Correlation between X-ray and gamma-ray emission in TeV blazars

Transcription

1 Correlation between X-ray and gamma-ray emission in TeV blazars Krzysztof Katarzyński Toruń Centre for Astronomy, Nicolaus Copernicus University, Poland Steady Jets and Transient Jets, Bonn 7-8 April 2010 Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 1/34

2 Outline Introduction Outline Observations observations, how we define the correlation why simple SSC model does not work two or more sources, more complex solution conclusions Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 2/34

3 Outline Observations Mrk 421 optical, X-ray & gamma-ray light curves optical [V mag.] X-ray [cts/s/pcu] γ-ray [Crab] TeV HEGRA & Whipple, X-ray RXTE-PCA, Fossati et. al Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 3/34

4 Mrk /19 March 2001 Outline Observations F TeV (F X ) x 2 Fossati et al Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 4/34

5 Definition of the correlation Outline Observations t - time F - flux F X t s F TeV t c t F 1/s X F TeV F c/s X x = c/s 2 Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 5/34

6 Mrk March 18/19, spectra Outline Observations Fossati et al Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 6/34

7 Mrk March 18/19, spectra Outline Observations Fossati et al Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 7/34

8 Mrk /23 March 2001 Outline Observations #5: March 22/23 (e) F TeV (F X ) x 2 Fossati et al Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 8/34

9 Outline Observations PKS /30 July 2006 H.E.S.S., Chandra & 32 cm Bronberg Observatory F TeV (F X ) x 3 Aharonian et al (H.E.S.S. Collaboration) Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 9/34

10 Mrk April 1997 Introduction Outline Observations Catanese et al. 1997, Pian et al. 1998, Djannati-Atai et al Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 10/34

11 Outline Observations Mrk correlation for April 1997 Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 11/34

12 Mrk February 2000 Outline Observations Krawczynski et al Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 12/34

13 Outline Observations Mrk correlation for February 2000 Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 13/34

14 Internal shock scenario Basic assumptions Evolution in time Estimated results compact jet component two or more colliding components BLR direction to observer source velocity NLR X-ray and gamma-ray source Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 14/34

15 Mrk 501 emission model Basic assumptions Evolution in time Estimated results active galaxy Katarzyński et al synch. IC Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 15/34

16 Basic assumptions Evolution in time Estimated results Homogeneous source - basic assumptions spherical homogeneous source (R [cm]) uniform electron density (K [cm 3 ]) uniform magnetic field intensity (B [G]) power law electron energy distribution: N(γ) = Kγ n for γ min γ γ max, or double (broken) power law distribution: { K1 γ n 1, γ min γ γ brk n1 N(γ) = K 2 γ n 2, γ brk < γ γ max log 10 N(γ) Ν(γ) γ n 1/2 n 2 where E = γm e c 2 and K 2 = K 1 γ n 2 n 1 brk. log 10 (γ) Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 16/34

17 Double power law spectrum Basic assumptions Evolution in time Estimated results Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 17/34

18 Basic assumptions Evolution in time Estimated results Time dependent SSC - basic assumptions The evolution of the source radius where R 0 is the initial radius. R(t) = R 0 ( t0 t ) re, The evolution of the magnetic field intensity inside the source ( ) m t0 B(t) = B 0, t where B 0 is the initial magnetic field intensity. Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 18/34

19 Evolution of electron spectrum Basic assumptions Evolution in time Estimated results { } N e (γ, t) = min Ne 1 (γ, t), Ne 2 (γ, t), where N 1 e (γ, t) = K 1 e (t)γ n1, N 2 e (γ, t) = K 2 e (t)γ n2 ) ra(n 1 1) ( Ke 1 t0 (t) = K 1 } t {{} adiabatic heating/cooling ( t0 ) 3rd, } t {{} density increase/decrease ) ra(n 2 1) ( Ke 2 t0 (t) = K 2 } t {{} adiabatic heating/cooling ( t0 ) 3rd, } t {{} density increase/decrease r a describes the adiabatic losses and r d describes the decrease of the electron density. Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 19/34

20 Evolution of synchrotron emission Basic assumptions Evolution in time Estimated results Evolution of the synchrotron flux is described by which below the peak gives and above the peak F s (t) R(t) 3 K e (t)b(t) m(α+1), Fs 1 (t) ( ) R0 3K s1 t 1B 1 t 0, s 1 = 3r e 3r d r a (n 1 1) m(α 1 + 1), Fs 2 (t) ( ) R0 3K s2 t 2B 2 t 0, s 2 = 3r e 3r d r a (n 2 1) m(α 2 + 1). Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 20/34

21 Basic assumptions Evolution in time Estimated results Evolution of inverse-compton emission Evolution of the inverse-compton flux below the peak, in the Thompson limit is given by F 1 c (t) R 4 0 K 2 1 B 1 ( t t 0 ) c1, c 1 = 4r e 6r d 2r a (n 1 1) m(α 1 + 1), whereas above the peak, in the Klein-Nishina regime we have F 2 c (t) R 4 0 K 1 K 2 B 1 ( t t 0 ) c2, c 2 = 4r e 6r d r a (n 1 1) r a (n 2 1) m(α 1 + 1). Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 21/34

22 Four basic correlations Basic assumptions Evolution in time Estimated results we have four basic evolutions: Fs 1 t s 1 for the synch. rad. before the νf s (ν) peak Fs 2 t s 2 for the synch. rad. above the νf s (ν) peak Fc 1 t c 1 for the IC emission before the νf c (ν) peak Fc 2 t c 2 for the IC emission above the νf c (ν) peak which give four basic correlations: F 1 c (F 1 s ) c 1/s 1 F 2 c (F 1 s ) c 2/s 1 F 1 c (F 2 s ) c 1/s 2 F 2 c (F 2 s ) c 2/s 2 Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 22/34

23 Four basic correlations Basic assumptions Evolution in time Estimated results Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 23/34

24 Basic estimations Introduction Basic assumptions Evolution in time Estimated results r e r d r a m c 1 /s 1 c 1 /s 2 c 2 /s 1 c 2 /s 2 a b c inf inf inf inf d e f g h i j inf inf k l Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 24/34

25 Correlations around the peaks Basic assumptions Evolution in time Estimated results Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 25/34

26 Impact of the radiative cooling Basic assumptions Evolution in time Estimated results Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 26/34

27 Basic assumptions Evolution in time Estimated results cannot explain observed correlations An injection of the relativistic particles into the source that increases the density could in principle explain the quadratic correlation during rising phase of a flare. However, this requires R = const., B = const. and negligible radiative cooling during the injection. By analogy to the injection, systematic energy independent escape of the particles that decreases the density could in principle explain the quadratic correlation during decay phase of a flare. However, the particles outside the source can still produce efficiently gamma rays through the inverse-compton scattering. In other words the gamma-ray emission will not decay fast enough to produce the quadratic correlation during the decay phase. What about observed more than quadratic correlations? Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 27/34

28 Two sources Injection and cooling Doppler effect Emission of two sources at the same time R cm K 1 K 2 R cm jet X-ray TeV F Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 28/34

29 Two sources Injection and cooling Doppler effect Mrk 421 variability of two sources model injection & cooling Katarzyński & Walczewska 2010 Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 29/34

30 Doppler boosting effect Two sources Injection and cooling Doppler effect ϕ V=βc transformations of: time t = (1 + z)t /δ frequency ν = δ 1+z ν intensity I ν = δ 3 I ν Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 30/34

31 Two sources Injection and cooling Doppler effect Mrk 421 variability due to the change of ϕ model ϕ(t) δ(t) Katarzyński & Walczewska 2010 Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 31/34

32 Two sources Injection and cooling Doppler effect PKS very rapid variability R cm R cm X-ray TeV F Katarzyński et al Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 32/34

33 Conclusions Introduction Two sources Injection and cooling Doppler effect The proposed approach has several advantages: it can explain any slope of the correlation, in the extreme case it is possible to explain the orphan flares, the approach does not involve a new model of the emission, it uses the standard SSC scenario to explain a single source radiation, it may explain why the correlation was well determined only in a few cases so far, in was already shown that using this approach it is possible to explain also the rapid variability. Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 33/34

34 References Introduction Two sources Injection and cooling Doppler effect Aharonian, F.; Akhperjanian, A. G.; Anton, G., et al. 2009, A&A, 502, 749 Catanese, M., Bradbury, S., M., Breslin, A., C., et al. 1997, ApJ, 487, L143 Djannati Atai, A., Piron, F., Barrau, A., et al., 1999, A&A, 350, 17 Fossati, G., Buckley, J., H., Bond, I. H., et al. 2008, ApJ, 677, 906 Katarzyński, K., Ghisellini, G., Tavecchio, F., et al. 2005, A&A, 433, 479 Katarzyński, K., Lenain, J.-P., Zech, A., et al. 2008, MNRAS, 390, 371 Katarzyński, K., & Walczewska, K., 2010, A&A, 510, 63 Krawczynski, H., Sambruna, R., Kohnle, A., et al., 2001, ApJ, 559, 187 Pian, E., Vacanti, G., Tagliaferri, G., et al., 1998, ApJ, 492, L17 Krzysztof Katarzyński TCfA Poland Correlation X/gamma, page 34/34