Orbital evolution of compact Black-hole binaries and white dwarf binaries

Wencong Chen

Astro-ph/0511760

Astro-ph/0510331

Astro-ph/0511760

1.Introduction:

Conventional magnetic braking (MB):

radiative envelopes inoperative, Md<1.5 solar mass

Author’s suggestion:

Compact binaries with Ap & Bp stars

Irradiation driven stellar wind

Lead to significant MB

Magnetic braking of Ap/Bp stars: application to compact BH X-ray binaries

9 of 17 compact BH X-ray binaries:

P<1d, Md<1 solar mass

Galactic:

1000 short period BH binaries (Wijers, 96; Romani, 98)

How to form short period and low donor mass BH binaries?

Intermediate mass (IM) star with Strong magnetic field, irradiation driven wind

A plausible AM loss mechanism

Produce short period low mass BH binaries

2 2 62

6

1

2 8 8s dB B R

vr

24windM v r

2 d

d

GMv

R

1/ 4

1/81/ 2 13/8windm s d dr B R M GM

1/ 2

1/ 42 13/ 4wind windMB d m d s d dJ r M B R M GM

Loss rate of AM due to MB:

2. Assumptions and derivations:

Assume wind corotates out to magnetospheric radius

11

2RLOFMB d

d BH

J a M M

J a M M

1/ 2RLOFMB totJ M GM a

2 2wind RLOFmM r M a

2

2 5/ 2 4d

wind RLOF

s d L

GMM M

B R r

/d La R r

1/ 2 1/ 2 1/ 2BH d TJ G M M M a

2.1 estimate of the required wind loss rate

Mass conservative

If adot<0

For a typical mass ratio

1/3Lr Mass –radius relation of donor star

4/5dM R

23/ 2

131 2 1

15 10

wind RLOFd

s

M M M

M yr B M M yr

10 1~ 4 10windM M yr

1000sB G

8 110RLOFM M yr

5dM M

2.2 Irradiation driven winds

Irradiation stellar wind loss rate

Stellar wind was driven irradiation in compact binaries ( Ruderman 89)

Wind driving parameter

maximum

2.3 analytic results for windM

MB torque:

Total AM of system

Mass conservative and adot=0

2.4 effects on the canonical LMXB population

3. BH binary populations

Suggest part of IM star possess strong magnetic field (Ap,Bp stars)New MB in strong field systems via irradiation induced stellar wind

Cause a subset of BH binaries to evolve to short periods

Assume Bs is a constant, even during mass loss

Use an updated version of Eggleton’s code

Initial conditions: 3,4,5dM M7BHM M

, 1orb iP day

3.1 long and short period: population statistics

Ap stars ~5% in A stars

Zero magnetic field: 0.2-0.4Gyr

Strong field: 10Gyr

3.2 observational test: spectral types

4. Summary and conclusions

New MB can cause BH binaries involving Ap/Bp donor stars to evolve to short periods (P<10hr)

BH binaries with IM donor star is reasonable than ones with low mass donor star

Author’s model is successful at reproducing the short periods and low donor mass

Shortcoming:

Calculative effective temperatures are significantly higher that for those of the observed donor stars.

Astro-ph/0510331

1.introduction:

CVs: white dwarf primary

low mass main sequence secondary

Main period distribution: 1.3-10 hours

Two major features:

Period gap 2-3 hours

period minimum 1.3 hour

Standard model

Detection of a period decrease in NN Ser with ULTRACAM: evidence for strong magnetic braking or an unseen companion

In this paper:

Measure mid-eclipse timing

find period change

To calculate AM loss

Pdot~5*10^(-4) s /yr

Contamination of light curve by accretion process

So choose pre-CV NN ser

NN ser:

WD and M dwarf with ~0.15 solar mass

High time resolution of ULTRACAM ~0.15S

Deeply eclipsing >4.8mag, strong reflection effect ~0.6mag

Orbital period 0.13days

2. Analysis & results:

A best fit linear ephemeris

A best fit quadratic ephemeris

Eclipse time

Rate of period decrease

The average rate of period change

The current rate of period change

3. discussion- mechanisms for period changes:

Applegate’s mechanism (92)

Presence of third body in a long orbit around binary

A genuine AM loss

3.1 Applegate’s mechanism

Gravitational coupling

Shape change of secondary

Change of quadrupole moment

Period change

3.2 third body

Light travel time variation leads to period change

0.0043 solar mass < M3 < 0.18 solar mass

30yr < P3 < 285 yr

A low mass companion could cause the observed changes in mid-eclipse timings

3.3 AM loss models

1. Gravitational radiation

2. Standard MB

(Rappaport, 83)

3. Reduced MB

(Sills, 2000)

4. conclusions:

Two possible explanations:

Presence of a third body

Genuine AM loss: standard MB by Rappaport, no cut off

Reduced MB underestimate ~ 2 orders of magnitude