Formation of double white dwarfs and AM CVn stars

Transcription

1 Formation of double white dwarfs and AM CVn stars Marc van der Sluys 1,2 Frank Verbunt 1, Onno Pols 1 1 Utrecht University, The Netherlands Mike Politano 3, Chris Deloye 2, Ron Taam 2, Bart Willems 2 2 Northwestern University, Evanston, IL, USA; 3 Marquette University, Milwaukee, WI, USA AM CVn workshop, Cape Town, September 2, 2008

2 Outline 1 Common envelopes Observed double white dwarfs Common-envelope evolution Envelope ejection 2 Progenitor models Single-star models 3 Reverse evolution Second mass-transfer phase Stable first mass-transfer phase Envelope ejection as first mass transfer 4 Future work

3 Observed double white dwarfs WD , Adapted from Maxted et al., 2002

4 Observed double white dwarfs System P orb a orb M 1 M 2 q 2 τ (d) (R ) (M ) (M ) (M 2 /M 1 ) (Myr) WD ± ± ± WD ± WD ± WD ± PG ± WD ± WD ± 0.05 HE ± ± ± WD a ± ± ± a HE ± ± ± a Unclear which white dwarf is older See references in: Maxted et al., 2002 and Nelemans & Tout, 2005.

5 Common envelope Average orbital separation: 7 R Typical progenitor: M c > 0.3 M R 100 R

6 Common envelope

7 Envelope ejection Classical α-common envelope (spiral-in): orbital energy is used to expel envelope (Webbink, 1984): [ G M1f M 2 U bind = α CE G M ] 1i M 2 2 a f 2 a i α CE is the common-envelope efficiency parameter γ-envelope ejection (EE, spiral-in not necessary): envelope ejection with angular-momentum balance (Nelemans et al., 2000): J i J f J i = γ CE M 1i M 1f M 1i + M 2 γ CE 1.5 is the efficiency parameter

8 Envelope ejection Assumption: Envelope ejection occurs much faster than nuclear evolution, hence: core mass does not grow during envelope ejection no accretion by companion during envelope ejection From Eggleton models: White-dwarf mass fixes evolutionary state of progenitor Giant radius determines orbital period of progenitor Envelope binding energy dictates what α CE is needed

9 Progenitor models Eggleton code 199 singe-star models M RGB AGB

10 Progenitor models R provides P orb at onset of EE RGB AGB

11 Progenitor models Envelope U bind provides α CE RGB AGB

12 Evolutionary scenarios Stable + unstable MS + MS Unstable + unstable MS + MS Stable M.T. (cons.) Unstable M.T. (γ-ee) WD + MS WD + MS Unstable M.T. (α-ce) Unstable M.T. (α, γ-ee) WD + WD WD + WD

13 Confusogram Confusogram Observation: M wd1, M wd2, P dwd Yes Possible progenitor: M wd1, M 2, Progenitor model: M 2, R 2, M c, U b R 2 = R max when M c = M wd2? No Not a progenitor P prog (M 1,M 2,R 2) P prog P dwd : acceptable α/γ? Yes No Accept this model as a possible progenitor Reject as progenitor Marc van der Sluys How the Giant lost its mantle and became a Dwarf NUTGM October 19, 2006

14 α-ce results Accept cases with: 0.1<α ce <10 Assume no errors in observed masses

15 α-ce results Accept cases with: 0.1<α ce <10 Introduce errors in observed masses: ± 0.05 M

16 Conservative first mass transfer Maximum P orb after stable mass transfer with q i = 0.62 (Nelemans et al., 2000) Only 5 systems have CE solutions with P orb < P max

17 Conservative first mass transfer CE solutions that may be formed by stable mass transfer Conservative mass transfer: M tot and J orb fixed One free parameter: q i

18 Conservative mass transfer: M, P 570 binary models, computed to match pre-ce systems spiral-in stable Results: 39% dynamical 18% contact 43% DWD

19 Conservative mass transfer: q, t 1414 fits 0957, 1101, 1704b and 2209 nearly fit Out of ten systems, 1 can be explained, 4 are close

20 Conclusions Conservative MT: More accurate models change α-ce only slightly After stable mass transfer, white-dwarf primaries have too low mass and too long orbital periods We can reproduce perhaps 1 4 out of 10 systems, all with α ce > 1.6 Conservative mass transfer cannot explain the observed double white dwarfs

21 Angular-momentum balance Average specific angular momentum of the system: J i J f J i = γ s M 1i M 1f M tot,i Specific angular momentum of the accretor: [ J i J f = γ a 1 M ( )] tot,i M1f M 1i exp J i M tot,f M 2 Specific angular momentum of the donor: J i J f J i = γ d M 1i M 1f M tot,f M 2i M 1i

22 Models Number of progenitor models: Filters: 10+1 observed systems 199 progenitor models in our grid 11 variations in observed mass: 0.05, 0.04,..., M total: P 198 n=1 n 2.4 million dynamical MT: R > R BGB and q > q crit age: τ 1 < τ 2 < 13 Gyr EE-parameter: 0.1 < α ce, γ < 10 Candidate progenitors left:

23 Results for γ s + α ce

24 Results for γ d + γ a

25 Results: overview Select systems with: 0.8 < α ce < < γ s < < γ a,d < 1.1 System 1: γ sα ce 2: γ sγ s 3: γ aα ce 4: γ aγ a 5: γ dα ce 6: γ dγ a Best: ,3,5, ,2,4,5, ,2,3,5, ,4,6 1704a + + 1,2 1704b ,2,4,5, ,2,5,6 +: α, γ within range, : α, γ outside range

26 Results: overview Select systems with: 0.8 < α ce < < γ s < < γ a,d < 1.1 System 1: γ sα ce 2: γ sγ s 3: γ aα ce 4: γ aγ a 5: γ dα ce 6: γ dγ a Best: 0135 / +/ +/ / +/ +/ 2,3,5, /+ +/+ +/ +/ +/+ +/+ 1,2,5, /+ +/+ / +/ +/+ +/+ 1,2,5, / +/ +/ / +/ +/ 1,5, / +/+ +/ +/ +/+ +/+ 2,5, / +/ +/ +/ +/ +/ /+ +/+ +/+ +/+ +/+ +/ / +/+ / +/+ / +/+ 2,4,6 1704a +/ +/ / / / / 1,2 1704b +/ +/ / +/ +/ +/ 1,2,4,5, /+ +/+ / / +/ +/+ 1,2,6 +: α, γ within range, : α, γ outside range +: ( t) < 50%, : 50% < ( t) < 500%, : ( t) > 500%

27 Results: example solution γ d = 0.96 γ a = 1.05 τ = 450 Myr

28 Results: solutions WD Mthd. γ 1 γ 2, τ/myr M 1i M 2i P i P m M 1f M 2f P f α ce2 obs mdl M M d d M M d 0135 γ d γ a γ d γ a γ d γ a γ d γ a γ d γ a γ d γ a γ d γ a γ d γ a a γ d γ a b γ d α ce γ d γ a

29 Conclusions Conservative mass transfer cannot explain the observed double white dwarfs Unstable envelope ejection can do this Several EE descriptions can reconstruct observed masses and periods γ s γ s and γ d γ a can in addition explain most observed cooling-age differences

30 Future work Population-synthesis code Based on grid of single-star models with Eggleton code Models provide M c, R, U bind Stellar wind, tidal coupling included Used for modelling binary mergers due to CE spiral-in (Politano et al., 2008) Second common-envelope phase implemented to study formation of double white dwarfs Need to: include naked helium-star models include more physics, e.g. magnetic braking

31 Future work Purpose: Study effect of e.g.: different α/γ-prescriptions wind mass loss angular-momentum loss on formation of e.g.: double white dwarfs He star/white dwarf binaries AM CVns CVs