Submitted to The Astrophysical Journal
Modeling the Spectral Energy Distribution and Variability of
3C 66A during the WEBT campaign of 2003 – 2004
M. Joshi1 and M. Böttcher1
ABSTRACT
The BL Lac object 3C 66A was observed in an extensive multiwavelength
monitoring campaign from July 2003 till April 2004. The spectral energy dis-
tribution (SED) was measured over the entire electromagnetic spectrum, with
flux measurements from radio to X-ray frequencies and upper limits in the very
high energy (VHE) γ-ray regime. Here, we use a time-dependent leptonic jet
model to reproduce the SED and optical spectral variability observed during our
multiwavelength campaign. Our model simulations could successfully reproduce
the observed SED and optical light curves and predict an intrinsic cutoff value
for the VHE γ-ray emission at ∼ 4 GeV. The effect of the optical depth due to
the intergalactic infrared background radiation (IIBR) on the peak of the high-
energy component of 3C 66A was found to be negligible. Also, the presence of
a broad line region (BLR) in the case of 3C 66A may play an important role in
the emission of γ-ray photons when the emission region is very close to the cen-
tral engine, but further out, the production mechanism of hard X-ray and γ-ray
photons becomes rapidly dominated by synchrotron self-Compton emission. We
further discuss the possibility of an observable X-ray spectral variability pattern.
The simulated results do not predict observable hysteresis patterns in the optical
or soft X-ray regimes for major flares on multi-day time scales.
Subject headings: galaxies: active — BL Lacertae objects: individual (3C 66A)
— gamma-rays: theory — radiation mechanisms: non-thermal
1Astrophysical Institute, Department of Physics and Astronomy,
Ohio University, Athens, OH 45701, USA
http://arxiv.org/abs/0704.0269v1
– 2 –
1. Introduction
Blazars are the most extreme class of Active Galactic Nuclei (AGN) exhibiting rapid
variability at all wavelengths and a high degree of linear polarization in the optical. They
have been observed at all wavelengths, from radio through VHE γ-rays and are characterized
by non-thermal continuum spectra and radio jets with individual components often exhibit-
ing apparent superluminal motion. This class of AGNs is comprised of BL Lac objects and
flat-spectrum radio quasars (FSRQs), which are distinguished primarily on the basis of the
absence or presence of broad emission lines in their optical spectra.
The broadband spectra of blazars are associated with non-thermal emission and exhibit
two broad spectral components. The low energy component is due to synchrotron emis-
sion from non-thermal electrons in a relativistic jet whereas the high energy component is
attributed either to the Compton upscattering of low energy radiation by the synchrotron
emitting electrons (for a recent review see, e.g., Böttcher (2006)) or the hadronic processes
initiated by relativistic protons co-accelerated with the electrons (Mücke & Protheroe 2001;
Mücke et al. 2003) . Blazars are often known to exhibit variability at all wavelengths, vary-
ing on time scales from months, to a few days, to even less than an hour in some cases.
The radio emission of blazars shows variability on a time scale of weeks to months whereas
the optical emission for some blazars might vary on a time scale of around one and a half
hours. At X-ray energies, some HBLs exhibit characteristic loop features when the pho-
ton energy spectral index, α, is plotted against the X-ray flux. These plots are known as
hardness-intensity diagrams (HIDs) and the loop structures are called spectral hysteresis.
This spectral hysteresis can be interpreted as the signature of synchrotron radiation, due to
the gradual injection and/or acceleration of ultrarelativistic electrons in the emitting region
and their subsequent radiative cooling (Kirk et al. 1998; Georganopoulos & Marscher 1998;
Kataoka et al. 2000; Kusunose et al. 2000; Li & Kusunose 2000; Böttcher & Chiang 2002).
3C 66A is classified as a low-frequency peaked (or radio selected) BL Lac object (LBL).
The peak of the low-frequency component of LBLs generally lie in the IR or optical regime,
whereas the high-energy component peak is located at several GeV, and the γ-ray output
is typically comparable to or slightly higher than the spectral output of the synchrotron
component. The redshift of 3C 66A has a relatively uncertain determination of z = 0.444
(Bramel et al. 2005). It has exhibited rapid microvariability at optical and near infrared
in the past and has been suggested as a promising candidate for detection by the new
generation of atmospheric Čerenkov telescope facilities like H.E.S.S., MAGIC, or VERITAS
(Costamante & Ghisellini 2002). This object has been studied in radio, IR, optical, X-rays
and γ-rays in the past. Its low-frequency component is known to peak in the IR - UV regime
whereas the high-frequency component generally peaks at multi MeV - GeV energies. The
– 3 –
multiwavelength SED and correlated broadband spectral variability behaviour of 3C 66A
have been very poorly understood. For this reason, Böttcher et al. (2005) organized an
intensive multiwavelength campaign to observe this object from July 2003 through April
2004, with the core campaign period being Sept. - Dec. 2003.
As described in Böttcher et al. (2005), the object exhibited several outbursts in the
optical. The variation was on the order of ∆m ∼ 0.3-0.5 over a timescale of several days.
The minimum variability timsecale of 2 hr provided an estimate for the size of the emitting
region to be on the order of 1015 cm. The optical flares suggested the presence of an optical
spectral hysteresis pattern with the B - R hardness peaking several days before the R- and B-
band flux peaked. The RXTE PCA data indicated a transition between the synchrotron and
the high-energy component at photon energies of & 10 keV. The broadband SED of 3C 66A
suggested that the synchrotron component peaked in the optical. In the VHE γ-ray regime,
STACEE provided an upper limit at Eγ & 150 GeV whereas an upper limit at Eγ > 390 GeV
resulted from simultaneous Whipple observations.
In this paper, we use a leptonic jet model to reproduce the broadband SED and the
observed optical spectral variability patterns of 3C 66A and make predictions regarding
observable X-ray spectral variability patterns and γ-ray emission. In §2, we describe the
time-dependent leptonic jet model used to reproduce the observed SED and optical spectral
variability patterns of 3C 66A. The parameters used to simulate the observed results are
described in §3. The modeling results and VHE γ-ray predictions are discussed in §4. We
summarize in §5.
Throughout this paper, we refer to α as the energy spectral index, Fν [Jy] ∝ ν
−α. A
cosmology with Ωm = 0.3, ΩΛ = 0.7, and H0 = 70 km s
−1 Mpc−1 is used. In this cosmology,
and using the redshift of z = 0.444, the luminosity distance of 3C 66A is dL = 2.46 Gpc.
2. Model Description
The SEDs and optical variability patterns of 3C 66A were modeled using a one-zone
homogeneous leptonic jet model. The model assumes injection of a population of ultrarel-
ativistic non-thermal electrons and positrons into a spherical emitting volume (the “blob”)
of comoving radius Rb at a time-dependent rate. Since the positrons lose equal amount of
energy as the electrons via the same radiative loss mechanisms so we do not distinguish
between them throughout the paper. The injected electron population is described by a
single power law distribution with a particle spectral index q, comoving injection density
Qinje (γ; t) (cm
−3s−1) and low- and high-energy cutoffs γ1 and γ2, respectively, such that
– 4 –
Qinje (γ) = Q
0 (t)γ
−q for γ1 ≤ γ ≤ γ2, where Q
0 (t) is the injection function and is given by,
0 (t) =
Linj(t)
if q 6= 2
Linj(t)
mec2ln(γ2/γ1)
if q = 2
where Linj specifies the power of the injected pair population and V
b is the blob volume
in the comoving frame.
The randomly oriented magnetic field B has uniform strength throughout the blob and
is determined by an equipartition parameter eB ≡ uB/ue (in the comoving frame), where
uB is the magnetic field energy density and ue is the electron energy density. We keep eB
constant so that the magnetic field value changes according to the evolving electron energy
density value as determined by equation 2. The initial injection of the electron population
into the blob takes place at a height z0 above the plane of the central accretion disk. The
emitting region travels relativistically with a speed v/c = βΓ = (1 − 1/Γ
2)1/2 along the jet.
The jet is directed at an angle θobs with respect to the line of sight. The Doppler boosting of
the emission region with respect to the observer’s frame is determined by the Doppler factor
δ = [Γ(1− βΓ cos θobs)]
−1, where Γ is the bulk Lorentz factor.
As the emission region propagates in the jet, the electron population inside the blob
continuously loses its energy due to synchrotron emission, Compton upscattering of syn-
chrotron photons (SSC) and/or Compton upscattering of external photons (EC). The seed
photons for the EC process include the UV soft X-ray emission from the disk entering the jet
either directly (Dermer et al. 1992; Dermer & Schlickeiser 1993) or after getting reprocessed
in the BLR or other circumnuclear material (Sikora et al., 1994; Dermer et al. 1997). The
time-dependent evolution of the electron and photon population inside the emission region
is governed, respectively, by,
∂ne(γ, t)
ne(γ, t)
+Qe(γ, t)−
ne(γ, t)
te,esc
∂nph(ǫ, t)
= ṅph,em(ǫ, t)− ṅph,abs(ǫ, t)−
nph(ǫ, t)
tph,esc
Here, (dγ/dt)loss is the radiative energy loss rate, due to synchrotron, SSC and/or EC
emission, for the electrons. Qe(γ, t) is the sum of external injection and intrinsic γ − γ pair
– 5 –
production rate and te,esc is the electron escape time scale. ṅph,em(ǫ, t) and ṅph,abs(ǫ, t) are the
photon emission and absorption rates corresponding to the electrons’ radiative losses and,
tph,esc = (3/4)Rb/c is the photon escape timescale. The time-dependent evolution of the
electron and photon population inside the blob is followed and radiative energy loss rates as
well as photon emissivities are calculated using the time-dependent radiation transfer code
of Böttcher & Chiang (2002).
The model only follows the evolution of the emission region out to sub-pc scales and
as a result only the early phase of γ-ray production can be simulated. Since the radiative
cooling is strongly dominant over adiabatic cooling during this phase and the emission region
is highly optically thick out to GHz radio frequencies, the simulated radio flux is well below
the actual radio data. We do not simulate the phase of the jet components in which they
are expected to gradually become transparent to radio frequencies as that would require the
introduction of several additional, poorly constrained parameters.
3. Model Parameters
The model independent parameters that were estimated using the SED and optical
intraday variability measurements (see Böttcher et al. 2005) were used to develop an initial
set of input parameters:
δ ≈ 15
R ≈ 3.3× 1015 cm
B ≈ 2.9 ǫ
γ1 ≈ 3.1× 10
γ2 ≈ 1.5× 10
p ≈ 4 (4)
Here p is the equilibrium spectral index that determines the optical synchrotron spec-
trum and p = q+1 for strongly cooled electrons. The initial set of parameters was modified
to reproduce the quiescent as well as the flaring state of 3C 66A. Approximately 350 sim-
ulations were carried out to study the effects of variations of various parameters, such as
γ1, γ2, q, B and Γ, on the resulting broadband spectra and light curves. The set of model
parameters that provided a satisfactory fit to the quiescent state of 3C 66A involved a value
of the Doppler factor, δ = Γ = 24 and a viewing angle of θobs = 2.4
o. These parameters
were chosen on the basis of VLBA observations that provided the limits on the superluminal
motion and indicated bending of the jet towards the line of sight thus resulting in a smaller
– 6 –
viewing angle and a higher Doppler boosting of the emission region as compared to the
values inferred from the superluminal measurements on larger scales (Jorstad et al. 2005;
Böttcher et al. 2005). The fitting of the SED both in the quiescent as well as flaring state
of 3C 66A was carried out such that the simulated quiescent state does not overpredict the
X-ray photon flux as X-ray photons are expected to be dominated by the flaring episodes.
On the other hand, the flaring state was simulated such that the resulting time-averaged
spectrum passes through the observed time-averaged optical as well as X-ray data points.
This was achieved by varying individual parameters, such as, γ1, γ2 and q between the values
for quiescent and flaring states with time profiles as discussed in the next section. A value
of γ1 = 2.1× 10
3, γ2 = 4.5× 10
4 and q = 2.4 provided a satisfactory fit to the flaring state.
Also, during our multiwavelength campaign of 2003 - 2004, flux upper limits at multi-GeV -
TeV energies could be obtained and as a result we could get upper limits on the respective
parameters governing the EC component. The various model parameters used to simulate
the two states of 3C 66A are listed in Table 1.
Figures 1 and 2 respectively show the reproduction of the SED of 3C 66A, for both the
quiescent and flaring state observed during the campaign period. The quiescent state is a
reproduction of the state observed around 1st October 2003 whereas the flaring state is the
reproduction of a generic 10 day flaring period corresponding to the timescale of several of
the major outbursts that were observed during the campaign. The simulated time-averaged
spectrum of 3C 66A in the flaring state is shown in Figure 3. The simulations, corresponding
to fits 1 and 2 of Table 1, were carried out for a pure SSC emission process by artificially
setting LD = 0, where LD is the bolometric disk luminosity. Fit 3 of Table 1 refers to an
EC+SSC case with LD = 1.0× 10
45 ergs s−1 and is shown in Figure 9. The value of LD was
chosen such that it is more than the value of the jet luminosity used in the simulations and
at the same time does not produce a blue bump in the simulated SED. In order to assess
the possible effect of EC emission in 3C66A, an upper limit to the optical depth of the BLR
was first determined using XSTAR, which returns the ionization balance and temperature,
opacity, and emitted line (Hα, Hβ) and continuum fluxes. The BLR was modeled as a
spherical shell with rBLR,in = 0.045 pc and rBLR,out = 0.050 pc, where rBLR,in and rBLR,out
stand for the inner and outer radii of the broad line region. A Thomson optical depth of
0.3 for the BLR was chosen as a reasonable upper limit such that the line emission is weak
enough or absent to be consistent with the observed featureless continuum.
– 7 –
ν [Hz]
Oct. 1
Nov. 1
Nov. 11
Dec. 28
STACEE
Whipple
(99 % UL)RXTE 2003
XMM−Newton
ROSAT
EXOSAT
EGRET
BeppoSAX
1999/2001
EINSTEIN
1979/1980
STACEE (99 % UL, Γ = 2.5)
(99 % UL, Γ = 3.0)
STACEE
(99 % UL)
Fig. 1.— Reproduction of the quiescent state of 3C 66A observed around October 1st 2003.
The simulation of this state was carried out using parameters that do not overpredict the X-
ray photon flux. The black colored solid line indicates the instantaneous spectrum generated
by the simulation after the system (blob + injected electron population) attains equilibrium.
The low-energy component peaks in the optical at νsyn ≈ 4.8 × 10
14 Hz whereas the high-
energy SSC component peaks in the MeV regime at νSSC ≈ 1.6× 10
21 Hz. The synchrotron
cooling timescale in the observer’s frame is ≈ 1.2 hours, which is on the order of observed
minimum optical variability timescale of 2 hours. The diamond shaped STACEE upper
limit is a new addition and is provided by Lindner (2006). All data that are indicated by
dotted curves are archival data and are shown for comparison. The historical average of the
5 EGRET pointings is also included to provide a guideline for our simulated VHE emission.
– 8 –
ν [Hz]
Oct. 1
Nov. 1
Nov. 11
Dec. 28
STACEE
Whipple
(99 % UL)
RXTE 2003
XMM−Newton
ROSAT
EXOSAT
EGRET
BeppoSAX
1999/2001
EINSTEIN
1979/1980
STACEE (99 % UL, Γ = 2.5)
(99 % UL, Γ = 3.0)
STACEE
(99 % UL)
Fig. 2.— Simulation of the flaring state for a generic 10 day flare corresponding to the
timescale of several major outbursts that were observed in the optical regime during our
campaign. The various curves show the instantaneous spectral energy distribution of 3C 66A
at several different times in the observer’s frame: black (red in the online version) dotted
line (∼ 5th hour), gray (green) dashed line (∼ 8th hour), black (blue) dot-dashed line (∼
14th hour), gray (yellow) long-dashed line (∼ 20th hour), long-dashed black line (∼ 8th day,
highest state attained by the system during flaring), gray solid line (∼ 9th day), dotted black
(violet) line (∼ 16th day), gray (cyan) colored solid line (∼ 18th day), dashed black (magenta)
colored line (∼ 20th day) and black (red) solid line (∼ 22nd day, equilibrium state reached
by the system after the flaring episode is over). The synchrotron component of the flaring
state peaks at νsyn ≈ 1.1× 10
15 Hz and the SSC component peaks at νSSC ≈ 2.7× 10
22 Hz.
The SSC component of this state cuts off at νSSC,cutoff ≈ 2.3 × 10
24 Hz. The synchrotron
cooling timescale in the optical regime is ≈ 37 minutes for the flaring state.
– 9 –
4. Results and Discussion
As can be seen in Figure 3, the time-averaged simulated spectrum passes through the
time-averaged optical data points whereas the high energy end of the synchrotron compo-
nent passes through the time averaged X-ray data indicating the dominance of synchrotron
emission in the production of such photons in case of flaring. For X-ray photons with energy
beyond 10-12 keV, the data is less reliable due to low count rates and possible source con-
fusion with 3C 66B. The spectral upturn at ≥ 7 keV occurs due to the presence of the SSC
component in the simulation. The presence of this component cannot be suppressed because
in order to suppress it the population of seed photons would have to be diluted, which can
be done by increasing the size of the emission region. But the size of the emission region
cannot be increased any further due to the strict constraint on the maximum size of the blob
that comes from the observed minimum variability timescale in the optical region, which
is 2 hrs. Hence, the emission region size cannot exceed 3.6 × 1015 (D/24) cm. Thus, our
model suggests that the harder X-ray photons come from the SSC and not the synchrotron
mechanism with the expected spectral hardening taking place at ∼ 7 keV. The high energy
component, due to the SSC emission, for the time-averaged spectrum (see Figure 3) cuts off
at ∼ 1.0× 1024 Hz or 4 GeV. From the simulated level of VHE emission we predict that the
object is well within the observational range of MAGIC, VERITAS and, especially, GLAST
(see Figure 3) whose sensitivity limit is 50 times lower than that of EGRET at 100 MeV
and even more at higher energies and its two year limit for source detection in an all-sky
survey is 1.6 × 10−9 photons cm−2 s−1 (at energies > 100 MeV). Thus it will be possible
to extract the spectral and variability information for this object at such high energies in
future observations.
Flaring above the quiescent state of 3C 66A was reproduced using a flaring profile for
the electron injection power (Linj(t)) that was Gaussian in time (see Figure 4):
Linj(t) = L
inj(t) +
(Lflinj − L
(z−rc)2
] (5)
Here, qu and fl stand for the quiescent and flaring state respectively, z determines the
position of the emission region in the jet at time t, rc indicates the position of the center of
the simulated flare and σ stands for the Gaussian width of the flare.
The rest of the parameters such as γ1 and γ2 and q were also changed accordingly.
In order to simulate the observed optical flare, the system was first allowed to come to an
equilibrium and after the equilibrium was set up the flare was introduced with a Gaussian
width, σ corresponding to 14 days in the observer’s frame. Although the flare was introduced
– 10 –
ν [Hz]
VERITAS
STACEE
Whipple
(99 % UL)
RXTE 2003
XMM−Newton
ROSAT
EXOSAT
EGRET
BeppoSAX
1999/2001
EINSTEIN
1979/1980
STACEE (99 % UL, Γ = 2.5)
(99 % UL, Γ = 3.0)
GLAST
MAGIC
(Large ZA)
STACEE
(99 % UL)
Fig. 3.— Time-averaged spectral energy distribution of 3C 66A for a period of 23 days
around a flare as shown in Figure 2. The filled black (colored in the online version) circles
are the time-averaged optical and IR data points for the entire campaign period and the
“RXTE 2003” denotes the time-averaged X-ray data points. The dot-dashed black line
is the contribution from the synchrotron component only whereas the long-dashed black
line indicates the contribution of the SSC component only. The time-averaged synchrotron
component peaks at νsyn ≈ 7.2× 10
14 Hz whereas the time-averaged SSC component peaks
at νSSC ≈ 5.3 × 10
21 Hz. The synchrotron component cuts off near 7 keV whereas the SSC
component cuts off at ∼ 4 GeV. The black colored dashed line indicates the attenuation due
to the optical depth at VHE energies. The γγ absorption effect becomes significant at ∼
200 GeV. The black (green, maroon and magenta) lines indicate the sensitivity limits for an
observation time of 50 hours for MAGIC, VERITAS and MAGIC (Large Zenith Angle) and
for GLAST for an observation time of 1 month.
– 11 –
in order to simulate the observed major optical outbursts lasting for 10 days, the choice of
14 days for the Gaussian width was made such that the width of the simulated flare matches
that of the observed flare, rc was adjusted such that the centre of the simulated flare aligns
with that of the observed one and the value of Linj was varied such that the peak of the
simulated flare matches that of the observed one.
The observed lightcurves did not agree well with a flaring profile that was top-hat or
triangular in time as can be seen in the figure. The presence of a flare that is Gaussian in
time might represent an initial injection of particles into the emission region at the base of
the jet. The particles slowly get accelerated as a shock wave ploughs through the region
and finally dies out in time. Crucial information on the dominant acceleration mechanism
comes from the change in the shape of the particle injection spectral index with time, which
might also indicate a possible change in the B-field orientation. According to the current
understanding of acceleration mechanisms, parallel shocks generally produce electron spectra
of Qe(γ) ∝ γ
−q with 2.2 . q . 2.3 (Achterberg et al. 2001; Galant et al. 1999), whereas
oblique shocks produce much softer injection spectral indices. On the other hand, 2nd order
Fermi acceleration behind the shock front might give rise to a harder injection index of the
order of q ∼ 1 or beyond (Virtanen & Vainio 2005). In order to reproduce the flaring state,
the simulation first starts out in the quiescent state with quiescent state parameters and
then the value of these parameters is changed to the flaring state parameters as the flaring
is introduced in the simulation. Since, the value of q, in our simulations, changes from 3.1
(quiescent state) to 2.4 (flaring state) it might indicate a possible change in the orientation
of the B-field from oblique to parallel during the flaring episode or an interplay between
the 1st and 2nd order Fermi acceleration thereby making the particle spectra harder. The
contribution from such acceleration mechanisms and the shear acceleration (Rieger & Duffy
2004) might play an important role in accelerating the particles to higher energies.
The simulated optical variability in the R band (0.55 mag) matches the observed value
(0.3-0.5 mag) for a 10 day period outburst. The predicted variability in B is more than
that of R by ∼ 0.15 mag as also observed, which indicates that the spectrum is becoming
harder (see Figure 5) with the spectral upturn occuring at B-R ≈ 0.72 mag as shown in
Figure 6. Figure 6 is a hardness intensity graph that shows that the object follows a positive
correlation of becoming harder in B-R while getting brighter in both the bands during the
10-day flare simulated in Figure 2. This agrees well with the observed optical variability
pattern. In this study, we are not addressing the variability that was observed on intraday
timescales as that analysis would open up an even larger parameter space, which cannot be
reasonably well constrained without any variability information in the X-ray regime.
The flare declines faster as compared to the time taken by the flare to rise. This might
– 12 –
2940 2945 2950
JD - 2450000
Fig. 4.— The simulated lightcurves for various flaring profiles that have been superimposed
on the observed R-band lightcurve (see Figure 7 of Böttcher et al. (2005)) for an outburst on
∼ November 1st 2003. The solid black line denotes a flaring profile that is Gaussian in time
as used for the flare in Figure 2, the dash-dotted black line is a trianglular flaring profile
whereas the dashed black line is a flaring profile that is top-hat in time. As can be seen, the
Gaussian flaring profile closely matches the width as well as the profile of the observed flare.
– 13 –
0.0e+00 2.0e+05 4.0e+05 6.0e+05 8.0e+05 1.0e+06 1.2e+06
time (sec)
2e+12
3e+12
4e+12
5e+12
0.0e+00
5.0e+11
1.0e+12
1.5e+12
1 keV
10 keV
15 keV
3 keV
0e+00
2e+12
4e+12
6e+12
1 MeV
100 MeV
10 GeV
∆R ~ 0.55 mag
Fig. 5.— Simulated lightcurves for the optical, X-rays and γ-ray energy regimes shown in
the three panels respectively. The simulated variability in the R band is ≈ 0.55 mag as
indicated by the arrows. The B band, denoted by the black dotted line exhibits a higher
variability of ≈ 0.7 mag, in the simulation, than that in the R band, which is consistent
with our observations. The simulated lightcurve at 1 keV is indicated by a black dashed
curve and exhibits an amplitude variation of ≈ 1.4 × 1012 Jy Hz. The 3, 10 and 15 keV
lightcurves, denoted by the black solid line, black long-dashed line and the black dot-dashed
curve, respectively, on the other hand do not exhibit much variability. In the VHE regime,
the 1 MeV lightcurve is denoted by a black solid line. The 100 MeV lightcurve is indicated
by a black long-dashed curve and the simulated variability amplitude in this energy regime
is on the order of 1012 Jy Hz. The black dot-dashed line indicates the lightcurve at 10 GeV.
– 14 –
13.6013.7013.8013.9014.0014.10
R magnitude
0.640
0.660
0.680
0.700
0.720
0.740
0.760
0.780
Fig. 6.— The simulated hardness-intensity diagram indicates a positive correlation between
R- and B-band for an outburst lasting for ∼ 10 days. The object becomes brighter in R and
harder in B-R as shown by the arrows. The spectral upturn takes place at B-R ≈ 0.72 mag
where the flux in B equals that in R (corresponding to αBR = 0).
– 15 –
indicate that the particles’ synchrotron cooling timescale is less than or equal to the light
crossing time.
τ obscool,sy ≈ 2.8× 10
−1/2 (
15 s (6)
We can calculate the observed synchrotron cooling timescale, τ obscool,syn in the optical
regime from equation 6 (Böttcher et al. 2005) using δ = 24, B = 2.4 G and ν15 = 0.48 for
the quiescent state and B = 2.8 G and ν15 = 1.1 for the flaring state (see Figures 1 and
2), where ν15 is the characteristic synchrotron frequency in units of 10
15 Hz. This yields a
value of τ obscool,sy ∼ 1.2 hours for the quiescent state whereas for the flaring state it reduces
to 37 minutes. The observed minimum variability timescale of ∼ 2 hours might therefore
correspond to the observed dynamical timescale, where
τ obsdyn ≈
1 + z
. (7)
This implies that it takes time to build up the electron population in the emission
region through flaring but once built up the electrons lose their energy efficiently to produce
synchrotron photons. This can be used to constrain the value of the magnetic field in the
jet, which has been allowed to evolve in time keeping eB = 1 and has an average value of 2.4
Gauss in the simulated quiescent state and 2.8 Gauss in the simulated flaring period.
The crossover of X-ray lightcurves, in our simulations, is a result of the dominance of
the SSC component in hard X-rays (see Figure 5). The lightcurve of soft X-ray photons of
energy 1 keV exhibits a greater variability of ∼ 1.4 × 1012 Jy Hz in its flux as compared
to their optical counterpart. This is expected because the soft X-ray photons, during the
flaring episode, are produced from synchrotron emission of electrons that are accelerated
to very high energies and as a result have a very short cooling timescale and thus greater
variability. In case of hard X-rays no significant variability is predicted. This is because such
photons are produced from Compton upscattering of synchrotron photons off the low-energy
electrons and as a result the cooling timescale is much longer as compared to the cooling
timescale of their soft X-ray and optical counterparts. Hence, the variability information
gets washed out. The predicted X-ray spectral variability pattern of large variability in the
low X-ray energy band and negligible variability in the high X-ray energy band is similar to
what has also been observed in BL Lacertae on several occasions (see for e.g., Ravasio et al.
2003, 2002).
As can be seen in Figure 7, spectral hysteresis patterns are not predicted for optical as
– 16 –
well as soft X-ray photons. This is expected because the cooling timescale of their parent
electron population is so short that what is observed is the average effect of this cooling
over the dynamical timescale and hence any hysteresis pattern gets smeared out. On the
other hand, one expects to see these patterns at higher energies because as explained earlier,
this photon population comes from Compton upscattering off low-energy electrons, which
have a longer cooling timescale and as a result the photon population gradually builds up
over time and then dies away giving rise to a hysteresis pattern (see Figure 8). The slight
spectral softening at 10 keV seen in its hysteresis pattern (see Figure 7) for higher values of
νFν indicates a small synchrotron contribution near the peak of the flare.
The simulated instantaneous SED, for a pure SSC model, shows a definite presence of
γ-ray emission in 3C66A, in the quiescent as well as the flaring state (see Figure 1 and 2).
The intrinsic cutoff of VHE emission in the flaring state, according to the simulations, for
the time averaged spectrum is ∼ 1.0 × 1024 Hz or 4 GeV. In our simulations, the emission
of VHE γ-ray photons is produced by the SSC mechanism in the quiescent as well as the
flaring state. Figure 5 shows the simulated lightcurves for VHE photons and as can be seen
the νFν value changes by ∼ 4.17×10
12 Jy Hz at 100 MeV. The variability in VHE photons is
expected as they are the result of Compton upscattering off the higher energy electrons and
due to this the hysteresis pattern is not seen at such high energies as the cooling timescale
of such high energy electrons is very short (see Figure 8).
From Figure 9, it can be seen that the high-energy component of 3C 66A, in the flaring
state, could start out with a dominant contribution of the EC emission, shown by the red
solid line. But as the blob travels further away and passes the outer edge of the broad line
region, the EC contribution becomes less significant and the SSC emission takes over. This
is indicated by the black long-dashed line in the figure. We might actually find that this
maximum contribution would be just enough to explain the historical EGRET flux and that
there could be GeV flaring due to early external Comptonization.
The effect of an optical depth due to the IIRB on the spectra of 3C 66A was also
evaluated and was found to be insignificant in the energy range we are interested in as
shown in Figure 3. The optical depth due to the IIRB was determined using the analytic
expression given in Stecker et al. (2006). The γ − γ absorption till ∼ 100 GeV is negligible
and becomes slightly observable at ∼ 200 GeV as the optical depth takes a value of, τγγ ≈
2.9. Hence, the SSC emission cutoff value at ∼ 4 GeV is intrinsic.
– 17 –
0.61 0.71 0.81 0.91
νFν [Jy Hz]
0.09 0.29 0.49 0.69 0.89
0.55 0.65 0.75 0.85 0.95
1 keV
10 keV
Fig. 7.— Simulated spectral hysteresis pattern in the R-band, 1 keV and 10 keV energy
regimes, shown in the three panels respectively. As can be seen, the hysteresis pattern starts
to show up in the 10 keV energy regime.
– 18 –
0.45 0.55 0.65 0.75 0.85 0.95
νFν [Jy Hz]
0.15 0.35 0.55 0.75 0.95
0.02 0.22 0.42 0.62 0.82
α 10 GeV
1 MeV
100 MeV
Fig. 8.— Simulated hysteresis pattern for 1 MeV, 100 MeV and 10 GeV energy regimes,
shown in the three panels repectively. The hysteresis pattern is prominent for the 1 MeV
energy regime but starts to become absent at higher energies.
– 19 –
ν [Hz]
Oct. 1
Nov. 1
Nov. 11
Dec. 28
STACEE
Whipple
(99 % UL)RXTE 2003
XMM−Newton
ROSAT
EXOSAT
EGRET
BeppoSAX
1999/2001
EINSTEIN
1979/1980
STACEE (99 % UL, Γ = 2.5)
(99 % UL, Γ = 3.0)
STACEE
(99 % UL)
Fig. 9.— Simulation of the effect of the BLR on the instantaneous spectral energy distri-
bution of 3C 66A for the first 3 days of a simulation similar to Figure 2. The curves in the
figure denote the instantaneous spectra obtained from the simulation. The gray (red in the
online version) solid line denotes one of the initial instantaneous spectrum at the beginning
of the simulation whereas the black long-dashed line indicates the last spectrum obtained
from the simulation.
– 20 –
5. Summary
An extensive analysis of the data of 3C 66A, obtained from the multiwavelength mon-
itoring campaign on 3C 66A from July 2003 to April 2004, was carried out using a time-
dependent leptonic jet model. The analysis was targeted towards understanding the dom-
inant radiation mechanism in the production of the high-energy component of the SED of
3C 66A in the quiescent as well as the flaring state. Our simulations yielded predictions
regarding the observable variability patterns in the X-ray as well as the VHE energy regimes
where such patterns could not be detected during the campaign. The object was well sam-
pled in the optical, especially in the R-band, during the campaign. It had exhibited several
major outbursts (∼10 days) in this regime with a varibility of ∆m ∼ 0.3-0.5. The X-ray
data covered the 3-10 keV range with the onset of the high-energy component expected at
≥ 10 keV photon energies. Only upper limits in the VHE regime had been obtained.
The simulations from our model could successfully reproduce the observed SED as well
as the optical spectral variability patterns. The model suggests the dominance of the SSC
mechanism in the production of hard X-ray as well as VHE photons. On the other hand, soft
X-ray photons exhibit spectral softening during flaring indicating the onset of the synchrotron
component in this energy range. According to the simulated time-averaged spectrum, the
synchrotron component is expected to cut off near 7 keV whereas the SSC component cuts
off at ∼ 4 GeV.
A flaring profile that was Gaussian in time could successfully reproduce the observed
flaring profile for a timescale of ∼ 10 days. The simulated varibility in R (∆m ∼ 0.55) agreed
well with the observed variability. According to the simulations, the object flares up in R
and B simultaneoulsy with τ obscool,syn (37 minutes) being less than or equal to the light crossing
time (2 hours) during flaring. No significant variability is predicted in the hard X-ray regime.
This is due to the production of such photons from Compton upscattering off low-energy
electrons with cooling timescales much longer than the light crossing time, 3Rb/4c. On the
other hand, the simulated lightcurves of VHE γ-ray photons exhibit significant variability as
such photons are produced from the Compton upscattering off higher energy electrons with
shorter cooling timescales than the light crossing time.
The effect of the optical depth due to γ − γ absorption by the IIBR on the SED of
3C 66A was also evaluated. The simulations do not predict a significant effect on the SED
due to the optical depth. The SSC emission cutoff predicted to be at ∼ 4 GeV can be
taken as the intrinsic SSC emission cutoff value for this object. We predict the object to
be well within the observational range of MAGIC, VERITAS and GLAST. Finally, the EC
emission for this object was also calculated and it appears that the EC emission could be
dominant in the high-energy component initially, but as the emission region travels further
– 21 –
away from the BLR, the EC contribution becomes less significant and the SSC emission
takes over. It is highly probable that this maximum contribution of the EC component
might explain the historical EGRET flux and that there could be GeV flaring due to early
external Comptonization.
This work was partially supported through NRL BAA 76-03-01, contract no. N00173-
05-P-2004.
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Böttcher, M., & Chiang, J., 2002, ApJ, 581, 127
Böttcher, M., Mause, H., & Schlickeiser, R., 1997, A&A, 324, 395
Bramel, D. A., et al., 2005, ApJ, 629, 108
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Li, H., & Kusunose, M., 2000, ApJ, 536, 729
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This preprint was prepared with the AAS LATEX macros v5.2.
– 23 –
Table 1. Model Parameters used to reproduce the quiescent and flaring state of 3C 66A as
shown in Figures 1 and 2, respectively. Note: Linj is the luminosity with which electron
population is injected into the blob. γ1,2 are the low- and high-energy cutoffs of electron
injection spectrum and q is the particle spectral index. Profile stands for the flare profile
used to reproduce the optical variability pattern, eB is the equipartition parameter and
magnetic field B is the equipartition value. Γ is the bulk Lorentz factor, Rb is the comoving
radius of the blob, θobs is the viewing angle and τT,BLR is the radial Thomson depth of the
Fit Linj [10
41 ergs/s] γ1 [10
3] γ2 [10
4] q Profile eB B [G] Γ Rb [10
15 cm] θobs [deg] τT,BLR
1 2.7 1.8 3.0 3.1 ——– 1 2.4 24 3.59 2.4 0
2 8.0 2.1 4.5 2.4 Gaussian 1 2.8 24 3.59 2.4 0
3 8.0 2.1 4.5 2.4 Gaussian 1 2.8 24 3.59 2.4 0.3
	Introduction
	Model Description
	Model Parameters
	Results and Discussion
	Summary

  The BL Lac object 3C 66A was observed in an extensive multiwavelength
monitoring campaign from July 2003 till April 2004. The spectral energy
distribution (SED) was measured over the entire electromagnetic spectrum, with
flux measurements from radio to X-ray frequencies and upper limits in the very
high energy (VHE) gamma-ray regime. Here, we use a time-dependent leptonic jet
model to reproduce the SED and optical spectral variability observed during our
multiwavelength campaign. Our model simulations could successfully reproduce
the observed SED and optical light curves and predict an intrinsic cutoff value
for the VHE gamma-ray emission at ~ 4 GeV. The effect of the optical depth due
to the intergalactic infrared background radiation (IIBR) on the peak of the
high-energy component of 3C 66A was found to be negligible. Also, the presence
of a broad line region (BLR) in the case of 3C 66A may play an important role
in the emission of gamma-ray photons when the emission region is very close to
the central engine, but further out, the production mechanism of hard X-ray and
gamma-ray photons becomes rapidly dominated by synchrotron self-Compton
emission. We further discuss the possibility of an observable X-ray spectral
variability pattern. The simulated results do not predict observable hysteresis
patterns in the optical or soft X-ray regimes for major flares on multi-day
time scales.

Introduction
Blazars are the most extreme class of Active Galactic Nuclei (AGN) exhibiting rapid
variability at all wavelengths and a high degree of linear polarization in the optical. They
have been observed at all wavelengths, from radio through VHE γ-rays and are characterized
by non-thermal continuum spectra and radio jets with individual components often exhibit-
ing apparent superluminal motion. This class of AGNs is comprised of BL Lac objects and
flat-spectrum radio quasars (FSRQs), which are distinguished primarily on the basis of the
absence or presence of broad emission lines in their optical spectra.
The broadband spectra of blazars are associated with non-thermal emission and exhibit
two broad spectral components. The low energy component is due to synchrotron emis-
sion from non-thermal electrons in a relativistic jet whereas the high energy component is
attributed either to the Compton upscattering of low energy radiation by the synchrotron
emitting electrons (for a recent review see, e.g., Böttcher (2006)) or the hadronic processes
initiated by relativistic protons co-accelerated with the electrons (Mücke & Protheroe 2001;
Mücke et al. 2003) . Blazars are often known to exhibit variability at all wavelengths, vary-
ing on time scales from months, to a few days, to even less than an hour in some cases.
The radio emission of blazars shows variability on a time scale of weeks to months whereas
the optical emission for some blazars might vary on a time scale of around one and a half
hours. At X-ray energies, some HBLs exhibit characteristic loop features when the pho-
ton energy spectral index, α, is plotted against the X-ray flux. These plots are known as
hardness-intensity diagrams (HIDs) and the loop structures are called spectral hysteresis.
This spectral hysteresis can be interpreted as the signature of synchrotron radiation, due to
the gradual injection and/or acceleration of ultrarelativistic electrons in the emitting region
and their subsequent radiative cooling (Kirk et al. 1998; Georganopoulos & Marscher 1998;
Kataoka et al. 2000; Kusunose et al. 2000; Li & Kusunose 2000; Böttcher & Chiang 2002).
3C 66A is classified as a low-frequency peaked (or radio selected) BL Lac object (LBL).
The peak of the low-frequency component of LBLs generally lie in the IR or optical regime,
whereas the high-energy component peak is located at several GeV, and the γ-ray output
is typically comparable to or slightly higher than the spectral output of the synchrotron
component. The redshift of 3C 66A has a relatively uncertain determination of z = 0.444
(Bramel et al. 2005). It has exhibited rapid microvariability at optical and near infrared
in the past and has been suggested as a promising candidate for detection by the new
generation of atmospheric Čerenkov telescope facilities like H.E.S.S., MAGIC, or VERITAS
(Costamante & Ghisellini 2002). This object has been studied in radio, IR, optical, X-rays
and γ-rays in the past. Its low-frequency component is known to peak in the IR - UV regime
whereas the high-frequency component generally peaks at multi MeV - GeV energies. The
– 3 –
multiwavelength SED and correlated broadband spectral variability behaviour of 3C 66A
have been very poorly understood. For this reason, Böttcher et al. (2005) organized an
intensive multiwavelength campaign to observe this object from July 2003 through April
2004, with the core campaign period being Sept. - Dec. 2003.
As described in Böttcher et al. (2005), the object exhibited several outbursts in the
optical. The variation was on the order of ∆m ∼ 0.3-0.5 over a timescale of several days.
The minimum variability timsecale of 2 hr provided an estimate for the size of the emitting
region to be on the order of 1015 cm. The optical flares suggested the presence of an optical
spectral hysteresis pattern with the B - R hardness peaking several days before the R- and B-
band flux peaked. The RXTE PCA data indicated a transition between the synchrotron and
the high-energy component at photon energies of & 10 keV. The broadband SED of 3C 66A
suggested that the synchrotron component peaked in the optical. In the VHE γ-ray regime,
STACEE provided an upper limit at Eγ & 150 GeV whereas an upper limit at Eγ > 390 GeV
resulted from simultaneous Whipple observations.
In this paper, we use a leptonic jet model to reproduce the broadband SED and the
observed optical spectral variability patterns of 3C 66A and make predictions regarding
observable X-ray spectral variability patterns and γ-ray emission. In §2, we describe the
time-dependent leptonic jet model used to reproduce the observed SED and optical spectral
variability patterns of 3C 66A. The parameters used to simulate the observed results are
described in §3. The modeling results and VHE γ-ray predictions are discussed in §4. We
summarize in §5.
Throughout this paper, we refer to α as the energy spectral index, Fν [Jy] ∝ ν
−α. A
cosmology with Ωm = 0.3, ΩΛ = 0.7, and H0 = 70 km s
−1 Mpc−1 is used. In this cosmology,
and using the redshift of z = 0.444, the luminosity distance of 3C 66A is dL = 2.46 Gpc.
2. Model Description
The SEDs and optical variability patterns of 3C 66A were modeled using a one-zone
homogeneous leptonic jet model. The model assumes injection of a population of ultrarel-
ativistic non-thermal electrons and positrons into a spherical emitting volume (the “blob”)
of comoving radius Rb at a time-dependent rate. Since the positrons lose equal amount of
energy as the electrons via the same radiative loss mechanisms so we do not distinguish
between them throughout the paper. The injected electron population is described by a
single power law distribution with a particle spectral index q, comoving injection density
Qinje (γ; t) (cm
−3s−1) and low- and high-energy cutoffs γ1 and γ2, respectively, such that
– 4 –
Qinje (γ) = Q
0 (t)γ
−q for γ1 ≤ γ ≤ γ2, where Q
0 (t) is the injection function and is given by,
0 (t) =
Linj(t)
if q 6= 2
Linj(t)
mec2ln(γ2/γ1)
if q = 2
where Linj specifies the power of the injected pair population and V
b is the blob volume
in the comoving frame.
The randomly oriented magnetic field B has uniform strength throughout the blob and
is determined by an equipartition parameter eB ≡ uB/ue (in the comoving frame), where
uB is the magnetic field energy density and ue is the electron energy density. We keep eB
constant so that the magnetic field value changes according to the evolving electron energy
density value as determined by equation 2. The initial injection of the electron population
into the blob takes place at a height z0 above the plane of the central accretion disk. The
emitting region travels relativistically with a speed v/c = βΓ = (1 − 1/Γ
2)1/2 along the jet.
The jet is directed at an angle θobs with respect to the line of sight. The Doppler boosting of
the emission region with respect to the observer’s frame is determined by the Doppler factor
δ = [Γ(1− βΓ cos θobs)]
−1, where Γ is the bulk Lorentz factor.
As the emission region propagates in the jet, the electron population inside the blob
continuously loses its energy due to synchrotron emission, Compton upscattering of syn-
chrotron photons (SSC) and/or Compton upscattering of external photons (EC). The seed
photons for the EC process include the UV soft X-ray emission from the disk entering the jet
either directly (Dermer et al. 1992; Dermer & Schlickeiser 1993) or after getting reprocessed
in the BLR or other circumnuclear material (Sikora et al., 1994; Dermer et al. 1997). The
time-dependent evolution of the electron and photon population inside the emission region
is governed, respectively, by,
∂ne(γ, t)
ne(γ, t)
+Qe(γ, t)−
ne(γ, t)
te,esc
∂nph(ǫ, t)
= ṅph,em(ǫ, t)− ṅph,abs(ǫ, t)−
nph(ǫ, t)
tph,esc
Here, (dγ/dt)loss is the radiative energy loss rate, due to synchrotron, SSC and/or EC
emission, for the electrons. Qe(γ, t) is the sum of external injection and intrinsic γ − γ pair
– 5 –
production rate and te,esc is the electron escape time scale. ṅph,em(ǫ, t) and ṅph,abs(ǫ, t) are the
photon emission and absorption rates corresponding to the electrons’ radiative losses and,
tph,esc = (3/4)Rb/c is the photon escape timescale. The time-dependent evolution of the
electron and photon population inside the blob is followed and radiative energy loss rates as
well as photon emissivities are calculated using the time-dependent radiation transfer code
of Böttcher & Chiang (2002).
The model only follows the evolution of the emission region out to sub-pc scales and
as a result only the early phase of γ-ray production can be simulated. Since the radiative
cooling is strongly dominant over adiabatic cooling during this phase and the emission region
is highly optically thick out to GHz radio frequencies, the simulated radio flux is well below
the actual radio data. We do not simulate the phase of the jet components in which they
are expected to gradually become transparent to radio frequencies as that would require the
introduction of several additional, poorly constrained parameters.
3. Model Parameters
The model independent parameters that were estimated using the SED and optical
intraday variability measurements (see Böttcher et al. 2005) were used to develop an initial
set of input parameters:
δ ≈ 15
R ≈ 3.3× 1015 cm
B ≈ 2.9 ǫ
γ1 ≈ 3.1× 10
γ2 ≈ 1.5× 10
p ≈ 4 (4)
Here p is the equilibrium spectral index that determines the optical synchrotron spec-
trum and p = q+1 for strongly cooled electrons. The initial set of parameters was modified
to reproduce the quiescent as well as the flaring state of 3C 66A. Approximately 350 sim-
ulations were carried out to study the effects of variations of various parameters, such as
γ1, γ2, q, B and Γ, on the resulting broadband spectra and light curves. The set of model
parameters that provided a satisfactory fit to the quiescent state of 3C 66A involved a value
of the Doppler factor, δ = Γ = 24 and a viewing angle of θobs = 2.4
o. These parameters
were chosen on the basis of VLBA observations that provided the limits on the superluminal
motion and indicated bending of the jet towards the line of sight thus resulting in a smaller
– 6 –
viewing angle and a higher Doppler boosting of the emission region as compared to the
values inferred from the superluminal measurements on larger scales (Jorstad et al. 2005;
Böttcher et al. 2005). The fitting of the SED both in the quiescent as well as flaring state
of 3C 66A was carried out such that the simulated quiescent state does not overpredict the
X-ray photon flux as X-ray photons are expected to be dominated by the flaring episodes.
On the other hand, the flaring state was simulated such that the resulting time-averaged
spectrum passes through the observed time-averaged optical as well as X-ray data points.
This was achieved by varying individual parameters, such as, γ1, γ2 and q between the values
for quiescent and flaring states with time profiles as discussed in the next section. A value
of γ1 = 2.1× 10
3, γ2 = 4.5× 10
4 and q = 2.4 provided a satisfactory fit to the flaring state.
Also, during our multiwavelength campaign of 2003 - 2004, flux upper limits at multi-GeV -
TeV energies could be obtained and as a result we could get upper limits on the respective
parameters governing the EC component. The various model parameters used to simulate
the two states of 3C 66A are listed in Table 1.
Figures 1 and 2 respectively show the reproduction of the SED of 3C 66A, for both the
quiescent and flaring state observed during the campaign period. The quiescent state is a
reproduction of the state observed around 1st October 2003 whereas the flaring state is the
reproduction of a generic 10 day flaring period corresponding to the timescale of several of
the major outbursts that were observed during the campaign. The simulated time-averaged
spectrum of 3C 66A in the flaring state is shown in Figure 3. The simulations, corresponding
to fits 1 and 2 of Table 1, were carried out for a pure SSC emission process by artificially
setting LD = 0, where LD is the bolometric disk luminosity. Fit 3 of Table 1 refers to an
EC+SSC case with LD = 1.0× 10
45 ergs s−1 and is shown in Figure 9. The value of LD was
chosen such that it is more than the value of the jet luminosity used in the simulations and
at the same time does not produce a blue bump in the simulated SED. In order to assess
the possible effect of EC emission in 3C66A, an upper limit to the optical depth of the BLR
was first determined using XSTAR, which returns the ionization balance and temperature,
opacity, and emitted line (Hα, Hβ) and continuum fluxes. The BLR was modeled as a
spherical shell with rBLR,in = 0.045 pc and rBLR,out = 0.050 pc, where rBLR,in and rBLR,out
stand for the inner and outer radii of the broad line region. A Thomson optical depth of
0.3 for the BLR was chosen as a reasonable upper limit such that the line emission is weak
enough or absent to be consistent with the observed featureless continuum.
– 7 –
ν [Hz]
Oct. 1
Nov. 1
Nov. 11
Dec. 28
STACEE
Whipple
(99 % UL)RXTE 2003
XMM−Newton
ROSAT
EXOSAT
EGRET
BeppoSAX
1999/2001
EINSTEIN
1979/1980
STACEE (99 % UL, Γ = 2.5)
(99 % UL, Γ = 3.0)
STACEE
(99 % UL)
Fig. 1.— Reproduction of the quiescent state of 3C 66A observed around October 1st 2003.
The simulation of this state was carried out using parameters that do not overpredict the X-
ray photon flux. The black colored solid line indicates the instantaneous spectrum generated
by the simulation after the system (blob + injected electron population) attains equilibrium.
The low-energy component peaks in the optical at νsyn ≈ 4.8 × 10
14 Hz whereas the high-
energy SSC component peaks in the MeV regime at νSSC ≈ 1.6× 10
21 Hz. The synchrotron
cooling timescale in the observer’s frame is ≈ 1.2 hours, which is on the order of observed
minimum optical variability timescale of 2 hours. The diamond shaped STACEE upper
limit is a new addition and is provided by Lindner (2006). All data that are indicated by
dotted curves are archival data and are shown for comparison. The historical average of the
5 EGRET pointings is also included to provide a guideline for our simulated VHE emission.
– 8 –
ν [Hz]
Oct. 1
Nov. 1
Nov. 11
Dec. 28
STACEE
Whipple
(99 % UL)
RXTE 2003
XMM−Newton
ROSAT
EXOSAT
EGRET
BeppoSAX
1999/2001
EINSTEIN
1979/1980
STACEE (99 % UL, Γ = 2.5)
(99 % UL, Γ = 3.0)
STACEE
(99 % UL)
Fig. 2.— Simulation of the flaring state for a generic 10 day flare corresponding to the
timescale of several major outbursts that were observed in the optical regime during our
campaign. The various curves show the instantaneous spectral energy distribution of 3C 66A
at several different times in the observer’s frame: black (red in the online version) dotted
line (∼ 5th hour), gray (green) dashed line (∼ 8th hour), black (blue) dot-dashed line (∼
14th hour), gray (yellow) long-dashed line (∼ 20th hour), long-dashed black line (∼ 8th day,
highest state attained by the system during flaring), gray solid line (∼ 9th day), dotted black
(violet) line (∼ 16th day), gray (cyan) colored solid line (∼ 18th day), dashed black (magenta)
colored line (∼ 20th day) and black (red) solid line (∼ 22nd day, equilibrium state reached
by the system after the flaring episode is over). The synchrotron component of the flaring
state peaks at νsyn ≈ 1.1× 10
15 Hz and the SSC component peaks at νSSC ≈ 2.7× 10
22 Hz.
The SSC component of this state cuts off at νSSC,cutoff ≈ 2.3 × 10
24 Hz. The synchrotron
cooling timescale in the optical regime is ≈ 37 minutes for the flaring state.
– 9 –
4. Results and Discussion
As can be seen in Figure 3, the time-averaged simulated spectrum passes through the
time-averaged optical data points whereas the high energy end of the synchrotron compo-
nent passes through the time averaged X-ray data indicating the dominance of synchrotron
emission in the production of such photons in case of flaring. For X-ray photons with energy
beyond 10-12 keV, the data is less reliable due to low count rates and possible source con-
fusion with 3C 66B. The spectral upturn at ≥ 7 keV occurs due to the presence of the SSC
component in the simulation. The presence of this component cannot be suppressed because
in order to suppress it the population of seed photons would have to be diluted, which can
be done by increasing the size of the emission region. But the size of the emission region
cannot be increased any further due to the strict constraint on the maximum size of the blob
that comes from the observed minimum variability timescale in the optical region, which
is 2 hrs. Hence, the emission region size cannot exceed 3.6 × 1015 (D/24) cm. Thus, our
model suggests that the harder X-ray photons come from the SSC and not the synchrotron
mechanism with the expected spectral hardening taking place at ∼ 7 keV. The high energy
component, due to the SSC emission, for the time-averaged spectrum (see Figure 3) cuts off
at ∼ 1.0× 1024 Hz or 4 GeV. From the simulated level of VHE emission we predict that the
object is well within the observational range of MAGIC, VERITAS and, especially, GLAST
(see Figure 3) whose sensitivity limit is 50 times lower than that of EGRET at 100 MeV
and even more at higher energies and its two year limit for source detection in an all-sky
survey is 1.6 × 10−9 photons cm−2 s−1 (at energies > 100 MeV). Thus it will be possible
to extract the spectral and variability information for this object at such high energies in
future observations.
Flaring above the quiescent state of 3C 66A was reproduced using a flaring profile for
the electron injection power (Linj(t)) that was Gaussian in time (see Figure 4):
Linj(t) = L
inj(t) +
(Lflinj − L
(z−rc)2
] (5)
Here, qu and fl stand for the quiescent and flaring state respectively, z determines the
position of the emission region in the jet at time t, rc indicates the position of the center of
the simulated flare and σ stands for the Gaussian width of the flare.
The rest of the parameters such as γ1 and γ2 and q were also changed accordingly.
In order to simulate the observed optical flare, the system was first allowed to come to an
equilibrium and after the equilibrium was set up the flare was introduced with a Gaussian
width, σ corresponding to 14 days in the observer’s frame. Although the flare was introduced
– 10 –
ν [Hz]
VERITAS
STACEE
Whipple
(99 % UL)
RXTE 2003
XMM−Newton
ROSAT
EXOSAT
EGRET
BeppoSAX
1999/2001
EINSTEIN
1979/1980
STACEE (99 % UL, Γ = 2.5)
(99 % UL, Γ = 3.0)
GLAST
MAGIC
(Large ZA)
STACEE
(99 % UL)
Fig. 3.— Time-averaged spectral energy distribution of 3C 66A for a period of 23 days
around a flare as shown in Figure 2. The filled black (colored in the online version) circles
are the time-averaged optical and IR data points for the entire campaign period and the
“RXTE 2003” denotes the time-averaged X-ray data points. The dot-dashed black line
is the contribution from the synchrotron component only whereas the long-dashed black
line indicates the contribution of the SSC component only. The time-averaged synchrotron
component peaks at νsyn ≈ 7.2× 10
14 Hz whereas the time-averaged SSC component peaks
at νSSC ≈ 5.3 × 10
21 Hz. The synchrotron component cuts off near 7 keV whereas the SSC
component cuts off at ∼ 4 GeV. The black colored dashed line indicates the attenuation due
to the optical depth at VHE energies. The γγ absorption effect becomes significant at ∼
200 GeV. The black (green, maroon and magenta) lines indicate the sensitivity limits for an
observation time of 50 hours for MAGIC, VERITAS and MAGIC (Large Zenith Angle) and
for GLAST for an observation time of 1 month.
– 11 –
in order to simulate the observed major optical outbursts lasting for 10 days, the choice of
14 days for the Gaussian width was made such that the width of the simulated flare matches
that of the observed flare, rc was adjusted such that the centre of the simulated flare aligns
with that of the observed one and the value of Linj was varied such that the peak of the
simulated flare matches that of the observed one.
The observed lightcurves did not agree well with a flaring profile that was top-hat or
triangular in time as can be seen in the figure. The presence of a flare that is Gaussian in
time might represent an initial injection of particles into the emission region at the base of
the jet. The particles slowly get accelerated as a shock wave ploughs through the region
and finally dies out in time. Crucial information on the dominant acceleration mechanism
comes from the change in the shape of the particle injection spectral index with time, which
might also indicate a possible change in the B-field orientation. According to the current
understanding of acceleration mechanisms, parallel shocks generally produce electron spectra
of Qe(γ) ∝ γ
−q with 2.2 . q . 2.3 (Achterberg et al. 2001; Galant et al. 1999), whereas
oblique shocks produce much softer injection spectral indices. On the other hand, 2nd order
Fermi acceleration behind the shock front might give rise to a harder injection index of the
order of q ∼ 1 or beyond (Virtanen & Vainio 2005). In order to reproduce the flaring state,
the simulation first starts out in the quiescent state with quiescent state parameters and
then the value of these parameters is changed to the flaring state parameters as the flaring
is introduced in the simulation. Since, the value of q, in our simulations, changes from 3.1
(quiescent state) to 2.4 (flaring state) it might indicate a possible change in the orientation
of the B-field from oblique to parallel during the flaring episode or an interplay between
the 1st and 2nd order Fermi acceleration thereby making the particle spectra harder. The
contribution from such acceleration mechanisms and the shear acceleration (Rieger & Duffy
2004) might play an important role in accelerating the particles to higher energies.
The simulated optical variability in the R band (0.55 mag) matches the observed value
(0.3-0.5 mag) for a 10 day period outburst. The predicted variability in B is more than
that of R by ∼ 0.15 mag as also observed, which indicates that the spectrum is becoming
harder (see Figure 5) with the spectral upturn occuring at B-R ≈ 0.72 mag as shown in
Figure 6. Figure 6 is a hardness intensity graph that shows that the object follows a positive
correlation of becoming harder in B-R while getting brighter in both the bands during the
10-day flare simulated in Figure 2. This agrees well with the observed optical variability
pattern. In this study, we are not addressing the variability that was observed on intraday
timescales as that analysis would open up an even larger parameter space, which cannot be
reasonably well constrained without any variability information in the X-ray regime.
The flare declines faster as compared to the time taken by the flare to rise. This might
– 12 –
2940 2945 2950
JD - 2450000
Fig. 4.— The simulated lightcurves for various flaring profiles that have been superimposed
on the observed R-band lightcurve (see Figure 7 of Böttcher et al. (2005)) for an outburst on
∼ November 1st 2003. The solid black line denotes a flaring profile that is Gaussian in time
as used for the flare in Figure 2, the dash-dotted black line is a trianglular flaring profile
whereas the dashed black line is a flaring profile that is top-hat in time. As can be seen, the
Gaussian flaring profile closely matches the width as well as the profile of the observed flare.
– 13 –
0.0e+00 2.0e+05 4.0e+05 6.0e+05 8.0e+05 1.0e+06 1.2e+06
time (sec)
2e+12
3e+12
4e+12
5e+12
0.0e+00
5.0e+11
1.0e+12
1.5e+12
1 keV
10 keV
15 keV
3 keV
0e+00
2e+12
4e+12
6e+12
1 MeV
100 MeV
10 GeV
∆R ~ 0.55 mag
Fig. 5.— Simulated lightcurves for the optical, X-rays and γ-ray energy regimes shown in
the three panels respectively. The simulated variability in the R band is ≈ 0.55 mag as
indicated by the arrows. The B band, denoted by the black dotted line exhibits a higher
variability of ≈ 0.7 mag, in the simulation, than that in the R band, which is consistent
with our observations. The simulated lightcurve at 1 keV is indicated by a black dashed
curve and exhibits an amplitude variation of ≈ 1.4 × 1012 Jy Hz. The 3, 10 and 15 keV
lightcurves, denoted by the black solid line, black long-dashed line and the black dot-dashed
curve, respectively, on the other hand do not exhibit much variability. In the VHE regime,
the 1 MeV lightcurve is denoted by a black solid line. The 100 MeV lightcurve is indicated
by a black long-dashed curve and the simulated variability amplitude in this energy regime
is on the order of 1012 Jy Hz. The black dot-dashed line indicates the lightcurve at 10 GeV.
– 14 –
13.6013.7013.8013.9014.0014.10
R magnitude
0.640
0.660
0.680
0.700
0.720
0.740
0.760
0.780
Fig. 6.— The simulated hardness-intensity diagram indicates a positive correlation between
R- and B-band for an outburst lasting for ∼ 10 days. The object becomes brighter in R and
harder in B-R as shown by the arrows. The spectral upturn takes place at B-R ≈ 0.72 mag
where the flux in B equals that in R (corresponding to αBR = 0).
– 15 –
indicate that the particles’ synchrotron cooling timescale is less than or equal to the light
crossing time.
τ obscool,sy ≈ 2.8× 10
−1/2 (
15 s (6)
We can calculate the observed synchrotron cooling timescale, τ obscool,syn in the optical
regime from equation 6 (Böttcher et al. 2005) using δ = 24, B = 2.4 G and ν15 = 0.48 for
the quiescent state and B = 2.8 G and ν15 = 1.1 for the flaring state (see Figures 1 and
2), where ν15 is the characteristic synchrotron frequency in units of 10
15 Hz. This yields a
value of τ obscool,sy ∼ 1.2 hours for the quiescent state whereas for the flaring state it reduces
to 37 minutes. The observed minimum variability timescale of ∼ 2 hours might therefore
correspond to the observed dynamical timescale, where
τ obsdyn ≈
1 + z
. (7)
This implies that it takes time to build up the electron population in the emission
region through flaring but once built up the electrons lose their energy efficiently to produce
synchrotron photons. This can be used to constrain the value of the magnetic field in the
jet, which has been allowed to evolve in time keeping eB = 1 and has an average value of 2.4
Gauss in the simulated quiescent state and 2.8 Gauss in the simulated flaring period.
The crossover of X-ray lightcurves, in our simulations, is a result of the dominance of
the SSC component in hard X-rays (see Figure 5). The lightcurve of soft X-ray photons of
energy 1 keV exhibits a greater variability of ∼ 1.4 × 1012 Jy Hz in its flux as compared
to their optical counterpart. This is expected because the soft X-ray photons, during the
flaring episode, are produced from synchrotron emission of electrons that are accelerated
to very high energies and as a result have a very short cooling timescale and thus greater
variability. In case of hard X-rays no significant variability is predicted. This is because such
photons are produced from Compton upscattering of synchrotron photons off the low-energy
electrons and as a result the cooling timescale is much longer as compared to the cooling
timescale of their soft X-ray and optical counterparts. Hence, the variability information
gets washed out. The predicted X-ray spectral variability pattern of large variability in the
low X-ray energy band and negligible variability in the high X-ray energy band is similar to
what has also been observed in BL Lacertae on several occasions (see for e.g., Ravasio et al.
2003, 2002).
As can be seen in Figure 7, spectral hysteresis patterns are not predicted for optical as
– 16 –
well as soft X-ray photons. This is expected because the cooling timescale of their parent
electron population is so short that what is observed is the average effect of this cooling
over the dynamical timescale and hence any hysteresis pattern gets smeared out. On the
other hand, one expects to see these patterns at higher energies because as explained earlier,
this photon population comes from Compton upscattering off low-energy electrons, which
have a longer cooling timescale and as a result the photon population gradually builds up
over time and then dies away giving rise to a hysteresis pattern (see Figure 8). The slight
spectral softening at 10 keV seen in its hysteresis pattern (see Figure 7) for higher values of
νFν indicates a small synchrotron contribution near the peak of the flare.
The simulated instantaneous SED, for a pure SSC model, shows a definite presence of
γ-ray emission in 3C66A, in the quiescent as well as the flaring state (see Figure 1 and 2).
The intrinsic cutoff of VHE emission in the flaring state, according to the simulations, for
the time averaged spectrum is ∼ 1.0 × 1024 Hz or 4 GeV. In our simulations, the emission
of VHE γ-ray photons is produced by the SSC mechanism in the quiescent as well as the
flaring state. Figure 5 shows the simulated lightcurves for VHE photons and as can be seen
the νFν value changes by ∼ 4.17×10
12 Jy Hz at 100 MeV. The variability in VHE photons is
expected as they are the result of Compton upscattering off the higher energy electrons and
due to this the hysteresis pattern is not seen at such high energies as the cooling timescale
of such high energy electrons is very short (see Figure 8).
From Figure 9, it can be seen that the high-energy component of 3C 66A, in the flaring
state, could start out with a dominant contribution of the EC emission, shown by the red
solid line. But as the blob travels further away and passes the outer edge of the broad line
region, the EC contribution becomes less significant and the SSC emission takes over. This
is indicated by the black long-dashed line in the figure. We might actually find that this
maximum contribution would be just enough to explain the historical EGRET flux and that
there could be GeV flaring due to early external Comptonization.
The effect of an optical depth due to the IIRB on the spectra of 3C 66A was also
evaluated and was found to be insignificant in the energy range we are interested in as
shown in Figure 3. The optical depth due to the IIRB was determined using the analytic
expression given in Stecker et al. (2006). The γ − γ absorption till ∼ 100 GeV is negligible
and becomes slightly observable at ∼ 200 GeV as the optical depth takes a value of, τγγ ≈
2.9. Hence, the SSC emission cutoff value at ∼ 4 GeV is intrinsic.
– 17 –
0.61 0.71 0.81 0.91
νFν [Jy Hz]
0.09 0.29 0.49 0.69 0.89
0.55 0.65 0.75 0.85 0.95
1 keV
10 keV
Fig. 7.— Simulated spectral hysteresis pattern in the R-band, 1 keV and 10 keV energy
regimes, shown in the three panels respectively. As can be seen, the hysteresis pattern starts
to show up in the 10 keV energy regime.
– 18 –
0.45 0.55 0.65 0.75 0.85 0.95
νFν [Jy Hz]
0.15 0.35 0.55 0.75 0.95
0.02 0.22 0.42 0.62 0.82
α 10 GeV
1 MeV
100 MeV
Fig. 8.— Simulated hysteresis pattern for 1 MeV, 100 MeV and 10 GeV energy regimes,
shown in the three panels repectively. The hysteresis pattern is prominent for the 1 MeV
energy regime but starts to become absent at higher energies.
– 19 –
ν [Hz]
Oct. 1
Nov. 1
Nov. 11
Dec. 28
STACEE
Whipple
(99 % UL)RXTE 2003
XMM−Newton
ROSAT
EXOSAT
EGRET
BeppoSAX
1999/2001
EINSTEIN
1979/1980
STACEE (99 % UL, Γ = 2.5)
(99 % UL, Γ = 3.0)
STACEE
(99 % UL)
Fig. 9.— Simulation of the effect of the BLR on the instantaneous spectral energy distri-
bution of 3C 66A for the first 3 days of a simulation similar to Figure 2. The curves in the
figure denote the instantaneous spectra obtained from the simulation. The gray (red in the
online version) solid line denotes one of the initial instantaneous spectrum at the beginning
of the simulation whereas the black long-dashed line indicates the last spectrum obtained
from the simulation.
– 20 –
5. Summary
An extensive analysis of the data of 3C 66A, obtained from the multiwavelength mon-
itoring campaign on 3C 66A from July 2003 to April 2004, was carried out using a time-
dependent leptonic jet model. The analysis was targeted towards understanding the dom-
inant radiation mechanism in the production of the high-energy component of the SED of
3C 66A in the quiescent as well as the flaring state. Our simulations yielded predictions
regarding the observable variability patterns in the X-ray as well as the VHE energy regimes
where such patterns could not be detected during the campaign. The object was well sam-
pled in the optical, especially in the R-band, during the campaign. It had exhibited several
major outbursts (∼10 days) in this regime with a varibility of ∆m ∼ 0.3-0.5. The X-ray
data covered the 3-10 keV range with the onset of the high-energy component expected at
≥ 10 keV photon energies. Only upper limits in the VHE regime had been obtained.
The simulations from our model could successfully reproduce the observed SED as well
as the optical spectral variability patterns. The model suggests the dominance of the SSC
mechanism in the production of hard X-ray as well as VHE photons. On the other hand, soft
X-ray photons exhibit spectral softening during flaring indicating the onset of the synchrotron
component in this energy range. According to the simulated time-averaged spectrum, the
synchrotron component is expected to cut off near 7 keV whereas the SSC component cuts
off at ∼ 4 GeV.
A flaring profile that was Gaussian in time could successfully reproduce the observed
flaring profile for a timescale of ∼ 10 days. The simulated varibility in R (∆m ∼ 0.55) agreed
well with the observed variability. According to the simulations, the object flares up in R
and B simultaneoulsy with τ obscool,syn (37 minutes) being less than or equal to the light crossing
time (2 hours) during flaring. No significant variability is predicted in the hard X-ray regime.
This is due to the production of such photons from Compton upscattering off low-energy
electrons with cooling timescales much longer than the light crossing time, 3Rb/4c. On the
other hand, the simulated lightcurves of VHE γ-ray photons exhibit significant variability as
such photons are produced from the Compton upscattering off higher energy electrons with
shorter cooling timescales than the light crossing time.
The effect of the optical depth due to γ − γ absorption by the IIBR on the SED of
3C 66A was also evaluated. The simulations do not predict a significant effect on the SED
due to the optical depth. The SSC emission cutoff predicted to be at ∼ 4 GeV can be
taken as the intrinsic SSC emission cutoff value for this object. We predict the object to
be well within the observational range of MAGIC, VERITAS and GLAST. Finally, the EC
emission for this object was also calculated and it appears that the EC emission could be
dominant in the high-energy component initially, but as the emission region travels further
– 21 –
away from the BLR, the EC contribution becomes less significant and the SSC emission
takes over. It is highly probable that this maximum contribution of the EC component
might explain the historical EGRET flux and that there could be GeV flaring due to early
external Comptonization.
This work was partially supported through NRL BAA 76-03-01, contract no. N00173-
05-P-2004.
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This preprint was prepared with the AAS LATEX macros v5.2.
– 23 –
Table 1. Model Parameters used to reproduce the quiescent and flaring state of 3C 66A as
shown in Figures 1 and 2, respectively. Note: Linj is the luminosity with which electron
population is injected into the blob. γ1,2 are the low- and high-energy cutoffs of electron
injection spectrum and q is the particle spectral index. Profile stands for the flare profile
used to reproduce the optical variability pattern, eB is the equipartition parameter and
magnetic field B is the equipartition value. Γ is the bulk Lorentz factor, Rb is the comoving
radius of the blob, θobs is the viewing angle and τT,BLR is the radial Thomson depth of the
Fit Linj [10
41 ergs/s] γ1 [10
3] γ2 [10
4] q Profile eB B [G] Γ Rb [10
15 cm] θobs [deg] τT,BLR
1 2.7 1.8 3.0 3.1 ——– 1 2.4 24 3.59 2.4 0
2 8.0 2.1 4.5 2.4 Gaussian 1 2.8 24 3.59 2.4 0
3 8.0 2.1 4.5 2.4 Gaussian 1 2.8 24 3.59 2.4 0.3
	Introduction
	Model Description
	Model Parameters
	Results and Discussion
	Summary
