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< Rc 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 lose24/

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

),(

),(

)( )(

)( )(

aah

qq

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

av

av

v

v

v

vn

v

v

v

vpGM

M

Mj

rel

r

arx

rel

x

r

x

rel

xorbX

ϕ

05.0~ 2

2

2

orb

g

p

rj Rcir= j2 /GM

22rxrel v+vv=v

xr

x

vv

vv

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<Rperiodlong

diskaccretionR>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

PP

RR

MM

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

R

R

M

M=

GMRM

ΩRM=

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=−23

μ2Ωs2

c3

I Ω s=−M d Rm,d2 Ω s T disk

I Ω s=−M sRm , s2 Ω s 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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