Draft version November 4, 2018
Preprint typeset using LATEX style emulateapj v. 3/25/03
THE RADIO EMISSION, X-RAY EMISSION, AND HYDRODYNAMICS OF G328.4+0.2: A COMPREHENSIVE
ANALYSIS OF A LUMINOUS PULSAR WIND NEBULA, ITS NEUTRON STAR, AND THE PROGENITOR
SUPERNOVA EXPLOSION
Joseph D. Gelfand, Patrick O. Slane, and Daniel J. Patnaude
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138
B. M. Gaensler∗
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 and
School of Physics, The University of Sydney, NSW 2006, Australia
John P. Hughes
Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019
Fernando Camilo
Columbia Astrophysics Lab, Columbia University, New York, NY 10027
Draft version November 4, 2018
ABSTRACT
We present new observational results obtained for the Galactic non-thermal radio source G328.4+0.2
to determine both if this source is a pulsar wind nebula or supernova remnant, and in either case,
the physical properties of this source. Using X-ray data obtained by XMM, we confirm that the
X-ray emission from this source is heavily absorbed and has a spectrum best fit by a power law
model of photon index Γ = 2 with no evidence for a thermal component, the X-ray emission from
G328.4+0.2 comes from a region significantly smaller than the radio emission, and that the X-ray
and radio emission are significantly offset from each other. We also present the results of a new
high resolution (7′′) 1.4 GHz image of G328.4+0.2 obtained using the Australia Telescope Compact
Array, and a deep search for radio pulsations using the Parkes Radio Telescope. By comparing this
1.4 GHz image with a similar resolution image at 4.8 GHz, we find that the radio emission has a flat
spectrum (α ≈ 0; Sν ∝ ν
α), though some areas of the eastern edge of G328.4+0.2 have a steeper radio
spectral index of α ∼ −0.3. Additionally, we searched without success for a central radio pulsar, and
obtain a luminosity limit of L1400 <. 30mJykpc
2, assuming a distance of 17 kpc. In light of these
observational results, we test if G328.4+0.2 is a pulsar wind nebula (PWN) or a large PWN inside
a supernova remnant (SNR) using a simple hydrodynamic model for the evolution of a PWN inside
a SNR. As a result of this analysis, we conclude that G328.4+0.2 is a young (. 10000 years old)
pulsar wind nebula formed by a low magnetic field (. 1012 G) neutron star born spinning rapidly
(. 10 ms) expanding into an undetected SNR formed by an energetic (& 1051 ergs), low ejecta mass
(Mej . 5M⊙) supernova explosion which occurred in a low density (n ∼ 0.03 cm
−3) environment.
If correct, the low magnetic field and fast initial spin period of this neutron star poses problems for
models of magnetar formation which require fast initial periods.
Subject headings: stars: neutron, stars: pulsars: general, ISM: supernova remnants, radio continuum:
ISM, X-rays: individual
1. introduction
Stars with initial masses between ∼9 and 25 M⊙ are
expected to end their lives in a giant supernova (SN) ex-
plosion during which neutron stars are created. The fast
moving ejecta from the SN create a supernova remnant
(SNR), while the particle wind produced by the neu-
tron star as it loses rotational energy inflates a pulsar
wind nebula (PWN; Gaensler & Slane 2006). Initially,
the PWN is inside the SNR – and when the PWN is
detected inside the SNR the system is called a “compos-
ite” SNR (Helfand & Becker 1987). The evolution of the
central neutron star and the outer SNR affect the PWN,
Electronic address: jgelfand@cfa.harvard.edu
∗Alfred P. Sloan Research Fellow, Australian Research Council
Federation Fellow
Electronic address: jgelfand@cfa.harvard.edu
and as a result the PWN goes through several evolution-
ary phases while it is inside the SNR. This evolution is
determined by the physical properties of the neutron star
(specifically the initial period P0, the braking index p
and the strength of the dipole component to the surface
magnetic field Bns), the SN explosion (explosion energy
Esn and ejecta mass Mej), and the surrounding medium
(ambient number density n). As a result, by measur-
ing the properties of the PWN inside a SNR at a given
time one is able to constrain these physical parameters
which allows one to study the mechanisms behind both
core-collapse SNe and massive star evolution.
With this in mind, we present results of new radio
1 The braking index is defined as Ω̇ ∝ Ωp, where Ω is the angular
velocity of the neutron star’s surface.
http://arxiv.org/abs/0704.0219v1
mailto:jgelfand@cfa.harvard.edu
mailto:jgelfand@cfa.harvard.edu
observations of this source with the Australia Telescope
Compact Array (ATCA), as well as a new X-ray (X-ray
Multi-mirror Mission; XMM) observation of G328.4+0.2
(MSH 15-57; Mills et al. 1961). This source is a distant
(d ≥ 17.4 ± 0.9 kpc; Gaensler et al. 2000), radio bright
(flux density Sν = 14.3 ± 0.1 Jy at ν =1.4 GHz), po-
larized, extended (diameter D ≃ 5.0′) radio source with
a relatively flat spectral index (α ≃ −0.12± 0.03 where
Sν ∝ ν
α; Gaensler et al. 2000). Based on these radio
properties, and the discovery of non-thermal X-ray emis-
sion from this source by ASCA (Hughes et al. 2000), this
source was classified as a PWN – the largest and most
radio-luminous PWN in the Galaxy. In this interpre-
tation, the expectation is that G328.4+0.2 is ∼ 7000
years old and powered by an extremely energetic neu-
tron star (Gaensler et al. 2000). However, follow up ra-
dio polarimetry work (Johnston et al. 2004) implied that
G328.4+0.2 is an older composite SNR in which the
PWN is just a small fraction of the total volume, and
as a result is powered by a significantly less energetic
neutron star then argued by Gaensler et al. (2000). In
this paper, we analyze new observations of this source in
order to determine the age of G328.4+0.2, the energet-
ics of the neutron star and the progenitor SN, and the
density of its environment.
In §2 we present new X-ray and radio observations of
G328.4+0.2. In §3, we first discuss the expected evolu-
tionary sequence for PWNe inside SNRs (§3.1), making
general comments regarding the expected observational
signature of each phase. In §3.2 use the observational
results presented in §2 to draw some initial conclusions
about the nature of G328.4+0.2. In §4, we present a sim-
ple hydrodynamical model for the evolution of a PWN
inside a SNR, which we apply to G328.4+0.2 assuming it
is a composite SNR (§4.1.1) or a PWN (§4.1.2). Finally,
in §5 we summarize our results.
2. observations
In this Section, we present the data gathered in a
XMM observation (§2.1), a 1.4 GHz ATCA observation
of G328.4+0.2 (§2.2), and a search for a radio pulsar in
this source (§2.3).
2.1. X-ray Observations
On 2003 March 9–10, G328.4+0.2 was observed for
∼50 ks by XMM. During this observation, the pn cam-
era was operated in Small Window Mode, and the Mos1
and Mos2 camera were operated in Full Frame Mode.
The “Thick” optical filter was used due to the presence of
numerous bright stars in the field-of-view of G328.4+0.2.
The data were reduced with the software package xmm-
sas v 6.0.0 with calibration files current throughXMM-
CCF-REL-174, using the standard procedure for re-
ducing XMM data outlined in the XMM-Newton ABC
Guide2 and the Birmingham XMM Guide3.
2.1.1. Image Analysis
A vignetting corrected 0.2–12 keV image from the
Mos1 and Mos2 instruments4, is shown in Fig. 1, in
2 Available at http://heasarc.gsfc.nasa.gov/docs/xmm/abc/
3 Available at http://www.sr.bham.ac.uk/xmm2/guide.html
4 We did not use the pn data due to the substantially larger pixel
size of this instrument.
which we observe three spatial components to the X-ray
emission: a bright, compact feature located along the
SW edge of the X-ray emission (“Clump 1”), a fainter,
slightly extended feature located NE of the compact fea-
ture described above (“Clump 2”), and extended diffuse
emission, roughly 1′ in diameter, surrounding the two
features described above (“Diffuse”). From the “Clump
1” region we detected 120 ± 12 counts above the back-
ground between 0.5–10 keV in the Mos1 detector and
136± 12 in the Mos2 detector, from the “Clump 2” re-
gion we detected 66 ± 9 counts in both the Mos1 and
Mos2 detectors, and from the “Diffuse” regions we de-
tected 360± 20 and 380± 20 counts from the Mos1 and
Mos2 detectors, respectively.
We determined the spatial properties of these com-
ponents using the Sherpa modeling software package
(Freeman et al. 2001). Due to the low number of counts
per pixel, we used the simplex fitting method and min-
imized the cash statistic (Cash 1979). We attempted
to model Clump 1 and Clump 2 as circular 2D Gaus-
sians, elliptical 2D Gaussians, or circular 2D Lorentzians,
the latter of which is a good model for XMM’s point
spread function (PSF; Ghizzardi & Molendi 2002). We
attempted to model the Diffuse region as a circular or
elliptical 2D Gaussian, and assumed a constant back-
ground. We fit the observed image to all model com-
binations of Clump 1, Clump 2, and Diffuse (attempts
to eliminate one of these components resulted in signif-
icantly worse fits), and the best fit was obtained for
a model in which Clump 1 is a 2D Lorentzian while
Clump 2 and Diffuse are elliptical 2D Gaussians. The
fit parameters for this model are given in Table 1, and
the model and residuals are shown in Fig. 1, and from
this conclude that the emission from Clump 1 is consis-
tent with the PSF of XMM. Additionally, from this fit
we estimate that Clump 1 and Clump 2 are separated
by ∼ 10′′, while the centers of Clump 1 and Diffuse are
separated by ∼ 15′′.
2.1.2. Spectral Results
In generating the spectra, only events with flag = 0
were used. Additionally, the event files were screened for
background flares by binning the 10–15 keV light curve
of each instrument by 50 s and then recursively flagging
all bins with a count rate > 3σ above the average. This
procedure removed 3.0 ks, 2.3 ks, and 0.6 ks of data from
the Mos1, Mos2, and pn detectors, respectively. Spec-
tra were extracted for the regions shown in Fig. 1, and
the resulting spectra were binned into a minimum of 25
counts per channel and modeled using Xspec v12.2.0.
The background regions used are also shown in Fig. 1.
To determine the composite spectra of G328.4+0.2, we
jointly fit the spectrum obtained by the Mos1, Mos2,
and pn detectors – shown in Fig. 2. The background-
subtracted observed 0.5–10 keV count rate of G328.4+0.2
was 0.012 ± 0.001 counts s−1 in the the Mos1 detector
(555± 29 counts), 0.012± 0.001 counts s−1 in the Mos2
detector (580±30 counts), and 0.045±0.001 counts s−1 in
the pn detector5 (1576±63 counts). We fit the spectra to
seven different models separately – a power-law, a black-
body, bremsstrahlung, a Raymond-Smith plasma, and a
5 The pn detector count rate does not account for 29% dead time
since this instrument was operated in Small Window Mode.
http://heasarc.gsfc.nasa.gov/docs/xmm/abc/
http://www.sr.bham.ac.uk/xmm2/guide.html
power-law plus one of these three thermal models – all
attenuated for interstellar absorption. Only the single-
component models produced reasonable fits (reduced
χ2 ∼ 1), and the fitted parameters are presented in Table
2. Both the blackbody (kTBB ∼ 1.7 keV, TBB ∼ 20 MK)
and the bremsstrahlung models (kT ∼ 9 keV) require
unrealistically high temperatures, especially if the X-rays
are from a PWN as argued by Hughes et al. (2000). The
derived parameters for the power law model are similar
to that observed in other PWN (e.g. Gotthelf 2003), and
agree well with the results obtained for G328.4+0.2 by
Hughes et al. (2000). There is no evidence for thermal
X-ray emission, which one would expect from a SNR, in
this source.
Since the individual regions discussed in §2.1.1 did not
have enough counts for spectral fitting, we measured
their hardness ratio (HR), defined as:
H − S
H + S
where H is the number of counts in the Hard (higher
energy) band and S is the number of counts in the Soft
(lower energy) band, of the regions discussed in §2.1.1 to
determine if there were any spatial variations in the X-
ray spectrum of G328.4+0.2. Using the X-ray spectrum
as a guide, we calculate HR with H as the number of
counts between 4 and 8 keV and S as the number of
counts between 2 and 4 keV. Since the pixels on the pn
detector are sufficiently large that it is not possible to
separate the emission from these regions, we only use
data from the mos1 and mos2 detectors. The calculated,
background subtracted HR of G328.4+0.2 is 0.25± 0.04,
of the Clump 1 region is 0.29±0.07, of the Clump 2 region
is 0.31 ± 0.11, and of the diffuse region is 0.24 ± 0.05
(1σ errors). As a result, we conclude that there is no
significant change in the X-ray spectrum of G328.4+0.2
between these features.
2.1.3. Timing Results
A clear signature for the presence of a neutron star
would be the detection of X-ray pulsations in the emis-
sion from G328.4+0.2. We searched for this using the Z2n
test defined by Buccheri et al. (1983), where n is the har-
monic number of periodic signal, for n = 1, 2, 3, 4. The
maximum frequency searched was νmax = 1/(2n∆t), the
minimum frequency searched was 1/20 Hz, and the fre-
quency step was 1/4tobs (5× 10
−6 Hz, oversampling the
Nyquist rate by a factor of 2), where ∆t is the time res-
olution of the dataset (5.7 ms) and tobs is the length of
the observation. We only used events from the pn in-
strument (5.7 ms since it was operated in Small Win-
dow Mode) due to the poor time resolution (2.6s) of
the mos data. Additionally, we only used events from
the Clump 1 region because only only emission from the
central NS should be pulsed and as the brightest X-ray
region of G328.4+0.2, this region is the most probable
location of any neutron star. Unfortunately, due to the
large pixel size of the pn instrument this region is con-
taminated by emission from Clump 2 and the Diffuse re-
gion. The event times from the resultant event list were
barycentered to the Solar System reference frame, and we
searched for a periodicity over multiple energy ranges in
order to maximize the sensitivity of our search. The most
significant period detected was in the dataset which only
included photons between 5 and 10 keV (159 photons),
in which for n = 4 a signal with period P = 336 ms had
Z23 = 49.5 in 2074786 independent trials for this value
of n and energy range, which has a 12% chance of being
a false positive, a < 2σ result. Statistically, the most
significant sinusoidal (n = 1) pulse was in the 1–20 keV
dataset (340 photons), and had a period P = 73.1 ms
with a Z21 = 34.4 in 8365396 trials, a 34% chance of
being a false positive. Assuming that this signal is not
significant, we derive an upper limit on the pulse fraction
of 45% for a sinusoidal pulse profile and 22.5% for a δ-
function pulse profile (Leahy et al. 1983). Using the pn
count rate and size of the Clump 2 and Diffuse regions,
∼ 1/3 of the counts in the Clump 1 region is contamina-
tion from these regions. Accounting for this, we are only
able to put an upper limit on the pulse fraction of 67%
for a δ-function pulse profile. This upper limit is consis-
tent with the pulse fraction observed from other young
neutron stars.
2.2. Australia Telescope Compact Array Observations
Based on previous radio observations of G328.4+0.2,
there was a dispute in the literature as to whether this
source is a PWN, as argued by Gaensler et al. (2000), or
a composite SNR, as argued by Johnston et al. (2004).
The argument for this source being a PWN centered
on the flat spectrum of the radio emission, as well
as the high degree of polarization observed from the
center (Gaensler et al. 2000), while the radial polariza-
tion angles observed at the edge of this is more consis-
tent with a SNR (Johnston et al. 2004). If there is a
SNR component in G328.4+0.2, we expect that some
of the radio emission from this source should have a
steep (α < −0.3) spectrum. To search for such emis-
sion, we observed G328.4+0.2 for 12 hours at 1.4 GHz
with the Australia Telescope Compact Array (ATCA)
on 2005 June 25. Flux density calibration was carried
out using an observation of PKS B1934-638, and phase
calibration was carried out with regular observations of
PMN J1603-4904. The observation was carried out using
two 128 MHz bands, one centered at 1.344 GHz and the
other at 1.432 GHz, and the data reduction was done
using the miriad software package. The observation
was conducted when the ATCA was in the 6B configu-
ration, which has a longest baseline of ∼6000 m (∼ 6.′′9)
and a shortest baseline of ∼200 m (∼ 3.′4). As a re-
sult, this dataset alone is not sensitive to large-scale
emission from G328.4+0.2. To improve the sensitivity
to diffuse emission, we combined this dataset with the
1.4 GHz data used by Gaensler et al. (2000) as well as
continuum data gathered in the Southern Galactic Plane
Survey (McClure-Griffiths et al. 2005). Total intensity
images from this combined dataset were formed using
natural weighting, multi-frequency synthesis, and maxi-
mum entropy deconvolution. The final image, shown in
Fig. 3, has a resolution of 7.′′0×5.′′8, and an rms noise of
∼ 0.15 mJy beam−1. The measured 1.4 GHz flux density
of G328.4+0.2 is 13.8±0.4 Jy – consistent with the value
measured by Gaensler et al. (2000). For a 4.5 GHz flux
of 12.5± 0.2 Jy (Gaensler et al. 2000), this implies that
G328.4+0.2 has a radio spectral index α = −0.03± 0.03.
As seen in Fig. 3, the radio emission from G328.4+0.2
is very complicated, and contains multiple morphological
features. The major features are:
• Central Bar: The Central Bar is the bright-
est morphological feature in G328.4+0.2, and
has been previously detected at both 4.8 GHz
(Gaensler et al. 2000) and 19 GHz (Johnston et al.
2004). The Central Bar runs roughly E-W, and the
western edge of the bar is bifurcated, first noticed
by Johnston et al. (2004). The length of the bar
is ∼ 1.′75 long, and inside the bar there are three
peaks in the radio emission.
• Filamentary Structure A: These are the curved
filaments near the center of G328.4+0.2 which ap-
pear to be connected to the Central Bar, the bright-
est of which is the “Y” shaped structure NE of the
eastern edge of the Central Bar. In general, these
filaments are more prominent on the eastern side
of G328.4+0.2 and appear confined to the central
region of G328.4+0.2, not extending much beyond
the inner half.
• Filamentary Structure B: These are the faint,
radial filaments predominantly found on the west-
ern side of G328.4+0.2, as shown in Fig. 4. The
inner parts of these filaments are located ∼ 2.′5
from the center of G328.4+0.2, and their length
varies across G328.4+0.2 – in the southern half,
two filaments appear to extend to the edge of the
source while in the northern and western parts of
G328.4+0.2 they are substantially shorter. While
some of these filaments are kinked or curved, most
are fairly straight and radial in orientation. These
features were not detected by Gaensler et al. (2000)
and Johnston et al. (2004) due to the insufficient
u–v coverage of those observations.
• Filamentary Structure C: As shown in Fig. 3,
these are features located near the outer edge of
G328.4+0.2 that are parallel to the outer edge.
These features are more prominent and more plen-
tiful in the eastern half of G328.4+0.2.
• Outer Protrusions: The Outer Protrusions are
faint features – the two most prominent of which
are in the NE quadrant of G328.4+0.2 – that ex-
tend beyond the outer boundary of G328.4+0.2.
Several of these structures have bow-shock mor-
phologies.
The physical interpretation of these features will be pre-
sented in §3.2. It is worthwhile to note here that several
of these morphological features (e.g. the Central Bar and
the internal filamentary structures) have been observed
in other PWNe such as MSH 15-56 (Dickel et al. 2000)
and 3C58 (Slane et al. 2004), while others (e.g. the Fil-
amentary Structure C and Protrusions) are more char-
acteristic of SNRs, such as the Vela SNR (Bock et al.
1998).
This XMM observation also allows, for the first time,
a comparison between the radio and X-ray morphology
of G328.4+0.2. As shown in Fig. 3, there is a signifi-
cant offset between the X-ray and the center of the radio
emission, with Clump 1 located ∼ 80′′ from the center
of the radio emission. Additionally, the extent of the
X-ray emission is significantly smaller than that of the
radio emission. A physical interpretation of the X-ray
morphology and its relation to the radio emission will be
discussed in §3.2.
2.2.1. Spectral Index Map
The previous 1.4 GHz dataset had a resolution (∼ 20′′)
significantly worse than that of the 4.5 GHz data, and
therefore is not suitable for determining if there are
small scale changes in α inside G328.4+0.2. With these
new, high-resolution 1.4 GHz observations, it was pos-
sible to make a spectral index map of G328.4+0.2 us-
ing our new 1.4 GHz data and the 4.5 GHz data pre-
sented by Gaensler et al. (2000) since these datasets have
comparable u–v coverage. To detect any variation in
α, we made a spectral tomography map of G328.4+0.2
(Katz-Stone & Rudnick 1997). To do this, we first
produced a 1.4 GHz image of G328.4+0.2 from data
matched in u–v coverage with the 4.5 GHz data, and then
smoothed both the new 1.4 GHz image and the 4.5 GHz
image to a resolution of 8′′ to account for the poorer reso-
lution of the 1.4 GHz data. Finally, we produced a series
of difference images (Idiff,α) using the following formula:
Idiff,α= I1.4 − I4.5
where I1.4 and I4.5 are the 1.4 and 4.5 GHz images
produced above. In this method, the spectral index of
a region is determined by the spectral index at which
it disappears from the difference image. As shown in
Fig. 5, most of the radio emission from G328.4+0.2 has
a spectral index between α ∼ −0.1 and α ∼ +0.1, while
the outer edges of G328.4+0.2 have a steeper spectrum
(α ∼ −0.4) than the center, particularly the western edge
of G328.4+0.2. This steeper spectrum material is coin-
cident with some of the Filamentary Structure C dis-
cussed in §2.2, but there are no spectral features associ-
ated with any of the other radio morphological features
in G328.4+0.2 or with the X-ray emission. A physical
interpretation of these results will be discussed in §3.2.
2.3. Search for the radio pulsar at Parkes
As part of a project to search for pulsar counterparts to
all Galactic PWNe (e.g. Camilo et al. 2002a), on 2005
October 13 we observed G328.4+0.2 using the ATNF
Parkes telescope in NSW, Australia. As for similar
such work, we employed the central beam of the Parkes
multibeam receiver at a central frequency of 1374MHz,
with 96 frequency channels across a total bandwidth of
288MHz in each of two polarizations. The integration
time was 24ks, during which total-power samples were
recorded every 0.25ms for off-line analysis.
We analyzed the data with standard pulsar searching
techniques using PRESTO (Ransom et al. 2002). We
searched the dispersion measure range 0–2600cm−3 pc
(twice the maximum Galactic DM predicted for this line
of sight by the Cordes & Lazio 2002 electron density
model), while maintaining close to optimal time reso-
lution. In our search we were sensitive to pulsars whose
spin period could have changed moderately during the
observation due to very large intrinsic spin-down. The
search followed very closely that described in more detail
in Camilo et al. (2006). We did not identify any promis-
ing pulsar candidate in this search.
Applying the standard modification to the radiometer
equation, for an assumed pulsation duty cycle of 10%,
and accounting for a sky temperature at this location
of 15K, we were nominally sensitive to long-period pul-
sars having a period-averaged flux density at 1.4GHz
of S1400 > 0.05mJy. In fact, this limit applies only
to such long-period pulsars as to not be of practical
interest for us: for a distance of ∼ 17 kpc along this
line of sight, the expected DM is ≈ 1200 cm−3 pc, and
the scatter-broadening of the radio pulses due to multi-
path propagation is expected to be ∼ 50ms at 1.4GHz
(Cordes & Lazio 2002). This would likely render pulsa-
tions undetectable from any short-period pulsar, such as
we expect to power G328.4+0.2, regardless of average
radio flux. We therefore repeated the search at a higher
radio frequency ν, since the scattering timescale is ap-
proximately ∝ ν−4.
On 2007 January 4 we observed G328.4+0.2 at Parkes
at a central frequency of 3078MHz, with 288 channels
spanning a bandwidth of 864MHz in each of two polar-
izations. The total-power samples were recorded every
1ms for 30 ks, and analyzed in a manner analogous to
that described previously for the 1.4GHz data. This time
a few somewhat-promising candidates were identified in
the analysis, and a second 3GHz observation was made,
on 2007 March 19, for 36 ks. Analysis of this second ob-
servation did not confirm the original candidates, and we
have therefore not detected any radio pulsar counterpart
for the PWN in G328.4+0.2. The sensitivity of our 3GHz
observations was about 0.03mJy for long-period pulsars
(P & 20ms) and decreasing gradually for shorter peri-
ods. For the predicted DM, at this frequency the scat-
tering timescale is expected to be ∼ 2ms, comparable to
the dispersion smearing across each individual channel,
∼ 1ms. Propagation effects should therefore not have
prevented the detection of signals with P & 5ms.
Converting the 3GHz flux density limit to a frequency
of 1.4GHz, using a typical pulsar spectral index of –1.6
(Lorimer et al. 1995), results in S1400 . 0.1mJy. For
a distance of ∼ 17 kpc, this corresponds to a pseudo-
luminosity limit of L1400 ≡ S1400d
2 . 30mJykpc2. This
is comparable to L1400 of the very young pulsars B1509–
58, J1119–6127, and Crab (Camilo et al. 2002b), but a
factor of about 60 greater than for the young pulsar
in 3C58 (Camilo et al. 2002c), which has the smallest
known radio luminosity among young pulsars. Based
on these results, it is therefore entirely possible that
G328.4+0.2 harbors an as-yet undetected young pulsar
beaming toward the Earth with an ordinary radio lumi-
nosity.
3. interpretation of x-ray and radio observations
of g328.4+0.2
The X-ray spectrum of G328.4+0.2 is characteristic of
PWNe (see Gotthelf 2003 for a compilation of the X-
ray properties of PWNe), and therefore conclude that
the X-ray emission from G328.4+0.2 comes from a PWN
and not from a SNR. The same is true for the polarized,
flat-spectrum radio emission detected from the center
of G328.4+0.2 which are also characteristic of PWNe.
Therefore, in the following discussion we assume that
the X-ray and flat spectrum radio emission are both pro-
duced by a PWN. In §3.1, we discuss the evolutionary
sequence of PWNe in SNRs and the observational signa-
tures of each stage. In §3.2, we use the results from the
observations presented in §2.1 and §2.2 to draw general
conclusion about the properties of G328.4+0.2.
3.1. Evolution of PWN in SNRs
Both PWNe and SNRs are dynamic objects, and when
the PWN is inside the SNR its evolution is affected by
the behavior of both the central neutron star and the sur-
rounding SNR. While the PWN is inside the SNR, it typ-
ically goes through three evolutionary phases (Chevalier
1998; van der Swaluw et al. 2004):
• The Free-Expansion Phase – In this phase, the
PWN freely expands into the cold material inside
the SNR, sweeping up and shocking the surround-
ing ejecta into a thin shell (Chevalier & Fransson
1992; van der Swaluw et al. 2001). Since the PWN
is confined only by the shock wave its expansion
drives into the surrounding SNR, and the velocity
of this shock wave is much larger than the neutron
star velocity, it is free to move inside the SNR with
the neutron star.
• Collision with the Reverse Shock – As the
SN sweeps up and shocks the surrounding a am-
bient material, a reverse shock (RS) is driven
into the ejecta. Eventually, the PWN will en-
counter the RS, and as a result, can not con-
tinue to freely expand inside the SNR because it
is no longer in an essentially pressureless environ-
ment. Initially, the pressure behind the RS is
higher than the pressure inside the PWN, and as
result the PWN is compressed. As it contracts,
the pressure inside the PWN increases adiabati-
cally and eventually will be higher than its sur-
rounding, and will as a result re-expand inside the
SNR (Blondin et al. 2001; Bucciantini et al. 2003;
Reynolds & Chevalier 1984; van der Swaluw et al.
2001). Once the PWN encounters the RS, the ex-
pansion velocity of the PWN decreases signficantly
and falls below that of the neutron star, which is
unaffected by this collision. As a result, the neu-
tron star can detach itself from its PWN.
• Relic PWN Phase – When the neutron star
detaches from the relic nebula, it forms a new
PWN from the relativistic e+/e− plasma it contin-
ues to inject into the SNR (van der Swaluw et al.
2004). The PWN around the neutron star and
relic nebula evolve differently. The relic nebula
continues to contract/expand inside the SNR un-
til it achieves pressure equilibrium with its sur-
roundings, a process that can take many tens of
thousands of years. The new PWN initially ex-
pands sub-sonically, but when the neutron star is
∼ 2/3 of the way to the SNR shell, its velocity
will become supersonic relative to the surrounding
material and the PWN will take on a bow-shock
morphology (van der Swaluw et al. 2004). Eventu-
ally, the neutron star will leave the SNR, and as it
passes through the SNR shell it may re-energize the
surrounding SNR material, as possibly observed in
SNRs G5.4-1.2 and CTB80 (Shull et al. 1989).
As the PWN evolves inside the SNR, its appearance
changes radically. During the Free-Expansion phase, the
morphology of the PWN is determined by the properties
of the particle wind expelled by the neutron star. In
these cases, the neutron star is in the center of the PWN,
and there is no significant offset between the radio and
X-ray emission from the PWN. In general, during this
stage the PWN is located near the center of the observed
SNR shell. Examples of PWNe in this evolutionary stage
are the PWNe in SNR 0540-693 in the LMC (Reynolds
1985), as well as those in the Milky Way SNRs G11.2-
0.3 (Roberts et al. 2003; Tam et al. 2002) and G21.5-0.9
(Matheson & Safi-Harb 2005).
Due to the offset in the PWN’s position with respect to
the SNR’s center as a result of the neutron star’s veloc-
ity or inhomogeneities in the ISM, it is expected that one
side of the PWN will encounter the RS before the other
side (Blondin et al. 2001; van der Swaluw et al. 2004).
As a result, the PWN will no longer be symmetrically
oriented around the neutron star (van der Swaluw et al.
2004), leading to an offset between the radio and X-ray
emission from the PWN. Because the cooling time for X-
ray producing electrons is very short compared to that of
radio emitting electrons, the X-ray emission of a PWN
is expected to be brightest at the current location of the
neutron star while the radio emission reflects the effect
of the RS on the PWN. The compression/re-expansion
cycle triggered by the PWN/RS collision will also affect
the appearance of the PWN. According to a spherically
symmetric MHD simulation of a PWN in this phase,
compression of the PWN by the RS leads to an over-
pressurized region forming in the center of the PWN.
Material injected by the neutron star after this point is
then confined to the small region, leading to the forma-
tion of a radio/infrared “hot spot” in the center of the
PWN (Bucciantini et al. 2003).
The PWN/RS interaction also leads to the forma-
tion of hydrodynamic, primarily Rayleigh-Taylor (R-T),
instabilities at the PWN/SNR interface (Blondin et al.
2001). During the PWN’s initial free-expansion phase,
the shell of material swept up by the PWN is subject to
both thin shell and R-T instabilities (Bucciantini et al.
2004; Jun 1998), but the growth rate of these features
is expected to be sufficiently small that the PWN is not
disrupted, especially if even a small percentage of the
total energy of the pulsar’s wind is in magnetic fields
(Bucciantini et al. 2004). However, during the PWN/RS
interaction, rapid mixing of pulsar wind and SNR ma-
terial is expected when the PWN re-expands into the
SNR (Blondin et al. 2001). In fact, numerical simula-
tions suggest that the PWN is disrupted after its first
re-expansion into the SNR as a result of these instabil-
ities (Blondin et al. 2001). It is important to note that
these instabilities are only expected to affect the relic
nebula and not the new PWN formed by the neutron
star further from the SNR’s center. Once the composite
SNR enters the Relic PWN phase, the X-ray emission is
expected to be dominated by the new PWN since it con-
tains the high energy particles recently injected by the
neutron star, while the radio emission is dominated by
the relic nebula which contains most of the older parti-
cles that are expected to contribute at low frequencies.
As a result, during this phase the radio-emitting elec-
trons are expected to be dominated by electrons injected
during the free-expansion phase, while the X-ray is from
electrons injected after the passage of the RS.
3.2. Observational Results
In this Section, we use the results from the observa-
tions presented in §2.1 and §2.2, as well as the basic evo-
lutionary sequence for PWN in SNRs described above
in §3.1 to make some initial statements on the nature,
evolutionary state, and properties of G328.4+0.2. The
discussion given below is a very general interpretation of
observed radio and X-ray features in G328.4+0.2, it pro-
vides a framework in which to test the various scenarios
for G328.4+0.2 discussed in §4.1.1 and §4.1.2.
As mentioned in §1, there is a debate in the
literature as to whether G328.4+0.2 is a PWN
(Gaensler et al. 2000; Hughes et al. 2000) or a composite
SNR (Johnston et al. 2004). In neither of the X-ray or
radio observations presented above is there clear evidence
(e.g. thermal X-ray emission or a bright, steep spec-
trum, radio shell) for a SNR component. If G328.4+0.2
is a composite SNR, then the outer boundary of the ra-
dio emission likely marks the outer radius of the SNR
component, while the observed flat-spectrum radio emis-
sion and power law X-ray emission are emitted by the
PWN. Using the extent of the flat-spectrum radio emis-
sion shown in Fig. 5 to estimate the size of the PWN
component, we obtain that the radius of the PWN in this
source must be & 2/3RG328, the radius of G328.4+0.2.
If G328.4+0.2 is a composite SNR, then Filamentary
Structure 3, which as mentioned in §2.2.1 might have
a steeper spectral index than the rest of the radio emis-
sion in G328.4+0.2, would be emission from the SNR.
This emission is then possibly analogous to the corru-
gated structures seen in the NE part of the Tycho’s SNR
(Velazquez et al. 1998). Additionally, in this case the
Outer Protrusions mentioned in §2.2 maybe are ejecta
“bullets”, similar to those observed in the Vela SNR
(Aschenbach et al. 1995) and SNR N63A (Warren et al.
2003).
If G328.4+0.2 is a PWN, then the outer boundary of
the radio emission is the outer radius of the PWN and
the SNR in which it resides is undetected, similar to the
case for the Crab Nebula. As a result, the steep spectrum
radio emission seen at the edge of G328.4+0.2, as well
as Filamentary Structure C and the Outer Protrusions
observed in the radio, correspond to material swept-up
by the PWN. This is because radio emission from the
pulsar wind is observed to have a flat spectrum, un-
like this material. As a result, Filamentary Structure C,
as well as the radial component seen by Johnston et al.
(2004) in the polarization angle along the outer edge of
G328.4+0.2, are the result of the hydrodynamical (HD)
instabilities at the PWN/SNR interface. Since these
instabilities only occur when the PWN is accelerating
the shell of swept-up material surrounding it, he current
pressure inside the PWN (Ppwn) must be higher than
that of the SNR material just of the PWN [Psnr(Rpwn)].
Additionally, in this case the Outer Protrusions would be
the result of the PWN currently expanding into a clumpy
medium (e.g. the PWN analog of the process described
for young SNR by Jun et al. 1996), which requires that
the expansion speed of the PWN, vpwn, is currently posi-
tive. In this case, it is possible that the SNR surrounding
G328.4+0.2 will be detected at a later date, as was the
case for G21.5-0.9 (Matheson & Safi-Harb 2005).
Regardless of whether G328.4+0.2 is a composite SNR
or a PWN, the offset between the radio and X-ray
emission from the PWN component implies that the
PWN/RS collision has already occurred. The Central
Bar is then the remains of the over-pressurized region
created when the PWN was compressed by the RS, with
the bar-like shape of this region the result of either an
asymmetric RS or the anisotropic wind emitted by the
neutron star. The Central Bar should then consist of
pulsar wind material, which accounts for the α ∼ 0 spec-
tral index of this region as shown in Fig. 5. Additionally,
the flat spectral index observed from Filamentary Struc-
tures A implies that this feature is emitted by pulsar
wind material. As mentioned in §3.1, when the PWN
re-expands after the initial compression by the RS, nu-
merical simulations suggest that the rapid mixing of the
SNR ejecta and pulsar wind material can then occur. In
their 2D simulations of this process, Blondin et al. (2001)
observe features similar to that of Filamentary Structure
A, and as a result we conclude that the existence of these
features requires that the PWN has re-expanded at least
once after its initial compression by the RS. Since the ra-
dius of flat-spectrum radio emission from G328 is larger
than the outer radius of Filamentary Structure A, the
instabilities formed during this expansion must not have
completely disrupted the PWN. This differs from the re-
sults of Blondin et al. (2001), in which the PWN is dis-
rupted during the first re-expansion. This is most likely
due to the damping effect of the PWN’s magnetic field
on Raleigh-Taylor instabilities, which is not accounted
for by Blondin et al. (2001).
Finally, we discuss the X-ray emission seen from
G328.4+0.2 which, based on its X-ray spectrum, is emit-
ted by pulsar wind material. The observed offset between
Clump 1, Clump 2, and the Diffuse regions of the X-ray
emission implies that the PWN is not freely expanding,
consistent with the explanation that the PWN has col-
lided with the RS. We identify Clump 1 as the current
location of the neutron star since it is the brightest X-ray
feature, Clump 2 as the location of the termination shock
in the PWN (Kennel & Coroniti 1984), and the Diffuse
emission is produced by recently injected plasma stream-
ing away from the neutron star. In this case, the extent
of the Diffuse component depends on the synchrotron
lifetime of the X-ray emitting particles in the PWN.
The X-ray emission also provides an estimate of the
physical properties of the central neutron star, namely
a measure of the neutron star’s rotational spin-down en-
ergy, Ė. A comparison of observed X-ray luminosity Lx
and Ė shows a trend that neutron stars with a higher Lx
have a higher Ė, and that the relationship between these
two quantities is (Possenti et al. 2002):
logLX,(2−10)=1.34 log Ė − 15.34 (3)
where LX,(2−10) is the X-ray luminosity of the source
between 2 and 10 keV, albeit with a significant scatter
(Possenti et al. 2002). For the absorbed power-law fit to
the X-ray emission from G328.4+0.2 given in Table 2,
the unabsorbed 2–10 keV flux of G328.4+0.2 is ∼ 1 ×
10−12 ergs cm−2 s−1. For a distance to G328.4+0.2 of
d = 17d17 kpc, we obtain that:
LX,(2−10)∼ 3.5d
17 × 10
34 ergs s−1, (4)
which, using Eq. (3), gives us an estimate of Ė:
Ė ∼ 1.7d1.4917 × 10
37 ergs s−1. (5)
This number is somewhat less than estimate obtained
byGaensler et al. (2000) (Ė = 8.3× 1038 ergs s−1), who
assumed that Ė = 4 × 10−4LR, where LR is the radio
luminosity of G328.4+0.2. Our estimate of Ė is similar
to the estimate by Hughes et al. (2000) (Ė ∼ 1037 − 2×
1038 ergs s−1), who also used the Lx − Ė relation.
4. simple hydrodynamic model for the evolution of
a pwn inside a snr
In order to determine what neutron star, SN, and am-
bient density properties are required to produce a system
with these properties described in §3.2, we have devel-
oped a simple hydrodynamic (HD) model for the evo-
lution of a PWN inside of a SNR, which we then ap-
ply to G328.4+0.2 in §4.1. This model is based largely
on the models developed by Blondin et al. (2001) and
van der Swaluw et al. (2001). The main goal of this
model is to determine the radius of the PWN, Rpwn,
as it progresses through the evolutionary sequence de-
scribed in §3.1. In this model, we assume that the PWN
can be treated as a perfect gas with adiabatic index
γ = 4/3 and that is expanding into a SNR filled with
a perfect gas with adiabatic index γ = 5/3. We also as-
sume that the material swept-up by the PWN initially
lies in a thin shell with inner radius R = 23/24 Rpwn
(van der Swaluw et al. 2001), as shown in Fig. 6. The
dynamics of this mass shell are determined by the dif-
ference in pressure between the PWN and SNR, and by
calculating the radius of this mass shell we determine
Rpwn(t). Once the PWN enters the Relic PWN phase
of its evolution, this model only determines the proper-
ties of the relic nebula. What follows is a brief qualitative
description of the model used, while the full suite of equa-
tions used to implement it quantitatively can be found
in Appendix A.
As mentioned above, we model Rpwn(t) by calculating
the outer radius of the mass shell swept up by the PWN,
ignoring the effect of any instabilities which could dis-
rupt this shell. We solve for Rpwn(t) by assuming that
we know the values for the relevant quantities at a time
t − ∆t, and then calculate them for a time t, since the
relevant equations can not be solved at all times analyt-
ically. we wrote a program in IDL to implement this
numerically using the following procedure:
1. Calculate Rpwn(t+∆t) by assuming that the mass
shell around the PWN between t and t+∆t moves
with a constant velocity vpwn(t).
2. Calculate the internal energy of the PWN, Epwn(t+
∆t), using the first law of thermodynamics:
∆Epwn= Ėt− Ppwn∆Vpwn (6)
which takes into account energy losses from the adi-
abatic expansion/contraction of the PWN as well
as any energy input from neutron star into the
PWN between t and t + ∆t if the neutron star is
still inside the PWN. Since we assume the PWN is
filled with a γ = 4/3 perfect gas, Epwn ∝ PpwnVpwn
from the ideal gas law, where Ppwn is the internal
pressure of the PWN and Vpwn is the volume of
the PWN, as defined in Equations (A5 and (A6).
Since Vpwn ∝ R
3, and γ = 4/3 requires that
Ppwn ∝ V
pwn , we derive that Ppwn ∝ R
−4. As
a result, if there is no input from the neutron star,
then Epwn ∝ R
pwn. The energy input from the
neutron star (∆Epsr) is calculated by integrating
Eq. (A7) between t and t+∆t.
3. Calculate Ppwn(t + ∆t) using Equations (A5) and
(A6).
4. Calculate the pressure inside the SNR (Psnr), the
density inside the SNR (ρej), the velocity of the
material inside the SNR (vej), and the sound speed
of the material inside the SNR (cs), at the outer
radius of the PWN, R = Rpwn(t + ∆t) using a
model for the evolution and structure of a SNR, as
described in Appendix A.
5. If the PWN is expanding faster than the SNR ma-
terial around it, increase the mass of the shell sur-
rounding the PWN, Msw,pwn(t+∆t), accordingly,
as described in Appendix A.
6. Calculate the force on the mass shell surrounding
the PWN, Fpwn(t + ∆t), using Eqs. (A14) and
(A15). During the initial free-expansion of the
PWN inside the SNR, these equations reduce to
Equation A4 of van der Swaluw et al. (2001) and
Equation 14 of Chevalier (2005).
7. Calculate the new velocity of the mass shell around
the PWN, vpwn(t + ∆t), assuming that any mass
swept up by the PWN between t and t+∆t is done
so inelastically:
vpwn(t+∆t)=
Msw(t)vpwn(t) + Fpwn(t+∆t)∆t
Msw(t+∆t)
This is believed to be a reasonable approximation
because the newly swept-up material is shocked by
the mass shell and, as a result, its pre-existing mo-
mentum is transferred to the internal energy of the
mass shell.
This model is assumes that both the SNR and PWN
are spherically symmetric, the PWN remains centered
on the center of the SNR at all times, the PWN has no
effect on the evolution of the SNR, and that the ma-
terial swept-up by the PWN is incompressible and has
a negligible internal pressure. Additionally, this model
ignores the effects of magnetic field (Bucciantini et al.
2003) and RT instabilities at the PWN/SNR interface
(Blondin et al. 2001; van der Swaluw et al. 2004) on the
properties of the PWN. Despite these simplifications, our
model does a reasonably good job of reproducing the re-
sults for Model A in Blondin et al. (2001), as shown in
Fig. 7. In general, relative to results of Blondin et al.
(2001) and other authors, our model tends to result in
larger oscillations in Rpwn/Rsnr and a larger initial com-
pression. The first discrepancy results from neglecting
the effect of instabilities at the PWN/SNR interface that
damp these oscillations, and the second from not includ-
ing the effect of reflected shocks that enter the PWN at
the time of the PWN/RS collision (Blondin et al. 2001).
Additionally, we find that scenarios with the same to-
tal amount of energy deposited by the neutron star into
the PWN, Epsr but with different neutron star properties
(e.g. different values of P0 and Bns) produce the same
behavior of Rpwn(t). This is different than the conclu-
sion of Blondin et al. (2001), and believe that this dis-
crepancy is the result of using a more realistic expression
for Ė, Eq. (A7), than a step function, the form used by
Blondin et al. (2001).
4.1. Application of Model to G328.4+0.2
In the following discussion, we use the model given in
§4 for a PWN’s evolution inside a SNR to examine the
different possibilities for the nature of G328.4+0.2 given
in §3.2. We first analyze the possibility that G328.4+0.2
is a composite SNR (§4.1.1), and then he possibility that
G328.4+0.2 is a PWN (§4.1.2). This model requires six
inputs: the characteristic timescale of the neutron star’s
spin-down, τ0, initial spin-down power of the neutron
star Ė0, the velocity of the neutron star, vns, the kinetic
energy of the SN ejecta Esn, the mass of the SN ejecta
Mej, and the number density of the surrounding material
n. In order to calculate these values, we use the following
information:
• The distance to G328.4+0.2 is 17 kpc (d17 ≡ 1),
which is the lower limit on the distance to this
source as determined by Gaensler et al. (2000) us-
ing Hi absorption. This implies that the current
radius of G328.4+0.2 is RG328 ≡ 12.5 pc.
• The neutron star inside G328.4+0.2 is spinning
down with a braking index p = 3, the braking in-
dex produced by a pure dipole surface magnetic
field. Additionally, we assume that the neutron
star’s moment of inertia is I = 1045 g cm2, the
value derived for standard equations of state for
a neutron star (Shapiro & Teukolsky 1983). Both
of assumptions are standard in the literature (e.g.
Blondin et al. 2001).
• The offset between the Clump 1, which as described
in §3.2 is believed to be the location of the neu-
tron star powering the PWN, and the center of the
radio emission is due to neutron star’s spatial ve-
locity, vns. Using §2.1.1, we determine that this
observed offset corresponds to physical distance of
∼ 6.6d17 pc. Since the observed offset is due only
to the neutron star’s velocity in the plane of the
sky, it is a lower limit on the true distance the neu-
tron star has traveled since the SN explosion, rns.
If we assume that vns = rns/tnow, where tnow is
the age of G328.4+0.2, the observed offset allows
us to estimate the minimum spatial velocity of the
neutron star, vminns , equal to:
vminns =
6.6d17 pc
. (8)
• Using Equation (A19), we determine that for stan-
dard initial periods (P0 ∼ 5− 20 ms) and magnetic
field strengths (Bns = 5× 10
11 − 1013 G), τ0 varies
from ∼ 100 − 2000 years. To cover this range, we
assume that τ0 of the neutron star in G328.4+0.2
can have one of three different values:
τ0 = 430, 770, and 1730 years. (9)
which respectively correspond to a neutron star
with B = 1012 G and P0 = 5 ms, B = 3 × 10
and P0 = 20 ms, or B = 5 × 10
11 G and P0 =
5 ms. This range of τ0 is similar to those used
by Blondin et al. (2001), van der Swaluw et al.
(2001), and Bucciantini et al. (2003).
• G328.4+0.2 is expanding into a uniform medium
(s = 0 in the notation of Chevalier 1982). This
assumes G328.4+0.2 is much larger than either
the main sequence and late-stage wind bubble
formed by its progenitor, both of which are ex-
pected to have an interior ρ ∝ r−2 density struc-
ture. While the typical size of these structures
is smaller than RG328, this is not the the case
for very massive stars (M & 15 M⊙) for which
these bubbles can reach sizes of ∼ 100 pc or
larger in low density (n . 1 cm−3) environments
(Chevalier & Emmering 1989; Chevalier & Liang
1989). In this case, our assumption of a constant
density medium would not be correct. However,
the effect of G328.4+0.2 still being inside a stellar
wind bubble since this does not significantly mod-
ify the evolution of the SNR. Since their no a priori
information on the density around G328.4+0.2, we
assume it is one of the assume it has one of the
following values:
logn = −1.5,−1.0, 0, 0.5 cm−3. (10)
which cover the range of densities in the warm ion-
ized medium and the warm neutral medium.
• The ejecta mass of the SN explosion that formed
G328.4+0.2, Mej has one of the following values:
Mej = 1, 5, 10M⊙ (11)
and that the kinetic energy of the ejecta, Esn is:
log(Esn/10
51ergs) = −0.5, 0, 0.5. (12)
This range of Mej and Esn incorporate the range
inferred from observations of “normal” SNe, but
do not include hypernovae.
• We assume that the Lx − Ė relationship used in
§3.2 is accurate to better than two orders of mag-
nitude. As a result, in §4.1.1, we assume that the
current spin-down luminosity of the neutron star
in G328.4+0.2 is one of the following:
Ė=0.017, 0.17, 1.7, 17, and 170× 1037 ergs s−1,(13)
and in §4.1.2 assume that 1.7 × 1035 < Ė < 1.7 ×
1039 ergs s−1.
These are the initial conditions used in both §4.1.1 and
§4.1.2. The remaining input parameters into the model
are the initial spin-down luminosity Ė0 and space ve-
locity vns of the neutron star, and the method for deter-
mining the possible values of these parameters is given in
§4.1.1 and §4.1.2. Finally, for all trials discussed in §4.1.1
and §4.1.2 the model begins at a time t = 0.5 years, with
∆t = 0.5 years.
4.1.1. G328.4+0.2 as a Composite SNR
In this Section, we evaluate the possibility that
G328.4+0.2 is a composite SNR. To do this, we first
assume that the outer edge of the radio emission from
this source denotes the edge of the SNR, and therefore
RG328 ≡ Rsnr. As a result, for a given value of Esn,
Mej, and n, we use the model for the evolution of a SNR
discussed in Appendix A to calculate the current age of
G328.4+0.2, tnow. With this value of tnow and assumed
values for the current spin-down luminosity of the neu-
tron star, Ė, and τ0, we are able to calculate both the
initial spin-down luminosity Ė0 and initial period P0 of
the neutron star in G328.4+0.2 using Eqs. (A7) and (A9),
respectively.
Using this procedure, we ran our model using all pos-
sible combinations of the input parameters (τ0, Ė, Esn,
Mej, and n) given in §4.1, for a total of 540 different com-
binations. To see which combination of these input pa-
rameters provide a plausible explanation for G328.4+0.2,
we require the following:
• Criterion 1: vminns < 2000 km s
−1, since a neu-
tron star with a higher velocity than this is ex-
tremely implausible based on pulsar observations
(Hobbs et al. 2005).
• Criterion 2: P0 > 2 ms, the minimum rota-
tion period of a young proto-neutron star before
it breaks up (Goussard et al. 1998).
• Criterion 3: The PWN is smaller than the SNR
for all t < tnow. While it is possible that PWN
could expand to fill the entire SNR, it is not con-
sidered likely, and is contrary to the model as-
sumption that the PWN does not affect the evolu-
tion of the SNR. Additionally, we also require that
Rpwn(tnow) ≥ 0.67Rsnr(tnow), due to the large ob-
served size of the flat-spectral index radio emission
which is produced from the PWN, as described in
§3.2.
• Criterion 4: G328.4+0.2 is currently in the Free-
Expansion or Sedov-Taylor phase of its expansion,
i.e. tnow < trad, where trad, the age when a SNR
goes radiative, is defined in Eq. A4. Once a SNR
has entered its Radiative phase, it is expected that
the radio emission from the SNR be confined to
thin, bright, filaments like those observed in SNR
G6.4-0.1 (Mavromatakis et al. 2004) – which are
not observed in G328.4+0.2, or that the SNR is
radio-quiet.
• Criterion 5: The PWN/RS collision has already
occurred, as described in §3.2, and the PWN has
been compressed as a result of its collision with the
RS. This is required to explain the Central Bar, as
described in §3.2. This requires that vpwn < 0 at
some point in the past – which can only occur at
a time t > tcol, the time when the PWN and RS
collide.
• Criterion 6: The Central Bar created by the
compression is still observable. This is satisfied
if either the PWN is currently being compressed,
vpwn(tnow) < 0, or if the compression ended suffi-
ciently recently such that it can be observed. The
Central Bar is believed to be formed by both a
pressure and a magnetic field enhancement at the
center of the PWN (Bucciantini et al. 2003). As a
result its observable lifetime is the synchrotron life-
time of electrons accelerated by the magnetic field
enhancement. Therefore, we assume that the life-
time of the central bar is the synchrotron age of
the accelerated electrons, τsynch, equal to:
τsynch = 3× 10
4ν−1/2B−3/2pwn years, (14)
where ν is the observed frequency, in units of Hz,
and Bpwn is the strength of the magnetic field in-
side of the PWN, in units of G. With this infor-
mation, in the case that vpwn(tnow) > 0 we deter-
mine if the central bar is still observable by eval-
uating τsynch at 22 GHz (since this is the highest
frequency at which the Central Bar is observed;
Johnston et al. 2004) at the time when the com-
pression ends, assuming that Bpwn can be derived
using the minimum energy estimate. This criterion
is satisfied if τsynch > tnow − tre−exp, where tre−exp
is the time when the compression phase ends.
That the above criteria fall into two categories: criteria
required for physical plausibility (Criteria 1–3) and those
which depend on our interpretation of the radio and X-
ray properties of G328.4+0.2 (Criteria 4–6).
Of the 540 possible combinations of the input parame-
ters, only one passes all six criteria. The predicted SNR,
PWN, and neutron star properties of this scenario are
given in Table 3, and the behavior of Rpwn as a function
of time is given in Figure 8. In this scenario, G328.4+0.2
is quite young, ∼ 4900 years old, and the energy in-
jected into the SNR by the neutron star is similar to
the kinetic energy of the SN explosion (∼ 1051 ergs).
However, in this scenario, as shown in Fig. 8, the pre-
dicted compression is very small; when the compression
begins, Rpwn = 3.838 pc, and when the PWN begins to
re-expand into the SNR, Rpwn = 3.834 pc. This small
decrease is not surprising given that, as shown in Table
3, the total energy inputed into the PWN by the pulsar
(Epsr) is very close to the kinetic energy of the SN ejecta
(Esn). This negligible decrease in the volume of the PWN
is unlikely to form a central bar as prominent as the one
observed (Fig. 3), and therefore we feel is unlikely to be
the correct explanation for G328.4+0.2.
4.1.2. G328.4+0.2 as a PWN
In order to evaluate if G328.4+0.2 is a PWN, we use
the model presented in §4 to determine the earliest time6
(tnow) at which a PWN powered by a neutron star with
a given initial period P0 reaches the observed size of
G328.4+0.2 (Rpwn = 12.5 pc) if it is expanding into as
yet unseen SNR formed by ejecta with initial mass Mej
and kinetic energy Esn which exploded in a constant-
density ambient medium with number density n. To
consider all reasonable cases, we ran our model using all
combinations of the values of τ0, Esn, Mej, and n given
in §4.1, as well as P0 = 5, 10, 25, 100 ms for a total of
432 different trials. In this scenario, since it is not pos-
sible to determine an independent estimate of the age
of the system, it is necessary to assume a value of P0.
To determine which of these combinations are possible
explanations for G328.4+0.2, we required that:
6 Due to oscillations in radius the PWN undergoes after its col-
lision with the RS, it can reach the current size at multiple times.
• Criterion 1: vminns < 2000 km s
−1. Since, in
this scenario, we have no prior estimate of the
age of G328.4+0.2, when we run our model we as-
sume that vns = 0. This does not effect our re-
sults because rns, as measured in §4.1, is less than
Rpwn ≡ RG328, and therefore the neutron star is
always injecting energy into the PWN as it does if
vns = 0. Once, for a given set of input parameters
we have determined tnow, we calculate v
ns using
Equation (8).
• Criterion 2: The current spin-down energy of the
neutron star in G328.4+0.2 is between 0.017 ≤
˙E,37 ≤ 170, where ˙E,37 ≡ Ė/10
37 ergs. This is
based on the work done in §3.2, and is consistent
with the initial values of Ė used in §4.1.1. Since
in this scenario we have no estimate of the age of
G328.4+0.2, we are unable to assume a value for
Ė of the central neutron star and then calculate its
initial spin-down luminosity, as we did in §4.1.1.
• Criterion 3: Rpwn < Rsnr for all times t < tnow,
as explained in §4.1.1.
• Criterion 4: The PWN has already collided, and
has been compressed by, the RS, as explained in
§3.2.
• Criterion 5: The Central Bar created by the
compression of the PWN is still observable. The
method of determining if this is satisfied is the same
as the one used in §4.1.1.
• Criterion 6: The PWN must have been able to
form RT instabilities after the PWN/RS collision.
As in §4.1.1, we implement this requirement by re-
quiring that Ppwn > Psnr(Rpwn) for some t > tcol.
Additionally, as explained in §3.2, in order for the
PWN to create Filamentary Structure C it must
currently be unstable to R-T instabilities – requir-
ing that Ppwn > Psnr(Rpwn) now.
• Criterion 7: As explained in §3.2, the ob-
served Outer Protrusions in the radio require that
the PWN currently be expanding into the SNR,
vpwn(tnow) > 0.
• Criterion 8: G328.4+0.2, must have only under-
gone one compression/re-expansion cycle. As ex-
plained in §3.2, numerical simulations of PWN in-
side SNRs finds that the PWN is disrupted after
the first such cycle (Blondin et al. 2001).
It is important to note that, if G328.4+0.2 is a PWN,
then the radio and X-ray observations provide little in-
formation on the evolutionary phase of the (unseen) SNR
and no information on the current ratio of the PWN and
SNR radii.
Out of the 432 possible combinations of the input pa-
rameters, only five satisfy all ten of the above criteria, as
listed in Table 4. While the neutron star appears to be
inside the PWN, it is possible that this is just a projec-
tion effect. To evaluate the possibility that the PWN in
G328.4+0.2 has already entered the Relic PWN phase of
its evolution, we calculated vmin,IIns , defined as:
vmin,IIns =
RG328
. (15)
If vns > v
min,II
ns , then the G328.4+0.2 is a Relic PWN, if
not, then it is still in the Collision with the RS phase of
its evolution.
As shown in this Table, the predicted properties of
G328.4+0.2 vary substantially if G328.4+0.2 is inside a
Sedov or Radiative SNR. In the Sedov case, G328.4+0.2
is quite young, and progenitor SN explosion had a normal
explosion energy but a low ejecta mass (Mej ∼ 1M⊙),
and it occurred in a low density environment. Ad-
ditionally, the neutron star formed in this explosion
was spinning rapidly, has a low surface magnetic field
strength (Bns < 10
12 G), and a high space velocity
(vns & 800 km s
−1). In the Radiative Case, G328.4+0.2
is substantially older, and the progenitor SN explosion
was a low kinetic energy (Esn ∼ 3 × 10
50 ergs) and high
ejecta mass expanding. The neutron star in this case
was born spinning somewhat slower and has a normal
magnetic field strength for a young neutron star.
With the information presented in Table 5, it is possi-
ble to further refine the expected SNR and PWN prop-
erties. As argued in §4.1.1, the prominence of the central
bar argues that, during the compression stage, the vol-
ume of the PWN decreased significantly. Though it is not
possible at this time to quantify the compression needed,
an examination of Table 5 shows that for only two mod-
els, ST 2 and Rad 1, did the volume of the PWN decrease
by more than 10% – and therefore these two models are
the most probable descriptions of G328.4+0.2. In the
case of Rad 1, vmin,IIns ∼ 100 km s
−1 is significantly less
then the average neutron star velocity, v ∼ 400 km s−1
(Faucher-Giguère & Kaspi 2006; Hobbs et al. 2005), im-
plying that the PWN is in the Relic PWN phase of its
evolution. Since the sound speed inside a Radiative SNR
is quite low, ∼ 100 km s−1, we expect that the PWN in
the Rad 1 scenario would have a bow-shock morphology.
Since there is no clear evidence for this in the X-ray or
radio emission from G328.4+0.2, this suggests that ST 2
is a better fit to the data.
The conclusion that ST 2 is an accurate description
of G328.4+0.2 is supported by circumstantial evidence
as well. For this scenario, the expected radius of the
termination shock around the neutron star, rts, defined
as (Slane et al. 2004):
r2ts =
4πcPpwn
, (16)
assuming a spherical wind, is rts ∼ 0.6 pc, which corre-
sponds to an angle of θts ∼ 8d17
′′ – a distance which is
comparable to the offset between Clump 1 and Clump 2
derived in §2.1.1. Another interesting feature for this
model is that, as shown in Fig. 4, the radius of the PWN
at the time of re-expansion is similar to that of the outer
parts of the central filamentary structures discussed in
§2.2. While this correlation might be coincidental, this
could imply that the hydrodynamic instabilities formed
at the PWN/SNR interface during the re-expansion dis-
rupted the shell of material swept up by the PWN –
consistent with the simulation of Blondin et al. (2001).
While not definitive, these two pieces of evidence argue
that ST 2 is a reasonable description of G328.4+0.2.
The properties of ST 2 are given in Table 6, and the
evolution of Rpwn is shown in Fig. 9. It is interesting to
note that in this scenario, the PWN collides with the RS
at a time tcol < τ0 (tcol ≈ 850 years) so energy injection
by the neutron star into the PWN after the PWN/RS
collision is important to the PWN’s evolution during this
stage. It is important to note that this model predicts
that the neutron star powering G328.4+0.2 is the most
energetic neutron star in the Milky Way, as well as one
of the fastest. Given that G328.4+0.2 is largest and has
the highest radio luminosity of any known PWN, it is not
surprising that it was formed by such a powerful neutron
star. Finally, the age and Ė predicted by this method
are similar to those predicted by Gaensler et al. (2000).
In order to better understand the limitations of the
approach in determining the properties of the neutron
star and SNR in G328.4+0.2, we have run the model
presented in §4 over a finer grid of parameters and eval-
uated the resulting PWN evolution using the same cri-
teria as above. In Fig. 10, we show which values of P0
and Bns pass all of this criteria for three different kind
of SN explosions: Esn = 10
51 ergs and Mej = 1 M⊙,
Esn = 3 × 10
51 ergs and Mej = 1 M⊙, and Esn =
4 × 1051 ergs and Mej = 3.25 M⊙, assuming an ambi-
ent density with n = 0.03. The first set of SN parame-
ters corresponds to ST 1, the second to ST 2, and third
to a higher ejecta mass SN explosion is compatible with
a neutron star with the same parameters as ST 2. For
the first case, we find that a wide range of P0 values
are allowed but that Bns . 10
12 G. In fact, for this set
of SN parameters a P0 ∼ 10 ms, Bns ∼ 8 × 10
11 G neu-
tron star results in a PWN which is compressed a similar
amount as in ST 2. In the second case, we find that P0
and Bns are tightly constrained around P0 ≈ 5 ms and
Bns ≈ 5× 10
11 G. In the third set of SN parameters, we
find that P0 . 6 ms, but that Bns spans a wide range of
values, ∼ 1011 − 2× 1012 G.
To determine the allowed values of Esn and Mej, we
followed the same procedure as above using two different
sets of neutron star parameters: P0 = 5 ms and Bns =
5× 1011 G (the neutron star parameters in the ST 1 and
ST 2 scenarios), and P0 = 10 ms and Bns = 8 × 10
11 G.
For the first case, only models with Esn ∼ 1−4×10
51 ergs
andMej ∼ 0.5−3.5M⊙ satisfy the criteria above – though
a substantial compression of the PWN requires Esn &
2 × 1051 ergs. In the second case, we find that only
models with Esn . 10
51 ergs and Mej ∼ 0.5− 3.5M⊙ are
allowed.
While this error analysis shows that the method used
above to determine the properties of the neutron star
and SN explosion which formed G328.4+0.2 is unable to
do so to much better than an order of magnitude, the
different combinations values of P0, Bns, Esn, and Mej
which are allowed predict different physical properties for
G328.4+0.2 which are testable with further observations.
For example, in the case of P0 = 10 ms, Bns = 8×10
11 G,
Esn = 1 × 10
51 ergs, and Mej = 1 M⊙, G328.4+0.2 is
∼ 13, 000 years old, twice the age predicted in the ST 2
model as shown in Table 6, and as a result the required
velocity of the neutron star is significantly lower, vminns ∼
500 km s−1. The predicted period for the neutron star
in this scenario is also significantly slower than required
by the ST 2 scenario, P ∼ 24 ms, with a value of Ė
approximately an order of magnitude lower than that
in the ST 2 scenario. The termination shock radius for
this set of parameters is ∼ 5′′, considerable smaller than
the ∼ 8′′ for the ST 2 scenario and detectable with the
Chandra X-ray Observatory.
5. conclusions
In this paper, we first presented new X-ray (§2.1) and
radio (§ §2.2, 2.3) and observations of Galactic non-
thermal radio and X-ray source, G328.4+0.2, from which
we infer the current properties and evolutionary history
of this source (§3.2). We then presented a simple hydro-
dynamic model for the evolution of a PWN inside a SNR
(§4), which is used to determine which values of Esn,
Mej, n, P0, and Bns are able to reproduce the properties
discussed in §3.2 if G328.4+0.2 was a Composite SNR
(§4.1.1) or a PWN (§4.1.2). As a result of this analysis,
we determine the G328.4+0.2 is a PWN inside an unde-
tected SNR. Though we are not able to precisely deter-
mine the properties of the SN explosion and the neutron
star which have created this system, our analysis implies
that the neutron star in G328.4+0.2 was born with an ini-
tial period P0 . 10 ms, has a lower than average surface
dipole magnetic field strength, and has a higher than av-
erage spatial velocity vns & 400 km s
−1. We assume de-
termining that the SN explosion which created the neu-
tron star had a normal explosion energy, Esn ∼ 10
51 ergs,
but a relative low ejecta mass, Mej . 4M⊙. Future X-
ray and radio observations can significantly decrease this
uncertainty, particularly if they are able to either detect
pulsations from the neutron star or continuum X-ray or
radio emission from the currently undetected SNR in this
system.
While we are not able to definitely determine the ini-
tial period (P0) or surface magnetic field strength (Bns)
of the neutron star, nor the kinetic energy (Esn) or ejecta
mass (Mej) of the progenitor SN explosion, the estimates
quoted above are of interest. Our non-detection of the
pulsar via radio pulsations is not particularly constrain-
ing, due to the very large distance of the PWN. The low
magnetic field but rapid initial period predicted for the
neutron star in G328.4+0.2 has implications for mod-
els concerning the origin of neutron star magnetic fields.
For example, according to the α − Ω dynamo model of
(Thompson & Duncan 1993), neutron star born spinning
rapidly (P0 . 5 ms) should have a strong dipole compo-
nent to their surface magnetic fields (Bns ≫ 10
12 G).
If the ST 2 scenario proves to be correct, then the low
magnetic field of the neutron star in this system would
be a problem for such a model. Additionally, the low
ejecta mass inferred in this scenario requires that the
progenitor of this system was either a single, massive
star (M & 35M⊙) which exploded in a Type Ib/c SN
(Woosley et al. 1995), or was initially in a binary sys-
Finally, the method used in this paper to study
G328.4+0.2 is complementary to other methods used
(e.g. Chevalier 2005) to infer the initial period and mag-
netic field strength of other neutron stars in young PWN
as well as the properties of the SN explosion in which
they were formed, and is easily applicable to other such
systems.
JDG would like to thank Niccolo Bucciantini, Shami
Chatterjee, Roger Chevalier, Tracey DeLaney, David Ka-
plan, Kelly Korreck, Cara Rakowski, and John Ray-
mond for useful discussions, and the anonymous referee
for many useful comments. We are extremely grateful
to John Reynolds for prompt scheduling and observing
assistance at Parkes in 2007. The Australia Telescope
is funded by the Commonwealth of Australia for oper-
ation as a National Facility managed by CSIRO. JDG
and BMG were supported in this work by XMM grant
NAG5-13202 and LTSA grant NAG5-13032.
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Table 1
Spatial components of the X-ray emission from G328.4+0.2
Component Parameter Value
background constant 0.09
+0.06
−0.07
Clump 1 r0 1.
′′1+1.
−0.′′7
Position 15h55m26.s68+0.
−0.s05
, −53◦18′02.′′7+0.
−0.′′6
A 6.6+27.6
α 0.9+1.0
Clump 2 FWHM 19′′
Position 15h55m27.s5
+0.s2
−0.s1
, −53◦17′54.′′6
+3.′′4
−3.′′8
e 0.4
θ 280◦
A 0.8
Diffuse FWHM 67
Position 15h55m26.s6
+0.s2
−0.s2
, −53◦17′48.′′3
e 0.4
θ 130◦+10
A 0.4+0.1
Note. – Results from the spatial fit to the X-ray emission from G328.4+0.2, as described in §2.1.1. Fitting was done using the Sherpa
software package, and the errors reflect the 90% confidence level. Clump 1 was fitted to a 2D Lorentzian, defined as f(r) = A
1 + r
where f(r) is the expected number of counts at radius r away from the center of the source, A is given in counts, and the core-radius r0 is in
arc-seconds. The background component is given in counts pixel−1. Both Clump 2 and Diffuse were modeled with elliptical 2D Gaussians,
where the full width, half maximum (FWHM) is given in arc-seconds, the ellipticity is e, defined as 1− b/a, where b and a are, respectively,
the major and minor axis of the source, the position angle θ is given in degrees counterclockwise from north, and the amplitude A is given
in counts.
Table 2
Spectral Fits to Mos1 + Mos2 + pn Data
Parameter Value
Model phabs * pow phabs * bbodyrad phabs * bremss phabs * ray
NH 11.6
× 1022 6.4
× 1022 10.4
× 1022 7.8
× 1022
Γ or kT 2.0
+>900
Absorbed Flux 4.6
× 10−13 4.4
× 10−13 4.5
× 10−13 4.9
× 10−13
Unabsorbed Flux 1.9
× 10−12 6.5
× 10−13 1.2
× 10−12 9.6
× 10−13
χ2 103.3/131 98.4/131 101.7/131 122.8/131
Reduced χ2 0.81/128 0.77/128 0.79/128 0.96/128
Note – Results from joint fits to the mos1, mos2, and pn spectrum between 0.5 and 10 keV. The model phabs * pow refers to a power-law
attenuated by interstellar absorption, phabs * bbodyrad refers to a blackbody attenuated by interstellar absorption, phabs * bremss
refers to a Bremsstrahlung source spectrum attenuated by interstellar absorption, and phabs * ray refers to a Raymond-Smith thermal
plasma spectrum attenuated by interstellar absorption. In the table, NH is given in cm
−2, kT in keV, and flux in ergs cm−2 s−1, both the
absorbed and unabsorbed flux are calculated between 0.5 and 10 keV, and the errors represent the 90% confidence level.
Table 3
Expected Properties of G328.4+0.2 if it is a Composite SNR
Supernova Remnant Properties Pulsar Wind Nebula Properties Neutron Star Properties
Parameter Value Parameter Value Parameter Value
Esn 1× 10
51 ergs Epwn 4.8× 10
50 ergs Ė0 2.5× 10
40 ergs s−1
Mej 1 M⊙ Rpwn 8.7 parsecs P0 3.8 ms
Phase Sedov-Taylor M
sw 5.3 M⊙ τ0 1730 years
Psnr(Rpwn) 1.4× 10
−9 dynes Ppwn 2.0× 10
−9 erg cm−4 Bns 1.1× 10
vej(Rpwn) 400 km s
−1 vpwn 700 km s
−1 vminns 1300 km s
tnow 4900 years rts 0.5 parsecs Ė 1.7× 10
39 ergs s−1
n 0.32 cm−3 θts 6.
′′7 P 7.5 ms
· · · · · · · · · · · · Ṗ 1.8× 10−14 s/s
· · · · · · · · · · · · τc 6700 years
· · · · · · · · · · · · Epsr 1.0× 10
51 ergs
Note. – The values in bold are model assumptions, while the others are predicted by the model presented in §4. Psnr(Rpwn) is the
pressure inside of the SNR just outside of the PWN, vej(Rpwn) is the velocity of material inside the SNR just outside of the PWN, Epwn is
the internal energy of the PWN, Rpwn is the radius of the PWN, M
sw is the mass of material swept up by the PWN, Ppwn is the internal
pressure of the PWN, vpwn is the expansion velocity of the PWN, rts is the radius of the termination shock around the neutron star inside
the PWN, calculated using Equation 16, θts is the angular size of this feature assuming d17 ≡ 1, Bns is the dipole magnetic field of the
neutron star in G328.4+0.2 according to this model, P is the period of the neutron star in G328.4+0.2, Ṗ is the period-derivative of the
neutron star, τc is the characteristic age of the neutron star, defined as τc = P/(2Ṗ ), and Epsr is the total amount of energy injected by
the neutron star into G328.4+0.2 for t < tnow. All values are given for t = tnow unless otherwise noted.
Table 4
Scenarios for G328 as a PWN inside an Undetected SNR
Scenario # τ0 P0 Esn,51 Mej n tnow SNR Phase Rsnr Bns,12 v
min,II
ST 1 1730 5.0 1.00 1 0.03 5100 Sedov-Taylor 19.8 0.5 1300 2400
ST 2 1730 5.0 3.16 1 0.03 6500 Sedov-Taylor 28.0 0.5 1000 1900
Rad 1 430 10.0 0.32 10 0.32 84200 Radiative 28.4 2.0 100 100
Rad 2 770 10.0 0.32 10 0.32 52400 Radiative 24.8 1.5 100 200
Rad 3 770 10.0 0.32 10 1.00 101400 Radiative 22.1 1.5 100 100
Note. – Values for τ0, P0, Esn, Mej, and n that satisfy the criteria listed in §4.1.2 for G328 being a PWN inside an undetected SNR.
The value of τ0 is given in years, P0 in ms, Esn,51 ≡ Esn/10
51 ergs, Mej in solar masses, n in cm
−3, tnow in years, Rsnr in parsecs,
Bns = Bns,12 × 10
12 G, vminns is in km s
−1, and v
min,II
ns is also in km s
Table 5
Compression/Expansion properties of G328.4+0.2 if it is a PWN
Scenario # t(vpwn = 0) Central Bar Lifetime Rpwn(vpwn = 0)
re−exp
compres
ST 1 1648.5, 2432.0 63930 8.20, 7.96 0.91
ST 2 969.0, 1837.0 35250 8.36, 6.34 0.44
Rad 1 12772.0, 26541.0 243480 8.53, 7.55 0.69
Rad 2 13336.5, 21112.5 256230 8.48, 8.27 0.93
Rad 3 9761.5, 11035.0 102640 5.72, 5.72 1.00
Note. – In this table, values Scenario # correspond to the values of τ0, P0, Esn, Mej, and n given in Table 4. t(vpwn = 0) and the Central
Bar lifetime are given in years, and Rpwn(vpwn = 0) is given in parsecs.
re−exp
compres
is the ratio of the volume of the PWN at re-expansion
and compression.
Table 6
Expected Properties of G328.4+0.2 if it is a PWN (ST 2 scenario in Table 4)
Supernova Remnant Properties Pulsar Wind Nebula Properties Neutron Star Properties
Parameter Value Parameter Value Parameter Value
Esn 3.2× 10
51 ergs Epwn 3.2× 10
50 ergs Ė0 1.5× 10
40 ergs s−1
Mej 1 M⊙ Rpwn 12.5 parsecs P0 5 ms
Phase Sedov-Taylor M
sw 0.4 M⊙ τ0 1730 years
Psnr(Rpwn) 3.6× 10
−10 dynes Ppwn 4.4× 10
−10 dynes Bns 5× 10
vej(Rpwn) 460 km s
−1 vpwn 790 km s
−1 vminns 990 km s
Age (tnow) 6500 years rts 0.6 parsecs Ė 6.4× 10
38 ergs s−1
n 0.03 cm−3 θts 7.
′′7 P 10.9 ms
· · · · · · · · · · · · Ṗ 2.1× 10−14 s/s
· · · · · · · · · · · · τc 8200 years
· · · · · · · · · · · · Epsr 6.3× 10
50 ergs
Note. – The model assumptions are given in bold. Psnr(Rpwn) is the pressure inside just outside of the PWN, vej(Rpwn) is the velocity
of material inside just outside of the PWN, Epwn is the internal energy of the PWN, Rpwn is the radius of the PWN, M
sw is the mass of
material swept up by the PWN, Ppwn is the internal pressure of the PWN, vpwn is the expansion velocity of the PWN, rts is the radius of
the termination shock around the neutron star inside the PWN, θts is the predicated angular radius of this feature assuming d17 ≡ 1, Bns
is the predicted dipole magnetic field of the neutron star in G328.4+0.2, P is the predicted period of the neutron star in G328.4+0.2, Ṗ
is the predicted period-derivative of the neutron star, τc is characteristic age of the neutron star, and Epsr is the total amount of energy
injected by the neutron star into G328.4+0.2 for t < tnow. All values are given for t = tnow unless otherwise noted.
Point Source
Background
Background Region for Spectral Analysis
Source Region for Spectral Analysis
Clump 1
DiffuseClump 2
Clump 2
Clump 1
Diffuse
Fig. 1.— Top: Exposure normalized, vignette corrected mos1 + mos2 image of G328.4+0.2 smoothed by a 5′′ Gaussian. The white
contours indicate 20, 40, 50, 70, and 90% of the peak X-ray flux in the smoothed image, while the boxes indicate the background and
source regions used for the spectral analysis described in §2.1.2. The background point source labeled in the image was excluded from
the background region. Additionally, the labels in this plot point to the morphological features discussed in §2.1.1. Bottom: Unsmoothed
normalized, vignette corrected mos1 and mos2 image of G328.4+0.2 overlaid with the regions used for the Hardness Ratio analysis discussed
in §2.1.2.
Fig. 2.— Mos1, Mos2, and pn spectrum of G328.4+0.2 overlaid with the absorbed power-law model whose parameters are given in
Table 2.
Fig. 3.— 1.4 GHz image of G328.4+0.2, overlaid with X-ray contours in green which represent 20%, 35%, ..., 90% of the peak flux in the
smooth X-ray image shown in Fig. 1. The beam size of this image is 7.′′0×5.′′8, and is shown in the lower left-hand corner of the image.
The labels indicate examples of the different radio morphological features discussed in §2.2.
Fig. 4.— 20cm radio image of G328.4+0.2 (same data as shown in Fig. 3), with a color scale chosen to enhance the visibility of Filamentary
Structure B discussed in §2.2. The yellow circle indicates the size of PWN predicted in the ST 2 model listed in Table 5 when it re-expanded
after the initial compression by the SNR reverse shock, and the white cross indicates the center of G328.4+0.2 (15h55m33s,−53◦17′00′′;
J2000) as determined by Gaensler et al. (2000).
Fig. 5.— Spectral tomography images of G328.4+0.2, as described in §2.2.1. The spectral index α is given in the upper left hand corner
of each image, where Sν ∝ ν
Contact Discontinuity
SNR Forward Shock
SNR Reverse
Shock
Outer Boundary
of PWN
Neutron Star
Shocked ISM Ambient ISM
Unshocked Ejecta
Material Swept
Up by PWN
Pulsar
Shocked Ejecta
Fig. 6.— Diagram of a Composite SNR in the Free Expansion stage of its evolution. In this image, the ratio between the thickness
of the mass shell surrounding the PWN and the radius of the PWN is 1/24, as determined by van der Swaluw et al. (2001), and the
radio of the SNR Forward Shock, Contact Discontinuity, and Reverse Shock radii are equal to the values given in Chevalier (1982) for his
n = 9, s = 0 case. The colors denote the nature of the material within each region.
1000 10000 100000
Time (years)
Fig. 7.— Rpwn/Rsnr for Models A (solid), B (long-dashed line), & C (short-dashed line) in Blondin et al. (2001). The top plot shows
the result of the model presented in §4, while the bottom is a reproduction of Fig. 3 by Blondin et al. (2001), reproduced by permission of
the AAS.
Fig. 8.— The radius of the PWN, SNR, and SNR reverse shock as well as the location of the neutron star as a function of time if
G328.4+0.2 is a composite SNR. The vertical line indicates the current age of the system, and the properties of this system are given in
Table 3.
Fig. 9.— The radius of the PWN, SNR, and SNR reverse shock as well as the location of the neutron star as a function of time for the
favored (ST 2; Table 4) scenario if G328.4+0.2 is a PWN. The vertical line indicates the current age of the system.
Fig. 10.— The results for varying P0 and Bns for a Esn = 10
51 ergs, Mej = 1M⊙ (top), Esn = 3× 10
51 ergs, Mej = 1M⊙ (middle), and
Esn = 4×10
51 ergs, Mej = 3.25M⊙ (bottom) SN explosion, assuming n = 0.03 cm
−3. The small black squares indicate models which failed
the criteria described in §4.1.2, while the colored circles indicate scenarios which passed. The color represents the Compression Fraction
of the PWN, defined as the ratio of the PWN’s volume at the beginning and end of the compression stage. The Compression Fraction of
the ST 2 case given in Table 4 is 0.44 (light blue on this color scale), and lower values correspond to a more substantial compression. The
star indicates the position of a P0 = 5 ms, Bns = 5 × 10
11 G neutron star, while the large square indicates the position of a P0 = 10 ms,
Bns = 8× 10
11 G neutron star – the two neutron stars used in Fig. 11.
Fig. 11.— The results of varying Esn and Mej for a P0 = 5 ms, Bns = 5 × 10
11 G (top) and P0 = 10 ms, Bns = 8 × 10
11 G (bottom)
neutron star, assuming n = 0.03 cm−3. The black squares indicate which scenarios failed the criteria described in §4.1.2, while the colored
circles indicate those that passed, with the color representing the Compression Fraction (defined as the ratio of the PWN’s volume at the
beginning and end of the compression stage) of the PWN. The star indicates a Esn = 1× 10
51 ergs, Mej = 1 M⊙ SN explosion, the square
indicates a Esn = 3× 10
51 ergs, Mej = 1 M⊙ SN explosion, and the circle indicates a Esn = 4× 10
51 ergs, Mej = 3.25 M⊙ SN explosion –
the SN explosion parameters used in Fig. 10.
APPENDIX
equations for the hd model for the evolution of a pwn inside a snr
In this Appendix, we provide many of the details concerning the properties of the neutron star, PWN, and SNR
needed to simulate the HD model for the evolution of a PWN inside a SNR described in §4.
For the SNR, we assume that the initial ejecta density profile consists of a constant density core surrounded by a
ρ ∝ r−9 envelope – the standard assumption for a SNR produced by a Type-II SNR (Blondin et al. 2001; Chevalier
1982) – and that the ejecta is expanding ballistically (vej ≡ rej/t). The boundary between the constant density core
and the outer ejecta envelope has a velocity vcore, defined as (Blondin et al. 2001):
vcore=
where Esn is the explosion energy of the SN and Mej is the ejecta mass. As a result, the density ρcore of the ejecta
core is (Blondin et al. 2001):
ρcore(t)=
Esn v
core t
−3. (A2)
As the SNR expands, it sweeps up and shocks the surrounding interstellar medium (ISM). This swept-up material has
a higher pressure than the cold ejecta driving the expansion of the SNR, and as a result drives a reverse shock (RS)
into the SN ejecta. In between the outer edge of the SNR, which marks the location of the forward shock (FS) and
the RS is a contact discontinuity which separates the shocked ISM from the ejecta shocked by the RS. The pressure
inside the SNR at r < rrs, where rrs is the radius of the RS, is assumed to be zero. A diagram of this is shown in
Fig. 6. Since we assume that both the SN ejecta and the shocked ISM behave as a γ = 5/3 perfect gas, the sound
speed cs of this material is:
When the RS is still in the ejecta envelope, we determine the pressure, velocity, and density profiles on the material
between the RS and FS using the self-similar equations given by Chevalier (1982), evaluating them for the n = 9, s = 0
case. However, when the RS enters the constant density ejecta core, it is no longer possibly to apply the self-similar
solution of Chevalier (1982), and we use the work of Truelove & McKee (1999) to determine the radius of the RS and
the results given by Bandiera (1984) to determine the pressure, velocity, and density profiles between the RS and FS.
It is also necessary to model the radius of the FS (Rsnr), which we do using the work of Truelove & McKee (1999).
This is valid while the SNR is in the Free Expansion and Sedov-Taylor phases of its evolutions. After the SNR goes
radiative, which occurs at a time t = trad defined as (Blondin et al. 1998):
trad≈ 2.9E
17 × 104 yr. (A4)
After this point, Rsnr ∝ t
2/7. An analytic model for the pressure, velocity, and density distribution of a SNR in this
phase does not currently exist, and therefore it is difficult to extend our model to this phase, though if one assumes
that the interior of the SNR evolves adiabatically, Rpwn/Rsnr ∝ t
0.075 for t > trad (Blondin et al. 2001).
For the PWN, as mentioned in §4, we assume that it is a bubble filled with a γ = 4/3 perfect gas. As a result, the
internal pressure of the PWN, Ppwn is equal to:
Ppwn=
3Vpwn
, (A5)
where Epwn is the internal energy of the PWN and Vpwn is the volume of the PWN, defined as:
Vpwn=
πR3pwn (A6)
where Rpwn is the radius of the PWN. The internal energy of the PWN is determined by the rate of energy injected
into the PWN by the neutron star (Ė), and energy loss due to its expansion inside the SNR ( ˙Eadpwn). For Ė, we use
the standard assumption that it is equal to:
Ė= Ė0
where t is the age of the neutron star, p is the pulsar braking index (p = 3 for a magnetic dipole), τ0 is the characteristic
timescale of pulsar spin-down, and Ė0 is the initial spin-down energy of the neutron star. Both τ0 and Ė0 depend on
the physical properties of the neutron star, with τ0 defined as (Blondin et al. 2001; Shapiro & Teukolsky 1983):
3c3 IP 20
4π2B2nsR
ns sin
where I is the neutron star’s moment of inertia, P0 is the initial spin period, Bns is the magnetic field of the neutron
star, Rns is the radius of the neutron star, α is the angle between the neutron star’s rotation axis and magnetic field,
and (Blondin et al. 2001):
Ė0= I
τ0(p− 1)
. (A9)
Since the PWN expands adiabatically, ˙Eadpwn is equal to:
˙Eadpwn=−
. (A10)
As a result, the change in the internal energy of the PWN over time ( ˙Epwn) is equal to:
˙Epwn=−
+ Ė0
(A11)
assuming that p = 3. This equation can be solved analytical, and we result that Epwn(t) can be expressed as:
Epwn(t)= Ė0τ0
ln(1 + t/τ0)
t/τ0 − 1
. (A12)
When we run our model, we use Eq. (A12) to determine the initial value of Epwn, but determine Epwn at later times
using the procedure described in Step 2 in §4.
During its free-expansion, the PWN is moving faster than its surroundings, and the mass of the shell surrounding
the PWN (Msw,pwn) is simply:
Msw,pwn(t)=
∫ Rpwn
4πR2ρej(r, t)dr (A13)
where ρej(r) is the density profile of the SNR. After the collision with the reverse shock, if the PWN is moving
faster than its surroundings we determine the mass of the ejecta shell recently swept up by the PWN and add it
to the value of Msw,pwn calculated at the time of the reverse shock collision. If the PWN is moving slower than its
surroundings, we assume that Msw,pwn remains constant, even if the PWN is being compressed by the surrounding
SNR. Due to the difference in pressure between the PWN interior to the mass shell and the SNR exterior to the mass
shell (Psnr(r = Rpwn)), the mass shell is subject to a force F∆P, defined as:
F∆P=4πR
pwn[Ppwn − Psnr(Rpwn)]. (A14)
In this notation, F∆P > 0 means that the PWN interior has a higher pressure than inside the surrounding SNR. If the
PWN has not yet encountered the RS, we assume that Psnr(r = Rpwn) = 0. If the mass shell is moving faster than the
sound speed of the surrounding material (vpwn > cs(Rpwn)), which is the case before the PWN interacts with the RS
(Chevalier & Fransson 1992), the mass shell is decelerated by ram pressure, and the total force on the mass swept-up
by the PWN, Fpwn, is:
Fpwn=F∆P − 4πR
pwnρej(Rpwn)[vpwn − vej(Rpwn)]
2. (A15)
If vpwn < cs, then Fpwn = F∆P. For t ≪ τ0, analytical solutions to these equations give Rpwn ∝ t
6/5 if the PWN is
still inside the central constant-density core – a result which is reproduced by our numerical implementation of the
model described in §4.
In this framework, the period P of a neutron star evolves as:
P =P0
, (A16)
the period-derivative Ṗ evolves as:
(A17)
and the surface magnetic field Bns of the neutron star, assuming p = 3, is:
Bns=1.5
˙E0,37
2P 20,ms
× 109 G (A18)
where ˙E0,37 = Ė0/10
37 ergs s−1, P0,ms is the initial period in ms, and R14 is the radius of the neutron star R/14 km.
Additionally, for p = 3 τ0 is equal to:
τ0=17.3
B212R
years (A19)
where I = 1045I45 g cm
2 and the angle between the spin and magnetic field axes of the neutron star is α = 45◦.

  We present new observational results obtained for the Galactic non-thermal
radio source G328.4+0.2 to determine both if this source is a pulsar wind
nebula or supernova remnant, and in either case, the physical properties of
this source. Using X-ray data obtained by XMM, we confirm that the X-ray
emission from this source is heavily absorbed and has a spectrum best fit by a
power law model of photon index=2 with no evidence for a thermal component, the
X-ray emission from G328.4+0.2 comes from a region significantly smaller than
the radio emission, and that the X-ray and radio emission are significantly
offset from each other. We also present the results of a new high resolution (7
arcseconds) 1.4 GHz image of G328.4+0.2 obtained using the Australia Telescope
Compact Array, and a deep search for radio pulsations using the Parkes Radio
Telescope. We find that the radio emission has a flat spectrum, though some
areas along the eastern edge of G328.4+0.2 have a steeper radio spectral index
of ~-0.3. Additionally, we obtain a luminosity limit of the central pulsar of
L_{1400} < 30 mJy kpc^2, assuming a distance of 17 kpc. In light of these
observational results, we test if G328.4+0.2 is a pulsar wind nebula (PWN) or a
large PWN inside a supernova remnant (SNR) using a simple hydrodynamic model
for the evolution of a PWN inside a SNR. As a result of this analysis, we
conclude that G328.4+0.2 is a young (< 10000 years old) pulsar wind nebula
formed by a low magnetic field (<10^12 G) neutron star born spinning rapidly
(<10 ms) expanding into an undetected SNR formed by an energetic (>10^51 ergs),
low ejecta mass (M < 5 Solar Masses) supernova explosion which occurred in a
low density (n~0.03 cm^{-3}) environment.

Draft version November 4, 2018
Preprint typeset using LATEX style emulateapj v. 3/25/03
THE RADIO EMISSION, X-RAY EMISSION, AND HYDRODYNAMICS OF G328.4+0.2: A COMPREHENSIVE
ANALYSIS OF A LUMINOUS PULSAR WIND NEBULA, ITS NEUTRON STAR, AND THE PROGENITOR
SUPERNOVA EXPLOSION
Joseph D. Gelfand, Patrick O. Slane, and Daniel J. Patnaude
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138
B. M. Gaensler∗
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 and
School of Physics, The University of Sydney, NSW 2006, Australia
John P. Hughes
Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019
Fernando Camilo
Columbia Astrophysics Lab, Columbia University, New York, NY 10027
Draft version November 4, 2018
ABSTRACT
We present new observational results obtained for the Galactic non-thermal radio source G328.4+0.2
to determine both if this source is a pulsar wind nebula or supernova remnant, and in either case,
the physical properties of this source. Using X-ray data obtained by XMM, we confirm that the
X-ray emission from this source is heavily absorbed and has a spectrum best fit by a power law
model of photon index Γ = 2 with no evidence for a thermal component, the X-ray emission from
G328.4+0.2 comes from a region significantly smaller than the radio emission, and that the X-ray
and radio emission are significantly offset from each other. We also present the results of a new
high resolution (7′′) 1.4 GHz image of G328.4+0.2 obtained using the Australia Telescope Compact
Array, and a deep search for radio pulsations using the Parkes Radio Telescope. By comparing this
1.4 GHz image with a similar resolution image at 4.8 GHz, we find that the radio emission has a flat
spectrum (α ≈ 0; Sν ∝ ν
α), though some areas of the eastern edge of G328.4+0.2 have a steeper radio
spectral index of α ∼ −0.3. Additionally, we searched without success for a central radio pulsar, and
obtain a luminosity limit of L1400 <. 30mJykpc
2, assuming a distance of 17 kpc. In light of these
observational results, we test if G328.4+0.2 is a pulsar wind nebula (PWN) or a large PWN inside
a supernova remnant (SNR) using a simple hydrodynamic model for the evolution of a PWN inside
a SNR. As a result of this analysis, we conclude that G328.4+0.2 is a young (. 10000 years old)
pulsar wind nebula formed by a low magnetic field (. 1012 G) neutron star born spinning rapidly
(. 10 ms) expanding into an undetected SNR formed by an energetic (& 1051 ergs), low ejecta mass
(Mej . 5M⊙) supernova explosion which occurred in a low density (n ∼ 0.03 cm
−3) environment.
If correct, the low magnetic field and fast initial spin period of this neutron star poses problems for
models of magnetar formation which require fast initial periods.
Subject headings: stars: neutron, stars: pulsars: general, ISM: supernova remnants, radio continuum:
ISM, X-rays: individual
1. introduction
Stars with initial masses between ∼9 and 25 M⊙ are
expected to end their lives in a giant supernova (SN) ex-
plosion during which neutron stars are created. The fast
moving ejecta from the SN create a supernova remnant
(SNR), while the particle wind produced by the neu-
tron star as it loses rotational energy inflates a pulsar
wind nebula (PWN; Gaensler & Slane 2006). Initially,
the PWN is inside the SNR – and when the PWN is
detected inside the SNR the system is called a “compos-
ite” SNR (Helfand & Becker 1987). The evolution of the
central neutron star and the outer SNR affect the PWN,
Electronic address: jgelfand@cfa.harvard.edu
∗Alfred P. Sloan Research Fellow, Australian Research Council
Federation Fellow
Electronic address: jgelfand@cfa.harvard.edu
and as a result the PWN goes through several evolution-
ary phases while it is inside the SNR. This evolution is
determined by the physical properties of the neutron star
(specifically the initial period P0, the braking index p
and the strength of the dipole component to the surface
magnetic field Bns), the SN explosion (explosion energy
Esn and ejecta mass Mej), and the surrounding medium
(ambient number density n). As a result, by measur-
ing the properties of the PWN inside a SNR at a given
time one is able to constrain these physical parameters
which allows one to study the mechanisms behind both
core-collapse SNe and massive star evolution.
With this in mind, we present results of new radio
1 The braking index is defined as Ω̇ ∝ Ωp, where Ω is the angular
velocity of the neutron star’s surface.
http://arxiv.org/abs/0704.0219v1
mailto:jgelfand@cfa.harvard.edu
mailto:jgelfand@cfa.harvard.edu
observations of this source with the Australia Telescope
Compact Array (ATCA), as well as a new X-ray (X-ray
Multi-mirror Mission; XMM) observation of G328.4+0.2
(MSH 15-57; Mills et al. 1961). This source is a distant
(d ≥ 17.4 ± 0.9 kpc; Gaensler et al. 2000), radio bright
(flux density Sν = 14.3 ± 0.1 Jy at ν =1.4 GHz), po-
larized, extended (diameter D ≃ 5.0′) radio source with
a relatively flat spectral index (α ≃ −0.12± 0.03 where
Sν ∝ ν
α; Gaensler et al. 2000). Based on these radio
properties, and the discovery of non-thermal X-ray emis-
sion from this source by ASCA (Hughes et al. 2000), this
source was classified as a PWN – the largest and most
radio-luminous PWN in the Galaxy. In this interpre-
tation, the expectation is that G328.4+0.2 is ∼ 7000
years old and powered by an extremely energetic neu-
tron star (Gaensler et al. 2000). However, follow up ra-
dio polarimetry work (Johnston et al. 2004) implied that
G328.4+0.2 is an older composite SNR in which the
PWN is just a small fraction of the total volume, and
as a result is powered by a significantly less energetic
neutron star then argued by Gaensler et al. (2000). In
this paper, we analyze new observations of this source in
order to determine the age of G328.4+0.2, the energet-
ics of the neutron star and the progenitor SN, and the
density of its environment.
In §2 we present new X-ray and radio observations of
G328.4+0.2. In §3, we first discuss the expected evolu-
tionary sequence for PWNe inside SNRs (§3.1), making
general comments regarding the expected observational
signature of each phase. In §3.2 use the observational
results presented in §2 to draw some initial conclusions
about the nature of G328.4+0.2. In §4, we present a sim-
ple hydrodynamical model for the evolution of a PWN
inside a SNR, which we apply to G328.4+0.2 assuming it
is a composite SNR (§4.1.1) or a PWN (§4.1.2). Finally,
in §5 we summarize our results.
2. observations
In this Section, we present the data gathered in a
XMM observation (§2.1), a 1.4 GHz ATCA observation
of G328.4+0.2 (§2.2), and a search for a radio pulsar in
this source (§2.3).
2.1. X-ray Observations
On 2003 March 9–10, G328.4+0.2 was observed for
∼50 ks by XMM. During this observation, the pn cam-
era was operated in Small Window Mode, and the Mos1
and Mos2 camera were operated in Full Frame Mode.
The “Thick” optical filter was used due to the presence of
numerous bright stars in the field-of-view of G328.4+0.2.
The data were reduced with the software package xmm-
sas v 6.0.0 with calibration files current throughXMM-
CCF-REL-174, using the standard procedure for re-
ducing XMM data outlined in the XMM-Newton ABC
Guide2 and the Birmingham XMM Guide3.
2.1.1. Image Analysis
A vignetting corrected 0.2–12 keV image from the
Mos1 and Mos2 instruments4, is shown in Fig. 1, in
2 Available at http://heasarc.gsfc.nasa.gov/docs/xmm/abc/
3 Available at http://www.sr.bham.ac.uk/xmm2/guide.html
4 We did not use the pn data due to the substantially larger pixel
size of this instrument.
which we observe three spatial components to the X-ray
emission: a bright, compact feature located along the
SW edge of the X-ray emission (“Clump 1”), a fainter,
slightly extended feature located NE of the compact fea-
ture described above (“Clump 2”), and extended diffuse
emission, roughly 1′ in diameter, surrounding the two
features described above (“Diffuse”). From the “Clump
1” region we detected 120 ± 12 counts above the back-
ground between 0.5–10 keV in the Mos1 detector and
136± 12 in the Mos2 detector, from the “Clump 2” re-
gion we detected 66 ± 9 counts in both the Mos1 and
Mos2 detectors, and from the “Diffuse” regions we de-
tected 360± 20 and 380± 20 counts from the Mos1 and
Mos2 detectors, respectively.
We determined the spatial properties of these com-
ponents using the Sherpa modeling software package
(Freeman et al. 2001). Due to the low number of counts
per pixel, we used the simplex fitting method and min-
imized the cash statistic (Cash 1979). We attempted
to model Clump 1 and Clump 2 as circular 2D Gaus-
sians, elliptical 2D Gaussians, or circular 2D Lorentzians,
the latter of which is a good model for XMM’s point
spread function (PSF; Ghizzardi & Molendi 2002). We
attempted to model the Diffuse region as a circular or
elliptical 2D Gaussian, and assumed a constant back-
ground. We fit the observed image to all model com-
binations of Clump 1, Clump 2, and Diffuse (attempts
to eliminate one of these components resulted in signif-
icantly worse fits), and the best fit was obtained for
a model in which Clump 1 is a 2D Lorentzian while
Clump 2 and Diffuse are elliptical 2D Gaussians. The
fit parameters for this model are given in Table 1, and
the model and residuals are shown in Fig. 1, and from
this conclude that the emission from Clump 1 is consis-
tent with the PSF of XMM. Additionally, from this fit
we estimate that Clump 1 and Clump 2 are separated
by ∼ 10′′, while the centers of Clump 1 and Diffuse are
separated by ∼ 15′′.
2.1.2. Spectral Results
In generating the spectra, only events with flag = 0
were used. Additionally, the event files were screened for
background flares by binning the 10–15 keV light curve
of each instrument by 50 s and then recursively flagging
all bins with a count rate > 3σ above the average. This
procedure removed 3.0 ks, 2.3 ks, and 0.6 ks of data from
the Mos1, Mos2, and pn detectors, respectively. Spec-
tra were extracted for the regions shown in Fig. 1, and
the resulting spectra were binned into a minimum of 25
counts per channel and modeled using Xspec v12.2.0.
The background regions used are also shown in Fig. 1.
To determine the composite spectra of G328.4+0.2, we
jointly fit the spectrum obtained by the Mos1, Mos2,
and pn detectors – shown in Fig. 2. The background-
subtracted observed 0.5–10 keV count rate of G328.4+0.2
was 0.012 ± 0.001 counts s−1 in the the Mos1 detector
(555± 29 counts), 0.012± 0.001 counts s−1 in the Mos2
detector (580±30 counts), and 0.045±0.001 counts s−1 in
the pn detector5 (1576±63 counts). We fit the spectra to
seven different models separately – a power-law, a black-
body, bremsstrahlung, a Raymond-Smith plasma, and a
5 The pn detector count rate does not account for 29% dead time
since this instrument was operated in Small Window Mode.
http://heasarc.gsfc.nasa.gov/docs/xmm/abc/
http://www.sr.bham.ac.uk/xmm2/guide.html
power-law plus one of these three thermal models – all
attenuated for interstellar absorption. Only the single-
component models produced reasonable fits (reduced
χ2 ∼ 1), and the fitted parameters are presented in Table
2. Both the blackbody (kTBB ∼ 1.7 keV, TBB ∼ 20 MK)
and the bremsstrahlung models (kT ∼ 9 keV) require
unrealistically high temperatures, especially if the X-rays
are from a PWN as argued by Hughes et al. (2000). The
derived parameters for the power law model are similar
to that observed in other PWN (e.g. Gotthelf 2003), and
agree well with the results obtained for G328.4+0.2 by
Hughes et al. (2000). There is no evidence for thermal
X-ray emission, which one would expect from a SNR, in
this source.
Since the individual regions discussed in §2.1.1 did not
have enough counts for spectral fitting, we measured
their hardness ratio (HR), defined as:
H − S
H + S
where H is the number of counts in the Hard (higher
energy) band and S is the number of counts in the Soft
(lower energy) band, of the regions discussed in §2.1.1 to
determine if there were any spatial variations in the X-
ray spectrum of G328.4+0.2. Using the X-ray spectrum
as a guide, we calculate HR with H as the number of
counts between 4 and 8 keV and S as the number of
counts between 2 and 4 keV. Since the pixels on the pn
detector are sufficiently large that it is not possible to
separate the emission from these regions, we only use
data from the mos1 and mos2 detectors. The calculated,
background subtracted HR of G328.4+0.2 is 0.25± 0.04,
of the Clump 1 region is 0.29±0.07, of the Clump 2 region
is 0.31 ± 0.11, and of the diffuse region is 0.24 ± 0.05
(1σ errors). As a result, we conclude that there is no
significant change in the X-ray spectrum of G328.4+0.2
between these features.
2.1.3. Timing Results
A clear signature for the presence of a neutron star
would be the detection of X-ray pulsations in the emis-
sion from G328.4+0.2. We searched for this using the Z2n
test defined by Buccheri et al. (1983), where n is the har-
monic number of periodic signal, for n = 1, 2, 3, 4. The
maximum frequency searched was νmax = 1/(2n∆t), the
minimum frequency searched was 1/20 Hz, and the fre-
quency step was 1/4tobs (5× 10
−6 Hz, oversampling the
Nyquist rate by a factor of 2), where ∆t is the time res-
olution of the dataset (5.7 ms) and tobs is the length of
the observation. We only used events from the pn in-
strument (5.7 ms since it was operated in Small Win-
dow Mode) due to the poor time resolution (2.6s) of
the mos data. Additionally, we only used events from
the Clump 1 region because only only emission from the
central NS should be pulsed and as the brightest X-ray
region of G328.4+0.2, this region is the most probable
location of any neutron star. Unfortunately, due to the
large pixel size of the pn instrument this region is con-
taminated by emission from Clump 2 and the Diffuse re-
gion. The event times from the resultant event list were
barycentered to the Solar System reference frame, and we
searched for a periodicity over multiple energy ranges in
order to maximize the sensitivity of our search. The most
significant period detected was in the dataset which only
included photons between 5 and 10 keV (159 photons),
in which for n = 4 a signal with period P = 336 ms had
Z23 = 49.5 in 2074786 independent trials for this value
of n and energy range, which has a 12% chance of being
a false positive, a < 2σ result. Statistically, the most
significant sinusoidal (n = 1) pulse was in the 1–20 keV
dataset (340 photons), and had a period P = 73.1 ms
with a Z21 = 34.4 in 8365396 trials, a 34% chance of
being a false positive. Assuming that this signal is not
significant, we derive an upper limit on the pulse fraction
of 45% for a sinusoidal pulse profile and 22.5% for a δ-
function pulse profile (Leahy et al. 1983). Using the pn
count rate and size of the Clump 2 and Diffuse regions,
∼ 1/3 of the counts in the Clump 1 region is contamina-
tion from these regions. Accounting for this, we are only
able to put an upper limit on the pulse fraction of 67%
for a δ-function pulse profile. This upper limit is consis-
tent with the pulse fraction observed from other young
neutron stars.
2.2. Australia Telescope Compact Array Observations
Based on previous radio observations of G328.4+0.2,
there was a dispute in the literature as to whether this
source is a PWN, as argued by Gaensler et al. (2000), or
a composite SNR, as argued by Johnston et al. (2004).
The argument for this source being a PWN centered
on the flat spectrum of the radio emission, as well
as the high degree of polarization observed from the
center (Gaensler et al. 2000), while the radial polariza-
tion angles observed at the edge of this is more consis-
tent with a SNR (Johnston et al. 2004). If there is a
SNR component in G328.4+0.2, we expect that some
of the radio emission from this source should have a
steep (α < −0.3) spectrum. To search for such emis-
sion, we observed G328.4+0.2 for 12 hours at 1.4 GHz
with the Australia Telescope Compact Array (ATCA)
on 2005 June 25. Flux density calibration was carried
out using an observation of PKS B1934-638, and phase
calibration was carried out with regular observations of
PMN J1603-4904. The observation was carried out using
two 128 MHz bands, one centered at 1.344 GHz and the
other at 1.432 GHz, and the data reduction was done
using the miriad software package. The observation
was conducted when the ATCA was in the 6B configu-
ration, which has a longest baseline of ∼6000 m (∼ 6.′′9)
and a shortest baseline of ∼200 m (∼ 3.′4). As a re-
sult, this dataset alone is not sensitive to large-scale
emission from G328.4+0.2. To improve the sensitivity
to diffuse emission, we combined this dataset with the
1.4 GHz data used by Gaensler et al. (2000) as well as
continuum data gathered in the Southern Galactic Plane
Survey (McClure-Griffiths et al. 2005). Total intensity
images from this combined dataset were formed using
natural weighting, multi-frequency synthesis, and maxi-
mum entropy deconvolution. The final image, shown in
Fig. 3, has a resolution of 7.′′0×5.′′8, and an rms noise of
∼ 0.15 mJy beam−1. The measured 1.4 GHz flux density
of G328.4+0.2 is 13.8±0.4 Jy – consistent with the value
measured by Gaensler et al. (2000). For a 4.5 GHz flux
of 12.5± 0.2 Jy (Gaensler et al. 2000), this implies that
G328.4+0.2 has a radio spectral index α = −0.03± 0.03.
As seen in Fig. 3, the radio emission from G328.4+0.2
is very complicated, and contains multiple morphological
features. The major features are:
• Central Bar: The Central Bar is the bright-
est morphological feature in G328.4+0.2, and
has been previously detected at both 4.8 GHz
(Gaensler et al. 2000) and 19 GHz (Johnston et al.
2004). The Central Bar runs roughly E-W, and the
western edge of the bar is bifurcated, first noticed
by Johnston et al. (2004). The length of the bar
is ∼ 1.′75 long, and inside the bar there are three
peaks in the radio emission.
• Filamentary Structure A: These are the curved
filaments near the center of G328.4+0.2 which ap-
pear to be connected to the Central Bar, the bright-
est of which is the “Y” shaped structure NE of the
eastern edge of the Central Bar. In general, these
filaments are more prominent on the eastern side
of G328.4+0.2 and appear confined to the central
region of G328.4+0.2, not extending much beyond
the inner half.
• Filamentary Structure B: These are the faint,
radial filaments predominantly found on the west-
ern side of G328.4+0.2, as shown in Fig. 4. The
inner parts of these filaments are located ∼ 2.′5
from the center of G328.4+0.2, and their length
varies across G328.4+0.2 – in the southern half,
two filaments appear to extend to the edge of the
source while in the northern and western parts of
G328.4+0.2 they are substantially shorter. While
some of these filaments are kinked or curved, most
are fairly straight and radial in orientation. These
features were not detected by Gaensler et al. (2000)
and Johnston et al. (2004) due to the insufficient
u–v coverage of those observations.
• Filamentary Structure C: As shown in Fig. 3,
these are features located near the outer edge of
G328.4+0.2 that are parallel to the outer edge.
These features are more prominent and more plen-
tiful in the eastern half of G328.4+0.2.
• Outer Protrusions: The Outer Protrusions are
faint features – the two most prominent of which
are in the NE quadrant of G328.4+0.2 – that ex-
tend beyond the outer boundary of G328.4+0.2.
Several of these structures have bow-shock mor-
phologies.
The physical interpretation of these features will be pre-
sented in §3.2. It is worthwhile to note here that several
of these morphological features (e.g. the Central Bar and
the internal filamentary structures) have been observed
in other PWNe such as MSH 15-56 (Dickel et al. 2000)
and 3C58 (Slane et al. 2004), while others (e.g. the Fil-
amentary Structure C and Protrusions) are more char-
acteristic of SNRs, such as the Vela SNR (Bock et al.
1998).
This XMM observation also allows, for the first time,
a comparison between the radio and X-ray morphology
of G328.4+0.2. As shown in Fig. 3, there is a signifi-
cant offset between the X-ray and the center of the radio
emission, with Clump 1 located ∼ 80′′ from the center
of the radio emission. Additionally, the extent of the
X-ray emission is significantly smaller than that of the
radio emission. A physical interpretation of the X-ray
morphology and its relation to the radio emission will be
discussed in §3.2.
2.2.1. Spectral Index Map
The previous 1.4 GHz dataset had a resolution (∼ 20′′)
significantly worse than that of the 4.5 GHz data, and
therefore is not suitable for determining if there are
small scale changes in α inside G328.4+0.2. With these
new, high-resolution 1.4 GHz observations, it was pos-
sible to make a spectral index map of G328.4+0.2 us-
ing our new 1.4 GHz data and the 4.5 GHz data pre-
sented by Gaensler et al. (2000) since these datasets have
comparable u–v coverage. To detect any variation in
α, we made a spectral tomography map of G328.4+0.2
(Katz-Stone & Rudnick 1997). To do this, we first
produced a 1.4 GHz image of G328.4+0.2 from data
matched in u–v coverage with the 4.5 GHz data, and then
smoothed both the new 1.4 GHz image and the 4.5 GHz
image to a resolution of 8′′ to account for the poorer reso-
lution of the 1.4 GHz data. Finally, we produced a series
of difference images (Idiff,α) using the following formula:
Idiff,α= I1.4 − I4.5
where I1.4 and I4.5 are the 1.4 and 4.5 GHz images
produced above. In this method, the spectral index of
a region is determined by the spectral index at which
it disappears from the difference image. As shown in
Fig. 5, most of the radio emission from G328.4+0.2 has
a spectral index between α ∼ −0.1 and α ∼ +0.1, while
the outer edges of G328.4+0.2 have a steeper spectrum
(α ∼ −0.4) than the center, particularly the western edge
of G328.4+0.2. This steeper spectrum material is coin-
cident with some of the Filamentary Structure C dis-
cussed in §2.2, but there are no spectral features associ-
ated with any of the other radio morphological features
in G328.4+0.2 or with the X-ray emission. A physical
interpretation of these results will be discussed in §3.2.
2.3. Search for the radio pulsar at Parkes
As part of a project to search for pulsar counterparts to
all Galactic PWNe (e.g. Camilo et al. 2002a), on 2005
October 13 we observed G328.4+0.2 using the ATNF
Parkes telescope in NSW, Australia. As for similar
such work, we employed the central beam of the Parkes
multibeam receiver at a central frequency of 1374MHz,
with 96 frequency channels across a total bandwidth of
288MHz in each of two polarizations. The integration
time was 24ks, during which total-power samples were
recorded every 0.25ms for off-line analysis.
We analyzed the data with standard pulsar searching
techniques using PRESTO (Ransom et al. 2002). We
searched the dispersion measure range 0–2600cm−3 pc
(twice the maximum Galactic DM predicted for this line
of sight by the Cordes & Lazio 2002 electron density
model), while maintaining close to optimal time reso-
lution. In our search we were sensitive to pulsars whose
spin period could have changed moderately during the
observation due to very large intrinsic spin-down. The
search followed very closely that described in more detail
in Camilo et al. (2006). We did not identify any promis-
ing pulsar candidate in this search.
Applying the standard modification to the radiometer
equation, for an assumed pulsation duty cycle of 10%,
and accounting for a sky temperature at this location
of 15K, we were nominally sensitive to long-period pul-
sars having a period-averaged flux density at 1.4GHz
of S1400 > 0.05mJy. In fact, this limit applies only
to such long-period pulsars as to not be of practical
interest for us: for a distance of ∼ 17 kpc along this
line of sight, the expected DM is ≈ 1200 cm−3 pc, and
the scatter-broadening of the radio pulses due to multi-
path propagation is expected to be ∼ 50ms at 1.4GHz
(Cordes & Lazio 2002). This would likely render pulsa-
tions undetectable from any short-period pulsar, such as
we expect to power G328.4+0.2, regardless of average
radio flux. We therefore repeated the search at a higher
radio frequency ν, since the scattering timescale is ap-
proximately ∝ ν−4.
On 2007 January 4 we observed G328.4+0.2 at Parkes
at a central frequency of 3078MHz, with 288 channels
spanning a bandwidth of 864MHz in each of two polar-
izations. The total-power samples were recorded every
1ms for 30 ks, and analyzed in a manner analogous to
that described previously for the 1.4GHz data. This time
a few somewhat-promising candidates were identified in
the analysis, and a second 3GHz observation was made,
on 2007 March 19, for 36 ks. Analysis of this second ob-
servation did not confirm the original candidates, and we
have therefore not detected any radio pulsar counterpart
for the PWN in G328.4+0.2. The sensitivity of our 3GHz
observations was about 0.03mJy for long-period pulsars
(P & 20ms) and decreasing gradually for shorter peri-
ods. For the predicted DM, at this frequency the scat-
tering timescale is expected to be ∼ 2ms, comparable to
the dispersion smearing across each individual channel,
∼ 1ms. Propagation effects should therefore not have
prevented the detection of signals with P & 5ms.
Converting the 3GHz flux density limit to a frequency
of 1.4GHz, using a typical pulsar spectral index of –1.6
(Lorimer et al. 1995), results in S1400 . 0.1mJy. For
a distance of ∼ 17 kpc, this corresponds to a pseudo-
luminosity limit of L1400 ≡ S1400d
2 . 30mJykpc2. This
is comparable to L1400 of the very young pulsars B1509–
58, J1119–6127, and Crab (Camilo et al. 2002b), but a
factor of about 60 greater than for the young pulsar
in 3C58 (Camilo et al. 2002c), which has the smallest
known radio luminosity among young pulsars. Based
on these results, it is therefore entirely possible that
G328.4+0.2 harbors an as-yet undetected young pulsar
beaming toward the Earth with an ordinary radio lumi-
nosity.
3. interpretation of x-ray and radio observations
of g328.4+0.2
The X-ray spectrum of G328.4+0.2 is characteristic of
PWNe (see Gotthelf 2003 for a compilation of the X-
ray properties of PWNe), and therefore conclude that
the X-ray emission from G328.4+0.2 comes from a PWN
and not from a SNR. The same is true for the polarized,
flat-spectrum radio emission detected from the center
of G328.4+0.2 which are also characteristic of PWNe.
Therefore, in the following discussion we assume that
the X-ray and flat spectrum radio emission are both pro-
duced by a PWN. In §3.1, we discuss the evolutionary
sequence of PWNe in SNRs and the observational signa-
tures of each stage. In §3.2, we use the results from the
observations presented in §2.1 and §2.2 to draw general
conclusion about the properties of G328.4+0.2.
3.1. Evolution of PWN in SNRs
Both PWNe and SNRs are dynamic objects, and when
the PWN is inside the SNR its evolution is affected by
the behavior of both the central neutron star and the sur-
rounding SNR. While the PWN is inside the SNR, it typ-
ically goes through three evolutionary phases (Chevalier
1998; van der Swaluw et al. 2004):
• The Free-Expansion Phase – In this phase, the
PWN freely expands into the cold material inside
the SNR, sweeping up and shocking the surround-
ing ejecta into a thin shell (Chevalier & Fransson
1992; van der Swaluw et al. 2001). Since the PWN
is confined only by the shock wave its expansion
drives into the surrounding SNR, and the velocity
of this shock wave is much larger than the neutron
star velocity, it is free to move inside the SNR with
the neutron star.
• Collision with the Reverse Shock – As the
SN sweeps up and shocks the surrounding a am-
bient material, a reverse shock (RS) is driven
into the ejecta. Eventually, the PWN will en-
counter the RS, and as a result, can not con-
tinue to freely expand inside the SNR because it
is no longer in an essentially pressureless environ-
ment. Initially, the pressure behind the RS is
higher than the pressure inside the PWN, and as
result the PWN is compressed. As it contracts,
the pressure inside the PWN increases adiabati-
cally and eventually will be higher than its sur-
rounding, and will as a result re-expand inside the
SNR (Blondin et al. 2001; Bucciantini et al. 2003;
Reynolds & Chevalier 1984; van der Swaluw et al.
2001). Once the PWN encounters the RS, the ex-
pansion velocity of the PWN decreases signficantly
and falls below that of the neutron star, which is
unaffected by this collision. As a result, the neu-
tron star can detach itself from its PWN.
• Relic PWN Phase – When the neutron star
detaches from the relic nebula, it forms a new
PWN from the relativistic e+/e− plasma it contin-
ues to inject into the SNR (van der Swaluw et al.
2004). The PWN around the neutron star and
relic nebula evolve differently. The relic nebula
continues to contract/expand inside the SNR un-
til it achieves pressure equilibrium with its sur-
roundings, a process that can take many tens of
thousands of years. The new PWN initially ex-
pands sub-sonically, but when the neutron star is
∼ 2/3 of the way to the SNR shell, its velocity
will become supersonic relative to the surrounding
material and the PWN will take on a bow-shock
morphology (van der Swaluw et al. 2004). Eventu-
ally, the neutron star will leave the SNR, and as it
passes through the SNR shell it may re-energize the
surrounding SNR material, as possibly observed in
SNRs G5.4-1.2 and CTB80 (Shull et al. 1989).
As the PWN evolves inside the SNR, its appearance
changes radically. During the Free-Expansion phase, the
morphology of the PWN is determined by the properties
of the particle wind expelled by the neutron star. In
these cases, the neutron star is in the center of the PWN,
and there is no significant offset between the radio and
X-ray emission from the PWN. In general, during this
stage the PWN is located near the center of the observed
SNR shell. Examples of PWNe in this evolutionary stage
are the PWNe in SNR 0540-693 in the LMC (Reynolds
1985), as well as those in the Milky Way SNRs G11.2-
0.3 (Roberts et al. 2003; Tam et al. 2002) and G21.5-0.9
(Matheson & Safi-Harb 2005).
Due to the offset in the PWN’s position with respect to
the SNR’s center as a result of the neutron star’s veloc-
ity or inhomogeneities in the ISM, it is expected that one
side of the PWN will encounter the RS before the other
side (Blondin et al. 2001; van der Swaluw et al. 2004).
As a result, the PWN will no longer be symmetrically
oriented around the neutron star (van der Swaluw et al.
2004), leading to an offset between the radio and X-ray
emission from the PWN. Because the cooling time for X-
ray producing electrons is very short compared to that of
radio emitting electrons, the X-ray emission of a PWN
is expected to be brightest at the current location of the
neutron star while the radio emission reflects the effect
of the RS on the PWN. The compression/re-expansion
cycle triggered by the PWN/RS collision will also affect
the appearance of the PWN. According to a spherically
symmetric MHD simulation of a PWN in this phase,
compression of the PWN by the RS leads to an over-
pressurized region forming in the center of the PWN.
Material injected by the neutron star after this point is
then confined to the small region, leading to the forma-
tion of a radio/infrared “hot spot” in the center of the
PWN (Bucciantini et al. 2003).
The PWN/RS interaction also leads to the forma-
tion of hydrodynamic, primarily Rayleigh-Taylor (R-T),
instabilities at the PWN/SNR interface (Blondin et al.
2001). During the PWN’s initial free-expansion phase,
the shell of material swept up by the PWN is subject to
both thin shell and R-T instabilities (Bucciantini et al.
2004; Jun 1998), but the growth rate of these features
is expected to be sufficiently small that the PWN is not
disrupted, especially if even a small percentage of the
total energy of the pulsar’s wind is in magnetic fields
(Bucciantini et al. 2004). However, during the PWN/RS
interaction, rapid mixing of pulsar wind and SNR ma-
terial is expected when the PWN re-expands into the
SNR (Blondin et al. 2001). In fact, numerical simula-
tions suggest that the PWN is disrupted after its first
re-expansion into the SNR as a result of these instabil-
ities (Blondin et al. 2001). It is important to note that
these instabilities are only expected to affect the relic
nebula and not the new PWN formed by the neutron
star further from the SNR’s center. Once the composite
SNR enters the Relic PWN phase, the X-ray emission is
expected to be dominated by the new PWN since it con-
tains the high energy particles recently injected by the
neutron star, while the radio emission is dominated by
the relic nebula which contains most of the older parti-
cles that are expected to contribute at low frequencies.
As a result, during this phase the radio-emitting elec-
trons are expected to be dominated by electrons injected
during the free-expansion phase, while the X-ray is from
electrons injected after the passage of the RS.
3.2. Observational Results
In this Section, we use the results from the observa-
tions presented in §2.1 and §2.2, as well as the basic evo-
lutionary sequence for PWN in SNRs described above
in §3.1 to make some initial statements on the nature,
evolutionary state, and properties of G328.4+0.2. The
discussion given below is a very general interpretation of
observed radio and X-ray features in G328.4+0.2, it pro-
vides a framework in which to test the various scenarios
for G328.4+0.2 discussed in §4.1.1 and §4.1.2.
As mentioned in §1, there is a debate in the
literature as to whether G328.4+0.2 is a PWN
(Gaensler et al. 2000; Hughes et al. 2000) or a composite
SNR (Johnston et al. 2004). In neither of the X-ray or
radio observations presented above is there clear evidence
(e.g. thermal X-ray emission or a bright, steep spec-
trum, radio shell) for a SNR component. If G328.4+0.2
is a composite SNR, then the outer boundary of the ra-
dio emission likely marks the outer radius of the SNR
component, while the observed flat-spectrum radio emis-
sion and power law X-ray emission are emitted by the
PWN. Using the extent of the flat-spectrum radio emis-
sion shown in Fig. 5 to estimate the size of the PWN
component, we obtain that the radius of the PWN in this
source must be & 2/3RG328, the radius of G328.4+0.2.
If G328.4+0.2 is a composite SNR, then Filamentary
Structure 3, which as mentioned in §2.2.1 might have
a steeper spectral index than the rest of the radio emis-
sion in G328.4+0.2, would be emission from the SNR.
This emission is then possibly analogous to the corru-
gated structures seen in the NE part of the Tycho’s SNR
(Velazquez et al. 1998). Additionally, in this case the
Outer Protrusions mentioned in §2.2 maybe are ejecta
“bullets”, similar to those observed in the Vela SNR
(Aschenbach et al. 1995) and SNR N63A (Warren et al.
2003).
If G328.4+0.2 is a PWN, then the outer boundary of
the radio emission is the outer radius of the PWN and
the SNR in which it resides is undetected, similar to the
case for the Crab Nebula. As a result, the steep spectrum
radio emission seen at the edge of G328.4+0.2, as well
as Filamentary Structure C and the Outer Protrusions
observed in the radio, correspond to material swept-up
by the PWN. This is because radio emission from the
pulsar wind is observed to have a flat spectrum, un-
like this material. As a result, Filamentary Structure C,
as well as the radial component seen by Johnston et al.
(2004) in the polarization angle along the outer edge of
G328.4+0.2, are the result of the hydrodynamical (HD)
instabilities at the PWN/SNR interface. Since these
instabilities only occur when the PWN is accelerating
the shell of swept-up material surrounding it, he current
pressure inside the PWN (Ppwn) must be higher than
that of the SNR material just of the PWN [Psnr(Rpwn)].
Additionally, in this case the Outer Protrusions would be
the result of the PWN currently expanding into a clumpy
medium (e.g. the PWN analog of the process described
for young SNR by Jun et al. 1996), which requires that
the expansion speed of the PWN, vpwn, is currently posi-
tive. In this case, it is possible that the SNR surrounding
G328.4+0.2 will be detected at a later date, as was the
case for G21.5-0.9 (Matheson & Safi-Harb 2005).
Regardless of whether G328.4+0.2 is a composite SNR
or a PWN, the offset between the radio and X-ray
emission from the PWN component implies that the
PWN/RS collision has already occurred. The Central
Bar is then the remains of the over-pressurized region
created when the PWN was compressed by the RS, with
the bar-like shape of this region the result of either an
asymmetric RS or the anisotropic wind emitted by the
neutron star. The Central Bar should then consist of
pulsar wind material, which accounts for the α ∼ 0 spec-
tral index of this region as shown in Fig. 5. Additionally,
the flat spectral index observed from Filamentary Struc-
tures A implies that this feature is emitted by pulsar
wind material. As mentioned in §3.1, when the PWN
re-expands after the initial compression by the RS, nu-
merical simulations suggest that the rapid mixing of the
SNR ejecta and pulsar wind material can then occur. In
their 2D simulations of this process, Blondin et al. (2001)
observe features similar to that of Filamentary Structure
A, and as a result we conclude that the existence of these
features requires that the PWN has re-expanded at least
once after its initial compression by the RS. Since the ra-
dius of flat-spectrum radio emission from G328 is larger
than the outer radius of Filamentary Structure A, the
instabilities formed during this expansion must not have
completely disrupted the PWN. This differs from the re-
sults of Blondin et al. (2001), in which the PWN is dis-
rupted during the first re-expansion. This is most likely
due to the damping effect of the PWN’s magnetic field
on Raleigh-Taylor instabilities, which is not accounted
for by Blondin et al. (2001).
Finally, we discuss the X-ray emission seen from
G328.4+0.2 which, based on its X-ray spectrum, is emit-
ted by pulsar wind material. The observed offset between
Clump 1, Clump 2, and the Diffuse regions of the X-ray
emission implies that the PWN is not freely expanding,
consistent with the explanation that the PWN has col-
lided with the RS. We identify Clump 1 as the current
location of the neutron star since it is the brightest X-ray
feature, Clump 2 as the location of the termination shock
in the PWN (Kennel & Coroniti 1984), and the Diffuse
emission is produced by recently injected plasma stream-
ing away from the neutron star. In this case, the extent
of the Diffuse component depends on the synchrotron
lifetime of the X-ray emitting particles in the PWN.
The X-ray emission also provides an estimate of the
physical properties of the central neutron star, namely
a measure of the neutron star’s rotational spin-down en-
ergy, Ė. A comparison of observed X-ray luminosity Lx
and Ė shows a trend that neutron stars with a higher Lx
have a higher Ė, and that the relationship between these
two quantities is (Possenti et al. 2002):
logLX,(2−10)=1.34 log Ė − 15.34 (3)
where LX,(2−10) is the X-ray luminosity of the source
between 2 and 10 keV, albeit with a significant scatter
(Possenti et al. 2002). For the absorbed power-law fit to
the X-ray emission from G328.4+0.2 given in Table 2,
the unabsorbed 2–10 keV flux of G328.4+0.2 is ∼ 1 ×
10−12 ergs cm−2 s−1. For a distance to G328.4+0.2 of
d = 17d17 kpc, we obtain that:
LX,(2−10)∼ 3.5d
17 × 10
34 ergs s−1, (4)
which, using Eq. (3), gives us an estimate of Ė:
Ė ∼ 1.7d1.4917 × 10
37 ergs s−1. (5)
This number is somewhat less than estimate obtained
byGaensler et al. (2000) (Ė = 8.3× 1038 ergs s−1), who
assumed that Ė = 4 × 10−4LR, where LR is the radio
luminosity of G328.4+0.2. Our estimate of Ė is similar
to the estimate by Hughes et al. (2000) (Ė ∼ 1037 − 2×
1038 ergs s−1), who also used the Lx − Ė relation.
4. simple hydrodynamic model for the evolution of
a pwn inside a snr
In order to determine what neutron star, SN, and am-
bient density properties are required to produce a system
with these properties described in §3.2, we have devel-
oped a simple hydrodynamic (HD) model for the evo-
lution of a PWN inside of a SNR, which we then ap-
ply to G328.4+0.2 in §4.1. This model is based largely
on the models developed by Blondin et al. (2001) and
van der Swaluw et al. (2001). The main goal of this
model is to determine the radius of the PWN, Rpwn,
as it progresses through the evolutionary sequence de-
scribed in §3.1. In this model, we assume that the PWN
can be treated as a perfect gas with adiabatic index
γ = 4/3 and that is expanding into a SNR filled with
a perfect gas with adiabatic index γ = 5/3. We also as-
sume that the material swept-up by the PWN initially
lies in a thin shell with inner radius R = 23/24 Rpwn
(van der Swaluw et al. 2001), as shown in Fig. 6. The
dynamics of this mass shell are determined by the dif-
ference in pressure between the PWN and SNR, and by
calculating the radius of this mass shell we determine
Rpwn(t). Once the PWN enters the Relic PWN phase
of its evolution, this model only determines the proper-
ties of the relic nebula. What follows is a brief qualitative
description of the model used, while the full suite of equa-
tions used to implement it quantitatively can be found
in Appendix A.
As mentioned above, we model Rpwn(t) by calculating
the outer radius of the mass shell swept up by the PWN,
ignoring the effect of any instabilities which could dis-
rupt this shell. We solve for Rpwn(t) by assuming that
we know the values for the relevant quantities at a time
t − ∆t, and then calculate them for a time t, since the
relevant equations can not be solved at all times analyt-
ically. we wrote a program in IDL to implement this
numerically using the following procedure:
1. Calculate Rpwn(t+∆t) by assuming that the mass
shell around the PWN between t and t+∆t moves
with a constant velocity vpwn(t).
2. Calculate the internal energy of the PWN, Epwn(t+
∆t), using the first law of thermodynamics:
∆Epwn= Ėt− Ppwn∆Vpwn (6)
which takes into account energy losses from the adi-
abatic expansion/contraction of the PWN as well
as any energy input from neutron star into the
PWN between t and t + ∆t if the neutron star is
still inside the PWN. Since we assume the PWN is
filled with a γ = 4/3 perfect gas, Epwn ∝ PpwnVpwn
from the ideal gas law, where Ppwn is the internal
pressure of the PWN and Vpwn is the volume of
the PWN, as defined in Equations (A5 and (A6).
Since Vpwn ∝ R
3, and γ = 4/3 requires that
Ppwn ∝ V
pwn , we derive that Ppwn ∝ R
−4. As
a result, if there is no input from the neutron star,
then Epwn ∝ R
pwn. The energy input from the
neutron star (∆Epsr) is calculated by integrating
Eq. (A7) between t and t+∆t.
3. Calculate Ppwn(t + ∆t) using Equations (A5) and
(A6).
4. Calculate the pressure inside the SNR (Psnr), the
density inside the SNR (ρej), the velocity of the
material inside the SNR (vej), and the sound speed
of the material inside the SNR (cs), at the outer
radius of the PWN, R = Rpwn(t + ∆t) using a
model for the evolution and structure of a SNR, as
described in Appendix A.
5. If the PWN is expanding faster than the SNR ma-
terial around it, increase the mass of the shell sur-
rounding the PWN, Msw,pwn(t+∆t), accordingly,
as described in Appendix A.
6. Calculate the force on the mass shell surrounding
the PWN, Fpwn(t + ∆t), using Eqs. (A14) and
(A15). During the initial free-expansion of the
PWN inside the SNR, these equations reduce to
Equation A4 of van der Swaluw et al. (2001) and
Equation 14 of Chevalier (2005).
7. Calculate the new velocity of the mass shell around
the PWN, vpwn(t + ∆t), assuming that any mass
swept up by the PWN between t and t+∆t is done
so inelastically:
vpwn(t+∆t)=
Msw(t)vpwn(t) + Fpwn(t+∆t)∆t
Msw(t+∆t)
This is believed to be a reasonable approximation
because the newly swept-up material is shocked by
the mass shell and, as a result, its pre-existing mo-
mentum is transferred to the internal energy of the
mass shell.
This model is assumes that both the SNR and PWN
are spherically symmetric, the PWN remains centered
on the center of the SNR at all times, the PWN has no
effect on the evolution of the SNR, and that the ma-
terial swept-up by the PWN is incompressible and has
a negligible internal pressure. Additionally, this model
ignores the effects of magnetic field (Bucciantini et al.
2003) and RT instabilities at the PWN/SNR interface
(Blondin et al. 2001; van der Swaluw et al. 2004) on the
properties of the PWN. Despite these simplifications, our
model does a reasonably good job of reproducing the re-
sults for Model A in Blondin et al. (2001), as shown in
Fig. 7. In general, relative to results of Blondin et al.
(2001) and other authors, our model tends to result in
larger oscillations in Rpwn/Rsnr and a larger initial com-
pression. The first discrepancy results from neglecting
the effect of instabilities at the PWN/SNR interface that
damp these oscillations, and the second from not includ-
ing the effect of reflected shocks that enter the PWN at
the time of the PWN/RS collision (Blondin et al. 2001).
Additionally, we find that scenarios with the same to-
tal amount of energy deposited by the neutron star into
the PWN, Epsr but with different neutron star properties
(e.g. different values of P0 and Bns) produce the same
behavior of Rpwn(t). This is different than the conclu-
sion of Blondin et al. (2001), and believe that this dis-
crepancy is the result of using a more realistic expression
for Ė, Eq. (A7), than a step function, the form used by
Blondin et al. (2001).
4.1. Application of Model to G328.4+0.2
In the following discussion, we use the model given in
§4 for a PWN’s evolution inside a SNR to examine the
different possibilities for the nature of G328.4+0.2 given
in §3.2. We first analyze the possibility that G328.4+0.2
is a composite SNR (§4.1.1), and then he possibility that
G328.4+0.2 is a PWN (§4.1.2). This model requires six
inputs: the characteristic timescale of the neutron star’s
spin-down, τ0, initial spin-down power of the neutron
star Ė0, the velocity of the neutron star, vns, the kinetic
energy of the SN ejecta Esn, the mass of the SN ejecta
Mej, and the number density of the surrounding material
n. In order to calculate these values, we use the following
information:
• The distance to G328.4+0.2 is 17 kpc (d17 ≡ 1),
which is the lower limit on the distance to this
source as determined by Gaensler et al. (2000) us-
ing Hi absorption. This implies that the current
radius of G328.4+0.2 is RG328 ≡ 12.5 pc.
• The neutron star inside G328.4+0.2 is spinning
down with a braking index p = 3, the braking in-
dex produced by a pure dipole surface magnetic
field. Additionally, we assume that the neutron
star’s moment of inertia is I = 1045 g cm2, the
value derived for standard equations of state for
a neutron star (Shapiro & Teukolsky 1983). Both
of assumptions are standard in the literature (e.g.
Blondin et al. 2001).
• The offset between the Clump 1, which as described
in §3.2 is believed to be the location of the neu-
tron star powering the PWN, and the center of the
radio emission is due to neutron star’s spatial ve-
locity, vns. Using §2.1.1, we determine that this
observed offset corresponds to physical distance of
∼ 6.6d17 pc. Since the observed offset is due only
to the neutron star’s velocity in the plane of the
sky, it is a lower limit on the true distance the neu-
tron star has traveled since the SN explosion, rns.
If we assume that vns = rns/tnow, where tnow is
the age of G328.4+0.2, the observed offset allows
us to estimate the minimum spatial velocity of the
neutron star, vminns , equal to:
vminns =
6.6d17 pc
. (8)
• Using Equation (A19), we determine that for stan-
dard initial periods (P0 ∼ 5− 20 ms) and magnetic
field strengths (Bns = 5× 10
11 − 1013 G), τ0 varies
from ∼ 100 − 2000 years. To cover this range, we
assume that τ0 of the neutron star in G328.4+0.2
can have one of three different values:
τ0 = 430, 770, and 1730 years. (9)
which respectively correspond to a neutron star
with B = 1012 G and P0 = 5 ms, B = 3 × 10
and P0 = 20 ms, or B = 5 × 10
11 G and P0 =
5 ms. This range of τ0 is similar to those used
by Blondin et al. (2001), van der Swaluw et al.
(2001), and Bucciantini et al. (2003).
• G328.4+0.2 is expanding into a uniform medium
(s = 0 in the notation of Chevalier 1982). This
assumes G328.4+0.2 is much larger than either
the main sequence and late-stage wind bubble
formed by its progenitor, both of which are ex-
pected to have an interior ρ ∝ r−2 density struc-
ture. While the typical size of these structures
is smaller than RG328, this is not the the case
for very massive stars (M & 15 M⊙) for which
these bubbles can reach sizes of ∼ 100 pc or
larger in low density (n . 1 cm−3) environments
(Chevalier & Emmering 1989; Chevalier & Liang
1989). In this case, our assumption of a constant
density medium would not be correct. However,
the effect of G328.4+0.2 still being inside a stellar
wind bubble since this does not significantly mod-
ify the evolution of the SNR. Since their no a priori
information on the density around G328.4+0.2, we
assume it is one of the assume it has one of the
following values:
logn = −1.5,−1.0, 0, 0.5 cm−3. (10)
which cover the range of densities in the warm ion-
ized medium and the warm neutral medium.
• The ejecta mass of the SN explosion that formed
G328.4+0.2, Mej has one of the following values:
Mej = 1, 5, 10M⊙ (11)
and that the kinetic energy of the ejecta, Esn is:
log(Esn/10
51ergs) = −0.5, 0, 0.5. (12)
This range of Mej and Esn incorporate the range
inferred from observations of “normal” SNe, but
do not include hypernovae.
• We assume that the Lx − Ė relationship used in
§3.2 is accurate to better than two orders of mag-
nitude. As a result, in §4.1.1, we assume that the
current spin-down luminosity of the neutron star
in G328.4+0.2 is one of the following:
Ė=0.017, 0.17, 1.7, 17, and 170× 1037 ergs s−1,(13)
and in §4.1.2 assume that 1.7 × 1035 < Ė < 1.7 ×
1039 ergs s−1.
These are the initial conditions used in both §4.1.1 and
§4.1.2. The remaining input parameters into the model
are the initial spin-down luminosity Ė0 and space ve-
locity vns of the neutron star, and the method for deter-
mining the possible values of these parameters is given in
§4.1.1 and §4.1.2. Finally, for all trials discussed in §4.1.1
and §4.1.2 the model begins at a time t = 0.5 years, with
∆t = 0.5 years.
4.1.1. G328.4+0.2 as a Composite SNR
In this Section, we evaluate the possibility that
G328.4+0.2 is a composite SNR. To do this, we first
assume that the outer edge of the radio emission from
this source denotes the edge of the SNR, and therefore
RG328 ≡ Rsnr. As a result, for a given value of Esn,
Mej, and n, we use the model for the evolution of a SNR
discussed in Appendix A to calculate the current age of
G328.4+0.2, tnow. With this value of tnow and assumed
values for the current spin-down luminosity of the neu-
tron star, Ė, and τ0, we are able to calculate both the
initial spin-down luminosity Ė0 and initial period P0 of
the neutron star in G328.4+0.2 using Eqs. (A7) and (A9),
respectively.
Using this procedure, we ran our model using all pos-
sible combinations of the input parameters (τ0, Ė, Esn,
Mej, and n) given in §4.1, for a total of 540 different com-
binations. To see which combination of these input pa-
rameters provide a plausible explanation for G328.4+0.2,
we require the following:
• Criterion 1: vminns < 2000 km s
−1, since a neu-
tron star with a higher velocity than this is ex-
tremely implausible based on pulsar observations
(Hobbs et al. 2005).
• Criterion 2: P0 > 2 ms, the minimum rota-
tion period of a young proto-neutron star before
it breaks up (Goussard et al. 1998).
• Criterion 3: The PWN is smaller than the SNR
for all t < tnow. While it is possible that PWN
could expand to fill the entire SNR, it is not con-
sidered likely, and is contrary to the model as-
sumption that the PWN does not affect the evolu-
tion of the SNR. Additionally, we also require that
Rpwn(tnow) ≥ 0.67Rsnr(tnow), due to the large ob-
served size of the flat-spectral index radio emission
which is produced from the PWN, as described in
§3.2.
• Criterion 4: G328.4+0.2 is currently in the Free-
Expansion or Sedov-Taylor phase of its expansion,
i.e. tnow < trad, where trad, the age when a SNR
goes radiative, is defined in Eq. A4. Once a SNR
has entered its Radiative phase, it is expected that
the radio emission from the SNR be confined to
thin, bright, filaments like those observed in SNR
G6.4-0.1 (Mavromatakis et al. 2004) – which are
not observed in G328.4+0.2, or that the SNR is
radio-quiet.
• Criterion 5: The PWN/RS collision has already
occurred, as described in §3.2, and the PWN has
been compressed as a result of its collision with the
RS. This is required to explain the Central Bar, as
described in §3.2. This requires that vpwn < 0 at
some point in the past – which can only occur at
a time t > tcol, the time when the PWN and RS
collide.
• Criterion 6: The Central Bar created by the
compression is still observable. This is satisfied
if either the PWN is currently being compressed,
vpwn(tnow) < 0, or if the compression ended suffi-
ciently recently such that it can be observed. The
Central Bar is believed to be formed by both a
pressure and a magnetic field enhancement at the
center of the PWN (Bucciantini et al. 2003). As a
result its observable lifetime is the synchrotron life-
time of electrons accelerated by the magnetic field
enhancement. Therefore, we assume that the life-
time of the central bar is the synchrotron age of
the accelerated electrons, τsynch, equal to:
τsynch = 3× 10
4ν−1/2B−3/2pwn years, (14)
where ν is the observed frequency, in units of Hz,
and Bpwn is the strength of the magnetic field in-
side of the PWN, in units of G. With this infor-
mation, in the case that vpwn(tnow) > 0 we deter-
mine if the central bar is still observable by eval-
uating τsynch at 22 GHz (since this is the highest
frequency at which the Central Bar is observed;
Johnston et al. 2004) at the time when the com-
pression ends, assuming that Bpwn can be derived
using the minimum energy estimate. This criterion
is satisfied if τsynch > tnow − tre−exp, where tre−exp
is the time when the compression phase ends.
That the above criteria fall into two categories: criteria
required for physical plausibility (Criteria 1–3) and those
which depend on our interpretation of the radio and X-
ray properties of G328.4+0.2 (Criteria 4–6).
Of the 540 possible combinations of the input parame-
ters, only one passes all six criteria. The predicted SNR,
PWN, and neutron star properties of this scenario are
given in Table 3, and the behavior of Rpwn as a function
of time is given in Figure 8. In this scenario, G328.4+0.2
is quite young, ∼ 4900 years old, and the energy in-
jected into the SNR by the neutron star is similar to
the kinetic energy of the SN explosion (∼ 1051 ergs).
However, in this scenario, as shown in Fig. 8, the pre-
dicted compression is very small; when the compression
begins, Rpwn = 3.838 pc, and when the PWN begins to
re-expand into the SNR, Rpwn = 3.834 pc. This small
decrease is not surprising given that, as shown in Table
3, the total energy inputed into the PWN by the pulsar
(Epsr) is very close to the kinetic energy of the SN ejecta
(Esn). This negligible decrease in the volume of the PWN
is unlikely to form a central bar as prominent as the one
observed (Fig. 3), and therefore we feel is unlikely to be
the correct explanation for G328.4+0.2.
4.1.2. G328.4+0.2 as a PWN
In order to evaluate if G328.4+0.2 is a PWN, we use
the model presented in §4 to determine the earliest time6
(tnow) at which a PWN powered by a neutron star with
a given initial period P0 reaches the observed size of
G328.4+0.2 (Rpwn = 12.5 pc) if it is expanding into as
yet unseen SNR formed by ejecta with initial mass Mej
and kinetic energy Esn which exploded in a constant-
density ambient medium with number density n. To
consider all reasonable cases, we ran our model using all
combinations of the values of τ0, Esn, Mej, and n given
in §4.1, as well as P0 = 5, 10, 25, 100 ms for a total of
432 different trials. In this scenario, since it is not pos-
sible to determine an independent estimate of the age
of the system, it is necessary to assume a value of P0.
To determine which of these combinations are possible
explanations for G328.4+0.2, we required that:
6 Due to oscillations in radius the PWN undergoes after its col-
lision with the RS, it can reach the current size at multiple times.
• Criterion 1: vminns < 2000 km s
−1. Since, in
this scenario, we have no prior estimate of the
age of G328.4+0.2, when we run our model we as-
sume that vns = 0. This does not effect our re-
sults because rns, as measured in §4.1, is less than
Rpwn ≡ RG328, and therefore the neutron star is
always injecting energy into the PWN as it does if
vns = 0. Once, for a given set of input parameters
we have determined tnow, we calculate v
ns using
Equation (8).
• Criterion 2: The current spin-down energy of the
neutron star in G328.4+0.2 is between 0.017 ≤
˙E,37 ≤ 170, where ˙E,37 ≡ Ė/10
37 ergs. This is
based on the work done in §3.2, and is consistent
with the initial values of Ė used in §4.1.1. Since
in this scenario we have no estimate of the age of
G328.4+0.2, we are unable to assume a value for
Ė of the central neutron star and then calculate its
initial spin-down luminosity, as we did in §4.1.1.
• Criterion 3: Rpwn < Rsnr for all times t < tnow,
as explained in §4.1.1.
• Criterion 4: The PWN has already collided, and
has been compressed by, the RS, as explained in
§3.2.
• Criterion 5: The Central Bar created by the
compression of the PWN is still observable. The
method of determining if this is satisfied is the same
as the one used in §4.1.1.
• Criterion 6: The PWN must have been able to
form RT instabilities after the PWN/RS collision.
As in §4.1.1, we implement this requirement by re-
quiring that Ppwn > Psnr(Rpwn) for some t > tcol.
Additionally, as explained in §3.2, in order for the
PWN to create Filamentary Structure C it must
currently be unstable to R-T instabilities – requir-
ing that Ppwn > Psnr(Rpwn) now.
• Criterion 7: As explained in §3.2, the ob-
served Outer Protrusions in the radio require that
the PWN currently be expanding into the SNR,
vpwn(tnow) > 0.
• Criterion 8: G328.4+0.2, must have only under-
gone one compression/re-expansion cycle. As ex-
plained in §3.2, numerical simulations of PWN in-
side SNRs finds that the PWN is disrupted after
the first such cycle (Blondin et al. 2001).
It is important to note that, if G328.4+0.2 is a PWN,
then the radio and X-ray observations provide little in-
formation on the evolutionary phase of the (unseen) SNR
and no information on the current ratio of the PWN and
SNR radii.
Out of the 432 possible combinations of the input pa-
rameters, only five satisfy all ten of the above criteria, as
listed in Table 4. While the neutron star appears to be
inside the PWN, it is possible that this is just a projec-
tion effect. To evaluate the possibility that the PWN in
G328.4+0.2 has already entered the Relic PWN phase of
its evolution, we calculated vmin,IIns , defined as:
vmin,IIns =
RG328
. (15)
If vns > v
min,II
ns , then the G328.4+0.2 is a Relic PWN, if
not, then it is still in the Collision with the RS phase of
its evolution.
As shown in this Table, the predicted properties of
G328.4+0.2 vary substantially if G328.4+0.2 is inside a
Sedov or Radiative SNR. In the Sedov case, G328.4+0.2
is quite young, and progenitor SN explosion had a normal
explosion energy but a low ejecta mass (Mej ∼ 1M⊙),
and it occurred in a low density environment. Ad-
ditionally, the neutron star formed in this explosion
was spinning rapidly, has a low surface magnetic field
strength (Bns < 10
12 G), and a high space velocity
(vns & 800 km s
−1). In the Radiative Case, G328.4+0.2
is substantially older, and the progenitor SN explosion
was a low kinetic energy (Esn ∼ 3 × 10
50 ergs) and high
ejecta mass expanding. The neutron star in this case
was born spinning somewhat slower and has a normal
magnetic field strength for a young neutron star.
With the information presented in Table 5, it is possi-
ble to further refine the expected SNR and PWN prop-
erties. As argued in §4.1.1, the prominence of the central
bar argues that, during the compression stage, the vol-
ume of the PWN decreased significantly. Though it is not
possible at this time to quantify the compression needed,
an examination of Table 5 shows that for only two mod-
els, ST 2 and Rad 1, did the volume of the PWN decrease
by more than 10% – and therefore these two models are
the most probable descriptions of G328.4+0.2. In the
case of Rad 1, vmin,IIns ∼ 100 km s
−1 is significantly less
then the average neutron star velocity, v ∼ 400 km s−1
(Faucher-Giguère & Kaspi 2006; Hobbs et al. 2005), im-
plying that the PWN is in the Relic PWN phase of its
evolution. Since the sound speed inside a Radiative SNR
is quite low, ∼ 100 km s−1, we expect that the PWN in
the Rad 1 scenario would have a bow-shock morphology.
Since there is no clear evidence for this in the X-ray or
radio emission from G328.4+0.2, this suggests that ST 2
is a better fit to the data.
The conclusion that ST 2 is an accurate description
of G328.4+0.2 is supported by circumstantial evidence
as well. For this scenario, the expected radius of the
termination shock around the neutron star, rts, defined
as (Slane et al. 2004):
r2ts =
4πcPpwn
, (16)
assuming a spherical wind, is rts ∼ 0.6 pc, which corre-
sponds to an angle of θts ∼ 8d17
′′ – a distance which is
comparable to the offset between Clump 1 and Clump 2
derived in §2.1.1. Another interesting feature for this
model is that, as shown in Fig. 4, the radius of the PWN
at the time of re-expansion is similar to that of the outer
parts of the central filamentary structures discussed in
§2.2. While this correlation might be coincidental, this
could imply that the hydrodynamic instabilities formed
at the PWN/SNR interface during the re-expansion dis-
rupted the shell of material swept up by the PWN –
consistent with the simulation of Blondin et al. (2001).
While not definitive, these two pieces of evidence argue
that ST 2 is a reasonable description of G328.4+0.2.
The properties of ST 2 are given in Table 6, and the
evolution of Rpwn is shown in Fig. 9. It is interesting to
note that in this scenario, the PWN collides with the RS
at a time tcol < τ0 (tcol ≈ 850 years) so energy injection
by the neutron star into the PWN after the PWN/RS
collision is important to the PWN’s evolution during this
stage. It is important to note that this model predicts
that the neutron star powering G328.4+0.2 is the most
energetic neutron star in the Milky Way, as well as one
of the fastest. Given that G328.4+0.2 is largest and has
the highest radio luminosity of any known PWN, it is not
surprising that it was formed by such a powerful neutron
star. Finally, the age and Ė predicted by this method
are similar to those predicted by Gaensler et al. (2000).
In order to better understand the limitations of the
approach in determining the properties of the neutron
star and SNR in G328.4+0.2, we have run the model
presented in §4 over a finer grid of parameters and eval-
uated the resulting PWN evolution using the same cri-
teria as above. In Fig. 10, we show which values of P0
and Bns pass all of this criteria for three different kind
of SN explosions: Esn = 10
51 ergs and Mej = 1 M⊙,
Esn = 3 × 10
51 ergs and Mej = 1 M⊙, and Esn =
4 × 1051 ergs and Mej = 3.25 M⊙, assuming an ambi-
ent density with n = 0.03. The first set of SN parame-
ters corresponds to ST 1, the second to ST 2, and third
to a higher ejecta mass SN explosion is compatible with
a neutron star with the same parameters as ST 2. For
the first case, we find that a wide range of P0 values
are allowed but that Bns . 10
12 G. In fact, for this set
of SN parameters a P0 ∼ 10 ms, Bns ∼ 8 × 10
11 G neu-
tron star results in a PWN which is compressed a similar
amount as in ST 2. In the second case, we find that P0
and Bns are tightly constrained around P0 ≈ 5 ms and
Bns ≈ 5× 10
11 G. In the third set of SN parameters, we
find that P0 . 6 ms, but that Bns spans a wide range of
values, ∼ 1011 − 2× 1012 G.
To determine the allowed values of Esn and Mej, we
followed the same procedure as above using two different
sets of neutron star parameters: P0 = 5 ms and Bns =
5× 1011 G (the neutron star parameters in the ST 1 and
ST 2 scenarios), and P0 = 10 ms and Bns = 8 × 10
11 G.
For the first case, only models with Esn ∼ 1−4×10
51 ergs
andMej ∼ 0.5−3.5M⊙ satisfy the criteria above – though
a substantial compression of the PWN requires Esn &
2 × 1051 ergs. In the second case, we find that only
models with Esn . 10
51 ergs and Mej ∼ 0.5− 3.5M⊙ are
allowed.
While this error analysis shows that the method used
above to determine the properties of the neutron star
and SN explosion which formed G328.4+0.2 is unable to
do so to much better than an order of magnitude, the
different combinations values of P0, Bns, Esn, and Mej
which are allowed predict different physical properties for
G328.4+0.2 which are testable with further observations.
For example, in the case of P0 = 10 ms, Bns = 8×10
11 G,
Esn = 1 × 10
51 ergs, and Mej = 1 M⊙, G328.4+0.2 is
∼ 13, 000 years old, twice the age predicted in the ST 2
model as shown in Table 6, and as a result the required
velocity of the neutron star is significantly lower, vminns ∼
500 km s−1. The predicted period for the neutron star
in this scenario is also significantly slower than required
by the ST 2 scenario, P ∼ 24 ms, with a value of Ė
approximately an order of magnitude lower than that
in the ST 2 scenario. The termination shock radius for
this set of parameters is ∼ 5′′, considerable smaller than
the ∼ 8′′ for the ST 2 scenario and detectable with the
Chandra X-ray Observatory.
5. conclusions
In this paper, we first presented new X-ray (§2.1) and
radio (§ §2.2, 2.3) and observations of Galactic non-
thermal radio and X-ray source, G328.4+0.2, from which
we infer the current properties and evolutionary history
of this source (§3.2). We then presented a simple hydro-
dynamic model for the evolution of a PWN inside a SNR
(§4), which is used to determine which values of Esn,
Mej, n, P0, and Bns are able to reproduce the properties
discussed in §3.2 if G328.4+0.2 was a Composite SNR
(§4.1.1) or a PWN (§4.1.2). As a result of this analysis,
we determine the G328.4+0.2 is a PWN inside an unde-
tected SNR. Though we are not able to precisely deter-
mine the properties of the SN explosion and the neutron
star which have created this system, our analysis implies
that the neutron star in G328.4+0.2 was born with an ini-
tial period P0 . 10 ms, has a lower than average surface
dipole magnetic field strength, and has a higher than av-
erage spatial velocity vns & 400 km s
−1. We assume de-
termining that the SN explosion which created the neu-
tron star had a normal explosion energy, Esn ∼ 10
51 ergs,
but a relative low ejecta mass, Mej . 4M⊙. Future X-
ray and radio observations can significantly decrease this
uncertainty, particularly if they are able to either detect
pulsations from the neutron star or continuum X-ray or
radio emission from the currently undetected SNR in this
system.
While we are not able to definitely determine the ini-
tial period (P0) or surface magnetic field strength (Bns)
of the neutron star, nor the kinetic energy (Esn) or ejecta
mass (Mej) of the progenitor SN explosion, the estimates
quoted above are of interest. Our non-detection of the
pulsar via radio pulsations is not particularly constrain-
ing, due to the very large distance of the PWN. The low
magnetic field but rapid initial period predicted for the
neutron star in G328.4+0.2 has implications for mod-
els concerning the origin of neutron star magnetic fields.
For example, according to the α − Ω dynamo model of
(Thompson & Duncan 1993), neutron star born spinning
rapidly (P0 . 5 ms) should have a strong dipole compo-
nent to their surface magnetic fields (Bns ≫ 10
12 G).
If the ST 2 scenario proves to be correct, then the low
magnetic field of the neutron star in this system would
be a problem for such a model. Additionally, the low
ejecta mass inferred in this scenario requires that the
progenitor of this system was either a single, massive
star (M & 35M⊙) which exploded in a Type Ib/c SN
(Woosley et al. 1995), or was initially in a binary sys-
Finally, the method used in this paper to study
G328.4+0.2 is complementary to other methods used
(e.g. Chevalier 2005) to infer the initial period and mag-
netic field strength of other neutron stars in young PWN
as well as the properties of the SN explosion in which
they were formed, and is easily applicable to other such
systems.
JDG would like to thank Niccolo Bucciantini, Shami
Chatterjee, Roger Chevalier, Tracey DeLaney, David Ka-
plan, Kelly Korreck, Cara Rakowski, and John Ray-
mond for useful discussions, and the anonymous referee
for many useful comments. We are extremely grateful
to John Reynolds for prompt scheduling and observing
assistance at Parkes in 2007. The Australia Telescope
is funded by the Commonwealth of Australia for oper-
ation as a National Facility managed by CSIRO. JDG
and BMG were supported in this work by XMM grant
NAG5-13202 and LTSA grant NAG5-13032.
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Table 1
Spatial components of the X-ray emission from G328.4+0.2
Component Parameter Value
background constant 0.09
+0.06
−0.07
Clump 1 r0 1.
′′1+1.
−0.′′7
Position 15h55m26.s68+0.
−0.s05
, −53◦18′02.′′7+0.
−0.′′6
A 6.6+27.6
α 0.9+1.0
Clump 2 FWHM 19′′
Position 15h55m27.s5
+0.s2
−0.s1
, −53◦17′54.′′6
+3.′′4
−3.′′8
e 0.4
θ 280◦
A 0.8
Diffuse FWHM 67
Position 15h55m26.s6
+0.s2
−0.s2
, −53◦17′48.′′3
e 0.4
θ 130◦+10
A 0.4+0.1
Note. – Results from the spatial fit to the X-ray emission from G328.4+0.2, as described in §2.1.1. Fitting was done using the Sherpa
software package, and the errors reflect the 90% confidence level. Clump 1 was fitted to a 2D Lorentzian, defined as f(r) = A
1 + r
where f(r) is the expected number of counts at radius r away from the center of the source, A is given in counts, and the core-radius r0 is in
arc-seconds. The background component is given in counts pixel−1. Both Clump 2 and Diffuse were modeled with elliptical 2D Gaussians,
where the full width, half maximum (FWHM) is given in arc-seconds, the ellipticity is e, defined as 1− b/a, where b and a are, respectively,
the major and minor axis of the source, the position angle θ is given in degrees counterclockwise from north, and the amplitude A is given
in counts.
Table 2
Spectral Fits to Mos1 + Mos2 + pn Data
Parameter Value
Model phabs * pow phabs * bbodyrad phabs * bremss phabs * ray
NH 11.6
× 1022 6.4
× 1022 10.4
× 1022 7.8
× 1022
Γ or kT 2.0
+>900
Absorbed Flux 4.6
× 10−13 4.4
× 10−13 4.5
× 10−13 4.9
× 10−13
Unabsorbed Flux 1.9
× 10−12 6.5
× 10−13 1.2
× 10−12 9.6
× 10−13
χ2 103.3/131 98.4/131 101.7/131 122.8/131
Reduced χ2 0.81/128 0.77/128 0.79/128 0.96/128
Note – Results from joint fits to the mos1, mos2, and pn spectrum between 0.5 and 10 keV. The model phabs * pow refers to a power-law
attenuated by interstellar absorption, phabs * bbodyrad refers to a blackbody attenuated by interstellar absorption, phabs * bremss
refers to a Bremsstrahlung source spectrum attenuated by interstellar absorption, and phabs * ray refers to a Raymond-Smith thermal
plasma spectrum attenuated by interstellar absorption. In the table, NH is given in cm
−2, kT in keV, and flux in ergs cm−2 s−1, both the
absorbed and unabsorbed flux are calculated between 0.5 and 10 keV, and the errors represent the 90% confidence level.
Table 3
Expected Properties of G328.4+0.2 if it is a Composite SNR
Supernova Remnant Properties Pulsar Wind Nebula Properties Neutron Star Properties
Parameter Value Parameter Value Parameter Value
Esn 1× 10
51 ergs Epwn 4.8× 10
50 ergs Ė0 2.5× 10
40 ergs s−1
Mej 1 M⊙ Rpwn 8.7 parsecs P0 3.8 ms
Phase Sedov-Taylor M
sw 5.3 M⊙ τ0 1730 years
Psnr(Rpwn) 1.4× 10
−9 dynes Ppwn 2.0× 10
−9 erg cm−4 Bns 1.1× 10
vej(Rpwn) 400 km s
−1 vpwn 700 km s
−1 vminns 1300 km s
tnow 4900 years rts 0.5 parsecs Ė 1.7× 10
39 ergs s−1
n 0.32 cm−3 θts 6.
′′7 P 7.5 ms
· · · · · · · · · · · · Ṗ 1.8× 10−14 s/s
· · · · · · · · · · · · τc 6700 years
· · · · · · · · · · · · Epsr 1.0× 10
51 ergs
Note. – The values in bold are model assumptions, while the others are predicted by the model presented in §4. Psnr(Rpwn) is the
pressure inside of the SNR just outside of the PWN, vej(Rpwn) is the velocity of material inside the SNR just outside of the PWN, Epwn is
the internal energy of the PWN, Rpwn is the radius of the PWN, M
sw is the mass of material swept up by the PWN, Ppwn is the internal
pressure of the PWN, vpwn is the expansion velocity of the PWN, rts is the radius of the termination shock around the neutron star inside
the PWN, calculated using Equation 16, θts is the angular size of this feature assuming d17 ≡ 1, Bns is the dipole magnetic field of the
neutron star in G328.4+0.2 according to this model, P is the period of the neutron star in G328.4+0.2, Ṗ is the period-derivative of the
neutron star, τc is the characteristic age of the neutron star, defined as τc = P/(2Ṗ ), and Epsr is the total amount of energy injected by
the neutron star into G328.4+0.2 for t < tnow. All values are given for t = tnow unless otherwise noted.
Table 4
Scenarios for G328 as a PWN inside an Undetected SNR
Scenario # τ0 P0 Esn,51 Mej n tnow SNR Phase Rsnr Bns,12 v
min,II
ST 1 1730 5.0 1.00 1 0.03 5100 Sedov-Taylor 19.8 0.5 1300 2400
ST 2 1730 5.0 3.16 1 0.03 6500 Sedov-Taylor 28.0 0.5 1000 1900
Rad 1 430 10.0 0.32 10 0.32 84200 Radiative 28.4 2.0 100 100
Rad 2 770 10.0 0.32 10 0.32 52400 Radiative 24.8 1.5 100 200
Rad 3 770 10.0 0.32 10 1.00 101400 Radiative 22.1 1.5 100 100
Note. – Values for τ0, P0, Esn, Mej, and n that satisfy the criteria listed in §4.1.2 for G328 being a PWN inside an undetected SNR.
The value of τ0 is given in years, P0 in ms, Esn,51 ≡ Esn/10
51 ergs, Mej in solar masses, n in cm
−3, tnow in years, Rsnr in parsecs,
Bns = Bns,12 × 10
12 G, vminns is in km s
−1, and v
min,II
ns is also in km s
Table 5
Compression/Expansion properties of G328.4+0.2 if it is a PWN
Scenario # t(vpwn = 0) Central Bar Lifetime Rpwn(vpwn = 0)
re−exp
compres
ST 1 1648.5, 2432.0 63930 8.20, 7.96 0.91
ST 2 969.0, 1837.0 35250 8.36, 6.34 0.44
Rad 1 12772.0, 26541.0 243480 8.53, 7.55 0.69
Rad 2 13336.5, 21112.5 256230 8.48, 8.27 0.93
Rad 3 9761.5, 11035.0 102640 5.72, 5.72 1.00
Note. – In this table, values Scenario # correspond to the values of τ0, P0, Esn, Mej, and n given in Table 4. t(vpwn = 0) and the Central
Bar lifetime are given in years, and Rpwn(vpwn = 0) is given in parsecs.
re−exp
compres
is the ratio of the volume of the PWN at re-expansion
and compression.
Table 6
Expected Properties of G328.4+0.2 if it is a PWN (ST 2 scenario in Table 4)
Supernova Remnant Properties Pulsar Wind Nebula Properties Neutron Star Properties
Parameter Value Parameter Value Parameter Value
Esn 3.2× 10
51 ergs Epwn 3.2× 10
50 ergs Ė0 1.5× 10
40 ergs s−1
Mej 1 M⊙ Rpwn 12.5 parsecs P0 5 ms
Phase Sedov-Taylor M
sw 0.4 M⊙ τ0 1730 years
Psnr(Rpwn) 3.6× 10
−10 dynes Ppwn 4.4× 10
−10 dynes Bns 5× 10
vej(Rpwn) 460 km s
−1 vpwn 790 km s
−1 vminns 990 km s
Age (tnow) 6500 years rts 0.6 parsecs Ė 6.4× 10
38 ergs s−1
n 0.03 cm−3 θts 7.
′′7 P 10.9 ms
· · · · · · · · · · · · Ṗ 2.1× 10−14 s/s
· · · · · · · · · · · · τc 8200 years
· · · · · · · · · · · · Epsr 6.3× 10
50 ergs
Note. – The model assumptions are given in bold. Psnr(Rpwn) is the pressure inside just outside of the PWN, vej(Rpwn) is the velocity
of material inside just outside of the PWN, Epwn is the internal energy of the PWN, Rpwn is the radius of the PWN, M
sw is the mass of
material swept up by the PWN, Ppwn is the internal pressure of the PWN, vpwn is the expansion velocity of the PWN, rts is the radius of
the termination shock around the neutron star inside the PWN, θts is the predicated angular radius of this feature assuming d17 ≡ 1, Bns
is the predicted dipole magnetic field of the neutron star in G328.4+0.2, P is the predicted period of the neutron star in G328.4+0.2, Ṗ
is the predicted period-derivative of the neutron star, τc is characteristic age of the neutron star, and Epsr is the total amount of energy
injected by the neutron star into G328.4+0.2 for t < tnow. All values are given for t = tnow unless otherwise noted.
Point Source
Background
Background Region for Spectral Analysis
Source Region for Spectral Analysis
Clump 1
DiffuseClump 2
Clump 2
Clump 1
Diffuse
Fig. 1.— Top: Exposure normalized, vignette corrected mos1 + mos2 image of G328.4+0.2 smoothed by a 5′′ Gaussian. The white
contours indicate 20, 40, 50, 70, and 90% of the peak X-ray flux in the smoothed image, while the boxes indicate the background and
source regions used for the spectral analysis described in §2.1.2. The background point source labeled in the image was excluded from
the background region. Additionally, the labels in this plot point to the morphological features discussed in §2.1.1. Bottom: Unsmoothed
normalized, vignette corrected mos1 and mos2 image of G328.4+0.2 overlaid with the regions used for the Hardness Ratio analysis discussed
in §2.1.2.
Fig. 2.— Mos1, Mos2, and pn spectrum of G328.4+0.2 overlaid with the absorbed power-law model whose parameters are given in
Table 2.
Fig. 3.— 1.4 GHz image of G328.4+0.2, overlaid with X-ray contours in green which represent 20%, 35%, ..., 90% of the peak flux in the
smooth X-ray image shown in Fig. 1. The beam size of this image is 7.′′0×5.′′8, and is shown in the lower left-hand corner of the image.
The labels indicate examples of the different radio morphological features discussed in §2.2.
Fig. 4.— 20cm radio image of G328.4+0.2 (same data as shown in Fig. 3), with a color scale chosen to enhance the visibility of Filamentary
Structure B discussed in §2.2. The yellow circle indicates the size of PWN predicted in the ST 2 model listed in Table 5 when it re-expanded
after the initial compression by the SNR reverse shock, and the white cross indicates the center of G328.4+0.2 (15h55m33s,−53◦17′00′′;
J2000) as determined by Gaensler et al. (2000).
Fig. 5.— Spectral tomography images of G328.4+0.2, as described in §2.2.1. The spectral index α is given in the upper left hand corner
of each image, where Sν ∝ ν
Contact Discontinuity
SNR Forward Shock
SNR Reverse
Shock
Outer Boundary
of PWN
Neutron Star
Shocked ISM Ambient ISM
Unshocked Ejecta
Material Swept
Up by PWN
Pulsar
Shocked Ejecta
Fig. 6.— Diagram of a Composite SNR in the Free Expansion stage of its evolution. In this image, the ratio between the thickness
of the mass shell surrounding the PWN and the radius of the PWN is 1/24, as determined by van der Swaluw et al. (2001), and the
radio of the SNR Forward Shock, Contact Discontinuity, and Reverse Shock radii are equal to the values given in Chevalier (1982) for his
n = 9, s = 0 case. The colors denote the nature of the material within each region.
1000 10000 100000
Time (years)
Fig. 7.— Rpwn/Rsnr for Models A (solid), B (long-dashed line), & C (short-dashed line) in Blondin et al. (2001). The top plot shows
the result of the model presented in §4, while the bottom is a reproduction of Fig. 3 by Blondin et al. (2001), reproduced by permission of
the AAS.
Fig. 8.— The radius of the PWN, SNR, and SNR reverse shock as well as the location of the neutron star as a function of time if
G328.4+0.2 is a composite SNR. The vertical line indicates the current age of the system, and the properties of this system are given in
Table 3.
Fig. 9.— The radius of the PWN, SNR, and SNR reverse shock as well as the location of the neutron star as a function of time for the
favored (ST 2; Table 4) scenario if G328.4+0.2 is a PWN. The vertical line indicates the current age of the system.
Fig. 10.— The results for varying P0 and Bns for a Esn = 10
51 ergs, Mej = 1M⊙ (top), Esn = 3× 10
51 ergs, Mej = 1M⊙ (middle), and
Esn = 4×10
51 ergs, Mej = 3.25M⊙ (bottom) SN explosion, assuming n = 0.03 cm
−3. The small black squares indicate models which failed
the criteria described in §4.1.2, while the colored circles indicate scenarios which passed. The color represents the Compression Fraction
of the PWN, defined as the ratio of the PWN’s volume at the beginning and end of the compression stage. The Compression Fraction of
the ST 2 case given in Table 4 is 0.44 (light blue on this color scale), and lower values correspond to a more substantial compression. The
star indicates the position of a P0 = 5 ms, Bns = 5 × 10
11 G neutron star, while the large square indicates the position of a P0 = 10 ms,
Bns = 8× 10
11 G neutron star – the two neutron stars used in Fig. 11.
Fig. 11.— The results of varying Esn and Mej for a P0 = 5 ms, Bns = 5 × 10
11 G (top) and P0 = 10 ms, Bns = 8 × 10
11 G (bottom)
neutron star, assuming n = 0.03 cm−3. The black squares indicate which scenarios failed the criteria described in §4.1.2, while the colored
circles indicate those that passed, with the color representing the Compression Fraction (defined as the ratio of the PWN’s volume at the
beginning and end of the compression stage) of the PWN. The star indicates a Esn = 1× 10
51 ergs, Mej = 1 M⊙ SN explosion, the square
indicates a Esn = 3× 10
51 ergs, Mej = 1 M⊙ SN explosion, and the circle indicates a Esn = 4× 10
51 ergs, Mej = 3.25 M⊙ SN explosion –
the SN explosion parameters used in Fig. 10.
APPENDIX
equations for the hd model for the evolution of a pwn inside a snr
In this Appendix, we provide many of the details concerning the properties of the neutron star, PWN, and SNR
needed to simulate the HD model for the evolution of a PWN inside a SNR described in §4.
For the SNR, we assume that the initial ejecta density profile consists of a constant density core surrounded by a
ρ ∝ r−9 envelope – the standard assumption for a SNR produced by a Type-II SNR (Blondin et al. 2001; Chevalier
1982) – and that the ejecta is expanding ballistically (vej ≡ rej/t). The boundary between the constant density core
and the outer ejecta envelope has a velocity vcore, defined as (Blondin et al. 2001):
vcore=
where Esn is the explosion energy of the SN and Mej is the ejecta mass. As a result, the density ρcore of the ejecta
core is (Blondin et al. 2001):
ρcore(t)=
Esn v
core t
−3. (A2)
As the SNR expands, it sweeps up and shocks the surrounding interstellar medium (ISM). This swept-up material has
a higher pressure than the cold ejecta driving the expansion of the SNR, and as a result drives a reverse shock (RS)
into the SN ejecta. In between the outer edge of the SNR, which marks the location of the forward shock (FS) and
the RS is a contact discontinuity which separates the shocked ISM from the ejecta shocked by the RS. The pressure
inside the SNR at r < rrs, where rrs is the radius of the RS, is assumed to be zero. A diagram of this is shown in
Fig. 6. Since we assume that both the SN ejecta and the shocked ISM behave as a γ = 5/3 perfect gas, the sound
speed cs of this material is:
When the RS is still in the ejecta envelope, we determine the pressure, velocity, and density profiles on the material
between the RS and FS using the self-similar equations given by Chevalier (1982), evaluating them for the n = 9, s = 0
case. However, when the RS enters the constant density ejecta core, it is no longer possibly to apply the self-similar
solution of Chevalier (1982), and we use the work of Truelove & McKee (1999) to determine the radius of the RS and
the results given by Bandiera (1984) to determine the pressure, velocity, and density profiles between the RS and FS.
It is also necessary to model the radius of the FS (Rsnr), which we do using the work of Truelove & McKee (1999).
This is valid while the SNR is in the Free Expansion and Sedov-Taylor phases of its evolutions. After the SNR goes
radiative, which occurs at a time t = trad defined as (Blondin et al. 1998):
trad≈ 2.9E
17 × 104 yr. (A4)
After this point, Rsnr ∝ t
2/7. An analytic model for the pressure, velocity, and density distribution of a SNR in this
phase does not currently exist, and therefore it is difficult to extend our model to this phase, though if one assumes
that the interior of the SNR evolves adiabatically, Rpwn/Rsnr ∝ t
0.075 for t > trad (Blondin et al. 2001).
For the PWN, as mentioned in §4, we assume that it is a bubble filled with a γ = 4/3 perfect gas. As a result, the
internal pressure of the PWN, Ppwn is equal to:
Ppwn=
3Vpwn
, (A5)
where Epwn is the internal energy of the PWN and Vpwn is the volume of the PWN, defined as:
Vpwn=
πR3pwn (A6)
where Rpwn is the radius of the PWN. The internal energy of the PWN is determined by the rate of energy injected
into the PWN by the neutron star (Ė), and energy loss due to its expansion inside the SNR ( ˙Eadpwn). For Ė, we use
the standard assumption that it is equal to:
Ė= Ė0
where t is the age of the neutron star, p is the pulsar braking index (p = 3 for a magnetic dipole), τ0 is the characteristic
timescale of pulsar spin-down, and Ė0 is the initial spin-down energy of the neutron star. Both τ0 and Ė0 depend on
the physical properties of the neutron star, with τ0 defined as (Blondin et al. 2001; Shapiro & Teukolsky 1983):
3c3 IP 20
4π2B2nsR
ns sin
where I is the neutron star’s moment of inertia, P0 is the initial spin period, Bns is the magnetic field of the neutron
star, Rns is the radius of the neutron star, α is the angle between the neutron star’s rotation axis and magnetic field,
and (Blondin et al. 2001):
Ė0= I
τ0(p− 1)
. (A9)
Since the PWN expands adiabatically, ˙Eadpwn is equal to:
˙Eadpwn=−
. (A10)
As a result, the change in the internal energy of the PWN over time ( ˙Epwn) is equal to:
˙Epwn=−
+ Ė0
(A11)
assuming that p = 3. This equation can be solved analytical, and we result that Epwn(t) can be expressed as:
Epwn(t)= Ė0τ0
ln(1 + t/τ0)
t/τ0 − 1
. (A12)
When we run our model, we use Eq. (A12) to determine the initial value of Epwn, but determine Epwn at later times
using the procedure described in Step 2 in §4.
During its free-expansion, the PWN is moving faster than its surroundings, and the mass of the shell surrounding
the PWN (Msw,pwn) is simply:
Msw,pwn(t)=
∫ Rpwn
4πR2ρej(r, t)dr (A13)
where ρej(r) is the density profile of the SNR. After the collision with the reverse shock, if the PWN is moving
faster than its surroundings we determine the mass of the ejecta shell recently swept up by the PWN and add it
to the value of Msw,pwn calculated at the time of the reverse shock collision. If the PWN is moving slower than its
surroundings, we assume that Msw,pwn remains constant, even if the PWN is being compressed by the surrounding
SNR. Due to the difference in pressure between the PWN interior to the mass shell and the SNR exterior to the mass
shell (Psnr(r = Rpwn)), the mass shell is subject to a force F∆P, defined as:
F∆P=4πR
pwn[Ppwn − Psnr(Rpwn)]. (A14)
In this notation, F∆P > 0 means that the PWN interior has a higher pressure than inside the surrounding SNR. If the
PWN has not yet encountered the RS, we assume that Psnr(r = Rpwn) = 0. If the mass shell is moving faster than the
sound speed of the surrounding material (vpwn > cs(Rpwn)), which is the case before the PWN interacts with the RS
(Chevalier & Fransson 1992), the mass shell is decelerated by ram pressure, and the total force on the mass swept-up
by the PWN, Fpwn, is:
Fpwn=F∆P − 4πR
pwnρej(Rpwn)[vpwn − vej(Rpwn)]
2. (A15)
If vpwn < cs, then Fpwn = F∆P. For t ≪ τ0, analytical solutions to these equations give Rpwn ∝ t
6/5 if the PWN is
still inside the central constant-density core – a result which is reproduced by our numerical implementation of the
model described in §4.
In this framework, the period P of a neutron star evolves as:
P =P0
, (A16)
the period-derivative Ṗ evolves as:
(A17)
and the surface magnetic field Bns of the neutron star, assuming p = 3, is:
Bns=1.5
˙E0,37
2P 20,ms
× 109 G (A18)
where ˙E0,37 = Ė0/10
37 ergs s−1, P0,ms is the initial period in ms, and R14 is the radius of the neutron star R/14 km.
Additionally, for p = 3 τ0 is equal to:
τ0=17.3
B212R
years (A19)
where I = 1045I45 g cm
2 and the angle between the spin and magnetic field axes of the neutron star is α = 45◦.
