Characterizing Xray Variability of Te V Blazars Jun

“Characterizing” X-ray Variability of Te. V Blazars Jun KATAOKA (Tokyo Tech, JAPAN) Blazar Variability across the Electromagnetic Spectrum, Apr. 22 -25, 2008 1

Outline X-ray observations of Te. V blazars ü Spectral evolution ü Variability (short/long), time lag++ Analysis tools for characterizing variability ü Normalized Power Spectrum Density (NPSD) ü Structure Function (SF) ü Discrete Correlation Function (DCF). . . w/ detailed MC simulations ü Recent news from Suzaku Summary 2

Extragalactic VHE sources z G Type Discovery M 87 0. 004 2. 9 FR-I HEGRA Mkn 421 0. 031 2. 2 HBL Whipple Mkn 501 0. 034 2. 4 HBL Whipple 1 ES 2344+514 0. 044 2. 9 HBL Whipple Mkn 180 0. 045 3. 3 HBL MAGIC 1 ES 1959+650 0. 047 2. 4 HBL 7 TA PKS 0548 -322 0. 069 　 HBL HESS BL Lac 0. 069 3. 6 LBL MAGIC PKS 2005 -489 0. 071 4. 0 HBL HESS PG 1553 >0. 09 4. 0 HBL HESS/MAGIC PKS 2155 -304 0. 116 3. 3 HBL Durham 1 ES 1426+428 0. 129 3. 3 HBL Whipple 0. 139 2. 5 　 HBL HESS H 2356 -309 0. 165 3. 1 HBL HESS 1 ES 1218+304 0. 182 3. 0 HBL MAGIC 1 ES 1101 -232 0. 186 2. 9 HBL HESS 0. 188 3. 1 　 HBL HESS 0. 212 4. 0 HBL MAGIC Source 1 ES 0229+200 1 ES 0347 -121 1 ES 1011+496 19 VHE emitters – mostly blazars except for a radio galaxy M 87. Most Te. V blazars are nearby (z < 0. 2) HBLs, but two exceptions. - BL Lac … LBL - 3 C 279 … QHB at z = 0. 536! 3

Why Te. V blazars in X-ray? Suzaku MAGIC QHB LBL HBL Synchrotron Inverse Compton Kubo+ 98, Fossati+ 98, JK 02 Takahashi+ 08 Probing the jet physics at very end of electron acceleration: gmax. Expecting a large amplitude, short time-scale variability. Multiband correlation - correlated or isolated (orphan) flares often reported in X-ray and Te. V bands. 4

e. g. , Mrk 421 with Suzaku X-ray spectral evolution within a few ksec up to ~ 40 ke. V. Mrk 421 count/sec An overall trend that the peak energy (Epeak) and peak flux (n. Fn, peak ) increase or decrease together. 65 60 55 50 45 40 35 XIS 0. 6~10 ke. V PIN 12~40 ke. V count/sec 1. 6 1. 4 1. 2 1 0. 8 0. 6 0 10000 (0 day) 20000 30000 40000 50000 (0. 5 day) 60000 70000 80000 (1 day) time [sec] Ushio+ 08 in preparation 5

X-ray Variability – daily flare Mrk 421 (1998) Int. shock Gfast Gslow Non-thermal emission collision （shock） Daily flare suggests R ~ c tvar d ~ 10 -3 pc. Only little variability on tvar << 1 d : “Internal shock” • Modulation of relativistic outflows - faster shell catches up with the slower one at D ~ 10 Gjet 2 Rg ~ 103 Rg ~ 0. 01 pc sub-pc jet (the first site of E-dissipation) 6

X-ray variability – time lag (1) Takahashi+ 96 cts/s Low (0. 5 -1. 5 ke. V) High(1. 5 -7. 5 ke. V) High/Low 0 0. 5 day Mrk 421 1 day Time-lag in the LCs has been claimed for several Te. V blazars. (e. g. , Takahashi+ 96, 98, Chiapetti+ 99, Zhang+ 99, JK+ 00) Energy dependence of electron cooling time? : Tsync B-3/2 E-1/2 Other groups voiced concerns about the reality of time-lag that are smaller than orbital periods (~ 6 ks) of satellites. (e. g. , Edelson et al. 01) 7

X-ray variability – time lag (2) lag +2000 s 0 -2000 s cts/s Perigee 7000 km Apogee 114000 km Inclination 40 deg Orbital period 48 hr Mrk 421 0 0. 2 day 0. 4 day 0. 6 day Brinkmann+ 03, 05 High eccentric orbit of XMM-Newton provided uninterrupted, high sensitivity data most suitable for detailed temporal studies. Lags of both signs, up to ± 2000 sec. HOWEVER, large amplitude variability has not been observed yet, over ~0. 8 day observations (only ± 10 % variation). 8

m. Crab X-ray Variability – long-term (1) Mrk 421 1 day 7 day RXTE-ASM (2 -10 ke. V) Sensitivity: 15 m. Crab @ 1 day Distance (light year) Unfortunately, even the brightest src like Mrk 421 is difficult to be detected with RXTE-ASM for 1 -day accumulation of data. 9

X-ray Variability – long-term (2) #7 #3 #1 #2 #6 #2 #3 JK+ 01 #4 #5 #5 #1 #6 #4 #7 Modern X-ray astronomy satellite is good at pointing observations, but not suitable for continuous monitoring. Highly under-sampling data! How to characterize variability? What about the periodic “orbital gap” ? Main topic of this talk. 10

Analysis Tools 11

Normalized PSD analysis Miyamoto+ 95, Hayashida+ 98 f 0. 5 f-0. 9 -1. 5 ff-1. 9 Fj : source count rate at tj T : data length of time series Fav: mean of F Similar to an usual PSD, but less affected by window sampling. If the LC contains a time gap, the NPSD is calculated for each segments before/after the gap, and take their average. Similarity of the PSD between the Gal. BHs and Seyferts. An efficient way of BH mass estimation (e. g. , Hayashida+ 98) 12

Te. V blazars: observed LC & PSD JK+ 01 ~f-1 Mrk 421 Mrk 501 ~f-2. 5 PKS 2155 Strong red noise: P(f) f-2. 5 with fbrk ~ 10 -5 Hz. Note, for Sy (1) variability is faster : fbrk, Sy ~ a few x 104 Hz (2) PSD index is a bit flatter : Psy(f) f-1. 5~ 2 How about the reality of this finding? need careful simulation! 13

MC simulation: method Assume that the PSD of the source (e. g. , Te. V blazar) is expressed by a convex broken power-law of the form: fb : break frequency (tb ~ 1/fb : characteristic timescale) Using a Monte Carlo simulation, we generate a set of random numbers, uniformly distributed between 0 and 2 p, and use them for the phase of each Fourier component of the assumed PSD. By a Fourier transform of this Monte Calro generated periodogram, we obtain a light curve of certain # of bins lengths, which covers the total span of the observation. C(t) = (1/2 p) Sf P(f)1/2 e-2 pift 14

MC simulation: ex. (1) An example of how the LC looks like for the different choice of the PSD index from -1. 0 (i. e. , fractal) to -3. 0 (strong red type). Small fluctuation large amplitude variations. 15

MC simulation: ex. (2) Example cases for f-2. 5 and fb = 10 -5 Hz: Close similarity to the observed LC in Te. V blazars. Note “wide variety” of the LC even if assuming the same PSD. 16

MC simulation: Orbital Gap orbital gap Simulation #1~ #10 To mimic the observed LC, the sampling window (orbital gap of ~ 5760 s) was applied to the simulated LC. By using more than ~ 1000 MC simulated LC, we confirm that the NPSD actually minimize the effects caused by sampling window. 17

Structure function analysis a(t) : a point of the LC t : time separation N : # of pairs some Simonetti+ 85, JK+01, Tanihata+03 ~ t 0. 5 But when the quality of each data are non-uniform; weight factor Firstly introduced to study flicker of extragalactic radio sources. While in theory the SF is completely equivalent to traditional PSD, it has several significant advantages: (1) much easier to calculate! (2) less affected by gaps in the LC, even if it is non-uniform. 18

SF: characteristics Paltani+ 99 t 0 t 2 tb ~2 e 2 Reg 1 : A plateau due to the measurement uncertainty e. t 2 as long as t < Tmin. Reg 3 : SF increases as tb (0 <b< 2) between Tmin and Tmax. Reg 2 : SF increases as Empirically, b a - 1 (a : PSD index) Reg 4 : For t > tmax , the SF flattens again 19

Te. V blazars: observed SF JK+ 01, Tanihata+ 03 Mrk 421 Mrk 501 PKS 2155 Mrk 421 t (ksec) Strong red noise: SF(t) t 1. 5 with tb ~ 0. 5 -3 day. Consistent with what has been implied from the NPSD analysis Reality of complicated features at t ~ tmax ? 20

MC simulation of the SF Mrk 421 artifacts? Observed Simulation Simulated LCs (P(f) f-2. 5 , fb = 10 -5 Hz) well reproduce the observed SF, but large uncertainty due to the finite length of data if t ≳ 1/3 tmax. Take special care about possible “artifacts” near tmax. 21

Warning – a case in literature Zhang+ 02 f o d n i k s ! i ” h t n o t i u t o a b c i a f l li u p f e -sim r a c ver e B “o PKS 2155 -304 22

Long-term variability: observed JK+ 01 observed Too sparse, unevenly sampled data prevent the analysis using “most common” Fourier technique (e. g. , NPSD). The SF seems to be much better, but obviously Important to know how the observed window affect the calculated SF. 23

Long-term variability: simulation JK+ 01 Actually, MC simulation of the LCs by applying same sampling window provides various spurious structures in the SF! 24

How to “robustly” evaluate the SF? Iyomoto+ 00, JK+ 01 Based on a set of 1000 fake LCs, we can compute the expected mean value <SFsim (t)> and variance ssf(t) at each t, for an assumed PSD. To evaluate the goodness of fit , we calculate the sum of squared difference: PL index a c 2 map X break: tb We then generate other sets of 1000 simulated LCs and fake SFs to evaluated the distribution of c 2 sim values. 25

Importance of Monitoring Obs. Takahashi & JK 00 t 0. 3 t 1. 4 Mrk 421 is the only Te. V blazar for which RXTE-ASM always detect its signal at > 4 s level, if 7 -day accumulation of data. Well-defined SF confirm the presence of characteristic time, but also another variability component at t ≳ 10 day. GLAST, MAXI monitoring important! 26

MAXI: Monitor of All-sky X-ray Imaging MAXI is an X-ray all-sky monitor on the Japanese Experimental Module (JEM) of the ISS, to be launched in 2009. 3. Sensitivity ~ 5 times better than RXTE-ASM, ~ 1 m. Crab @ 1 week. See, more details: http: //www-maxi. tksc. nasda. go. jp X-ray CCD Camera (SSC) 0. 5 -10 ke. V Gas Slit Camera (GSC) 2 -30 ke. V 27

Underlying Physics? Perturvation in jets, including accel, cooling, R/c? (beamed) t 1. 4 t 0. 3 Time variation of accreting flow ? (non-beamed) Surely two components exist in the variability of Te. V blazars - the one due to the perturbation produced in the jet, and the other is due to time variation of accreting matter near the central BH. evenly sampled data awaited to test this speculation. 28

DCF analysis Edelson & Krolik 88 ai, bj: a point of data set {a}, {b} a, b : means of {a} {b} sa, sb : standard deviation ea, eb : mesurement error Firstly introduced to test variability correlation of optical continuum and Hb flux. Specifically designed to analyze unevenly sampled data. ü Relatively easy to calculate by using all data points available. ü Does not introduce new errors through interpolation. 29

DCF amplitude ex 1: a case of PKS 2155 -304 JK+ 00 3 -8 ke. V vs 0. 5 -1 ke. V +4 ks D -1 0 Time lag (day) +1 During the flare, change in the hard X-ray flux led the change in the soft X-ray flux by ~ 4 ksec, similar to the case of Mrk 421. The energy dependent time-lag is consistent with the differential Sync cooling time, if B ~ 0. 1 G (tcool B-3/2 E-1/2 d-1/2). … but, could be artifacts ? ? ? ( orbital gap ~ 6 ksec) 30

Again, MC simulation! w/o orbitgap w/ orbit w/o orbitgap Simulating thousand pairs of LCs, one is artificially shifted by ~ 4 ksec to mimic the observed LC. Although periodic gaps introduce larger uncertainties, lags on ~ 4 ksec cannot be the result of periodic gaps. e. g. , Tanihata+ 03, Zhang+ 04 31

ex 2: a case of 1 ES 1218+304 See poster by R. Sato -20 ks 4 -10 kev vs 0. 4 -1 ke. V 4 -10 ke. V 2 -4 ke. V 1 -2 ke. V 0. 4 -1 ke. V Opposite sense of time-lag was clearly detected, with the maximum “hard-lag” of ~ 20 ksec - much larger than orbital gap! A wide variety of flare shape measured at different energies, suggesting energy dependence in the rise/fall time-scales. 32

Direct fit of the “flare shape” Sato+ 08 Ap. JL (astro-ph/0804. 2529) tacc tcool (i) Low energy • Rapid rise & slow decay • Asymmetric LC 0. 3 -1 ke. V tacc tcool (ii) High energy • Slow rise & fast decay 5 -10 ke. V “rise time” ~ tacc & “fall time” ~ tcool • tacc (E) = 9. 7× 10 -2 (1+z)3/2 x B-3/2 d-3/2 E 1/2 • t cool (E) = 3. 0× 103 (1+z)1/2 B-3/2 d-1/2 E-1/2 • Symmetric LC (tacc~tcool) B = 0. 049 x 5 G (x 5 : Gyro factor) 33

Comparison w/ SED Sato+ 08 Ap. JL (astro-ph/0804. 2529) Suzaku γmin γbrk γmax α 1. 0 8× 103 8× 105 -1. 7 B 0. 05 G R 8× 1016 cm d 20. 0 z 0. 182 MAGIC Ue 8. 3× 10 -3 erg/cm 3 UB 8. 8× 10 -5 erg/cm 3 Ue/UB 94 Very consistent with LC! 34

Summary: I have overviewed the sync X-ray variability of blazars and detailed temporal technique to evaluate the LCs. Temporal techniques, such as PSD, SF, DCF are indeed powerful tool, but special care must be taken if (1) the data are not well sampled and (2) short compared to the variability timescale of the system. MC simulation is one of the best way to evaluate the effects caused by sampling window and finite length of data. If evaluating properly, the LC provides independent and/or complementary information to the X-ray spectrum of Te. V blazars. 35