Variability of VHE γ -ray sources
NNuclear Physics B Proceedings Supplement 00 (2018) 1–6
Nuclear Physics BProceedingsSupplement
Variability of VHE γ –ray sources Stanislav Stefanik a, ∗ , Dalibor Nosek a a Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles UniversityV Holesovickach 2, 180 00 Prague 8, Czech Republic
Abstract
We study changes in the γ –ray intensity at very high energies observed from selected active galactic nuclei. Publiclyavailable data collected by Cherenkov telescopes were examined by means of a simple method utilizing solely thenumber of source and background events. Our results point to some degree of time variability in signal observed fromthe investigated sources. Several measurements were found to be excessive or deficient in the number of source eventswhen compared to the source intensity deduced from other observations. Keywords: γ –astronomy, Statistical methods, Time variability, BL Lacertae objects: individual (PKS 2005–489,1ES 0229 +
1. Introduction
Precise knowledge of variability in γ –ray fluxes ob-served from various emitters is considered essential forprobing their intrinsic properties. Among the mostprominent sources of such transient γ –ray emission areactive galactic nuclei (AGN). Measurements of variabil-ity time scales of their activities can be useful, for exam-ple, for putting constraints on size and location of the γ –ray production region [1].Spectral energy distributions (SED) of AGN exhibittwo distinctive peaks and they are commonly describedby the synchrotron self–Compton model (SSC) [2].This scenario assumes that a population of relativisticelectrons present in the AGN jets gives rise to the syn-chrotron photons at X–ray wavelengths in the vicin-ity of the first SED peak. High energy radiation ofthe second spectral bump is believed to be a result ofinverse Compton scattering of lower energy photonsby the same ensemble of electrons that is responsible ∗ Corresponding author.
Email addresses: [email protected] (Stanislav Stefanik), [email protected] (DaliborNosek) for the synchrotron emission. Information on tempo-ral changes of di ff erent SED components of AGN andtheir mutual relations can be beneficial for predictionson the mechanisms of the particle acceleration and pho-ton emission [1].In particular, analysis of data gathered during ob-servations of the PKS 2005–489 blazar provided noconclusive proof of the flux variability at very highenergies (VHE) in the GeV–TeV γ –ray band betweenyears 2004 and 2005 [3]. This is contrary to the find-ings at other wavelengths which indicate that the X–rayflux increased significantly during the two consecutiveyears [3]. If the VHE radiation is to be related to thelower energy contributions to the SED through the SSCmechanism, a rise in the X–ray activity should be ac-companied by corresponding increase of the flux in theTeV band [2]. The lack of the γ –ray flux variabilitymight be explained by an additional jet component ofelectrons contributing to the VHE emission [3]. Suchcomponent, emerging only in the hard X–ray energyrange, should be separated from the production regionof the observed synchrotron emission and thus not inter-act with these photons in order to preserve the measuredVHE flux [3].Besides studying the origin of γ –ray emission, pos- a r X i v : . [ a s t r o - ph . H E ] D ec . Stefanik and D. Nosek / Nuclear Physics B Proceedings Supplement 00 (2018) 1–6 sible time variations in the source intensities of hard–spectrum blazars located at large redshifts can have alsoimplications for cosmological observations. Constraintscan be put on the strength of the intergalactic magneticfield (IGMF) from measurements of time delay betweenarrivals of photons in di ff erent energy bands as long asthe emission of the parent very high energetic γ –raysis steady [4]. The condition of the constant flux thuscalls for reliable investigations of multiwavelength vari-ability of AGN. Distant blazar 1ES 0229 +
200 has beenfor a long time considered to be a good candidate forIGMF studies [4, 5]. This belief has been based on ap-parent steadiness of the VHE γ –ray flux observed dur-ing 2005–2006 [6]. However, analysis of more recentdata casts doubt upon this assumption with the recom-mendation not to include this object in the IGMF re-search relying on a constant flux or at least account forsystematic uncertainties arising from the variability ofits flux [7]. The case of 1ES 0229 +
200 is thus anotherexample of strong need for precise measurements andreliable statistical methods for variability studies.Future improvement in the experimental techniquesin γ –astronomy will provide us with vast amount ofdata on various transient phenomena with better tem-poral resolution. In particular, one of the goals of thenext generation of imaging atmospheric telescopes, theCherenkov Telescope Array [8], will be extensive stud-ies of the AGN populations [1]. Time variability of in-trinsic activities of not only these γ –ray emitters will bea crucial question in most analyses, for which our mod-ification [9] of the no–source on–o ff method [10] couldbe useful.The modified on–o ff technique attempts to determinea level of significance for an excess or deficit of countsin individual measurements when compared to the refer-ence source intensity previously ascertained from otherobservations [9]. In the on–o ff method there is no de-mand for the calculation of the flux or other quantities.It works only with the numbers of events detected inthe on–source and reference o ff –source region providedthat their exposures are known. The method is equallysuitable for any observations regardless of the experi-mental technique, thus making the comparison of datadetected by di ff erent instruments possible.The modified on–o ff method is briefly described inSection 2. It allows to check for intensity changes inthe ranges of times, energies or zenith angles, for ex-ample, as long as reasonable estimates for the sourceintensity exist. Section 3 deals with the analysis ofthe data gathered by experiments using imaging atmo-spheric Cherenkov telescopes along with the previousfindings on the considered sources. We use the on– o ff technique to examine whether two selected AGN,PKS 2005–489 and 1ES 0229 + γ –ray events detectedfrom their directions.
2. Method
The Li–Ma method is widely employed in VHE γ –ray astronomy for determining a level of significance ofa photon excess above background when validating thesource presence in a given region [10]. In this method,one assumes the test of the null hypothesis stating thatthere is no source present in the investigated on–sourceregion. The on–source region encompasses the potential γ –ray emitter whereas the o ff –source region is consid-ered to be free of point sources and thus suitable for thebackground estimation. In order to account for di ff erentextent (e.g. temporal or spatial) and unequal observingconditions of both regions, an on–o ff parameter α , theratio of the on– and o ff –source exposures, is needed.A straightforward modification of this technique al-lows one to estimate the significance of an excess ordeficit of the number of events when compared to theknown source activity [9]. The modified on–o ff methodassumes that the γ –ray emitter has already been posi-tively identified in the potential hotspot. A source pa-rameter β > β ,i.e. N on = αβ N o ff [9], where N on and N o ff are the num-bers of events detected in the on– and o ff –source re-gions, respectively.A level of significance for the rejection of the no–source assumption is given in terms of either binomialor Li–Ma statistics [10]. A modification of the origi-nal significance formulae (Eqs. 9 and 17 in [10]) for theassumption of the constant source intensity leads to acouple of similar equations, the only di ff erence beingthe transformation α → αβ [9], i.e. S Bi = N on − αβ N o ff (cid:112) αβ ( N on + N o ff ) , (1) S LM = s √ { N on ln X + N o ff ln X } , (2)for the binomial and Li–Ma statistics, respectively.Here, the logarithmic arguments are X = + αβαβ N on N on + N o ff and X = (1 + αβ ) N o ff N on + N o ff . The s –term in Eq. 2 ( s = ± S Bi , S LM >
0) or deficit( S Bi , S LM <
0) of events is observed. . Stefanik and D. Nosek / Nuclear Physics B Proceedings Supplement 00 (2018) 1–6 Taking the source parameter β being equal to unityone recovers the original no–source assumption. Alter-natively, the inequality β > < β < S Bi and S LM and the reference standard Gaussian distribu-tion should be regarded as a sign of change in the tested γ –ray intensity. It is worth noting, that the Li–Ma statis-tic can be alternatively exploited to derive confidenceintervals for the source parameter β at a given level ofsignificance. Sequence of such confidence intervals car-ries information about temporal evolution of the source γ –ray activity.
3. Data analysis
We used published data obtained during observationsof two VHE γ –ray emitters by imaging atmosphericCherenkov telescopes. The only necessities for themodified on–o ff method are the numbers of detectedon– and o ff –source events, N on and N o ff , and the on–o ff parameter α . These quantities are the direct outcome ofthe experiment and its particular setup. On contrary, thesource parameter β is set at our discretion. We used esti-mates of the source parameter derived as average valuesof the ratio of observed and expected on–source eventsover individual time intervals, i.e. β = (cid:104) N on /α N o ff (cid:105) . Us-ing a particular value of the source parameter, the in-vestigated data were tested for the assumption of givenintensity.In the following, our results are visualized inquantile–quantile (QQ) plots, see Figs. 1 and 3. Inthese plots, both binomial and Li–Ma significances re-trieved from data are arranged in ascending order andthen paired with the quantiles of the reference Gaus-sian distribution with zero mean and unit variance. Inorder to cover evenly the unit interval, the quantilesof the standardized normal distribution were chosen tobe k / ( m +
1) where m denotes the number of observedevents and k = . . . m . In QQ–plots, the observationaltime sequence is indicated as increasing sizes of mark-ers.In the case of a steady γ –ray intensity, the values ofbinomial and Li–Ma statistics lie on the diagonal of thefirst quadrant represented by a dashed line in QQ–plotsprovided the source parameter was chosen correctly. Disagreement between the observed data and the cho-sen source intensity manifests itself in QQ–plots as dis-persion of sample significances from the reference diag-onal. Those distributions of sample significances whichprovide curved QQ–plots (di ff erently skewed than thereference standard normal distribution) indicate a pro-gressive change in the source intensity. The non–linearrelationship between the sample and reference distribu-tions is thus regarded as a hint of the time variability ofthe source activity.In individual observations, we consider a large valueof the statistical significance as a signature of a consid-erable deviation of the source intensity from its prede-fined constant value. The upward (downward) shift ofthe sample statistic from the reference distribution sug-gests that the intensity of the source was found to beabove (below) the benchmark value.Due to the arbitrariness of the source intensity rep-resented by the source parameter β we derived also itsconfidence intervals at a 3 σ ( ≈ . N on , N o ff , α ), confidence in-tervals for the source parameter β were determined nu-merically such that the Li–Ma significance in Eq. 2 sat-isfies | S LM ( N on , N o ff , α ; β ) | <
3. Plots of 99.7% con-fidence intervals, (cid:104) β − , β + (cid:105) , were constructed as MJD–ordered time sequence, see Figs. 2 and 4. In these plots,comparison of the source intensity in individual obser-vations is possible, thus allowing one to see the progressof the γ –ray activity in time. High–frequency peaked BL Lac (HBL) objectPKS 2005–489 ( z = . γ –ray fluxchanged annually by less than 40% between 2004 and2005. On the other hand, observations by the satellitesXMM–Newton and RXTE indicate variations of the X–ray flux by a factor of ∼
16 during the same period [3]. Itwas also found that the flux increased by approximately40% in the ultraviolet and by 20% in the optical band.In our analysis, we used 14 sets of data from Ta-ble 1 in Ref. [3] arranged according to the calendar . Stefanik and D. Nosek / Nuclear Physics B Proceedings Supplement 00 (2018) 1–6 N(0,1) q S
2 1 0 1 2 B i , S L M S PKS 2005 489, 2004 2007 (HESS)=1.29 β Bin, =1.29 β Li Ma, September ’06 August ’06June ’06 July ’06
Figure 1: QQ–plots of asymptotic binomial (empty symbols) and Li–Ma significances (full symbols) for the γ –ray events detected from thedirection of PKS 2005–489 [3]. Average source parameter β = . months during four years of HESS observations. Num-bers of on– and o ff –source events detected in these pe-riods range from 93 to several thousand. The data takenduring September 2007 were not included in the anal-ysis due to the small number of registered on–sourceevents N on =
11. We set the average source parameter β = (cid:104) N on /α N o ff (cid:105) = .
29 as a benchmark value of theblazar γ –ray intensity. Resultant sample significancesare depicted in QQ–plots in Fig. 1.Curvatures of QQ–plots indicate that the γ –ray inten-sity evolved in time during the observations. Disperseddistributions of the sample significances show that theintrinsic activity of the blazar is not consistent with thechosen intensity. One pair of sample statistics, well be-low the reference diagonal, suggests that a deficit of γ –ray events was observed during September 2006 ata 3 . σ level of significance. On the other hand, twomeasurements of June and July 2006 can be consid-ered excessive compared to the average expectation ata 2 . σ and 3 . σ level of significance, respectively. Weconclude that the PKS 2005–489 blazar exhibited vari-ability of its emissive intensity on time scales of monthsduring 2006.Confidence intervals for the source parameter β weredetermined for each of the 14 observational epochs,see Fig. 2. Non–overlapping confidence intervals ob-tained using July and September 2006 data (MJD53938–53940, 53995–54002) indicate consistently withcorresponding points in QQ–plots in Fig. 1 that a change MJD σ > + β , β < =1.29 β PKS 2005 489, 2004 2007 (HESS), monthsyears
Figure 2: 99 .
7% confidence intervals for the source parameter β ofPKS 2005–489 [3] are shown as a function of observational time. Ver-tical lines with points indicate the span of monthly confidence inter-vals. Hatched bands represent confidence intervals in calendar yearsfrom 2004 to 2007. The average source parameter β = .
29 is depictedas the horizontal dashed line. of the source intensity happened during this period. Ob-servations of August 2006 (MJD 53967–53977) pro-vide possible values of the source parameter consistentwith both the preceding and subsequent measurements.Therefore, there is a considerable hint that a gradual de-crease of the source intensity occured during consec-utive months in 2006, see Figs. 1 and 2. The rest ofmeasurements provide overlapping confidence intervalscontaining the average value of the source parameter(dashed line). The data thus suggests that the HBL ob-ject PKS 2005–489 spent most of the time during theobservational campaign in a quiescent steady state. Weevaluated also confidence intervals for the sum of countsdetected in individual calendar years (hatched bands inFig. 2). All four annual confidence intervals correspondwith each other as well as with the reference source in-tensity. No variations of the blazar activity can be rec-ognized on annual time scales.Lack of correlations between the increase of the fluxat lower wavelengths (optical to X–ray) and the steadyVHE emission during 2004–2005 would spoil the con-nection between these energy bands observed com-monly in a number of blazars [2]. In order to overcomethis problem, the HESS collaboration suggested that anadditional component contributing to the X–ray part ofthe SED might be present in the AGN jet in a way beingconsistent with the SSC modelling [3]. We confirmedthe previous HESS statement of constant γ –ray activityby analysing the sequence of confidence intervals us-ing the modified on–o ff method. We also verified that . Stefanik and D. Nosek / Nuclear Physics B Proceedings Supplement 00 (2018) 1–6 N(0,1) q S
2 1 0 1 2 B i , S L M S β =1.20, 2009 2012 (VERITAS) β Figure 3: QQ–plots of sample significances for the γ –ray activity of1ES 0229 +
200 are depicted. Circles represent the observations of theHESS collaboration in the 2005–2006 campaign [6]. Squares denotethe VERITAS data from measurements with MJD 55118–55951 [7].Source parameter β = .
20 was assumed. See also caption to Fig. 1. confidence intervals inconsistent with the assumptionof steady source activity corresponding to the 2004 and2005 measurements are obtained only when constructedat most at a 1 . σ level of significance. + HBL object 1ES 0229 +
200 ( z = . .
7% of the Crab Nebula fluxwas found to approach the value measured by the HESScollaboration. An excess of the γ –ray flux was observedduring October 2009 when it was almost twice as highas its average value [7]. The probability of the flux be-ing constant on annual time scales was evaluated to be1 . ff –source counts ranging from ten tothousands. In QQ–plots in Fig. 3, we compare dis- MJD σ > + β , β < β HESS 2005 2006, = 1.22 β VERITAS 2009 2012, yearsmonthsyears
Figure 4: 99.7% confidence intervals for the source parameter β of1ES 0229 +
200 are depicted. Yearly HESS observations [6] (circles)are compared with the monthly measurements of the VERITAS col-laboration [7] (squares). Hatched bands represent the confidence in-tervals obtained from joint sets of VERITAS data obtained in threeyearly observational periods. tributions of sample significances evaluated using datacollected by both collaborations. The average sourceparamater β HESS = (cid:104) N on /α N o ff (cid:105) = .
20 used as a ref-erence value of the blazar intensity was derived fromthe HESS data set. Note that the average source pa-rameter extracted from the VERITAS measurements is β VER = . S Bi and S LM for the HESS data (cir-cles) do not exhibit any significant deviations from thereference diagonal. The majority of the VERITAS mea-surements of 1ES 0229 +
200 (squares) provide samplesignificances not inconsistent with the chosen sourceintensity. However, two pairs of on– and o ff –sourcecounts coming from the VERITAS observations dur-ing October and November 2009 (MJD 55118–55131,55144–55159) yield large test significances, pointing tothe increase of overall source intensity. These two in-stances show that the 1ES 0229 +
200 activity cannot beconsidered steady at least on time scales of months.Confidence intervals for the source parameter β at a3 σ level of significance are displayed in Fig. 4. Theconsistency of the source intensities measured by theHESS (segments with circles) and VERITAS (segmentswith squares) collaborations, as visualized in QQ–plotsin Fig. 3, is also well visible in the time sequence ofconfidence intervals.Monthly confidence intervals contain the average val-ues of the source parameter derived using the HESSand VERITAS data with the only exceptions being . Stefanik and D. Nosek / Nuclear Physics B Proceedings Supplement 00 (2018) 1–6 two months in the observational period 2009–2010, seeFig. 4. Moreover, the confidence interval correspondingto October 2009 does not overlap with intervals at twolatter occasions with MJD 55476–55482 and 55555–55570 observed during the 2010–2011 VERITAS cam-paign. Thus, we state that the blazar varied its γ –ray emission on monthly time scales during the VER-ITAS observations. The joint sets of the on– and o ff –source counts taken over yearly time intervals exhibitsignificant excesses in the beginning of the 2009–2010epoch (MJD 55118–55212) with respect to the HESSand VERITAS measurements of 2006 and 2010–2011.The rest of the annual observations agree with the aver-age source intensities deduced from both the HESS andVERITAS data sets. It is worth noting that the VERI-TAS collaboration reported the evidence of source vari-ability supported by the 2009–2012 runs [7].
4. Conclusions
Temporal changes in the observed γ –ray intensi-ties of selected AGN were studied by the means ofthe modified on–o ff method with the emphasis puton its usefulness in the analyses of data gathered byCherenkov telescopes. The assumption of the constantsource activity was ruled out consistently with the pre-vious findings on time variability of PKS 2005–489 [3]and 1ES 0229 +
200 [7]. In particular, our results on1ES 0229 +
200 indicate intensity changes in the 2009–2010 period, thus rejecting the long–held conjecture ofits steadiness, in agreement with the conclusions of theVERITAS collaboration. Interestingly, temporal evolu-tion of the PKS 2005–489 activity during successivemonths in 2006 emerges and time variability of thisblazar is stated.The modified on–o ff scheme is not only backed bya compelling statistical motivation, but also relativelysimple to implement, yet su ffi ciently general. Freedomof the method from more complex calculations of fluxesmakes it suitable for the examination and comparison ofobserved intensity changes in VHE γ –astronomy. Acknowledgements
This work was supported by the Czech Science Foun-dation grant 14-17501S.