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’Observed’ double-star statistics from population synthesis Consequences for Gaia simulations

’Observed’ double-star statistics from population synthesis Consequences for Gaia simulations. Staffan Söderhjelm, 2004-07-05. Basic assumptions. ’Standard’ IMF, low-mass limit 0.03 Msun Fixed proportion f D made to binaries with ’reasonable’ f(q) and f(a)

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’Observed’ double-star statistics from population synthesis Consequences for Gaia simulations

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  1. ’Observed’ double-star statistics from population synthesisConsequences for Gaia simulations Staffan Söderhjelm, 2004-07-05

  2. Basic assumptions • ’Standard’ IMF, low-mass limit 0.03 Msun • Fixed proportion fD made to binaries with ’reasonable’ f(q) and f(a) • Rest (1-fD) remains single (25% in what follows) • All ages (0-12 Gyr) equally probable (constant SFR) • Full binary evolution with Hurley et al BSE-code

  3. Analysis in absolute magnitude bins and division in four classes: • single: True singles • visual: ’Visual’ pairs with magnitude difference between comp. Dm < 6 • ast(*): ’Astrometric’ pairs with stellar secondary • ast(w): ’Astrometric’ pairs with white dwarf secondary

  4. Large ’spurious’ variations along the Main Sequence (fD=75% at all masses) 'easy' doubles, defined (ad hoc) to have Dm < 2 and a=10-1000 a.u. represent 4 to 10% only

  5. Apparent variation of the binary frequency (fD=75%) visual ast(*) ast(w)

  6. ’Observational’ distributions • a=semi-major axis, Dm = magnitude difference • Reasonably decoupled f(a,Dm)~f(a)f(Dm) • Input (Duquesnoy-Mayor) f(a) unchanged above some ac lower limit • f(Dm) highly variable with absolute magnitude • Distribution of astrometric secondary stellar masses almost rectangular

  7. ac,the lower limit for log-normal a depends on the masses ’F-G’ ’B’ ’O’

  8. The ’observed’ f(Dm) varies greatly with the absolute magnitude O OB B A FG K bright M faint M

  9. Stellar secondary masses ’uniformly’ distributed to an upper limit depending on primary mass(primary=B,A,FG,K,bright M,faint M type stars) K FG A B bright M faint M

  10. White dwarf secondaries are more massive for massive primaries primary mass, wd secondary mass

  11. Adding binaries to a single-star Galaxy model • Replace each single star with one of the four categories (single,visual,ast(*),ast(w)) • For ’visual’, select Dm according to ’observed’ distribution, adjust MV(primary) to keep MV(system)=original MV • For ’ast(*)’ select secondary mass from uniform distr, for ’ast(w)’ take mean mass • For any binary, select (log-normal) a between ac and 105 au

  12. Conclusions • Observed ’binary frequencies’ not easy to interpret in relation to ’birth frequency’ • Large variations with mass/absolute magnitude need careful normalizations • A single-star Galaxy model can be relatively easily modified to give realistic numbers of ’long-period’ (P> weeks) binaries • Evolutionary aspects (fraction of wd secondaries!) smoothly variable with mass

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