Transcript - Lorentz Center

Bojan Arbutina
University of Belgrade, Serbia
The Minimum Mass Ratio for Contact Close Binary
Systems of W Ursae Majoris-type
Stellar Mergers workshop, Lorentz center
Leiden, 21 Sept 2009 - 2 Oct 2009
The Minimum Mass Ratio for Contact CBS of W UMa-type
CBs of W UMa-type
-
contact systems
- Roche model:
 eff  
2 
GM1 GM 2 1 2

2 R
r1
r2
G(M 1  M 2 )
a3
- spectral type: late F-K
- common convective envelope, nearly
equal temperatures (although q =M2/M1
~ 0.5)
- two sub-types: A and W
- primary components seems to be
normal MS stars, secondaries are
oversized for their ZAMS masses, and
can be found left from the mainsequence (see e.g. Hilditch 2001)
O
B
A
F
G
K
M
- critical equipotential surfaces (Roche lobes):
 IL ,  OL
- degree of contact (overcontact degree):
f 
   IL
 OL   IL
The Minimum Mass Ratio for Contact CBS of W UMa-type
Dynamical evolution
- driven presumably by angular
momentum loss (AML)
- magnetic activity, starspots,
magnetized stellar wind
- secular, tidal or Darwin instability
- tidal forces
circulization and synchronization
- if the timescale for the synchronization is smaller
that the AML timescale, system will remain
synchronized and orbit will shrink until, at some
critical separation, the instability sets in
- rotational and orbital angular momentum become
comparable
- instability condition: d Jtot = 0 (Jorb = 3 Jspin)
(Rasio 1995, Rasio & Shapiro 1995)
- MERGER!
W UMa
blue stragglers, FK Com
- a significant number of W UMa-type binary systems
among blue stragglers in open and globular clusters
(Kaluzny & Shara 1988).
Sir George Howard Darwin (1845-1912)
The Minimum Mass Ratio for Contact CBS of W UMa-type
The minimum mass ratio for W UMa-type CBs
(Eggleton 1983, Yakut & Eggleton 2005)
- qmin = 0.085-0.095
- AW UMa, q = 0.075
- critical separation (Rasio 1995)
- k is dimensionless gyration radius which depends on the
density distribution (for homogenous sphere k2 = 2/5)
polytrope
polytrope
Sun:
(Paczynski 1964,
Rucinski 1992,
Pribulla & Rucinski 2008)
– disagreement between theory and
observations – there are systems with the
mass ratio smaller than qmin observed !
The Minimum Mass Ratio for Contact CBS of W UMa-type
- contribution of the rotational AM of the secondary (Li & Zhang 2006, Arbutina 2007)
- qmin = 0.094-0.109
- deformation of the primary due to rotation and companion – nonzero quadrupole moment –
“apsidal motion constant”
- qmin = 0.091-0.103
(
)
- structure of the primary (k depends on the central condensation, or
- “spherical symmetry”, r
R volume radius, see Eggleton (2006)
)
The Minimum Mass Ratio for Contact CBS of W UMa-type
- instability condition:
The Minimum Mass Ratio for Contact CBS of W UMa-type
- significantly lower minimum mass ratio (Arbutina 2009) :
qmin = 0.070-0.074
- contact CBs of W UMa-type with an extremely low mass ratio
The Minimum Mass Ratio for Contact CBS of W UMa-type
The Minimum Mass Ratio for Contact CBS of W UMa-type
Interesting systems
- AW UMa
Pribulla & Rucinski (2008) find higher
mass ratio q = 0.1 and suggest that
AW UMa may not be a contact binary?
- V857 Her, q = 0.065? (Qian et al. 2006)
- spectroscopic mass ratio, Pribulla et al. (2009)
- qmin could be slightly higher if contribution from the secondary is taken into account, but it
could be lower if the star is more evolved (more centrally condensed than n = 3 polytrope)
- differential rotation (Hilditch 2001) - Yakut & Eggleton (2005) proposed it as a possible
mechanism for thermal energy transfer from the primary to the secondary component in contact
binaries, which leads to the equalization of temperatures in the common envelope.
- unstable
merger?