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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