D O I: 10.1051/0004-6361/201629419
© E S O 2017
Astronomy &
Astrophysics
Characterizing the γ -ray long-term variability of PKS 2 1 5 5 -3 0 4 with H.E.S.S. and Fermi-LAT
H.E.S.S. Collaboration, H. Abdalla1, A. Abramowski2, F. Aharonian3,4' 5, F. AitBenkhali3, A. G. Akhperjanian6,5' ł , T. Andersson10, E. O. Anguner7, M. Arrieta15, P. Aubert23, M. Backes8, A. Balzer9, M. Barnard1, Y. Becherini10, J. Becker Tjus11, D. Berge12, S. Bernhard13, K. Bernlohr3, R. Blackwell14, M. Bottcher1, C. Boisson15, J. Bolmont16, P. Bordas3, J. Bregeon17, F. Brun25, P. Brun18, M. Bryan9, T. Bulik19,
M. Capasso27, J. Carr20, S. Casanova21,3, M. Cerruti16, N. Chakraborty3, R. Chalme-Calvet16, R. C. G. Chaves17, A. Chen22, J. Chevalier23,*, M. Chrćtien16, S. Colafrancesco22, G. Cologna24, B. Condon25, J. Conrad26, Y. Cui27, I. D. Davids1,8, J. Decock18, B. Degrange28, C. Deil3,
J. Devin17, P. deWilt14, L. Dirson2, A. Djannati-Atai29, W. Domainko3, A. Donath3, L. O ’C. Drury4, G. Dubus30, K. Dutson31, J. Dyks32, T. Edwards3, K. Egberts33, P. Eger3, J.-P. Ernenwein20, S. Eschbach34, C. Farnier26,10, S. Fegan28, M. V. Fernandes2, A. Fiasson23, G. Fontaine28,
A. Forster3, S. Funk34, M. FuBling35, S. Gabici29, M. Gajdus7, Y. A. Gallant17, T. Garrigoux1, G. Giavitto35, B. Giebels28, J. F. Glicenstein18, D. Gottschall27, A. Goyal36, M.-H. Grondin25, D. Hadasch13, J. Hahn3, M. Haupt35, J. Hawkes14, G. Heinzelmann2, G. Henri30, G. Hermann3,
O. Hervet15,42, J. A. Hinton3, W. Hofmann3, C. Hoischen33, M. Holler28, D. Horns2, A. Ivascenko1, A. Jacholkowska16, M. Jamrozy36, M. Janiak32, D. Jankowsky34, F. Jankowsky24, M. Jingo22, T. Jogler34, L. Jouvin29, I. Jung-Richardt34, M. A. Kastendieck2,*, K. Katarzynski37,
U. Katz34, D. Kerszberg16, B. Khćlifi29, M. Kieffer16, J. King3, S. Klepser35, D. Klochkov27, W. Kluzniak32, D. Kolitzus13, Nu. Komin22, K. Kosack18, S. Krakau11, M. Kraus34, F. Krayzel23, P. P. Kruger1, H. Laffon25, G. Lamanna23, J. Lau14, J.-P. Lees23, J. Lefaucheur15, V. Lefranc18,
A. Lemifere29, M. Lemoine-Goumard25, J.-P. Lenain16, E. Leser33, T. Lohse7, M. Lorentz18, R. Liu3, R. López-Coto3, I. Lypova35, V. Marandon3, A. Marcowith17, C. Mariaud28, R. Marx3, G. Maurin23, N. Maxted14, M. Mayer7, P. J. Meintjes38, M. Meyer26, A. M. W. Mitchell3, R. Moderski32, M. Mohamed24, L. Mohrmann34, K. Mora26, E. Moulin18, T. Murach7, M. de Naurois28, F. Niederwanger13, J. Niemiec21, L. Oakes7, P. O ’Brien31, H. Odaka3, S. Ottl13, S. Ohm35, M. Ostrowski36, I. Oya35, M. Padovani17, M. Panter3, R. D. Parsons3, N. W. Pekeur1, G. Pelletier30, C. Perennes16,
P.-O. Petrucci30, B. Peyaud18, Q. Piel23, S. Pita29, H. Poon3, D. Prokhorov10, H. Prokoph10, G. Puhlhofer27, M. Punch29,10, A. Quirrenbach24, S. Raab34, A. Reimer13, O. Reimer13, M. Renaud17, R. de los Reyes3, F. Rieger3,39,*, C. Romoli4, S. Rosier-Lees23, G. Rowell14, B. Rudak32, C. B. Rulten15, V. Sahakian6,5, D. Salek40, D. A. Sanchez23, A. Santangelo27, M. Sasaki27, R. Schlickeiser11, F. Schussler18, A. Schulz35, U. Schwanke7, S. Schwemmer24, M. Settimo16, A. S. Seyffert1, N. Shafi22, I. Shilon34, R. Simoni9, H. Sol15, F. Spanier1, G. Spengler26, F. Spies2, Ł. Stawarz36, R. Steenkamp8, C. Stegmann33,35, F. Stinzing34,ł , K. Stycz35, I. Sushch1, J.-P. Tavernet16, T. Tavernier29, A. M. Taylor4, R. Terrier29,
L. Tibaldo3, D. Tiziani34, M. Tluczykont2, C. Trichard20, R. Tuffs3, Y. Uchiyama41, D. J. van der Walt1, C. van Eldik34, C. van Rensburg1, B. van Soelen38, G. Vasileiadis17, J. Veh34, C. Venter1, A. Viana3, P. Vincent16, J. Vink9, F. Voisin14, H. J. Volk3, T. Vuillaume23, Z. Wadiasingh1, S. J. Wagner24, P. Wagner7, R. M. Wagner26, R. White3, A. Wierzcholska21, P. Willmann34, A. Wornlein34, D. Wouters18, R. Yang3, V. Zabalza31,
D. Zaborov28, M. Zacharias24, A. A. Zdziarski32, A. Zech15, F. Zefi28, A. Ziegler34, and N. Zywucka36 (Affiliations can be found after the references)
Received 28 July 2016 / Accepted 29 September 2016
ABSTRACT
Studying the temporal variability of BL Lac objects at the highest energies provides unique insights into the extreme physical processes occurring in relativistic jets and in the vicinity of super-massive black holes. To this end, the long-term variability of the BL Lac object PKS 2155-304 is analyzed in the high (HE, 100MeV< E < 300 GeV) and very high energy (VHE, E > 200 GeV) y-ray domain. Over the course of ~ 9 y r of H.E.S.S. observations the VHE light curve in the quiescent state is consistent with a log-normal behavior. The VHE variability in this state is well described by flicker noise (power-spectral-density index/3
VHE
= 1.10+0 1 0
) on timescales larger than one day. An analysis of ~5.5 yr of HE Fermi-LAT data gives consistent results (3HE
= 1.20+0 21
, on timescales larger than 10 days) compatible with the VHE findings. The HE and VHE power spectral densities show a scale invariance across the probed time ranges. A direct linear correlation between the VHE and HE fluxes could neither be excluded nor firmly established. These long-term-variability properties are discussed and compared to the red noise behavior (/3 ~ 2) seen on shorter timescales during VHE-flaring states. The difference in power spectral noise behavior at VHE energies during quiescent and flaring states provides evidence that these states are influenced by different physical processes, while the compatibility of the HE and VHE long-term results is suggestive of a common physical link as it might be introduced by an underlying jet-disk connection.Key words. galaxies: active - BL Lacertae objects: individual: PKS 2155-304 - gamma rays: galaxies - galaxies: jets - galaxies: nuclei - radiation mechanisms: non-thermal
1. Introduction
O ne o f the m o st striking properties o f BL L acertae objects is their variability across the electrom agnetic spectrum from r a dio to y rays and accros the tem poral spectrum from m inutes to
* Corresponding authors: H.E.S.S. Collaboration, e-mail: c o n ta c t.h e s s @ h e s s - e x p e rim e n t.e u t Deceased.
years. In the current standard p aradigm o f active galactic nuclei (e.g., U rry & Padovani 1995) th e observed nontherm al em ission is pro d u ced in tw o-sided collim ated, relativistic p lasm a outflows (jets) closely aligned w ith th e line o f sight, so th at th e intrinsic em ission appears enhanced b ecause o f D oppler-boosting effects.
T he je ts are pow ered by a central engine consisting o f a super- m assive b lack hole surrounded by an accretion disk. C h aracter
izing the tem poral variability provides one o f the key diagnostics
Year a ± <ra b ±
and 56 246 (15 N ovem ber 2012), using three o r four telescopes.
T he high flux state from 27 July to 8 A ug u st 2006, w ith an average flux o f (75.2 ± 0.8) x 10-11 c m -2 s-1 above 200 G eV is excluded from the data set. T he rem aining data constitutes the basis fo r the tim e-series analysis, and is referred to as the q u ies
cent d ata set in the follow ing.
In total, abo u t 328 h o f data p assed standard quality cuts as defined in A haronian et al. (2006), w ith a m ean zenith angle o f 21° resulting in an average energy threshold o f 178 GeV. The data set has been analyzed w ith the M odel analysis chain using standard cuts (de N aurois & R o llan d 2009) above 200 GeV.
T he total detection significance in the quiescent data set cor
responds to 3 4 1 ^ . T he lig h t curve o f nightly fluxes is calculated assum ing a log-parabolic energy spectrum ,
d N /d E k E -a-b log E, (1)
w ith a an d b corresponding to the best-fit pow er-law index and curvature index, respectively. In order to take indications o f a spectral variability in the V H E dom ain during the q uiescent state (A bram ow ski e t al. 2010) into account, the n ightly fluxes are d e
riv ed w ith a separate log-parabola fit o f the spectrum for each inant em ission processes.
T he B L L ac P K S 2 1 5 5 -3 0 4 (redshift z = 0.116;
F alom o e t al. 1993) has been observed w ith th e H igh E n ergy S tereoscopic S ystem (H .E.S.S.; H inton 2004) at very high-energy y-rays (V H E; E > 200 G eV ) since 2002 (e.g., A bram ow ski e t al. 20 1 0 , and references therein). T he source u n derw ent an extrem e V H E flux outburst in July/A ugust 2006 w ith peak fluxes exceeding the average flux level o f th e lo n g term em ission b y a factor o f ~ 100, during w hich it show ed rap id variability on tim escales as short as 3 m in (A haronian et al.
2007) . T he stochastic V H E variability during this flaring state has been ch aracterized as pow er-law n o ise (<xf~P, w here f is the frequency) w ith an index j3 ~ 2. A detailed analysis o f the V H E d ata from 2 0 0 5 -2 0 0 7 revealed th at the run-by-run light curve o f PKS 2 1 5 5 -3 0 4 follow s a skew ed flux distribution, w hich is w ell represented by tw o superposed lognorm al distribu
tions (A bram ow ski et al. 20 1 0 , Fig. 3). E xcluding the flare data, the flux distribution satisfies a sim ple lognorm al distribution.
This provides evidence th at the source sw itches from a q u ies
cent V H E state w ith m inim al activity to a flaring state, and the flux distribution in each state follow s a lognorm al distribution.
L ognorm al behavior was first established for accreting G alac
tic sources such as X -ray binaries by U ttley & M cH ardy (2001), linking such a b ehavior to the underlying accretion process. In a lognorm al process, the fluctuations o f the flux are on average proportional, o r a t least correlated, to the flux itself, ruling out additive processes in favor o f m ultiplicative processes. In the case o f blazars, a lognorm al behavior could thus m ark the influ
ence o f the accretion d isk on the je t (e.g., G iebels & D egrange 2 0 0 9 ; M cH ardy 2010) . C ascade-like events are an exam ple o f m ultiplicative lognorm al processes. D ensity fluctuations in the accretion d isk provide one possible realization. If dam ping is negligible, these fluctuations can propagate inw ard an d couple together to p roduce a m ultiplicative behavior. If this is efficiently transm itted to th e je t, the y -ra y em ission cou ld be m o dulated accordingly.
In Sect. 2 w e presen t V H E data from 9 y r o f H .E .S.S. o b servations o f PKS 2 1 5 5 - 3 0 4 in th e q uiescent state, and partially contem poraneous H E data from 5.5 y r o f observations from the L arge A rea T elescope (Ferm i-LA T), are p resented in Sect. 2.
In Sect. 3, a d etailed tim e-series analysis is perform ed. First, the lig h t curves are tested for a lognorm al behavior. Then, their variability is characterized as pow er-law noise w ith a forw ard folding m eth o d w ith sim ulated lig h t curves, taking th e sam pling o f the data, d escribed in K astendieck e t al. (2011) into account.
A nd, finally, the V H E and H E em issions are also analyzed for a possible d irect linear correlation. This is the first tim e th at such an extended analysis is p erform ed on the V H E y -ray em ission o f a BL L ac o bject on tim escales as long as n in e years. In Sect. 4 the results o f the tw o energy ranges are com pared and their im plications on the p hysical properties o f PKS 2 1 5 5 -3 0 4 are discussed.
2. Observations and analysis
H .E .S.S. (VHE): H .E .S.S. is an array o f five Im aging A t
m ospheric C herenkov Telescopes (IA CTs). T he first p hase o f H .E.S.S. began in 2003 w ith four 12-m telescopes giving an en ergy threshold ~ 1 0 0 GeV. In 2012, a fifth 28-m telescope was added to the array, reducing the energy threshold to ~ 5 0 GeV.
T he p rese n t analysis is b ased on V H E data taken w ith the com pleted H .E .S.S. P hase-I betw een M JD 53 200 (14 July 2004)
year.
T he values for a and b are su m m arize d in Table 1; the aver
age values are a = 3.209 and b = 0.164. T he unbiased sam ple variance for th e first param eter
(2)
is larger than the expected variance <r2a = 0.005 b ecause o f the uncertainties <ra on th e individual best-fit values. T he sam e is true for the second p aram eter w ith s2 = 0.114 and a 2b = 0.005.
This could be indicative o f a variable spectrum .
Variations w ithin a season, however, are unlikely to affect the analysis p resen ted here as the inferred sm all changes in the spectral param eters only re su lt in sm all changes in the integral flux.
T he resulting quiescent lig h t curve has an average flux o f (5.10 ± 0.41) x 10-11 cm -2 s-1 above 200 G eV an d is show n in Fig. 1. It is characterized b y a fractional ro o t m ean square (rm s) variability (Vaughan e t al. 2003)
(3)
w here $ is the m ean flux, S $ is the variance o f the fluxes and is the contribution to the variance caused by the m easurem ent for the p hysical conditions in these system s, for exam ple
the je t-d isk connection, location o f the em itting region, o r dom -
fable 1. Values of the log-parabola parameters of the spectrum (Eq. (1)) of PKS 2155-304 used to derive the light curve.
2004 2.95 ± 0.03 0.37 ± 0.03 2005 3.27 ± 0.12 0.25 ± 0.12 2006 3.27 ± 0.04 0.24 ± 0.04 2007 3.38 ± 0.08 - 0 .0 3 ± 0.07 2008 3.28 ± 0.04 0.12 ± 0.03 2009 3.14 ± 0.08 0.18 ± 0.07 2010 3.24 ± 0.08 0.10 ± 0.07 2011 3.08 ± 0.10 0.13 ± 0.08 2012 3.27 0.01 0.12 0.09
1 n
s2a = — ^ ( a . - - a ) = 0.017 i=1
F var = _ --- = 0.66 ± 0.01,
$
Fig. 1. H .E.S.S. light curve of nightly fluxes above 200 GeV excluding the high state in July/August 2006 (gray shaded area). The gray dashed horizontal line indicates the average flux of the quiescent state.
Table 2. Values of the reduced y 2 and associated probability for the Gaussian fits of the flux and log flux distributions for each light curve.
1 h t t p : / / f e r m i . g s f c . n a s a . g o v / s s c / d a t a / a n a l y s i s / d o cu m en ta tio n /P a ss7 R E P _ u sag e .h tm l
2 Cf. the Fermi Science Support Center web site h t t p : / / f e r m i . g s f c . n a s a .g o v / s s c /
$ log $
X 2 /d.o.f. Prob X / d . o .f . Prob a H .E .S.S. 50.8/17 10-5 11.9/13 0.54 5.39
Ferm i 21.6/12 0.04 15.0/11 0.18 2.57
Notes. The parameter a is the significance level on which a lognormal distribution is preferred to a normal distribution.
Table 3. Values of the reduced x 2 of the constant and linear fits of the scatter plots shown in Fig. 3 for each light curve with values for the significance a , correlation factor p, and Kendall rank t .
Tim e (MJD)
Fig. 2. Light curve of the integral fluxes between 0.1 and 300 GeV in bins of ten days measured with Fermi-LAT. The dashed line indicates the average flux.
errors. T he analysis results w ere cross-checked using different analysis m ethods and calibration chains (e.g., A haronian et al.
2006), yielding com patible results.
Ferm/-LAT (HE): T he Ferm i-LA T (A tw ood e t a l. 2009) on board the F erm i satellite is a pair-conversion telescope designed to detect H E y-rays in the energy range from below 20 M eV to m ore than 30 0 GeV.
T he set o f observational d ata for PKS 2 1 5 5 -3 0 4 used here covers abo u t 5.5 yr, from M JD 5 4 6 8 8 (10 A ugust 2008) to 5 6 6 8 8 (31 January 2014). E vents are selected betw een 100 M eV and 300 G eV in a region o f interest (ROI) o f 15° around PKS 2 1 5 5 -3 0 4 . T he detector is d escribed by the P 7R E P _S O U R C E _V 15 instrum ent response function 1. T he H E light curve is obtained w ith th e tool E nrico (S anchez & D eil 2013) using the Ferm i S cience Tools v9r3 2 p 52, w ith a 10-day binning to ensure enough statistics in each bin. T he prefactor o f the diffuse galactic b ackground (gll_iem _v05) and the n o rm al
ization o f th e isotropic diffuse em ission (iso_source_v05) are left free to vary in the likelihood fit.
A ll sources from th e th ird LAT source catalog (3FG L ; A cero e t al. 2015) w ithin 15° o f PKS 2 1 5 5 -3 0 4 are included in the m odel to ensure a good b ackground m odeling. T he H E spec
tra o f PKS 2 1 5 5 - 3 0 4 and all sources w ithin 3° are fitted fo l
low ing the spectral shape o f th e 3FG L catalog. T he spectra o f PKS 2 1 5 5 -3 0 4 , 3FG L J2151.6-2744 and 3FG L J2159.2-2841 are m odeled w ith a sim ple pow er law, w hile for 3FG L J2151.8- 3025 a log-parabolic shape is assum ed. T he indices an d p re factors are left free. A ll o ther com ponents are fixed to the values in th e 3FG L catalog. PKS 2 1 5 5 -3 0 4 is d etected w ith a sig nificance o f 1 5 6 a w ith a spectral index o f 1.83 ± 0.01. The photon counts o f PKS 2 1 5 5 -3 0 4 are integrated into 201 bins o f ten days. T he resulting light curve has an average flux o f 1.20 ± 0.03 x 10-7 c m -2 s-1 betw een 100 M eV and 300 G eV w ith a F var = 0.41 ± 0.02 (Eq. (3)) and is show n in Fig. 2 .
C onstant L in e ar increase
/d.o.f. ^ 2/d.o.f. a
H .E.S.S. 5.78 0.89 6.33
Ferm i 0.936 0.107 2.75
p t
H .E.S.S. 0.86 ± 0.11 0.78 ± 0.26 Ferm i 0.93 ± 0.19 0.69 ± 0.25
3. Time-series analysis
To characterize the long-term variability o f PKS 2 1 5 5 -3 0 4 , the H E and V H E data sets are an alyzed w ith resp ect to lognorm ality and pow er-law noise.
Lognorm ality: A possible lognorm al behavior o f PKS 2 1 5 5 -3 0 4 is investigated by exam ining the distribu
tion o f the fluxes and studying the correlation betw een the flux levels and the intrinsic variability. T he flux and log-flux distributions o f each lig h t curve are fitted b y a G aussian using a x 2 fit. T he goodness o f th e fits are sum m arized in Table 2 . In both cases, a G aussian fits the log-flux distribution b etter than the flux distribution, w ith a significance level o f a > 5 for the V H E an d a > 2 for th e H E data, respectively. F or th e V H E data the probability representing the goodness o f fit is about 104 tim es h igher for the log-flux distribution w hen com pared to the flux distribution. F o r the H E data this ratio is on th e order o f 10. Thus, w hile th e H E y -ray flux o f PKS 2 1 5 5 -3 0 4 in this approach shows only an indication, the V H E y -ray flux data p rovide evidence fo r a lognorm al behavior.
In addition, the variability-flux relation, estim ated by the excess rm s (Eq. (4 )), is investigated fo r a possible correlation (U ttley e t al. 2005) . T he excess rm s estim ates the intrinsic vari
ability o f a tim e series b y subtracting th e contribution o f the m e a
surem ent errors. It is defined as
a xs = J S 2 - a err (4)
w here S 2 is the variance and a 2rr th e m ean square o f the statis
tical erro r o f the data (V aughan et al. 2003) . H ere aXS is calcu lated for bins o f the light curves each containing at least 20 light curve points. T hey are p lotted versus the average fluxes $ o f the corresponding bins fo r both lig h t curves in F ig. 3 .
To test th e p ossible correlation betw een the flux and its vari
ability, the scatter plots are fitted b y a co nstant as w ell as a linear ascending slope. T he fit results are sum m arized in Table 3 . The results reveal a p reference g reater than 6 a fo r the lin e ar fit to the V H E data w hile H E data only show an indication o f linear
ity. To characterize this b ehavior b eyond the fit o f a lin e ar cor
relation, the nonparam etric correlation factor S pearm an p and
Fig. 3. Scatter plot of the excess rms and the average flux for the H.E.S.S. (left) and Fermi-LAT (right) data. Each flux and excess rms values are computed using at least 20 adjacent light curve points. A linear fit is shown in red.
the K endall ran k t, w hich m easure the ordering o f the points, (G leissner et al. 2004) are calculated. In all cases p > 0.85 and t > 0.65, m eaning th at t xs and $ show a strong correlation.
This im plies th at th e fluctuations o f the flux are in fact co rre
lated w ith the flux.
T he preceding analysis show s that the H E and V H E flux distributions o f PKS 2 1 5 5 -3 0 4 during the quiescent state are com patible w ith lognorm al distributions. W hen the tw o energy bands are com pared, the lognorm al b ehavior is m uch m o re ev
ident in th e V H E d ata set. In addition, for both energy bands the variability am plitude o f the flux is correlated w ith the flux level, supporting the conclusion th at lognorm ality is an intrinsic characteristic o f the long-term y -ra y em ission in PKS 2 1 5 5 -3 0 4 . A sim ilar resu lt has also been reported for the V H E flaring state o f PK S 2 1 5 5 -3 0 4 in 2006 (A bram ow ski e t al. 2010) .
Pow er-law noise: the flux variability o f active g alax ies has frequently been characterized as pow er-law noise (e.g., L aw rence & Papadakis 1993) . T he pow er spectral density (PSD), i.e., th e square m odulus o f th e discrete F ourier transform (Priestley 1967) , o f such a lig h t curve follow s a pow er law <xf ~P, w here f is th e tem poral frequency and usually 1 ś j3 ś 2. The PSD reveals how th e variability am plitude is distributed am ong the tim escales. In a pow er-law n oise lig h t curve (6 > 0) the flux variations on longer tim escales d o m inate the variations on shorter tim escales. T he total variance o f such a light curve tends to grow w ith its length. F or = 0 the variability pow er is equal on each tim e cale, resulting in w hite noise, w here the fluxes at all tim es are uncorrelated.
To study the variability characteristics, w e first hypothesize that the lig h t curves can b e described b y pow er-law n oise w ith a lognorm al b ehavior w ith j3 > 0 as the only free param eter.
T hree different m ethods are then u sed to characterize th e vari
ability o f th e lig h t curves: the L om b-S cargle P eriodogram (LSP), w hich is a m eth o d to approxim ate the PSD (L om b 1976; Scargle 1982) ; the first-order S tructure F unction (SF; Sim onetti et al.
1985) and the M ultiple F ragm ents V ariance F unction (M FV F;
K astendieck e t al. 2011) , w hich are both representations o f the PSD in the tim e dom ain.
A forw ard-folding m eth o d w ith sets o f 104 sim ulated light curves for each value o f j3 an d a m axim um likelihood e sti
m ato r are applied to estim ate the best-fit p aram eter j3, as d e
scribed in K astendieck e t al. (2011) . T he lig h t curves are sim ulated w ith a lognorm al behavior, so th at the logarithm o f the
intrinsic light curve $ intr is pow er-law n oise w ith a G aussian b e havior o f m ean u and standard deviation t .
log($intr) ^ N (U , t ) . (5)
T he PSD o f th e sim ulated pow er-law n oise is generated on a frequency ran g e [(10T )-1 , 5 d -1] w here T H.E.S.S. = 3047 d and T Fermi = 2000 d are the lengths o f th e m easured light curves, respectively. T he pow er-law n oise is rebinned to ten days for the F erm i-L A T analysis corresponding to the binning o f the PKS 2 1 5 5 -3 0 4 lightcurve. T he light curves are then dow nsam p le d to the real observation tim es, the fluxes are rescaled to the average and variance o f the m easu red fluxes, and m easurem ent errors are sim ulated. T he p aram eter space is sam pled w ith = 0 .0 ,0 .1 , . . . , 3.0. T he SFs, L SPs and M F V F s are equally binned in lo g 10 scale w ith 50, 20, and 5 bins p er decade, respectively.
O w ing to the binning, th e sm allest resolvable tim escale in the F erm i-L A T light curve is t 0 = 10 d and the corresponding frequency is fhigh = ( 2 t 0) -1 = (20 d )-1 . F or the H .E.S.S. light curve the sm allest resolvable tim escale is t 0 = 1 d correspond
ing to fhigh = (2 d )-1 . T he L SP s are characterized on a frequency ran g e [10-4 d -1 , fhigh], w hile the low est tim escale for the SFs and M F V F s is t 0. T he m ethods are also sensitive to variations that occur on tim escales larger than th e lengths o f the light curves and th at appear as long-term trends. It is therefore also useful to cal
culate th e L S P on frequencies < T -1 to reveal such inform ation.
T he application o f these m ethods to the H .E .S.S. lig h t curve in the quiescent state gives best-fit param eters
>6lsp = 1.1 0 - ^ 6 , ,6sf = 1.00- ^ ^ , j6mfvf = 1.1 0 -^ 1°.
A goodness o f fit test is applied w here the m axim um likelihood values o f sim ulated L SP s, SFs and M F V F s, respectively, are used as test statistics. F or this, new sim ulated sets o f 1 0 4 light curves o f th e best-fit param eters are analyzed w ith the likelihood estim ator. T he distribution o f their m axim um likelihood values is com pared w ith the respective value o f PKS 2 1 5 5 -3 0 4 . A ssum ing th e m odel to b e correct, th e values should b e com patible. The quantile th at has a sm aller likelihood than the PKS 2 1 5 5 -3 0 4 d ata is used to estim ate the p -v alu e p . T he sm allest value o f p = 11% is found w ith th e M FVF. T he hypothesis th at th e data can b e described by a single pow er-law noise m odel is thus not rejected.
T he M F V F gives the m o st p recise value, w hich is taken here as th e final value:
jSvHE = 1.10X13.
T he best-fit values o f the o th e r m ethods are com patible w ithin the uncertainties.
T he LSP, SF an d M F V F o f the m easured lig h t curves to gether w ith the p robability density functions (PD F) o f the sim ple pow er-law noise m o d el th at b est fits the data are show n in Fig. A .1 . T he probability is n orm alized to unity in each fre
quency bin. T he uncertainties o f 3 are found w ith th e distribu
tions illustrated in Fig. A .2 .
F o r com parison, as a second hypothesis, an extended m odel is investigated: a m axim um tim escale is considered, above w hich the variance does n o t increase any further. T he existence o f such a tim escale is expected, as otherw ise the variance o f the light curve and therefore the flux w ould increase to infinity w ith tim e.
This is represented b y a b reak in the PSD to a co nstant level (3 = 0) a t the corresponding frequency / min, w hich is treated as an additional free param eter, w ith a sam pling lo g 10( / min/ d -1) = - 4 .4 , - 4 . 2 , . . . , - 1 .0 .
T he likelihood estim ators w ith th e three m ethods give best- fit values o r 1 a u p p er lim its,
3lSP = k 10- ^ ^
log10 (/min,LSP/d-1) = -3.80-1.12 < - 2 .6 8 ,
^SF = 1.00-0.07,
log10 (/min,SF/d-1) = -3 .8 0 -1 .¾ < -2 .1 9 ,
3mFVF =
lo g 10 (/min,MFVF/d-1) = -3.60-1.34,.
T he best-fit values o f lo g 10( / min/ d -1) = - 3 .8 0 fo r th e L S P and SF is n ea r th e form al lim it o f o u r analysis, w hich is constrained to - 4 .4 by the lengths o f the sim ulated lig h t curves. T he results together w ith the 1 a uncertainties to higher values (+ 1.12 and + 1.61) are therefore treated as 1 a u pper lim its. T he b est lik eli
hood fo r the M F V F is given fo r a b rea k in the PSD . However, the goodness-of-fit p value o f 10% is n o t im proved com pared to 11% for the first hypothesis (assum ing no break). This and the L SP and M F V F findings thus do n o t reveal any p reference for the existence o f such a b rea k in th e sam pled frequency range.
A n analogous analysis is p erform ed on the F erm i-LAT light curve. T he follow ing best-fit param eters for the sim ple pow er- law m odel are com patible:
3lSP = ^^-0.31+ ^SF = k 2 0 -!.22, ^MFVF = k 20 - ^ .
T he m o st constraining result, again given by th e M FVF, is taken as th e final value:
3he = 1.20-1.¾.
T he goodness-of-fit tests yield p values > 6% . Inspection o f the L SP p lo t in Fig. A.1 for the F erm i-L A T data reveals a p ea k at
~ (6 7 0 -7 0 0 ) days, w hich is indicative o f a possible H E p erio d icity on th e n oted tim escale an d influencing the p value fo r this analysis. It is interesting to no te that a tentative H E periodicity o f ~ (6 2 0 -6 6 0 ) days has already been reported (S andrinelli et al.
2014) .
A com parative analysis o f the extended m o d el (pow er law w ith a break) gives com patible results w ith
^lsp = 1.10-0.11,
log10 (/min,LSp/d-1) = -4 .2 0 -1 .¾ < - 2 .7 8 ,
^sf = 1.20-0.11,
log10 (/min,SF/d-1) = -4.20-1.10 < -2 .8 0 ,
jSmfvf = 1.30-0.08,
log10 (/min,MFVF/d-1) = -3.40-0.12.
T he best-fit values fo r the L SP and the SF are both lo g 10( / min/ d -1) = -4 .2 0 . Including the 1 a uncertainties to higher values (+ 1 .4 2 and +1.40) they are treated as 1 a upper lim its.
T he goodness-of-fits do n o t im prove. T he results therefore give no indication fo r th e p resence o f a b reak frequency in the PSD in the sam pled frequency range. S ee Table 4 for a sum m ary o f these an d related results.
C orrelations: T he V H E an d H E lig h t curves are furtherm ore an alyzed fo r a possible d irect correlation w ith the discrete co rre
lation function (D C F; E delson & K rolik 1988) using a binning o f 30 d. T he results are com pared w ith the D C F s o f sim ulated H .E.S.S. and F erm i-L A T lig h t curves follow ing one o f the tw o hypotheses: (1) th e H .E .S.S. an d the F erm i-L A T light curves are characterized by flicker n oise (3 = 1.1) w ith o u t any correlation;
(2) the fluxes o f such light curves obey a perfect, d irect linear correlation.
F o r each hypothesis 104 pairs o f corresponding lig h t curves are sim ulated an d th eir D C F s are calculated. T hese D C F s are then com bined in a tw o-dim ensional histogram w hich is treated as a PDF. T he hypotheses are tested according to the goodness- of-fit te st described above: for the m easu red D C F th e likelihood is calculated w ith the PDF. A lso for the sim ulated D C F s the lik e
lihoods are calculated and are used as a test statistic for calculat
ing the p value. B oth hypotheses are com patible w ith th e m e a
sured data w ith p values for (1) o f 41% , and for (2) o f 59% , respectively. A ccordingly, these results n eith er give a clear p re f
erence n o r do they allow the rejection o f a d irect correlation.
4. Discussion and conclusions
F or th e first tim e th e tem poral variability o f the V H E em is
sion o f PKS 2 1 5 5 -3 0 4 in th e quiescent state has been analyzed on tim escales from days up to m ore than nin e years. T he vari
ability o f the long-term quiescent V H E lig h t curve as m e a
sured w ith H .E .S.S. provides evidence for a lognorm al behavior and is com patible w ith pow er-law n oise process on tim escales
>1 d. T he V H E PSD on these tim escales is co nsistent w ith a pow er law ( k f -3) w ith an index o f 3 VhE = 1.10+013 (flicker noise). O n the other hand, th e PSD for the H .E .S.S. d ata du r
ing th e flaring p erio d in 2006 is consistent w ith a po w er law o f slope 3 = 2.06 ± 0.21 (red noise) on tim escales <3 h w ith indications for a possible b rea k in the SF betw een 3 an d 20 h (A bram ow ski e t al. 2010) . In the context o f accretion-pow ered sources, X -ray variability w ith sim ilar characteristics (power- law noise w ith
3
~ 1 -2 , and lognorm al behavior) has often been related to ran d o m fluctuations o f the disk p aram eter a on local viscous tim escales (e.g., L yubarskii 1997; K ing e t al. 2004) . The> 2 0 0 G eV H .E .S .S .a [0.9,2.6] SF, F F 2.06 ± 0.21 [0.1,0.9] - ( 1 0.1 - 300 G eV F erm i-L A T b [ -2 .0 , - 0 .9 ] PSD , fit 0.577 ± 0.332 - - (2;
0.1 - 300 G eV F erm i-L A T c [ -3 .2 , - 0 .7 ] PSD , fit 0.64+070 < - 1 .7 - (3)
2 .5 -2 0 keV R X T E d [ -0 .9 ,0 .0 ] PSD , fit 1.46 ± 0 .1 0 - - (4;
2 .5 -2 0 keV R X T E d [0.0,1.9] PSD , fit 2.23 ± 0.10 - - (4;
O ptical G eneva [ -1 .2 ,2 .0 ] SF, fit 2.4+0 3 - - (5)
O ptical RO TSE [ - 4 . 4 ,- 1 .3 ] M FV F, F F 1.8:+00.:2 -3.0+ 04 - (6:
O ptical SM AR TS [ -2 .4 , - 0 .9 ] PSD , fit 2 .2 -°2 - ' - (7;
Notes. Range of log10( f /d -1): the range over which the PSD is characterized. Method: the methods used for the analysis; forward folding method (FF), best fit of the slope by, e.g. a y 2-test (fit), Structure Function (SF), Lomb-Scargle Periodogram (LSP) and Multiple Fragments Variance Function (MFVF). Goodness of fit: the p-value obtained with simulated light curves. Upper part - results from this work. Lower part - results reported in the literature with superscripts referring to: (a) H.E.S.S. flaring state: a break was detected with a 95% confidence in the SF. It shall be noted that a break in the SF is at a ~3 times larger frequency than in the intrinsic PSD. (b) Based on aperture photometric Fermi-LAT light curves provided by the Fermi Science Support Center at h t t p : / / f e r m i . g s f c . n a s a . g o v / s s c / d a t a / a c c e s s / l a t / m s l _ l c / . (c) Model results assuming a superposition of Ornstein-Uhlenbeck processes (OU) and using 4 yr of Fermi-LAT data. A slight preference for a single OU with different slope is reported.(d) Based on non-simultaneous data.
References. (1) Abramowski et al. (2010); (2) Nakagawa & Mori (2013); (3) Sobolewska et al. (2014); (4) Kataoka et al. (2001); (5) Paltani et al.
(1997); (6) Kastendieck et al. (2011); (7) Chatterjee et al. (2012).
current V H E findings can in p rinciple b e interpreted in tw o d if
ferent w ays:
(1) T he PSD slope o f the V H E variability is stationary. It fo l
lows a pow er law w ith a transition (break) from f i ~ 2 to
~1 som ew here betw een 0.1 and ~1 d. This can be co m pared to the X -ray PSD s o f S eyfert A G N and radio g alax ies. T he P SD o f S eyfert A G N exhibit a pow er-law behavior f i - 1 a t low frequency, steepening to f i ^ 2 on tim escales shorter than som e b rea k tim e Tbr (e.g., M cH ardy et al.
2006) . Two radio galaxies, 3C 111 an d 3C 120 show a sim ilar behavior in X -ray w ith a pow er-law slope o f ~ 2 for 3C 111 (C hatterjee e t a l. 2011) and a steepening o f the PSD a t high frequency for 3C 120 (C hatterjee e t al. 2009) . Interestingly, for PKS 2 1 5 5 - 3 0 4 a b reak tim e Tbr ~ 1 d has been suggested earlier (K ataoka et al. 2 0 0 1 , cf. also Table 1), b ased on (nonsim ultaneous) X -ray data (cf. also E m m anoulopoulos et al. 20 1 0 , for caveats). In the case o f S eyfert A G N a sim ple quantitative relationship b etw een Tbr, the observed (bolom etric) lum inosity LB and the b lack hole m ass M BH has been found (M cH ardy et al. 2006) . A lthough PKS 2 1 5 5 - 3 0 4 is n o t a radio-quiet object, a sim ilar re la tion could apply if its characteristic tim ing properties are caused by an external process (e.g., o riginate in th e ac cre
tion flow, see fo r instance; M cH ardy 2010). In term s o f the accretion rate mE (expressed in units o f th e E ddington rate),
the relevant scaling relation for a standard d isk configuration becom es (Tbr/1 d) - 0.7 (Mbh/ 108 M 0 ) L12/m£'98. If this w ould apply to PKS 2 1 5 5 -3 0 4 , then relatively h igh ac cre
tion rates (^ 0 .1 E ddington rate for M BH > 108 M 0 ) w ould be im plied even fo r the quiescent V H E state. This m ay suggest th at in this context th e break tim e is m o re likely rela ted to a change in accretion flow conditions such as a transition from an advection-dom inated to a standard d isk configuration.
(2) A lternatively, the pow er-law indices o f the PSD could be different during the quiescent and flaring states, as they are possibly rela ted to different p hysical processes and/or spatial locations. T he extrem e characteristics o f the flaring state (including apparent lognorm ality an d a red -n o ise b e havior dow n to m inutes) seem to req u ire rath e r exceptional conditions to account for it (e.g., R ieger & Volpe 2 0 1 0 ; B iteau & G iebels 2 0 1 2 ; N arayan & P iran 2012) . This could support a variability origin differing from the origin in the q uiescent state. F u rth er lim its on the possible cross-over tim escale w ill b e im portant to distinguish betw een these tw o scenarios.
T he H E lig h t curve, as m easured w ith F erm i-LAT, is found to be com patible w ith a pow er-law n o ise o f slope j6he = 1.20+0 23 on tim escales larger than ten days. This value differs slightly from the earlier reported best-fit f i = 1.7 ± 0.3 fo r the average PSD o f the six brig h test F erm i-L A T BL L acs (including PKS 2 1 5 5 -3 0 4 )
> 2 0 0 G eV H .E.S.S. [ -4 .0 , - 0 .3 ] LSP, FF 1.10+0.14
. -0.16 no break (fixed) 56%
> 2 0 0 G eV H .E.S.S. [-3 .5 ,0 .0 ] SF, FF 1.00+- 0..11 1.00-0.15
1 .10+- 00..1105 no break (fixed) 48%
> 2 0 0 G eV H .E.S.S. [-3 .5 ,0 .0 ] M FVF, F F . -0.13 no break (fixed) 11%
> 2 0 0 G eV H .E.S.S. [ -4 .0 , - 0 .3 ] LSP, FF 1.10+- 0.28
. -0.09 -3 .8 0 +- 10..1312 < - 2 .6 8 51%
> 2 0 0 G eV H .E.S.S. [-3 .5 ,0 .0 ] SF, FF 1.00+- 0.24
. -0.07 -3 .8 0 -+001...136118 < -2 .1 9 43%
> 2 0 0 G eV H .E.S.S. [-3 .5 ,0 .0 ] M FV F, F F 1 .10+- 0..23
. -0.06 - . -0.34- 3 6 0 +141 10%
0 .1 -3 0 0 G eV F erm i-LAT [ - 4 . 0 ,- 1 .3 ] LSP, FF 1 .10+- 0..26
. -0.31 no break (fixed) 6.3%
0 .1 -3 0 0 G eV F erm i-LAT [ - 3 . 3 ,- 1 .0 ] SF, FF 1.20+- 0.22 . -0.31
1 .20+- 00..2311 no break (fixed) 46%
0 .1 -3 0 0 G eV F erm i-LAT [ - 3 . 3 ,- 1 .0 ] M FV F, F F . -0.23 no break (fixed) 40 % 0 .1 -3 0 0 G eV F erm i-LAT [ - 4 . 0 ,- 1 .3 ] LSP, FF 1.10+- 0.46
. -0.11 -4.20+++3 < - 2 .7 8 2.4%
0 .1 -3 0 0 G eV F erm i-LAT [ - 3 . 3 ,- 1 .0 ] SF, FF 1.20+- 0.44
. -0.11 - 4 .2 0 + ™ < - 2 .8 0 33%
0 .1 -3 0 0 G eV F erm i-LAT [ - 3 . 3 ,- 1 .0 ] M FV F, F F 1.30+- 0.54 - -30..4102+0.74
30%
Table 4. Characteristics of the power spectral densities of PKS 2155-304 at different energies and timescales.
E nergy Instrum ent R ange o f M ethod f i lo g 10 ( f min/ d -1 ) G oodness Ref.
range__________________________ lo g ^ ( f / d -1)______________________________________________________ o f f it
based on the first 11 m onths o f d ata (A bdo e t al. 2010) . It is co m patible w ith m o re recen t indications for a flatter slope (6 ~ 1) for high-frequency-peaked B L L ac (H B L) objects (S. Larsson, priv. com m .). T he H E slope is also com patible w ith the V H E results for the quiescent d ata set, suggesting th at th e PSD s on these tim escales are shaped by sim ilar processes. O w ing to in strum ental n oise and observational gaps a possible d irect co rre
lation betw een the V H E and the H E lig h t curves could neither be excluded n o r firm ly established.
T he H E and V H E PSD s show a scale invariance on tim escales from w eeks up to at least the 1T -low er lim its Ś 6 0 0 d and > 200 d, respectively. A m axim um tim escale o f 103 days has been reported in the optical range (see Table 1). If the m axim um tim escale w as related to the radial infall tim e in the accretion disk, then a possible o uter radius o f r d ^ ( a VG M BHfmi1n)2/3 >
4 x 1016 ( a /0 .3 ) 2/3(tmax/1 0 0 0 d )2/3 (M BH/1 0 8 M 0) 1/3 cm m ight be in ferred for an advection-dom inated system (L yubarskii 1997) . H ow ever a significant detection o f such a m axim um tim escale in the y -ray ran g e w ill probably require longer light curves that exceed this tim escale by an o rder o f m agnitude.
F or both d ata sets o f PKS 2 1 5 5 -3 0 4 , th e flux distributions during th e quiescent state are com patible w ith lognorm al d istri
butions, w here the resu lt is m o re significant for the V H E data than for the H E data. A hint o f lognorm al b ehavior was found in A bram ow ski et al. (2010) w here the distribution o f the fluxes o f th e quiescent state o f 2 0 0 5 -2 0 0 7 w ere follow ing a lognorm al distribution. This suggests th at m ultiplicative, i.e., self-boosting processes dom inate the variability. It is interesting to note th at in the context o f galactic X -ray binaries, w here lognorm al flux v ari
ability has first been established, such a b ehavior is thou g h t to be linked to the underlying accretion process (U ttley & M cH ardy 2001) . In the A G N context, evidence for lognorm ality on d if
ferent tim escales has in th e m eantim e also been found in sev
eral sources, for exam ple, in the X -ray b an d for the B L L ac o b je c t B L L acertae (G iebels & D egrange 2009) , in the TeV b and
for th e BL L ac o bject M arkarian 501 (T luczykont et al. 2 0 1 0 ; C hakraborty e t al. 2015) , and in the X -ray b an d for the Seyfert 1 galaxy IR A S 13 244-3809 (G askell 2004) .
F urther observations w ith H .E .S.S. II and th e p lanned C herenkov T elescope A rray w ill allow us to im prove the char
acterization o f the P SD at high frequencies due to their b etter sensitivities (Sol e t al. 2013) . T he larger energy ran g e w ill m ake it p ossible to close th e gap to th e Ferm i band, helping to im prove o ur u nderstanding o f the degree o f convergence (e.g., p o s
sible correlations and sim ilar processes) betw een the H E an d the V H E dom ain. A clear characterization o f the y -ra y variability o f different sources sim ilar to PKS 2 1 5 5 - 3 0 4 w ill also b e im p o rtan t to im prove ou r understanding o f the p hysical processes separating different source classes.
Acknowledgements. The support of the Namibian authorities and of the Uni
versity of Namibia in facilitating the construction and operation of H.E.S.S. is gratefully acknowledged, as is the support by the German Ministry for Edu
cation and Research (BMBF), the Max Planck Society, the German Research Foundation (DFG), the French Ministry for Research, the CNRS-IN2P3 and the Astroparticle Interdisciplinary Programme of the CNRS, the UK Science and Technology Facilities Council (STFC), the IPNP of the Charles University, the Czech Science Foundation, the Polish Ministry of Science and Higher Educa
tion, the South African Department of Science and Technology and National Research Foundation, the University of Namibia, the Innsbruck University, the Austrian Science Fund (FWF), and the Austrian Federal Ministry for Science, Research and Economy, and by the University of Adelaide and the Australian Research Council. We appreciate the excellent work of the technical support staff in Berlin, Durham, Hamburg, Heidelberg, Palaiseau, Paris, Saclay, and in Namibia in the construction and operation of the equipment. This work benefited
from services provided by the H.E.S.S. Virtual Organisation, supported by the national resource providers of the EGI Federation.
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1 Centre for Space Research, North-West University, 2520 Potchefstroom, South Africa
2 Universitat Hamburg, Institut fur Experimentalphysik, Luruper Chaussee 149, 22761 Hamburg, Germany
3 Max-Planck-Institut fur Kernphysik, PO Box 103980, 69029 Heidelberg, Germany
4 Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland
5 National Academy of Sciences of the Republic of Armenia, Marshall Baghramian Avenue, 24, 0019 Yerevan, Republic of Armenia
6 Yerevan Physics Institute, 2 Alikhanian Brothers St., 375036 Yerevan, Armenia
7 Institut fur Physik, Humboldt-Universitat zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
8 University of Namibia, Department of Physics, Private Bag, 13301 Windhoek, Namibia
9 GRAPPA, Anton Pannekoek Institute for Astronomy, Univer
sity of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
10 Department of Physics and Electrical Engineering, Linnaeus Uni
versity, 351 95 Vaxjo, Sweden
11 Institut fur Theoretische Physik, Lehrstuhl IV: Weltraum und Astrophysik, Ruhr-Universitat Bochum, 44780 Bochum, Germany
12 GRAPPA, Anton Pannekoek Institute for Astronomy and Institute of High-Energy Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
13 Institut fur Astro- und Teilchenphysik, Leopold-Franzens Univer- sitat Innsbruck, 6020 Innsbruck, Austria
14 School of Physical Sciences, University of Adelaide, Adelaide 5005, Australia
15 LUTH, Observatoire de Paris, PSL Research University, CNRS, Universitó Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France
16 Sorbonne Universitós, UPMC Universitó Paris 06, Universitó Paris Diderot, Sorbonne Paris Citó, CNRS, Laboratoire de Physique Nu- clćaire et de Hautes Energies (LPNHE), 4 place Jussieu, 75252 Paris Cedex 5, France
17 Laboratoire Univers et Particules de Montpellier, Universitó Mont
pellier, CNRS/IN2P3, CC 72, Place Eugfene Bataillon, 34095 Montpellier Cedex 5, France
18 DSM/Irfu, CEA Saclay, 91191 Gif-Sur-Yvette Cedex, France 19 Astronomical Observatory, The University of Warsaw,
Al. Ujazdowskie 4, 00-478 Warsaw, Poland
20 Aix-Marseille University CNRS/IN2P3, CPPM UMR 7346, 13288 Marseille, France
21 Instytut Fizyki Jadrowej PAN, ul. Radzikowskiego 152, 31-342 Kraków, Poland
22 School of Physics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, 2050 Johannesburg, South Africa
23 Laboratoire d ’Annecy-le-Vieux de Physique des Particules, Uni- versitó Savoie Mont-Blanc, CNRS/IN2P3, 74941 Annecy-le-Vieux, France
24 Landessternwarte, Universitat Heidelberg, Konigstuhl, 69117 Heidelberg, Germany
25 Universitó Bordeaux, CNRS/IN2P3, Centre d ’Etudes Nuclćaires de Bordeaux Gradignan, 33175 Gradignan, France
26 Oskar Klein Centre, Department of Physics, Stockholm University, Albanova University Center, 10691 Stockholm, Sweden
27 Institut fur Astronomie und Astrophysik, Universitat Tubingen, Sand 1, 72076 Tubingen, Germany
28 Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, 91128 Palaiseau, France
29 APC, AstroParticule et Cosmologie, Universitó Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Citó, 10 rue Alice Domon et Lćonie Duquet, 75205 Paris Cedex 13, France
30 Univ. Grenoble Alpes, IPAG, 38000 Grenoble, France CNRS, IPAG, 38000 Grenoble, France
31 Department of Physics and Astronomy, The University of Leicester, University Road, Leicester, LE1 7RH, UK
32 Nicolaus Copernicus Astronomical Center, ul. Bartycka 18, 00-716 Warsaw, Poland
33 Institut fur Physik und Astronomie, Universitat Potsdam, Karl-Liebknecht-Strasse 24/25, 14476 Potsdam, Germany 34 Friedrich-Alexander-Universitat Erlangen-Nurnberg, Erlangen
Centre for Astroparticle Physics, Erwin-Rommel-Str. 1, 91058 Erlangen, Germany
35 DESY, 15738 Zeuthen, Germany
36 Obserwatorium Astronomiczne, Uniwersytet Jagiellonski, ul. Orla 171, 30-244 Kraków, Poland
37 Centre for Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland
38 Department of Physics, University of the Free State, PO Box 339, 9300 Bloemfontein, South Africa
39 Heisenberg Fellow (DFG), ITA Universitat Heidelberg, Germany 40 GRAPPA, Institute of High-Energy Physics, University of Amster
dam, Science Park 904, 1098 XH Amsterdam, The Netherlands 41 Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro,
Toshima-ku, 171-8501 Tokyo, Japan
42 Now at Santa Cruz Institute for Particle Physics and Department of Physics, University of California at Santa Cruz, Santa Cruz, CA 95064, USA
Appendix A: Additional figures
Fig. A.1. LSPs, SFs, and MFVFs. Left panel a) the red solid lines are the LSP (top), SF (middle), and MFVF (bottom) for the H.E.S.S. quiescent lightcurve. The best-fit PDFs of simulated LSP, SF, and MFVF values are represented by the blue histograms in color scale. Right panel b) same plots for the Fermi-LAT data.
Fig. A.2. Uncertainties on the LSP, SF, and MFVF best-fit parameters. Left panel a) the histograms represent the distributions of estimates for 3 for simulated H.E.S.S. light curves with the LSP (top), SF (middle), and MFVF (bottom) respectively. For the simulated light curves, the true value for3 is the best-fit value found for the H.E.S.S. light curve. The vertical red bars are the 1 a uncertainties on the best fit obtained from the histograms by removing equal tails. Right panel b) same plots for the Fermi-LAT data.
