Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://hea.iki.rssi.ru/conf/hea2010/Presentations/24/Titarchuk.pdf Äàòà èçìåíåíèÿ: Wed Jan 26 13:25:09 2011 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:58:16 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: annular solar eclipse

On the Non-Relativistic Origin of Red-skewed lines in CV, NS and BH

Lev Titarchuk, Philippe Laurent & Nikolai Shaposhnikov

TALK@Moscow, High Energy Astrophysics December 24, 2010


X-ray Binary (artistic conception)
X - ra y b i nari e s


Model of Accretion Process Surrounding a Compact Object (NS or BH)
Outflow (jet, wind)

soft photon illumination ( Q

d

)
Outflow (jet)

coronal heating ( Qcor) by shock disk

( 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 )


v

1

v1-v

2

Diverging Flow (Wind)
2

Converging Flow (Inflow)
v External photon illumination
1

-v

2

n

-v

n v1 -v

2

v

1

Internal photon illumination

v

2

n

v

1

n v
2

BH

Inner radius

Inner radius (BH horizon)

On the left side: A photon emitted near the inner boundary and subsequently scattered by an electron moving with velocity v1, impinges on an electron moving with velocity v2 as shown. The change in frequency is 2= 1 [1+ (v1 - v2} · n/c]. In a diverging flow (v1 - v2} · n/c<0 and photons are successively redshifted, until scattered off electrons to an observer at infinity. The color of photon path indicates the frequency shift in the rest frame of the receiver (electron or the Earth observer). On the right side: In a converging flow (v1 - v2} · n/c>0 and photons are blueshifted.


Observational evidence of wind. I. Main idea of smearing out a pulsed signal
The emergent signal is a convolution

where ( ) is a pulsed signal and X (R, ) exp(IS A SCATTERING REPROCESSING FUNCTION

0

))

THE RESULTING POWER SPECTRUM


II. POWER SPECTRUM
blue, red and black lines present power spectra of reprocessing function, pulsed signal and resulting pds respectively

T, Laurent & shaposhnikov (2008)


GK Per XMM Spectrum
The XMM- Newton observation of GK Per on March 9 2002 (revolution 412)

T, laurent & Shaposhnikov (2009)


Red-skewed line in GK Per (CV)


Relativistic interpretaion (CV)


Ser X-1


Red skewed line in Cyg X-2. Suzaku observations


BH GX 339-4


Red skewed line in GX 339-4 (rev. 514). XMM-RXTE observations


Best-fit parameters of the XMM Iron Line Spectra for GK Per, Ser X-1 and GX 339-4


Summary
1. We utilize XMM-Newton and RXTE data to study the red-skewed iron lines in GK Per, Ser X-1, and GX 339-4 as representatives of WD, NS, and BH X-ray binary sources, respectively. 2. We analyze the iron line profiles in terms of both relativistic reflection and wind outflow models. 3. (i) all three types of accretion compact objects show redskewed iron K lines, (ii) outflow is a common phenomenon for CVs, NS and BH. 4. The K line iron emission with redskewed features in CV GK Per indicates that the red skewness of the line cannot be a BH particular signature related to the redshift effects of General Relativity (GR).



Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States

Dragulescu, & Yakovenko Physica A 299, 213 (2001))


Spectral index of the converging inflow spectrum
· Main idea of the : power law formation

I



p

K

,

where p is a probability of single scattering .

/ 0 = 1+ ,

after k scatterings

k / 0 = (1 + ) .
k

Thus

I = ( / o )

-

where = ln(1 / p) / ln(1 + )


The index saturation is a BH signature Spectral index =-1

Number of scatterings

average fractional energy change per scattering

spectral index saturates when CF optical depth increase!


Black Hole Mass Determination. The Main Idea
QPO frequency L by definition is a ratio:

where V is a characteristic (acoustic) velocity in a given configuration and L is a size of the configuration. But velocity V and dimensionless size Lds= L/R are funcition of the spectral Hardness (photon index ) (T, Lapidus & Muslimov 1998)
S

L V/L

Thus for a given index (spectral state) and for two black hole sources of masses m1=M1/M , m2=M2/M Log 1- Log 2=log (m2/m1)


Shaposhnikov & T (2006)


BH XTE J1650-500. BeppoSAX

Montanari, T & Frontera 2008


Montanari, T & Frontera 2006


Montanari, T & Frontera 2006


Montanari, T & Frontera 2006


QPO-Photon Index Correlations in BH sources Cygnus X-1 GRS 1915+105

J1859+226 and 1550+564

GRO J1655-40


Index-Mdot saturation. GRS 1915+105

Seifina & T (2009)


BH mass and distance determinations

Shaposhnikov &T (2008)



Black Hole Mass Determination. The Main Idea
QPO frequency L by definition is a ratio:

where V is a characteristic (acoustic) velocity in a given configuration and L is a size of the configuration. But velocity V and dimensionless size Lds= L/R are funcition of the spectral Hardness (photon index ) (T, Lapidus & Muslimov 1998)
S

L V/L

Thus for a given index (spectral state) and for two black hole sources of masses m1=M1/M , m2=M2/M Log 1- Log 2=log (m2/m1)


BH mass determination:Cyg X-1


The scaling method vs other methods BH masses and distances


Summary II
1. A new method for evaluation of the BH mass using this observable index-frequency correlation is demonstrated. 2. In the soft state this index-QPO and Mdot correlations show the saturation to the photon index at high values of the low frequency which are identified as a black hole signature. 3. The K line iron emission with redskewed features in CV GK Per indicates that the red skewness of the line cannot be a BH particular signature related to the redshift effects of General Relativity (GR). 4. If the mechanism of the K line formation is the same in CVs, NSs and BHs then it is evident that the GR effects would be ruled out as a cause of red skewness of the iron line.


K line formation in the wind. Direct component


Shaposhnikov, T & Laurent (2008)


Composite spectrum of Cyg X-2

EXOSAT-ASM-PCA (RXTE) power spectrum of Cyg X-2 in frequency range that covers 10 orders of magnitude. One can clearly see low and high frequency (LF and HF) white-red noise components in PDS, related to the extended Keplerian disk and relatively compact, innner disklike configuration (sub-Keplerian Compton corona) respectively. Each of these two components is perfectly fitted by our white-red noise model (dotted and solid lines are for LF and HF best-fit models respectively.


Soft state power spectrum of Cyg X-1

The composite soft state PDS is made by PCA (blue) and ASM (red) PDSs. The PCA PDS is for ObsID 50110-01-52-00. Data are fitted by LF-HF diffusion model: 2/Ndof = 184/228 = 0.81, the best -fit parameters t0,D = (6 1.7) 105 s, D = 2.93

0.01.


LF QPOs in Black Holes
Cygnus X-1
GRO J1655-40

QuickTimeTM and a QuickTimeTM and a TIFF (LZW) decompressor TIFF (LZW) decompressor are needed to see this picture. are needed to see this picture.

(ShaposhnikoSShaposhnikov & T 2006, ApJ, 643,1098

(Shaposhnikov, Swank, Rupen, Shrader, Beckmann, Markwardt & Smith 2007, ApJ, 655,434)


Simultaneous Power and energy spectra evolution


The inferred scenario of the spectral transition in Cyg X-1. Strength of disk and outflow (wind) increase towards the soft states


Index- low QPO frequency correlation in BH candidates

Shaposhnikov & T (2006)


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.


Index-QPO frequency correlation for NS source 4U 1728-34

T & Shaposhnikov (2005)



Transition Layer. Scaling method I.


Transition Layer. Scaling method II.


Transition Layer. Scaling method III.


Verification of the Scaling Method

GRS 1915+105 & GRO J1655-40
·Scaling Coefficient M
1655/

M

1915=0.41

±0.01

· Given that MGRO J1655+40=(6.3±0.5) solar masses we obtain that

·MGRS

1915+105=

(15.6±1.5) solar masses
Optical: 10.0-18.0 M_Sun (Griener et al. 2001)

Shaposhnikov & T (2007)


BH Mass Determination in Cygnus X-1

Cygnus X-1 & GRO J1655-40
·M
Cyg X-1

=

8.7 ± 0.8 solar masses Optical: 6.85-13.25 Msun

Shaposhnikov & T (2007)


NASA PRESS RELEASE
NASA Scientists Pioneer Technique for "Weighing" Black Holes 05.09.07 Two astrophysicists at NASA's Goddard Space Flight Center in Greenbelt, Md., Nikolai Shaposhnikov and Lev T, have successfully tested a new method for determining the masses of black holes. This elegant technique, which Lev T. first suggested in 1998, shows that the black hole in a binary system known as Cygnus X-1 contains 8.7 times the mass of our sun, with a margin of error of only 0.8 solar mass. Working independently, Tod Strohmayer and Richard Mushotzky of Goddard and four colleagues used T's technique to estimate that an ultra-luminous X-ray source in the small, nearby galaxy NGC 5408 harbors a black hole with a mass of about 2,000 suns.


Observable Index-QPO and Index-Mdot correlations

PCA Standard1 count rate (top row) and hardness (second row) for three outbursts from GX 339-4 on 2002 (left), 2004 (middle) and 2007 (right). Third and bottom rows: Index versus QPO frequency (left), and Mdot normalization (middle) and Comptonized fraction (right) for transitions in GX 339-4 ( each transition is indicated by different color).

Shaposhnikov & T (2008)


Index-Mdot saturation. GRS 1915+105

Seifina & T (2009)


·W

­O

· · ·

QPO I QPO

QPO M

­P

· ·

QPO I C ·P ·W M ­C ­S

C

BH

1 MBH BH


Condition for supression of pulsed signal
||FW(p)||2/ ||FW(p)||2
which leads to inequality NS case: 0.7e2(p /400 Hz)2 (L/107 cm) or e >1 BH case:
2

max

= [(pt0)2+1]-1<<1

>>1

(e /0.02)2(p /100 Hz)2 (L/1011 cm)
attenuated as exponential exp(- ). e

2

>>1

The above relations are for scattered component of the resulting signal. The direct component of the pulsed radiation is

or e > 0.02.

T, Laurent & shaposhnikov (2008)



Redskewed iron line profiles in CV (GK Per). Wind model

T, laurent & Shaposhnikov (2008)


Redskewed iron line profiles in CV (GK Per). ``Relativistic model''

T, laurent & Shaposhnikov (2009)


Fit quality (GK Per). Wind model

T, laurent & Shaposhnikov (2009)


Fit quality (GK Per). ``Relativistic model''

T, laurent & Shaposhnikov (2009)


Summary II of first part
1. 2. 3. QPO-spectral index data contain information about the mass of compact object. QPO-index scaling is a good alternative to dynamical mass measurement. QPO-Index scaling method applied gives: M M M
GRS 1915+105

= (15.6

1.5) MSUN

Cygnus X-1

= (8.7 0.8) MSUN, BHC -> BH BHC -> BH

H1743-322 339-4

= (10 1)MSUN
J1859+226

MGX

MXTE

~ (9.7 ±0.8) MSUN

4. Simultaneous timing and spectral analysis is essential for diagnostics of astrophysical compact objects. Missions like RXTE and BeppoSAX are crucial.


Formulation of the problem



The boundary condition at the outer boundary Assumed that at the inner boundary which is equivalent to

We assume that perturbations of the mass accretion rate at the inner disk edge into perturbations of the X-ray luminosity, i.e. is converted with efficiency

Because

then

Now we consider a general case of problems where a. Viscosity linearly distributed over radius:

where the viscous time scale Then the power spectrum of Y(t) is:


The series in the right hand side of this equation can be calculated exactly

where As it follows from this formula that

and


General case
Although the series of power spectrum

has to be calculated numerically the asymptotic form of PDS can be easily evaluated analytically:

where

,

and



Integrated Power of X-ray emission vs total integrated power of the disk configuration
We obtain that the integrated total power of X-ray resulting signal

We arrive to the conclusion that the resulting integrated power Px, which is related to the perturbation amplitude at the inner disk edge, is much less than the total integrated power of the driving oscillation in the disk Pdr


Evolution of Power density spectrum and energy spectrum

Cyg X-1: Observable power spectrum (PDS) (left panel) vs photon spectrum (right panel). The first observation is a pure low/hard state with no LF WRN component in the PDS. During the second observation the source energy spectrum is still hard, but LF WRN is already detectable.


The first observation is taken during the intermediate state just before the transition to high/soft state, which is presented by the second observation.No HF WRN is present in PDS during high/soft state.


Power spectra of Cyg X-1: Hard and intermediate states

Two composite PDSs: EXOSAT spectra with matching high frequency PCA PDS. Data are fitted by LF-HF diffusion model: 2/Ndof = 250.1/267 = 0.94, corona = 2.32 0.12, t0,C = 1.8 0.3, D = 2.5 and 2/Ndof = 278.5/267 = 1.04, corona = 2.07 0.7, t0,C = 1.24 0.12, D= 0.3 0.3.


Reynolds number of the flow and Shakura-Sunyaev disk - alpha parameter as observable quantities
Using the best-fit parameters of the PDS model we can infer the evolution of the physical parameters of the source such the disk diffusion time t0, magnetoacoustic QPO frequency and Reynolds number of the accretion flow Re, with the change of photon index. We can relate t0 with Re and magnetoacoustic QPO frequency

,
because

These formulas leads to equation

that allows us to infer a value of Re using the best-fit model parameters t0 and the QPO low frequency presumably equals to .


Determination of Reynolds number of accretion flow from Observations I

T, Shaposhnikov & Arefiev 2007


Determination of Reynolds number of accretion flow from Observations II


Determination of Reynolds number of accretion flow from Observations III


Observational Evidence of Compton Cloud Contraction

Cyg X-1: a product of QPO low frequency QPO(L) and the best-fit diffusion time of HF WRN t0 vs . Decrease of QPO t0 with implies that Compton cloud contracts when the source evolves to the softer states.


Driving QPOs in the observed power spectra

RXTE/PCA power spectra (left panels) and power frequency diagrams (right panels) of GRO J1655-40 (top) and XTE 1859+226 (bottom). One can clearly see QPO frequencies dr at 10 20 Hz for GRO J1655-40 and 185 Hz for XTE 1859+226 before a high-frequency cut-off. The rms2 power at dr is comparable (GRO J1655-40) or higher (XTE 1859+226) than that at low frequencies (see right panels).


Power vs Driving QPO frequency


Low QPO frequency vs Driving QPO frequency


Summary I.
We present a model of Fourier Power Density Spectrum (PDS) formation in accretion powered X-ray binary systems derived from the first principles of the diffusion theory.

The resulting PDS continuum is a sum of two components, a low frequency (LF) component is presumably originated in an extended accretion disk and a high frequency (HF) component is originated in the innermost part of the source (Compton cloud).


Summary II.
The LF PDS component has a power law shape with index about 1.5 at higher frequencies ("red" noise) and a flat spectrum below a characteristic (break) frequency ("white" noise). This white-red noise (WRN) continuum spectrum holds information about physical parameters of bounded extended medium, diffusion time scale and dependence of viscosity vs radius. We offer a method to measure an effective Reynolds number, Re using the basic PDS parameters (PDS index and characteristic frequencies). We obtain that the inferred Re increases from 8 in low/hard state to 70 high/soft state.


This cartoon illustrates the different emission patterns responsible for the time lags of the pulsed emission. Cill is the disk illumination fraction. Soft time lag of the pulsed emission is the result of downscattering of hard X-ray photons in the relative cold plasma of the disk. A fraction of hard X-ray photons 1- Cill that are upscattered soft disk photons coming from the disk and NS and directly are seen by the Earth Observer.


Time lags and density variations in compact objects

The measured soft time lag of the pulse profile versus energy (crosses) with respect to the first energy channel. The best- fit curve using the Comptonization model is shown with the solid line. The upper and lower limit of the electron number density of the Comptonization emission area, are given in dot-dashed line 1.6-2.6 x 1018 cm-3 . The panels corresponds (a) for IGR J00291+5934 including also the upper and lower limit of the electron number density of the reflector, 6.1-8 x 1018 cm-3, and (b) that for XTE J1751305, 6-6.6 x 1018 cm-3 and (c) that for SAX J1808.4-3658, 2.9-3.6 x 1018 cm-3.


Time lag model




W01 demonstrated that the mass accretion rate in the disk

can be calculated as

Furthermore, we assume that the mass accretion rate at the inner disk edge is converted into the X-ray luminosity, L(t) i.e. with efficiency and thus

Now we consider a general case of problems where a. Viscosity linearly distributed over radius:

where the viscous time scale Then the power spectrum of X(t) is:

where


BH Candidate: GX 339-4

M

GX 339-4

M

XTE J1859+226

~ (9.7 ±0.8) MSUN