1.3. 1.3. Treatment of the mass transfer Treatment of the mass transfer

episodesepisodes The Roche lobe radius has been modelled The Roche lobe radius has been modelled according to Eggelton (1983).according to Eggelton (1983).

The common envelope phase has been The common envelope phase has been treated according to Nelemans & Tout (2005).treated according to Nelemans & Tout (2005).

For the overflow treatment we have used For the overflow treatment we have used the formalism of Webbink (1985) except when the formalism of Webbink (1985) except when the two stars enter in the CE with convective the two stars enter in the CE with convective envelope, then we use double CE phase of envelope, then we use double CE phase of Belczynski et al. (2008). Belczynski et al. (2008).

Monte Carlo simulations of the binary Monte Carlo simulations of the binary white dwarf population: a progress white dwarf population: a progress

reportreport

Monte Carlo simulations of the binary Monte Carlo simulations of the binary white dwarf population: a progress white dwarf population: a progress

reportreportJudit Camacho1, Santiago Torres1,2 & Enrique García-Berro1,2

AbstractAbstractWe present a detailed Monte Carlo simulator of We present a detailed Monte Carlo simulator of

the population of binary stars within the solar the population of binary stars within the solar

neighborhood. We have used the most updated neighborhood. We have used the most updated

models for stellar evolution (Hurley et al. 2000), models for stellar evolution (Hurley et al. 2000),

a complete treatment of the Roche lobe overflow a complete treatment of the Roche lobe overflow

episodes, as well as a full implementation of the episodes, as well as a full implementation of the

orbital evolution. Special emphasis has been orbital evolution. Special emphasis has been

placed on processes leading to the formation of placed on processes leading to the formation of

binary systems in which one of the members is a binary systems in which one of the members is a

white dwarf. white dwarf.

1Departament Física Aplicada, Universitat Politècnica de Catalunya, (UPC) 2Institut d'Estudis Espacials de Catalunya (IEEC)

11. The model11. The model

1.11.1 The simulatorThe simulatorMonte Carlo simulator of the binary Monte Carlo simulator of the binary

population within the solar neighborhood population within the solar neighborhood

based, based in our Monte Carlo simulator of based, based in our Monte Carlo simulator of

the single white dwarf population.the single white dwarf population.

1.2 Underlying physics1.2 Underlying physics We have used the stellar evolutionary We have used the stellar evolutionary tracks of Hurley et al. (2000).tracks of Hurley et al. (2000).

A standard IMF (Scalo 1998), for M < 20MA standard IMF (Scalo 1998), for M < 20M☉☉ was adopted.

We have used an constant SFR. We have used an constant SFR.

A disk age of 11 Gyr was adopted.A disk age of 11 Gyr was adopted.

Orbital separations have been computed Orbital separations have been computed according to a logarithmic distribution according to a logarithmic distribution ψψ==LnLn(a)=k(a)=k for for 2 R2 R☉ ≤ ≤ aa ≤ 104 R ≤ 104 R☉ (Nelemans (Nelemans

2001).2001).

Eccentricities have been calculated Eccentricities have been calculated according to a thermal distribution according to a thermal distribution f(e)f(e)=2e=2e between between 0 ≤ 0 ≤ ee ≤ 0.9 ≤ 0.9 (Heggie 1975).(Heggie 1975).

Tidal effects (circularization and Tidal effects (circularization and synchronization) have been taken into account synchronization) have been taken into account (Zahn 1977, 1989, Hut 1981).(Zahn 1977, 1989, Hut 1981).

Wind mass-loss was considered.ind mass-loss was considered.

33. General statistics33. General statistics

CASE A (single)

CO WD 92 %

ONe WD 8 %

CASE C

He-giant +He-WD 100 %

CASE B

He-WD+ MS 99 %

He-WD+He-WD 1 %

TPAGB

CO WD + MS 81.7 %

CO WD + He-MS 8.5 %

ONe WD + MS 8.0 %

CO WD + He-WD 1.4 %

ONe WD + He-MS 0.4 %

DETACHED BINARIES

CO WD + MS 61.92 %

CO WD + CO WD 30.36 %

ONe WD + CO WD 2.92 %

CO WD + Giant 1.86 %

ONe WD + MS 1.19 %

ONe WD + ONe WD 0.81 %

CO WD + CHeB 0.76 %

ONe WD + Giant 0.07 %

ONe WD + CHeB 0.07 %

CO WD + AGB 0.04 %

Progenitor He WDs

CASE B 95.5 %

CASE C 4 %

TPAGB CASE

0.5 %

Progenitor CO WDs

DETACHED BINARY

91 %

TPAGB CASE 9 %

Progenitor ONe WDs

DETACHED BINARY

85 % (443)

TPAGB CASE 15 % (69)

66. Final mass ratio of the components q=mWD/M2final versus semi axis66. Final mass ratio of the components q=mWD/M2final versus semi axis

Red points: CASE B

Blue points: RLOF during the TPAGB

Green points: detached binaries

In all cases the secondary is a MS star

Detached binaries:

• White dwarf + giant.

• White dwarf + core helium burning (CHeB).

He DWD = He WD + He WD via CASE B

CO/ONe DWD = CO/ONe Wd + CO/ONe WD via binary detached or TPAGB case

CO/ONe WD + He WD via TPAGB case

CO WD + He-MS via TPAGB case

55. Eccentricity versus orbital period55. Eccentricity versus orbital period

Red points: white dwarfs resulting from CASE B RLOF.

Blue points: white dwarfs resulting from RLOF during the TPAGB

Green points: detached binaries.

Magenta points: white dwarfs resulting from CASE C RLOF.

Systems resulting in a double white dwarf or a white dwarf plus a He-star, circularize after CE.

Most of the systems resulting in white dwarf plus a main sequence star with Porb < 10 days, circularize after CE, and the rest are very likely to circularize during the main sequence phase of the secondary.

44. White dwarf formation44. White dwarf formation

ReferencesReferencesBelczynski, K., Kalogera, V., Bulik, T., 2008, arXiv:0802.2748Belczynski, K., Kalogera, V., Bulik, T., 2008, arXiv:0802.2748

Catalán, S., Isern, J., García-Berro, E., Ribas, I., 2008, Catalán, S., Isern, J., García-Berro, E., Ribas, I., 2008, arXiv:0804.3034v1arXiv:0804.3034v1

Eggleton, P.P., 1983, ApJ, Eggleton, P.P., 1983, ApJ, 268268, 368, 368

Heggie, D.C., 1975, MNRAS,Heggie, D.C., 1975, MNRAS, 173 173, 729, 729

Hurley, J.R., Pols, O.R., & Tout, C.A., 2000, MNRAS, Hurley, J.R., Pols, O.R., & Tout, C.A., 2000, MNRAS, 315315, 543, 543

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Iben, I., Ritossa, C., García-Berro, E. , 1997, ApJ, Iben, I., Ritossa, C., García-Berro, E. , 1997, ApJ, 489489, 772, 772

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Scalo, J., 1988, in ‘’The Stellar Initial Mass function’’, E.d.: G. Scalo, J., 1988, in ‘’The Stellar Initial Mass function’’, E.d.: G. Gilmore and D. Howell, PASP Conf. Ser., Gilmore and D. Howell, PASP Conf. Ser., 142142, 201 , 201

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Entire binary population generated: 88896

Relative to the entire binary population

with t ≤ tdisk

White dwarfs in binaries

CASE AOverflow during the

core hydrogen burning (MS)

15 % 0 %

CASE BOverflow before He-ignition (subgiant /

giant)7 % 17 %

CASE COverflow before C-ignition (supergiant) 6 % 1 %

TPAGBCASE

Overflow during TPAGB (supergiant) 1 % 6 %

DETACHED BINARIES 71 % 76 %

22. Example of mass transfer22. Example of mass transfer

•Initial conditions:

•The overflow episodes take place during the MS The overflow episodes take place during the MS of the donor and the accreted star.of the donor and the accreted star.•Mass transfer proceeds in a nuclear timescale Mass transfer proceeds in a nuclear timescale with the exception of two thermodynamic with the exception of two thermodynamic episodes.episodes.•Mass transfer is highly non-conservative.Mass transfer is highly non-conservative.•The donor finishes the MS in a detached system.The donor finishes the MS in a detached system.•Final conditions:Final conditions:

•The dThe donor will overflow again before He ignition, having a degenerate He core.•Afterwards, a CE phase will happen, leading to a merger.

Mdon=0.84M☉ Macc=0.77M☉

a= 3.49 R☉ Porb=0.59 days

Mdon=1.13M☉ Macc=0.74M☉

a= 3.60 R☉ Porb=0.58 days