G.S. Bianovatyi-Kogan, Yu.N. Krivosheev

Space Research Institute, Moscow (IKI RAN)

Thermal balance of the jet in the microquasar SS433

HEPRO-III, Barcelona28 June, 2011

SS433 is a unique massive X-ray binary system with precessing relativistic jets. It is situated at a distance of approximately 5 kpc = 1.5 10^22 cm nearly in the galactic plane. The optical companion V1343 Aquilae was first identified in the survey of stars exhibiting H_alpha (656 nm) emission by Stephenson and Sanduleak in 1977.

This binary has been observed in radio, optical, ultraviolet and X-ray for three decades, and nevertheless there are several puzzles concerning this object that remain to be solved, for instance, the nature of the relativistic object and the mechanism of collimation and acceleration of matter in jets to relativistic velocity.

orbital period of binary system

1. The origin of the broad-band X-ray spectrum of SS433 from 3 to 100 keV

2. Getting the values of some physical parameters of the source

3. Thermal balance of the jet

• It is almost certain that there is a black hole in SS433 system.

• This binary system consists of an optical star and a black hole, surrounded by an accretion disk with a couple of jets. Mass ratio of SS433 components is

• One of SS433 pecularities is supercritical regime of accretion onto relativistic object

( ~ , ~ )

• Powerful jets of conical shape have kinetic luminosity about ~ , the velocity of matter in jets is almost one third of light speed (0.26с)

SS433

410 /sunM M yr 710 / ( 10 )cr sun X sunM M yr M M

/ 0.2 0.3X Vq M M

39 4010 /kL erg s

Fabrika S.,2004 ,ApSS Reviews, 12, 1

121.5 10diskr cm

1310jetr cm

01.2jet

04disk 7bh SunM M

0.3bh

opt

Mq

M

124 10a cm Binary separation

In this figure the SS433 spectrum in the range from 3 to 90 keV is presented. It was obtained from INTEGRAL data (JEM-X points from 3 to 20 keV and IBIS (ISGRI) points from 20 to 90 keV). The spectum corresponds to precessional moment T3, i.e. when the angle between jet axis and the line of sight is equal 60 degrees and the disk is maximally ‘face-on’.

Cherepashchuk A.M.,Sunyaev R.A., Fabrika S.N., Postnov K.A. et al., 2005, A&A, 437, 561

Cherepashchuk A.M.,Sunyaev R.A. et al., 2006, Proceeding of 6th INTEGRAL Workshop, Moscow, Russia

10 100

10-5

10-4

10-3

10-2

lg I

, pho

t/cm

2 /sec

/keV

lg h, keV

Monte-Carlo simulations of the X-ray spectrum of SS433

Yu. M. Krivosheyev, G. S. Bisnovatyi-Kogan,A. M. Cherepashchuk and K. A. Postnov

MNRAS, 394, 1674–1684 (2009)

It follows from observations, that jet’s opening angle in X-ray range is about 1.2 degrees. That leads us to the assumption that jet is of conical shape.

Temperature profile:

2 4 6 8 100,0

0,2

0,4

0,6

0,8

1,0

F(r/r0)

r/r0

4

30

jet cor

rT T

r

corresponds to adiabatic cooling of expanding ideal gas.

Density profile:

2

00

r

rnn

Follows from the equation of continuity with the following expression for n0:

0 20 0p

Mn

m v r

0v

M is mass loss rate in the jet

0 0.26v c is the radial velocity in the jet

is the solid angle, occupied by the jet

• The corona has a spherical shape, its inner radius is , the outer one is .

• It was considered to be isothermal, with temperature equal to .

• The density profile was taken to be the same as in the jet for simplicity, but with different value at .

0r corr

20corT keV

0r

0

00 0( ) 1

corr

cor T Tcorr

rn r dr n r

r

- optical depth of corona with

respect to Thomson scattering

And thus we can obtain the formula for the outer radius of the corona: 0

0 01 /corcor T

rr

n r

• It was assumed that the size of the accretion disk coincides with that of Roche lobe and is equal .

• One can find the half thickness of the disk using the standard disk accretion theory in the gas-dominated region with free-free opacity, which begins from the radius (Shakura&Syunyaev, 1973, A&A, 24, 337-355) and then, assuming linear growth of thickness with radius , obtain the disk’s half-opening angle. It is equal 2 degrees (approximately).

121.5 10diskr cm

tan2diskh r

104·10bcr cm

3/20 3/209/8 1/29/10

3 1/10˙6.1·10 1

3 3Sun g gcr

M M R Rh

M R RM

110 10r cm

corr

0.26jetV c

Geometry of the computational domain

Angle dependence of SS433 spectrum

In the figure the spectra of the source for three angles of observation is shown: 60 degrees (solid line), 82 degrees (dotted line) and 90 degrees (dash-dotted line). In the last case the contribution of both hemispheres was taken into account, in the first two cases it wasn’t necessary.

10 100

10-5

10-4

10-3

10-2

I , pho

t/cm

2 /sec

/keV

h, keV

The observed X-ray flux is small at 90 degrees, so the second hemisphere is not visible, and outer parts of the disk have larger thickness, that SS model.The observational points correspond to the angle ~60 degrees.

Heating mechanisms of the jet in SS433

B.-K., K. Astron. Zh. (in press)

Sources of heating

1. Compton effect of hard X rays from corona on jet electrons

2. Heating due to dissipation of the energy of shock waves moving along the jet, and generated near the origin

3. Heating due to transformation of the jet kinetic energy into the heat in the collisions of the corona and jet

protons.

Density profile

Equation of a thermal balance of the jet

Radiative energy losses

Temperature profiles of the jet temperature with account of adiabatic expansion only (hard curve), and with account of radiative energy losses (dotted curve).

Solution of the equation of the energy balance in jet

Radiative losses curve due to free-free (dotted curve), and with account of free-bound, and bound-bound losses

Account of Compton heating

Integrating over the frequency::

Energy density of photons

Input into the thermal balance

Jet heating due to dissipation of shock waves

Hugonit adiabate

This expression is used in the equation of the balance of the internal energy, together with radiative losses. The value Delta (t) is established from the observations of the X ray variability of SS 433, on the time scale ~ 1 second.

To close the system, we derive the equation, determining the change of the energy flux in the shock, propagating along the jet..

The density of the flux of the energy of the shock wave, equal to the energy moving through the unit of square in a unit time

$D$ is the a velocity of the shock relative to the jet

The system describing the thermal balance of the jet with shocks

Jet temperature profile with account of shock wave heating

Shocks heat only a small region of the jet, around the place of the shock origin.

The whole jet could be heated only by a system of shocks formed along the jet, and

dissipating at different lengths.May be the “clumpy” structure of jets is

connected with a shock heating.

Coulomb collisions of protons

Thermal protons from corona enter the jet, becoming targets, on which jet protons, moving with a speed 0.27 c are scattered. Jet protons loose their kinetic energy due to scattering. The kinetic energy of jet is transformed

into heat.

Estimate a maximal heating rate by this mechanism, when the proton entering the jet is thermolised inside the jet, transforming into the heat the energy (М_р vjet^2/2)

(erg/g/sec)

The mean free path of the proton due to Coulomb collisions is much less than the jet radius, therefore the heating by collisions is much less than the maximally

possible. On the corona radius

Magnetic field influence

Jet temperature profilewith radiative losses and collisionalheating at a=const

1.0, 0.5, 0.3, 0

Same forvariable

a

Optical jet:

r ~10^14-15 cm (10^3-4 r0), almost constant temperature T ~ 10^4 Ê.Heating is necessary to balance radiative and adiabatic losses

Heating by collisions with the protons of corona and stellar wind

T_0 = 2.2 10^8 K until r = r_cor = 6. 4 10^11 cm,

Adiabatic law at larger radius T ~ rho^{2/3}~r^{-4/3}.

Heating of the optical jet in SS 433

Temperature profile of the jet:

Solid line – best fit byanalytic formula

Dotted line – pure adiabatic profile

Dashed line – simpler for heating

1. SS433 spectrum in the region form 3 to 90 keV origins from comptonized free-free emission of corona and jet (with the exception of small region near 7 keV, where line formation is important)

2. Еmission from accretion disk plays an important role in spectrum formation for lower energies and makes no contribution to the source’s spectrum in the range considered.

3. Most effective heating mechanism of the jet in SS 433 is connected with kinetic energy losses by collisions with surrounding matter (protons), in presence of a very moderate magnetic field. Collisions may support T~10^4 Ê in the optical jet. Shocks distributed over the jet may give an input into heating.

4. The losses of the kinetic energy are relatively very small ~10^{-4}, and the velocity change along the jet is hardly observable..