Evolution of low-mass binaries with black-hole components

L. Yungelson et al.Ref: arXiv:0806.2235

1. Model- Formation of black holes with low-mass companions

• Population of zero-age LMBHB code: SEBA 250000 initial binaries M10>25Msun

a 50% binarity (2/3 of stars in binaries) for the CE phase: αCE×λ=2

1. Model- Angular momentum loss

• Low mass components KV/MV spectral type AML via MSW:

AML via GWR:

Eqs.(1)+(2)- a “standard” model

)1(121021ln

21

42

3/1

3/2

3/10228

fMRM

GPk

dtJd t

1~1.0~2 fk

1. Model - Population of unevolved LMBHB

• Within Hubble time(13.5 Gyr) 49000 BH+MS Porb < 2 day M20<1.6Msun

MBH=12Msun

MBH=4Msun

In standard model: overflow < 15 hr → shorter period

2. Evolution of LMBHB

• In the figures below, q=M2/M1≥0.02• q=M2/M1<0.02: - circularization radius of accretion stream>outer

radius of accretion disc - how mass transfer occurs ? - Porb ≤ 2 hr mass-transfer rate < 10-10 Msun yr-1

• In “standard” model 75% q<0.02

2. Evolution of LMBHB - Luminous persistent LMBHB?• Irradiated discs are hot and stable if accre-tion rate exceeds

• No persistent LMBHB with Porb<4 hr are observed• Stable model:

370 objects

2900 objects

2. Evolution of LMBHB - Reduced angular momentum loss?

2. Evolution of LMBHB - Observational parameters of short-period LMBHB

a. Effective temperatures• Essential information of donor: spectral type• Emission of the cool star is contaminated by

radiation from disc and hot spot

b. Masses of donors

c. Mass-transfer rate

• Non-stationary quiescent accretion disc:

• According to DIM, disc is in cold thermal equilibrium if :

48.0 tcirctin frfr

Menou et al. 1999 MNL

MNL point out that if the truncation radii were slightly larger than estimated to fit observations of quiescent SXTs the discs would be globally stable

3. Cold, stable system

4. Conclusion

• Under various assumptions about the AML “standard” model unobserved persistent LMBHB pure GWR only transient systems• Mass-transfer rate consistent with upper limits on Mdot • Truncation of discs at radii close to Rcirc make disc cold

and stable, in this case not relate to DIM “external factors” – enforced mass transfer ,Rin •

2CE