Astronomy & Astrophysics manuscript no. ms c© ESO 2018
November 4, 2018
The Boundary Conditions of the Heliosphere: Photoionization
Models Constrained by Interstellar and In Situ Data
Jonathan D. Slavin1 and Priscilla C. Frisch2
1 Harvard-Smithsonian Center for Astrophysics, 60 Garden St., MS 83, Cambridge, MA 02138
e-mail: jslavin@cfa.harvard.edu
2 University of Chicago, Department of Astronomy and Astrophysics, 5640 S. Ellis Ave., Chicago, IL 60637
e-mail: frisch@oddjob.uchicago.edu
Received – / Accepted –
ABSTRACT
Context. The boundary conditions of the heliosphere are set by the ionization, density and composition of inflowing interstellar matter.
Aims. Constraining the properties of the Local Interstellar Cloud (LIC) at the heliosphere requires radiative transfer ionization models.
Methods. We model the background interstellar radiation field using observed stellar FUV and EUV emission and the diffuse soft
X-ray background. We also model the emission from the boundary between the LIC and the hot Local Bubble (LB) plasma, assuming
that the cloud is evaporating because of thermal conduction. We create a grid of models covering a plausible range of LIC and LB
properties, and use the modeled radiation field as input to radiative transfer/thermal equilibrium calculations using the Cloudy code.
Data from in situ observations of He0, pickup ions and anomalous cosmic rays in the heliosphere, and absorption line measurements
towards ǫ CMa were used to constrain the input parameters.
Results. A restricted range of assumed LIC H i column densities and LB plasma temperatures produce models that match all the
observational constraints. The relative weakness of the constraints on N(H i) and Th contrast with the narrow limits predicted for the
H0 and electron density in the LIC at the Sun, n(H0) = 0.19 − 0.20 cm−3, and ne = 0.07 ± 0.01 cm
−3. Derived abundances are mostly
typical for low density gas, with sub-solar Mg, Si and Fe, possibly subsolar O and N, and S about solar; however C is supersolar.
Conclusions. The interstellar gas at the Sun is warm, low density, and partially ionized, with n(H) ≈ 0.23 − 0.27 cm−3, T ≈ 6300 K,
X(H+) ∼ 0.2, and X(He+) ∼ 0.4. These results appear to be robust since acceptable models are found for substantially different input
radiation fields. Our results favor low values for the reference solar abundances for the LIC composition.
Key words. ISM: clouds — ISM: abundances — ultraviolet: ISM — X-rays: diffuse background – solar system: general — ISM:
cosmic rays
1. Introduction
The solar wind evacuates a cavity in the interstellar medium
(ISM) known as the heliosphere, from which interstellar ions
are excluded. In contrast, neutral interstellar gas flows through
the heliosphere until destroyed by charge-transfer with the solar
wind and photoionization. These neutrals form the parent popu-
lation of pickup ions (PUI) and anomalous cosmic rays (ACR)
observed inside of the heliosphere. The properties of the sur-
rounding interstellar medium set the boundary conditions of the
heliosphere and determine its configuration and evolution. An
ionization gradient is expected in the cloud feeding ISM into the
heliosphere because of the hardness of the interstellar radiation
field and the low opacity of the ISM (Cheng & Bruhweiler 1990;
Vallerga 1996; Slavin & Frisch 2002, hereafter SF02). Because
of this ionization gradient, the densities of partially ionized
species in the local interstellar cloud (LIC) will differ from the
values in the circumheliosphere interstellar medium (CHISM)
that forms the boundary conditions of the heliosphere. Hence
we have undertaken a series of studies to determine the bound-
ary conditions of the heliosphere based on both astronomical and
heliospheric data. In turn our results provide tighter constraints
on the heliosphere models used to calculate the filtration factors
Send offprint requests to: J. Slavin
for neutrals that then permit comparisons between ISM inside
and outside of the heliosphere.
The distribution and velocity of interstellar H0 inside
of the heliosphere were first determined over 30 years ago
from the florescence of solar Lyα radiation from these
atoms (Thomas & Krassa 1971; Bertaux & Blamont 1971;
Adams & Frisch 1977). Similar observations of solar 584Å flo-
rescence from interstellar He0 showed that H/He ∼ 6 for in-
terstellar gas inside of the heliosphere, in contrast to the cos-
mic value H/He = 10 (Ajello 1978; Weller & Meier 1981).
More recent measurements of n(H0) compared to n(He0) in-
side of the heliosphere find a similar ratio of H/He ∼ 6 − 7
(Richardson et al. 2004; Gloeckler & Geiss 2004; Witte 2004;
Möbius et al. 2004). This difference can be attributed to two ef-
fects: the loss of 40–60% of interstellar H0 due to charge-transfer
with protons in the heliosheath region, a process denoted “filtra-
tion” (Ripken & Fahr 1983), and the hardness of the interstellar
radiation field at the Sun that ionizes more He than H (§4).
The Copernicus satellite first showed that the local inter-
stellar cloud (LIC) surrounding the Sun is low density, ∼ 0.1
atoms cm−3, partially ionized (n(H+) ∼ n(H0), York 1974;
McClintock et al. 1975), and warm (temperature < 104 K, e.g.
McClintock et al. 1978). Copernicus, FUSE and HST data have
shown that the cluster of local interstellar clouds (CLIC, low
density clouds within ∼ 30 pc), has low column densities, N(H i)
< 1018.7, and N ionization levels of > 30% (e.g. Lehner et al.
http://arxiv.org/abs/0704.0657v2
2 Slavin and Frisch: Boundary Conditions of the Heliosphere
2003; Wood et al. 2005), indicating partially ionized gas because
H and N ionization are coupled by charge-transfer. The low col-
umn densities of the LIC itself, N(H i) < 1018 cm−2, indicate
it is partially opaque to H ionizing radiation but not to He ion-
izing radiation. Cloud opacities of unity are reached for N(H i)
∼ 1017.2 cm−2 for photons close to the ionization threshold of
hydrogen (13.6 eV), and N(H i) ∼ 1017.7 cm−2 for photons at the
He0 ionization edge (24.6 eV). The result is that the LIC is par-
tially ionized with a significant ionization gradient between the
edge and center. Because of this radiative transfer effects are im-
portant and need to be modeled carefully in order to determine
the boundary conditions of the heliosphere.
The LIC belongs to a flow of low density ISM embedded
in the very low density and apparently hot (T ∼ 106 K) Local
Bubble (Frisch 1981; Frisch & York 1986; McCammon et al.
1983; Snowden et al. 1990). The bulk motion of the CLIC
through the local standard of rest1 corresponds to a velocity of
−17.0 to −19.4 km s−1 from the direction ℓ ∼ 331◦, b ∼ −5◦
(Frisch & Slavin 2006). This upwind direction is near the center
of the Loop I superbubble and the center of the “ring” shadow
that has been attributed to the merging of Loop I and the Local
Bubble (Frisch & York 1986; Frisch 2007; Egger & Aschenbach
1995). Individual cloudlets with distinct velocities are identified
in this flow (Lallement et al. 1986; Frisch et al. 2002). The ve-
locity of the cloud feeding gas into the heliosphere has been de-
termined by the velocity of interstellar He0 in the heliosphere
measured by the GAS detector on Ulysses, −26.3 km s−1 (Witte
2004).
Curiously, absorption lines at the LIC velocity are not ob-
served in the nearest interstellar gas in the upwind hemisphere,
such as towards the closest star α Cen or towards 36 Oph lo-
cated ∼ 5 pc beyond the heliosphere nose (Adams & Frisch
1977; Landsman et al. 1984; Linsky & Wood 1996; Wood et al.
2000a,b). This lack of an absorption component at the LIC ve-
locity in the closest stars in the upstream direction indicates that
the Sun is near the edge of the LIC, so the CHISM may vary
over short distances (and hence timescales).
We are able to test for possible past variations by compar-
ing the first interplanetary H0 Lyα glow spectrum obtained by
Copernicus in 1975 with Hubble Space Telescope observations
of the Lyα spectra obtained during the mid-1990’s solar min-
imum conditions. The observed H0 velocity and intensity has
not varied to within uncertainties over the twenty-year period
separating these two sets of observations, so that the CHISM
velocity field is relatively smooth over spatial scales of ∼ 120
AU in the downwind direction (Frisch & Slavin 2005). The 1975
Copernicus data were acquired in the direction corresponding
to ecliptic longitudes of λ = 264.3◦, β = +15.0◦, or ∼ 13.3◦
from the most recent upwind direction derived from SOHO H i
Lyα data (Quémerais et al. 2006b,a, Q06). The Copernicus look
direction was just outside of the “groove” expected in the Lyα
glow in the ecliptic during solar minimum. The groove is caused
by increased charge-transfer in the solar wind current sheet,
which has a small tilt during minimum conditions (Bzowski
2003). The velocity of the Lyα profile observed by Copernicus
corresponds to −24.8±2.6 km s−1, after correction to the SOHO
upwind direction. Since Q06 measured H0 upwind velocities
during the solar minimum years of 1996 and 1997 of −25.7±0.2
km s−1 and −25.3 ± 0.2 km s−1, which is consistent with the
Copernicus results, we must arrive at the conclusion that the flow
of interstellar H0 into the heliosphere was relatively constant be-
1 Heliocentric motions are converted to the local standard of rest,
LSR, using the Standard solar apex motion.
tween the years of 1975 and 1997, so that any observations of
variations in the interplanetary Lyα glow properties must be due
to solar activity properties alone. The thermal broadening of the
Copernicus spectrum corresponded to a temperature of ∼ 5400
K, however measurement uncertainties allowed temperatures of
up to 20, 000 K.
In this paper we present new photoionization models of the
LIC and show they reproduce both the densities of the ISM at the
heliosphere and column densities in the LIC component towards
the star ǫ CMa. In earlier papers, photoionization models of both
the “LIC” and “Blue Cloud” components observed towards ǫ
CMa were used to constrain the models (SF02, Frisch & Slavin
2003). SF02 grouped the properties of the LIC and Blue Cloud,
both of which are with 2.7 pc of the Sun because they are also
observed towards Sirius, ∼ 12◦ from the ǫ CMa sightline. The
LIC velocity and density are sampled by observations of inter-
stellar He i inside of the heliosphere (−26.3 km s−1, Witte 2004),
and Gry & Jenkins (2001) show that the properties of the LIC
and Blue Cloud differ somewhat. The present study therefore fo-
cuses on obtaining the best model of heliosphere boundary con-
ditions by using only data on the LIC inside of the heliosphere,
and the LIC component towards ǫ CMa. The present study also
benefits from new atomic rates for the critical Mg ii→Mg i di-
electronic recombination coefficient, improved cooling rates in
the radiative transfer code Cloudy, recent values for the pickup
ion densities at the termination shock, and recent values for solar
abundances.
The most truly unique quality of the LIC is that we are inside
of it and therefore have the ability to sample the cloud directly
via in situ observations carried out by a variety of spacecraft
within the Solar System. Of all the available measurements of
LIC gas flowing into the Solar System, the observations of the
density and temperature of neutral He are apparently the most
robust. Helium, unlike hydrogen, undergoes little ionization or
heating in traversing the heliosheath regions, no deflection due
to radiation pressure, and is destroyed by photoionization and
electron-impact ionization within ∼ 1 AU of the Sun, so we ex-
pect that the density and temperature of He0 derived from the
observations in the Solar System are truly representative of the
values in the LIC (Möbius et al. 2004). In this paper we put a
special emphasis on matching these He i data by determining
model parameters that yield close agreement with the n(He0) and
T (He0) data simultaneously.
2. Photoionization Model Constraints and
Assumptions
The primary data constraints on our photoionization mod-
els are the LIC component column densities towards ǫ CMa,
(Gry & Jenkins 2001, hereafter GJ01), in situ observations
of He0 (Witte 2004; Möbius et al. 2004), pickup ions (PUI,
Gloeckler & Fisk 2007), and anomalous cosmic rays (ACR,
Cummings et al. 2002). The astronomical and in situ observa-
tional constraints are summarized in Table 1.
2.1. Astronomical Constraints – The LIC towards ǫ CMa
The data toward ǫ CMa of GJ01 show four separate veloc-
ity components detected in several different ions including C ii,
Si iii, Si ii, and Mg ii. One of these velocity components, with
a heliocentric velocity of ∼ 17 km s−1, is identified as the LIC.
Another is identified with a second local cloud, the “Blue Cloud”
(BC) at ∼ 10 km s−1. In our previous study of LIC ioniza-
Slavin and Frisch: Boundary Conditions of the Heliosphere 3
Table 1. Observational Constraints
Observed Observeda Notesb
Quantity Value
N(C ii) (cm−2) 1.4 − 2.1 × 1014 1, S
N(C ii∗) (cm−2) 1.3 ± 0.2 × 1012 1
N(C iv) (cm−2) 1.2 ± 0.3 × 1012 1
N(N i) (cm−2) 1.70 ± 0.05 × 1013 1
N(O i) (cm−2) 1.4+0.5
−0.2 × 10
14 1, S
N(Mg i) (cm−2) 7 ± 2 × 109 1
N(Mg ii) (cm−2) 3.1 ± 0.1 × 1012 1
N(Si ii) (cm−2) 4.52 ± 0.2 × 1012 1
N(Si iii) (cm−2) 2.3 ± 0.2 × 1012 1
N(S ii) (cm−2) 8.6 ± 2.1 × 1012 1
N(Fe ii) (cm−2) 1.35 ± 0.05 × 1012 1
N(H i)/N(He i) 14 ± 0.4c 2
T (K) 6300 ± 340 4
n(He0) (cm−3) 0.015 ± 0.003 4, f = 1d
n(N0)e (cm−3) 5.47 ± 1.37 × 10−6 3, f = 0.68 − 0.95d
n(O0)e (cm−3) 4.82 ± 0.53 × 10−5 3, f = 0.64 − 0.99d
n(Ne0)e (cm−3) 5.82 ± 1.16 × 10−6 3, f = 0.84 − 0.95d
n(Ar0)e (cm−3) 1.63 ± 0.73 × 10−7 3, f = 0.53 − 0.95d
a N(C ii∗), N(N i), N(O i), N(Mg ii), N(Si ii), N(S ii) and N(Fe ii) are
used to constrain the input abundances of the models.
b The first number indicates the reference (below), and “S” indi-
cates that the column density is based on a saturated line. Filtration
factors ( f , §2.2) are listed for neutrals that have been observed as
pickup ions.
c The uncertainty given is only that due to uncertainties listed in
Dupuis et al. (1995) for the observed H i and He i column densities
with the implicit assumption that the ratio is the same on all lines of
sight. Given the substantial intrinsic variation in this ratio, however,
the quoted uncertainty must be regarded as a lower limit to the true
uncertainty.
d We assume in this paper that for He fHe = 1, and f is not allowed
to exceed 1. Heliosphere models predict the range fHe = 0.92 − 1
for He and fH = 0.50 − 0.74 for H (see filtration factors in
Cummings et al. 2002; Müller & Zank 2004a; Müller et al. 2007;
Izmodenov et al. 2004).
e Note that the pickup ion ratios are for values at the termination
shock. N0, O0, Ne0, and Ar0 densities need to be corrected for fil-
tration in the heliosheath regions (2.2).
References: (1) Gry & Jenkins (2001) Note that the values shown are
for the LIC component towards ǫ CMa.; (2) Dupuis et al. (1995); (3)
Gloeckler & Fisk (2007); (4) Witte (2004).
tion (SF02) we noted that since the BC is close to the LIC,
and both are detected towards Sirius at 2.7 pc (Lallement et al.
1994; Hébrard et al. 1999), perhaps actually abutting the LIC,
we should treat the two as a single cloud for this line of sight.
Counter arguments to this line of reasoning include the fact that
the BC apparently has different properties than the LIC, though
whether it is colder or hotter is unclear (see Hébrard et al. 1999,
GJ01). For this reason and because we wish to find the ioniza-
tion models that best predict interstellar neutral densities inside
and outside of the heliosphere, we assume in this paper that the
LIC and BC are truly separate clouds and select only the LIC
components towards ǫ CMa to constrain the models.
In the context of these models, the best astronomical con-
straints on the neutral ISM component are N i, the saturated O i
line, and to some extent Mg i (though the line is weak). The elec-
tron density can be deduced from the ratio Mg ii/Mg i, which is
determined by photoionization and both dielectronic and radia-
tive recombination, and the excitation of the C ii fine-structure
lines, C ii/C ii∗. However, the heavy saturation of the C ii 1335
Å line in the ISM limits the accuracy of the determination of
N(C ii), so in this paper we have de-emphasized C ii/C ii∗ as an
ionization diagnostic. For a discussion of the use of C ii/C ii∗ and
other observations in diagnosing the C abundance and C/S ratio
see Slavin & Frisch (2006). Elements with first ionization po-
tentials (FIP) < 13.6 eV (e.g. Mg, Si, S, and Fe) are generally
almost entirely singly ionized in the LIC and thus the column
densities of these ions are close to the total column densities for
the elements.
2.2. In situ Constraints – He0, Pickup Ions, and Anomalous
Cosmic Rays
Neutral atoms in the LIC penetrate the outer heliosphere regions,
and become ionized primarily by charge-transfer with the so-
lar wind ions, photoionization, and electron impact ionization
(Rucinski et al. 1996). The composition of this neutral popula-
tion reflects the partially ionized state of the LIC, rather than
indicating a pure FIP effect. Thus the observed abundances of
neutrals representing high FIP elements, such as He, Ne, and Ar,
as well as H, N, and O, do not reflect their elemental abundances
directly. As a result, these neutrals provide an interesting and
unique constraint on the photoionization models. Once ionized,
these interstellar wind particles form a population of ions with
a distinct velocity distribution that are “picked up” by the solar
wind and convected outwards, where they are measured by var-
ious spacecraft (Möbius et al. 2004; Gloeckler & Geiss 2004).
These pickup ions (PUI) are accelerated in the heliosheath re-
gion and form a population of cosmic rays with an anomalous
composition reflective of their origin as interstellar neutrals in
a partially ionized gas (Cummings et al. 2002). In situ observa-
tions of these byproducts of the ISM interaction with the helio-
sphere, H, He, N, O, Ar, and Ne, provide a unique opportunity
to constrain theoretical models of an interstellar cloud using the
combination of sightline-integrated data, and data from a “sin-
gle” spatial location, the heliosphere.
We adopt the Ulysses He measurements as the best set of
constraints on the ISM inside of the heliosphere. The Ulysses
satellite provides direct measurements of interstellar He0 at
high ecliptic latitudes throughout the solar cycle (the GAS de-
tector, Witte 2004) and also measurements of the He pickup
ion component (the SWICS detector Gloeckler & Geiss 2004;
Gloeckler & Geiss 2007). Although interstellar He0 close to the
Sun is detected through the resonant scattering of solar 584 Å
radiation, geocoronal contamination of the interstellar signal is
present so we prefer the Ulysses data (Möbius et al. 2004). We
adopt the Ulysses GAS and SWICS results, n(He0) = 0.0151 ±
0.0015 cm−3, T (He0) = 6, 300 ± 340 K.
Data on the density of neutral N, O, Ne, and Ar in the sur-
rounding ISM are provided by PUI and ACR data. The densities
of interstellar N0, O0, Ne0, and Ar0 at the termination shock are
listed in Table 1. These densities must be corrected by the fil-
tration factors, which correspond to the ratios of the densities
at the termination shock to those in the LIC. Filtration occurs
when neutral interstellar atoms are removed from the inflow by
charge-transfer with interstellar protons as the atom crosses the
heliosheath regions. Filtration values are listed in Table 1, based
on values in Cummings et al. (2002); Müller & Zank (2004b);
Izmodenov et al. (2004). Filtration values larger than 1 are not
considered, although some models suggest possible net creation
of O0 through charge-transfer between O+ and H0 in the he-
liosheath regions (Müller & Zank 2004a). We adopt fHe = 1 for
He. Our models must be compared to the interstellar densities
4 Slavin and Frisch: Boundary Conditions of the Heliosphere
Fig. 1. The modeled interstellar radiation field at the Sun (model
26) is shown as a function of wavelength (bottom X-axis) and
energy (top X-axis). The black histogram is the modeled hot
gas (i.e. Local Bubble) spectrum while the gray histogram is
the cloud boundary contribution. The other line is the stellar
EUV/FUV background. The list of elements at the top of the
plot identifies the ionization potentials for neutrals and ions of
interest. The energy/wavelength at which an optical depth of 1 is
reached for several different H i column densities is shown along
the bottom of the plot. Observed flux levels of the soft X-ray dif-
fuse background in the Wisconsin Be and B bands are plotted as
lines (Bloch et al. 1986; McCammon et al. 1983).
obtained by correcting densities at the termination shock by fil-
tration factors.
2.3. Interstellar Radiation Field at the Cloud Surface
The spectrum and flux of the cosmic radiation field control
the ionization of the very local warm partially ionized medium
(WPIM). The local interstellar radiation field (ISRF) that ionizes
the LIC and other nearby cloudlets is determined by the location
of the Sun in the interior of a hole in the neutral interstellar gas
and dust referred to as the Local Bubble. The clustering tendency
of hot O and B stars, and attenuation of radiation by interstellar
dust and gas, yield the well known spatial variation of the in-
tensity and spectrum of the ISRF. We ignore possible temporal
variations of the radiation field (e.g. Parravano et al. 2003), and
model the ISRF throughout the LIC based on the observations
of the present-day radiation field.
The radiation field we use in our models is based on obser-
vations of the ISRF at the Sun, supplemented by theoretical cal-
culations of the spectra in the EUV and soft X-rays where lack
of sensitivity and/or spectral resolution require the use of mod-
els to create a realistic spectrum. The directly observed radiation
field includes the far ultraviolet (FUV) field created primarily
by B stars, the extreme ultraviolet (EUV) field from two B stars
(ǫ CMa and β CMa) and hot nearby white-dwarf stars, and the
diffuse soft X-ray background (SXRB). We show the radiation
field at the cloud surface in Fig. 1. Because the interstellar opac-
ity for radiation with E > 13.6 eV is vastly greater than for
E < 13.6 eV, the EUV part of the ISRF originates in nearby
regions with N(H i) <∼ 10
18 cm−2 while the FUV comes from a
much larger volume.
We use the EUV field of Vallerga (1998), which is based
on data collected by the Extreme Ultraviolet Explorer (EUVE)
satellite. The EUVE spectrometers were sensitive over the wave-
length range of 504 – 730 Å and showed that the stellar part of
the EUV background is dominated by ǫ CMa and β CMa with
substantial contributions from nearby hot white dwarfs at shorter
wavelengths. Vallerga extrapolated those measurements to the
H0 ionization edge at 912 Å using a total interstellar H0 density
towards ǫ CMa of N(H i) = 9 × 1017 cm−2. This value for N(H i)
appears somewhat high based on observations of Gry & Jenkins
(2001) which, though dependent on assumptions for gas phase
abundances, indicate a value for N(H i) of ∼ 7× 1017 cm−2. This
uncertainty in the total N(H i) affects only the extrapolated por-
tion of the spectrum in our models since the other portion of the
spectrum is derived by de-absorbing the observed spectrum by
the value of N(H i) assumed just for the LIC. For the results pre-
sented here we have assumed that the total N(H i) towards ǫ CMa
is 7×1017 cm−2. Assuming a larger value would increase the flux
in the extrapolated region, though our calculations indicate that
the overall affect on our results is only at the ∼ 2% level at most.
The FUV field is important because it sets the ionization rate
of Mg0, which has a first ionization potential of 7.65 eV (1621
Å). The radiation field shortwards of 1600 Å is heavily domi-
nated by O and B stars in Gould’s Belt, particularly those oc-
cupying the unattenuated regions of the third and fourth galac-
tic quadrants. A pronounced spatial asymmetry in the 1565 Å
radiation field has been observed by the TD-1 satellite S2/68
telescope survey of the interstellar radiation field, and we use
those data and the extrapolation down to 912 Å from the 1564 Å
measurements as calculated by Gondhalekar et al. (1980). The
asymmetries in the TD-1 1565 Å radiation field are reproduced
by diffuse interstellar radiation field models (Henry 2002).
The diffuse soft X-ray background (SXRB) has been ob-
served over the entire sky at relatively low spatial and spectral
resolution by ROSAT (Snowden et al. 1997) and proportional
counters flown on sounding rockets by the Wisconsin group
(e.g., McCammon et al. 1983). The broadband count rates in
the low energy bands, particularly the B and C bands (130–
188 eV and 160–284 eV respectively) have been modeled as
coming from an optically thin, hot plasma at a temperature of
∼ 106 K that occupies the low density cavity extending to ∼ 50–
200 pc from the Sun in all directions (Snowden et al. 1990).
Refinements to this picture have been required by ROSAT data
showing absorption by relatively distant clouds (e.g. MBM12,
Snowden et al. 1993). Snowden et al. (1998) propose a picture
in which the emission is divided between a LB component (un-
absorbed except for the LIC) and a distant absorbed component,
mainly in the Galactic halo. More recently there has been grow-
ing evidence that some, possibly large, fraction of the SXRB is
generated within the heliosphere from charge exchange between
solar wind ions and neutral atoms (SWCX). We discuss this fur-
ther in §5.6.
We model the spectrum measured by the broad-band soft X-
ray observations by assuming that the SXR background consists
of a local (unabsorbed) component and a distant (halo) com-
ponent absorbed by an H i column density of 1019 cm−2. The
emission measure or intrinsic intensity of the local and distant
components are assumed to be equal. The spectrum is calculated
using the Raymond & Smith (1977, updated) plasma emission
code assuming a hot, optically thin plasma in collisional ion-
ization equilibrium. We explore temperatures for the hot gas of
log Th = 5.9, 6.0 and 6.1. The total flux, scaled by the emission
measure, is fixed so that the B band flux matches the all-sky av-
erage from McCammon et al. (1983).
Slavin and Frisch: Boundary Conditions of the Heliosphere 5
The boundary region between the warm LIC and the adja-
cent Local Bubble plasma may be another significant source of
EUV radiation and we include this flux in our models 1–30. We
model this transition region as a conductive interface between
the LIC and Local Bubble plasma in the same way as described
in Slavin & Frisch (2002). The cloud is assumed to be steadily
evaporating into the surrounding hot gas. The partially ionized
gas of the LIC is heated and ionized as it flows into the Local
Bubble. The ionization falls out of equilibrium, with low ion-
ization stages persisting into the hot gas. The non-equilibrium
ionization is followed and the emission in the boundary is calcu-
lated again using the Raymond & Smith (1977) code. Ions in the
outflow are typically excited several times before being ionized
and the boundary region radiates strongly in the 13.6 − 54.4 eV
band. The contribution of the interface emission to the total B
band flux is taken into account in the calculation of the emission
measure for the hot gas of the Local Bubble so that the B band
flux still matches the all-sky average.
We note that no attempt is made to make this model con-
sistent with the size of the local cavity, which is proposed to
contain the hot gas in the standard model for the SXRB (e.g.,
Snowden et al. 1998). The pressure in the hot gas is not adjusted
to fit such models. Rather the total pressure in the hot gas for an
evaporating cloud model is dictated by the assumed density, tem-
perature and magnetic field in the cloud. In fact the pressures in
our models come out far too low for the standard model to pro-
duce the SXRB within the confines of the Local Cavity as de-
duced, e.g., from Na i observations (Lallement et al. 2003). This
in turn means that if the thermal pressure in the Local Bubble
turns out to be much lower than was assumed in those models
because a substantial fraction of the SXRB comes from SWCX
then the emission from the cloud boundary would be unaffected.
An example of the profiles of the hydrodynamic variables
for two different models is shown in Fig. 2. The magnetic field
strength in these calculations is assumed to be proportional to
the density at every point in the outflow. The treatment here is
the same as in Slavin (1989) which contains a more thorough
discussion of the issues involved in this sort of calculation. The
effect of the field on the conductivity is parametrized in a simple
way by a constant reduction factor of 0.5. The importance of the
magnetic field for our calculations lies in the way it affects the
thermal pressure in the layer. Since the density drops sharply in
the outflow and |B| ∼ n, any magnetic pressure (∼ B2) drops
even more sharply. The total pressure is roughly constant in the
boundary, so the thermal pressure necessarily rises to make up
for the decreasing magnetic pressure. Since all our models have
nearly the same thermal pressure in the cloud, the primary effect
of the magnetic field is to help determine the thermal pressure
in the interface and thus radiative flux from the boundary. Since
the total soft X-ray flux is fixed by requiring a match with the
Wisconsin B band all-sky average count rate (McCammon et al.
1983), a larger assumed magnetic field increases only the EUV
flux which is not constrained by the B-band data. The affect on
the cloud of a larger EUV flux is to increase its temperature and
ionization.
A secondary effect of the magnetic field can be seen in the
temperature profiles in Figure 2. In evaporating clouds in the
ISM, if the temperature gradient is large enough and the thermal
pressure is low enough, the conduction becomes “saturated”,
which means that the heat flux expected from the gas temper-
ature and temperature gradient exceeds the flux that can be car-
ried by the electrons (Cowie & McKee 1977). Saturation leads
to a steepening of the temperature gradient and a relative slow-
ing of the mass loss rate. In the two cases shown in Figure 2,
Fig. 2. Profiles of hydrodynamic variables in two different cloud
boundary calculations. The solid lines are for model 6 which has
nH = 0.273 cm
−3, log Th = 6.0, B0 = 2 µG and NHI = 4.5 × 10
cm−2, while the dashed lines are for model 8, which differs from
model 6 only in the strength of the magnetic field, B0 = 5 µG.
Note that in the upper right panel, the plot of thermal pressure,
the radial scale is much smaller in order to show the variation in
thermal pressure. The higher magnetic pressure inside the cloud
for model 8 leads to the higher external thermal pressure for that
case. The temperature profile differs in the two cases because the
degree of heat flux saturation is reduced for the higher thermal
pressure of model 8, which in turn leads to a shallower tempera-
ture gradient.
the lower magnetic field case (B0 = 2 µG) is moderately satu-
rated (in terms of Cowie & McKee’s parameter, σ0 = 3) while
the other case (B0 = 5 µG), because of the higher magnetic pres-
sure, is less saturated.
3. Photoionization Models
The photoionization models of the LIC are developed follow-
ing the same underlying procedure as in SF02, but selecting
only the LIC absorption component towards ǫ CMa for com-
parison. Improvements include using updated values for in situ
ISM observations and using a recent version of the Cloudy
radiative transfer/thermal equilibrium code (version 06.02.09a,
Ferland et al. 1998). We run Cloudy with the assumption of a
plane-parallel cloud geometry and format our calculated pho-
toionizing spectrum to be used as input. The selected options
include utilizing recent calculations for the dielectronic recom-
bination rates for Mg+ → Mg0 (e.g. Altun et al. 2006, and the
commands “set dielectronic recombination Badnell” and “set ra-
diative recombination Badnell”) , the assumption of constant
pressure, and the inclusion of interstellar dust grains at 50%
abundance compared to a standard ISM value. As we discuss
below, the only role that dust plays is net heating of the gas since
there is far too little column for extinction to be important (ex-
pected E(B − V) ∼ 10−4.2). The fraction of the heating provided
by dust is ∼ 4% of the total heating, while dust provides ∼ 2% of
the cooling (mainly by capture of electrons onto grain surfaces).
A cosmic ray ionization rate at the default background level of
2.5×1017 s−1 (for H ionization) is included. The LIC is assumed
to be in ionization and thermal equilibrium, and Cloudy calcu-
lates the detailed transfer of radiation, including absorption and
6 Slavin and Frisch: Boundary Conditions of the Heliosphere
Table 2. Model Input Parameter Values
Input Parameter
nH log Th B0 NHI
Model No. (cm−3) (K) (µG) (1017 cm−2)
1 0.273 5.9 2.0 3.0
2 0.273 5.9 2.0 4.5
3 0.273 5.9 5.0 3.0
4 0.273 5.9 5.0 4.5
5 0.273 6.0 2.0 3.0
6 0.273 6.0 2.0 4.5
7 0.273 6.0 5.0 3.0
8 0.273 6.0 5.0 4.5
9 0.273 6.1 2.0 3.0
10 0.273 6.1 2.0 4.5
11 0.273 6.1 5.0 3.0
12 0.273 6.1 5.0 4.5
13 0.218 5.9 2.0 3.0
14 0.218 5.9 2.0 4.5
15 0.218 5.9 5.0 3.0
16 0.218 5.9 5.0 4.5
17 0.218 6.0 2.0 3.0
18 0.218 6.0 2.0 4.5
19 0.218 6.0 5.0 3.0
20 0.218 6.0 5.0 4.5
21 0.218 6.1 2.0 3.0
22 0.218 6.1 2.0 4.5
23 0.218 6.1 5.0 3.0
24 0.218 6.1 5.0 4.5
25 0.226 5.9 4.7 3.0
26 0.213 5.9 2.5 4.0
27 0.226 6.0 3.8 3.0
28 0.216 6.0 2.1 4.0
29 0.232 6.1 3.4 3.0
30 0.223 6.1 0.05 4.0
42 0.218 6.1 – 4.5
scattering of the radiation incident on the cloud surface, as well
as the diffuse continuum and emission lines generated within the
cloud.
The procedure for creating a model begins with generating
the incident radiation field at the cloud surface (§2.3). The ra-
diative transfer model is then run, and the output predictions of
the model are compared to observations of interstellar absorp-
tion lines in the LIC towards ǫ CMa (N(C ii∗), N(N i), N(O i),
N(Mg ii), N(S ii), N(Si ii), N(Fe ii)) and in situ observations of
n(He0) by spacecraft inside of the solar system. The abundances
of C, N, O, Mg, Si, S and Fe are then adjusted to be consistent
with the observed column densities. With these new abundances,
the Cloudy run is repeated and this process is continued until no
adjustment of the abundances is needed. Because the abundances
do have an impact on the emission from the cloud boundary, the
cloud evaporation model is then re-run with the new abundances
as well to re-generate the input ionizing spectrum. The iterative
process of generating the spectrum and doing the Cloudy pho-
toionization runs generally requires only a couple runs of the
cloud evaporation program and a few runs of Cloudy.
4. Model Results
To investigate the dependence of the results on the input pa-
rameters we calculate a grid of 24 models. We explore total H
density, nH = 0.273, 0.218; Local Bubble hot gas temperature,
log Th = 5.9, 6.0, 6.1; magnetic field strength, B0 = 2, 5 µG; and
H i column density, NH I = 3 × 10
17, 4.5 × 1017 cm−2. The val-
Fig. 3. Model results for the He0 density and temperature in the
ISM just outside the heliosphere. The squares, circles, and trian-
gles are for models that are part of the initial grid of 24 models,
while the stars are for models 25 − 30 for which the magnetic
field, B, and the total H density, nH, were varied to match the ob-
served n(He0) and T . For the grid models, the empty symbols are
for models with N(H i)= 3 × 1017 cm−2, while the filled symbol
models have N(H i)= 4.5 × 1017 cm−2. As the legend shows, the
color (black vs. gray) indicates the magnetic field strength and
the symbol shape indicates the temperature assumed for the hot
gas of the Local Bubble. For identical kinds of points, the one to
the left is for a model with n(H0) = 0.218 cm−3 and the one to
the right has n(H0) = 0.273 cm−3. The ellipse is the error range
around the observed values for n(He0) and T .
ues for T and n(He i) at the solar location, the endpoint of the
calculations, are shown in Fig. 3 for this set of models. We then
explore another six models in which we do the calculations over
a grid in log Th and NH I but vary the values of nH and B0 in or-
der to match the observed T and n(He i). We employed a multiple
linear regression to assist in narrowing down the search region
for the values of nH and B0 needed to match the observations.
Since the dependencies of the results on the parameters really
are quite non-linear, this procedure could not work to predict
exactly correct values for the required parameters, but was use-
ful for getting close to the correct values. Based on the results
for the initial grid of models, we use log Th = 5.9, 6.0, 6.1 and
NH I = 3 × 10
17, 4 × 1017 cm−2 for this smaller grid, models
25 − 30. We chose to use 4 × 1017 cm−2 rather than 4.5 × 1017
cm−2 because the higher column density models, for the most
part, produced temperatures that were too high. As can be seen
from Fig. 3, all of these models (25–30), plotted as stars, are con-
sistent with the observed T and n(He i), indicated by the ellipse
in the figure. Table 2 gives the input parameters for each model.
Model predictions for the ǫ CMa sightline integrated through the
LIC are presented in Table 3. Model predictions for the CHISM
(i.e. at the solar location) are shown in Table 4.
In SF02 we tested models with no emission from the cloud
boundary. This amounts to assuming that the boundary is a sharp
transition from the hot gas of the Local Bubble to the warm gas
of the LIC. We have again explored such models using the LIC
data as constraints in the same way as for the models discussed
above with a conductive interface. When there is no evaporative
boundary, our models do not depend on the magnetic field in the
cloud since in that case the ionizing flux consists only of dif-
fuse emission from the hot gas of the Local Bubble and EUV
Slavin and Frisch: Boundary Conditions of the Heliosphere 7
Table 3. Model Column Density Results
Modela log N(Htot) log N(Ar i) log N(Ar ii) log N(Si iii)
N(Mg II)
N(Mg I)
N(C II)
N(C II∗)
N(H I)
N(He I)
Obs.b – – – 12.40 443+197
−110 93 − 430
c 12 − 16
1 17.58 11.48 11.76 8.895 706.3 213.0 11.36
2 17.78 11.67 11.95 9.641 325.3 234.1 11.40
3 17.65 11.33 11.84 9.844 246.1 182.1 11.44
4 17.82 11.55 12.00 10.12 136.5 198.0 11.80
5 17.58 11.49 11.75 8.961 717.8 230.0 11.62
6 17.78 11.67 11.94 9.711 286.7 244.9 11.62
7 17.64 11.34 11.81 9.909 207.4 194.8 12.47
8 17.82 11.56 11.97 10.17 119.7 208.2 12.66
9 17.59 11.46 11.75 9.289 553.0 239.5 12.27
10 17.78 11.66 11.93 9.861 210.3 248.1 12.14
11 17.64 11.33 11.78 9.993 171.2 201.7 13.44
12 17.82 11.54 11.95 10.23 104.3 210.6 13.52
13 17.60 11.44 11.78 9.100 768.9 255.1 11.52
14 17.79 11.64 11.96 9.738 336.4 274.4 11.47
15 17.67 11.30 11.85 9.944 251.2 215.9 11.65
16 17.84 11.51 12.01 10.21 140.6 232.1 12.01
17 17.58 11.47 11.76 8.926 840.1 262.5 11.65
18 17.79 11.65 11.95 9.792 308.9 286.3 11.64
19 17.66 11.30 11.82 10.02 208.5 229.2 12.76
20 17.84 11.52 11.98 10.26 123.5 242.1 12.95
21 17.59 11.43 11.76 9.318 633.1 280.8 12.41
22 17.79 11.63 11.94 9.926 224.9 288.4 12.25
23 17.66 11.29 11.79 10.10 175.0 235.5 13.81
24 17.84 11.50 11.96 10.31 110.2 245.5 13.85
25 17.66 11.32 11.84 9.887 271.3 213.6 11.71
26 17.74 11.56 11.91 9.676 383.9 270.1 11.70
27 17.63 11.36 11.79 9.751 331.1 242.0 12.51
28 17.73 11.59 11.90 9.625 411.6 284.5 11.79
29 17.62 11.38 11.77 9.720 329.3 251.6 13.01
30 17.72 11.60 11.88 9.642 386.6 295.1 12.08
42 17.77 11.70 11.92 9.555 482.9 317.9 11.51
a The best models, consistent with all observational data (see §4), are indicated by bold face.
b Observational results from Gry & Jenkins (2001) (see table 1). The values listed for N(H i)/N(He i) are the range of values observed excluding
Feige 24 which is one of the most distant stars observed by Dupuis et al. (1995) and has unusually large N(H i) and ratio values.
c The upper limit on N(C ii) is not well determined observationally because of the saturation of the line. Gry & Jenkins (2001) define it by
assuming a solar C/S abundance ratio and using the observed S ii column density. We find (see Slavin & Frisch 2006) that the abundance of C
required to match the N(C ii∗) observations is supersolar, with C/S∼ 36 − 44, which results in a much higher upper limit on N(C ii).
emission from nearby hot stars and the spectrum is not related
to the properties of the cloud. For these models our model grid
consists of total H density, nH = 0.273, 0.218, Local Bubble hot
gas temperature, log Th = 5.9, 6.0, 6.1, and H i column density,
NH I = 3×10
17, 4.5×1017 cm−2, for a total of twelve models that
we label as models 31–42. Of these models, however, only two
resulted in ionizing fluxes sufficient to heat the cloud to a tem-
perature ∼ 6000 K at the same time as matching the constraints
on the ion column densities. These models were the ones with
log Th = 6.1 and NH I = 4.5 × 10
17 cm−2 (models 36 and 42).
For the other cases, either at the surface or deeper into the cloud,
there are insufficient photons to provide the heating to balance
the cooling and the cloud temperature drops sharply to < 1000
K. The model with nH = 0.218 (model 42) is consistent with the
observed value of n(He0) and with the column density data as
well.
From these 42 models we have selected those that provide
acceptable results for the observational constraints, according to
prioritized requirements. The first requirement is that the model
predict the density and temperature of He i observed inside of
the solar system. Models 14 (marginally), 15 and 25–30 and 42
predict a He density and temperature consistent with the ob-
served values within the reported errors. They also predict the
PUI Ne densities, for an assumed Ne/H=123 ppm. Models 26
and 28 successfully match the PUI data for Ne/H as low as
∼ 100 ppm. These models are also required to match the ob-
served Mg ii/Mg i ratio in the LIC towards ǫ CMa. Models 14,
27, and 29 marginally fit this criterion, while 26, 28, 30, and 42
successfully fit this criterion. Note that the new models now pro-
vide acceptable predictions for the CHISM temperature, which
was not the case for the best models in SF02. These models are
also consistent with the observed C ii/C ii∗ ratios in the LIC com-
ponent towards ǫ CMa though this constraint is weak because of
the large uncertainties in N(C ii). Based on these comparisons,
and given the uncertainties in both data and models, Models 14,
26-30, and 42 are plausible models, but Models 26 and 28 appear
to best match the observational constraints.
Based on the constraints and assumptions presented in the
previous section, we select models 14, 26–30 and 42 as the best
models for the LIC ionization, with models 26 and 28 favored
by the PUI Ne data provided that Ne/H > 100 ppm. We believe
that these seven models then give a realistic range for the uncer-
tainties in the boundary conditions of the heliosphere, providing
that the underlying assumptions implicit in the Cloudy code, e.g.
8 Slavin and Frisch: Boundary Conditions of the Heliosphere
Table 4. Model Results for Solar Location
Modela X(H) X(He) n(H0) n(He0) n(N0) n(O0) n(Ne0) n(Ar0) ne np T
Obs.b 0.015 5.5 × 10−6 4.8 × 10−5 5.8 × 10−6 1.6 × 10−7 6300
1 0.176 0.299 0.318 0.0269 1.84 × 10−5 1.48 × 10−4 1.39 × 10−5 3.47 × 10−7 0.0800 0.0678 4310
2 0.196 0.352 0.251 0.0201 9.63 × 10−6 7.71 × 10−5 8.51 × 10−6 2.69 × 10−7 0.0724 0.0611 6450
3 0.286 0.404 0.230 0.0191 1.34 × 10−5 1.07 × 10−4 7.81 × 10−6 1.82 × 10−7 0.106 0.0922 6280
4 0.259 0.428 0.229 0.0175 8.86 × 10−6 6.95 × 10−5 6.45 × 10−6 1.92 × 10−7 0.0937 0.0799 7560
5 0.174 0.310 0.300 0.0249 1.72 × 10−5 1.39 × 10−4 1.13 × 10−5 3.30 × 10−7 0.0750 0.0631 4610
6 0.197 0.363 0.242 0.0190 9.13 × 10−6 7.44 × 10−5 7.08 × 10−6 2.61 × 10−7 0.0707 0.0593 6770
7 0.278 0.441 0.225 0.0173 1.33 × 10−5 1.04 × 10−4 5.75 × 10−6 1.78 × 10−7 0.101 0.0866 6670
8 0.257 0.459 0.223 0.0161 8.65 × 10−6 6.79 × 10−5 4.92 × 10−6 1.89 × 10−7 0.0918 0.0773 7860
9 0.193 0.357 0.265 0.0209 1.53 × 10−5 1.23 × 10−4 7.52 × 10−6 2.71 × 10−7 0.0761 0.0634 5410
10 0.203 0.392 0.235 0.0177 9.06 × 10−6 7.24 × 10−5 5.52 × 10−6 2.43 × 10−7 0.0723 0.0600 7230
11 0.278 0.474 0.220 0.0158 1.29 × 10−5 1.02 × 10−4 4.42 × 10−6 1.69 × 10−7 0.0999 0.0847 7020
12 0.262 0.490 0.219 0.0148 8.41 × 10−6 6.66 × 10−5 3.83 × 10−6 1.78 × 10−7 0.0928 0.0776 8160
13 0.201 0.333 0.230 0.0191 1.34 × 10−5 1.08 × 10−4 8.94 × 10−6 2.32 × 10−7 0.0681 0.0580 4720
14 0.215 0.376 0.193 0.0152 7.29 × 10−6 5.95 × 10−5 5.99 × 10−6 1.94 × 10−7 0.0625 0.0528 6650
15 0.310 0.436 0.176 0.0143 1.02 × 10−5 8.18 × 10−5 5.35 × 10−6 1.28 × 10−7 0.0905 0.0789 6470
16 0.284 0.461 0.175 0.0131 6.76 × 10−6 5.36 × 10−5 4.40 × 10−6 1.35 × 10−7 0.0812 0.0695 7750
17 0.178 0.315 0.255 0.0211 1.47 × 10−5 1.19 × 10−4 9.51 × 10−6 2.75 × 10−7 0.0656 0.0553 4360
18 0.214 0.383 0.188 0.0146 7.16 × 10−6 5.81 × 10−5 5.07 × 10−6 1.91 × 10−7 0.0610 0.0513 6900
19 0.302 0.472 0.173 0.0129 1.01 × 10−5 8.03 × 10−5 3.93 × 10−6 1.26 × 10−7 0.0872 0.0748 6860
20 0.282 0.491 0.172 0.0120 6.61 × 10−6 5.26 × 10−5 3.37 × 10−6 1.33 × 10−7 0.0802 0.0677 8050
21 0.204 0.374 0.211 0.0164 1.20 × 10−5 9.85 × 10−5 5.54 × 10−6 2.04 × 10−7 0.0648 0.0541 5390
22 0.221 0.414 0.184 0.0136 6.96 × 10−6 5.69 × 10−5 3.90 × 10−6 1.78 × 10−7 0.0628 0.0523 7350
23 0.305 0.506 0.168 0.0117 9.91 × 10−6 7.82 × 10−5 2.97 × 10−6 1.18 × 10−7 0.0868 0.0737 7220
24 0.286 0.520 0.169 0.0111 6.57 × 10−6 5.16 × 10−5 2.60 × 10−6 1.25 × 10−7 0.0808 0.0676 8310
25 0.297 0.427 0.187 0.0151 1.09 × 10−5 8.67 × 10−5 5.75 × 10−6 1.41 × 10−7 0.0907 0.0789 6360
26 0.224 0.385 0.192 0.0151 8.32 × 10−6 6.66 × 10−5 5.96 × 10−6 1.83 × 10−7 0.0653 0.0554 6320
27 0.258 0.426 0.195 0.0149 1.13 × 10−5 8.97 × 10−5 5.03 × 10−6 1.63 × 10−7 0.0796 0.0677 6240
28 0.212 0.376 0.194 0.0152 8.24 × 10−6 6.73 × 10−5 5.49 × 10−6 1.95 × 10−7 0.0622 0.0523 6350
29 0.242 0.429 0.202 0.0150 1.17 × 10−5 9.30 × 10−5 4.53 × 10−6 1.74 × 10−7 0.0769 0.0646 6300
30 0.203 0.379 0.197 0.0151 8.51 × 10−6 6.81 × 10−5 4.78 × 10−6 2.01 × 10−7 0.0605 0.0502 6500
42 0.189 0.355 0.186 0.0145 6.91 × 10−6 5.71 × 10−5 4.60 × 10−6 2.04 × 10−7 0.0522 0.0433 6590
a The best models (see §4) are indicated by bold face.
b Observational results from Gloeckler & Geiss (2004), Gloeckler (2005, private communication) and Witte et al. (1996) (see table 1 for uncer-
tainties).
photoionization equilibrium, are correct. The predictions of the
best models provide excellent matches to the observational con-
straints. Based on these models, we find the boundary conditions
of the heliosphere to be describable as n(H0) = 0.19−0.20 cm−3,
ne = 0.05−0.08 cm
−3, and X(H) ≡ H+/(H0+H+) = 0.19−0.26,
X(He) ≡ He+/(He0 + He+) = 0.36 − 0.43. For these models, we
find abundances of O/H = 295 − 437 ppm, C/H = 589 − 813
ppm, and N/H = 40.7 − 64.6 ppm (Table 7). The total LIC den-
sity is n(H)0 = 0.213 − 0.232 cm
−3, while the strength of the
interstellar magnetic in the cloud varies between 0 and 3.8 µG.
The Ne PUI data further favor densities of n(H0) ≈ 0.19 cm−3
and ne = 0.06 − 0.07 cm
In this analysis we have assumed negligible filtration for He
in the heliosheath regions. Modeling of the He filtration factor
however allows values as small as fHe = 0.92, which yields
n(He i)= 0.0164 cm−3 for the CHISM (Table 1). The predictions
of Model 21 agree with this value for n(He i), as well as with
the ratios Mg ii/Mg i and C ii/C ii∗ towards ǫ CMa and the pickup
ion Ne and Ar data (Table 3). The predicted cloud temperature
is low by ∼ 1000 K. The density and ionization for Model 21 are
n(H0) = 0.21 cm−3 and ne= 0.06 cm
−3. We therefore conclude
that our best models listed above are robust in the sense that they
predict consistent values for the n(H0) to within 5%, and electron
densities to within 25%.
The radiation field incident on the LIC for Model 26 is shown
in Fig. 1 and the spectral characteristics of the field for each
model are listed in Table 5. The wavelengths regions λ ≤ 912 Å
and λ ∼ 1500 Å are of primary importance for the photoioniza-
tion of the cloud, the former because it determines H0 and He0
ionization, and the latter because it determines Mg0 ionization.
The ionization parameter is defined as U ≡ Φ/n(H)c, where
Φ is the H ionizing photon flux, n(H) is the total (neutral + ion-
ized) hydrogen density at the cloud surface and c is the speed
of light. The total ionizing photon fluxes at the cloud surface
(photons cm−2 s−1) for the three bands 13.6–24.6, 24.6–54.4, and
54.4–100 eV, are given by ΦH, ΦHe0 , and ΦHe+ , respectively. The
ratio of the total number of H0 and He0 ionizing photons in the
incident radiation field is given by Q(He0)/Q(H0). The quantity
〈E〉 (eV) is the mean energy of an ionizing photon, equal to the
integrated energy flux from 13.6 to 100 eV divided by the inte-
grated photon flux over the same energy range.
In Figure 3 we show n(He0) and temperature of the CHISM
for our model calculations. In Figure 4 we show N ii/N i vs.
Mg ii/Mg i, illustrating an anti-correlation of the ratios caused
by the fact that Mg ii/Mg i decreases with electron density while
N ii/N i indicates the ionization level in the cloud. The ionization
of the CHISM is listed in Table 6 for Model 26, where com-
monly observed elements are listed. The abundances of He, Ne,
Slavin and Frisch: Boundary Conditions of the Heliosphere 9
Table 5. Characteristics of the Model Radiation Field
Modela U φH φHe0 φHe+ Q(He
0)/Q(H0) 〈E〉
photons cm−2 s−1 photons cm−2 s−1 photons cm−2 s−1 eV
1 2.0 × 10−6 4.6 × 103 7.5 × 103 2.8 × 103 0.46 74.6
2 2.0 × 10−6 5.3 × 103 7.3 × 103 2.7 × 103 0.44 72.4
3 3.1 × 10−6 9.0 × 103 1.3 × 104 2.7 × 103 0.49 57.7
4 3.0 × 10−6 8.6 × 103 1.2 × 104 2.6 × 103 0.49 58.6
5 2.0 × 10−6 4.0 × 103 7.0 × 103 3.8 × 103 0.43 79.0
6 2.1 × 10−6 4.9 × 103 6.9 × 103 3.8 × 103 0.41 76.2
7 3.2 × 10−6 7.4 × 103 1.4 × 104 3.8 × 103 0.53 61.3
8 3.1 × 10−6 7.4 × 103 1.3 × 104 3.7 × 103 0.52 61.5
9 2.2 × 10−6 3.8 × 103 7.4 × 103 5.6 × 103 0.40 80.0
10 2.3 × 10−6 4.8 × 103 7.2 × 103 5.6 × 103 0.38 77.3
11 3.5 × 10−6 6.6 × 103 1.5 × 104 5.6 × 103 0.53 63.4
12 3.4 × 10−6 6.9 × 103 1.5 × 104 5.5 × 103 0.52 63.2
13 2.3 × 10−6 4.3 × 103 7.0 × 103 2.8 × 103 0.46 76.9
14 2.4 × 10−6 5.1 × 103 6.8 × 103 2.7 × 103 0.43 74.3
15 3.7 × 10−6 8.5 × 103 1.2 × 104 2.7 × 103 0.49 58.8
16 3.6 × 10−6 8.2 × 103 1.2 × 104 2.6 × 103 0.49 59.5
17 2.3 × 10−6 3.7 × 103 6.4 × 103 3.8 × 103 0.42 81.8
18 2.4 × 10−6 4.7 × 103 6.2 × 103 3.8 × 103 0.39 78.4
19 3.9 × 10−6 7.1 × 103 1.4 × 104 3.8 × 103 0.53 62.2
20 3.8 × 10−6 7.2 × 103 1.3 × 104 3.7 × 103 0.52 62.2
21 2.6 × 10−6 3.6 × 103 6.8 × 103 5.6 × 103 0.39 82.0
22 2.7 × 10−6 4.6 × 103 6.6 × 103 5.6 × 103 0.36 78.9
23 4.2 × 10−6 6.3 × 103 1.5 × 104 5.6 × 103 0.52 64.4
24 4.2 × 10−6 6.7 × 103 1.4 × 104 5.5 × 103 0.51 64.1
25 3.5 × 10−6 7.9 × 103 1.2 × 104 2.7 × 103 0.49 60.3
26 2.5 × 10−6 5.0 × 103 7.5 × 103 2.7 × 103 0.45 73.2
27 3.1 × 10−6 5.4 × 103 1.0 × 104 3.8 × 103 0.50 68.9
28 2.4 × 10−6 4.3 × 103 6.4 × 103 3.8 × 103 0.40 79.5
29 3.0 × 10−6 4.6 × 103 9.7 × 103 5.6 × 103 0.45 73.6
30 2.4 × 10−6 3.8 × 103 5.5 × 103 5.6 × 103 0.33 84.6
42 2.2 × 10−6 3.6 × 103 3.6 × 103 5.6 × 103 0.25 91.1
a The best models (see §4) are indicated by bold face.
Fig. 4. Model results for N(N ii)/N(N i) versus Mg ii/Mg i. The
symbols have the same meaning as in Figure 3. In this case the
models with higher n(H0) lie below and slightly to the left of
those with lower density. N(N ii)/N(N i) is an indicator of cloud
ionization fraction while Mg ii/Mg i goes as 1/ne. The dotted line
is the observed value for Mg ii/Mg i and the dashed lines indi-
cate the 1 − σ error range for the value. We see that models that
match the observed ratio all correspond to relatively low ioniza-
tion, X(H) ∼ 0.20 − 0.27 in the CHISM.
Na, Al, P, Ar, and Ca were assumed, based on solar abundances,
and were not adjusted in the modeling process. The abundances
of C, N, O, Mg, Si, S and Fe were adjusted for each model to
match observed column densities towards ǫ CMa (see §2). The
elemental abundances that have been assumed, with the excep-
tion of that for He, are not expected to have any significant im-
pact on the model results.
5. Discussion
5.1. Heliosphere Boundary Conditions
As discussed above, the best models of those we calculated
are determined by the match to the CHISM He0 density and
temperature found by the in situ Ulysses measurements (§2.2),
combined with the matching the LIC component column den-
sity ratios Mg ii/Mg i and C ii/C ii∗. These models span a fairly
large range in the model parameters: nH = 0.213 − 0.232
cm−3, log Th = 5.9 − 6.1 K, B0 = 0.05 − 3.8 µG, and N(H i)
= 3.0 × 1017 − 4.5 × 1017 cm−2. Despite this, the predicted val-
ues for neutral H density and electron density in the CHISM lie
within a remarkably small range: n(H0) = 0.19 − 0.20 cm−3,
ne = 0.05 − 0.08 cm
−3, for models that include the conductive
boundary. For the one model without evaporation that is consis-
tent with the data we find n(H0) = 0.186 cm−3, ne = 0.052 cm
Including the PUI Ne data as a constraint narrows the density re-
sults to n(H0) ≈ 0.19 cm−3 and ne = 0.06− 0.07 cm
−3. For these
10 Slavin and Frisch: Boundary Conditions of the Heliosphere
Table 6. Model 26 Results for Ionization Fractionsa
Element PPM I II III IV
H 106 0.776 0.224 – –
He 105 0.611 0.385 4.36(-3) –
C 661 2.68(-4) 0.975 0.0244 0.000
N 46.8 0.720 0.280 8.52(-5) 0.000
O 331 0.814 0.186 4.71(-5) 0.000
Ne 123 0.196 0.652 0.152 2.79(-6)
Na 2.04 1.47(-3) 0.843 0.155 6.34(-6)
Mg 6.61 1.98(-3) 0.850 0.148 0.000
Al 0.0794 5.37(-5) 0.976 0.0118 0.0123
Si 8.13 4.21(-5) 0.999 8.02(-4) 3.10(-5)
P 0.219 1.35(-4) 0.977 0.0232 9.29(-5)
S 15.8 6.47(-5) 0.971 0.0288 1.95(-6)
Ar 2.82 0.263 0.500 0.238 2.83(-6)
Ca 4.07(-4) 9.21(-6) 0.0155 0.984 1.87(-4)
Fe 2.51 7.01(-5) 0.975 0.0245 5.75(-6)
a Numbers less than 10−3 are written as x(y) where y is the exponent
and x is the mantissa (or significand).
densities to stray out of this range would appear to require sig-
nificant errors in the underlying comparison data, e.g. n(He0) in
the CHISM, or substantial non-equilibrium ionization effects in
the LIC. The variation in the interstellar radiation field between
the different models that match the data give us some degree of
confidence that these densities are not highly sensitive to the de-
tails of the radiation field. The range ne = 0.05 − 0.08 cm
corresponds to an electron plasma frequency of 2.0–2.5 kHz,
which is the frequency of the mysterious weak radio emission
detected beyond the termination shock in the outer heliosphere
(Gurnett & Kurth 2005; Mitchell et al. 2004).
5.2. Hydrogen Filtration Factor
Tracers of H0 inside of the termination shock, after filtration, in-
clude the H i Lyα backscattered radiation, H pickup ions, and
the slowdown of the solar wind at distances beyond 5 AU from
mass-loading by H PUIs. The range of n(H0) found above to
best fit the combined heliospheric n(He0) and LIC data towards
ǫ CMa, n(H0) = 0.19− 0.20 cm−3, represents the density of neu-
tral interstellar H atoms outside of the heliosphere, and removed
from heliospheric influences. The hydrogen filtration factor, fH,
can be obtained from comparisons between these models and in-
terstellar H0 densities at the termination shock as inferred from
in situ observations of interstellar H inside of the heliosphere.
The accompanying papers in this special section provide es-
timates of the interstellar H0 density at the termination shock.
The solar wind slows down due to massloading by interstel-
lar H, yielding n(H0)= 0.09 ± 0.01 cm−3 at the termination
shock (Richardson et al. 2007). The density of H pickup ions ob-
served by Ulysses is inferred at the termination shock, yielding
n(H0)= 0.11 ± 0.01 cm−3; models of H atoms traversing the he-
liosheath regions then yield for the CHISM n(H0)= 0.20 ± 0.02
cm−3 and np= 0.04±0.02 cm
−3, or ne∼ 0.05 cm
−3 (Bzowski et al.
2007). The radial variation in the response of the interplanetary
Lyα 1215 Å backscattered radiation to the solar rotational mod-
ulation of the Lyα “beam” that excites the florescence yields
n(H0)∼ 0.085−0.095 cm−3, depending on the heliosphere model
(Pryor et al. 2007). From these n(H0) values at the termination
shock, we estimate that 43%–58% of the H-atoms successfully
traverse the heliosheath region, or fH ∼ 0.43−0.58. Müller et al.
(2007) evaluate filtration using five different plasma-neutral
Table 7. Elemental Gas Phase Abundances (ppm)
Element
Model No. C N O Mg Si S Fe
14 589 40.7 295 5.89 7.24 14.1 2.24
21 955 60.3 447 9.77 11.5 22.9 3.55
25 631 66.1 437 7.76 10.0 19.5 3.09
26 661 46.8 331 6.61 8.13 15.8 2.51
27 759 64.6 437 8.71 10.7 20.9 3.31
28 708 45.7 331 7.08 8.32 16.6 2.57
29 813 64.6 437 9.33 11.0 21.9 3.39
30 741 46.8 331 7.41 8.51 17.0 2.63
42 724 39.8 295 6.76 7.76 15.1 2.34
models, and find a range of fH = 0.52 − 0.74. A hydrogen filtra-
tion of fH = 0.55 ± 0.03 is consistent with both in situ data and
radiative transfer models.
5.3. Gas-Phase Abundances
The LIC photoionization models are forced to match the ob-
served set of column densities (Tables 1 and 3). The gas-phase
abundances of most elements are treated as free parameters that
can be varied in order to match observed column densities, so
that the successful models yield elemental abundances for the
LIC that are automatically corrected for unobserved H+ (Table
7). The exceptions are that He, Ne, and Ar abundances, being
unconstrained by the observations toward ǫ CMa, are not ad-
justed but are assumed to be 105 ppm, 123 ppm and 2.82 ppm,
respectively. In the models, N(C ii∗) is a constraint on both the
C abundance (in place of the heavily saturated C ii 1335Å line)
and ne, such that the product of the abundance and ne is more
tightly limited than either quantity individually. The requirement
to match both N(C ii∗) and n(He0) effectively restricts the ioniza-
tion fraction of H, which in turn limits O and N ionization whose
ionization fractions are tied by charge-transfer to the H ioniza-
tion at LIC temperatures.
Early studies showed that the abundances of refractory el-
ements in the very local ISM are enhanced compared to abun-
dances in cold disk gas (Marschall & Hobbs 1972; Stokes 1978;
Frisch 1981). Throughout warm and cold disk gas, the un-
derabundances of refractory elements compared to solar abun-
dances (by factors of 10−1 − 10−4) are taken to represent deple-
tion onto interstellar dust grains (e.g. Savage & Sembach 1996).
This view is supported by the correlation found between elemen-
tal depletions and the temperature characteristic of condensa-
tion at solar pressure and composition (Ebel 2000), and assumes
that there is a reference abundance pattern that characterizes the
cloud, and remains constant over the cloud lifetime as atoms are
exchanged between the gas and dust phases. Below (§5.4) we
compare solar abundances with observed gas-phase abundances
to predict the gas-to-dust mass ratios for the LIC, based on the
assumption that LIC gas and dust have remained coupled over
the cloud lifetime.
An important question is whether the LIC has solar abun-
dances. Isotopes of 18O and 22Ne isotopes measured in the ACR
population suggest that this is so. ACRs are characterized by
a rising particle flux for energies below 10–50 MeV/nucleon,
and this characteristic spectral signature is seen for 16O, 18O,
20Ne, and 22Ne. Ratios of 16O/18O ∼ 500 and 20Ne/22Ne ∼
13.7 are found for both the ACRs and solar material, indicat-
ing that the CHISM and solar material have similar composi-
Slavin and Frisch: Boundary Conditions of the Heliosphere 11
Table 8. Solar Abundances (ppm)
Grevesse Holweger Lodders Grevesse
Sauval et al.
(1998) (2001) (2003) (2007)a
C 334 ± 46 391(+110,−86) 290 ± 27 275 ± 34
N 84 ± 12 85.3+25
−19 82 ± 20 67 ± 10
O 683 ± 94 545+107
−90 579 ± 66 513 ± 63
Ne 121 ± 17 100+17
−15 91 ± 21 77 ± 12
Mg 38 ± 4 34.5+5.1
−4.5 41 ± 2 38 ± 9
Si 35 ± 4 34.4+4.1
−3.7 41 ± 2 36 ± 4
S 22 ± 5 - 18 ± 2 15 ± 2
Ar 2.54 ± 0.35 - 4.24 ± 0.77 1.70 ± 0.34
Fe 32 ± 4 28.15.84.8 35 ± 2 32 ± 4
a Protosolar abundances are obtained by increasing the photospheric
abundances by 0.05 dex for elements heavier than He, as suggested
by Grevesse et al. (2007)
tions (Leske et al. 2000; Leske 2000). We therefore adopt solar
abundances as the underlying reference abundance pattern for
the LIC.
Unfortunately a prominent uncertainty exists in the correct
solar abundances of volatile elements such as O and S, which
have low condensation temperatures (Tcond, 180 K and 700 K
respectively), and noble elements such as Ne and Ar. Solar
abundances are determined from photospheric data (C, N, O,
Mg, Si, S, Fe), the solar wind (Ar, Ne), solar active regions
(Ne), and helioseismic data (He); abundances of non-volatile el-
ements are also found from meteoritic data (Grevesse & Sauval
1998; Holweger 2001; Lodders 2003; Grevesse et al. 2007).
Solar abundances from these studies are listed in Table 8. Our
results, discussed below, indicate that if the LIC has a solar abun-
dance composition, as indicated by the 18O and 22Ne data, then
the lower abundances found by Grevesse et al. (2007) are pre-
ferred by our models.
Ne: In these models we have assumed the Ne abundance
is 123 ppm (Anders & Grevesse 1989), which is based on a
combination of photospheric and interstellar data. Solar sys-
tem Ne abundances are difficult to measure because of FIP
effects, however values include 77 ppm (Grevesse et al. 2007,
after adding 0.05 dex to account for gravitational settling of
the elements), and ∼ 41 ppm for solar wind in coronal holes
(Gloeckler & Geiss 2007). The predicted densities of n(Ne0) in
the CHISM for models 26 and 28 (Table 4) are in agreement with
the most recent PUI results for Ne (Table 1), and Ne densities as
low as ∼ 100 ppm are allowed when filtration is included.
The CHISM Ne abundances indicated by these results ap-
pear to be consistent with Ne abundances and ionization levels
in the global ISM. The Ne abundance in the Orion nebula is 100
ppm (Simpson et al. 2004). Takei et al. (2002) measured X-ray
absorption edges formed by Ne and O in the interstellar gas and
dust towards Cyg X-2, and found abundances of Ne/H ∼ 92 ppm
and O/H ∼ 579 ppm when both atomic and compound forms
in the sightline were included. Juett et al. (2006) observed the
X-ray absorption edges of Ne and O towards nine X-ray bina-
ries which sampled both neutral and ionized warm material, and
found that the ionized states formed in the ionized material have
the ratio Ne iii/Ne ii ∼ 0.23. This value is identical to the pre-
dictions of model 26, Ne iii/Ne ii ∼ 0.23, a fortuitous agreement
that may indicate that the EUV radiation field in the CHISM is
similar to the generic galactic EUV field in the solar vicinity.
Ar: Solar Ar abundance determinations range between Ar/H
∼ 1.4 − 5.0 ppm (Table 8); we have assumed Ar/H = 2.82 ppm.
The predicted Ar density at the Sun is within the uncertainties
of the PUI data, although the range of possible filtration factors
(0.64 – 0.95, see §2.2) also allow considerable leeway.
O: In the warm ISM such as the LIC, the ionization of oxy-
gen and hydrogen is tightly coupled over timescales of ∼100
years by charge transfer (Field & Steigman 1971), so that the
assumed N(H i) combined with N(O i) measurements act to con-
strain the deduced O abundance in the gas. The two best models
(26, 28) correspond to O/H = 331 ppm, however the O column
density measurements are based on the saturated 1302Å line, and
have ∼ 35% uncertainty. The modeled LIC value of O/H ∼ 331
ppm indicates that ∼ 35% of the O atoms are depleted onto dust
grains. An oxygen filtration factor of fO ∼ 0.75 is required by
the PUI data and Model 26.
These models yield gas-phase O abundances that are con-
sistent with observations of more distant interstellar sightlines.
The ratio N(O i)/N(H i) is measured in both low and high extinc-
tion clouds. Oliveira et al. (2003) used unsaturated O i lines in
the 910–1100Å interval and found O i/H i = 317 ± 19 ppm for
∼ 30 sightlines that included both types of material. Sightlines
with detected H2, N(H) > 10
20.5 cm−2 and 〈nH〉 = 0.1−3.3 cm
yield O/H = 319 ± 14 ppm (Meyer et al. 1997). A survey of 19
stars with an average distance of 2.6 kpc by André et al. (2003)
found O i/H i = 408± 14 ppm, where the long sightline and high
average value N(H)/E(B− V) = 6.3 × 1021 cm−2 mag−1 indicate
a bias towards sightlines containing many clouds that individu-
ally have low extinctions. A larger sample of 56 sightlines for
a range of extinctions and distances show that sightlines with
higher average mean densities, 〈nH〉, show O/H = 284±12 ppm,
versus O/H = 390 ± 10 ppm for stars with low values of 〈nH〉
(Cartledge et al. 2004). For comparison, solar abundance stud-
ies yield a range of ∼ 450 − 780 ppm.
C: The best Models 26 and 28 yield a gas-phase abundance
of C of C/H = 661 and 708 compared to solar abundances
of ∼ 240 − 500 ppm, which is consistent with our earlier re-
sults (Slavin & Frisch 2006) indicating an overabundance of C
in the LIC. We speculate that shock destruction of carbonaceous
grains, perhaps combined with some local spatial decoupling be-
tween carbonaceous and silicate grains, may explain these find-
ings.
Singly-ionized carbon is an important coolant in the LIC
(§5.5), so the C overabundance is required to maintain the tem-
perature of the CHISM at the observed value. The carbon abun-
dance obtained here indirectly depends on the Mg ii→Mg i di-
electronic recombination coefficient that determines the ratio
Mg ii/Mg i, since that ratio is used as a criteria for the best mod-
els. The same ionization correction that gives the C abundance
also successfully predicts Ne ionization in global WPIM and the
S abundances in the LIC, although this may be a fortuitous co-
incidence. In the adjacent sightline towards Sirius the LIC has
N(C ii)/N(H i) = 1, 050 ppm (Hebrard et al. 1999). An ionization
correction of 300% is required to make this value consistent with
solar abundances, and such a large ionization correction is not
consistent with the ionization levels of X(H) ∼ 20 − 26% found
here. In contrast, sightlines with cold ISM show C abundances
on the order of 135 ± 46 ppm (Sofia et al. 1997; Sembach et al.
2000).
N: The best models (26 and 28) find N/H = 46–47 ppm, com-
pared to solar values of ∼ 57−110 ppm. These results are consis-
tent with the PUI results, N/H ∼ 19−47 ppm, after filtration fac-
tor uncertainties are included. The N and O results and favor an
12 Slavin and Frisch: Boundary Conditions of the Heliosphere
ISM abundance pattern for volatiles similar to the Grevesse et al.
(2007) photospheric abundances.
S: The best models predict S/H = 16–17, compared to solar
values of ∼ 13−27 (including uncertainties, see Table 8). Sulfur
is found to have little or no depletion onto dust grains in warm
diffuse ISM (e.g. Welty et al. 1999).
Mg, Si, Fe: These refractory elements are observed in the
LIC gas with abundances far below solar (factors of 3–15).
Approximately 92%, 82%, and 77% of the Fe, Mg, and Si, re-
spectively, are presumably depleted onto interstellar dust grains.
If (Grevesse et al. 2007) abundances are assumed for the LIC,
then to within the uncertainties the LIC dust has the relative com-
position of Fe:Mg:Si:O = 1:1:1:4, as is consistent with amor-
phous olivines MgFeSiO4. Fe and Si are dominantly singly ion-
ized, while Mg has a significant fraction (∼ 15%) that is twice
ionized. The gas-phase abundances of these refractory elements
are highly subsolar, even after ionization corrections are made,
indicating that these elements are substantially depleted onto in-
terstellar dust grains. In contrast to C, however, the silicate dust
in the LIC that carries the missing Mg, Si, and Fe has experi-
enced far less destruction than the carbonaceous grains.
Ca ii, Na i: Weak lines of the trace ionization species Ca ii
and Na i are common diagnostics of ionization and abundance
for interstellar clouds, including the partially ionized LIC; Na i
is also frequently used as a diagnostic of the H column density.
We note that our models show that the ratios N(Ca ii)/N(Na i),
N(Na i)/N(H), and N(Na i)/N(H i) vary by 30%, 77%, and 93%,
respectively, between the best models (Models 26–30, 42). As
trace ionization species, the densities of Na i and Ca ii are highly
sensitive to volume density, n(Na0), n(Ca+) ∝ n(H)ne. We there-
fore conclude that Na i and Ca ii are imprecise diagnostics of
ionization levels, H density, and abundances in warm partially
ionized clouds.
5.4. Gas-to-Dust Mass Ratio
Because the abundances are automatically corrected for unob-
served H+, we use the model results to infer the total mass of the
interstellar dust, providing that the gas and dust in the LIC form
a coupled and closed system that evolves together as the cloud
moves through the LSR. The LIC LSR velocity is 16–21 pc/Myr,
so that a LIC origin related to the Loop I or Scorpius-Centaurus
superbubble would require that the LIC gas and dust remained
a closed system over timescales of 4–5 Myr (Frisch & Slavin
2006; Frisch 1981). Gas-to-dust mass ratios calculated from the
best models (26 and 28) using the missing-mass argument2 are
in the range RG/D= 149 − 217, depending on solar abundances.
The detailed information about RG/D for different assumptions
and the different models is listed in table 9.
For comparison, RG/D determined from comparisons of in
situ observations of interstellar dust inside of the solar system,
compared to the gas densities of these models, yield RG/D = 115–
125 (Table 9, Landgraf et al. 2000; Altobelli et al. 2004). The in
situ RG/D is an upper limit, since the smallest interstellar dust
grains (radii ≤ 0.15 µm) with large charge-to-mass ratios (and
thus small Larmor radii) are excluded from the heliosphere by
the interstellar magnetic field which is draped over the helio-
sphere.
For all the models, the RG/D determined from comparing
in situ dust measurements with the CHISM gas mass flux is
2 This argument assumes that the ISM reference abundances, in this
case solar abundances, represent the sum of the atoms in the gas plus
the dust (Frisch et al. 1999).
Table 9. Gas-to-Dust Mass Ratios from Models and In Situ
Observations
Modela
Source 14 26 27 28 29 30 42
GS98 137 149 196 149 197 150 138
Lodders 158 174 238 174 239 175 160
Grevesse 194 217 321 217 323 218 196
In Situ 115 116 123 116 125 116 107
a The source of the comparison solar abundances is listed in column
1 (Table 8. The in situ dust flux is from Landgraf et al. (2000),
corrected downwards by 20% as recommended by Altobelli et al.
(2004) to account for side-wall impacts.
Table 10. Major Heat Sources in LIC Gasa
Sourceb Fraction of Heating
H i 0.657
He i 0.248
dust 0.055
He ii 0.016
cosmic rays 0.010
a Results for model 26. Other models are qualitatively the same,
though there are some quantitative variations.
b For lines with ion names, the source here denotes the ion that is
photoionized. Dust heating comes from photoelectric ejection by
photons of the background FUV radiation field. Cosmic ray heating
comes from electron impact ionization of the gas and direct heating
of the electrons in the LIC plasma by the cosmic ray electrons.
lower than that determined by assuming solar abundances and
using the gas phase abundances we determine to find RG/D.
This suggests that somehow the dust flowing into the helio-
sphere is concentrated relative to the gas, compared to the over-
all LIC sightline towards ǫ CMa. The lower solar abundances
of Grevesse et al. (2007) result in lower required depletions, and
produces stronger disagreements with RG/D determined from in
situ data. We do not understand this result, which we have found
previously (Frisch et al. 1999). Since RG/D is sensitive to the
mass of Fe in the dust grains (Frisch & Slavin 2003), we sug-
gest that this difference may indicate inhomogeneous mixing of
the gas and silicate dust over the ∼ 0.64 pc extent of the LIC.
5.5. Heating and Cooling Rates
The heating and cooling rates for Model 26 are listed in Tables
10 and 11. The primary heat sources are photoelectrons from
the ionization of H0 and He0, with dust and cosmic ray heating
contributing less than 7% of the heating. The dominant source
of cooling is the [C ii] 157.6 µm fine-structure line, making up
43% of the total. This is more than twice the contribution of
any other coolant. Nearly all the cooling is due to optical and
infrared forbidden lines with many lines contributing at the ∼
1% level. H recombination, free-free emission and dust, through
the capture of electrons onto grain surfaces, also contribute at
about a 2% level. The importance of C ii as both a constraint
on the C abundance in our models as well as a major coolant
means that any model that aims to reduce the abundance of C
to a solar level faces severe difficulties. The models with LIC
temperatures in the THe0 = 6 300 ± 340 K range indicated by
Slavin and Frisch: Boundary Conditions of the Heliosphere 13
Table 11. Major Coolants in LIC Gasa
Ion/Line Fraction of Cooling
[C ii] 157.6 µm 0.428
[S ii] 6731 Å 0.145
Fe ii (total) 0.074
[Si ii] 34.8 µm 0.065
[Ne ii] 12.8 µm 0.035
[O i] 63.2 µm 0.028
H recomb. 0.024
dust 0.024
[Ne iii] 15.6 µm 0.020
[N ii] 6584 Å 0.018
net free-free 0.018
[O i] 6300 Å 0.017
[O ii] 3727 Å 0.011
[Ar ii] 6.98 µm 0.011
a Results for model 26. Other models show similiar results.
the in situ He0 data all require supersolar abundances of C. The
total heating/cooling rate for the LIC at the Sun for this model is
3.55 × 10−26 ergs cm−3 s−1.
5.6. Radiation Field
Recently it has been proposed that a significant portion
of the SXRB can be attributed to charge-transfer (a.k.a.
charge exchange) between the solar wind ions (e.g., O+7 and
O+8) and interstellar neutrals (Cravens 2000; Snowden et al.
2004; Wargelin et al. 2004; Smith et al. 2005; Koutroumpa et al.
2006). While it seems at present that some fraction of the low
energy X-rays are from this mechanism, it is unclear how large
that fraction is. We note that basing the properties of the local
hot plasma in the galactic plane on SXRB emission at energies
E > 0.3 keV is problematical. (Bellm & Vaillancourt 2005) have
compared the Wisconsin B and Be band data with the ROSAT
R12 data, and concluded that the observed anticorrelation be-
tween R12 and N(H i) indicates that more than 34% of the SXRB
generated in the Galactic disk must come from the Local Bubble.
They also concluded that a heavily depleted plasma with log
T ∼ 5.8 is consistent both with the McCammon et al. (2002);
Sanders et al. (2001) X-ray spectral data, and the upper limits
set on the EUV emission by CHIPS (Hurwitz et al. 2004). When
the Robertson & Cravens (2003) models of SXRB production
by charge-transfer with the solar wind are considered, then only
half of the SXRB in the plane is required to arise from a hot local
plasma. We also note that the atomic physics for the calculation
of the low energy part of the emission is still quite uncertain
(V. Kharchenko, private communication). At this point we take
the simple approach of ignoring the charge-transfer emission,
though we plan to consider its possible impact in future work by
reducing the assumed SXRB flux from hot gas. As noted previ-
ously, a lower SXRB flux due to a lower pressure in the hot gas
does not necessarily have any impact on our calculated flux from
the evaporative cloud boundary.
5.7. LIC Pressure
The strength of the interstellar magnetic field in the LIC is un-
known, though modeling of its effects on the heliosphere sets
some constraints. Our best models (26 and 28) presented here
have a thermal pressure of ∼ 2100 cm−3 K for the LIC. If the
thermal and magnetic pressures are equal, this indicates a mag-
netic field strength B ∼ 2.7 µG, in agreement with field strengths
for these models. As noted is §2.3, the main effect of the field
strength in the models is to regulate the pressure in the evapo-
rative cloud boundary, which in turn affects the flux of diffuse
EUV radiation incident on the cloud. The amount of EUV flux
helps determine the temperature in the cloud, which is how the
observational constraints fix the magnetic field strength in the
context of our modeling. Thus we do not explicitly fix the mag-
netic field strength with the goal of achieving equipartition and
indeed some of our successful models have lower or higher field
strengths. It is probably coincidental that the field strength re-
quired to match the in situ He0 temperature for our best models
is also close to the equipartition field strength, but it is at least
encouraging that this field strength is consistent with our pho-
toionization models. We note that if thermal, cosmic ray, and
magnetic pressures are approximately equal the LIC has a pres-
sure of ∼ 6300 cm−3 K.
5.8. Comparisons with other LISM Sightlines
There have been a number of efforts to understand the
LISM ionization and abundances (Frisch et al. 1986;
Cheng & Bruhweiler 1990; Lallement & Bertin 1992;
Vallerga 1996; Lallement & Ferlet 1997; Holberg et al. 1999;
Kimura et al. 2003). The studies that attempt to derive gas
phase elemental abundances find a range of results, generally
fairly consistent with ours. A point of particular interest is the
abundance of carbon that is surprisingly overabundant in our
results. As an example, Kimura et al. (2003) find (based on four
sightlines and excluding the ǫ CMa and β CMa sightlines), a
subsolar C abundance in contradiction with our results. Results
for thirteen sightlines from Redfield & Linsky (2004) with
velocity components consistent with the LIC velocity vector
show that N(C ii)/N(O i) > 1 for 8 of them, especially those
at lower column density indicating a solar or supersolar C
abundance. For our best models N(C ii)/N(O i) ≈ 2. Our series
of studies are unique in that we model the radiation field incident
on the cloud, include radiative transfer effects, and calculate
the thermal equilibrium within the cloud. The ionization varies
through the cloud as does the temperature and density (slightly)
and we compare observations within the heliosphere with the
physical conditions at that point in the cloud rather than basing
the model on line-of-sight averages.
Our present results indicate that n(N ii)/n(N i)∼ 0.32 − 0.50
at the solar location, with N becoming more ionized as the
sightline approaches the cloud surface. The column density ra-
tio is thus higher, ranging from 0.38 − 0.62. Observed values
of N(N ii)/N(N i) toward other nearby stars are 0.58+0.56
−0.77 toward
Capella (Wood et al. 2002), 1.29±0.23 toward HZ43 (Kruk et al.
2002), 1.91+0.87
−0.69 towards WD1634-573 (Lehner et al. 2003), and
1.13 ± 0.24 towards η UMa (Frisch et al. in preparation). The
total H i column density towards each of these stars is greater
than the N(H i)∼ 4 × 1017 cm−2 found for the best models here.
The nearest of these stars, Capella, has an ionization compara-
ble to that of the LIC. The two high-latitude stars HZ43 and η
UMa appear to sample low opacity regions where the ionization
is larger than at the Sun, as does the WD1634-573 sightline that
appears to cross the nearby diffuse H ii region seen towards λ
Sco (York 1983). As we have noted the ǫ CMa line of sight is
special because that star is the dominant source of stellar EUV
photons for the LIC. Thus for sightlines at a large angle from
the ǫ CMa sightline, if the H i column between points along the
sightline and ǫ CMa is small the apparently high column points
14 Slavin and Frisch: Boundary Conditions of the Heliosphere
are subject to a strong EUV field. Such geometry dependent ion-
ization effects can be important for non-spherical clouds subject
to a strongly spatially variable ionizing radiation source.
The variation in the fractional ionization of the CLIC gas
has a direct impact on our understanding of the distribution and
physical properties of low column density clouds for several rea-
sons. (1) Abundances of elements with FIP < 13.6 eV must al-
ways be calculated with respect to N(H i)+ N(H ii) for very low
column density clouds. (2) Cloud geometry affects the opacity
of observed sightlines so that the opacity to ionizing radiation
is not directly traced by the observed value of N(H i). For lines
of sight other than that towards ǫ CMa, this could require more
complex radiative transfer models in which the difference be-
tween the line of sight toward the star and that toward one of the
primary sources of ionizing flux, ǫ CMa, at each point is taken
into account.
6. Conclusions
There are many uncertainties regarding the detailed properties of
the ionizing interstellar radiation field incident on the LIC. The
data we have on the LIC, both from absorption line studies and
in situ measurements by spacecraft in the heliosphere, provide us
with strong constraints on the ionization and composition of the
LIC and particularly the CHISM. By exploring a range of models
for the ISRF we find that while a fairly broad range of radiation
fields can produce photoionization consistent with the data, other
outputs from the models fall within a relatively narrow range of
values. Our results for the models explored in this paper in which
we require our models to be consistent with the LIC component
of the absorption lines observed towards ǫ CMa include:
1. For a range of assumptions regarding the H i column density
of the LIC, N(H i) = (3.0−4.5)×1017 cm−2, and temperature
of the hot gas of the Local Bubble, log Th = 5.9, 6.0 and
6.1, we are able to find model parameters that allow a match
of the model results with best observed quantities, n(He0),
T (He0) and N(Mg ii)/N(Mg i). For these models we assume
that the cloud is evaporating because of thermal conduction
between the hot Local Bubble gas and the warm LIC gas and
include the emission from the cloud boundary.
2. For the best models in terms of fits to data, the required input
parameters are: initial (i.e. at the outer edge of the cloud)
total H density, n(H) ≈ 0.21−0.23 cm−3; and cloud magnetic
field, B0 ≤ 3.8 µG.
3. If we assume that the magnetic field configuration reduces
thermal conductivity at the boundary enough to prevent
evaporation and ignore any radiation from the cloud bound-
ary, we find that for most cases the radiation field does not
cause sufficient heating to maintain the LIC at the temper-
ature observed, T = 6, 300 ± 340 K. One set of parameter
choices, though, yields a successful model. These parame-
ters are N(H i) = 4.5 × 1017 cm−2 and log Th = 6.1.
4. Despite the wide range of possible input parameters, the out-
put values for quantities important for shaping the helio-
sphere are confined to a fairly small range: n(H0) = 0.19 −
0.20 cm−3, and ne = 0.05 − 0.08 cm
5. A H filtration factor of fH = 0.55 ± 0.03 yields good agree-
ment between the radiative transfer model predictions for
n(H i) in the CHISM, and n(H i) at the termination shock as
found from observations of PUIs, the H i Lyα glow, and the
solar wind slow-down in the outer heliosphere. This filtra-
tion value is also consistent with heliosphere models of the
ionization of interstellar H atoms traversing the heliosheath
regions.
6. Elements with ionization potentials 13.6− 25 eV, e.g. H, He,
N, O, Ne, and Ar, are partially ionized with ionization frac-
tions of ∼ 0.2 − 0.7.
7. By requiring that the models match the column densities de-
rived from absorption line data we are able to determine the
necessary elemental abundances for several elements. We
find that the abundances of N and O may be somewhat sub-
solar. Sulfur is roughly solar, and C is substantially super-
solar. Mg, Si and Fe are all sub-solar by factors of 3 − 15.
The depletions of Fe, Mg, Si and O in the LIC are consis-
tent with a dust population consisting of amorphous silicate
olivines MgFeSiO4, though other compositions for the dust
are possible as well. We conclude that any carbonaceous dust
in the LIC must have been destroyed, while silicate dust has
persisted. Except for the gas-to-dust mass ratio, these results
are in better agreement with the lower solar abundances of
Grevesse et al. (2007). However we note that the O and Ne
abundances of Lodders (2003) are in better agreement with
other astronomical data such as the X-ray absorption edges.
8. The gas-to-dust mass ratio derived from missing mass in the
gas-phase for our best models depends strongly on the as-
sumed reference abundance set and range from 137 − 323.
Our two best models, nos. 26 and 28, give a range of
149−217. For these same models RG/D = 115−125 based on
the observed flux of dust into the heliosphere. The discrep-
ancy of these values is minimized, in fact leading to con-
sistency within the errors, if one assumes an abundance set
such as that of GS98 which has large abundances of the met-
als. The GS98 abundances lead to substantial O depletion,
however, which is not easily explained and conflict with the
S abundances found for models 26 and 28.
9. These models also show that the densities of the trace ion-
ization species Ca ii and Na i are extremely sensitive to den-
sity and ionization. Therefore the ratios N(Ca ii)/N(Na i),
N(Na i)/N(H i), and N(Na i)/N(H) are, by themselves, inade-
quate diagnostics of warm low density diffuse gas.
Acknowledgements. We would like to thank George Gloeckler for sharing data
with us prior to publication, and Alan Cummings for pointing out that the
ACR isotopic data indicate that the LIC abundances are solar. We also thank
the International Space Science Institute in Bern, Switzerland for hosting the
working group on “Interstellar Hydrogen in the Heliosphere.” This research was
supported by NASA Solar and Heliospheric Program grants NNG05GD36G
and NNG06GE33G to the University of Chicago, and by the NASA grant
NNG05EC85C to SWRI.
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List of Objects
‘ǫ CMa’ on page 2
‘Sirius’ on page 3
	Introduction
	Photoionization Model Constraints and Assumptions 
	Astronomical Constraints – The LIC towards  CMa  
	In situ Constraints – He0, Pickup Ions, and Anomalous Cosmic Rays 
	Interstellar Radiation Field at the Cloud Surface 
	Photoionization Models
	Model Results 
	Discussion
	Heliosphere Boundary Conditions
	Hydrogen Filtration Factor
	Gas-Phase Abundances 
	Gas-to-Dust Mass Ratio 
	Heating and Cooling Rates 
	Radiation Field
	LIC Pressure
	Comparisons with other LISM Sightlines
	Conclusions

  The boundary conditions of the heliosphere are set by the ionization, density
and composition of inflowing interstellar matter. Constraining the properties
of the Local Interstellar Cloud (LIC) at the heliosphere requires radiative
transfer ionization models. We model the background interstellar radiation
field using observed stellar FUV and EUV emission and the diffuse soft X-ray
background. We also model the emission from the boundary between the LIC and
the hot Local Bubble (LB) plasma, assuming that the cloud is evaporating
because of thermal conduction. We create a grid of models covering a plausible
range of LIC and LB properties, and use the modeled radiation field as input to
radiative transfer/thermal equilibrium calculations using the Cloudy code. Data
from in situ observations of He^O, pickup ions and anomalous cosmic rays in the
heliosphere, and absorption line measurements towards epsilon CMa were used to
constrain the input parameters. A restricted range of assumed LIC HI column
densities and LB plasma temperatures produce models that match all the
observational constraints. The relative weakness of the constraints on N(HI)
and T_h contrast with the narrow limits predicted for the H^O and electron
density in the LIC at the Sun, n(H^0) = 0.19 - 0.20 cm^-3, and n(e) = 0.07 +/-
0.01 cm^-3. Derived abundances are mostly typical for low density gas, with
sub-solar Mg, Si and Fe, possibly subsolar O and N, and S about solar; however
C is supersolar. The interstellar gas at the Sun is warm, low density, and
partially ionized, with n(H) = 0.23 - 0.27 cm^-3, T = 6300 K, X(H^+) ~ 0.2, and
X(He^+) ~ 0.4. These results appear to be robust since acceptable models are
found for substantially different input radiation fields. Our results favor low
values for the reference solar abundances for the LIC composition.

Introduction
The solar wind evacuates a cavity in the interstellar medium
(ISM) known as the heliosphere, from which interstellar ions
are excluded. In contrast, neutral interstellar gas flows through
the heliosphere until destroyed by charge-transfer with the solar
wind and photoionization. These neutrals form the parent popu-
lation of pickup ions (PUI) and anomalous cosmic rays (ACR)
observed inside of the heliosphere. The properties of the sur-
rounding interstellar medium set the boundary conditions of the
heliosphere and determine its configuration and evolution. An
ionization gradient is expected in the cloud feeding ISM into the
heliosphere because of the hardness of the interstellar radiation
field and the low opacity of the ISM (Cheng & Bruhweiler 1990;
Vallerga 1996; Slavin & Frisch 2002, hereafter SF02). Because
of this ionization gradient, the densities of partially ionized
species in the local interstellar cloud (LIC) will differ from the
values in the circumheliosphere interstellar medium (CHISM)
that forms the boundary conditions of the heliosphere. Hence
we have undertaken a series of studies to determine the bound-
ary conditions of the heliosphere based on both astronomical and
heliospheric data. In turn our results provide tighter constraints
on the heliosphere models used to calculate the filtration factors
Send offprint requests to: J. Slavin
for neutrals that then permit comparisons between ISM inside
and outside of the heliosphere.
The distribution and velocity of interstellar H0 inside
of the heliosphere were first determined over 30 years ago
from the florescence of solar Lyα radiation from these
atoms (Thomas & Krassa 1971; Bertaux & Blamont 1971;
Adams & Frisch 1977). Similar observations of solar 584Å flo-
rescence from interstellar He0 showed that H/He ∼ 6 for in-
terstellar gas inside of the heliosphere, in contrast to the cos-
mic value H/He = 10 (Ajello 1978; Weller & Meier 1981).
More recent measurements of n(H0) compared to n(He0) in-
side of the heliosphere find a similar ratio of H/He ∼ 6 − 7
(Richardson et al. 2004; Gloeckler & Geiss 2004; Witte 2004;
Möbius et al. 2004). This difference can be attributed to two ef-
fects: the loss of 40–60% of interstellar H0 due to charge-transfer
with protons in the heliosheath region, a process denoted “filtra-
tion” (Ripken & Fahr 1983), and the hardness of the interstellar
radiation field at the Sun that ionizes more He than H (§4).
The Copernicus satellite first showed that the local inter-
stellar cloud (LIC) surrounding the Sun is low density, ∼ 0.1
atoms cm−3, partially ionized (n(H+) ∼ n(H0), York 1974;
McClintock et al. 1975), and warm (temperature < 104 K, e.g.
McClintock et al. 1978). Copernicus, FUSE and HST data have
shown that the cluster of local interstellar clouds (CLIC, low
density clouds within ∼ 30 pc), has low column densities, N(H i)
< 1018.7, and N ionization levels of > 30% (e.g. Lehner et al.
http://arxiv.org/abs/0704.0657v2
2 Slavin and Frisch: Boundary Conditions of the Heliosphere
2003; Wood et al. 2005), indicating partially ionized gas because
H and N ionization are coupled by charge-transfer. The low col-
umn densities of the LIC itself, N(H i) < 1018 cm−2, indicate
it is partially opaque to H ionizing radiation but not to He ion-
izing radiation. Cloud opacities of unity are reached for N(H i)
∼ 1017.2 cm−2 for photons close to the ionization threshold of
hydrogen (13.6 eV), and N(H i) ∼ 1017.7 cm−2 for photons at the
He0 ionization edge (24.6 eV). The result is that the LIC is par-
tially ionized with a significant ionization gradient between the
edge and center. Because of this radiative transfer effects are im-
portant and need to be modeled carefully in order to determine
the boundary conditions of the heliosphere.
The LIC belongs to a flow of low density ISM embedded
in the very low density and apparently hot (T ∼ 106 K) Local
Bubble (Frisch 1981; Frisch & York 1986; McCammon et al.
1983; Snowden et al. 1990). The bulk motion of the CLIC
through the local standard of rest1 corresponds to a velocity of
−17.0 to −19.4 km s−1 from the direction ℓ ∼ 331◦, b ∼ −5◦
(Frisch & Slavin 2006). This upwind direction is near the center
of the Loop I superbubble and the center of the “ring” shadow
that has been attributed to the merging of Loop I and the Local
Bubble (Frisch & York 1986; Frisch 2007; Egger & Aschenbach
1995). Individual cloudlets with distinct velocities are identified
in this flow (Lallement et al. 1986; Frisch et al. 2002). The ve-
locity of the cloud feeding gas into the heliosphere has been de-
termined by the velocity of interstellar He0 in the heliosphere
measured by the GAS detector on Ulysses, −26.3 km s−1 (Witte
2004).
Curiously, absorption lines at the LIC velocity are not ob-
served in the nearest interstellar gas in the upwind hemisphere,
such as towards the closest star α Cen or towards 36 Oph lo-
cated ∼ 5 pc beyond the heliosphere nose (Adams & Frisch
1977; Landsman et al. 1984; Linsky & Wood 1996; Wood et al.
2000a,b). This lack of an absorption component at the LIC ve-
locity in the closest stars in the upstream direction indicates that
the Sun is near the edge of the LIC, so the CHISM may vary
over short distances (and hence timescales).
We are able to test for possible past variations by compar-
ing the first interplanetary H0 Lyα glow spectrum obtained by
Copernicus in 1975 with Hubble Space Telescope observations
of the Lyα spectra obtained during the mid-1990’s solar min-
imum conditions. The observed H0 velocity and intensity has
not varied to within uncertainties over the twenty-year period
separating these two sets of observations, so that the CHISM
velocity field is relatively smooth over spatial scales of ∼ 120
AU in the downwind direction (Frisch & Slavin 2005). The 1975
Copernicus data were acquired in the direction corresponding
to ecliptic longitudes of λ = 264.3◦, β = +15.0◦, or ∼ 13.3◦
from the most recent upwind direction derived from SOHO H i
Lyα data (Quémerais et al. 2006b,a, Q06). The Copernicus look
direction was just outside of the “groove” expected in the Lyα
glow in the ecliptic during solar minimum. The groove is caused
by increased charge-transfer in the solar wind current sheet,
which has a small tilt during minimum conditions (Bzowski
2003). The velocity of the Lyα profile observed by Copernicus
corresponds to −24.8±2.6 km s−1, after correction to the SOHO
upwind direction. Since Q06 measured H0 upwind velocities
during the solar minimum years of 1996 and 1997 of −25.7±0.2
km s−1 and −25.3 ± 0.2 km s−1, which is consistent with the
Copernicus results, we must arrive at the conclusion that the flow
of interstellar H0 into the heliosphere was relatively constant be-
1 Heliocentric motions are converted to the local standard of rest,
LSR, using the Standard solar apex motion.
tween the years of 1975 and 1997, so that any observations of
variations in the interplanetary Lyα glow properties must be due
to solar activity properties alone. The thermal broadening of the
Copernicus spectrum corresponded to a temperature of ∼ 5400
K, however measurement uncertainties allowed temperatures of
up to 20, 000 K.
In this paper we present new photoionization models of the
LIC and show they reproduce both the densities of the ISM at the
heliosphere and column densities in the LIC component towards
the star ǫ CMa. In earlier papers, photoionization models of both
the “LIC” and “Blue Cloud” components observed towards ǫ
CMa were used to constrain the models (SF02, Frisch & Slavin
2003). SF02 grouped the properties of the LIC and Blue Cloud,
both of which are with 2.7 pc of the Sun because they are also
observed towards Sirius, ∼ 12◦ from the ǫ CMa sightline. The
LIC velocity and density are sampled by observations of inter-
stellar He i inside of the heliosphere (−26.3 km s−1, Witte 2004),
and Gry & Jenkins (2001) show that the properties of the LIC
and Blue Cloud differ somewhat. The present study therefore fo-
cuses on obtaining the best model of heliosphere boundary con-
ditions by using only data on the LIC inside of the heliosphere,
and the LIC component towards ǫ CMa. The present study also
benefits from new atomic rates for the critical Mg ii→Mg i di-
electronic recombination coefficient, improved cooling rates in
the radiative transfer code Cloudy, recent values for the pickup
ion densities at the termination shock, and recent values for solar
abundances.
The most truly unique quality of the LIC is that we are inside
of it and therefore have the ability to sample the cloud directly
via in situ observations carried out by a variety of spacecraft
within the Solar System. Of all the available measurements of
LIC gas flowing into the Solar System, the observations of the
density and temperature of neutral He are apparently the most
robust. Helium, unlike hydrogen, undergoes little ionization or
heating in traversing the heliosheath regions, no deflection due
to radiation pressure, and is destroyed by photoionization and
electron-impact ionization within ∼ 1 AU of the Sun, so we ex-
pect that the density and temperature of He0 derived from the
observations in the Solar System are truly representative of the
values in the LIC (Möbius et al. 2004). In this paper we put a
special emphasis on matching these He i data by determining
model parameters that yield close agreement with the n(He0) and
T (He0) data simultaneously.
2. Photoionization Model Constraints and
Assumptions
The primary data constraints on our photoionization mod-
els are the LIC component column densities towards ǫ CMa,
(Gry & Jenkins 2001, hereafter GJ01), in situ observations
of He0 (Witte 2004; Möbius et al. 2004), pickup ions (PUI,
Gloeckler & Fisk 2007), and anomalous cosmic rays (ACR,
Cummings et al. 2002). The astronomical and in situ observa-
tional constraints are summarized in Table 1.
2.1. Astronomical Constraints – The LIC towards ǫ CMa
The data toward ǫ CMa of GJ01 show four separate veloc-
ity components detected in several different ions including C ii,
Si iii, Si ii, and Mg ii. One of these velocity components, with
a heliocentric velocity of ∼ 17 km s−1, is identified as the LIC.
Another is identified with a second local cloud, the “Blue Cloud”
(BC) at ∼ 10 km s−1. In our previous study of LIC ioniza-
Slavin and Frisch: Boundary Conditions of the Heliosphere 3
Table 1. Observational Constraints
Observed Observeda Notesb
Quantity Value
N(C ii) (cm−2) 1.4 − 2.1 × 1014 1, S
N(C ii∗) (cm−2) 1.3 ± 0.2 × 1012 1
N(C iv) (cm−2) 1.2 ± 0.3 × 1012 1
N(N i) (cm−2) 1.70 ± 0.05 × 1013 1
N(O i) (cm−2) 1.4+0.5
−0.2 × 10
14 1, S
N(Mg i) (cm−2) 7 ± 2 × 109 1
N(Mg ii) (cm−2) 3.1 ± 0.1 × 1012 1
N(Si ii) (cm−2) 4.52 ± 0.2 × 1012 1
N(Si iii) (cm−2) 2.3 ± 0.2 × 1012 1
N(S ii) (cm−2) 8.6 ± 2.1 × 1012 1
N(Fe ii) (cm−2) 1.35 ± 0.05 × 1012 1
N(H i)/N(He i) 14 ± 0.4c 2
T (K) 6300 ± 340 4
n(He0) (cm−3) 0.015 ± 0.003 4, f = 1d
n(N0)e (cm−3) 5.47 ± 1.37 × 10−6 3, f = 0.68 − 0.95d
n(O0)e (cm−3) 4.82 ± 0.53 × 10−5 3, f = 0.64 − 0.99d
n(Ne0)e (cm−3) 5.82 ± 1.16 × 10−6 3, f = 0.84 − 0.95d
n(Ar0)e (cm−3) 1.63 ± 0.73 × 10−7 3, f = 0.53 − 0.95d
a N(C ii∗), N(N i), N(O i), N(Mg ii), N(Si ii), N(S ii) and N(Fe ii) are
used to constrain the input abundances of the models.
b The first number indicates the reference (below), and “S” indi-
cates that the column density is based on a saturated line. Filtration
factors ( f , §2.2) are listed for neutrals that have been observed as
pickup ions.
c The uncertainty given is only that due to uncertainties listed in
Dupuis et al. (1995) for the observed H i and He i column densities
with the implicit assumption that the ratio is the same on all lines of
sight. Given the substantial intrinsic variation in this ratio, however,
the quoted uncertainty must be regarded as a lower limit to the true
uncertainty.
d We assume in this paper that for He fHe = 1, and f is not allowed
to exceed 1. Heliosphere models predict the range fHe = 0.92 − 1
for He and fH = 0.50 − 0.74 for H (see filtration factors in
Cummings et al. 2002; Müller & Zank 2004a; Müller et al. 2007;
Izmodenov et al. 2004).
e Note that the pickup ion ratios are for values at the termination
shock. N0, O0, Ne0, and Ar0 densities need to be corrected for fil-
tration in the heliosheath regions (2.2).
References: (1) Gry & Jenkins (2001) Note that the values shown are
for the LIC component towards ǫ CMa.; (2) Dupuis et al. (1995); (3)
Gloeckler & Fisk (2007); (4) Witte (2004).
tion (SF02) we noted that since the BC is close to the LIC,
and both are detected towards Sirius at 2.7 pc (Lallement et al.
1994; Hébrard et al. 1999), perhaps actually abutting the LIC,
we should treat the two as a single cloud for this line of sight.
Counter arguments to this line of reasoning include the fact that
the BC apparently has different properties than the LIC, though
whether it is colder or hotter is unclear (see Hébrard et al. 1999,
GJ01). For this reason and because we wish to find the ioniza-
tion models that best predict interstellar neutral densities inside
and outside of the heliosphere, we assume in this paper that the
LIC and BC are truly separate clouds and select only the LIC
components towards ǫ CMa to constrain the models.
In the context of these models, the best astronomical con-
straints on the neutral ISM component are N i, the saturated O i
line, and to some extent Mg i (though the line is weak). The elec-
tron density can be deduced from the ratio Mg ii/Mg i, which is
determined by photoionization and both dielectronic and radia-
tive recombination, and the excitation of the C ii fine-structure
lines, C ii/C ii∗. However, the heavy saturation of the C ii 1335
Å line in the ISM limits the accuracy of the determination of
N(C ii), so in this paper we have de-emphasized C ii/C ii∗ as an
ionization diagnostic. For a discussion of the use of C ii/C ii∗ and
other observations in diagnosing the C abundance and C/S ratio
see Slavin & Frisch (2006). Elements with first ionization po-
tentials (FIP) < 13.6 eV (e.g. Mg, Si, S, and Fe) are generally
almost entirely singly ionized in the LIC and thus the column
densities of these ions are close to the total column densities for
the elements.
2.2. In situ Constraints – He0, Pickup Ions, and Anomalous
Cosmic Rays
Neutral atoms in the LIC penetrate the outer heliosphere regions,
and become ionized primarily by charge-transfer with the so-
lar wind ions, photoionization, and electron impact ionization
(Rucinski et al. 1996). The composition of this neutral popula-
tion reflects the partially ionized state of the LIC, rather than
indicating a pure FIP effect. Thus the observed abundances of
neutrals representing high FIP elements, such as He, Ne, and Ar,
as well as H, N, and O, do not reflect their elemental abundances
directly. As a result, these neutrals provide an interesting and
unique constraint on the photoionization models. Once ionized,
these interstellar wind particles form a population of ions with
a distinct velocity distribution that are “picked up” by the solar
wind and convected outwards, where they are measured by var-
ious spacecraft (Möbius et al. 2004; Gloeckler & Geiss 2004).
These pickup ions (PUI) are accelerated in the heliosheath re-
gion and form a population of cosmic rays with an anomalous
composition reflective of their origin as interstellar neutrals in
a partially ionized gas (Cummings et al. 2002). In situ observa-
tions of these byproducts of the ISM interaction with the helio-
sphere, H, He, N, O, Ar, and Ne, provide a unique opportunity
to constrain theoretical models of an interstellar cloud using the
combination of sightline-integrated data, and data from a “sin-
gle” spatial location, the heliosphere.
We adopt the Ulysses He measurements as the best set of
constraints on the ISM inside of the heliosphere. The Ulysses
satellite provides direct measurements of interstellar He0 at
high ecliptic latitudes throughout the solar cycle (the GAS de-
tector, Witte 2004) and also measurements of the He pickup
ion component (the SWICS detector Gloeckler & Geiss 2004;
Gloeckler & Geiss 2007). Although interstellar He0 close to the
Sun is detected through the resonant scattering of solar 584 Å
radiation, geocoronal contamination of the interstellar signal is
present so we prefer the Ulysses data (Möbius et al. 2004). We
adopt the Ulysses GAS and SWICS results, n(He0) = 0.0151 ±
0.0015 cm−3, T (He0) = 6, 300 ± 340 K.
Data on the density of neutral N, O, Ne, and Ar in the sur-
rounding ISM are provided by PUI and ACR data. The densities
of interstellar N0, O0, Ne0, and Ar0 at the termination shock are
listed in Table 1. These densities must be corrected by the fil-
tration factors, which correspond to the ratios of the densities
at the termination shock to those in the LIC. Filtration occurs
when neutral interstellar atoms are removed from the inflow by
charge-transfer with interstellar protons as the atom crosses the
heliosheath regions. Filtration values are listed in Table 1, based
on values in Cummings et al. (2002); Müller & Zank (2004b);
Izmodenov et al. (2004). Filtration values larger than 1 are not
considered, although some models suggest possible net creation
of O0 through charge-transfer between O+ and H0 in the he-
liosheath regions (Müller & Zank 2004a). We adopt fHe = 1 for
He. Our models must be compared to the interstellar densities
4 Slavin and Frisch: Boundary Conditions of the Heliosphere
Fig. 1. The modeled interstellar radiation field at the Sun (model
26) is shown as a function of wavelength (bottom X-axis) and
energy (top X-axis). The black histogram is the modeled hot
gas (i.e. Local Bubble) spectrum while the gray histogram is
the cloud boundary contribution. The other line is the stellar
EUV/FUV background. The list of elements at the top of the
plot identifies the ionization potentials for neutrals and ions of
interest. The energy/wavelength at which an optical depth of 1 is
reached for several different H i column densities is shown along
the bottom of the plot. Observed flux levels of the soft X-ray dif-
fuse background in the Wisconsin Be and B bands are plotted as
lines (Bloch et al. 1986; McCammon et al. 1983).
obtained by correcting densities at the termination shock by fil-
tration factors.
2.3. Interstellar Radiation Field at the Cloud Surface
The spectrum and flux of the cosmic radiation field control
the ionization of the very local warm partially ionized medium
(WPIM). The local interstellar radiation field (ISRF) that ionizes
the LIC and other nearby cloudlets is determined by the location
of the Sun in the interior of a hole in the neutral interstellar gas
and dust referred to as the Local Bubble. The clustering tendency
of hot O and B stars, and attenuation of radiation by interstellar
dust and gas, yield the well known spatial variation of the in-
tensity and spectrum of the ISRF. We ignore possible temporal
variations of the radiation field (e.g. Parravano et al. 2003), and
model the ISRF throughout the LIC based on the observations
of the present-day radiation field.
The radiation field we use in our models is based on obser-
vations of the ISRF at the Sun, supplemented by theoretical cal-
culations of the spectra in the EUV and soft X-rays where lack
of sensitivity and/or spectral resolution require the use of mod-
els to create a realistic spectrum. The directly observed radiation
field includes the far ultraviolet (FUV) field created primarily
by B stars, the extreme ultraviolet (EUV) field from two B stars
(ǫ CMa and β CMa) and hot nearby white-dwarf stars, and the
diffuse soft X-ray background (SXRB). We show the radiation
field at the cloud surface in Fig. 1. Because the interstellar opac-
ity for radiation with E > 13.6 eV is vastly greater than for
E < 13.6 eV, the EUV part of the ISRF originates in nearby
regions with N(H i) <∼ 10
18 cm−2 while the FUV comes from a
much larger volume.
We use the EUV field of Vallerga (1998), which is based
on data collected by the Extreme Ultraviolet Explorer (EUVE)
satellite. The EUVE spectrometers were sensitive over the wave-
length range of 504 – 730 Å and showed that the stellar part of
the EUV background is dominated by ǫ CMa and β CMa with
substantial contributions from nearby hot white dwarfs at shorter
wavelengths. Vallerga extrapolated those measurements to the
H0 ionization edge at 912 Å using a total interstellar H0 density
towards ǫ CMa of N(H i) = 9 × 1017 cm−2. This value for N(H i)
appears somewhat high based on observations of Gry & Jenkins
(2001) which, though dependent on assumptions for gas phase
abundances, indicate a value for N(H i) of ∼ 7× 1017 cm−2. This
uncertainty in the total N(H i) affects only the extrapolated por-
tion of the spectrum in our models since the other portion of the
spectrum is derived by de-absorbing the observed spectrum by
the value of N(H i) assumed just for the LIC. For the results pre-
sented here we have assumed that the total N(H i) towards ǫ CMa
is 7×1017 cm−2. Assuming a larger value would increase the flux
in the extrapolated region, though our calculations indicate that
the overall affect on our results is only at the ∼ 2% level at most.
The FUV field is important because it sets the ionization rate
of Mg0, which has a first ionization potential of 7.65 eV (1621
Å). The radiation field shortwards of 1600 Å is heavily domi-
nated by O and B stars in Gould’s Belt, particularly those oc-
cupying the unattenuated regions of the third and fourth galac-
tic quadrants. A pronounced spatial asymmetry in the 1565 Å
radiation field has been observed by the TD-1 satellite S2/68
telescope survey of the interstellar radiation field, and we use
those data and the extrapolation down to 912 Å from the 1564 Å
measurements as calculated by Gondhalekar et al. (1980). The
asymmetries in the TD-1 1565 Å radiation field are reproduced
by diffuse interstellar radiation field models (Henry 2002).
The diffuse soft X-ray background (SXRB) has been ob-
served over the entire sky at relatively low spatial and spectral
resolution by ROSAT (Snowden et al. 1997) and proportional
counters flown on sounding rockets by the Wisconsin group
(e.g., McCammon et al. 1983). The broadband count rates in
the low energy bands, particularly the B and C bands (130–
188 eV and 160–284 eV respectively) have been modeled as
coming from an optically thin, hot plasma at a temperature of
∼ 106 K that occupies the low density cavity extending to ∼ 50–
200 pc from the Sun in all directions (Snowden et al. 1990).
Refinements to this picture have been required by ROSAT data
showing absorption by relatively distant clouds (e.g. MBM12,
Snowden et al. 1993). Snowden et al. (1998) propose a picture
in which the emission is divided between a LB component (un-
absorbed except for the LIC) and a distant absorbed component,
mainly in the Galactic halo. More recently there has been grow-
ing evidence that some, possibly large, fraction of the SXRB is
generated within the heliosphere from charge exchange between
solar wind ions and neutral atoms (SWCX). We discuss this fur-
ther in §5.6.
We model the spectrum measured by the broad-band soft X-
ray observations by assuming that the SXR background consists
of a local (unabsorbed) component and a distant (halo) com-
ponent absorbed by an H i column density of 1019 cm−2. The
emission measure or intrinsic intensity of the local and distant
components are assumed to be equal. The spectrum is calculated
using the Raymond & Smith (1977, updated) plasma emission
code assuming a hot, optically thin plasma in collisional ion-
ization equilibrium. We explore temperatures for the hot gas of
log Th = 5.9, 6.0 and 6.1. The total flux, scaled by the emission
measure, is fixed so that the B band flux matches the all-sky av-
erage from McCammon et al. (1983).
Slavin and Frisch: Boundary Conditions of the Heliosphere 5
The boundary region between the warm LIC and the adja-
cent Local Bubble plasma may be another significant source of
EUV radiation and we include this flux in our models 1–30. We
model this transition region as a conductive interface between
the LIC and Local Bubble plasma in the same way as described
in Slavin & Frisch (2002). The cloud is assumed to be steadily
evaporating into the surrounding hot gas. The partially ionized
gas of the LIC is heated and ionized as it flows into the Local
Bubble. The ionization falls out of equilibrium, with low ion-
ization stages persisting into the hot gas. The non-equilibrium
ionization is followed and the emission in the boundary is calcu-
lated again using the Raymond & Smith (1977) code. Ions in the
outflow are typically excited several times before being ionized
and the boundary region radiates strongly in the 13.6 − 54.4 eV
band. The contribution of the interface emission to the total B
band flux is taken into account in the calculation of the emission
measure for the hot gas of the Local Bubble so that the B band
flux still matches the all-sky average.
We note that no attempt is made to make this model con-
sistent with the size of the local cavity, which is proposed to
contain the hot gas in the standard model for the SXRB (e.g.,
Snowden et al. 1998). The pressure in the hot gas is not adjusted
to fit such models. Rather the total pressure in the hot gas for an
evaporating cloud model is dictated by the assumed density, tem-
perature and magnetic field in the cloud. In fact the pressures in
our models come out far too low for the standard model to pro-
duce the SXRB within the confines of the Local Cavity as de-
duced, e.g., from Na i observations (Lallement et al. 2003). This
in turn means that if the thermal pressure in the Local Bubble
turns out to be much lower than was assumed in those models
because a substantial fraction of the SXRB comes from SWCX
then the emission from the cloud boundary would be unaffected.
An example of the profiles of the hydrodynamic variables
for two different models is shown in Fig. 2. The magnetic field
strength in these calculations is assumed to be proportional to
the density at every point in the outflow. The treatment here is
the same as in Slavin (1989) which contains a more thorough
discussion of the issues involved in this sort of calculation. The
effect of the field on the conductivity is parametrized in a simple
way by a constant reduction factor of 0.5. The importance of the
magnetic field for our calculations lies in the way it affects the
thermal pressure in the layer. Since the density drops sharply in
the outflow and |B| ∼ n, any magnetic pressure (∼ B2) drops
even more sharply. The total pressure is roughly constant in the
boundary, so the thermal pressure necessarily rises to make up
for the decreasing magnetic pressure. Since all our models have
nearly the same thermal pressure in the cloud, the primary effect
of the magnetic field is to help determine the thermal pressure
in the interface and thus radiative flux from the boundary. Since
the total soft X-ray flux is fixed by requiring a match with the
Wisconsin B band all-sky average count rate (McCammon et al.
1983), a larger assumed magnetic field increases only the EUV
flux which is not constrained by the B-band data. The affect on
the cloud of a larger EUV flux is to increase its temperature and
ionization.
A secondary effect of the magnetic field can be seen in the
temperature profiles in Figure 2. In evaporating clouds in the
ISM, if the temperature gradient is large enough and the thermal
pressure is low enough, the conduction becomes “saturated”,
which means that the heat flux expected from the gas temper-
ature and temperature gradient exceeds the flux that can be car-
ried by the electrons (Cowie & McKee 1977). Saturation leads
to a steepening of the temperature gradient and a relative slow-
ing of the mass loss rate. In the two cases shown in Figure 2,
Fig. 2. Profiles of hydrodynamic variables in two different cloud
boundary calculations. The solid lines are for model 6 which has
nH = 0.273 cm
−3, log Th = 6.0, B0 = 2 µG and NHI = 4.5 × 10
cm−2, while the dashed lines are for model 8, which differs from
model 6 only in the strength of the magnetic field, B0 = 5 µG.
Note that in the upper right panel, the plot of thermal pressure,
the radial scale is much smaller in order to show the variation in
thermal pressure. The higher magnetic pressure inside the cloud
for model 8 leads to the higher external thermal pressure for that
case. The temperature profile differs in the two cases because the
degree of heat flux saturation is reduced for the higher thermal
pressure of model 8, which in turn leads to a shallower tempera-
ture gradient.
the lower magnetic field case (B0 = 2 µG) is moderately satu-
rated (in terms of Cowie & McKee’s parameter, σ0 = 3) while
the other case (B0 = 5 µG), because of the higher magnetic pres-
sure, is less saturated.
3. Photoionization Models
The photoionization models of the LIC are developed follow-
ing the same underlying procedure as in SF02, but selecting
only the LIC absorption component towards ǫ CMa for com-
parison. Improvements include using updated values for in situ
ISM observations and using a recent version of the Cloudy
radiative transfer/thermal equilibrium code (version 06.02.09a,
Ferland et al. 1998). We run Cloudy with the assumption of a
plane-parallel cloud geometry and format our calculated pho-
toionizing spectrum to be used as input. The selected options
include utilizing recent calculations for the dielectronic recom-
bination rates for Mg+ → Mg0 (e.g. Altun et al. 2006, and the
commands “set dielectronic recombination Badnell” and “set ra-
diative recombination Badnell”) , the assumption of constant
pressure, and the inclusion of interstellar dust grains at 50%
abundance compared to a standard ISM value. As we discuss
below, the only role that dust plays is net heating of the gas since
there is far too little column for extinction to be important (ex-
pected E(B − V) ∼ 10−4.2). The fraction of the heating provided
by dust is ∼ 4% of the total heating, while dust provides ∼ 2% of
the cooling (mainly by capture of electrons onto grain surfaces).
A cosmic ray ionization rate at the default background level of
2.5×1017 s−1 (for H ionization) is included. The LIC is assumed
to be in ionization and thermal equilibrium, and Cloudy calcu-
lates the detailed transfer of radiation, including absorption and
6 Slavin and Frisch: Boundary Conditions of the Heliosphere
Table 2. Model Input Parameter Values
Input Parameter
nH log Th B0 NHI
Model No. (cm−3) (K) (µG) (1017 cm−2)
1 0.273 5.9 2.0 3.0
2 0.273 5.9 2.0 4.5
3 0.273 5.9 5.0 3.0
4 0.273 5.9 5.0 4.5
5 0.273 6.0 2.0 3.0
6 0.273 6.0 2.0 4.5
7 0.273 6.0 5.0 3.0
8 0.273 6.0 5.0 4.5
9 0.273 6.1 2.0 3.0
10 0.273 6.1 2.0 4.5
11 0.273 6.1 5.0 3.0
12 0.273 6.1 5.0 4.5
13 0.218 5.9 2.0 3.0
14 0.218 5.9 2.0 4.5
15 0.218 5.9 5.0 3.0
16 0.218 5.9 5.0 4.5
17 0.218 6.0 2.0 3.0
18 0.218 6.0 2.0 4.5
19 0.218 6.0 5.0 3.0
20 0.218 6.0 5.0 4.5
21 0.218 6.1 2.0 3.0
22 0.218 6.1 2.0 4.5
23 0.218 6.1 5.0 3.0
24 0.218 6.1 5.0 4.5
25 0.226 5.9 4.7 3.0
26 0.213 5.9 2.5 4.0
27 0.226 6.0 3.8 3.0
28 0.216 6.0 2.1 4.0
29 0.232 6.1 3.4 3.0
30 0.223 6.1 0.05 4.0
42 0.218 6.1 – 4.5
scattering of the radiation incident on the cloud surface, as well
as the diffuse continuum and emission lines generated within the
cloud.
The procedure for creating a model begins with generating
the incident radiation field at the cloud surface (§2.3). The ra-
diative transfer model is then run, and the output predictions of
the model are compared to observations of interstellar absorp-
tion lines in the LIC towards ǫ CMa (N(C ii∗), N(N i), N(O i),
N(Mg ii), N(S ii), N(Si ii), N(Fe ii)) and in situ observations of
n(He0) by spacecraft inside of the solar system. The abundances
of C, N, O, Mg, Si, S and Fe are then adjusted to be consistent
with the observed column densities. With these new abundances,
the Cloudy run is repeated and this process is continued until no
adjustment of the abundances is needed. Because the abundances
do have an impact on the emission from the cloud boundary, the
cloud evaporation model is then re-run with the new abundances
as well to re-generate the input ionizing spectrum. The iterative
process of generating the spectrum and doing the Cloudy pho-
toionization runs generally requires only a couple runs of the
cloud evaporation program and a few runs of Cloudy.
4. Model Results
To investigate the dependence of the results on the input pa-
rameters we calculate a grid of 24 models. We explore total H
density, nH = 0.273, 0.218; Local Bubble hot gas temperature,
log Th = 5.9, 6.0, 6.1; magnetic field strength, B0 = 2, 5 µG; and
H i column density, NH I = 3 × 10
17, 4.5 × 1017 cm−2. The val-
Fig. 3. Model results for the He0 density and temperature in the
ISM just outside the heliosphere. The squares, circles, and trian-
gles are for models that are part of the initial grid of 24 models,
while the stars are for models 25 − 30 for which the magnetic
field, B, and the total H density, nH, were varied to match the ob-
served n(He0) and T . For the grid models, the empty symbols are
for models with N(H i)= 3 × 1017 cm−2, while the filled symbol
models have N(H i)= 4.5 × 1017 cm−2. As the legend shows, the
color (black vs. gray) indicates the magnetic field strength and
the symbol shape indicates the temperature assumed for the hot
gas of the Local Bubble. For identical kinds of points, the one to
the left is for a model with n(H0) = 0.218 cm−3 and the one to
the right has n(H0) = 0.273 cm−3. The ellipse is the error range
around the observed values for n(He0) and T .
ues for T and n(He i) at the solar location, the endpoint of the
calculations, are shown in Fig. 3 for this set of models. We then
explore another six models in which we do the calculations over
a grid in log Th and NH I but vary the values of nH and B0 in or-
der to match the observed T and n(He i). We employed a multiple
linear regression to assist in narrowing down the search region
for the values of nH and B0 needed to match the observations.
Since the dependencies of the results on the parameters really
are quite non-linear, this procedure could not work to predict
exactly correct values for the required parameters, but was use-
ful for getting close to the correct values. Based on the results
for the initial grid of models, we use log Th = 5.9, 6.0, 6.1 and
NH I = 3 × 10
17, 4 × 1017 cm−2 for this smaller grid, models
25 − 30. We chose to use 4 × 1017 cm−2 rather than 4.5 × 1017
cm−2 because the higher column density models, for the most
part, produced temperatures that were too high. As can be seen
from Fig. 3, all of these models (25–30), plotted as stars, are con-
sistent with the observed T and n(He i), indicated by the ellipse
in the figure. Table 2 gives the input parameters for each model.
Model predictions for the ǫ CMa sightline integrated through the
LIC are presented in Table 3. Model predictions for the CHISM
(i.e. at the solar location) are shown in Table 4.
In SF02 we tested models with no emission from the cloud
boundary. This amounts to assuming that the boundary is a sharp
transition from the hot gas of the Local Bubble to the warm gas
of the LIC. We have again explored such models using the LIC
data as constraints in the same way as for the models discussed
above with a conductive interface. When there is no evaporative
boundary, our models do not depend on the magnetic field in the
cloud since in that case the ionizing flux consists only of dif-
fuse emission from the hot gas of the Local Bubble and EUV
Slavin and Frisch: Boundary Conditions of the Heliosphere 7
Table 3. Model Column Density Results
Modela log N(Htot) log N(Ar i) log N(Ar ii) log N(Si iii)
N(Mg II)
N(Mg I)
N(C II)
N(C II∗)
N(H I)
N(He I)
Obs.b – – – 12.40 443+197
−110 93 − 430
c 12 − 16
1 17.58 11.48 11.76 8.895 706.3 213.0 11.36
2 17.78 11.67 11.95 9.641 325.3 234.1 11.40
3 17.65 11.33 11.84 9.844 246.1 182.1 11.44
4 17.82 11.55 12.00 10.12 136.5 198.0 11.80
5 17.58 11.49 11.75 8.961 717.8 230.0 11.62
6 17.78 11.67 11.94 9.711 286.7 244.9 11.62
7 17.64 11.34 11.81 9.909 207.4 194.8 12.47
8 17.82 11.56 11.97 10.17 119.7 208.2 12.66
9 17.59 11.46 11.75 9.289 553.0 239.5 12.27
10 17.78 11.66 11.93 9.861 210.3 248.1 12.14
11 17.64 11.33 11.78 9.993 171.2 201.7 13.44
12 17.82 11.54 11.95 10.23 104.3 210.6 13.52
13 17.60 11.44 11.78 9.100 768.9 255.1 11.52
14 17.79 11.64 11.96 9.738 336.4 274.4 11.47
15 17.67 11.30 11.85 9.944 251.2 215.9 11.65
16 17.84 11.51 12.01 10.21 140.6 232.1 12.01
17 17.58 11.47 11.76 8.926 840.1 262.5 11.65
18 17.79 11.65 11.95 9.792 308.9 286.3 11.64
19 17.66 11.30 11.82 10.02 208.5 229.2 12.76
20 17.84 11.52 11.98 10.26 123.5 242.1 12.95
21 17.59 11.43 11.76 9.318 633.1 280.8 12.41
22 17.79 11.63 11.94 9.926 224.9 288.4 12.25
23 17.66 11.29 11.79 10.10 175.0 235.5 13.81
24 17.84 11.50 11.96 10.31 110.2 245.5 13.85
25 17.66 11.32 11.84 9.887 271.3 213.6 11.71
26 17.74 11.56 11.91 9.676 383.9 270.1 11.70
27 17.63 11.36 11.79 9.751 331.1 242.0 12.51
28 17.73 11.59 11.90 9.625 411.6 284.5 11.79
29 17.62 11.38 11.77 9.720 329.3 251.6 13.01
30 17.72 11.60 11.88 9.642 386.6 295.1 12.08
42 17.77 11.70 11.92 9.555 482.9 317.9 11.51
a The best models, consistent with all observational data (see §4), are indicated by bold face.
b Observational results from Gry & Jenkins (2001) (see table 1). The values listed for N(H i)/N(He i) are the range of values observed excluding
Feige 24 which is one of the most distant stars observed by Dupuis et al. (1995) and has unusually large N(H i) and ratio values.
c The upper limit on N(C ii) is not well determined observationally because of the saturation of the line. Gry & Jenkins (2001) define it by
assuming a solar C/S abundance ratio and using the observed S ii column density. We find (see Slavin & Frisch 2006) that the abundance of C
required to match the N(C ii∗) observations is supersolar, with C/S∼ 36 − 44, which results in a much higher upper limit on N(C ii).
emission from nearby hot stars and the spectrum is not related
to the properties of the cloud. For these models our model grid
consists of total H density, nH = 0.273, 0.218, Local Bubble hot
gas temperature, log Th = 5.9, 6.0, 6.1, and H i column density,
NH I = 3×10
17, 4.5×1017 cm−2, for a total of twelve models that
we label as models 31–42. Of these models, however, only two
resulted in ionizing fluxes sufficient to heat the cloud to a tem-
perature ∼ 6000 K at the same time as matching the constraints
on the ion column densities. These models were the ones with
log Th = 6.1 and NH I = 4.5 × 10
17 cm−2 (models 36 and 42).
For the other cases, either at the surface or deeper into the cloud,
there are insufficient photons to provide the heating to balance
the cooling and the cloud temperature drops sharply to < 1000
K. The model with nH = 0.218 (model 42) is consistent with the
observed value of n(He0) and with the column density data as
well.
From these 42 models we have selected those that provide
acceptable results for the observational constraints, according to
prioritized requirements. The first requirement is that the model
predict the density and temperature of He i observed inside of
the solar system. Models 14 (marginally), 15 and 25–30 and 42
predict a He density and temperature consistent with the ob-
served values within the reported errors. They also predict the
PUI Ne densities, for an assumed Ne/H=123 ppm. Models 26
and 28 successfully match the PUI data for Ne/H as low as
∼ 100 ppm. These models are also required to match the ob-
served Mg ii/Mg i ratio in the LIC towards ǫ CMa. Models 14,
27, and 29 marginally fit this criterion, while 26, 28, 30, and 42
successfully fit this criterion. Note that the new models now pro-
vide acceptable predictions for the CHISM temperature, which
was not the case for the best models in SF02. These models are
also consistent with the observed C ii/C ii∗ ratios in the LIC com-
ponent towards ǫ CMa though this constraint is weak because of
the large uncertainties in N(C ii). Based on these comparisons,
and given the uncertainties in both data and models, Models 14,
26-30, and 42 are plausible models, but Models 26 and 28 appear
to best match the observational constraints.
Based on the constraints and assumptions presented in the
previous section, we select models 14, 26–30 and 42 as the best
models for the LIC ionization, with models 26 and 28 favored
by the PUI Ne data provided that Ne/H > 100 ppm. We believe
that these seven models then give a realistic range for the uncer-
tainties in the boundary conditions of the heliosphere, providing
that the underlying assumptions implicit in the Cloudy code, e.g.
8 Slavin and Frisch: Boundary Conditions of the Heliosphere
Table 4. Model Results for Solar Location
Modela X(H) X(He) n(H0) n(He0) n(N0) n(O0) n(Ne0) n(Ar0) ne np T
Obs.b 0.015 5.5 × 10−6 4.8 × 10−5 5.8 × 10−6 1.6 × 10−7 6300
1 0.176 0.299 0.318 0.0269 1.84 × 10−5 1.48 × 10−4 1.39 × 10−5 3.47 × 10−7 0.0800 0.0678 4310
2 0.196 0.352 0.251 0.0201 9.63 × 10−6 7.71 × 10−5 8.51 × 10−6 2.69 × 10−7 0.0724 0.0611 6450
3 0.286 0.404 0.230 0.0191 1.34 × 10−5 1.07 × 10−4 7.81 × 10−6 1.82 × 10−7 0.106 0.0922 6280
4 0.259 0.428 0.229 0.0175 8.86 × 10−6 6.95 × 10−5 6.45 × 10−6 1.92 × 10−7 0.0937 0.0799 7560
5 0.174 0.310 0.300 0.0249 1.72 × 10−5 1.39 × 10−4 1.13 × 10−5 3.30 × 10−7 0.0750 0.0631 4610
6 0.197 0.363 0.242 0.0190 9.13 × 10−6 7.44 × 10−5 7.08 × 10−6 2.61 × 10−7 0.0707 0.0593 6770
7 0.278 0.441 0.225 0.0173 1.33 × 10−5 1.04 × 10−4 5.75 × 10−6 1.78 × 10−7 0.101 0.0866 6670
8 0.257 0.459 0.223 0.0161 8.65 × 10−6 6.79 × 10−5 4.92 × 10−6 1.89 × 10−7 0.0918 0.0773 7860
9 0.193 0.357 0.265 0.0209 1.53 × 10−5 1.23 × 10−4 7.52 × 10−6 2.71 × 10−7 0.0761 0.0634 5410
10 0.203 0.392 0.235 0.0177 9.06 × 10−6 7.24 × 10−5 5.52 × 10−6 2.43 × 10−7 0.0723 0.0600 7230
11 0.278 0.474 0.220 0.0158 1.29 × 10−5 1.02 × 10−4 4.42 × 10−6 1.69 × 10−7 0.0999 0.0847 7020
12 0.262 0.490 0.219 0.0148 8.41 × 10−6 6.66 × 10−5 3.83 × 10−6 1.78 × 10−7 0.0928 0.0776 8160
13 0.201 0.333 0.230 0.0191 1.34 × 10−5 1.08 × 10−4 8.94 × 10−6 2.32 × 10−7 0.0681 0.0580 4720
14 0.215 0.376 0.193 0.0152 7.29 × 10−6 5.95 × 10−5 5.99 × 10−6 1.94 × 10−7 0.0625 0.0528 6650
15 0.310 0.436 0.176 0.0143 1.02 × 10−5 8.18 × 10−5 5.35 × 10−6 1.28 × 10−7 0.0905 0.0789 6470
16 0.284 0.461 0.175 0.0131 6.76 × 10−6 5.36 × 10−5 4.40 × 10−6 1.35 × 10−7 0.0812 0.0695 7750
17 0.178 0.315 0.255 0.0211 1.47 × 10−5 1.19 × 10−4 9.51 × 10−6 2.75 × 10−7 0.0656 0.0553 4360
18 0.214 0.383 0.188 0.0146 7.16 × 10−6 5.81 × 10−5 5.07 × 10−6 1.91 × 10−7 0.0610 0.0513 6900
19 0.302 0.472 0.173 0.0129 1.01 × 10−5 8.03 × 10−5 3.93 × 10−6 1.26 × 10−7 0.0872 0.0748 6860
20 0.282 0.491 0.172 0.0120 6.61 × 10−6 5.26 × 10−5 3.37 × 10−6 1.33 × 10−7 0.0802 0.0677 8050
21 0.204 0.374 0.211 0.0164 1.20 × 10−5 9.85 × 10−5 5.54 × 10−6 2.04 × 10−7 0.0648 0.0541 5390
22 0.221 0.414 0.184 0.0136 6.96 × 10−6 5.69 × 10−5 3.90 × 10−6 1.78 × 10−7 0.0628 0.0523 7350
23 0.305 0.506 0.168 0.0117 9.91 × 10−6 7.82 × 10−5 2.97 × 10−6 1.18 × 10−7 0.0868 0.0737 7220
24 0.286 0.520 0.169 0.0111 6.57 × 10−6 5.16 × 10−5 2.60 × 10−6 1.25 × 10−7 0.0808 0.0676 8310
25 0.297 0.427 0.187 0.0151 1.09 × 10−5 8.67 × 10−5 5.75 × 10−6 1.41 × 10−7 0.0907 0.0789 6360
26 0.224 0.385 0.192 0.0151 8.32 × 10−6 6.66 × 10−5 5.96 × 10−6 1.83 × 10−7 0.0653 0.0554 6320
27 0.258 0.426 0.195 0.0149 1.13 × 10−5 8.97 × 10−5 5.03 × 10−6 1.63 × 10−7 0.0796 0.0677 6240
28 0.212 0.376 0.194 0.0152 8.24 × 10−6 6.73 × 10−5 5.49 × 10−6 1.95 × 10−7 0.0622 0.0523 6350
29 0.242 0.429 0.202 0.0150 1.17 × 10−5 9.30 × 10−5 4.53 × 10−6 1.74 × 10−7 0.0769 0.0646 6300
30 0.203 0.379 0.197 0.0151 8.51 × 10−6 6.81 × 10−5 4.78 × 10−6 2.01 × 10−7 0.0605 0.0502 6500
42 0.189 0.355 0.186 0.0145 6.91 × 10−6 5.71 × 10−5 4.60 × 10−6 2.04 × 10−7 0.0522 0.0433 6590
a The best models (see §4) are indicated by bold face.
b Observational results from Gloeckler & Geiss (2004), Gloeckler (2005, private communication) and Witte et al. (1996) (see table 1 for uncer-
tainties).
photoionization equilibrium, are correct. The predictions of the
best models provide excellent matches to the observational con-
straints. Based on these models, we find the boundary conditions
of the heliosphere to be describable as n(H0) = 0.19−0.20 cm−3,
ne = 0.05−0.08 cm
−3, and X(H) ≡ H+/(H0+H+) = 0.19−0.26,
X(He) ≡ He+/(He0 + He+) = 0.36 − 0.43. For these models, we
find abundances of O/H = 295 − 437 ppm, C/H = 589 − 813
ppm, and N/H = 40.7 − 64.6 ppm (Table 7). The total LIC den-
sity is n(H)0 = 0.213 − 0.232 cm
−3, while the strength of the
interstellar magnetic in the cloud varies between 0 and 3.8 µG.
The Ne PUI data further favor densities of n(H0) ≈ 0.19 cm−3
and ne = 0.06 − 0.07 cm
In this analysis we have assumed negligible filtration for He
in the heliosheath regions. Modeling of the He filtration factor
however allows values as small as fHe = 0.92, which yields
n(He i)= 0.0164 cm−3 for the CHISM (Table 1). The predictions
of Model 21 agree with this value for n(He i), as well as with
the ratios Mg ii/Mg i and C ii/C ii∗ towards ǫ CMa and the pickup
ion Ne and Ar data (Table 3). The predicted cloud temperature
is low by ∼ 1000 K. The density and ionization for Model 21 are
n(H0) = 0.21 cm−3 and ne= 0.06 cm
−3. We therefore conclude
that our best models listed above are robust in the sense that they
predict consistent values for the n(H0) to within 5%, and electron
densities to within 25%.
The radiation field incident on the LIC for Model 26 is shown
in Fig. 1 and the spectral characteristics of the field for each
model are listed in Table 5. The wavelengths regions λ ≤ 912 Å
and λ ∼ 1500 Å are of primary importance for the photoioniza-
tion of the cloud, the former because it determines H0 and He0
ionization, and the latter because it determines Mg0 ionization.
The ionization parameter is defined as U ≡ Φ/n(H)c, where
Φ is the H ionizing photon flux, n(H) is the total (neutral + ion-
ized) hydrogen density at the cloud surface and c is the speed
of light. The total ionizing photon fluxes at the cloud surface
(photons cm−2 s−1) for the three bands 13.6–24.6, 24.6–54.4, and
54.4–100 eV, are given by ΦH, ΦHe0 , and ΦHe+ , respectively. The
ratio of the total number of H0 and He0 ionizing photons in the
incident radiation field is given by Q(He0)/Q(H0). The quantity
〈E〉 (eV) is the mean energy of an ionizing photon, equal to the
integrated energy flux from 13.6 to 100 eV divided by the inte-
grated photon flux over the same energy range.
In Figure 3 we show n(He0) and temperature of the CHISM
for our model calculations. In Figure 4 we show N ii/N i vs.
Mg ii/Mg i, illustrating an anti-correlation of the ratios caused
by the fact that Mg ii/Mg i decreases with electron density while
N ii/N i indicates the ionization level in the cloud. The ionization
of the CHISM is listed in Table 6 for Model 26, where com-
monly observed elements are listed. The abundances of He, Ne,
Slavin and Frisch: Boundary Conditions of the Heliosphere 9
Table 5. Characteristics of the Model Radiation Field
Modela U φH φHe0 φHe+ Q(He
0)/Q(H0) 〈E〉
photons cm−2 s−1 photons cm−2 s−1 photons cm−2 s−1 eV
1 2.0 × 10−6 4.6 × 103 7.5 × 103 2.8 × 103 0.46 74.6
2 2.0 × 10−6 5.3 × 103 7.3 × 103 2.7 × 103 0.44 72.4
3 3.1 × 10−6 9.0 × 103 1.3 × 104 2.7 × 103 0.49 57.7
4 3.0 × 10−6 8.6 × 103 1.2 × 104 2.6 × 103 0.49 58.6
5 2.0 × 10−6 4.0 × 103 7.0 × 103 3.8 × 103 0.43 79.0
6 2.1 × 10−6 4.9 × 103 6.9 × 103 3.8 × 103 0.41 76.2
7 3.2 × 10−6 7.4 × 103 1.4 × 104 3.8 × 103 0.53 61.3
8 3.1 × 10−6 7.4 × 103 1.3 × 104 3.7 × 103 0.52 61.5
9 2.2 × 10−6 3.8 × 103 7.4 × 103 5.6 × 103 0.40 80.0
10 2.3 × 10−6 4.8 × 103 7.2 × 103 5.6 × 103 0.38 77.3
11 3.5 × 10−6 6.6 × 103 1.5 × 104 5.6 × 103 0.53 63.4
12 3.4 × 10−6 6.9 × 103 1.5 × 104 5.5 × 103 0.52 63.2
13 2.3 × 10−6 4.3 × 103 7.0 × 103 2.8 × 103 0.46 76.9
14 2.4 × 10−6 5.1 × 103 6.8 × 103 2.7 × 103 0.43 74.3
15 3.7 × 10−6 8.5 × 103 1.2 × 104 2.7 × 103 0.49 58.8
16 3.6 × 10−6 8.2 × 103 1.2 × 104 2.6 × 103 0.49 59.5
17 2.3 × 10−6 3.7 × 103 6.4 × 103 3.8 × 103 0.42 81.8
18 2.4 × 10−6 4.7 × 103 6.2 × 103 3.8 × 103 0.39 78.4
19 3.9 × 10−6 7.1 × 103 1.4 × 104 3.8 × 103 0.53 62.2
20 3.8 × 10−6 7.2 × 103 1.3 × 104 3.7 × 103 0.52 62.2
21 2.6 × 10−6 3.6 × 103 6.8 × 103 5.6 × 103 0.39 82.0
22 2.7 × 10−6 4.6 × 103 6.6 × 103 5.6 × 103 0.36 78.9
23 4.2 × 10−6 6.3 × 103 1.5 × 104 5.6 × 103 0.52 64.4
24 4.2 × 10−6 6.7 × 103 1.4 × 104 5.5 × 103 0.51 64.1
25 3.5 × 10−6 7.9 × 103 1.2 × 104 2.7 × 103 0.49 60.3
26 2.5 × 10−6 5.0 × 103 7.5 × 103 2.7 × 103 0.45 73.2
27 3.1 × 10−6 5.4 × 103 1.0 × 104 3.8 × 103 0.50 68.9
28 2.4 × 10−6 4.3 × 103 6.4 × 103 3.8 × 103 0.40 79.5
29 3.0 × 10−6 4.6 × 103 9.7 × 103 5.6 × 103 0.45 73.6
30 2.4 × 10−6 3.8 × 103 5.5 × 103 5.6 × 103 0.33 84.6
42 2.2 × 10−6 3.6 × 103 3.6 × 103 5.6 × 103 0.25 91.1
a The best models (see §4) are indicated by bold face.
Fig. 4. Model results for N(N ii)/N(N i) versus Mg ii/Mg i. The
symbols have the same meaning as in Figure 3. In this case the
models with higher n(H0) lie below and slightly to the left of
those with lower density. N(N ii)/N(N i) is an indicator of cloud
ionization fraction while Mg ii/Mg i goes as 1/ne. The dotted line
is the observed value for Mg ii/Mg i and the dashed lines indi-
cate the 1 − σ error range for the value. We see that models that
match the observed ratio all correspond to relatively low ioniza-
tion, X(H) ∼ 0.20 − 0.27 in the CHISM.
Na, Al, P, Ar, and Ca were assumed, based on solar abundances,
and were not adjusted in the modeling process. The abundances
of C, N, O, Mg, Si, S and Fe were adjusted for each model to
match observed column densities towards ǫ CMa (see §2). The
elemental abundances that have been assumed, with the excep-
tion of that for He, are not expected to have any significant im-
pact on the model results.
5. Discussion
5.1. Heliosphere Boundary Conditions
As discussed above, the best models of those we calculated
are determined by the match to the CHISM He0 density and
temperature found by the in situ Ulysses measurements (§2.2),
combined with the matching the LIC component column den-
sity ratios Mg ii/Mg i and C ii/C ii∗. These models span a fairly
large range in the model parameters: nH = 0.213 − 0.232
cm−3, log Th = 5.9 − 6.1 K, B0 = 0.05 − 3.8 µG, and N(H i)
= 3.0 × 1017 − 4.5 × 1017 cm−2. Despite this, the predicted val-
ues for neutral H density and electron density in the CHISM lie
within a remarkably small range: n(H0) = 0.19 − 0.20 cm−3,
ne = 0.05 − 0.08 cm
−3, for models that include the conductive
boundary. For the one model without evaporation that is consis-
tent with the data we find n(H0) = 0.186 cm−3, ne = 0.052 cm
Including the PUI Ne data as a constraint narrows the density re-
sults to n(H0) ≈ 0.19 cm−3 and ne = 0.06− 0.07 cm
−3. For these
10 Slavin and Frisch: Boundary Conditions of the Heliosphere
Table 6. Model 26 Results for Ionization Fractionsa
Element PPM I II III IV
H 106 0.776 0.224 – –
He 105 0.611 0.385 4.36(-3) –
C 661 2.68(-4) 0.975 0.0244 0.000
N 46.8 0.720 0.280 8.52(-5) 0.000
O 331 0.814 0.186 4.71(-5) 0.000
Ne 123 0.196 0.652 0.152 2.79(-6)
Na 2.04 1.47(-3) 0.843 0.155 6.34(-6)
Mg 6.61 1.98(-3) 0.850 0.148 0.000
Al 0.0794 5.37(-5) 0.976 0.0118 0.0123
Si 8.13 4.21(-5) 0.999 8.02(-4) 3.10(-5)
P 0.219 1.35(-4) 0.977 0.0232 9.29(-5)
S 15.8 6.47(-5) 0.971 0.0288 1.95(-6)
Ar 2.82 0.263 0.500 0.238 2.83(-6)
Ca 4.07(-4) 9.21(-6) 0.0155 0.984 1.87(-4)
Fe 2.51 7.01(-5) 0.975 0.0245 5.75(-6)
a Numbers less than 10−3 are written as x(y) where y is the exponent
and x is the mantissa (or significand).
densities to stray out of this range would appear to require sig-
nificant errors in the underlying comparison data, e.g. n(He0) in
the CHISM, or substantial non-equilibrium ionization effects in
the LIC. The variation in the interstellar radiation field between
the different models that match the data give us some degree of
confidence that these densities are not highly sensitive to the de-
tails of the radiation field. The range ne = 0.05 − 0.08 cm
corresponds to an electron plasma frequency of 2.0–2.5 kHz,
which is the frequency of the mysterious weak radio emission
detected beyond the termination shock in the outer heliosphere
(Gurnett & Kurth 2005; Mitchell et al. 2004).
5.2. Hydrogen Filtration Factor
Tracers of H0 inside of the termination shock, after filtration, in-
clude the H i Lyα backscattered radiation, H pickup ions, and
the slowdown of the solar wind at distances beyond 5 AU from
mass-loading by H PUIs. The range of n(H0) found above to
best fit the combined heliospheric n(He0) and LIC data towards
ǫ CMa, n(H0) = 0.19− 0.20 cm−3, represents the density of neu-
tral interstellar H atoms outside of the heliosphere, and removed
from heliospheric influences. The hydrogen filtration factor, fH,
can be obtained from comparisons between these models and in-
terstellar H0 densities at the termination shock as inferred from
in situ observations of interstellar H inside of the heliosphere.
The accompanying papers in this special section provide es-
timates of the interstellar H0 density at the termination shock.
The solar wind slows down due to massloading by interstel-
lar H, yielding n(H0)= 0.09 ± 0.01 cm−3 at the termination
shock (Richardson et al. 2007). The density of H pickup ions ob-
served by Ulysses is inferred at the termination shock, yielding
n(H0)= 0.11 ± 0.01 cm−3; models of H atoms traversing the he-
liosheath regions then yield for the CHISM n(H0)= 0.20 ± 0.02
cm−3 and np= 0.04±0.02 cm
−3, or ne∼ 0.05 cm
−3 (Bzowski et al.
2007). The radial variation in the response of the interplanetary
Lyα 1215 Å backscattered radiation to the solar rotational mod-
ulation of the Lyα “beam” that excites the florescence yields
n(H0)∼ 0.085−0.095 cm−3, depending on the heliosphere model
(Pryor et al. 2007). From these n(H0) values at the termination
shock, we estimate that 43%–58% of the H-atoms successfully
traverse the heliosheath region, or fH ∼ 0.43−0.58. Müller et al.
(2007) evaluate filtration using five different plasma-neutral
Table 7. Elemental Gas Phase Abundances (ppm)
Element
Model No. C N O Mg Si S Fe
14 589 40.7 295 5.89 7.24 14.1 2.24
21 955 60.3 447 9.77 11.5 22.9 3.55
25 631 66.1 437 7.76 10.0 19.5 3.09
26 661 46.8 331 6.61 8.13 15.8 2.51
27 759 64.6 437 8.71 10.7 20.9 3.31
28 708 45.7 331 7.08 8.32 16.6 2.57
29 813 64.6 437 9.33 11.0 21.9 3.39
30 741 46.8 331 7.41 8.51 17.0 2.63
42 724 39.8 295 6.76 7.76 15.1 2.34
models, and find a range of fH = 0.52 − 0.74. A hydrogen filtra-
tion of fH = 0.55 ± 0.03 is consistent with both in situ data and
radiative transfer models.
5.3. Gas-Phase Abundances
The LIC photoionization models are forced to match the ob-
served set of column densities (Tables 1 and 3). The gas-phase
abundances of most elements are treated as free parameters that
can be varied in order to match observed column densities, so
that the successful models yield elemental abundances for the
LIC that are automatically corrected for unobserved H+ (Table
7). The exceptions are that He, Ne, and Ar abundances, being
unconstrained by the observations toward ǫ CMa, are not ad-
justed but are assumed to be 105 ppm, 123 ppm and 2.82 ppm,
respectively. In the models, N(C ii∗) is a constraint on both the
C abundance (in place of the heavily saturated C ii 1335Å line)
and ne, such that the product of the abundance and ne is more
tightly limited than either quantity individually. The requirement
to match both N(C ii∗) and n(He0) effectively restricts the ioniza-
tion fraction of H, which in turn limits O and N ionization whose
ionization fractions are tied by charge-transfer to the H ioniza-
tion at LIC temperatures.
Early studies showed that the abundances of refractory el-
ements in the very local ISM are enhanced compared to abun-
dances in cold disk gas (Marschall & Hobbs 1972; Stokes 1978;
Frisch 1981). Throughout warm and cold disk gas, the un-
derabundances of refractory elements compared to solar abun-
dances (by factors of 10−1 − 10−4) are taken to represent deple-
tion onto interstellar dust grains (e.g. Savage & Sembach 1996).
This view is supported by the correlation found between elemen-
tal depletions and the temperature characteristic of condensa-
tion at solar pressure and composition (Ebel 2000), and assumes
that there is a reference abundance pattern that characterizes the
cloud, and remains constant over the cloud lifetime as atoms are
exchanged between the gas and dust phases. Below (§5.4) we
compare solar abundances with observed gas-phase abundances
to predict the gas-to-dust mass ratios for the LIC, based on the
assumption that LIC gas and dust have remained coupled over
the cloud lifetime.
An important question is whether the LIC has solar abun-
dances. Isotopes of 18O and 22Ne isotopes measured in the ACR
population suggest that this is so. ACRs are characterized by
a rising particle flux for energies below 10–50 MeV/nucleon,
and this characteristic spectral signature is seen for 16O, 18O,
20Ne, and 22Ne. Ratios of 16O/18O ∼ 500 and 20Ne/22Ne ∼
13.7 are found for both the ACRs and solar material, indicat-
ing that the CHISM and solar material have similar composi-
Slavin and Frisch: Boundary Conditions of the Heliosphere 11
Table 8. Solar Abundances (ppm)
Grevesse Holweger Lodders Grevesse
Sauval et al.
(1998) (2001) (2003) (2007)a
C 334 ± 46 391(+110,−86) 290 ± 27 275 ± 34
N 84 ± 12 85.3+25
−19 82 ± 20 67 ± 10
O 683 ± 94 545+107
−90 579 ± 66 513 ± 63
Ne 121 ± 17 100+17
−15 91 ± 21 77 ± 12
Mg 38 ± 4 34.5+5.1
−4.5 41 ± 2 38 ± 9
Si 35 ± 4 34.4+4.1
−3.7 41 ± 2 36 ± 4
S 22 ± 5 - 18 ± 2 15 ± 2
Ar 2.54 ± 0.35 - 4.24 ± 0.77 1.70 ± 0.34
Fe 32 ± 4 28.15.84.8 35 ± 2 32 ± 4
a Protosolar abundances are obtained by increasing the photospheric
abundances by 0.05 dex for elements heavier than He, as suggested
by Grevesse et al. (2007)
tions (Leske et al. 2000; Leske 2000). We therefore adopt solar
abundances as the underlying reference abundance pattern for
the LIC.
Unfortunately a prominent uncertainty exists in the correct
solar abundances of volatile elements such as O and S, which
have low condensation temperatures (Tcond, 180 K and 700 K
respectively), and noble elements such as Ne and Ar. Solar
abundances are determined from photospheric data (C, N, O,
Mg, Si, S, Fe), the solar wind (Ar, Ne), solar active regions
(Ne), and helioseismic data (He); abundances of non-volatile el-
ements are also found from meteoritic data (Grevesse & Sauval
1998; Holweger 2001; Lodders 2003; Grevesse et al. 2007).
Solar abundances from these studies are listed in Table 8. Our
results, discussed below, indicate that if the LIC has a solar abun-
dance composition, as indicated by the 18O and 22Ne data, then
the lower abundances found by Grevesse et al. (2007) are pre-
ferred by our models.
Ne: In these models we have assumed the Ne abundance
is 123 ppm (Anders & Grevesse 1989), which is based on a
combination of photospheric and interstellar data. Solar sys-
tem Ne abundances are difficult to measure because of FIP
effects, however values include 77 ppm (Grevesse et al. 2007,
after adding 0.05 dex to account for gravitational settling of
the elements), and ∼ 41 ppm for solar wind in coronal holes
(Gloeckler & Geiss 2007). The predicted densities of n(Ne0) in
the CHISM for models 26 and 28 (Table 4) are in agreement with
the most recent PUI results for Ne (Table 1), and Ne densities as
low as ∼ 100 ppm are allowed when filtration is included.
The CHISM Ne abundances indicated by these results ap-
pear to be consistent with Ne abundances and ionization levels
in the global ISM. The Ne abundance in the Orion nebula is 100
ppm (Simpson et al. 2004). Takei et al. (2002) measured X-ray
absorption edges formed by Ne and O in the interstellar gas and
dust towards Cyg X-2, and found abundances of Ne/H ∼ 92 ppm
and O/H ∼ 579 ppm when both atomic and compound forms
in the sightline were included. Juett et al. (2006) observed the
X-ray absorption edges of Ne and O towards nine X-ray bina-
ries which sampled both neutral and ionized warm material, and
found that the ionized states formed in the ionized material have
the ratio Ne iii/Ne ii ∼ 0.23. This value is identical to the pre-
dictions of model 26, Ne iii/Ne ii ∼ 0.23, a fortuitous agreement
that may indicate that the EUV radiation field in the CHISM is
similar to the generic galactic EUV field in the solar vicinity.
Ar: Solar Ar abundance determinations range between Ar/H
∼ 1.4 − 5.0 ppm (Table 8); we have assumed Ar/H = 2.82 ppm.
The predicted Ar density at the Sun is within the uncertainties
of the PUI data, although the range of possible filtration factors
(0.64 – 0.95, see §2.2) also allow considerable leeway.
O: In the warm ISM such as the LIC, the ionization of oxy-
gen and hydrogen is tightly coupled over timescales of ∼100
years by charge transfer (Field & Steigman 1971), so that the
assumed N(H i) combined with N(O i) measurements act to con-
strain the deduced O abundance in the gas. The two best models
(26, 28) correspond to O/H = 331 ppm, however the O column
density measurements are based on the saturated 1302Å line, and
have ∼ 35% uncertainty. The modeled LIC value of O/H ∼ 331
ppm indicates that ∼ 35% of the O atoms are depleted onto dust
grains. An oxygen filtration factor of fO ∼ 0.75 is required by
the PUI data and Model 26.
These models yield gas-phase O abundances that are con-
sistent with observations of more distant interstellar sightlines.
The ratio N(O i)/N(H i) is measured in both low and high extinc-
tion clouds. Oliveira et al. (2003) used unsaturated O i lines in
the 910–1100Å interval and found O i/H i = 317 ± 19 ppm for
∼ 30 sightlines that included both types of material. Sightlines
with detected H2, N(H) > 10
20.5 cm−2 and 〈nH〉 = 0.1−3.3 cm
yield O/H = 319 ± 14 ppm (Meyer et al. 1997). A survey of 19
stars with an average distance of 2.6 kpc by André et al. (2003)
found O i/H i = 408± 14 ppm, where the long sightline and high
average value N(H)/E(B− V) = 6.3 × 1021 cm−2 mag−1 indicate
a bias towards sightlines containing many clouds that individu-
ally have low extinctions. A larger sample of 56 sightlines for
a range of extinctions and distances show that sightlines with
higher average mean densities, 〈nH〉, show O/H = 284±12 ppm,
versus O/H = 390 ± 10 ppm for stars with low values of 〈nH〉
(Cartledge et al. 2004). For comparison, solar abundance stud-
ies yield a range of ∼ 450 − 780 ppm.
C: The best Models 26 and 28 yield a gas-phase abundance
of C of C/H = 661 and 708 compared to solar abundances
of ∼ 240 − 500 ppm, which is consistent with our earlier re-
sults (Slavin & Frisch 2006) indicating an overabundance of C
in the LIC. We speculate that shock destruction of carbonaceous
grains, perhaps combined with some local spatial decoupling be-
tween carbonaceous and silicate grains, may explain these find-
ings.
Singly-ionized carbon is an important coolant in the LIC
(§5.5), so the C overabundance is required to maintain the tem-
perature of the CHISM at the observed value. The carbon abun-
dance obtained here indirectly depends on the Mg ii→Mg i di-
electronic recombination coefficient that determines the ratio
Mg ii/Mg i, since that ratio is used as a criteria for the best mod-
els. The same ionization correction that gives the C abundance
also successfully predicts Ne ionization in global WPIM and the
S abundances in the LIC, although this may be a fortuitous co-
incidence. In the adjacent sightline towards Sirius the LIC has
N(C ii)/N(H i) = 1, 050 ppm (Hebrard et al. 1999). An ionization
correction of 300% is required to make this value consistent with
solar abundances, and such a large ionization correction is not
consistent with the ionization levels of X(H) ∼ 20 − 26% found
here. In contrast, sightlines with cold ISM show C abundances
on the order of 135 ± 46 ppm (Sofia et al. 1997; Sembach et al.
2000).
N: The best models (26 and 28) find N/H = 46–47 ppm, com-
pared to solar values of ∼ 57−110 ppm. These results are consis-
tent with the PUI results, N/H ∼ 19−47 ppm, after filtration fac-
tor uncertainties are included. The N and O results and favor an
12 Slavin and Frisch: Boundary Conditions of the Heliosphere
ISM abundance pattern for volatiles similar to the Grevesse et al.
(2007) photospheric abundances.
S: The best models predict S/H = 16–17, compared to solar
values of ∼ 13−27 (including uncertainties, see Table 8). Sulfur
is found to have little or no depletion onto dust grains in warm
diffuse ISM (e.g. Welty et al. 1999).
Mg, Si, Fe: These refractory elements are observed in the
LIC gas with abundances far below solar (factors of 3–15).
Approximately 92%, 82%, and 77% of the Fe, Mg, and Si, re-
spectively, are presumably depleted onto interstellar dust grains.
If (Grevesse et al. 2007) abundances are assumed for the LIC,
then to within the uncertainties the LIC dust has the relative com-
position of Fe:Mg:Si:O = 1:1:1:4, as is consistent with amor-
phous olivines MgFeSiO4. Fe and Si are dominantly singly ion-
ized, while Mg has a significant fraction (∼ 15%) that is twice
ionized. The gas-phase abundances of these refractory elements
are highly subsolar, even after ionization corrections are made,
indicating that these elements are substantially depleted onto in-
terstellar dust grains. In contrast to C, however, the silicate dust
in the LIC that carries the missing Mg, Si, and Fe has experi-
enced far less destruction than the carbonaceous grains.
Ca ii, Na i: Weak lines of the trace ionization species Ca ii
and Na i are common diagnostics of ionization and abundance
for interstellar clouds, including the partially ionized LIC; Na i
is also frequently used as a diagnostic of the H column density.
We note that our models show that the ratios N(Ca ii)/N(Na i),
N(Na i)/N(H), and N(Na i)/N(H i) vary by 30%, 77%, and 93%,
respectively, between the best models (Models 26–30, 42). As
trace ionization species, the densities of Na i and Ca ii are highly
sensitive to volume density, n(Na0), n(Ca+) ∝ n(H)ne. We there-
fore conclude that Na i and Ca ii are imprecise diagnostics of
ionization levels, H density, and abundances in warm partially
ionized clouds.
5.4. Gas-to-Dust Mass Ratio
Because the abundances are automatically corrected for unob-
served H+, we use the model results to infer the total mass of the
interstellar dust, providing that the gas and dust in the LIC form
a coupled and closed system that evolves together as the cloud
moves through the LSR. The LIC LSR velocity is 16–21 pc/Myr,
so that a LIC origin related to the Loop I or Scorpius-Centaurus
superbubble would require that the LIC gas and dust remained
a closed system over timescales of 4–5 Myr (Frisch & Slavin
2006; Frisch 1981). Gas-to-dust mass ratios calculated from the
best models (26 and 28) using the missing-mass argument2 are
in the range RG/D= 149 − 217, depending on solar abundances.
The detailed information about RG/D for different assumptions
and the different models is listed in table 9.
For comparison, RG/D determined from comparisons of in
situ observations of interstellar dust inside of the solar system,
compared to the gas densities of these models, yield RG/D = 115–
125 (Table 9, Landgraf et al. 2000; Altobelli et al. 2004). The in
situ RG/D is an upper limit, since the smallest interstellar dust
grains (radii ≤ 0.15 µm) with large charge-to-mass ratios (and
thus small Larmor radii) are excluded from the heliosphere by
the interstellar magnetic field which is draped over the helio-
sphere.
For all the models, the RG/D determined from comparing
in situ dust measurements with the CHISM gas mass flux is
2 This argument assumes that the ISM reference abundances, in this
case solar abundances, represent the sum of the atoms in the gas plus
the dust (Frisch et al. 1999).
Table 9. Gas-to-Dust Mass Ratios from Models and In Situ
Observations
Modela
Source 14 26 27 28 29 30 42
GS98 137 149 196 149 197 150 138
Lodders 158 174 238 174 239 175 160
Grevesse 194 217 321 217 323 218 196
In Situ 115 116 123 116 125 116 107
a The source of the comparison solar abundances is listed in column
1 (Table 8. The in situ dust flux is from Landgraf et al. (2000),
corrected downwards by 20% as recommended by Altobelli et al.
(2004) to account for side-wall impacts.
Table 10. Major Heat Sources in LIC Gasa
Sourceb Fraction of Heating
H i 0.657
He i 0.248
dust 0.055
He ii 0.016
cosmic rays 0.010
a Results for model 26. Other models are qualitatively the same,
though there are some quantitative variations.
b For lines with ion names, the source here denotes the ion that is
photoionized. Dust heating comes from photoelectric ejection by
photons of the background FUV radiation field. Cosmic ray heating
comes from electron impact ionization of the gas and direct heating
of the electrons in the LIC plasma by the cosmic ray electrons.
lower than that determined by assuming solar abundances and
using the gas phase abundances we determine to find RG/D.
This suggests that somehow the dust flowing into the helio-
sphere is concentrated relative to the gas, compared to the over-
all LIC sightline towards ǫ CMa. The lower solar abundances
of Grevesse et al. (2007) result in lower required depletions, and
produces stronger disagreements with RG/D determined from in
situ data. We do not understand this result, which we have found
previously (Frisch et al. 1999). Since RG/D is sensitive to the
mass of Fe in the dust grains (Frisch & Slavin 2003), we sug-
gest that this difference may indicate inhomogeneous mixing of
the gas and silicate dust over the ∼ 0.64 pc extent of the LIC.
5.5. Heating and Cooling Rates
The heating and cooling rates for Model 26 are listed in Tables
10 and 11. The primary heat sources are photoelectrons from
the ionization of H0 and He0, with dust and cosmic ray heating
contributing less than 7% of the heating. The dominant source
of cooling is the [C ii] 157.6 µm fine-structure line, making up
43% of the total. This is more than twice the contribution of
any other coolant. Nearly all the cooling is due to optical and
infrared forbidden lines with many lines contributing at the ∼
1% level. H recombination, free-free emission and dust, through
the capture of electrons onto grain surfaces, also contribute at
about a 2% level. The importance of C ii as both a constraint
on the C abundance in our models as well as a major coolant
means that any model that aims to reduce the abundance of C
to a solar level faces severe difficulties. The models with LIC
temperatures in the THe0 = 6 300 ± 340 K range indicated by
Slavin and Frisch: Boundary Conditions of the Heliosphere 13
Table 11. Major Coolants in LIC Gasa
Ion/Line Fraction of Cooling
[C ii] 157.6 µm 0.428
[S ii] 6731 Å 0.145
Fe ii (total) 0.074
[Si ii] 34.8 µm 0.065
[Ne ii] 12.8 µm 0.035
[O i] 63.2 µm 0.028
H recomb. 0.024
dust 0.024
[Ne iii] 15.6 µm 0.020
[N ii] 6584 Å 0.018
net free-free 0.018
[O i] 6300 Å 0.017
[O ii] 3727 Å 0.011
[Ar ii] 6.98 µm 0.011
a Results for model 26. Other models show similiar results.
the in situ He0 data all require supersolar abundances of C. The
total heating/cooling rate for the LIC at the Sun for this model is
3.55 × 10−26 ergs cm−3 s−1.
5.6. Radiation Field
Recently it has been proposed that a significant portion
of the SXRB can be attributed to charge-transfer (a.k.a.
charge exchange) between the solar wind ions (e.g., O+7 and
O+8) and interstellar neutrals (Cravens 2000; Snowden et al.
2004; Wargelin et al. 2004; Smith et al. 2005; Koutroumpa et al.
2006). While it seems at present that some fraction of the low
energy X-rays are from this mechanism, it is unclear how large
that fraction is. We note that basing the properties of the local
hot plasma in the galactic plane on SXRB emission at energies
E > 0.3 keV is problematical. (Bellm & Vaillancourt 2005) have
compared the Wisconsin B and Be band data with the ROSAT
R12 data, and concluded that the observed anticorrelation be-
tween R12 and N(H i) indicates that more than 34% of the SXRB
generated in the Galactic disk must come from the Local Bubble.
They also concluded that a heavily depleted plasma with log
T ∼ 5.8 is consistent both with the McCammon et al. (2002);
Sanders et al. (2001) X-ray spectral data, and the upper limits
set on the EUV emission by CHIPS (Hurwitz et al. 2004). When
the Robertson & Cravens (2003) models of SXRB production
by charge-transfer with the solar wind are considered, then only
half of the SXRB in the plane is required to arise from a hot local
plasma. We also note that the atomic physics for the calculation
of the low energy part of the emission is still quite uncertain
(V. Kharchenko, private communication). At this point we take
the simple approach of ignoring the charge-transfer emission,
though we plan to consider its possible impact in future work by
reducing the assumed SXRB flux from hot gas. As noted previ-
ously, a lower SXRB flux due to a lower pressure in the hot gas
does not necessarily have any impact on our calculated flux from
the evaporative cloud boundary.
5.7. LIC Pressure
The strength of the interstellar magnetic field in the LIC is un-
known, though modeling of its effects on the heliosphere sets
some constraints. Our best models (26 and 28) presented here
have a thermal pressure of ∼ 2100 cm−3 K for the LIC. If the
thermal and magnetic pressures are equal, this indicates a mag-
netic field strength B ∼ 2.7 µG, in agreement with field strengths
for these models. As noted is §2.3, the main effect of the field
strength in the models is to regulate the pressure in the evapo-
rative cloud boundary, which in turn affects the flux of diffuse
EUV radiation incident on the cloud. The amount of EUV flux
helps determine the temperature in the cloud, which is how the
observational constraints fix the magnetic field strength in the
context of our modeling. Thus we do not explicitly fix the mag-
netic field strength with the goal of achieving equipartition and
indeed some of our successful models have lower or higher field
strengths. It is probably coincidental that the field strength re-
quired to match the in situ He0 temperature for our best models
is also close to the equipartition field strength, but it is at least
encouraging that this field strength is consistent with our pho-
toionization models. We note that if thermal, cosmic ray, and
magnetic pressures are approximately equal the LIC has a pres-
sure of ∼ 6300 cm−3 K.
5.8. Comparisons with other LISM Sightlines
There have been a number of efforts to understand the
LISM ionization and abundances (Frisch et al. 1986;
Cheng & Bruhweiler 1990; Lallement & Bertin 1992;
Vallerga 1996; Lallement & Ferlet 1997; Holberg et al. 1999;
Kimura et al. 2003). The studies that attempt to derive gas
phase elemental abundances find a range of results, generally
fairly consistent with ours. A point of particular interest is the
abundance of carbon that is surprisingly overabundant in our
results. As an example, Kimura et al. (2003) find (based on four
sightlines and excluding the ǫ CMa and β CMa sightlines), a
subsolar C abundance in contradiction with our results. Results
for thirteen sightlines from Redfield & Linsky (2004) with
velocity components consistent with the LIC velocity vector
show that N(C ii)/N(O i) > 1 for 8 of them, especially those
at lower column density indicating a solar or supersolar C
abundance. For our best models N(C ii)/N(O i) ≈ 2. Our series
of studies are unique in that we model the radiation field incident
on the cloud, include radiative transfer effects, and calculate
the thermal equilibrium within the cloud. The ionization varies
through the cloud as does the temperature and density (slightly)
and we compare observations within the heliosphere with the
physical conditions at that point in the cloud rather than basing
the model on line-of-sight averages.
Our present results indicate that n(N ii)/n(N i)∼ 0.32 − 0.50
at the solar location, with N becoming more ionized as the
sightline approaches the cloud surface. The column density ra-
tio is thus higher, ranging from 0.38 − 0.62. Observed values
of N(N ii)/N(N i) toward other nearby stars are 0.58+0.56
−0.77 toward
Capella (Wood et al. 2002), 1.29±0.23 toward HZ43 (Kruk et al.
2002), 1.91+0.87
−0.69 towards WD1634-573 (Lehner et al. 2003), and
1.13 ± 0.24 towards η UMa (Frisch et al. in preparation). The
total H i column density towards each of these stars is greater
than the N(H i)∼ 4 × 1017 cm−2 found for the best models here.
The nearest of these stars, Capella, has an ionization compara-
ble to that of the LIC. The two high-latitude stars HZ43 and η
UMa appear to sample low opacity regions where the ionization
is larger than at the Sun, as does the WD1634-573 sightline that
appears to cross the nearby diffuse H ii region seen towards λ
Sco (York 1983). As we have noted the ǫ CMa line of sight is
special because that star is the dominant source of stellar EUV
photons for the LIC. Thus for sightlines at a large angle from
the ǫ CMa sightline, if the H i column between points along the
sightline and ǫ CMa is small the apparently high column points
14 Slavin and Frisch: Boundary Conditions of the Heliosphere
are subject to a strong EUV field. Such geometry dependent ion-
ization effects can be important for non-spherical clouds subject
to a strongly spatially variable ionizing radiation source.
The variation in the fractional ionization of the CLIC gas
has a direct impact on our understanding of the distribution and
physical properties of low column density clouds for several rea-
sons. (1) Abundances of elements with FIP < 13.6 eV must al-
ways be calculated with respect to N(H i)+ N(H ii) for very low
column density clouds. (2) Cloud geometry affects the opacity
of observed sightlines so that the opacity to ionizing radiation
is not directly traced by the observed value of N(H i). For lines
of sight other than that towards ǫ CMa, this could require more
complex radiative transfer models in which the difference be-
tween the line of sight toward the star and that toward one of the
primary sources of ionizing flux, ǫ CMa, at each point is taken
into account.
6. Conclusions
There are many uncertainties regarding the detailed properties of
the ionizing interstellar radiation field incident on the LIC. The
data we have on the LIC, both from absorption line studies and
in situ measurements by spacecraft in the heliosphere, provide us
with strong constraints on the ionization and composition of the
LIC and particularly the CHISM. By exploring a range of models
for the ISRF we find that while a fairly broad range of radiation
fields can produce photoionization consistent with the data, other
outputs from the models fall within a relatively narrow range of
values. Our results for the models explored in this paper in which
we require our models to be consistent with the LIC component
of the absorption lines observed towards ǫ CMa include:
1. For a range of assumptions regarding the H i column density
of the LIC, N(H i) = (3.0−4.5)×1017 cm−2, and temperature
of the hot gas of the Local Bubble, log Th = 5.9, 6.0 and
6.1, we are able to find model parameters that allow a match
of the model results with best observed quantities, n(He0),
T (He0) and N(Mg ii)/N(Mg i). For these models we assume
that the cloud is evaporating because of thermal conduction
between the hot Local Bubble gas and the warm LIC gas and
include the emission from the cloud boundary.
2. For the best models in terms of fits to data, the required input
parameters are: initial (i.e. at the outer edge of the cloud)
total H density, n(H) ≈ 0.21−0.23 cm−3; and cloud magnetic
field, B0 ≤ 3.8 µG.
3. If we assume that the magnetic field configuration reduces
thermal conductivity at the boundary enough to prevent
evaporation and ignore any radiation from the cloud bound-
ary, we find that for most cases the radiation field does not
cause sufficient heating to maintain the LIC at the temper-
ature observed, T = 6, 300 ± 340 K. One set of parameter
choices, though, yields a successful model. These parame-
ters are N(H i) = 4.5 × 1017 cm−2 and log Th = 6.1.
4. Despite the wide range of possible input parameters, the out-
put values for quantities important for shaping the helio-
sphere are confined to a fairly small range: n(H0) = 0.19 −
0.20 cm−3, and ne = 0.05 − 0.08 cm
5. A H filtration factor of fH = 0.55 ± 0.03 yields good agree-
ment between the radiative transfer model predictions for
n(H i) in the CHISM, and n(H i) at the termination shock as
found from observations of PUIs, the H i Lyα glow, and the
solar wind slow-down in the outer heliosphere. This filtra-
tion value is also consistent with heliosphere models of the
ionization of interstellar H atoms traversing the heliosheath
regions.
6. Elements with ionization potentials 13.6− 25 eV, e.g. H, He,
N, O, Ne, and Ar, are partially ionized with ionization frac-
tions of ∼ 0.2 − 0.7.
7. By requiring that the models match the column densities de-
rived from absorption line data we are able to determine the
necessary elemental abundances for several elements. We
find that the abundances of N and O may be somewhat sub-
solar. Sulfur is roughly solar, and C is substantially super-
solar. Mg, Si and Fe are all sub-solar by factors of 3 − 15.
The depletions of Fe, Mg, Si and O in the LIC are consis-
tent with a dust population consisting of amorphous silicate
olivines MgFeSiO4, though other compositions for the dust
are possible as well. We conclude that any carbonaceous dust
in the LIC must have been destroyed, while silicate dust has
persisted. Except for the gas-to-dust mass ratio, these results
are in better agreement with the lower solar abundances of
Grevesse et al. (2007). However we note that the O and Ne
abundances of Lodders (2003) are in better agreement with
other astronomical data such as the X-ray absorption edges.
8. The gas-to-dust mass ratio derived from missing mass in the
gas-phase for our best models depends strongly on the as-
sumed reference abundance set and range from 137 − 323.
Our two best models, nos. 26 and 28, give a range of
149−217. For these same models RG/D = 115−125 based on
the observed flux of dust into the heliosphere. The discrep-
ancy of these values is minimized, in fact leading to con-
sistency within the errors, if one assumes an abundance set
such as that of GS98 which has large abundances of the met-
als. The GS98 abundances lead to substantial O depletion,
however, which is not easily explained and conflict with the
S abundances found for models 26 and 28.
9. These models also show that the densities of the trace ion-
ization species Ca ii and Na i are extremely sensitive to den-
sity and ionization. Therefore the ratios N(Ca ii)/N(Na i),
N(Na i)/N(H i), and N(Na i)/N(H) are, by themselves, inade-
quate diagnostics of warm low density diffuse gas.
Acknowledgements. We would like to thank George Gloeckler for sharing data
with us prior to publication, and Alan Cummings for pointing out that the
ACR isotopic data indicate that the LIC abundances are solar. We also thank
the International Space Science Institute in Bern, Switzerland for hosting the
working group on “Interstellar Hydrogen in the Heliosphere.” This research was
supported by NASA Solar and Heliospheric Program grants NNG05GD36G
and NNG06GE33G to the University of Chicago, and by the NASA grant
NNG05EC85C to SWRI.
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List of Objects
‘ǫ CMa’ on page 2
‘Sirius’ on page 3
	Introduction
	Photoionization Model Constraints and Assumptions 
	Astronomical Constraints – The LIC towards  CMa  
	In situ Constraints – He0, Pickup Ions, and Anomalous Cosmic Rays 
	Interstellar Radiation Field at the Cloud Surface 
	Photoionization Models
	Model Results 
	Discussion
	Heliosphere Boundary Conditions
	Hydrogen Filtration Factor
	Gas-Phase Abundances 
	Gas-to-Dust Mass Ratio 
	Heating and Cooling Rates 
	Radiation Field
	LIC Pressure
	Comparisons with other LISM Sightlines
	Conclusions
