The Astrophysical Journal, 836:83 (9pp), 2017 February 10 doi:10.3847/1538-4357/836/1/83
© 2017. The American Astronomical Society. All rights reserved.
On the Spectral Curvature of VHE Blazar 1ES 1011+496:
Effect of Spatial Particle Diffusion
Atreyee Sinha1, S. Sahayanathan2, B. S. Acharya1, G. C. Anupama3, V. R. Chitnis1, and B. B. Singh1
1 Department of High Energy Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India; atreyee@tifr.res.in
2 Nuclear Research Laboratory, Bhabha Atomic Research Center, Mumbai, India
3 Indian Institute of Astrophysics, II Block, Koramangala, Bangalore, 560 034, India
Received 2016 January 15; revised 2016 November 29; accepted 2016 November 30; published 2017 February 9
Abstract
A detailed multi-epoch study of the broadband spectral behavior of the very high energy (VHE) source 1ES 1011
+496 provides us with valuable information regarding the underlying particle distribution. Simultaneous
observations of the source at optical/UV/X-ray/γ-ray during three different epochs, as obtained from Swift-
UVOT/Swift-XRT/Fermi-LAT, are supplemented with the information available from the VHE telescope array,
HAGAR. The long-term flux variability at the Fermi-LAT energies is clearly found to be lognormal. It is seen that
the broadband spectral energy distribution of 1ES 1011+496 can be successfully reproduced by synchrotron and
synchrotron self Compton emission models. Notably, the observed curvature in the photon spectrum at X-ray
energies demands a smooth transition of the underlying particle distribution from a simple power law to a power
law with an exponential cutoff, or a smooth broken power law distribution, which may possibly arise when the
escape of the particles from the main emission region is energy dependent. Specifically, if the particle escape rate is
related to its energy as E0.5, then the observed photon spectrum is consistent with the ones observed during the
various epochs.
Key words: BL Lacertae objects: individual (1ES 1011+496) – galaxies: active – radiation mechanisms: non-thermal
1. Introduction (synchrotron self Compton, SSC) or from external sources such
Blazars are a peculiar subclass of radio loud active galactic as the broad line region, the accretion disc, the cosmic
microwave background, and so on (external Compton, EC).
nuclei where a powerful relativistic jet is pointed close to the
( For a comprehensive review of these mechanisms, seeline of sight of the observer Urry & Padovani 1995). They Böttcher (2007).
show high optical polarization, intense and highly variable non- 1ES 1011+496 (R.A.=10:15:04.14, decl.=49:26:00.70;
thermal radiation throughout the entire electromagnetic spectra J2000) is an HBL located at a redshift of z=0.212. It was
in timescales extending from minutes to years, apparent super- discovered as a very high energy (VHE) emitter by the MAGIC
luminal motion in high resolution radio maps, large Doppler collaboration in 2007, following an optical outburst in March
factors, and beaming effects. Blazars can be broadly classified 2007 (Albert et al. 2007). The flux above 200 GeV was roughly
into two subgroups, BLLacs and flat spectrum radio quasars 7% of the Crab Nebula, and the observed spectrum was
(FSRQs), where the former are identified by the absence of reported to be a power law with a very steep index of
emission/absorption lines. The broadband spectral energy 4.0±0.5. After correction for attenuation of VHE photons by
distribution (SED) of blazars is characterized by two peaks, the extragalactic background light (EBL; Kneiske & Dole
one in the IR–X-ray regime, and the second one in the γ-ray 2010), the intrinsic spectral index was computed to be
regime. According to the location of the first peak, BLLacs are 3.3±0.7. At its epoch of discovery, it was the most distant
further classified into low energy peaked BL lacs (LBLs), TeV source. Albert et al. (2007) had constructed the SED with
intermediate energy peaked BLLacs (IBLs), and high energy simultaneous optical R-band data, and other historical data
peaked BLLacs (HBLs; Padovani & Giommi 1995). Both from Costamante & Ghisellini (2002), and modeled it with a
leptonic (e.g., Maraschi et al. 1992; Dermer & Schlickeiser single zone radiating via SSC processes. However, the model
1993; Sikora et al. 1994; Bloom & Marscher 1996; parameters could not be constrained due to the sparse sampling
Błażejowski et al. 2000) and hadronic (e.g., Mannheim & and the non-simultaneity of the data. Hartman et al. (1999) had
Biermann 1992; Mücke & Protheroe 2001; Mücke et al. 2003) suggested the association of this source with the EGRET
models have been proposed to explain the broadband SED with source 3EG J1009+4855, but this association has later been
varying degrees of success. While the origin of the low energy challenged (Sowards-Emmerd et al. 2003). This source has
component is well established to be caused by synchrotron been detected in the 0.1–300 GeV band by Fermi-LAT, and in
emission from relativistic electrons gyrating in the magnetic the 0.3–10 keV band by Swift-XRT (Abdo et al. 2010). A
field of the jet, the physical mechanisms responsible for the detailed study of its optical spectral variability has been
high energy emission are still under debate. It can be produced performed by Böttcher et al. (2010). Results of multiwave-
either via inverse Compton scattering (IC) of low frequency length campaigns carried out in 2008 (Ahnen et al. 2016b) and
photons by the same electrons responsible for the synchrotron 2011–2012 (Aleksić et al. 2016) have recently been published
emission (leptonic models), or via hadronic processes initiated by the MAGIC collaboration.
by relativistic protons, neutral and charged pion decays, or In 2014 February, 1ES 1011+496 was reported to be in its
muon cascades (hadronic models). The seed photons for IC in highest flux state to date, as seen by Fermi-LAT (Corbet &
leptonic models can be either the source synchrotron photons Shrader 2014) and Swift-XRT (Kapanadze 2014). During this
1
The Astrophysical Journal, 836:83 (9pp), 2017 February 10 Sinha et al.
functions P7REP_SOURCE_V15 are used for the analysis.
All the sources lying within a 10° region of interest (ROI)
centered at the position of 1ES 1011+496 and defined in the
third Fermi-LAT catalog (Acero et al. 2015) are included in
the XML file. All the parameters except the scaling factor of
the sources within the ROI are allowed to vary during the
likelihood fitting. The source spectrum is assumed to be a
power law.
Analysis of all data for this source from 2008 to 2014 yields a
spectrum consistent with a simple power law with an index of
1.82±0.01 (Figure 1), and the flux is found to be variable on a
timescale of 10 days, with a significance of 12.7s. The fractional
variability amplitude parameter (Vaughan et al. 2003; Chitnis
et al. 2009) is computed to be Fvar = 0.35  0.01, where
S2 - s2
Figure 1. Energy spectrum of 1ES1 1011+496 from 6 years of Fermi-LAT F errvar = . (1)
data during 2008–2014. The last point is an upper limit and is shown by x¯2
an inverted triangle. The spectrum is well fit by a power law of
index a = 1.82  0.01. Here s2err is the mean square error, x̄ the unweighted sample
mean, and S2 the sample variance, and the error on Fvar is given as
time, the VERITAS collaboration also detected a strong VHE
flare from this source, at an integral flux level of~20%–75% of ⎛ 2 ⎞2 ⎛ 2⎜ 1 · serr ⎟ ⎜ s
2 1 ⎞
the Crab flux, which was almost a factor of 10 higher than its s errF ⎟var = + · , (2)2
baseline flux (Cerruti 2015). Ahnen et al. (2016a) have used the ⎝ 2N x¯ Fvar ⎠ ⎝⎜ N x¯ ⎠⎟
TeV spectrum during this flare to put constraints on the EBL
density. This source was observed by the High Altitude with N as the number of points.
Gamma-Ray (HAGAR) Telescope array during the 2014 There is no significant trend of spectral hardening with
February–March season. In this paper, we study the simulta- increasing flux (Spearman’s rank correlation, rs = -0.25),
neous SED of this source, as seen by Swift, Fermi-LAT, and which has been seen in many HBL. The light curve for a 3-year
HAGAR during this epoch. To understand the broadband period during 2011–2014 is shown in the bottom panel of
spectral behavior, we also construct SEDs using quasi- Figure 2.
simultaneous data from two previous epochs. Spectra are extracted in five logarithmically binned energy bins
In Section 2, we describe our data reduction procedure for three epochs contemporaneous with Swift observations,
and study the temporal variability in the lightcurves. The corresponding to MJD (a) 56005 to 56020 (state s1), (b) 56280
distribution function of the flux at the γ-ray energies is studied to 56310 (state s2), and (c) 56692 to 56720 (state s3). LAT fluxes
in Section 3. We model the SED using an SSC model having a and spectral parameters during these epochs are given in Table 1.
smoothly varying power law spectrum of the underlying The state s3 corresponds to the period for which the highest
electron energy distribution, and the results are outlined in gamma-ray flux from this source is seen to date.
Section 4. We discuss the implications in Section 5, and show
that such a situation may arise when the escape of the particles 2.2. Swift-XRT
from the emission region is energy dependent. The results are A total of 16 Swift pointings are available during the
summarized in Section 6. A cosmology with wm = 0.3, studied epochs, the ids of which are given in Table 1. Swift-
wL = 0.7, and H0=70 km s−1 Mpc is used in this work. XRT data (Burrows et al. 2005) are processed with the
XRTDAS software package (v.3.0.0) available within the
2. Data Analysis and Lightcurves HEASOFT package (6.16). Event files are cleaned and
calibrated using standard procedures (xrtpipeline
2.1. Fermi-LAT v.0.13.0), and xrtproducts v.0.4.2 is used to
Fermi-LAT data are extracted from a region of 20° obtain the lightcurves and spectra. Observations are available
centered on the source. The standard data analysis procedure in both Windowed Timing (WT) and Photon Counting (PC)
as mentioned in the Fermi-LAT documentation4 is used. modes, and full grade selections (0–2 for WT and 0–12 for
Events belonging to the energy range 0.2−300 GeV and PC) are used. PC observations during the 2014 flare are
SOURCE class are used. To select good time intervals, a lter heavily piled up (counts >0.5 c/s), and are corrected for byfi
DATA_QUAL>0, && LAT_CONFIG==1 is used, and following the procedure outlined in the Swift analysis“ ” “ ”
only events with less than 105° zenith angle are selected to threads.
5 The XRT Point Spread Function is modeled by a
avoid contamination from the Earth limb -rays. The galactic King function,γ
diffuse emission component gll_iem_v05_rev1.fits and an PSF(r) = [1 + (r r )2]-bc , (3)
isotropic component iso_source_v05_rev1.txt are used as
the background models. The unbinned likelihood method with rc = 5.8 and b = 1.55 (Moretti et al. 2005). Depending on
included in the pylikelihood library of Science Tools the source brightness, annular regions are chosen to exclude
(v9r33p0) and the post-launch instrument response pixels deviating from the King’s function. The tool xrtmkarf
4 http://fermi.gsfc.nasa.gov/ssc/data/analysis/documentation/ 5 http://www.swift.ac.uk/analysis/xrt/pileup.php
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The Astrophysical Journal, 836:83 (9pp), 2017 February 10 Sinha et al.
Figure 2.Multiwavelength light curve during MJD 55600 to 56800 (calendar days 2011–2014), showing from top: Panel 1: OVRO flux in Jy; Panel 2: Optical U band
flux in mJy; Panel 3: UV flux in UW2 band in mJy; Panel 4: MAXI flux (with monthly binning) in counts/sec; Panel 5: Swift-XRT flux in counts/sec; Panel 6: Fermi-
LAT flux (with 10 days binning) in ph cm-2 s-1. The three states for which SED has been studied are marked and labelled as s1, s2, and s3, respectively.
is then executed with PSF correction set to “yes” to create an 2.4. Other Multiwavelength Data
ARF corrected for the loss of counts due to the exclusion of this We supplement the previous information with other multi-
central region. For example, for observation id 00035012032 wavelength flux measurements at different energies:
(see Figure 4), an annular region of 16–25 arcsec centered on
the source position is taken as the source region. (i) Radio.
The lightcurves are finally corrected for telescope vignet- As a part of the Fermi monitoring program, the Owens
ting and PSF losses with the tool xrtlccorr v.0.3.8. Valley Radio Observatory (OVRO; Richards et al. 2011)
The spectra are combined using the tool addspec for all has been regularly observing this source since 2008. Flux
observations within each of the states s1, s2, and s3, as measurements at 15 GHz taken directly from their website
6
de ned in Section 2.1. Spectra are grouped to ensure a show negligible variability with fvar ~ 0.07.fi
minimum of 30 counts in each bin by using the tool (ii) X-ray.
grppha v.3.0.1. Daily binned source counts in the 2–20 keV range
A slight curvature is detected in the XRT spectrum, and a log from the Monitor of All-sky X-ray Image (MAXI) on
parabolic spectral model given by board the International Space Station (ISS; Matsuoka
et al. 2009) are available from their website.7 The X-ray
( )-a-b log(E E ) ( ) counts binned on monthly timescales show highdN dE = K E Eb b , 4 variability, with fvar = 1.34  0.08.
(iii) VHE.
is used to model the observed spectrum. Here α gives the HAGAR (Gothe et al. 2013) is a hexagonal array of
spectral index at Eb, which is fixed at 1 keV during the fitting. seven Atmospheric Cherenkov Telescopes (ACT) that
Parameters obtained during the fitting are given in Table 1. To uses the wavefront sampling technique to detect celestial
correct for the line of sight absorption of soft X-rays due to the gamma-rays. It is located at the Indian Astronomical
interstellar gas, the neutral hydrogen column density is fixed at Observatory site (32°46′46″ N, 78°58′35″ E), in Hanle,
NH=8.38×10
19 cm−2 (Kalberla et al. 2005). Ladakh, in the Himalayan mountain ranges, at an altitude
of 4270 m. The energy threshold for the HAGAR array
for vertically incident γ-ray showers is 208 GeV, with a
2.3. Swift-UVOT sensitivity of detecting a Crab Nebula–like source in
17 hr for a 5σ significance. Detailed descriptions of
Swift-UVOT observations cycled through the six filters, the HAGAR instrumentation and simulations can be found in
optical U, V, B, and the UV UW1, UW2, and UM2. The Shukla et al. (2012) and Saha et al. (2013). HAGAR
individual exposures during each of the states are summed observations of 1ES 1011+496 were carried out during
using uvotimsum v.1.6, and the uvotsource v.3.3 the 2014 February–March season following an alert by
tool is used to extract the fluxes from the images using aperture MAGIC and VERITAS collaborations of a VHE flare
photometry. The observed fluxes are corrected for galactic from this source during February 3–11 (Mirzoyan 2014).
extinction using the dust maps of Schlegel et al. (1998), and for
contribution from the host galaxy following Nilsson et al. 6 http://www.astro.caltech.edu/ovroblazars/
(2007), with R-mag=16.41±0.09. 7 http://maxi.riken.jp/
3
The Astrophysical Journal, 836:83 (9pp), 2017 February 10 Sinha et al.
Table 1
Observation Details (XRT Observation Ids and the Total Exposure Time) and Spectral Parameters in the X-ray and GeV Bands
for the Different States for which the SED Has Been Extracted
State Start Date End Date XRT Obs id XRT Exp XRT Spectral Parameters LAT Spectral Parameters
ISO ISO Time (ks) α β F2–10 keV Index F0.2–300 GeV
s1 2012 Mar 19 2012 Apr 03 00035012020 6.3 2.27±0.19 0.17±0.10 1.6±0.3 1.81±0.16 4.3±0.9
00035012021
00035012022
00035012023
00035012024
s2 2012 Dec 19 2013 Jan 18 00035012025 5.1 2.37±0.11 0.61±0.22 0.82±0.07 1.74±0.13 2.8±0.6
00035012026
00035012027
00035012028
00035012029
00035012030
s3 2014 Feb 04 2014 Mar 04 00035012031 7.3 1.94±0.04 0.16±0.0.03 4.11±0.12 1.77±0.22 9.8±0.3
00035012032
00035012033
00035012035
00035012036
Note.The X-ray 2–10 keV flux is quoted in 10−11 erg cm−2 s−1, and the Fermi-LAT 0.2–300 GeV Flux in 10−8 ph cm−2 s−1.
The observations were carried out in clear moonless blazars was first clearly detected in the X-ray regime in BLLac
conditions, between 2014 February 19 and March 8 (Giebels & Degrange 2009) and has hence been seen across the
(MJD 56707 to 56724). Each pointing source (ON) run of entire electromagnetic spectrum in PKS2155−304 (Chevalier
approximately 60 minutes duration was followed (or et al. 2015) and Mkn421 (Sinha et al. 2016).
preceded) by a background (OFF) run of the the same Since for the present source the variability is minimal in the
time duration at the same zenith angle, having similar MAXI and OVRO bands, and the sampling sparse in the
night sky brightness as the source region. A total of 23 UVOT and XRT bands, we restrict our study of lognormal flux
run pairs were taken, corresponding to a total duration of variability to the Fermi band only. We fit the histogram of the
1035 minutes with a common ON–OFF hour angle. observed fluxes with a Gaussian and a lognormal function
(Figure 3(a)), and find that a lognormal fit (chi-sq/dof=11/
The data are reduced following the procedures outlined in 12) is statistically preferred over a Gaussian fit (chi-sq/
Shukla et al. (2012), with various quality cuts imposed. Only dof=22.8/12). We further plot the excess variance,
events with signals seen in at least five telescopes are retained,
2 2
for which the energy threshold is calculated to be 234 GeV. No sEXCESS = S - serr , versus the mean flux in Figure 3(b).
significant signal is seen from the source with 600 minutes of The two parameters show a strong linear correlation, r
clean data. The excess of signal over background is computed (prob)=76% (1.6e–5), and are well fit by a straight line of
-8
to be 706±566 photons, corresponding to a significance of slope 1.17±0.18 and an intercept of (-3.9  0.8) ´ 10
1.3s. A 3 - s upper limit of 1.2 * 10-10 erg cm-2 s-1 for the (chi-sq/dof=24.1/22). This indicates a clear detection of
flux of gamma-rays above 234 GeV is calculated from the lognormal temporal behavior in this source.
previously provided data, which corresponds to roughly 70%
of the Crab Nebula flux. 4. Spectral Energy Distribution
This is supplemented with VHE spectra of this source
obtained during its epoch of discovery (Albert et al. 2007) by The broadband SED of 1ES 1011+496, during different
the Major Atmospheric Gamma-ray Imaging Cherenkov activity states, is modeled under the ambit of a simple leptonic
(MAGIC). These spectral points have been plotted for scenario. This, in turn, helps us understand the the nature of
representative purposes in Figure 5 and provide a lower limit the electron distribution responsible for the emission through
for the SED modeling during the VHE flare in 2014, epoch s3. synchrotron and SSC processes. We assume the electrons to
be confined within a spherical zone of radius R permeated
3. Detection of Lognormality by a tangled magnetic field B. As a result of the relativistic
motion of the jet, the radiation is Doppler boosted along
Lognormal flux distributions and linear rms-flux relations the line of sight. A good sampling of the SED from radio
have often been claimed as universal features of accretion to γ-rays allows one to obtain a reasonable estimation of
powered sources like X-ray binaries (Uttley & McHardy 2001; the physical parameters, under appropriate assumptions
Scaringi et al. 2012). Lognormal fluxes have fluctuations that (Ghisellini et al. 1996; Tavecchio et al. 1998; Sahayanathan
are, on average, proportional to the flux itself, and are indicative & Godambe 2012). Notably, the smooth spectral curvatures,
of an underlying multiplicative, rather than additive, physical observed around the peak of the SED, may result from a
process. It has been suggested that a lognormal flux behavior in convolution of the single particle emissivity with the assumed
blazars could be indicative of the variability imprint of the particle distribution. If the chosen particle distribution has a
accretion disk onto the jet (McHardy 2008). This behavior in sharp break, then the observed curvature in the photon
4
The Astrophysical Journal, 836:83 (9pp), 2017 February 10 Sinha et al.
Figure 3. Detection of lognormality in 1ES 1011+496 in the Fermi energy band. The first panel shows the histogram of the observed fluxes (black points) fitted with a
Gaussian (dotted blue line) and lognormal (solid red line) function. A lognormal fit is clearly preferred. The second panel shows the strong linear relationship between
the flux and the excess rms. The black points denote data points averaged over 100 days, and the solid gray line indicates the linear fit.
Figure 4. XRT PSF for obs 00035012032 fitted by a King function. The deviation from the model is seen for regions smaller than 16 arcsec, which are thus excluded
from the source region.
spectrum could be due to the emissivity function. On the other law with index p and an exponentially decreasing tail,
hand, the underlying particle distribution itself can show a given by
gradual transition causing the observed curvatures. To
investigate this, the observed SED is modeled with the ⎛ g ⎞N (g)dg = N0g-p exp ⎜- ⎟dg, gmin < g < gmax. (7)
following choices of particle distributions. ⎝ gc ⎠
(i) Broken power law (BPL). In this case, we assume the
electron spectrum to be a sharp BPL with indices p and q, Here, gmin and gmax are the minimum and maximum dimension-
given by less energies (E = gmc
2) of the non-thermal electron distribution,
and gb is the electron energy associated with the peak of the SED
⎧N g-pdg, g < g < g and N0 the normalization. To reduce the number of unknowns, the
( ) ⎨ 0 min bN g dg = . (5) radius R is fixed at 1.3 ´ 1016 cm, corresponding to a variability⎩N g(q-p) -q0 b g dg, gb < g < gmax timescale of tvar » 1 day (for the Doppler factor d » 10). In
2
addition, the magnetic Bfield energy density, UB(= ), is
(ii) Smooth broken power law (SBPL). Here the electron 8pconsidered to be in near equipartition with the particle energy
distribution is an SBPL with low energy index p and the density (Ue). The resultant model spectra, corresponding to epochhigh energy index q: s3, for the previously provided three choices of particle
(g )-p distribution are shown in Figure 6, along with the observed
N (g)dg = N b0 dg, gmin < g < gmax . (6) fluxes. The governing physical parameters are given in Table 2.(g g )pb + (g g )qb We compare the different fit models by incorporating the
(iii) Power law with an exponential cutoff (CPL). The numerical SSC model into the XSPEC spectral fitting software
particle distribution in this case is chosen to be a power to perform a c2 minimization as followed in Sinha et al. (2016).
5
The Astrophysical Journal, 836:83 (9pp), 2017 February 10 Sinha et al.
Table 2
Models Parameters, the Total Bolometric Luminosity (L) and the Computed Reduced-c2 for the Different Particle Distributions during the Three Epochs. while the
BPL Cannot Reproduce the Observed Spectrum Satisfactorily, the SBPL and the CPL Can
Broken Power Law (BPL)
State Particle Index Magnetic Field Doppler Factor Break Energy Particle Energy Density Luminosity c2/dof
p q B (G) δ gb Ue (erg/cc) L (erg/cc)
s1 2.35 4.20 0.82 10.0 7.7e4 5.1e-2 3.2e46 10.3
s2 2.20 4.60 0.78 10.2 8.1e4 3.8e-2 2.6e46 9.4
s3 2.26 4.30 0.73 9.8 1.9e5 7.4e-2 7.7e46 12.1
Smooth Broken Power Law (SBPL)
p q B (G) δ gb Ue (erg/cc) L (erg/cc)
s1 2.35 4.22 0.83 10.0 9.5e4 7.8e-2 3.7e46 1.3
s2 2.20 4.60 0.78 10.2 7.7e4 4.7e-2 2.3e46 1.1
s3 2.22 4.20 0.73 9.8 1.7e5 8.6e-2 7.8e46 1.2
Cutoff Power Law (CPL)
p B (G) δ gmax Ue (erg/cc) L (erg/cc)
s1 2.30 0.78 10.9 1.1e5 8.2e-2 3.4e46 1.2
s2 2.02 0.76 10.7 7.0e4 4.6e-2 2.1e46 1.4
s3 2.10 0.74 10.3 1.6e5 8.6e-2 6.6e46 1.3
Figure 5. Spectral energy distribution of 1ES 1011+496 during the three epochs studied in the paper, with simultaneous data from Swift-UVOT, Swift-XRT, and the
Fermi-LAT. The orange inverted triangle gives the HAGAR upper limit during the 2014 February–March season. The green stars show the MAGIC spectrum during
its discovery in 2007 (Albert et al. 2007). The SEDs are modeled with a one zone SSC, with the underlying electron distribution as (a) a power law with exponential
cutoff and (b) a smooth broken power law.
Swift-XRT is binned to have eight spectral points to avoid from distinguishing between the two models. Particularly, with
biasing the fit toward X-ray energies. Since we are dealing with the current sampling, the index q and the gmax for the SBPL
several different instruments over a broad energy range, we cannot be well constrained, and the latter is fixed at 10
7. The
assume model systematics of 5%. Our study shows that the model parameters describing the observed SED for the three
commonly used electron spectrum, the BPL (e.g., Ghisellini epochs for the SBPL and the CPL are also listed in Table 2.
et al. 1996; Krawczynski et al. 2004), cannot explain the The different flux states can be reproduced mainly by changing
smooth curvature observed at the X-ray energies for this the particle indices and the break energy, whereas the variations in
source, implying that the synchrotron emissivity function alone other parameters like the Doppler factor and the magnetic field are
is not suf cient to give rise to the observed curvature, and that minimal. While the total bolometric luminosity, L, changes byfi
the underlying particle spectrum itself must have a gradual more than a factor of three, the variations in B and δ are less than
10%. This probably suggests that the variation in the flux states
transition as opposed to a sharp break. This suggests that the may occur mainly due to changes in the underlying particle
SBPL and CPL are the better choices to represent the observed distributions, rather than the other jet properties.
SED, and in Figure 5 we show the model spectra corresponding
to these particle distributions for all three epochs considered in
this study. Both these models can well reproduce the observed 5. Discussions
spectrum, during all three epochs, and the absence of high The observations of lognormality in the long term (6 years)
energy X-ray/simultaneous TeV measurements prevents us gamma-ray flux distribution and the linear flux-rms relation
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The Astrophysical Journal, 836:83 (9pp), 2017 February 10 Sinha et al.
Figure 6. State s3 modeled with the underlying spectrum as a BPL (dotted Figure 7. Model curves obtained by changing the energy dependence of the
black line); a SBPL (dashed red line); and a CPL (dashed blue line). The BPL escape timescale for the state s3. The blue line is obtained for a energy
fails to reproduce the smooth curvature of the observed SED (shown in green). independent escape (x = 0), and fails to reproduce the observed spectrum. The
best match between the data and the model is obtained for x = -0.5 and is
imply that the γ-ray flux variability of 1ES1011+496 represented by the solid green line. The magnetic field B is assumed to be 0.4 G
is lognormal. Since similar trends have been seen in the and the Doppler factor d = 10. The injected particle spectrum is a power of
X-ray band in sources like the Seyfert 1 galaxy; Mkn 766 index 2.1.
(Vaughan et al. 2003), where the physical process responsible
for the X-ray emission originates in the galactic disc; and at VHE energies suggests that the Thomson scattering
other compact accreting systems like cataclysmic variables approximation of SSC process may not be valid and one
(Giannios 2013), such trends have been claimed as universal needs to incorporate Klein–Nishina correction in the cross-
signs of accretion induced variability. The other option might section (Tavecchio et al. 1998). Hence, we numerically solve
be that the underlying parameters responsible for the observed Equation (8) using a fully implicit finite difference scheme
emission (e.g., the Doppler factor, magnetic field, etc.) (Chang & Cooper 1970; Chiaberge & Ghisellini 1999), while
themselves have a lognormal time dependence (Giebels & incorporating the exact Klein–Nishina cross-section for IC
Degrange 2009). Since the result of our spectral modeling scattering (Blumenthal & Gould 1970).
indicates that the flux variability is mainly induced by changes The case tesc  ¥ (no escape) gives rise to a BPL with the
in the particle spectrum rather than the other jet properties, it break occurring at the energy where the observation time is
seems reasonable to believe that lognormal fluctuations in the equal to the cooling timescale of the particle, while for the case
accretion rate give rise to an injection rate into the jet with x = 0 (constant tesc), a steady state BPL particle distribution is
similar properties. eventually attained where the break corresponds to the particle
Moreover, a detailed study of the multiwavelength spectral energy at which the escape timescale equates to its cooling
behavior of the source during three different epochs under timescale. However, in these cases, the spectral transition at
simple synchrotron and SSC models demands an underlying the break energy is too sharp to reproduce the observed SED,
electron distribution with a smooth curvature. Though such a and a gradual transition can be achieved by considering x ¹ 0.
requirement can be satisfied by assuming the underlying We found that the smooth spectral curvature demanded by the
electron distribution as either SBPL or CPL, the absence of observation can be attained by fixing x » 0.5. In Figure 7,
hard X-ray data prevents one from distinguishing between we show the resultant model SED corresponding to x = 0
these two choices. To interpret this, we consider a scenario (blue line) and x = 0.5, along with the observed fluxes for the
where a non-thermal distribution of electronsQ (g) = Q -p0g is state s3. The underlying particle distribution corresponding to
continuously injected into a cooling region (CR) where they these values of ξ is shown in Figure 8.
lose their energy through radiative processes as well as escape Alternate to this interpretation, a smooth curvature in the
out at a rate defined by a characteristic timescale, tesc. The particle distribution can also be a result of time averaging of an
evolution of the particle number density, N (g, t), in the CR evolving particle distribution. For instance, an episodic injection
can then be conveniently described by the kinetic equation of a power-law particle distribution into CR can cause the high
(Kardashev 1962) energy cutoff to shift toward lower energy with time, which will
¶ ¶ be reflected as a smooth curvature at high energy in the timeN
- (P (g)N ) N+ averaged spectrum. Also, an episodic injection with an energy-
¶t ¶g tesc (g) dependent escape gives rise to a particle distribution similar to a
= Q (g)Q(g - gmin)Q(gmax - g), (8) cutoff power law. However, this interpretation fails to explain
the observed variability of the gamma-ray flare, since the
where P (g) is the energy loss rate due to synchrotron and observed cooling timescale of the GeV gamma-ray emitting
SSC processes. Assuming a power law dependence of electrons will come out to be (Kushwaha et al. 2014)
escape timescale with energy tesc = tgx, a semianalytical ⎛ ⎞1 4
solution of Equation (8) can be attained when the dtcool,GeV » 3 ´ 1010B-7 4 ⎜ ⎟ s (9)
loss processes are confined within the Thomson regime ⎝nGeV ⎠
(Atoyan & Aharonian 1999). However, detection of the source »0.5 days. (10)
7
The Astrophysical Journal, 836:83 (9pp), 2017 February 10 Sinha et al.
particle power law index p ~ 2.1 indicates that the particles are
most likely accelerated at relativistic shocks (Sironi
et al. 2015). However, the non-availability of hard X-ray
observation presently prevents us from distinguishing between
CPL and SBPL particle spectra. Future observations in the hard
X-ray band from the newly launched ASTROSAT (Singh
et al. 2014) can be crucial in resolving this uncertainty.
The detection of lognormal flux variability in this source
follows similar recent detections in other blazars. While the γ-
ray flux distribution could be modeled by a single lognormal
distribution for other HBLs (Mkn421; Sinha et al. 2016 and
PKS2155-304; Chevalier et al. 2015), the FSRQ PKS1510-
089 (Kushwaha et al. 2016) required a sum of two such
distributions. With the Fermi mission now into its ninth year of
operation, we have unprecedented continuous flux measure-
ments for a large sample of blazars. A systematic study of the
Figure 8. Underlying particle spectra for the model curves shown in Figure 7. same can shed new light on the origin of the jet launching
The dashed blue line is obtained for an energy independent escape (x = 0;
which fails to reproduce the observed SED), and the solid black line mechanisms in supermassive blackholes.
corresponds to the particle spectrum that best models the observed
SED (x = -0.5). We thank the scientific and technical personnel of HAGAR
groups at IIA, Bengaluru, and TIFR, Mumbai, for observations
Here the cooling timescale is estimated for the parameters with the HAGAR system. This research has made use of data,
provided in Table 2, and nGeV corresponds to the frequency of software, and/or web tools obtained from NASA’s High
the gamma-ray photon falling on the Compton peak. This time Energy Astrophysics Science Archive Research Center (HEA-
is much smaller than the observed are duration of »30 days, SARC), a service of Goddard Space Flight Center and thefl
as seen in Figure 2. Similarly, the particle spectrum injected Smithsonian Astrophysical Observatory. Part of this work is
based on archival data, software, and online services provided
into the CR itself can show smooth curvatures, due to an by the ASI Science Data Center (ASDC). This research has
underlying complex particle acceleration prices. For example, made use of the XRT Data Analysis Software (XRTDAS)
an energy-dependent acceleration process is known to give rise developed under the ASI Science Data Center (ASDC), Italy,
to significant curvature in the accelerated particle distribution and the NuSTAR Data Analysis Software (NuSTARDAS)
(Massaro et al. 2004; Zirakashvili & Aharonian 2007). jointly developed by the ASI Science Data Center (ASDC,
However, in this present work, we only consider a simplistic Italy) and the California Institute of Technology (Caltech,
scenario where the smooth curvature can be introduced by USA). The OVRO 40 M Telescope Fermi Blazar Monitoring
considering an energy-dependent escape from the main Program is supported by NASA under awards NNX08AW31G
emission region. and NNX11A043G, and by the NSF under awards AST-
0808050 and AST-1109911. We are grateful to the anonymous
6. Conclusions referee for the constructive criticism and helpful comments,
which lead to a major change in the discussions section.
The blazar, 1ES 1011+496, underwent a major γ-ray flare
during 2014 February, triggering observations at other wave-
bands, thereby providing simultaneous observations of the References
source at radio/optical/X-ray/γ-ray energies. The TeV flare Abdo, A. A., Ackermann, M., Agudo, I., et al. 2010, ApJ, 716, 30
seen by VERITAS on 2014 February 3–11 decayed down by Acero, F., Ackermann, M., Ajello, M., et al. 2015, ApJS, 218, 23
2014 February 19, as indicated by the HAGAR upper limits. Ahnen, M. L., Ansoldi, S., Antonelli, L. A., et al. 2016a, A&A, 590, A24
This is also seen in the flux decrease in the Fermi and the X-ray Ahnen, M. L., Ansoldi, S., Antonelli, L. A., et al. 2016b, MNRAS, 459, 2286
bands. In this work, we analyzed the simultaneous multi- Albert, J., Aliu, E., Anderhub, H., et al. 2007, ApJL, 667, L21
Aleksić, J., Ansoldi, S., Antonelli, L. A., et al. 2016, A&A, 591, A10
wavelength spectrum of the source and obtained the broadband Atoyan, A. M., & Aharonian, F. A. 1999, MNRAS, 302, 253
SED during three different epochs. The observed SEDs over Błażejowski, M., Sikora, M., Moderski, R., & Madejski, G. M. 2000, ApJ,
these epochs clearly show a trend of the synchrotron peak 545, 107
moving to higher energies during increased flux states, similar Bloom, S. D., & Marscher, A. P. 1996, ApJ, 461, 657
to the “bluer when brighter Blumenthal, G. R., & Gould, R. J. 1970, RvMP, 42, 237” trend seen by Böttcher et al. Böttcher, M. 2007, Ap&SS, 309, 95
(2010) during 5 years of optical observations of this source. Böttcher, M., Hivick, B., Dashti, J., et al. 2010, ApJ, 725, 2344
However, Böttcher et al. (2010) attributed the observed Burrows, D. N., Hill, J. E., Nousek, J. A., et al. 2005, SSRv, 120, 165
variability primarily due to magnetic field changes in the jet, Cerruti, M. 2015, arXiv:1501.03554
whereas our broadband spectral modeling results indicate the Chang, J. S., & Cooper, G. 1970, JCoPh, 6, 1
Chevalier, J., Kastendieck, M. A., Rieger, F., et al. 2015, ICRC, 34, 829
spectral behavior is dominated by changes in the particle Chiaberge, M., & Ghisellini, G. 1999, MNRAS, 306, 551
spectrum. Chitnis, V. R., Pendharkar, J. K., Bose, D., et al. 2009, ApJ, 698, 1207
The spectra during all the states demand a smooth curvature Corbet, R. H. D., & Shrader, C. R. 2014, ATel, 5888, 1
in the underlying particle spectrum (e.g., an SBPL or a CPL). Costamante, L., & Ghisellini, G. 2002, A&A, 384, 56
We show that such a smoothly varying particle spectrum can be Dermer, C. D., & Schlickeiser, R. 1993, ApJ, 416, 458Ghisellini, G., Maraschi, L., & Dondi, L. 1996, A&AS, 120, C503
easily obtained by assuming an energy-dependent particle Giannios, D. 2013, MNRAS, 431, 355
escape (t xesc µ g ) mechanism in the jet. The inferred injected Giebels, B., & Degrange, B. 2009, A&A, 503, 797
8
The Astrophysical Journal, 836:83 (9pp), 2017 February 10 Sinha et al.
Gothe, K. S., Prabhu, T. P., Vishwanath, P. R., et al. 2013, ExA, 35, 489 Nilsson, K., Pasanen, M., Takalo, L. O., et al. 2007, A&A, 475, 199
Hartman, R. C., Bertsch, D. L., Bloom, S. D., et al. 1999, ApJS, 123, 79 Padovani, P., & Giommi, P. 1995, ApJ, 444, 567
Kalberla, P. M. W., Burton, W. B., Hartmann, D., et al. 2005, A&A, 440, 775 Richards, J. L., Max-Moerbeck, W., Pavlidou, V., et al. 2011, ApJS, 194, 29
Kapanadze, B. 2014, ATel, 5866, 1 Saha, L., Chitnis, V. R., Vishwanath, P. R., et al. 2013, APh, 42, 33
Kardashev, N. S. 1962, SvA, 6, 317 Sahayanathan, S., & Godambe, S. 2012, MNRAS, 419, 1660
Kneiske, T. M., & Dole, H. 2010, A&A, 515, A19 Scaringi, S., Körding, E., Uttley, P., et al. 2012, MNRAS, 421, 2854
Krawczynski, H., Hughes, S. B., Horan, D., et al. 2004, ApJ, 601, 151 Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525
Kushwaha, P., Chandra, S., Misra, R., et al. 2016, ApJL, 822, L13 Shukla, A., Chitnis, V. R., Vishwanath, P. R., et al. 2012, A&A, 541, A140
Kushwaha, P., Sahayanathan, S., Lekshmi, R., et al. 2014, MNRAS, 442, 131 Sikora, M., Begelman, M. C., & Rees, M. J. 1994, ApJ, 421, 153
Mannheim, K., & Biermann, P. L. 1992, A&A, 253, L21 Singh, K. P., Tandon, S. N., Agrawal, P. C., et al. 2014, Proc. SPIE,
Maraschi, L., Ghisellini, G., & Celotti, A. 1992, ApJL, 397, L5 9144, 1
Massaro, E., Perri, M., Giommi, P., & Nesci, R. 2004, A&A, 413, 489 Sinha, A., Shukla, A., Saha, L., et al. 2016, A&A, 591, A83
Matsuoka, M., Kawasaki, K., Ueno, S., et al. 2009, PASJ, 61, 999 Sironi, L., Keshet, U., & Lemoine, M. 2015, SSRv, 191, 519
McHardy, I. 2008, in Blazar Variability across the Electromagnetic Spectrum, Sowards-Emmerd, D., Romani, R. W., & Michelson, P. F. 2003, ApJ,
Workshop Proc. (Trieste: PoS), 14 590, 109
Mirzoyan, R. 2014, ATel, 5887, 1 Tavecchio, F., Maraschi, L., & Ghisellini, G. 1998, ApJ, 509, 608
Moretti, A., Campana, S., Mineo, T., et al. 2005, Proc. SPIE, 5898, 360 Urry, C. M., & Padovani, P. 1995, PASP, 107, 803
Mücke, A., & Protheroe, R. J. 2001, APh, 15, 121 Uttley, P., & McHardy, I. M. 2001, MNRAS, 323, L26
Mücke, A., Protheroe, R. J., Engel, R., Rachen, J. P., & Stanev, T. 2003, APh, Vaughan, S., Edelson, R., Warwick, R. S., & Uttley, P. 2003, MNRAS, 345, 1271
18, 593 Zirakashvili, V. N., & Aharonian, F. 2007, A&A, 465, 695
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