Spectral Index and QPO Frequency Correlation in Black Hole Neutron Star Sources: Observational Evidence of Black Hole S

1. Spectral Index and QPO Frequency Correlation in Black Hole Neutron Star Sources: Observational Evidence of Black Hole Signature L. Titarchuk*, R.B. Fiorito** and N. Shaposhnikov*** *Naval Research Laboratory/George Mason University **University of Maryland and NASA/GSFC *** NASA/GSFC/USRA

2. Introduction We examine the observed correlations between photon index of the power-law component of the X-ray spectrum with low QPO frequencies in BH and NS Sources. We compare these observations of QPO’s and X-ray spectra for BH’s and NS’s and demonstrate how the differences can be used to uniquely identify BH’s.

3. Observational Background and Motivation

4. Observations show inconsistent correlations of low frequency QPO with disk parameters for a number of BHC’s GRS 1915+105 c State Observations Correlation of LFQPO frequency and the apparent disk flux for XTE J1550-564 during its 1998-1999 outburst. The plotting symbols distinguish the QPO type: Type A (broad QPOs with phase lags in soft X-rays) – open triangles, Type B (narrow QPOs with hard lags)– open squares, Type C (small lags and strong harmonics) – filled circles, and anomalous QPOs– ‘x’. The correlation between these quantities is only demonstrated for the C type LFQPOS. From R. Remillard, et. al., 2002. Correlation of LFQPO with disk flux for OBSID 20402 (1997) data are in agreement with observations of Markwardt, et. al.(1999); anticorrelation of frequency with disk flux for OBSID 10408 (1996); and no correlation of frequency with disk flux for OBSID 10258 (1996). From Fiorito, et. al. 2003.

5. QPO LOW FREQUENCY - SPECTRAL INDEX CORRELATIONS FOR BHC’s OBSERVED IN OUTBURST DECAY From E. Kalemci, et.al., (2003)

6. Observed Correlations and Interpretations Using Transition Layer Model GRS 1915+105 Observations in Plateau (Fender) or c states (Belloni) which are associated with jet emission GRS 1915+105 Observations in Transient States Plot of power-law index vs QPO low frequency for the plateau observations from: Vignarca, et. al. 2003 along with a fit using TL model with m=12 and 0 1.25. Plot of power-law index vs QPO low frequency for the observations of class  and  (red points =obs.15.16) and  and  from: Vignarca, et. al. 2003 along with a fit using TL model with m=12 and 0 1.25. Values for plateau observations (on the left) are plotted for comparisons (blue points).

7. Predicted Low-High Frequency Correlation Valid across neutron stars, black holes and certain cataclysmic variables Mauche (2002) for SS Cyg, Woudt & Warner (2002) for VW Hyi, Belloni et al. (2002) for BH and NS Empirical correlation Relationusing MA model (Titarchuk &Wood, 2002) and It is found that

8. BH mass determination using the index- low QPO frequency correlation Comparison of the observed (points) and theoretical correlations (solid lines) of photon index vs QPO low frequency between GRS 1915 +105 (Vignarca et al. 2003) and XTE J1550-564 [Sobczak et al. (1999), (2000); Remillard et al. (2002a, b)]. Red points and line for XTE J1550-564 and black points and line for GRS 1915+105. The XTE J1550-564 curve is produced by sliding the GRS 1915+105 curve along the frequency axis with factor 12/10.

9. Spectral states in BHC candidates Binaries Categorized in Two Generic Classes or States • Low/hard state: thermal Comptonization spectrum , Te ~ 50 keV , optical depth t ~`1- 4, photon index G ~ 1.5- 1.8 • Soft state: black body bump, power law with G ~ 2.5-3, Te Tdisk ~ 1 keV From: Grove et al. (1998)

10. Index-QPO frequency correlation for NS source The observed correlations of photon index vs break frequency b (black), QPO low frequency L (blue) and sub-harmonic SL (red) in NS source 4U 1728-34.

11. Spectral evolution of the NS source Spectral evolution of the source from low/hard state to high/soft state. Photon index of the upscattering Green function  changes from 2.25 to 6.5 respectively. In the embedded panel we show the evolution of the upscattering Green function. One can clearly see an evolution of the broken power law with the high-energy power-law tail of index 2.25 to almost Delta-function distribution.

12. Soft State (Two Black body) Spectrum Hard State (Comptonization) Spectrum Spectral components of low/hard state (left hand panel) and high/soft state (right hand panel). The low/hard state spectrum consists of two Comptonized blackbody components for which color temperatures are 0.93 keV and 2.92 keV and K-iron line component. The high/soft state spectrum consist of two pure blackbody components which color temperatures 0.83 keV and 2.2 keV and K-iron line component.

13. Ratio of sub-harmonic frequency to the low frequency  Observed ratio of sub-harmonic frequency of the low frequency SL to low frequency L as a function of L . Two horizontal lines indicate the corridor where the most of ratio points are situated.

14. Low-frequency oscillation modes We treat L and SL as normal mode oscillation frequencies of spherical and cylindrical components respectively. The wave equation for displacement u(t,r) reads where a is sound speed of plasma, r a radius vector for a given point in the configuration and  is the Laplace operator for a given configuration. The ratio of eigen frequencies c and S related to L and SL is c /s=[(3.85)2-2(R0/H)2]1/2 /1.43  It is easy to that c /s monotonically decreases with R0/H. In a case of R0<<H one can obtain c /s =0.86 and for R0~H c /s =0.5.

15. Transition Layer (Compton Cloud) Model of Accretion Process Surrounding a Compact Object Outflow (jet, wind) coronal heating ( Q ) cor by shock soft photon illumination ( ) Q d disk Outflow (jet) Standings shock ( rin for BH, NS, or WD) ( compact region of sub-Keplerian bulk inflow which Comptonizes soft disk photons and radiates them as the hard component )

16. The adjustment is not smooth and shock occurs at Radj . Hot matter is bounced from the disk forming Compton cloud around the central object • Disk model features near the adjustment radius correlated with features of the power spectrum, i.e, QPO frequencies in formulae are evaluated at Radj: • Transition Layer as an adjustment of Kepler disk to sub-Keplerian rotated central object (either NS or BH) change from Keplerian to sub-Keplerian flow occurs at Radj • Scaling of other frequencies relative to high=K is predicted by model equation of angular momentum radial transport The TL adjustment radius, is determined by an equation of angular momentum radial transport and inner and outer boundary conditions (Titarchuk, Lapidus & Muslimov 1998): inner and outer boundary conditions and is the Reynolds number.

17. Conclusions We have presented the observed index-QPO frequency correlations for BH and NS sources. developed which greatly simplifies and reclassifies the plethora of “states” observational assigned to categorize the X-ray observations of variable BH’c and NS’s into two generic phases (states): a. A hard phase (state) in NS’s and BH’s related to an extended Compton cloud (cavity) characterized by the photon index around 1.7 and the low QPO frequencies below 1 Hz. This is the regime where thermal Comptonization dominates the upscattering of soft disk photons and the spectral shape (index) is almost independent of mass accretion rate. The low-hard spectrum is a result of the Fermi accelaration of the second order with respect to V/c, i.e , <>/E~(V/c)2. The effect of the first order on V/c is smeared out by the quasi-symmetry of the particular dynamic, predominantly thermal motion of the Compton cloud plasma. b. Ina soft phase (state) of BH candidate sources we see the effect of the BH as a ``drain’’. The system does not reach the thermal equilibrium: along with a strong blackbody component one can see a prominent power-law component which photon index saturates to 2.8 when mass accretion rate increases. The observed high energy spectrum are emitted from a compact region, where soft energy photons of the disk are upscattered by accreting material (electrons) forming the steep power law with photon index around 2.8 and low QPO frequencies (above 10 Hz ) and high QPO frequencies (of order of 100 Hz) are observed. Ina soft phase (state) of NS source The index saturation seen in BH sources at high values of L (or mass accretion rate) is not observed in NS sources. The index increases without any limit when L and break frequency b increase. In the high/soft state of NS accreting source the thermal equilibrium is achieved and two blackbody components related to the disk and the NS are seen in the data. The temperature of the Compton cloud is of order of the temperature of the blackbody component ( a few keV).

18. Conclusions (continued) c. We offer a new method of BH mass estimate using the index-frequency correlations. Namely, if the theoretical curve of the index-frequency dependence (low) related to the BH mass m1 fits the data for a given source then the simple slide of the frequency axis `low =(m1/ m2) low with respect low may allow us to obtain the mass m2 by fit of (`low ) to the observable correlation for another source.

19. Model Predictions for BH’s • Black Hole acts as a “drain” which manifests itself as a power law with index saturating at G = 2.5-2.7 in the soft state; in the low/hard state the spectrum is flat with G 1.7. • Origin and behavior of low and high frequency QPO’s: • 1) nlowassociated with the magneto-acoustic oscillation of Comptonization cavity size L, i.e. nlow ~ V/L ; cavity size is anticorrelated with mass accretion rate, . • 2) In the low hardstatenlow is correlated with but is independent of index , which is constant G  1.7 at low values of frequency. • 3) nhigh is anticorrelated with the inner disk or cavity boundary radius; hence nlow is correlated with nhigh. • 4) In transition from low hard to soft statenlow is correlated with G up to saturation ( G = 2.5-2.7 ) and then remains almost constant. • 5) At very high accretion rate, pair production heating in the bulk inflow overcomes bulk Comptonization, and nlow is anticorrelated with index.

20. Soft State Model Picture: The “Drain” • Gravitational attraction of BH in presence of plenty of accreting mass develops mass accretion flow rate of order of Eddington. • At such a high mass accretion rate a specific X-ray spectrum is formed as a result of the photon trapping effect. • Photon is trapped by the accretion flow, as it attempts to diffuse out of the hot accreting plasma • Result: steep spectrum, low Compton upscatter efficiency. • The photon index varies from 2.5-2.8 depending on the temperature of the flow. The soft photon component is characterized by blackbody-like spectrum that temperature is around 1 keV (for galactic sources) and 10-50 eV for extragalactic sources – UV bump. From: Laurent and Titarchuk, 2001

21. Source Photon Spatial Distribution in Converging Inflow Our Monte Carlo simulations (Laurent & T 2001) reproduce the source function spatial distribution: 2-5 keV (curve a), 5-13 keV (curve b), 19-29 keV (curve c), and 60-150 keV (curve d). • We confirm the analytical results that the density of the highest energy X-ray photons is concentrated near the BH horizon. From: Laurent and Titarchuk, 2001

22. From: Titarchuk and Laurent, 1999

23. Predicted Correlations: QPO Frequency vs. Mass Accretion Rate and Photon Index vs. Mass Accretion Rate Plot of QPO low frequency in Hz, vs. g parameter Photon spectral index vs the TL optical depth 0 From: Titarchuk, Fiorito (2004)

24. Summary • Black hole sources are usually in two phases (states): • 1) Soft state, where we see the BH function as a “drain” • BH Spectrum is dominated by photon-trapping in this situation and which is steep. • The observed high energy photons are emitted from a compact region, where soft energy photons of the disk are upscattered by bulk inflow forming the steep power law with photon index around 2.7, and low QPO frequencies (above 10 Hz) and high QPO frequencies are of order 100 Hz are observed. • The bulk inflow is present in BH when the high mass accretion is highbut not in NS, where the presence of the firm surface leads to the high radiation pressure which eventually stops the accretion. The bulk inflow and all its features are absent in NS’s. This phase is a particular signature of the black hole. • 2) Low/hard state, which is comparatively starved for accretion • The hard phase (state) is related to an extended thermal Compton scattering cloud (cavity) characterized by a photon index around 1.5 and the presence of low QPO frequencies (below 1 Hz).