X-ray spectral variations of synchrotron peak in BL Lacs
Yijun Wang, Shifu Zhu, Yongquan Xue, Minfeng Gu, Shanshan Weng, Huynh Anh N. Le
DDraft version September 17, 2019Typeset using L A TEX twocolumn style in AASTeX62
X-ray spectral variations of synchrotron peak in BL Lacs
Yijun Wang,
1, 2
Shifu Zhu,
3, 4
Yongquan Xue,
1, 2
Minfeng Gu, Shanshan Weng, and Huynh Anh N. Le
1, 2 CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei 230026, China;[email protected], [email protected] School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China Department of Astronomy & Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA; [email protected] Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai200030, China Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China (Received; Revised; Accepted)
Submitted to ApJABSTRACTThe spectral energy distribution of blazars around the synchrotron peak can be well described by the log-parabolic model that has three parameters: peak energy ( E p ), peak luminosity ( L p ) and the curvature parameter( b ). It has been suggested that E p shows relations with L p and b in several sources, which can be used toconstrain the physical properties of the emitting region and/or acceleration processes of the emitting particles.We systematically study the E p – L p and E p –(1 / b ) relations for 14 BL Lac objects using the 3–25 keV RXTE /PCAand 0.3–10 keV
Swift /XRT data. Most objects (9/14) exhibit positive E p – L p correlations, three sources show nocorrelation, and two sources display negative correlations. In addition, most targets (7/14) present no correlationbetween E p and 1 / b , five sources pose negative correlations, and two sources demonstrate positive correlations.1ES 1959+650 displays two different E p – L p relations in 2002 and 2016. We also analyze E p – L p and E p –(1 / b )relations during flares lasting for several days. The E p – L p relation does not exhibit significant differences betweenflares, while the E p –(1 / b ) relation varies from flare to flare. For the total sample, when L p < 10 erg s -1 , thereseems to be a positive E p – L p correlation. L p and the slope of E p – L p relation present an anti-correlation, whichindicates that the causes of spectral variations might be different between luminous and faint sources. E p showsa positive correlation with the black hole mass. We discuss the implications of these results. Keywords: galaxies: active — BL Lacertae objects: general — X-rays: galaxies INTRODUCTIONBlazars, including BL Lac objects and flat-spectrum radioquasars (FSRQs), are one type of radio-loud active galacticnuclei (AGNs), with the direction of one of their relativisticjets nearly aligned with our line of sight (Urry & Padovani1995). The emission from blazars is dominated by jet emis-sion whose spectral energy distribution (SED) consists ofa low-energy hump that peaks from sub-millimeter wave-lengths to X-ray energies and a high-energy hump that peaksfrom hard X-rays up to TeV γ -rays. The low-energy compo-nent is thought to be produced by synchrotron emission ofrelativistic electrons in the jet, while the high-energy compo-nent is probably dominated by the emission from the inverseCompton scattering process (i.e., the leptonic scenario; e.g.,Maraschi et al. 1992; Dermer et al. 1992) or related to protonemission processes (i.e., the hadronic scenario; e.g., Aharo-nian 2000). According to the peak frequency ( ν p ) of the low-energy hump, BL Lac objects can be divided into high-energypeaked BL Lac objects (HBLs; ν p > Hz), intermediate- energy peaked BL Lac objects (IBLs; 10 Hz < ν p ≤ Hz) and low-energy peaked BL Lac objects (LBLs; ν p ≤ Hz; Abdo et al. 2010). The synchrotron peak of FSRQs isusually located in the regime from the sub-millimeter band tofar-infrared band, and even to optical/UV wavelengths.The SED around the synchrotron peak can be well describedby the log-parabolic model (e.g., Landau et al. 1986; Massaroet al. 2004; Donato et al. 2005; Tramacere et al. 2007; Chen2014; Wierzcholska & Wagner 2016; Sinha et al. 2017; Bhattaet al. 2018; Goswami et al. 2018; Pandey et al. 2018), which ischaracterized by peak energy ( E p ), peak luminosity ( L p ), andthe curvature parameter around the peak ( b ). For the entireblazar populations, there is an apparent anti-correlation be-tween L p and E p , widely known as the blazar sequence (e.g.,Fossati et al. 1998; Ghisellini et al. 1998; Chen & Bai 2011;Ghisellini et al. 2017). However, it is suggested that this trendmight be due to the selection bias (e.g., Giommi et al. 2012)or might disappear after applying the Doppler boosting cor-rection (e.g., Nieppola et al. 2008; Wu et al. 2009; Huang et a r X i v : . [ a s t r o - ph . GA ] S e p Y.J. Wang et al. al. 2014; Fan et al. 2017; Wang et al. 2018). Blazars exhibitintense variability in all detectable wavelengths, which, for in-stance, is illustrated by their seemingly scale-invariant X-rayflares that last from years down to days and even to minutes(e.g., Cui 2004; Xue & Cui 2005; Zhu et al. 2018). Duringthese flaring periods, E p , L p , and b may change with fluxes.For an individual object, there appears to be an apparent posi-tive correlation between E p and L p (e.g., Tanihata et al. 2004;Tramacere et al. 2007; Massaro et al. 2008; Tramacere et al.2009; Kapanadze et al. 2016, 2017, 2018), which might beconnected with the physical conditions in the emitting region,e.g., the average electron energy, magnetic field and beamingfactor (e.g., Tramacere et al. 2009). It is also suggested thatthere might be an apparent anti-correlation between E p and1 / b , which could be related to the acceleration processes ofemitting particles (e.g., Massaro et al. 2004; Tramacere et al.2011).However, only a few studies have focused on E p – L p and E p –(1 / b ) relations in individual sources and the largest sample ofsuch previous studies only includes five objects (Massaro etal. 2008). Therefore, in this work, we use the hitherto largestsample of this kind, which includes 14 BL Lac objects, to sys-tematically study the E p – L p and E p –(1 / b ) relations for everysingle source, aiming to provide stringent observational con-straints upon the physical properties and acceleration mecha-nisms of emitting particles during flares for future theoreticalstudies. We combined the data from the Rossi X-Ray Tim-ing Explorer ( RXTE ) and
Neil Gehrels Swift Observatory ( Swift ), for the following reasons: (1) generally, both of themhad performed more X-ray observations for multiple blazarsthan other satellites used in the previous studies (see Table 1);and (2) the combination of their different spectral coveragessignificantly enlarges the observational energy range reached.This paper is organized as follows. In Section 2, we de-scribe the criteria to select our sample and relevant observa-tional data reduction. In Section 3, we show the empiricalmodels that are used to fit the X-ray spectra and the method ofcalculating parameters. In Section 4, we analyze the E p – L p and E p –(1 / b ) relations of each source during flaring periods,and discuss the correlations of the total sample. Finally, wesummarize our results in Section 5. We adopt the followingflat Λ CDM cosmological parameters: H =67.8 km s -1 Mpc -1 , Ω m =0.308, and Ω Λ =0.692 (Planck Collaboration et al. 2016). SAMPLE AND DATA REDUCTION2.1.
Sample Construction
Our sample of 14 representative BL Lac objects (hereafterthe total sample; see Table 1) was built upon the
RXTE
TeVblazar sample of Wang et al. (2018), which includes 2 FS-RQs, 1 LBLs, 5 IBLs and 24 HBLs. The total sample wasconstructed in three steps. Firstly, we only focused on HBLsbecause their synchrotron peaks fall into the X-ray bands thatare covered by
RXTE and
Swift . Secondly, in order to assurereasonable signal-to-noise ratios, we required that the average3–25 keV flux of each source (presented in Table 1 of Wanget al. 2018) is larger than 10 − erg cm − s − and the totalcounts are larger than 200/20 for each RXTE / Swift observa- tion. Finally, we excluded the sources with a total number of
RXTE and
Swift observations less than 15.2.2.
RXTE Data ReductionRXTE carries on board the All-Sky Monitor (ASM; 1.5–12keV), Proportional Counter Array (PCA; 2–60 keV) and HighEnergy X-Ray Timing Experiment (HEXTE; 15–250 keV). Inorder to obtain high-quality spectra, we utilized the 3–25 keVdata of PCA that consists of five nearly identical proportionalcounter units (PCUs). Following Rivers et al. (2011), before1998 December 23, we extracted spectra from PCUs 0, 1 and2; from 1998 December 23 to 2000 May 12, the spectra wereextracted from PCUs 0 and 2; after 2000 May, because PCUs1, 3 and 4 had high-voltage breakdown issues and the propanelayer of PCU 0 could not operate after 2000 May 12, we onlyextracted the spectra from PCU 2.We used ftools (version 6.21) to reduce the data. Firstly,we followed the standard procedure to create the data filterfile and corresponding good time intervals (GTIs) file. Sec-ondly, we used the latest faint and bright background modelsto simulate background events of low-flux observations (countrates < 40 counts s –1 PCU –1 ) and high-flux observations(count rates ≥
40 counts s –1 PCU –1 ), respectively. Finally,we extracted the total spectrum and background spectrum foreach observation. We obtained the net source spectrum bysubtracting the background contribution from the total spec-trum. The net source spectra were binned to ensure at least 20counts per bin in order to utilize the χ minimization fittingmethod. 2.3. Swift Data Reduction
We collected the 0.3–10 keV data from the X-ray Telescope(XRT) carried by
Swift . To obtain high-quality spectra, weutilized its Photon Counting (PC) mode observations in thiswork. The data reduction was performed with the XRT DataAnalysis Software (xrtdas; v.2.4) that is a part of the heasoftpackage (v.6.21). The cleaned event files were produced usingthe xrtpipeline task with standard filtering criteria. Thespectra of the source and background were extracted usingthe xselect task. Firstly, we extracted the source spectrumfrom a circular region with a radius of 30 pixels (1 pixel =2.36 arcseconds). If the source count rate was above 0.5 counts − , the pile-up effect should be considered. To remove thiseffect, we re-extracted the source spectrum from an annularregion with an inner radius of 1–17 pixels and an outer radiusof 30 pixels. The inner radius was selected according to thedeviation of the observed point spread function (PSF) fromthe known, un-piled-up PSF. The background events wereextracted from a source-free circular region with a radius of60 pixels. The ancillary response files (ARFs) were createdusing the xrtmkarf task after correcting for the pile-up effect.Source spectra were binned to ensure at least 1 count per bin inorder to use the Cash-statistics fitting method. For Mrk 501 See http://heasarc.gsfc.nasa.gov/docs/xte/recipes/cook_book.html fordetails. -ray spectral variations of synchrotron peak in BL Lacs 3
Table 1.
Source sample a z b Data Origin c log ( M BH / M (cid:12) ) Ref. d , M08 ± ± −
232 0.186 This work (16,8) , M08 · · · · · · , M08 ± ± , G06 , M08 , K18 ± ± , M08 ± , M08 ± , M08 , K17 ± , M08 ± −
489 0.071 This work (24,4) , M08 ± −
304 0.116 This work (47,2) , M08 ± ± Notes. a All sources are HBLs. b Redshift, provided by http://tevcat.uchicago.edu/. c Superscript numbers indicate different data origins: 1:
RXTE ; 2:
Swift ; 3:
BeppoSAX ; and 4:
XMM-Newton . The two numbers in the parentheses denote the numbers of
RXTE and
Swift observationsused in this work, respectively (also see Figure A1). Previous studies are showed in the abbreviated forms: G06: Gutierrez et al. (2006); M08:Massaro et al. (2008); K17: Kapanadze et al. (2017); and K18: Kapanadze et al. (2018). d References of the black hole mass: Wu09: Wuet al. (2009); Woo05: Woo et al. (2005); Wagner08: Wagner (2008). Wu et al. (2009) estimated the black hole mass using the correlationbetween the R -band absolute magnitude of host galaxy and the black hole mass. Woo et al. (2005) and Wagner (2008) estimated the blackhole mass through the measured stellar velocity dispersion of host galaxies. and 1ES 1959+650, given that most of their Swift spectrawere analyzed in detail in the previous works (Kapanadze etal. 2017, 2018), we did not perform the data reduction fortheir
Swift data in this work. METHODWe used the log-parabolic model (Massaro et al. 2004) to fiteach
RXTE or Swift spectrum with the xspec software pack-age (version 12.9.0). The log-parabolic model can describecurved spectra without invoking a sharp high-energy cut-off.Massaro et al. (2004) provided a physical explanation of thismodel in the framework of statistical acceleration process.This model has two forms in xspec: logpar and eplogpar ,both of which are used in this work. The Galactic hydrogencolumn density ( N H ) derived from Dickey & Lockman (1990)for each source was fixed during the fitting process.3.1. logpar model The log-parabolic model is given by
F(E) = K ( E / E ) (− a − b log ( E / E )) , (1)in units of photons cm − s − keV − (e.g., Massaro et al. 2004). E is the reference energy, generally fixed to 1 keV. The pa-rameter a is the spectral index at the energy of E , while b isthe curvature parameter around the peak. If b = 0, it becomes a power-law model. K is the normalization. The location ofthe synchrotron peak is calculated by E p,logpar = E ( − a )/ b ( keV ) (2)and the peak height is calculated by S p,logpar = (cid:0) × − (cid:1) KE E p (cid:0) E p / E (cid:1) − a / , (3) = (cid:0) × − (cid:1) KE ( − a ) / b (cid:0) erg cm − s − (cid:1) . (4)3.2. eplogpar model Even though the maximum-likelihood estimates for E p and S p can be obtained using Eq. 2 and Eq. 4, their error prop-agation is complex. We thus adopted another form of thelog-parabolic model, which is given by F(E) = K − b ( log ( E / E p )) / E , (5)in units of photons cm − s − keV − (e.g., Tramacere et al.2007, 2009). E p is the synchrotron peak in units of keV(hereafter E p,eplog ), while b is the curvature parameter, whichis the same as the parameter b in the logpar model. Theparameter K is the flux in ν F ν units at energy E p keV. Thesynchrotron peak height is calculated by S p,eplog = × − × K (cid:0) erg cm − s − (cid:1) . (6) Y.J. Wang et al. Table 2.
Fitting results of E p – L p and E p –(1 / b ) relations E p – L p relation E p –(1 / b ) relationObject Spearman log L p = α log E p + β Spearman 1 / b = C log E p + D Name r s p s α β r s p s C D ± − ± − · · · · · · ± ± − · · · · · · − − − ± ± − − ± ± ± ± − · · · · · · ± − ± · · · · · · ± ± ± ± ± ± ± ± ± − ± − · · · · · · · · · · · · − − ± ± ± − ± · · · · · ·
10 Mrk 501 0.61 < 0.001 0.89 ± − ± ± ± · · · · · · − − ± ± − − · · · · · · − − ± ± − − − ± ± − − ± ± ± ± · · · · · · Notes.
Column (1): Source name. Columns (2) and (3): Spearman’s rank correlation coefficient and probability of the hypothesis test of E p – L p relation. Columns (4) and (5): Best-fitting α and β of log L p = α log E p + β , where E p is in units of keV and L p is in units of 10 erg s − .Columns (6) and (7): Spearman’s rank correlation coefficient and probability of the hypothesis test of E p –(1 / b ) relation. Columns (8) and (9):Best-fitting C and D of 1 / b = C log E p + D , where E p is in units of keV. Spectral Analysis
Firstly, we fitted the spectra with the power-law and the logpar models, and then used the F-test to compare the fittingresults of these two models. In order to sift out the spectrapreferring the log-parabolic model, we excluded the spectrawith p -value larger than 0.05, because if a spectrum is welldescribed by the power-law model, then the peak energy andcurvature parameter could not be well constrained. Secondly,we derived the peak parameters from the best-fit spectralparameters with the logpar model using Eq. 2 and Eq. 4.Thirdly, we fitted the spectra with the eplogpar model bysetting the initial parameter values to those obtained fromthe previous step. Following the method in Tramacere et al.(2009), we used two criteria to test the reliability of the fittingresults:• The ratio between E p,eplog and 1-sigma uncertainty of E p,eplog should be larger than 1 to assure the statisticalsignificance of the peak energy.• E p,logpar should be consistent with E p,eplog within 1-sigma uncertainty. We excluded observations with E p,eplog not satisfying theabove criteria. Finally, we required that the parameter b should be larger than 0, because when b < 0, the resultingpeak energy might straddle the cavity location of the concavespectrum, which might be the intersection of the two compo-nents from the synchrotron and inverse Compton scatteringradiation processes, respectively. The resulting numbers of RXTE and
Swift observations adopted for each source in thetotal sample are shown in Table 1, and these observations areannotated in the corresponding source light curves as pre-sented in Figure A1.The rest-frame peak energy is calculated by E p = ( + z ) E p,eplog ( keV ) . (7)The rest-frame isotropic peak luminosity is calculated by L p (cid:39) π D × S p,eplog (cid:0) erg s − (cid:1) , (8)where D L is the luminosity distance. RESULTS AND DISCUSSIONS-ray spectral variations of synchrotron peak in BL Lacs 5
Figure 1. E p – L p relations of the 14 sources in the total sample. The filled circles with black edges represent the literature data, while thosewithout black edges represent the data analyzed in this work (see Table 1). Different colors indicate different observational dates. The linesdenote the best-fitting E p – L p relations when applicable; for 1ES 1959+650, the two dashed lines are for the 2002 and 2016 data, respectively(see Table 2). Y.J. Wang et al.
Figure 1 (Cont.).
We tested the correlations between E p , L p , and 1 / b in eachsource of the total sample with the Spearman’s rank cor-relation coefficients ( r s ) and associated p -values ( p s ). Forthe objects displaying significant correlations (i.e., with p s ≤ L p = α log E p + β and 1 / b = C log E p + D to describe the E p – L p relation (see Figure 1) and E p –(1 / b )relation (see Figure 2) following the fitting method of Kelly(2007), respectively. All the fitting results are shown in Table2. 4.1. Properties of Individual Sources (1) 1ES 0229+200 had outbursts from 2010 to 2011, duringwhich its peak luminosity reached 10 erg s − , peak energy reached 9.4 keV, and curvature maintained nearly at 1. Thefive observations in 2008, 2015 and 2016 represented the low-flux states of this source, whose peak luminosity decreased to10 erg s − , peak energy decreased to 2 keV, and curvaturedecreased to about 0.5. Our result is consistent with that ofMassaro et al. (2008).(2) 1ES 0647+250 showed a gradually increasing trend ofX-ray flux from 2010 to 2012. During this period, its peakluminosity increased from 10 to 10 erg s − , while itspeak energy ranged between 0.5 and 2 keV, and curvaturearound the peak ranged between 0.25 and 1. Given the largeerror bars of the fitting result of E p – L p relation (see Table 1),-ray spectral variations of synchrotron peak in BL Lacs 7 Figure 2.
Same as Figure 1, but for E p –(1 / b ) relations. Y.J. Wang et al.
Figure 2 (Cont.). we do not show the best-fit linear model of this source inFigure 1.(3) 1ES 1101-232 had an average peak energy of 2.5 keV,an average peak luminosity of 10 erg s -1 , and a curvaturevalue of 0.5 in 2005. In 2010, its peak energy increasedto 4.5 keV, peak luminosity decreased to 10 erg s -1 , andcurvature increased to about 1. Between 2015 and 2016,its peak energy decreased to about 2 keV, peak luminosityincreased to 10 erg s -1 , and the curvature decreased to 0.3(similar to that in 2005). Our result based on the 2005 RXTE data is consistent with that of Massaro et al. (2008) based onthe 2005
Swift data. (4) 1ES 1218+304 showed its peak luminosity increasingto 10 erg s -1 and peak energy increasing to 7 keV during anoutburst in 2009. In 2005, 2016 and 2017, it was in relativelylow-flux states, whose peak luminosity decreased to 10 erg s -1 and peak energy decreased to 0.6 keV. From 2005to 2017, the curvature ranged between 0.25 and 1. It had asimilar peak luminosity in 2005–2006 and 2016–2017, buthad a lower peak energy range during the former period.(5) 1ES 1727+502 showed its peak luminosity increasingfrom 10 to 10 erg s -1 or even higher, and peak energyincreasing from 0.8 to 3.5 keV during a large outburst in 2015.In the relatively low-flux state, its peak luminosity decreased-ray spectral variations of synchrotron peak in BL Lacs 9to 10 erg s -1 . From 2015 to 2017, its curvature had a veryweak increase. It had a similar peak energy range in 2015and 2017, but had a larger peak luminosity in 2015 than thatin 2017.(6) 1ES 2344+514 underwent a large outburst in December2007, and the observation with the highest peak luminosityand peak energy in the E p – L p plot corresponds to the peakposition of this flare. During this period, its peak luminosityreached 10 erg s -1 and peak energy reached 8 keV. Thethree observations between 2009 and 2010 represented thelow-flux states, whose peak luminosity decreased to 10 erg s -1 and peak energy decreased to 1 keV. In addition, itscurvature displayed no significant changes.(7) 1ES 1959+650 was in large outbursts in 2002 and 2016.In 2002 ( RXTE observations), its peak luminosity increasedfrom 10 to 10 erg s -1 and peak energy increased from0.7 to 30 keV. In 2016 ( Swift observations of Kapanadze etal. 2018), its peak luminosity increased from 10 to 10 erg s -1 and peak energy increased from 0.4 to 13 keV. In thesame peak energy range, the peak luminosity in 2016 wasfive times larger than that in 2002. For the observations inboth 2002 and 2016, there is a significant positive correlationbetween E p and L p as well as between E p and 1 / b . Theobservations in 2005 and 2006 showed a similar trend withthat in 2016. Interestingly, in 2000, 2001, 2003, 2008 and2011, E p and L p seem to stay in a transitional region betweenthe relations in 2002 and 2016 in the E p – L p plot (see Figure1).(8) H 1426+428 went through a large outburst in May 2001,which was excluded by one of our observation selection crite-ria (i.e., the logpar model was not required to fit the spectraas the synchrotron peak was much larger than the RXTE spec-tral coverage; see Section 3.3); during the peak of this flare, itspeak energy and peak luminosity were estimated to be largerthan 25 keV and 10 erg s -1 , respectively. In 2002, its peakenergy ranged between 5 and 25 keV, and peak luminosityranged between 10 and 10 erg s -1 . After 2004, its peakenergy ranged between 0.9 and 5 keV, which is lower thanthat in 2002, but its peak luminosity ranged between 10 and 10 erg s -1 , which is quite similar to that in 2002. Ourresult is consistent with that of Massaro et al. (2008).(9) Mrk 180 was in a high-flux state between 2008 and2009. During this period, its peak energy changed between0.5 and 3 keV, while peak luminosity changed between 10 and 10 erg s -1 . In 2015, it was in a relatively low-flux statewith peak luminosity decreasing to 10 erg s -1 . Our result isconsistent with that of Massaro et al. (2008).(10) Mrk 501 experienced a large outburst in 1997, whosepeak luminosity reached 10 erg s -1 and peak energy couldreach 100 keV. From 1997 to 2011, its peak energy decreasedfrom 100 to 0.4 keV, while peak luminosity decreased from10 to 10 erg s -1 . Our result based on the RXTE databetween 1997 and 2011 is consistent with that of Massaroet al. (2008) based on the
BeppoSAX and
Swift data. Inaddition, our result is also consistent with that of Kapanadzeet al. (2017). (11) PG 1553+113 showed its peak luminosity ranging be-tween 10 and 10 erg s -1 , and peak energy ranging be-tween 0.5 and 1.5 keV from 2015 to 2018. Our result issimilar to that of Massaro et al. (2008).(12) PKS 2005-489 was in a large outburst in 1998, whosepeak luminosity reached 10 erg s -1 . In 2014, it was ina relatively low-flux state with peak luminosity decreasingto 10 erg s -1 and the curvature value similar to that of thehigh-flux state in 2009. Its peak energy ranged between 0.5and 2.5 keV. Our result based on the 1998 RXTE data isconsistent with that of Massaro et al. (2008) based on the1998
BeppoSAX data. Given the large error bars of the fittingresult of E p –(1 / b ) relation, we do not show the best-fit linearmodel in Figure 2.(13) PKS 2155-304 underwent at least two large outburstsbetween 1996 and 2000, whose peak luminosity reached 10 erg s -1 and peak energy ranged between 0.5 and 3 keV. Theobservations in 2009 were in a relatively low-flux state, whosepeak luminosity decreased to 10 erg s -1 but peak energyreached 4 keV. Within uncertainties, our result is consistentwith that of Massaro et al. (2008).(14) RGB J0710+591 showed its peak luminosity reaching10 erg s -1 and peak energy reaching 10 keV in the outburstsof 2009 and 2011, while the curvature in 2011 was muchhigher than that in 2009. In the low-flux state in 2017, itspeak luminosity decreased to 10 erg s -1 and peak energydecreased to 2 keV. 4.2. E p -L p Relation
According to the synchrotron theory (Rybicki & Lightman1979), the synchrotron peak energy ( E p ) and luminosity ( L p )follow a power-law relation of L p ∝ E α p . If the electrons in theemitting region follow a log-parabolic distribution, the peakluminosity is given by L p ∝ n ( γ ) γ B δ ∼ N γ B δ , andthe peak energy follows E p ∝ γ B δ ∼ γ B δ (e.g., Tramacereet al. 2009). γ represents the peak of n ( γ ) γ where γ isthe electron Lorentz factor, γ p represents the peak of n ( γ ) γ , N ∼ n ( γ p ) γ p is the total electron number, B is the magneticfield and δ represents the Doppler beaming factor.If α = 1, the spectral changes might be mainly caused by thevariations of the average electron energy, and the total elec-tron number remains constant; if α = 1.5, the spectral changesmight be mainly caused by the variations of the average elec-tron energy, but the total electron number also changes; if α =2, the spectral variations might be correlated with the changesof the magnetic field; and if α = 4, the spectral changes mightbe then dominated by the variations of the beaming factor.According to the fitting results (see Table 2), five ob-jects (i.e., 1ES 0229+200, 1ES 1727+502, 1ES 1959+650in 2002, 1ES 2344+514, RGB J0710+591) have α ≈
1, thustheir spectral variations are mainly caused by the changesof the electron energy while the total electron number mayremain constant. The spectral variations of 1ES 1218+304,1ES 1727+502 and Mrk 180 might also be due to the changesof the electron energy but the total electron number changes.1ES 1959+650 in 2016 and Mrk 501 have α <
1, which0 Y.J. Wang et al. could not be explained by any mechanism mentioned above.In addition, both 1ES 1101 −
232 and PKS 2155 −
304 showan anti-correlation between E p and L p , which is significantlydifferent from the other sources. H 1426+428, PG 1553+113and PKS 2005 −
489 show no correlation between E p and L p .For 1ES 0647+250, due to the large errors of α , we could notdraw any solid conclusion.In a word, most of the sources (9/14) show a positive corre-lation between E p and L p , which indicates that their spectralvariations might be due to the variations of electron energies.For the sources that show a negative or no correlation between E p and L p , the aforementioned mechanisms could not explaintheir results and it might be related to the source luminosity(see Section 4.5). In addition, 1ES 1959+650 has two dif-ferent E p – L p relations in 2002 and 2016, indicating that thecauses of spectral variations likely changed during these twoperiods. 4.3. E p -b Relation It has been suggested that the statistical and stochastic ac-celeration mechanisms could explain the correlation between E p and b (e.g., Massaro et al. 2004; Tramacere et al. 2011).These two mechanisms can produce the electron energy dis-tribution that follows the log-parabolic law, resulting in alog-parabolic SED.The first scenario is described by the statistical accelera-tion process. For the energy-dependent acceleration prob-ability process, the electron energy distribution follows thelog-parabolic law and the acceleration efficiency of the parti-cles is inversely proportional to their energy (Massaro et al.2004). In this process, E p and b follow the correlation oflog E p ≈ Const. + / (5 b ), given the assumption of b = r /4where r is the curvature of the electron energy distribution(Chen 2014). While for the fluctuations of fractional accel-eration gain process, electron energies are distributed in alog-normal law, and the energy gain fluctuations are a ran-dom variable around the systematic energy gain (Tramacereet al. 2011). In this case, E p and b follow the correlation oflog E p ≈ Const. + / (10 b ) given b = r /4 (Chen 2014).Another scenario is described by the stochastic accelera-tion process, and its kinetic equation includes a momentum-diffusion term, which leads to energy gain fluctuations inthe diffusive shock acceleration process (Tramacere et al.2011). For this explanation, E p and b follow the relationof log E p ≈ Const. + / (2 b ) given b = r /4 (Chen 2014).Therefore, the theoretically expected values of C are 10 / / E p and 1 / b . For 1ES 1959+650in 2002, C = ± C = ± C = ± E p and 1 / b : 1ES 1101–232, H 1426+428,PG 1553+113, PKS 2005 −
489 and PKS 2155 − E p and 1 / b in seven sources, i.e., 1ES 0229+200, 1ES 0647+250,1ES 1218+304, 1ES 1727+502, 1ES 2344+514, Mrk 180and RGB J0710+591. For PKS 2005 − C , we could not draw any solid conclusion.None of these three mechanisms could explain all the E p –(1 / b ) behaviors of these sources. One possible reason is thatthe E p –(1 / b ) relation might be different from flare to flarein each source (see Section 4.4), as different accelerationprocesses might be at work during flares and hence cause largescatters of the E p –(1 / b ) relation for each source. Therefore,we would not expect a simple and good E p –(1 / b ) relation thatcan be explained by one single acceleration model.4.4. Correlations during the Single Flares
Tanihata et al. (2004) found that for Mrk 421, E p and L p showed an overall positive correlation but this relation seemedto vary between individual flares lasting for hundreds of kilo-seconds. We here focus on the flares lasting for several days.We require that in each flare, at least four observations shouldsatisfy the selection criteria in Sections 2.1 and 3.3. Finally,we selected out ten flares of four objects that were observedby RXTE (see Figure 3).For Flares 3–5 of 1ES 1959+650 and Flares 6–10 ofMrk 501 in Figure 3, there are positive correlations between E p and L p , which are consistent with the trends revealed withtheir respective all observations (see Figure 1). In addition,most of these flares share a similar slope of E p – L p relationto that for their respective all observations, which indicatesthat the E p – L p relation did not vary significantly during theseindividual flares. During these flares, the peak energy shiftedto the higher energy and reached the highest value at thepeak of flare, then returned to the lower energy with the fluxdecreasing. Assuming that the flaring events are due to thecontribution from a new component, the positive correlationbetween E p and L p might indicate that this new component hasa higher synchrotron peak energy than the preexisting com-ponent. In addition, in some cases, the observations duringthe rising periods had the higher peak energy compared withthat in the decay periods, such as, Flares 4, 5, 7, 9, 10 and thesecond flare of Flare 8; while other cases show the oppositetrend, such as, Flares 3, 6 and the first flare of Flare 8. ForFlare 1 of PKS 2005 −
489 and Flare 2 of PKS 2155 − E p and L p seem to follow the negative or no correlation, but giventhe large error bars, we could not draw any solid conclusion.For Flare 5 of 1ES 1959+650 and Flares 7–9 of Mrk 501,there are two adjacent and comparable flares, where the peakenergies of the second flares of Flares 5 and 7 are lower thanthat of their respective first flares, while the first and secondflares of Flares 8 and 9 have similar peak energies. Given thatthe two flares of Flare 5 or 7 lasted for about 2–4 days whilethe two flares of Flare 8 or 9 lasted for about 10–20 days, it-ray spectral variations of synchrotron peak in BL Lacs 11 Figure 3.
RXTE /PCA light curve (first column), time evolution of E p – L p and E p –(1 / b ) relations (second and third columns,respectively) for PKS 2005 −
489 (Flare 1), PKS 2155 −
304 (Flare 2), 1ES 1959+650 (Flares 3–5) and Mrk 501 (Flares 6–10), respectively. Inthe first column, the filled circles with black edges of the light curves represent the observations satisfying the selection criteria in Sections 2.1and 3.3. In the second and third columns, the beginning of each flare is marked with a star, the peak of each flare is marked with an open circle,the red and green arrowed lines represent the first and second flares (see the first column) respectively, and the arrows indicate the time order. Itseems that the E p – L p relation does not exhibit significant differences between flares, while the E p –(1 / b ) relation differs from flare to flare. et al. Figure 3 (Cont.). -ray spectral variations of synchrotron peak in BL Lacs 13is likely that the two flares of Flares 5 and 7 are from twodifferent small-scale regions while the two flares of Flares 8and 9 are from the same large-scale region.For Flare 1 of PKS 2005 − − E p and 1 / b , while forFlares 3 and 5 of 1ES 1959+650 and Flares 6, 7, and 10 ofMrk 501, it shows an opposite trend. Therefore, the E p –(1 / b )relation differs from flare to flare for the same source. ForFlares 1, 3, 5 and 10, the peak of the flare has the lowestcurvature around the synchrotron peak compared with thatof other observations during flares, while for other cases, thepeak of the flare has a medium curvature value. The changesof curvature around the peak do not follow the flux variationtrend during flares.In conclusion, for the same source (Mrk 501 and1ES 1959+650), the E p – L p relation does not show any signif-icant change between different flares lasting for several days,which is inconsistent with the result of shorter-timescale (i.e.,hundreds of kilo-seconds) flares in Tanihata et al. (2004).However, the E p –(1 / b ) relation differs from flare to flare,which might explain the lack of correlation between E p and1 / b in most objects, or the large scatters of E p –(1 / b ) relations.4.5. Correlations for the Total Sample
In Figure 4, we show the correlations between α and L p , α and E p , E p and L p , C and α , black hole mass ( M BH ) and L p , and M BH and E p of all the sources (using their respectivemedian values of E p and L p as well as best-fitting C and α ),respectively. Given that the small sample size of this work, weassume that the Doppler factors are similar for all the HBLsin our sample.In the panel (1) of Figure 4, there seems to be an anti-correlation between L p and α , which indicates that the causesof spectral variations might be different between luminous andfaint sources. For the sources with L p lower than 8 × (∼ ) erg s -1 , they have the α value larger than 0.5, while forthe sources with higher L p , they usually have much smaller α values. Therefore, we divided the total sample into twosubsamples according to the peak luminosity: low L p sources( L p < 8 × erg s -1 , hereafter LLP) and high L p sources ( L p >8 × erg s -1 , hereafter HLP). In addition, it seems that thereis no correlation between E p and α (see the panel 2 of Figure4), which indicates that the causes of spectral variations showno significant difference between sources with different peakenergies.In the panel (3) of Figure 4, for HLP subsample, there seemsto be an anti-correlation between E p and L p , but it is not sta-tistically significant. While for LLP subsample, there is anapparent positive correlation between E p and L p . In addition,the trend of E p – L p correlation in each individual object is con-sistent with that of the subsample it belongs to. For example,Mrk 180 shows a positive E p – L p correlation ( α > 0), and it be-longs to LLP subsample, which also shows a positive E p – L p correlation. These results might be explained by that with thenumber of high-energy electrons increasing, E p will become larger and the number of photons produced by synchrotronradiation will increase ( L p will increase). However, when L p is larger than 8 × erg s -1 , the synchrotron self-Compton(SSC) cooling effect might be significant, which might resultin a trend that E p decreases with increasing L p .We test the correlation between the causes of the spectralvariations and possible acceleration processes by studying thecorrelation between α and C (see the panel 4 of Figure 4),because α and C might represent the causes of the spectralvariations and the acceleration processes, respectively. How-ever, it seems that there is no significant correlation between α and C according to the statistical test.There is no significant correlation between L p and M BH (from previous works, see Table 1) either in the total sam-ple or in the two subsamples, while E p shows a significantpositive correlation with M BH (see panels 5 and 6 of Figure4). Our result is different from that of Xiong et al. (2015),which suggested that there is no apparent correlation betweensynchrotron peak frequency and black hole mass in a sampleof more than 100 BL Lacs. There are several reasons thatmight cause such a discrepancy. Firstly, we mainly focus onHBLs, while they focus on all types of BL Lacs. Secondly,they fitted broadband SEDs or used empirical relationshipsto obtain E p and L p , while we fitted the X-ray spectra of eachobservation of each source, and then obtained median E p and L p values. In addition, the different methods of estimating M BH might also affect the result.Finally, we also study the correlations between E p and 1 / b , L p and 1 / b , but it seems that there is no correlation. Chen(2014) fitted the broadband SEDs of 48 blazars with two log-parabolic models and found a positive correlation betweenthe synchrotron peak and 1/ b for the whole sample. Xue etal. (2016) used a larger sample including 200 FSRQs and79 BL Lacs, and found a similar trend of E p –(1 / b ) relationbut the slope of this relation is different between FSRQs andBL Lacs. Our result seems to be inconsistent with theirs,which might be due to the following reasons: (1) both of theirsamples only included two or three sources with synchrotronpeaks larger than 0.3 keV where our sources mainly peak; (2)their curvature values were obtained by fitting the broadbandSEDs, while our result is obtained using the X-ray data, whichusually shows larger curvature values. However, the result ofXue et al. (2016) showed that the E p –(1 / b ) relation has alarge scatter for HBLs, which might lead to a weak E p –(1 / b )correlation for the high-peaked sources. SUMMARY AND CONCLUSIONSFor the 14 BL Lacs in the total sample (see Table 1), we uti-lized the log-parabolic model to fit the 3–25 keV
RXTE /PCAand 0.3–10 keV
Swift /XRT spectra, and then obtained the fol-lowing three parameters to characterize the synchrotron peak:peak energy ( E p ), peak luminosity ( L p ) and the curvature pa-rameter around the peak ( b ). Further, we studied the E p – L p and E p –(1 / b ) relations in these sources and their trends dur-ing flaring periods. We also analyzed these correlations forthe total sample and the correlations with the black hole mass.4 Y.J. Wang et al. L p (erg s )1.010.0 E p ( k e V ) r s = -0.46 p -value=0.294 r s = 0.79 p -value=0.036 (3) L p = log E p +642024 C o f / b = C l og E p + D
123 456 78 910111213 1466 r s = 0.55 p -value=0.064(4) L p (erg s )1.51.00.50.00.51.01.5 o f l og L p = l og E p + r s = -0.59 p -value=0.035
11 1ES 0229+200 22 1ES 0647+250 33 1ES 1101-232 44 1ES 1218+304 55 1ES 1727+502 66 1ES 1959+65077 1ES 2344+514 88 H 1426+42899 Mrk 180 1010 Mrk 501 1111 PG 1553+113 1212 PKS 2005-489 1313 PKS 2155-304 1414 RGB J0710+5916 1ES 1959 (2002)6 1ES 1959 (2016) (1) E p (keV)1.51.00.50.00.51.01.52.02.5 o f l og L p = l og E p +
12 3 45 67 89 1011 12 13 14 r s = 0.04 p -value=0.900 (2) L p (erg s )10 M B H ( M fl ) r s = -0.77 p -value=0.072 r s = 0.46 p -value=0.294 (5) E p (keV)10 M B H ( M fl )
12 45 67 89 1011 12 13 14 r s = 0.73 p -value=0.004 (6) Figure 4.
Correlations between α and L p (panel 1), between α and E p (panel 2), between E p and L p (panel 3), between C and α (panel 4),between M BH and L p (panel 5), and between M BH and E p (panel 6) for the 14 sources in the total sample. The black filled circles representthe median values of E p and L p of respective all observations as well as best-fitting C and α of each source. The triangle and inverted-trianglesymbols represent the data of 1ES 1959+650 in 2016 and 2002, respectively. The red dashed line annotates that L p = 8 × erg s -1 . The errorbars of E p and L p represent the standard deviations. In the panel (4), the Spearman’s rank test is performed without Sources 2 and 12 due totheir large error bars. In panels (1) and (2), the Spearman’s rank test is performed without Source 2 due to its large error bars. -ray spectral variations of synchrotron peak in BL Lacs 15The results regarding the E p – L p relations of individualsources are as follows: (1) The positive E p – L p relations of1ES 0229+200, 1ES 1727+502, 1ES 1959+650 in 2002,1ES 2344+514, and RGB J0710+591 indicate that theirspectral variations might be related to the electron energyvariations, while the total electron number remains con-stant; and the positive E p – L p relations of 1ES 1218+304,1ES 1727+502, and Mrk 180 indicate that their spectral vari-ations might be related to the electron energy variations butthe total electron number changes. (2) 1ES 1959+650 in2016 and Mrk 501 show a positive E p – L p relation but noneof the four aforementioned mechanisms could explain theirspectral variations. (3) H 1426+428, PKS 2005 −
489 andPG 1553+113 show no correlation between E p and L p . (4)1ES 1101 −
232 and PKS 2155 −
304 show an anti-correlationbetween E p and L p . None of the four mechanisms could ex-plain the causes of spectral variations in these sources. (5)1ES 1959+650 shows two significantly different E p – L p rela-tions in 2002 and 2016.The results on the E p –(1 / b ) relations of individual sourcesare the following: (1) Mrk 501 and 1ES 1959+650 show thepositive correlation between E p and 1 / b . For 1ES 1959+650,both the energy-dependent acceleration probability andstochastic acceleration processes could be the possiblemechanisms. (2) The following five sources show an anti-correlation: 1ES 1101 − −
489 and PKS 2155 − E p and 1 / b for the sources in the totalsample. For the total sample, α shows an anti-correlation with L p ,which indicates that the causes of spectral variations mightbe different between luminous and faint sources. In contrast, α shows no correlation with E p . When L p is lower than 8 × erg s -1 , there is a significant positive correlation between E p and L p . In addition, E p shows a positive correlation with M BH , while L p shows no correlation with M BH .During flares lasting for several days, the E p – L p relationdoes not exhibit the significant change between differentflares, which is not consistent with the previous result basedon shorter-timescale (hundreds of kilo-seconds) flares. The E p –(1 / b ) relation differs from flare to flare, which might ex-plain the lack of correlation between E p and 1 / b in mostobjects.In the future and in light of our results in this work, we willuse more data and larger samples when available to furtherinvestigate the correlations between the synchrotron peak pa-rameters ( E p , L p , and 1 / b ) and the black hole properties (e.g., M BH ) of blazars, aiming to better confront observational re-sults with theoretical considerations and explore whether thecorrelation between the synchrotron E p and M BH could pro-vide a method to estimate the black hole mass of blazars.We are grateful to Zhenyi Cai for helpful discussion.Y.J.W., Y.Q.X., and H.A.N.L. acknowledge support fromthe 973 Program (2015CB857004), the National Natural Sci-ence Foundation of China (NSFC-11890693, 11421303), theCAS Frontier Science Key Research Program (QYZDJ-SSW-SLH006), and the K.C. Wong Education Foundation. M.F.G.acknowledges support from the National Science Foundationof China (grants 11873073 and U1531245). S.S.W. acknowl-edges support from the National Natural Science Foundationof China (NSFC-11673013). Software:
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Figure A1.
Long-term light curves of the 14 sources in the total sample. The red segmented line represents the 3–25 keV
RXTE /PCA lightcurve and the green dashed line represents the 0.3–10 keV
Swift /XRT light curve. The black open squares denote the observations selected inthis work. Note that for
RXTE /PCA light curves, the units of y-axis are c s − PCU − . et al. Figure 1 (Cont.). -ray spectral variations of synchrotron peak in BL Lacs 19-ray spectral variations of synchrotron peak in BL Lacs 19