Quasi-spherical accretion onto magnetized neutron

stars

Nikolai Shakura (Moscow University, Sternberg

Astronomical Institute)

Zeldovich-100

OSA seminar

March 20-21, 2014

Plan

• Introduction: supersonic and subsonic wind accretion

• Two regimes of plasma entrance the magnetosphere: Compton and radiative cooling

• High and low (‘off”) states in X-ray pulsars• Pencil (in ‘off’) and fan (in ‘high’ state)

beam from accretion column • Comparison with observations: off-states in

Vela X-1 and bright flares in SFXTs• Conclusions

First paper with YaB:

• Pulsating X-ray sources accreting magnetized neutron stars in binary systems

• P from ms to 10000 s, dP/dt negative or positive (spin-up/spin-down), variable, Lx~1034-1038 erg/s, spectrum with exp. cutoff at E~20-30 keV

• Cyclotron resonance scattering features direct estimation of NS magnetic field 1012-1013 G

Wind-fed pulsars• Matter is captured from

(generally inhomogeneous) stellar wind. Specific angular momentum can be prograde or retrograde (from 2D (Fryxell & Taam, 1988 etc.) and 3D (Ruffert 1997,1999…) calculations

• Disc can or cannot be formed, depending on the specific angular momentum at the magnetosphere

Nagae et al 2004

Key physical parameters

• NS magnetic field – Directly probed by CRSF energy (local -in the site of the

line generation!) B= 1012G x Ec/(11.6 keV) (1+z)

- Indirectly – from matter-magnetospheric interaction (only large-scale dipole component!)

• Mass accretion rate– Derived from X-ray luminosity, but the distance is

usually uncertain

• Stellar wind velocity (for wind-fed XPSR)

• Binary orbital period Pb

• Pulsar spin period P*• Pulsar spin-up/down rate dP*/dt

Accretion Bondi-Hoyle-Littleton

cool freefallt t

22

3

2

(2 )~

2

B

B

GMM vR

vGM

Rv

~2GM/V2 (Bondi radius)characterizes bow shock location in the wind

shock

Bondi (supersonic) accretion regime• If plasma cooling time << free fall time • Free fall with velocity ur=uff

• Shock close to magnetosphere (hs<<RA)

• RA is Alfven radius determined from ram and magnetic pressure balance

• Plasma rapidly cools and enters magnetosphere due to Rayleigh-Taylor instability (Arons, Lea’76)

• Plasma carries angular momentum (Illarionov, Sunyaev’75) • Happens at high X-ray luminosities Lx> 4 x 1036 erg/s

2~ binary Bj M R

Subsonic settling accretion without shock near magnetosphere

Convective isomomentumshell ω(R)~1/R2

Matter subsonicallysettles down inside the

the shell with radius ~RB

1/3

~ ffBondi

cool

tM M

t

cool freefallt t

Shakura et al. 2012

Settling subsonic accretion regime• If plasma cooling time >> free fall time• Settling with velocity ur=f(u)uff, f(u)<1, determined

by plasma cooling rate (Compton cooling, radiative cooling)

• f(u)≈(tff/tcool)1/3

• Happens for moderate X-ray luminosities Lx< 4 x 1036 erg/s (Shakura et al. 2012)

2 24 ( ) ( )A A

A

GMM R R f u

R RA is Alfven radius from

gas and magnetic pressurebalance

Vertical structure

• Hydrostatic equilibrium

Adiabatic solution:

2

10

dP GM

dR R

1

m

T GM

R

Alfven surface: from gas pressure balance (cf. in supersonic accretion – from

dynamic pressure balance!)

• Gas pressure balance

• Change density from mass continuity

Settling accretion:

K2~7.6 , f(u)~0.1(Arons & Lea, 1976) model

2( )

8A

g mm

B RTP P

2/ 72

2

4( )

1 2AR f u K

M GM

Plasma entering magnetosphere

• Critical temperature:

• Effective gravity:

(Elsner, Lamb’77)

• Need for plasma to cool

Alfven surface

Neutron star

χcos

2

1/ ( )

mcr

A A

GMT

R R

curvature radius

Stable : T>Tcr

Unstable : T<Tcr

Stability of magnetosphereincreases when it becomesmore curved (concave)

Two cooling regimes

• Compton cooling time:

At given Lx cooling occurs at R<Rx . At higher radii – Compton heating takes place.

Radiative cooling time1

9 36

( )300 , ~

10 10 / 0.1xA

rad

LR f u dTt s T

cm erg s dt

1/3 1/3

9 2/11 6/11 4/11 1/11, 16 30 16 30

9 6/27 16/27 6/27 2/27, 16 30 16 30

2

10 ( ) ~ 0.22

10 ( ) ~ 0.1

ff ffff

cool A cool

cA C C

ff

radA rad rad

ff

t tGMu u

t R t

uR cm M f u M

u

uR cm M f u M

u

Plasma entry rate

Example light curves of Vela X−1, 4U 1907+09 and GX 301−2 ( HEASARCH archive data).

Shakura N et al. MNRAS 2013;428:670-677

• Observed as sudden drops in X-ray luminosity with a duration of a few 100-1000 s

• Most studied in: Vela X-1, 4U1907+09, GX 301-2, etc.

II. Application to real sources

Vela X-1 off state (Doroshenko et al. 2011)

Suzaku XIS data

Low state: spectrum is softer Lx~3x1035

High state, Lx ~3x1036

Most important: At off-state, phase of hard X-ray pulse changes by 90 degrees

cusp is almost stable

Pulse profiles of Vela X−1 as observed by Suzaku (in normalized counts from Doroshenko et al. 2011) at normal luminosity levels (four upper panels) and in an ‘off’ state (four lower

panels).

Shakura N et al. MNRAS 2013;428:670-677

© 2012 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society

• High state: Pulse maximum in the hardest channels is shifted by ~90 deg relative to low state

• Low state: Pencil-beam at E>Ecyc~20 keV, fan near Ecyc , absorption dominates scattering below 12 keV

Scheme of the different regimes of quasi-spherical accretion including supersonic (Bondi) accretion and subsonic (our model) accretion.

Shakura N et al. MNRAS 2013;428:670-677

III. Non-stationary wind accretion:The nature of SFXTs

• SFXT= Supergiant Fast X-ray Transients

• New class of high-mass X-ray binaries (HMXBs), heavily obscured in soft X-rays. Mostly discovered by INTEGRAL in hard X-rays (Sunyaev et al. 2003a,b; Grebenev et al. 2003, 2004; Lutovinov et al.2004; Molkov et al. 2004)

HMXRB classes: a summary

Persistent wind fed accreting X-ray pulsars with supergiant companions

“typical” HMXRBs, Vela X-1 like

Be/X-ray binariestypically Transient X-ray sourceswith Be companions

A new class -> Supergiant Fast X-ray Transients

with supergiant companionstransient emission, with

short duration outbursts, typically few hours, less than Be/XRBs

outbursts

highly absorbed HMXRBsdiscovered with INTEGRAL

a growing number of membershave been discovered

with INTEGRAL

Bright persistent disk-fedmassive X-ray binaries (Cen X-3 like) in close orbits

(from L. SIdoli’s talk)

Final lightcurve from Swift / XRT observations of IGR J11215-5952IGR J11215-5952

9th February 2007Romano et al. 2007

Role of stellar wind magnetic field

Solar wind: Tangent magnetic field smaller solar wind velocity by a factor of 2 (Milovanov & Zeleny 2006)

Along radial field600-700 km/s

With tangent fieldup to 350 km/s

Magnetized winds from O-B stars

• ~10% of hot O-B stars are known to have magnetic fields up to a few kG (Braithwaite 2013)

How to produce an outburst?• Observed amplitude of outbursts up to 1000 times as the quiescent

value (~ 1034 -1035 erg/s) = low state (radiative plasma cooling)

• At low state:

• Magnetized wind Decrease wind velocity (factor 2) increase in Bondi accretion rate f(u)=1

2.76 2/3 41 4/3,2 35

,

2/9 2/27 2/9 2/2736 30 34 30

0.1 5 10 [ ] ( )10 1000 / 500 / 10

( ) ~ 0.1 ~ 0.036

w NSx low low rad

radrad

ff

vverg M PL M c f u

s M km s km s d

uf u L L

u

5,outburst , ,2 10 ~ (300 1000)x x low x lowL L L

2

2.76

1( ) ( )

4

0.4 1 / 19 /

Blow B o

o

RM f u M f u M

a

LM L L L L

cv

Plasma without magnetic field entries magnetosphere due toRT instability

MagBound, Geneva26.06.2013

Plasma with magnetic field opens magnetospheric boundary

RA

SFXT IGR J11215, P*=187 s

Sidoli et al. 2007

Conclusions• At < 4 x 1036 erg/s wind-fed pulsars can be at

subsonic settling accretion accretion rate onto NS is determined by the ability of plasma to enter magnetosphere.

• Two states of plasma entrance the magnetopshere depending on cooling mechanism:

L>3 x1035 erg/s Compton cooling dominates in the equatorial region of magnetosphere HIGH state

L<3 x1035 erg/s radiative cooling dominates in the equatorial region of magnetosphere LOW state. Transition from high to low state is accompanied by ~90 degree phase shift of hard pulse maximum

• Settling accretion can be realized at low (quiescent) states of SFXTs. SFXT outbursts can be triggered by magnetic field in stellar winds of O-B supergiants (low velocity + Bondi accretion in outbursts)

References

1. Theory of quasi-spherical accretion in X-ray pulsars. N. Shakura, Postnov, Kochetkova, Hjalmarsdotter (MNRAS, 2012, 420, 216; arXiv:1110.3701)

2. On the nature of “Off” states in slowly rotating low-luminosity X-ray pulsars, Shakura,Postnov, Hjalmarsdotter, 2013, MNRAS, 428, 670 (arXiv:1209.4962)

3. Bright flares in Supergiant Fast X-ray Transients, Shakura,Postnov, Sidoli, Paizis, 2014, MNRAS,

submittedThank you for your attention