https://doi.org/10.1051/0004-6361/201833628 Astronomy
&
cESO 2018
Astrophysics
HardX-rayproperties of NuSTAR blazars
Gopal Bhatta1, Maksym Mohorian2, and Illya Bilinsky2
1 Astronomical Observatory, Jagiellonian University, ul. Orla 171, 30-244 Krak, Poland e-mail: gopal@oa.uj.edu.pl 2TarasShevchenko NationalUniversityofKyiv, Akademika HlushkovaAve4b, 02000Kyiv, Ukraine
Received 13 June 2018 / Accepted8August 2018
ABSTRACT
Context.InvestigationofthehardX-ray emission propertiesof blazarsiskeytothe understandingofthe centralengineofthe sources and associated jet process. In particular, simultaneous spectral and timing analyses of the intraday hard X-ray observations provide us a means to peer into the compact innermost blazar regions that are not accessible to our current instruments. Aims. The primary objective of the work is to associate the observed hard X-ray variability properties in blazars with their fux and spectral states, thereby, based on the correlation among these states, extract the details about the emission regions and processes occurring near the central engine. Methods.Wecarried out timing, spectral, and cross-correlation analysis of 31 NuSTAR observationsof13 blazars.Weinvestigatedthe spectral shapes of the sources using single power-law, broken power-law, and log-parabola models.We also studied the co-relation between the soft and hard emission using z-transformed discrete correlation function. In addition, we attempted to constrain the smallest emission regions using minimum variability timescales derived from the light curves. Results.We found that, for most of the sources, the hard X-ray emission can be well represented by the log-parabola model and that the spectral slopes for different blazar subclasses are consistent with the so-called blazar sequence.We also report the steepest spectra (Γ ∼ 3)in the BL Lacertae PKS 2155–304 and the hardest spectra(Γ ∼ 1.4) in the fat-spectrum radio quasar PKS 2149–306. In addition,wenotedaclose connectionbetweenthefuxandspectralslopewithinthe sourcesubclassinthesensethathighfuxand/or fux states tend to be harder in spectra. In BL Lacertae objects, assuming particle acceleration by diffusive shocks and synchrotron cooling as the dominant processes governing the observed fux variability, we constrain the magnetic feld of the emission region to be a few Gauss; whereas in fat-spectrum radio quasars, using external Compton models, we estimate the energy of the lower end of the injected electronstobeafew Lorentzfactors.
Keywords. accretion, accretion disks – radiation mechanisms: non-thermal –galaxies: active –BL Lacertae objects: general
1. Introduction
Blazars,a subclass of activegalactic nuclei(AGN), are radio-loud sources with their relativistic jets closely aligned to the line of sight. The Doppler boosted nonthermal emission is highly variable over a wide range of spatial and temporal frequencies. The broadband spectral energy distribution (SED) of blazars features twodistinct spectral peaks. The lower peak, usu-ally observed between radio and X-ray wavelengths, is widely acceptedtobe resultof synchrotron emissionby energetic particles; however, the origin of a high energy component, mostly peaking between UV and γ-ray, is still debated. There are two widely discussed models based on the origin of seed photons. According to the synchrotron self-Compton (SSC) model (e.g., Maraschi et al. 1992;Mastichiadis&Kirk 2002),the same population of the electrons emitting synchrotron radiation up-scatters the softer photon to high energy, whereas in the external Compton (EC) model the seed photons for the Compton up-scattering are provided by the various components of an AGN, such as accretion disk (AD;Dermer&Schlickeiser 1993), broad-line region (BLR; Sikora 1994), and dusty torus (DT; B a˙zejowski et al. 2000).
Blazars consistsof furthertwosubclasses: fat-spectrum radio quasars(FSRQ)andBLLacertae(BLLac)sources.Themorelumi-nous sources,FSRQs,showemissionlinesoverthe continuumand their synchrotron peak is in the lower frequency. As the sources arefoundtohaveabundantseed photonsduetotheAD,BLR,and DT,the high energy emission is most likely due to the EC process as opposedtoSSC(Ghisellinietal. 2011).BLLac objects con-stitute less powerful subclass that has weak or no emission lines over the continuum and the synchrotron peak in these objects lies intheUVtoX-raysbands.BLLacs representanextremeclassof sourceswithanexcessofhighenergyemission(hardX-raystoTeV emission) resulting from the synchrotron and inverse-Compton (IC) processes. However, their apparent low luminosity could be due to lack of strong circumnuclear photon felds and relatively low accretion rates. Blazar sources can have further subdivision based on the frequencyof the synchrotron peak(νs): high synchrotron peaked blazars (HSP; νs > 1015 Hz), intermediate synchrotron peaked blazars (ISP; 1014 <νs < 1015 Hz), and lowsynchrotronpeakedblazars(LSP; νs < 1014 Hz;seeAbdo et al. 2010). In the unifying scheme known as blazar sequence, the bolometric luminosity decreases as we movefrom FSRQ to HSPbut γ-ray emission increases(Fossati et al.1998;Ghisellini et al.2017).This means that while FSRQs are γ-ray dominated,inHSP sourcessynchrotron and γ-ray emission become comparable.In otherwords, withthe increaseintheir bolometric luminosities, blazars become redderandCompton dominantastheratioofthe luminositiesatthe Compton peak to the synchrotron peak frequencyincreases.
Blazar continuum emission is characterized by broadband emission, which is variable on diverse timescales. The variability timescales can be long term (years to decades), short term
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(weeks to months) and intraday/night (minutes to hours). Long-term variability most likely arises owing to variable accretion rates; short-term faring episodes lasting a few weeks could be due to the shock waves propagating down the jets; and the low-amplitude rapid variability known as intraday variability might arise owing to the turbulent fow of the plasma in the innermost regions of the jets (e.g., Bhatta et al. 2013; Cawthorne 2006; Lister&Homan 2005; Hughes et al. 1998; Marscher&Travis 1996).In general, thevariability shownbyAGNs appears pre
dominantly aperiodic in nature, although quasi-periodic oscillations on various timescales have been detected for a number of sources (see Bhatta 2017;Bhatta et al. 2016b;Zola et al. 2016)
Blazar variability in X-ray bands has been extensively studied using numerous instruments over the past several decades. In a study including a large sample of BL Lac sources observed with Einstein Observatory Imaging Proportional Counter (IPC), the source spectra were well described by single power-law model with spectral slope indexes(αX )in the range of 0.1–0.5 (Worrall&Wilkes 1990). The soft X-ray study of a sample of radio-selected BL Lacs (RBL; Urry et al. 1996) and X-ray-selected BL Lac objects (XBL; Perlman et al. 1996) using ROSAT Position Sensitive Proportional Counter (PSPC) showed that the 0.2–2.0keV spectra of the sources could be well described mostly by single power law with αX between
0.5 and 2.3. The single power-law and the broken power-law models were successfully used to describe the X-ray spectra from various instruments such as Advanced Satellite for Cosmology and Astrophysics (ASCA; e.g., Kubo et al. 1998), BeppoSAX(Wolter et al. 1998;Padovani et al. 2002), European X-ray Observatory Satellite (EXOSAT; e.g., Sambruna et al. 1994),andtheROentgenSATellite(ROSAT;e.g., Perlmanetal. 1996; Urry et al. 1996). In the ASCA spectra of four FSRQs, Sambruna et al. (2000) found steep (ΓX ∼ 2−2.5) soft X-ray (0.2–2.4keV) photon indexes similar to those observed in synchrotron-dominated BL Lac objects; and the spectra were found to be consistent with power-law models. However, the ASCA spectra were observed to be fatter than their ROSAT spectra. Similarly, in some cases continuously curved, log-parabola models provided better representation for the X-ray spectral distributionof some sources(Donatoetal.2005).Also, Massaro et al. (2004a,b) found the log-parabola as the best model for the characterization of X-ray spectra of Mrk 421 and Mrk 501 in their multiple fux states. Spectral curvature has also been detected in the XMM-Newton spectra of a number of X-ray bright BL Lac objects from the Einstein Slew Survey (see Perlman et al. 2005)and several BeppoSAX blazars (see Donato et al. 2005).UsingSwift/XRTspectraofasampleofTeV blazars,Wierzcholska&Wagner(2016b)decomposed the syn-chrotronandIC components. Furthermore,inafewsourcesalinear relation between the fux and hardness ratio, also called the “harder-when-brighter” trend, has been reported by Zhang et al. (2005, 2006). Similarly, soft and hard lags were observed during the correlation study between the emission in various X-ray bands (e.g., Fossati et al. 2000b; Zhang et al. 2006). In addition,hysteresis loopsin the spectral index and fux intensity planehavebeen reported(e.g., Ravasioetal.2004;Falconeetal. 2004; Brinkmann et al. 2005). To sum up, these studies over the decades have suggested that the sources exhibit high ampli-tude rapid variability on diverse timescales ranging from a few hours to a few months and that the nature of X-ray blazar spectra in various energy bands behave in variable and complex fashions.
Recently, several sources have been observed in the hard X-ray regime by Nuclear Spectroscopic Telescope Array
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(NuSTAR), mostly to complement the contemporaneous multifrequencyobserving campaigns. Madsen et al. (2015)described the NuSTAR spectra of the blazar 3C 273 by an exponentially cutoff power-law with a weak refection component from cold, dense material; the spectra revealed an evidence of a weak neutral iron line as well. In the NuSTAR observations of the FSRQ 3C 279, Hayashida et al. (2015)observed a spectral softening by ΔΓX ≈ 0.4 at ∼4keV between the two observation epochs. Blazar S5 0836+71 was found to be highly variable in hard X-ray during the broadband studyby Paliya (2015). Similarly, Furniss et al. (2015)found that the combined Swift and NuS-TAR of the blazar Mrk 501, during both a low and high fux state, could be well ftted by a log-parabolic spectrum. In the combined NuSTAR and Swift/XRT spectra of S5 0716+714, Wierzcholska&Siejkowski (2016a)reporteda break energy at ∼8keV revealing both low and high energy components. In their study of the two high red-shifted blazars, S5 0014+81 and B0222+185, Sbarrato et al. (2016)concluded that the two sources harbored the most luminous AD and the most power-ful jet, respectively, placing these sources at the extreme end of the disk-jet relation for γ-ray blazars. Rani et al. (2017)observed rapid hard X-ray variability on hour timescales in a few blazar sources. Similarly, Pandeyetal. (2017)reported the instances of intraday variability in the NuSTAR light curves of a number ofTeV blazars, and also noticeda general harder-when-brighter trend.
In this paper, we conduct a thorough analysis of all the blazar sources from the NuSTAR data archive by carrying out timing, spectral, and cross-correlation analyses to study the nature of the variability properties of blazars in the hard X-ray regime.Ourworkismainlymotivatedto understandthephysical process in the blazars by exploring the possible relation of variability properties, particularly variability and the minimum variability timescale, with the mean fux and spectral state of the sample sources, and thereby shed light into the innermost regions of blazars hidden from our direct view. We organize our presentations in the following way: in Sect. 2, the obser
vation and the data processing of 31 NuSTAR observations of 13 blazar sources are discussed. We present our timing, spec-tral, and cross-correlation study on the light curves and the spectra in Sect. 3. In Sect. 4, we report several interesting observa
tional features such as rapid fux and spectra variability, a con-nection between higher fux and harder spectra, and hard and soft lags, and we discuss the observed features in the light of current blazar models. Finally we summarize our conclusions in Sect.5.
2. Observations and data reduction
2.1. Source sample
We selected the sample sources from the NuSTAR archive that were classifed as blazar sources. Moreover, only the observations with observation period greater than ten kiloseconds (ks) and carrying the issue fag 0 were included in the study. The name, class, position and redshift of the sources are listed in Table1.The source sample consistsofseven FSRQs,two ISPs, and four HSPs1, which are alsoTeV blazars. The redshiftof the sources has a diverse range from the nearest(z = 0.0334; Mrk
501) to thefarthest source(z = 3.366; S5 0014+81).
1 We did not include Mrk 421 in the sample because it is being exclusively studiedby our research group.
G. Bhatta et al.: NuSTAR blazars Table 1. General information about the studied blazar sources.
Source name Source class RA (J2000) Dec (J2000) Redshift (z)
S5 0014+81 FSRQ 00h17m08.4748s +81d35m08.136s 3.366
B0222+185 FSRQ 02h25m04.6688s +18d46m48.766s 2.690
HB 0836+710 FSRQ 08h41m24.3652s +70d53m42.173s 2.172
3C 273 FSRQ 12h29m06.6997s +02d03m08.598s 0.158
3C 279 FSRQ, TeV 12h56m11.1665s −05d47m21.523s 0.536
PKS 1441+25 FSRQ, TeV 14h43m56.9s +25d01m44s 0.939
PKS 2149−306 FSRQ 21h51m55.5239s −30d27m53.697s 2.345
1ES 0229+200 BL Lac, HSP, TeV 02h32m48.616s +20d17m17.45s 0.140
S5 0716+714 BL Lac, ISP, TeV 07h21m53.4s +71d20m36s 0.300
Mrk 501 BL Lac, HSP, TeV 16h53m52.2167s +39d45m36.609s 0.0334
1ES 1959+650 BL Lac, HSP, TeV 19h59m59.8521s +65d08m54.652s 0.048
PKS 2155–304 BL Lac, HSP, TeV 21h58m52.0651s −30d13m32.118s 0.116
BL Lac BL Lac, ISP, TeV 22h02m43.3s +42d16m40s 0.068
2.2. NuSTAR Observations
Nuclear SpectroscopicTelescope Array(NuSTAR)is a sensitive hard X-ray (3–79keV) instrument with two focal plane mod-ules: FPMA and FPMB. The observatory operates within the bandpass with spectral resolution of ∼1keV. The feld of view of each telescope is ∼130 and the half-power diameter of an image of a point source is ∼10 (see Harrison et al. 2013). The raw data products were processed using NuSTAR Data Analysis Software (NuSTARDAS) packageversion 1.3.1.Wereduced and analyzed the observations via HEASOFT2 version 6.21 and CALDB version 2017-06-14. By using the standard nupipeline script, cali-brated and cleaned event fles were produced. Source fux and spectra were extracted from a region of 3000 radius centered around the source location, and the background was extracted from a 7000 radius region relatively close to the sourcebut also farenoughtobefreefrom contaminationbythe source.Thelight curves were generated with a time bin of 15 min. Similarly, the spectra were re-binned with the task grppha to have at least 30 counts per channel.
3. Analysis
The NuSTAR observations of the blazar sources discussed in this paper along with their observation ID and observation dates are listed in Table 2. The light curve of the source 3C 279 (Obs. ID: 60002020002), displaying modulations in the hard X-ray emission, is presented in the top panel of Fig. 1. To see the spectral states of the individual fux points, the plot symbols are color-coded according to the hardness ratio (defned below). The light curves for the other observations are presented sim-ilarly in Appendix A. Timing, spectral, and cross-correlation analyses are performed to examine the hard X-ray variability properties of the sample sources; these analyses are discussed below.
3.1. Flux variability
Most of the observations for the sample sources are found to be rapidly variable within the observation period. The observed variability is quantifed by defning two measures. Variability amplitude (VA) measuring the peak-to-peak fux oscillations is
https://heasarc.nasa.gov/lheasoft/
given as
Fmax − Fmin
VA = , (1) Fmin
where Fmax and Fmin are the maximum and minimum fux in counts/sec. This kind of variability measure, derived only from the extreme fuxes, may not represent the overall variability. In such a case, fractional variability (FV; see Vaughan et al. 2003;Bhatta&Webb 2018), which considers all the fuxes in the light curve, may be a more suitable measure to represent the observedvariability.Following Burbidgeetal. (1974), the minimum timescale of such variability is determined using the expression
Δt
,
τvar = (2)
ΔlnF
where Δt is the time interval between fux measurements (see also Hagen-Thorn et al. 2008). To compute the uncertainty in τvar, we followed the general error propagation rule, i.e., for a general function y = f (x1, x2, ..xn)with the corresponding uncertainties Δx1, Δx2, ..Δxn in x1, x2, ..xn, respectively, uncertainty in y can be expressed as (similar to Eq. (3.14) in Bevington&Robinson 2003)
s
!2 !2 !2
∂y ∂y ∂y
Δy ' Δx1 +Δx2 + ... +Δxn · (3)
∂x1 ∂x2 ∂xn
Thus using Eq.(3), uncertainty in τvar are estimated as
s
F12 ΔF22 + F22 ΔF2 Δτvar ' 1 Δt, (4) F2 F2(ln[F1/F2])4
12
where F1 and F2 are the count rates used to estimate the minimum variability timescales, and ΔF1 and ΔF2 their corresponding uncertainties.
All these quantities characterizing fux variability in the sources, i.e., FV, VA, and minimum variability timescales for the source sample are listed in Cols. 6, 7, and 8, respectively, of Table2.
Now, using the causality argument, the minimum variability timescale τvar can be used to estimate the upper limit for the minimum sizeof the emission region(R)asgivenby
δ
R ≥ cτvar, (5)
(1+ z)
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# Source Obs. date Obs. ID Obs. time (ks) Fvar (percent) VA τvar (ks)
1 S5 0014+81 2014-12-21 60001098002 46.80 30.02 ± 1.38 3.15 ± 1.23 0.91 ± 0.83
2 2015-01-23 60001098004 39.60 14.29 ± 1.73 2.02 ± 1.07 1.77 ± 0.74
3 B0222+185 2014-12-24 60001101002 61.00 6.92 ± 1.37 0.97 ± 0.40 4.48 ± 2.96
4 2015-01-18 60001101004 70.00 8.90 ± 1.40 1.12 ± 0.60 3.58 ± 1.67
5 HB 0836+710 2013-12-15 60002045002 47.00 12.92 ± 0.87 1.43 ± 0.35 2.53 ± 0.91
6 2014-01-18 60002045004 67.00 8.85 ± 0.52 1.11 ± 0.35 4.99 ± 1.94
7 3C 273 2016-06-26 10202020002 74.70 10.05 ± 6.01 1.48 ± 2.16 8.81 ± 3.34
8 2017-06-26 10302020002 72.00 14.86 ± 4.79 4.06 ± 6.09 1.24 ± 1.70
9 3C 279 2013-12-16 60002020002 78.00 16.59 ± 0.77 2.28 ± 0.52 2.31 ± 1.26
10 2013-12-31 60002020004 78.00 17.26 ± 0.28 1.50 ± 0.17 5.61 ± 3.99
11 PKS 1441+25 2015-04-25 90101004002 72.00 26.01 ± 3.82 2.82 ± 1.34 1.24 ± 0.62
12 PKS 2149–306 2013-12-17 60001099002 71.10 9.30 ± 0.65 1.21 ± 0.21 3.31 ± 2.27
13 2014-04-18 60001099004 90.00 10.60 ± 0.88 1.64 ± 0.80 2.24 ± 1.00
14 1ES 0229+200 2013-10-05 60002047004 38.00 13.33 ± 0.85 1.61 ± 0.47 2.35 ± 1.23
15 S5 0716+714 2015-01-24 90002003002 32.00 14.93 ± 1.45 1.49 ± 0.58 2.79 ± 1.43
16 Mrk 501 2013-04-13 60002024002 35.00 5.24 ± 0.66 0.75 ± 0.14 6.30 ± 2.21
17 2013-05-08 60002024004 55.00 17.76 ± 0.42 1.52 ± 0.14 4.89 ± 1.56
18 2013-07-12 60002024006 20.00 5.23 ± 0.43 0.59 ± 0.17 18.79 ± 10.01
19 2013-07-13 60002024008 20.40 9.79 ± 0.30 1.05 ± 0.11 2.25 ± 0.89
20 1ES 1959+650 2014-09-17 60002055002 32.00 33.60 ± 0.58 2.48 ± 0.35 3.76 ± 1.14
21 2014-09-22 60002055004 32.00 13.93 ± 0.66 0.68 ± 0.14 8.31 ± 5.59
22 PKS 2155–304 2012-07-08 10002010001 71.00 19.66 ± 0.75 3.44 ± 2.65 0.95 ± 0.64
23 2013-04-23 60002022002 90.00 25.17 ± 1.07 2.21 ± 0.80 1.86 ± 0.84
24 2013-07-16 60002022004 26.10 27.78 ± 0.98 5.65 ± 3.40 0.79 ± 0.40
25 2013-08-02 60002022006 29.70 22.03 ± 1.92 2.96 ± 3.33 0.30 ± 0.12
26 2013-08-08 60002022008 36.00 18.67 ± 6.63 2.10 ± 1.59 1.93 ± 1.09
27 2013-08-14 60002022010 31.50 37.69 ± 6.61 3.76 ± 2.89 1.59 ± 0.86
28 2013-08-26 60002022012 24.30 19.74 ± 1.33 1.70 ± 0.26 3.13 ± 1.98
29 2013-09-04 60002022014 29.70 18.90 ± 1.98 1.52 ± 0.24 3.41 ± 1.41
30 2013-09-28 60002022016 25.20 31.34 ± 2.42 7.28 ± 7.74 0.77 ± 0.66
31 BL Lac 2012-12-11 60001001002 42.30 25.03 ± 4.12 3.55 ± 2.86 1.88 ± 0.96
where δ, Dopplerfactor, is defned as δ = (Γ (1− βcosθ))−1 and for the velocity β = v/c thebulk Lorentzfactor can be written
pas Γ= 1/ 1− β2. It is assumed that the emission originates from the innermost regions of the blazar jets, which move with high speeds along the path that makes an angle, θ, with the line of sight.Fora moderatevalueof δ = 10, the distribution of the emission region sizes are shownin Fig. 2.
3.2. Spectral analysis: Hardness ratio and spectral ftting
To study the spectral variability of the X-ray emission from the sources, the source light curves are produced in two energy bands: a soft band between 3 and 10keV and a hard band between 10 and 79keV. Then we defne hardness ratio (HR) as
Fhard
HR = , (6) Fsoft
where Fhard and Fsoft are the fux in count rates in the hard (10–79keV) and soft (3–10keV) bands, respectively. The HR is a commonly used model-independent method to study spectral variationsover timeand fux states.In thiswork,we particularly examine the relation between fux and HRs over the observation period to constrain the underlying physics. The middle panel of Fig.1shows the fux-HR plot for the source Mrk 501 (Obs. ID: 6000202400), with clearly visible harder-when-brighter trend.
To look for possiblehysteresis loops in the fux-HR plane, the symbols are color-coded according to the time.
Spectral analyses of the NuSTAR blazars were carried out by the spectral ftting the source spectra using xspec (Arnaud 1996) models and using the χ2 minimization statistics. The spectra from the instruments FPMA and FPMB were simultaneously ftted in xspec.To account for any possible subtle differences between the instruments, an intercalibration constant was included in the spectral models. The values of the constant, ranging from 0.97 to 1.04, indicate that there are no major differences betweenthe observations obtainedbythetwo instruments. To ascertain the best representation of the spectral behavior, we ft each spectrum using three spectral models: power law (PL), log-parabola (LP) and broken power law (BPL). The power-law model can be given as
dN = NE−Γ , (7)
dE where N, E, and Γ are normalization, photon energy, and photon index, respectively. Similarly, the log-parabola model that has a continuous break is given by
!−(Γ+βlog(E/E0))
dNE
= N0 , (8)
dEE0
where N0 and E0 are the normalization and reference energy fxed to 10keV, and Γ and β are the photon index and the
A93, page4of 19
G. Bhatta et al.: NuSTAR blazars
(
E−Γ1
dN , if E ≥ Eb
= N0(9)
E−Γ2
dE , otherwise
where Γ1 and Γ2 represent the high and low energy pho-ton indexes and N0 and Eb are the normalization and break energy,respectively.To account for thegalactic absorption tbabs (Tuebingen–Boulder ISM absorption model; Wilms et al. 2000) is multiplied with these models, while thehydrogen column den-sity are taken from Kalberla et al. (2005).
Of the three models, we chose the best-ft spectral model after performing F-test3. In particular the signifcance of LP and BPLwas estimatedagainstPL (nullhypothesis) and the model was accepted as a better ft if the probability under the null hypothesis was equal or smaller than 0.1 – equivalently, a signifcance equal or greater than 90%. If not, PL was considered to be the best representation. Further, between two models, i.e., LP and BPL, the model with higher signifcance (or lower probability value) was chosen to be the best model. Based on such criteria,outof31 observation spectra,7,17,and7spectra were found to be best represented by PL, LP, and BPL spectral mod-els, respectively. The ftting parameters for all the observations are listedinTable 3. Spectral ftting for the sourceS5 0716+714 is presented in the bottom panel of Fig. 1 and similar fgures for the rest of the observations are presented in Appendix A. The distribution of the photon indexes, resulting from the best-ft models, over the mean fux in count rates is shown in Fig.6.
3.3. Discrete correlation function
Cross-correlation study between emission in different energy bands offers insights that can shed light into the ongoing pro-cesses at the emission sites, for instance, the dominant radia-tive processes involved and distribution of the emitting particles (see, e.g., Zhang 2002).We analyzed the correlation between the NuSTAR blazar light curves in the soft energy (3–10keV) and hard energy (10–79keV) using z-transformed discrete correlation function (ZDCF) along with the likelihood of the ZDCF peaks and the associated uncertainties as described in Alexander
3 The F-test tool used in this work is available in xpsec.
A93, page5of 19 Table 3. Spectral ftting of the NuSTAR blazars.
(1) (2) (3) (4) (5) (6) (7) (8) Source Obs. ID Model Γ, Γ1 Eb(keV) β, Γ2 χred2 /d.o.f. F-value (prob.)
S5 0014+81 60001098002 PL 1.82 ± 0.03 – – 1.1851/153 LP 1.84 ± 0.04 – 0.36 ± 0.12 1.1226/152 9.52 (2.42 × 10−3) BPL 1.73 ± 0.04 21.79 ± 2.56 3.40 ± 0.73 1.0706/151 9.18 (1.73 × 10−4) 60001098004 PL 1.70 ± 0.03 – – 1.1128/164 LP 1.70 ± 0.03 – 0.00 ± 0.11 1.1197/163 – BPL 1.71 ± 0.04 19.55 ± 16.11 1.56 ± 0.28 1.1231/162 0.25 (7.81 × 10−1)
B0222+185 60001101002 PL 1.54 ± 0.02 – – 0.9783/479 LP 1.54 ± 0.02 – 0.22 ± 0.05 0.9380/478 21.58 (4.39 × 10−6) BPL 1.47 ± 0.03 14.04 ± 2.09 1.75 ± 0.07 0.9405/477 10.63 (3.06 × 10−5) 60001101004 PL 1.64 ± 0.02 – – 0.9882/366 LP 1.66 ± 0.02 – 0.29 ± 0.06 0.9270/365 25.16 (8.24 × 10−7) BPL 1.34 ± 0.08 6.54 ± 0.70 1.75 ± 0.03 0.9149/364 15.66 (2.99 × 10−7)
HB 0836+710 60002045002 PL 1.69 ± 0.02 – – 0.9106/452 LP 1.69 ± 0.02 – –0.08 ± 0.05 0.9075/451 2.54 (1.11 × 10−1) BPL 1.73 ± 0.03 12.65 ± 4.07 1.60 ± 0.06 0.9045/450 2.52 (8.13 × 10−2) 60002045004 PL 1.66 ± 0.01 – – 1.0267/664 LP 1.66 ± 0.01 – 0.10 ± 0.04 1.0146/663 8.92 (2.93 × 10−3) BPL 1.59 ± 0.03 7.98 ± 1.83 1.70 ± 0.03 1.0156/662 4.63 (1.01 × 10−2)
3C 273 10202020002 PL 1.62 ± 0.00 – – 1.0871/1335 LP 1.62 ± 0.00 – 0.11 ± 0.01 1.0326/1334 71.46 (7.31 × 10−17) BPL 1.57 ± 0.01 13.43 ± 1.05 1.72 ± 0.02 1.0299/1333 38.07 (8.32 × 10−17) 10302020002 PL 1.66 ± 0.01 – – 0.9334/1017 LP 1.66 ± 0.01 – 0.08 ± 0.02 0.9164/1016 19.87 (9.23 × 10−6) BPL 1.64 ± 0.01 19.35 ± 3.23 1.78 ± 0.05 0.9190/1015 8.97 (1.38 × 10−4)
3C 279 60002020002 PL 1.73 ± 0.02 – – 0.9442/480 LP 1.73 ± 0.02 – 0.08 ± 0.05 0.9411/479 2.58 (1.09 × 10−1) BPL 1.71 ± 0.02 29.87 ± 8.06 2.15 ± 0.33 0.9386/478 2.43 (8.90 × 10−2) 60002020004 PL 1.74 ± 0.01 – – 0.9031/691 LP 1.74 ± 0.01 – 0.07 ± 0.03 0.8982/690 4.77 (2.93 × 10−2) BPL 1.69 ± 0.03 8.66 ± 2.40 1.78 ± 0.03 0.8980/689 2.96 (5.24 × 10−2)
PKS 1441+25 90101004002 PL 2.08 ± 0.08 – – 1.030/49 LP 2.01 ± 0.09 – –0.32 ± 0.28 1.027/48 1.14 (2.90 × 10−1) BPL 2.09 ± 0.09 23.56 ± 23.32 1.51 ± 1.38 1.070/47 0.08 (9.19 × 10−1)
PKS 2149–306 60001099002 PL 1.37 ± 0.01 – – 0.9722/824 LP 1.36 ± 0.01 – 0.05 ± 0.03 0.9686/823 4.06 (4.42 × 10−2) BPL 1.34 ± 0.02 12.48 ± 3.57 1.42 ± 0.03 0.9668/822 3.30 (3.73 × 10−2) 60001099004 PL 1.46 ± 0.01 – – 0.9730/744 LP 1.46 ± 0.01 – 0.04 ± 0.03 0.9716/743 2.07 (1.50 × 10−1) BPL 1.42 ± 0.03 8.86 ± 2.94 1.49 ± 0.02 0.9701/742 2.11 (1.22 × 10−1)
1ES 0229+200 60002047004 PL 2.03 ± 0.02 – – 1.0547/387 LP 2.06 ± 0.02 – 0.23 ± 0.07 1.0255/386 12.02 (5.86 × 10−4) BPL 1.99 ± 0.03 16.04 ± 3.42 2.30 ± 0.15 1.0390/385 3.92 (2.06 × 10−2)
S5 0716+714 90002003002 PL 1.90 ± 0.03 – – 1.2050/194 LP 1.87 ± 0.03 – –0.33 ± 0.09 1.1428/193 11.56 (8.19 × 10−4) BPL 1.94 ± 0.04 19.60 ± 5.08 1.50 ± 0.23 1.1922/192 2.04 (1.33 × 10−1)
Mrk 501 60002024002 PL 2.27 ± 0.01 – – 0.8889/562 LP 2.30 ± 0.02 – 0.16 ± 0.04 0.8649/561 16.59 (5.29 × 10−5) BPL 2.26 ± 0.01 19.77 ± 5.55 2.48 ± 0.16 0.8848/560 2.30 (1.01 × 10−1) 60002024004 PL 2.24 ± 0.01 – – 1.0918/730 LP 2.26 ± 0.01 – 0.13 ± 0.03 1.0650/729 19.37 (1.24 × 10−5) BPL 2.23 ± 0.01 24.50 ± 4.37 2.55 ± 0.14 1.0786/728 5.47 (4.40 × 10−3)
Notes. Column 1: source name, Col. 2: Obs. ID, Col. 3: spectral models, power-law (PL), log-parabola (LP), broken power-law (BPL), Col. 4: photonindex(PLandLP), high-energyphotonindex(BPL),Col.5:break energy(keV),Col.6:CurvatureParameter(LP),low-energyphoton index (BPL), Col. 7: reduced χ2/degrees of freedom, and Col. 8: F-test and probability value. The best-ft spectral models are given in bold font.
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Table 3. continued.
(1) Source (2) Obs. ID (3) Model (4) Γ, Γ1 (5) Eb(keV) (6) β, Γ2 (7) χ2 red/d.o.f. (8) F-value (prob.)
60002024006 PL 2.09 ± 0.01 – – 1.0474/765 LP 2.12 ± 0.01 – 0.19 ± 0.03 0.9817/764 52.20 (1.22 × 10−12) BPL 2.00 ± 0.02 8.45 ± 0.70 2.20 ± 0.02 0.9836/763 25.81 (1.42 × 10−11) 60002024008 PL 2.13 ± 0.01 – – 1.0916/720 LP 2.17 ± 0.01 – 0.29 ± 0.03 0.9538/719 105.02 (4.27 × 10−23) BPL 1.98 ± 0.02 8.04 ± 0.47 2.28 ± 0.02 0.9548/718 52.58 (4.90 × 10−22)
1ES 1959+650 60002055002 PL 2.28 ± 0.01 – – 1.0531/561 LP 2.30 ± 0.02 – 0.10 ± 0.04 1.0444/560 5.67 (1.76 × 10−2) BPL 2.27 ± 0.01 20.25 ± 8.80 2.41 ± 0.15 1.0537/559 0.84 (4.32 × 10−1) 60002055004 PL 2.54 ± 0.01 – – 1.1642/540 LP 2.59 ± 0.02 – 0.21 ± 0.05 1.1230/539 20.81 (6.28 × 10−6) BPL 2.50 ± 0.02 13.69 ± 1.55 2.86 ± 0.10 1.1192/538 11.86 (9.15 × 10−6)
PKS 2155-304 10002010001 PL 3.00 ± 0.02 – – 1.1986/377
LP BPL 3.10 ± 0.04 2.84 ± 0.06 – 5.92 ± 0.70 0.26 ± 0.09 3.13 ± 0.05 1.1774/376 1.1612/375 7.79 (5.53 × 10−3) 7.07 (9.67 × 10−4)
60002022002 PL 2.70 ± 0.03 – – 0.9128/307
LP BPL 2.63 ± 0.04 2.72 ± 0.03 – 15.40 ± 3.32 –0.21 ± 0.10 2.25 ± 0.26 0.9023/306 0.9031/305 4.57 (3.33 × 10−2) 2.65 (7.24 × 10−2)
60002022004 PL 2.55 ± 0.04 – – 0.9447/151
LP BPL 2.48 ± 0.05 2.59 ± 0.04 – 21.85 ± 3.19 –0.23 ± 0.14 0.87 ± 0.52 0.9366/150 0.8691/149 2.31 (1.31 × 10−1) 7.57 (7.41 × 10−4)
60002022006 PL 3.04 ± 0.05 – – 0.9465/120
LP BPL 3.05 ± 0.08 3.04 ± 0.05 – 17.42 ± 131.65 0.02 ± 0.19 3.13 ± 4.34 0.9543/119 0.9624/118 0.02 (8.90 × 10−1) 0.01 (9.91 × 10−1)
60002022008 PL 2.88 ± 0.05 – – 0.9755/94
LP BPL 2.70 ± 0.08 2.99 ± 0.09 – 9.14 ± 2.01 –0.51 ± 0.20 2.48 ± 0.21 0.9242/93 0.9381/92 6.22 (1.44 × 10−2) 2.87 (6.16 × 10−2)
60002022010 PL 2.98 ± 0.05 – – 0.7921/106
LP BPL 3.03 ± 0.09 2.94 ± 0.06 – 13.74 ± 4.22 0.16 ± 0.22 3.80 ± 1.07 0.7939/105 0.7792/104 0.76 (3.85 × 10−1) 1.88 (1.58 × 10−1)
60002022012 PL 2.66 ± 0.03 – – 1.0162/210
LP BPL 2.79 ± 0.05 2.55 ± 0.04 – 11.14 ± 1.44 0.48 ± 0.13 3.20 ± 0.22 0.9483/209 0.9413/208 16.04 (8.63 × 10−5) 9.35 (1.29 × 10−4)
60002022014 PL 2.80 ± 0.04 – – 0.9787/182
LP BPL 2.79 ± 0.06 2.80 ± 0.04 – 39.70 ± 48.09 –0.02 ± 0.15 -2.50 ± 26.91 0.9840/181 0.9788/180 0.02 (8.88 × 10−1) 0.99 (3.73 × 10−1)
60002022016 PL 2.61 ± 0.06 – – 1.024/78
LP BPL 2.52 ± 0.07 2.71 ± 0.11 – 8.21 ± 2.92 –0.35 ± 0.20 2.41 ± 0.17 1.000/77 1.013/76 2.87 (9.42 × 10−2) 1.42 (2.47 × 10−1)
BL Lac 60001001002 PL 1.85 ± 0.02 – – 0.9482/409 LP 1.85 ± 0.02 – 0.02 ± 0.06 0.9503/408 0.10 (7.57 × 10−1) BPL 1.84 ± 0.03 13.76 ± 14.96 1.89 ± 0.09 0.9515/407 0.29 (7.48 × 10−1)
(20134;see alsoBhatta&Webb 2018).The ZDCFs between the lower energy (LE) and higher energy (HE) light curves for the source 3C 279 (Obs. ID 60002020002) are shown in the bottom panelof Fig. 1, and similar plots for the restof the observations discussed in the paper are presented in Appendix A;the results are also tabulated inTable 4. In the fgure, we see that in most cases we do not fnd a strong correlation between low and high energy emission at the zero lag, and in a few cases hints of hard and soft lags can be seen. It should be pointed out that between two similar DCF values at the different lags, the value closer to zero lag would be statistically more signifcant as the number of
The software is publicly available at http://www.weizmann.ac.
il/particle/tal/research-activities/software
observations that go into the calculation of DCF value decreases with the increase in the lead/lag.
4. Results
The results of all of the above analyses on the individual sources along with their brief introduction are presented below.
4.1. S5 0014+81
FSRQ S5 0014+81, detectedbymultiple X-ray instruments, possesses the most luminous AD among blazars (see Sbarrato et al. 2016, and references therein). Also, of the sources discussed in
A93, page7of 19 Table 4. Discrete cross-correlation function between the low (3– 10keV) and high energy (10–79keV) emission of the NuSTAR blazars.
Source Obs. ID Lag (ks) ZDCF Likelihood
S5 0014+81 60001098002 +5.40+0.58 −10.43 0.32+0.14 −0.13 0.22
60001098004 −0.90+0.40 −0.72 0.34+0.14 −0.13 0.62
B0222+185 60001101002 +9.00+0.44 −10.36 0.48+0.17 −0.18 0.29
60001101004 +2.00+0.75 −3.89 0.53+0.15 −0.14 0.42
HB 0836+710 60002045002 −6.70+9.13 −7.72 0.31+0.12 −0.18 0.35
60002045004 +3.00+9.36 −2.34 0.30+0.17 −0.18 0.33
3C 273 10202020002 0.00+0.91 −0.58 0.45+0.15 −0.16 0.44
10302020002 −4.80+1.04 −2.13 0.46+0.15 −0.16 0.45
3C 279 60002020002 0.00+5.53 −0.68 0.63+0.12 −0.11 0.43
60002020004 +7.00+5.97 −10.07 0.79+0.06 −0.05 0.45
PKS 1441+25 90101004002 +4.00+4.29 −10.21 0.15+0.23 −0.24 0.08
PKS 2149–306 60001099002 −1.80+5.71 −4.27 0.47+0.14 −0.13 0.72
60001099004 −3.60+6.46 −4.34 0.23+0.14 −0.14 0.19
S5 0716+714 90002003002 +3.00+6.37 −7.02 0.50+0.20 −0.18 0.13
Mrk 501 60002024002 +3.00+0.58 −6.45 0.40+0.27 −0.24 0.13
60002024004 +0.00+0.47 −0.48 0.92+0.37 −0.28 0.57
60002024006 −4.00+6.02 −0.44 0.75+0.16 −0.12 0.40
60002024008 0.00+1.98 −2.52 0.78+0.98 −0.81 0.72
1ES 1959+650 60002055002 0.00+1.12 −0.52 0.95+0.31 −0.23 0.41
60002055004 +0.00+0.62 −0.57 0.67+0.18 −0.15 0.54
PKS 2155–304 10002010001 0.00+0.52 −3.56 0.49+0.15 −0.14 0.61
60002022002 −1.25+1.63 −1.78 0.49+0.13 −0.13 0.37
60002022004 −1.50+1.55 −0.94 0.75+0.15 −0.12 0.38
60002022006 −1.50+4.37 −2.67 0.29+0.24 −0.22 0.15
60002022008 +0.00+3.69 −0.42 0.75+0.14 −0.11 0.53
60002022010 +1.88+1.39 −1.17 0.49+0.27 −0.23 0.36
60002022012 +2.02+1.55 −1.42 0.55+0.24 −0.19 0.37
60002022014 −5.27+3.12 −1.02 0.32+0.27 −0.25 0.30
60002022016 −2.70+1.76 −0.65 0.32+0.29 −0.28 0.20
BL Lac 60001001002 −2.70+2.14 −7.72 0.31+0.12 −0.18 0.35
Notes. The +ve lag indicates hard lag.
this paper, it is the most distant source at the redshift of 3.366. The high-redshift blazar reveals contributions due to thermal emission from the AD in its optical continuum(Ghisellini et al. 2010a). We looked into two NuSTAR observations separated by one month. The frst observation (Obs. ID: 60001098002) shows one of the largest variability with FV ∼ 30% and rapid (τvar = 0.91 ± 0.93 ks) minimum variability timescale within 46ks observation period, while the second observation showsa moderatevariability (FV ∼ 14%) within 39 ks. No obvious trend in fux-HR plane could be observed. While in the frst observation, we do not see anysignifcant correlation between the low and high energy emission, in the second observation we found a hint of soft lag of ∼0.9ks with ZDCF coefficient ∼0.34 and likelihood(LH)= 0.62. The spectra for the frst observation is ftted with BPL with a break at ∼20keV energy, whereas the power-law model with ΓX ∼ 1.7 is ftted well for the second observation.
4.2. B0222+185
Blazar B0222+185 has been widely studied by X-ray instruments, for example, Swift/BAT (Ajello et al. 2012; Baumgartner et al. 2013). In the hard X-ray study, it was found to be one the most powerful blazars ever observed (Sbarrato et al. 2016); the optical fux showed evidence for the thermal emission from the AD(Ghisellini et al. 2010a). It is one of the most distant sources(z = 2.69) discussedin thiswork.We studied two NuSTAR observations spanning 61 and 70 ks. In the light curves, the fux points appear to be scattered showing no coherent variability pattern. Similarly, no clear trend in the fux-HR plane can be observed. The correlation between the soft and hard emissionshowsasignofhardlagof ∼9.0ks and∼2ks with ZDCF ∼0.48 and ∼0.53. However the larger associated errors and smallvaluesofLHmake them inconclusive.The frst observation is ftted with LP with β ∼ 0.2and the second observation is well ftted with BPL with Eb ∼ 6.5keV.
4.3. HB 0836+710
Source HB 0836+710 is a high-redshift blazar, extensively studied in multiband emission (see Akyuz et al. 2013, and refer
ence therein).The sourceis identifedwithaprominent kpc-scale radio jet(Hummel et al. 1992).The optical-UV spectrum is dom-inatedbythermal emissionfromtheAD(Ghisellinietal. 2010a) and the γ-ray emission region is found to be located ∼35pcaway from the central engine(Jorstad et al. 2013). In the two NuSTAR observationsthatweexamined,the sourceshowsrapidvariability withthe minimumvariability timescalesas smallas2.53±0.91ks. The second observation shows a systematic modulation of fuxHRplane.However,the ZDCFvalues∼0.31 and∼0.30 at the zero lag show that there is not much correlation between the low and high energy emission.For the frst and second observations BPL and LP models are ftted, respectively.
4.4. 3C 273
3C 273 is the nearest bright quasar with a large-scale visible jet. Because it is highly variable across nearly all energies, the source has been the subject of numerous broadband observation campaigns (e.g., Soldi et al. 2008;Abdo et al. 2010). In the optical-UV band there is a bright excess, commonly called blue bump, possibly a signature of thermal reprocessing from the AD(Paltanietal. 1998).Weexamined two NuSTAR observations(Obs.ID 10202020002and 10302020002)exactlyoneyear apart. In the frst observation, we fnd moderate (FV ∼ 10%)but rapid variability(τvar = 8.81 ± 3.34ks).We observe that the fux is stable and HR changes randomly,whereas in the second observation the source became more variable with FV ∼ 15% and rapid(τvar = 1.24 ± 1.70 ks) in fux and HR. In the frst observation, we fnd a good correlation (ZDCF= 0.45 and LH = 0.44) between the high and the low energy emission at zero lag. In the second epoch, although not very signifcant (ZDCF = 0.46 and LH = 0.45),we seea possible softlagof ∼4.8ks. The spectra for both of the observations are well ftted with LP with β ∼ 0.1.
4.5. 3C 279
Blazar 3C 279 is a FSRQ source profusely emitting in hard X-ray and γ-rays. The source, highly variable across a wide range of spectral bands (see Hayashida et al. 2015, and the references therein), is one of a handful of sources detected above 100 GeV (MAGIC Collaboration 2008). The source reveals a compact, milliarcsecond-scale radio core ejecting radio knots withabulk Lorentz factor, Γ= 15.5 ± 2.5, along the direction making an angle, θobs = 2.1 ± 1.1◦,to the line of sight(Jorstad et al. 2005, 2004). Our study concerning two NuSTAR observations
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shows that the source displays moderate variability in hour-like timescales(τvar = 2.31 ± 1.26ks and5.61 ± 3.99 ks), the correlation betweensoftandhard emissionshowsahardlagbya few ks, particularly distinguished (ZDCF ∼ 0.79 and LH= 0.45) inthe second observation (Obs. ID: 60002020004).Wecannot see anyclear trend in fux-HR plane. Of the three spectral models, the frst observation is ftted with BPL model with Eb ∼ 30keV and the secondis well representedbyLP witha small β ∼ 0.07.
4.6. PKS 1441+25
PKS 1441+25, a TeV blazar, has been detected in very high energy (VHE) γ-rays by VERITAS and MAGIC (see Abeysekara et al. 2015). The source shows rapid variability when fux doubled within a few hours and it also exhibits one of the most rapid(τvar = 1.24 ± 0.62 ks) and largest variability (FV ∼ 26%) observed within the observation period of 72ks. Wedonotseeasimple correlation betweenthefuxandHR,and there is no apparent correlation (ZDCF ∼ 0.00) between the low and high energy emission at the zero lag. The spectrum is ftted well with a PL model with photon index ∼2.
4.7. PKS 2149–306
PKS 2149-306 is a X-ray bright FSRQ often marked by dra-matic fux and spectral variability as observed by most of the X-ray telescopes (see D’Ammando&Orienti 2016, and refer
ences therein). In both of the NuSTAR observation we studied, the source shows signifcant variability (FV ∼10%) in the timescale of a few hours. In the frst observation, we see a hint ofa softlag near1.8ks with ZDCF = 0.47 and LH = 0.72 anda harder-when-brighter trend, whereas in the second there is not much correlation between the low and high energy emission and a complex fux HR relation is observed.For both the observations, the source spectra are ftted with BPL and PL with the fattest photon indexes of ∼1.5.
4.8. 1ES 0229+200
BL Lac 1ES 0229+200is oneof the importantTeV sources that has been used to study the properties of the extragalactic background light and intergalactic magnetic feld through its very high energy emission(Aliu et al. 2014, and references therein). We examined the 38ks long NuSTAR observation for its hard X-ray properties. The source displays a signifcant (FV ∼ 13%) and rapid(τvar = 2.35 ± 1.23 ks) variability. The fux does not appear to be correlated with the HR. The source spectra are best ftted using LP model with photon index, ΓX ∼ 2.
4.9. S5 0716+714
S5 0716+714 is one of the best-studied sources across broad bands.TheTeV sourceis widelyfamousforitsvariability with almost 100% duty cycle (see Bhatta et al. 2016a, and the ref-erences therein). In the NuSTAR observation we studied, the source shows rapidvariability; the fux nearly doubled within the observation period of 32ks. In addition, signifcant average fux variability (FV∼ 15%) with 2.79 ± 1.43ks minimum variability timescale is noticed.We do not detect anyobvious HR-fux relation,howeverthe correlation betweenthehighandlowenergy emissionrevealsapossiblehardlagof ∼3.00ks with ZDCFvalue ∼0.5howeverwithasmallLH,0.13.The spectrumisfttedusing LP model with ΓX ∼ 1.9anda negative curvature,β ∼−0.33.
4.10. Mrk501
Mrk501,which shinesbrightinX-ray,isoneofthemostfavored targets for multifrequencyobservations (see Furniss et al. 2015, and references therein).We studied four NuSTAR observations between April and July 2013. The light curve of the frst observation (Obs. ID: 60002024002) shows low variability (FV ∼ 5%) and no clear trend in HR variability. In the second observation (Obs. ID: 60002024004), the overall fux fol-lows a rising trend for ∼47ks and later declines during the remaining 8ks; the source displays signifcant variability with FV ∼17%. The harder-when-brighter behavior is clearly visible in the fux-HR plane as shown in Fig. 1(middle panel). During the third observation (60002024006) the source is nearly twice as bright asin the other observationsbut has decreasedvariability (FV ∼ 5%). The last data set for Mrk 501 (60002024008) shows the source getting fainter with random fux-HR trend. Similarly, we found that of the four observations, the correlation between LE and HE light curves were signifcant for Obs ID 60002024004 and 60002024008, whereas for the other two observations we do not fnd anyclear lead/lag. The spectra are ftted well with different power-law models for different observations, the ΓX ranging from2.1−2.3(refer toTable3).
4.11. 1ES 1959+650
BL Lac 1ES 1959+650, a HSP (Giebels et al. 2002) and a TeV blazar (see Holder et al. 2003), was frst detected in X-raysby Elvisetal. (1992).We analyzed data for the two observations 60002055002 and 60002055004. In the frst observation, we see the fux rising by the factor ∼2, displaying the harder-when-brighter trend. Although the FV does not differ signifcantly from the frst observation, in the second epoch the light curve is relatively stable and does not display a well-defned trend in the fux-HR plane. The ZDCF analysis shows that LE and HE light curves have a relatively strong correlation around zero lag.For both of the observations, LP model with ΓX ∼2.3 and 2.6 best describes the source spectra.
4.12. PKS 2155–304
PKS 2155–304 is one of the brightest HSP blazars and has been widely studied in X-ray bands (see Madejski et al. 2016, and references therein). The source is known to frequently exhibit rapid variability in the X-ray bands on hourly timescales (e.g., Rani et al. 2017; Tanihata et al. 2001; Zhang et al. 1999). We analyzed nine NuSTAR observations between July 2012 and October 2013, and found that the source displayed several inter-esting features including large FV(∼27%) and the most rapid variability with smallest minimumvariability timescale0.30 ±
0.12 ks. In addition, in three of the observations, the fux changes by twice withinafew hours.However,the fux-HR relation does not show anyobvious trend. The ZDCF analysis does not reveal anyclear lead/lag betweenLEandHElight curves(refertoTable 4). The spectra for different observations are ftted separately with all three models, i.e., PL, LP, and BPL models, while the photon indexes range between ∼2.5 and 3.0.We note that with ΓX ∼ 3.0the source displays one of the steepest spectra usually found in anyBL Lac objects.
4.13. BL Lac
BL Lac is a prototype source of the class with the same name. The source has been observedbyseveral multiwavelength
A93, page9of 19
campaigns (see Bhatta&Webb 2018, and the references therein). The 42ks long NuSTAR observation that we examined shows large (FV ∼ 25%) and rapid(τvar = 1.88 ± 0.96 ks) variability. However, the HR does not appear to be correlated with the fux.Weobservearelatively smaller correlation(∼0.30) between the high and low energy emission at the zero lag. The source spectra is best-ftted with PL model with ΓX ∼ 1.85.
5. Discussion
In this section, we attempt to explain the results of the above analyses in the light of the existing blazar models.
5.1. Rapid hard X-ray variability
Hard X-ray observations offer a direct access to the heart of an AGN revealing important processes occurring at the innermost regions of the central engine. The variable hard X-ray emission inAGNis consideredto originateatthe corona, whichisa compact region above the AD. Hard X-ray emission from most of theAGNs mainly consistsof three components: soft-access, neutral iron line, and the Compton hump.InSeyfertItypegalaxies, these components are distinctly observedintheir spectra (e.g., see Walton et al. 2014). However, in case of blazars, as the Doppler boosted jet emission is dominant over the coronal emission, the spectra exhibits pure power-law shapes devoid of emission or absorption features. Hard X-rayvariabilityinblazarsovervarious timescales couldbe resultedbythe up-scatteringofthesoftpho-ton felds locatedatvarious geometrical componentsofanAGN including AD, jets, DT,and BLR. Consequently,anymodulation inthe photon feld, high energyelectron population, and magnetic feld in situ can produce hard X-ray variability, which can propagate along the jets. In addition, the distribution of the emission region sizes, as presentedin Fig. 2,points out that suchvariability originates in compact(∼1012cm)volumesofthe sources.
Thus estimated sizes of the emission regions are smaller than thegravitational radiusofanAGNwithatypicalblackhole mass of 109 M∼ 1.5 × 1012 cm. This suggests the observed short timescale modulations could either be ascribed to changes occur-ring at a fraction of the entire black hole region or the fuctuations could refect small-scale instabilities intrinsic to the jet (see Begelman et al. 2008).In the relativistic turbulencescenario byNarayan&Piran (2012),magnetohydrodynamic turbulencein thejetcanleadtocompact substructuresthatmoverelativistically in random directions. Alternatively,very highbulk Lorentzfac-tors (e.g., Γ ∼ 100) associated with the emitting regions can make the size of these regions appear comparable to rg. It is possible to achieveasuch high Γswith the jets-in-a-jet model in which mag-netic reconnection (e.g., Giannios et al. 2009)or turbulence (e.g., Narayan&Piran 2012)can produce relativistic outfows thebulk jet frame.
Therapidfuxvariationscouldalsobeexplainedasthe emission from the shocked regions in the blazar jets viewed close to line of sight (e.g., Marscher&Gear 1985;Spada et al. 2001; Joshi&Btcher 2011). The nonthermal emission modulations can also be attributed to various instabilities in the jet such as turbulence behind the shocks (see Bhatta et al. 2013;Marscher 2014).
In HSPs, the hard X-ray emission is probably due to the high energy tail of the synchrotron emission from large-scale jets. The variable emission then can be related to the particle accel-eration and synchrotron emission by the electrons of the high-est energy. In such a scenario, the variability timescales can be directly linked with particle acceleration and cooling timescales.
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3 mec
tcool = ∼ 7.74 × 108γ−1B−2 s, (10)
4 σTUBγβ2
where we use β ∼ 1 considering ultra-relativistic electrons. We note that such energy dependent cooling timescale can produce more rapid variability at hard X-ray energies than at soft X-ray energies. If we assume that the cooling takes place mainly because of the synchrotron process and that the most of the synchrotron emission is emitted in the NuSTAR energy band(∼15keV; logarithmic mean of the NuSTAR range), then following Zhang(2002), magnetic feld corresponding to the cooling timescales can be given as
2.09 × 102(1 + z)1/3
B = , (11)
t2/3
coolδ1/3E1/3
where E is the energy of the observed photons expressed in keV, and B and δ are the magnetic feld and Doppler fac-tor of the emitting region, respectively. Similarly, assuming the particle acceleration due to diffusive shock acceleration (e.g., Blandford&Eichler 1987), magnetic feld corresponding to the particle acceleration timescales canbegiven as
21.04 × 10−2(1+ z)ξ2/3E1/3
B = , (12)
t2/3
acc δ
where ξ is the acceleration parameter conveniently expressed in the fducial scale of 105 (for details see Zhang 2002)indicating the acceleration rate of electrons. For moderate δ and z = 0.1, the curves showing the relation between the magnetic feld and the acceleration and synchrotron cooling timescales within the NuSTAR band,are presentedinFig. 3.Itis interestingtonotethat for a reasonable ξ = 0.2× 105, the cooling curves closely follow the acceleration curves. From these curves, it can be inferred that for the given variability timescales of a few hours as seen in the source (refer toTable 2last column),a reasonablevalue of the magnetic feld could be in the order of a few Gauss. Once we constrain the magnetic feld, we can also estimate the energy of the high-tail synchrotron emitting electrons. Assuming most