The Minimum Mass Ratio for Contact Close Binary 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

CBs of W UMa-type Roche model: O B A F G K M The Minimum Mass Ratio for Contact CBS of W UMa-type CBs of W UMa-type contact systems Roche model: 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 main-sequence (see e.g. Hilditch 2001) O B A F G K M critical equipotential surfaces (Roche lobes): - degree of contact (overcontact degree):

Dynamical evolution driven presumably by angular momentum loss (AML) 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) MERGER! (Rasio 1995, Rasio & Shapiro 1995) 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 W UMa-type CBs 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 (Paczynski 1964, Rucinski 1992, Pribulla & Rucinski 2008) - critical separation (Rasio 1995) - k is dimensionless gyration radius which depends on the density distribution (for homogenous sphere k2 = 2/5) polytrope – disagreement between theory and observations – there are systems with the mass ratio smaller than qmin observed ! polytrope Sun:

- “spherical symmetry”, r R volume radius, see Eggleton (2006) 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)

- instability condition: The Minimum Mass Ratio for Contact CBS of W UMa-type - instability condition:

- significantly lower minimum mass ratio (Arbutina 2009) : 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

Interesting systems - AW UMa Pribulla & Rucinski (2008) find higher 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? - 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? V857 Her, q = 0.065? (Qian et al. 2006) - spectroscopic mass ratio, Pribulla et al. (2009)