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1.1 What's BeXBs? HMXBs SGXBsBeXBs Be/star NS Be/star Characteristics: 1. Usually 8-18 solar mass 2. Rapid rotation 3. Equatorial disk 4. Infrared excess 5. Emission lines of H and He Characteristics of BeXBs: 1. Orbital period s days 2. High orbital eccentricity 3. Mass transfer driven by stellar wind or equatorial disk 4. Drastically X-ray flux change between outburst and quiet states NS Super Giant
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BeBe//XX -Ray-Ray 双星中的中子星自传演化双星中的中子星自传演化成忠群
南京大学2013.8.17
Contents
1. Introduction (1) Observed period gap for BeXBs
(2) Possible interpretation by the authors
2. What we have did (1) The theoretical considerations
(2) Our model and detailed calculation process
(3) The results of our calculation
3. Contrast and discussion (1) Something we have ignored
(2) Comparing and discussion
1.1 What's BeXBs?
HMXBs
SGXBs BeXBs
Be/starNS
Be/star Characteristics:1. Usually 8-18 solar mass2. Rapid rotation 3. Equatorial disk4. Infrared excess5. Emission lines of H and He
Characteristics of BeXBs:1. Orbital period 10-100s days2. High orbital eccentricity3. Mass transfer driven by stellar wind or equatorial disk4. Drastically X-ray flux change between outburst and quiet states
NS Super Giant
The bimodal spin period distribution of BeXBs, with two peaks at 10s and 200s and a spin period gap around 40s.
The two types of BeXBs have a percentage of 35% and 65% in the total BeXBs, respectively. Ref. (Christian Knigge, etal 2011)
1.1 HMXBs on the Corbet diagram.
1.2 The equilibrium spin period of X-ray binaries
For disk accretion neutron star, the spin will reach a equilibrium spin period when the co-rotation radius equal the magnetosphere radius.
Rm> Rc spin down propeller phaseRm< R c spin up accretion phase
3/122
7/124
4/
2/
πPGM=R
MGMμ=R
snc
nm
7/37/57/6 222 MGMμπ=P neq
cm RR
The bimodal spin period distribution of BeXBs, with two peaks at 10s and 200s and a spin period gap around 40s.
The two types of BeXBs have a percentage of 35% and 65% in the total BeXBs, respectively. Ref. (Christian Knigge, etal 2011)
1.1 HMXBs on the Corbet diagram.
1.1 Two spin period peaks for BeXBs.
1.2 Is the supernovae responsible for the bimodal?
Two types of supernovae
Electron-capturing Supernovae (ECS)
Core collapse Supernovae (CCS)
Lower kick velocity (<50km/s)Less NS mass (<1.3 solar mass)
Higher kick velocity (>200km/s)Large NS mass (~1.4 solar mass)
Shorter orbital periods and little eccentricity
Longer orbital periods and higher eccentricity
Lower spin period Higher spin period
1.2 Problems with the explanation.
1. The equilibrium spin period of wind-fed pulsar is determined by the mass accretion rate and magnetic field. If the two groups of pulsar is formed by the supernova, then the orbital period gap should be more clear than the spin period gap.
2. The mass accretion rate of pulsar in BeXBs change violently, then there's no reason to neglect the influence of pulsar spin evolution history on the bimodal distribution.
2.1 The equatorial disk of Be/star
(1). Within the equatorial disk(Water 1989):
(2). Outside the equatorial disk or it's disappeared: vπrM=rρ lose
24/
10.161.240.8115109.6 yrMMLR=M sunBelose
βrRv=rv /1
0=rv
ρ(r )=ρ0(r /R)−n
v (r )=v0(r /R)n−2
v ϕ (r )= v eq (R / r )
h(r )=α r
2.1 Mass transfer rate for BeXBs
Within the equatorial disk:
Outside the equatorial disk or during the disk-loss episodes:
Compare with the X-ray luminosity:
relldlg
relgdgl
relgdgl
relldlg
vrMrrah
vrMrrah
vahrMahrr
vahrMahrr
ρ
ρ
ρ
ρ
2
2
),(
),(
)( )(
)( )(
aahqq
aqr
vGMr
l
relXg
)1.0~01.0()(1ln(6.0
49.0
/2
)3/13/2
3/2
2
relgs vaρπr=M 2 22rxrel v+vv=v
Loutburst
Lquiescence=103−104 M d
Ms=103−104
ds PP
7/3 MPeq
2.1 Specific angular momentum capture rate.
(2). Within the spherical stellar wind, numerical simulation shows (Livio etal 1986, Ruffert 1999):
(1). Within the equatorial disk and the NS orbital plane coplanar with the equatorial disk of Be/star (Wang 1981, Li & van den Heuvel 1996 ):
)()(sin
|]coscossin)2(cos[cos
)()2
()()(6
22
43/13/22
avav
vv
vvn
vv
vvpGM
MMj
rel
r
arx
rel
x
r
x
rel
xorbX
ϕ
05.0~ 22
2
orb
g
pr
j Rcir= j2 /GM
22rxrel v+vv=v
xr
x
vvvv
xrel vv
Rcir∝ j2∝(v x
vrel)8
2.2 Accretion flow configuration.
If the accretion material circularization radius is bigger than the magnetosphere radius, the accretion flow can evolve into accretion disk before contact the NS magnetic field (Ghosh and Lamb 1979).
Otherwise a atmosphere envelope probably formed replace the accretion disk to mediate the energy and angular momentum transfer between the NS magnetic field and accretion flow (Davies & Pringle 1981, Ikhasanov 2007, Shakura etal 2011)
Spherical stellar wind:
Equatorial disk:
envelopesphericalR<R mcir
envelopesphericalR<RperiodlongdiskaccretionR>Rperiodshort
mcir
mcir
::
2.2 The influence of wind structure change.
The observed Be/star equatorial disk formed and disappeared erratically on a timescale range from months to years, so both the mass and specific angular momentum captured from wind change alternatively from between the two cases.
If the accretion flow can evolve into accretion disk during the equatorial disk existing duration
seq,deq,
sm,dm,
sd
lossdisk
PPRRMM
TT
windSphericaldiskEquatorial
propeller Rc< Rm , d< Rm , s
Diskaccretion sm,dm,cdisk R<RRT :
propeller sm,cdm,loss R<R<RT :
Spin down
Spin down
Spin up
12/37/32
c
dm,
d
s
dm,d
ssm,s
up
down
RR
MM=
GMRMΩRM
=N
N
For the case of no accretion disk formed around NS, the subsonic propeller set in and the co-rotation radius can exceed the magnetosphere radius.
2.2 The influence of wind structure change.
propeller
Subsonic propeller
Subsonic accretion
Rc< Rm , d< Rm , s
sm,dm,cdisk R<RRT :
Spin down
Spin down
sm,cdm,disk R<R<RT :
propeller sm,cdm,loss R<R<RT :
Spin down
Spin up not efficient
The co-rotation radius can be an order of magnitude larger than the magnetosphere radius in spherical accretion (Shakura etal 2011).
The spin up torque depend on the coupling between the envelope and the NS magnetic field, the limit spin up torque is when all the captured momentum transfer to the NS.
2.2 The detailed spin evolution paths in our model
New born NS:10-100 ms
Propeller: two spin down rates
work alternatively
P eq ,d
P eq ,d P eq , s
I Ω s=−23μ2Ωs
2
c3
I Ω s=−M d Rm,d2 Ω s T disk
I Ω s=−M sRm , s2 Ωs T loss
I Ωs=0 T disk
I Ω s=−Ms Rm,s2 Ωs T loss
Accretion disk
No accretion disk
2.2 Parameters input
Binaries population synthesis (BPS) to produce BeXBs with new born NS and particular distribution of orbital period, Be/star mass, other parameters is assumed to be:
NS mass, radius: 1.4 solar mass, 10 km
Magnetic field: Gaussian, no decay, Log B=12.3, deviation: 0.3
Be/star rotation : around [0.7, 0.8] of critical Keplerian rotation rate
Equatorial disk parameters near Be/star: density: 10^[-12, -11] g/cm^3,
velocity: [2, 20] km/s, \alpha=[0.01, 0.1], n=[2, 4]
Spherical stellar wind: mass lose rate (Nieuwenhuijzen 1990), \beta=0.8
v_\infinity =[0.4, 1] v_escape.
Time proportion for two wind structure: k = T_disk/T_loss=0.05
2.3 Calculation results
2.3 Calculation results
2.3 Calculation results
2.3 Calculation results
2.3 Calculation results
2.3 Calculation results
3.1 Discussion
High eccentricity and large angle between the orbital plane and equatorial disk plane for BeXBs can be ascribed to the supernovae and kick velocity when the NS was born. A isotropic Maxwellian velocity distribution is imparted to the NS when supernovae happens in the BPS.
For ECS BeXBs :
For CCS BeXBs :skm=vkick /50
skm=vkick /265
3.1 Discussion
3.1 The contrast of two types of supernovae
3.2 conclusion
We have calculated the spin evolution of NS in a large number of BeXBs with particular orbital and mass distribution get from the BPS. Our result showed that the observed bimodal spin period distribution of BeXBs should be ascribed to the pulsar spin evolution history rather than the supernova channel.Accretion disk formed BeXBs will stay at a lower equilibrium spin period since the spin up of pulsar is much efficient than the spin down. They are responsible to the observed lower spin period peak of BeXBs.No accretion disk formed BeXBs will evolve to a higher spin period and then formed the other peak of the bimodal peak
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