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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?