University of Belgrade, Serbia

1. 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

2. 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 leftfrom 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):

3. The Minimum Mass Ratio for Contact CBS of W UMa-type W UMa blue stragglers, FK Com • 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) • 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)

4. 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) - kis dimensionless gyration radius which depends on the density distribution (for homogenous spherek2 = 2/5) polytrope –disagreement between theory and observations – there are systems with the mass ratio smaller than qminobserved ! polytrope Sun:

5. 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 (kdepends on the central condensation, or ) - “spherical symmetry”, r R volume radius, see Eggleton (2006)

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

7. 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

8. The Minimum Mass Ratio for Contact CBS of W UMa-type

9. 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)