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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). The Work is based on published papers by our group.

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Anti-Correlated Lags in Compact Stellar X-ray Sources

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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)

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


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

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.

Two mechanisms of mass transfer in a binary system

Accretion through Roche lobe outflow

Accretion from stellar wind

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




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

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)

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

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


  • 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

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.

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


  • 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

For non-stationary electron:


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:


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

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

Disk Corona Geometries..

slab, sandwich

sphere+disk geometry


RXTE Satellite


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


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

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

COSPAR Workshop, Udaipur 2003


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.

COSPAR Workshop, Udaipur 2003


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.

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.

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


confidence ranges of these


Compare to data

Basic Spectral states in GBHs

Soft State,


Hard State,

thermal Comp.



IM state/VHS/SPL

Cyg X-1

Soft State,


Figure is taken from Zdziarski et al. 2002

Three-state classification

In this classification the luminosity is not used as one of parameters.

Remillard & McClintock 2006

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

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)

Typical outburst of BH source

QPO propagation during an Outburst

Truncated disc and X-ray spectral states

Spectral states – moving truncation radius


hard state

soft state

hard state

soft state

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

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

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????

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


Two series are highly correlated,

with no lag, then

CCF peak points to Zero

In anti-correlation,

CCF peak shift to the -tive side.

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

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


Sriram et al. 2009, RAA

XTE J1550-564,

Sriram et al. ApJ, 2007

First Neutron stars source to show ACL

Lei et al. 2008, ApJL

Cyg X-2

GX 339-4, first BH source to show AC soft lag

Sriram, Rao & Choi submitted to ApJ

ACL for GX339-4 using RXTE and INTEGRAL

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)

Typical timescales in different size BH

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)

QPO changes???

XTE J1550-564

Sriram et al. 2007, ApJ

GRS 1915+105, Choudhury et al. 2005

For source H1743-322

For GX 339-4 QPO changes

Spectral changesModel independent changes

GRS 1915+105

Cyg X-3

XTE J1550-564

For H1743-322

GX 339-4 spectral changes

Spectral Ratio

Spectral changes

  • More importance is given to know the change in spectral parameters.

  • spectral fitting was carried for H1743-322, XTE J1550-564 , GRS 1915+105 (all of them were in VHS or SPL state)

  • Spectra were obtained from initial and final part of the Lc, for the resp. sources for which QPO shift was found

  • Model used : Smedge(Diskbb+Gaussian+ThComp+PL)‏

  • PL index =2.2 and Gaussian Line=6.4 keV were fixed

Simultaneous Spectral fitting

  • Data is not sufficient to know which parameter is changing

  • Fitted the initial and final part spectra simultaneously

  • all the parameters tied to the initial spectrum

  • Initially the χ2 was very high

  • Nthcomp of two parts allowed to vary independently(χ2 improved).

  • Then Ndisk and kTin were allowed to vary one by one

  • continued the process no considerable improvement was observed in the fit

  • Suggest that Normalisation and disk parameters significantly varied between these two parts.

Most important result is change in disk and Corona flux (unit: 10-9 ergs/cm2/sec) during lag in different source

XTE J1550-564

flux A B


soft 20.9 22

hard 56.5 52.5


2nd Obsev.

flux A B


soft 17.3 23.2

hard 52.5 42

H1743 A1 B1 A2 B2 A3 B3 A4 B4


Soft7.90 7.41 61.10 100.20 119.1 84.10 4.3 3.9

Hard 41.17 46.50 10.1 8.10 12.6 10 3.9 5.6

GRS 1915+105 A B

Soft8.5 6.2

Hard 11.4 22.0

For GRS 1915+105, we found electron temperature is changed by ~4 keV

Sriram et al. 2007, ApJ

GX 339 -4 unfolded residual with same model used for A section spectrum

Physical Interpretation of temporal and spectral delays of VH state In GBHs

Corona, Compton cloud,

thermal Comptonized hard photons

Disk, seed soft photons

As Disk goes in, Soft photons increases and cools the cororna and hard photons decreases


  • Still the Hard X-ray source location in accretion process in BH, NS and CV is poorly know.

  • Cross-Correlation method is one of the powerful tool to constrain the physical location in accretion disk (BH, NH)/ column (polar).

  • Similar kind of work can be extended to other BHs, NSs, CVs inorder to constrain the geometrical and physical regions in the accretion processes


  • Still the Hard X-ray source location in accretion process in BH, NS and CV is poorly known.

  • Cross-Correlation method is one of the powerful tool to constrain the physical location in accretion disk (BH, NH)/ column (polar) or IPs

  • Similar kind of work can be extended to other BHs, NSs, CVs inorder to constrain the geometrical and physical regions in the accretion processes .

Work carried out at KASI during Dec 16-till Now

X-ray Work

  • Anti-Correlated soft lags in Intermediate state of BH source

    GX 339-4 (Sriram, Rao & Choi submitted to ApJ)

  • XMM-Newton observation of a cataclysmic variable candidate: AX J1853.3-0128 (Hui, Sriram & Choi planning to submit in ApJ)

    Optical Work

  • Photometric study of Contact binary systems in omega Centauri

    (Sriram et al. , submitted to Ap&SS)

  • Photometric study of W Uma type variable in LMC

    (Shanti, Sriram and Vivekananda Rao submitted to RAA)

Thank you

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