Anti-Correlated Lags in Compact Stellar X-ray Sources

1. Dr. Kandulapati Sriram Anti-Correlated Lags in Compact Stellar X-ray Sources Collaborators: Prof A. R. Rao (TIFR) Dr. Vivek Kumar Agrawal (ISRO/TIFR). Dr. Ranjeev Misra (IUCAA)

2. The Work is based on published papers by our group 1. Anticorrelated Hard X-Ray Time Lag in GRS 1915+105: Evidence for a Truncated Accretion Disk Choudhury, M., Rao, A. R., Dasgupta, S., Pendharkar, J., Sriram, K., & Agrawal, V. K. 2005, ApJ 2. Anticorrelated Hard X-Ray Time Lags in Galactic Black Hole Sources Sriram, K., Agrawal, V. K., Pendharkar, Jayant, & Rao, A. R., 2007, ApJ 3. Energy-dependent Time Lags in the Seyfert 1 Galaxy NGC 4593 Sriram,K.; Agrawal, V. K.; Rao, A. R., 2009, ApJ 4. A truncated accretion disk in the galactic black hole candidate source H1743-322 Sriram, K.; Agrawal, V. K.; Rao, A. R., 2009, RAA And some other work carried out at KASI

3. Overview A. Introduction 1. Mass transfer and Disk formation 2. SS disk and Why ADAF? 3. Basic X-ray continuum models B. About 1. RXTE Satellites 2. X-ray spectral states in GBHs 3.VH/SPL/IM state and possible geometry C. Method, Application & Results 1. CCF 2. ACL in GBHS, NS 3. physical interpretation and Results D. Conclusion

4. Mass Transfer in Binary Stars In a binary system, each star controls a finite region of space, bounded by the Roche Lobes (or Roche surfaces). Lagrange points = points of stability, where matter can remain without being pulled towards one of the stars. Matter can flow over from one star to another through the Inner Lagrange Point L1.

5. Two mechanisms of mass transfer in a binary system Accretion through Roche lobe outflow Accretion from stellar wind

6. How Disk forms? • Accretion in LMXB is due Roche Lobe Overflow • As secondary star evolves it fill up its Roche lobe (equipotential surface) • Mass transfer take place from Lagrange point L1 Jet disk L1

7. Formation of disk.. • Matter passing through L1 has AM • forms an elliptical orbit around primary • For continues stream of matter, form a ring • to sink in the gravitational potential of primary, it loses AM • matter slowly spiral inwards in circular orbit and forms an accretion disk Low AM High AM

8. How does disk heats up? Two main process responsible for heating up the disk 1. Gravitational Binding energy : Matter goes in -----> decrease in GBE results in hot disk 2. Viscous Dissipation: Friction between two layer----transport the AM outside—heat up the disk 3. Because of heating---->~disk temp. goes to 107-8 K (X-ray band)

9. Black Body approximation SS Disk • For steady geometrically thin (h<<r) and optically thick disk • Each ring “dR” loses GΩ'dR of mechanical energy into heat energy (G is torque) • for upper and lower face of disk D(R)=9/8*νΣGM/R3 (D(R)=rate / unit surface area ν- kinematic viscosity Σ-surface density)‏ changing νΣ in terms of Mdot and R, we get D(R)=3GMMdot / 8ΠR3 [1-(R*/R)1/2] • Total rate at which energy is dissipated 3GMMdot/2ΠR2 [1-(R*/R)1/2] • Emitted spectrum σT4=D(R)---> T= (3GMMdot / 8ΠR3 σ)1/4

10. Multi BB components in Disk Standard accretion disk spectrum looks like super-positon of blackbody spectra multi-color disk-blackbody approximation works (diskbb in xspec) Each disk annuli is responsible for obs. Disk temperature

11. Problems.. • SS disks are ideal and occasionally seen • Remedy: ADAF, radiative inefficient (developed by Narayan and collaborators) • Most probable model to explain the low luminous episodes in X-ray binaries

12. Why Is the Flow Advection-dominated? • Radiation comes primarily from electrons • At low , ion-electron (Coulomb) coupling is weak • Plasma becomes two-temperature --- heat energy is locked up in the ions and advected to the center • Radiative efficiency of electrons is also low, so electrons also advect their energy • Very hot, optically thin gas. Quasi-spherical. Non-blackbody spectrum (Shapiro, Lightman & Eardley 1976; Ichimaru 1977; Bisnovatyi–Kogan & Lovelace 1997; Quataert 1998; Gruzinov 1998; Quataert & Gruzinov 1998 ; Blackman 1998; Medvedev 2000) Too Many changes in disk theory to explain observations, ADIOS, CDAF, slim disk model etc.

13. Basic Continuum models • Two kind spectral components In BHB • 1. Soft X-ray component ( few eV to ~ 1 keV) • Thermal in nature, black body radiation • No census of BB component • Each radii in disk emits a BB spectrum know MCD model

14. Conti.. • 2. Hard X-ray Component • Not exactly known in terms of physical location, exact mechanism (thermal,non-thermal, processes) etc. • Spectral domain is vast (few keV to GeV) • Many possible Mechanism • Thermal Comptonization • Non thermal Comptonization • Syncrhoton • Bremmstrulung

15. For non-stationary electron: Compton Inverse Compton The Comptonization Process • Discovered by A.H. Compton in 1923 • gain/loss of energy of a photon after collision with an electron If electron at rest:

16. Tsoft Thermal Comptonization Hot phase = corona Comptonization on a thermal plasma of electrons characterized by a temp. T and optical depth τ Tc,  mean relative energy gain per collision Cold phase = acc. disc for E < kT, unsaturated Compt. for E ≳ kT For E~KT saturated Comptonization mean number of scatterings ➨ Compton parameter

17. Non-thermal Comptonizaton For electron with large Lorentz factor Comptonization by a non-thermal distribution of electrons ➥ very efficient energy transfert ⇒ Possible non-thermal electrons are from jets close to X-ray binaries

18. Disk Corona Geometries.. slab, sandwich sphere+disk geometry patchy

19. RXTE Satellite PCA Energy range: 2 - 60 keV Energy resolution: < 18% at 6 keV Time resolution: 1 microsec Spatial resolution: 1 degree Detectors: 5 proportional counters Collecting area: 6500 square cm HEXTE Energy range 15-200 keV Time resolution min 32 sec 4 NaI/CsI Scintillation counter Area : 1600 sq. cm All Sky Monitor (ASM) Remarkable temporal resolution and covers spectrum domain of 2.5-200 keV

20. COSPAR Workshop, Udaipur 2003 Unfolding Spectrum: the Basic Problem Suppose we observe D(I) counts in channel I (of N) from some source. Then : D(I) = T ∫ R(I,E) A(E) S(E) dE • T is the observation length (in seconds) • R(I,E) is the probability of an incoming photon of energy E being registered in channel I (dimensionless) • A(E) is the energy-dependent effective area of the telescope and detector system (in cm2) • S(E) is the source flux at the front of the telescope (in photons/cm2/s/keV

21. COSPAR Workshop, Udaipur 2003 Conti.. D(I) = T ∫ R(I,E) A(E) S(E) dE We assume that T, A(E) and R(I,E) are known and want to solve this integral equation for S(E). We can divide the energy range of interest into M bins and turn this into a matrix equation : Di= T ∑Rij Aj Sj where Sj is now the flux in photons/cm2/s in energy bin J. We want to find Sj.

22. COSPAR Workshop, Udaipur 2003 Conti.. Di = T ∑Rij Aj Sj The obvious tempting solution is to calculate the inverse of Rij, premultiply both sides and rearrange : (1/T Aj) ∑(Rij)-1Di = Sj This does not work ! The Sj derived in this way are very sensitive to slight changes in the data Di. This is a great method for amplifying noise.

23. COSPAR Workshop, Udaipur 2003 Mathematical Methods In mathematics the integral is known as a Fredholm equation of the first kind. Tikhonov showed that such equations can be solved using “regularization” - applying prior knowledge to damp the noise. A familiar example is maximum entropy but there are a host of others. Some of these have been tried on X-ray spectra - none have had any impact on the field.

24. COSPAR Workshop, Udaipur 2003 Define Model Solution: Forward-fitting algorithm Calculate Model Convolve with detector response Change model parameters The aim of the forward-fitting is then to obtain the best-fit and confidence ranges of these parameters. Compare to data

25. Basic Spectral states in GBHs Soft State, thermalBB Hard State, thermal Comp. or Non-thermal IM state/VHS/SPL Cyg X-1 Soft State, Non-thermal Figure is taken from Zdziarski et al. 2002

26. Three-state classification In this classification the luminosity is not used as one of parameters. Remillard & McClintock 2006

27. VH state, special spectral state.. • Most often brightest state among all • Steep unbroken (X-ray to gamma-ray) PL ( ≥ 2.4-2.8), no evidence for high-energy cutoff • transitions between TD and LH states usually pass through SPL state • essentially radio-quiet; though sometimes shows impulsive jets • QPOs in 0.1–30 Hz range and HFQPO are also found in this state • Both soft (disk) and hard (Compton cloud/corona) component dominates GRO J1655–40

28. Disk and jet connection The model for systems with radio jets LS – low/hard state HS – high/soft state VHS/IS –very high andintermediate states The shown data arefor the sourceGX 339-4. (Fender et al. 2004, Remillard, McClintock astro-ph/0606352)

29. Typical outburst of BH source

30. QPO propagation during an Outburst

31. Truncated disc and X-ray spectral states Spectral states – moving truncation radius Lh/Ls hard state soft state hard state soft state

32. Possible generalized geometry of AD • LH- large truncation of accretion disk • VHS/SPL/IM- less truncation of disk • High state/Thermal dominated disk: No truncation

33. More about SPL state.. • Steep Power-Law (SPL)‏/VHS/IM • physical origin still an outstanding problem • spectrum extends to ~1MeV, may be higher • possible physical model: • Inverse Compton scattering for a radiation mechanism • Perhaps scattering occurs in a thermal corona below 100 keV and non thermal corona at high energies. • Disk is observationally found to be truncated at ~10-30 Rs • PL gets stronger and steeper as disk luminosity and radius decrease, while keeping high temperature

34. Possible geometrical configuration of VH state Corona, Compton cloud, thermal Comptonized hard photons Disk, seed soft photons How can we detect these signatures in a short time of few kiloseconds instead of waiting for whole long outbusrt of typical duration few days to few 100 days????

35. Method: Cross-correlation Method • To understand the disk Geometry, we use three different ways • 1.Cross-Correlation • 2. Model independent & dependent Spectral study • 3. QPO analysis • Cross correlation is a standard method of estimating the degree to which two time series are correlated. ALL the data used belongs to SPL/VH/IM state

36. CCF? Two series are highly correlated, with no lag, then CCF peak points to Zero In anti-correlation, CCF peak shift to the -tive side.

37. First such source to show lags is Cyg X-3 • First source in which ACL was detected was Cyg X-3 • Brightest X-ray source in Radio band • Orbital period ~4.8 hrs • no optical counterpart has been found • no information on Compact object • strong evidence of jetlike structures • Spectral studies reflects typical BH spectrum Choudhury & Rao 2004, ApJL

38. Chi state • GRS 1915+105 • Harbours Most massive BH (~14 solar mass)‏ • Orbital period~33 days (largest among GBHs)‏ • LMXB, secondary is K/MIII type star • Show relativistic jet • Highly variable X-ray source among all the BH • distance 6~10kpc Choudhury et al. 2005, ApJ

39. H1743-322, Sriram et al. 2009, RAA XTE J1550-564, Sriram et al. ApJ, 2007

40. First Neutron stars source to show ACL Lei et al. 2008, ApJL Cyg X-2

41. GX 339-4, first BH source to show AC soft lag Sriram, Rao & Choi submitted to ApJ

42. ACL for GX339-4 using RXTE and INTEGRAL

43. Various Timescale is Accretion disk • Viscous timescale : tv~R/vr • Dynamical time scale : tφ~1/Ωk (QPO ???) • Deviation in vertical structure timescale : tz~tφ • Thermal time scale : tth~M-2tv • Compton cooling timescale: tcool = 10−6 × R37 Ṁ−117 m−110T8 tcool <~ tφ ~tz <tth <<tv (for complete derivation of Compton cooling time scale see Sriram et al. 2009, RAA)

44. Typical timescales in different size BH

45. Truncation radius assuming that they indicate small viscous delays α is the viscosity parameter in units of 0.01, M is the mass of the compact object in solar mass units, R is the radial location in the accretion disk in units of 107 cm, and Mdot is the mass accretion rate in units of 1018 g s-1 Taking α = 1, M = 10, and Mdot= 3 , we get R ~ 7 for a viscous timescale of 1000 s. Thus ~25 Schwarzschild radius. Similar dimension for truncation radius is observed in SPL state using QPO frequency (see Done et al. 2007)

46. QPO changes??? XTE J1550-564 Sriram et al. 2007, ApJ GRS 1915+105, Choudhury et al. 2005

47. For source H1743-322

48. For GX 339-4 QPO changes

49. Spectral changesModel independent changes GRS 1915+105 Cyg X-3

50. XTE J1550-564