Transcript Document

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
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.
Observational Background and Motivation
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 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.
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.
QPO LOW FREQUENCY - SPECTRAL INDEX CORRELATIONS FOR
BHC’s OBSERVED IN OUTBURST DECAY
From E. Kalemci, et.al., (2003)
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
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.
GRS 1915+105 Observations in Transient
States
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).
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
 lo w  0.08 high
Relation using MA model (Titarchuk &Wood, 2002)
 MA  CMA K
CMA  21 /2 4[( f  ) /(1  )]1 /2 (H / Rou t)
It is found that
H / Rou t  0.015
and
  0.1
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.
Spectral states in BHC candidates Binaries Categorized
in Two Generic Classes or States
• Low/hard state: thermal
Comptonization spectrum , Te ~
50 keV , optical depth  ~`14, 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)
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.
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 G 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.
Hard State (Comptonization) Spectrum
Soft State (Two Black body) 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.
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.
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
 2u
2

a
u ,
2
t
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.
Transition Layer (Compton Cloud) Model of
Accretion Process Surrounding a Compact Object
Outflow (jet, wind)
soft photon illumination ( Q
d
coronal heating ( Qcor)
by shock
disk
)
Outflow (jet)
( rin for BH, NS, or WD)
Standings shock
( compact region of sub-Keplerian
bulk inflow which Comptonizes soft
disk photons and radiates them as the
hard component )
•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
 MA  VA / Radj .
3 1/ 2
 high  (GMstar / Radj
) / 2 ,
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):

d
d
d
(R 2 ) 
( R3
),
dR
dR
dR
inner and outer boundary conditions
( Radj )  K ( Radj ),( Radj )  K ( Radj )
 
M
4H
is
and
the Reynolds number.
 ( R0 )  0 ,
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 Xray 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. In a 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.
In a 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).
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 G(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 G(`low ) to the observable correlation
for another source.
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) low associated with the magneto-acoustic oscillation of Comptonization cavity
size L, i.e. low ~ V/L ; cavity size is anticorrelated with mass accretion rate, m .
2) In the low hard state low is correlated with m but is independent of index ,
which is constant G ~ 1.7 at low values of frequency.
3) high is anticorrelated with the inner disk or cavity boundary radius; hence low is
correlated with high.
4) In transition from low hard to soft state low 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 low is anticorrelated with index.
Soft State Model Picture: The “Drain”
•
•
From: Laurent and Titarchuk, 2001
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.
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
From: Titarchuk and Laurent, 1999
Predicted Correlations: QPO Frequency vs. Mass Accretion Rate
and Photon Index vs. Mass Accretion Rate
Plot of QPO low frequency in Hz, vs. 
parameter
(  M )
)
Photon spectral index vs the TL optical depth ( 0  M
0
From: Titarchuk, Fiorito (2004)
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
high but 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).