1.3. Treatment of the mass transfer episodes

1. Monte Carlo simulations of the binary white dwarf population: a progress report Judit Camacho1, Santiago Torres1,2 & Enrique García-Berro1,2 1Departament Física Aplicada, Universitat Politècnica de Catalunya, (UPC) 2Institut d'Estudis Espacials de Catalunya (IEEC) 2. Example of mass transfer Abstract We present a detailed Monte Carlo simulator of the population of binary stars within the solar neighborhood. We have used the most updated models for stellar evolution (Hurley et al. 2000), a complete treatment of the Roche lobe overflow episodes, as well as a full implementation of the orbital evolution. Special emphasis has been placed on processes leading to the formation of binary systems in which one of the members is a white dwarf. • Initial conditions: • The overflow episodes take place during the MS of the donor and the accreted star. • Mass transfer proceeds in a nuclear timescale with the exception of two thermodynamic episodes. • Mass transfer is highly non-conservative. • The donor finishes the MS in a detached system. • Final conditions: • The donor will overflow again before He ignition, having a degenerate He core. • Afterwards, a CE phase will happen, leading to a merger. Mdon=1.13M☉ Macc=0.74M☉ a= 3.60 R☉ Porb=0.58 days Mdon=0.84M☉ Macc=0.77M☉ a= 3.49 R☉ Porb=0.59 days 1. The model • 1.1The simulator • Monte Carlo simulator of the binary population within the solar neighborhood based, based in our Monte Carlo simulator of the single white dwarf population. 3. General statistics 1.2 Underlying physics • We have used the stellar evolutionary tracks of Hurley et al. (2000). • A standard IMF (Scalo 1998), for M < 20M☉ was adopted. • We have used an constant SFR. • A disk age of 11 Gyr was adopted. • Orbital separations have been computed according to a logarithmic distribution ψ=Ln(a)=kfor2 R☉ ≤ a ≤ 104 R☉(Nelemans 2001). • Eccentricities have been calculated according to a thermal distribution f(e)=2ebetween0 ≤ e ≤ 0.9(Heggie 1975). • Tidal effects (circularization and synchronization) have been taken into account (Zahn 1977, 1989, Hut 1981). • Wind mass-loss was considered. 5. Eccentricity versus orbital period 4. White dwarf formation 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. 1.3. Treatment of the mass transfer episodes • The Roche lobe radius has been modelled according to Eggelton (1983). • The common envelope phase has been treated according to Nelemans & Tout (2005). • For the overflow treatment we have used the formalism of Webbink (1985) except when the two stars enter in the CE with convective envelope, then we use double CE phase of Belczynski et al. (2008). 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. References Belczynski, K., Kalogera, V., Bulik, T., 2008, arXiv:0802.2748 Catalán, S., Isern, J., García-Berro, E., Ribas, I., 2008, arXiv:0804.3034v1 Eggleton, P.P., 1983, ApJ, 268, 368 Heggie, D.C., 1975, MNRAS, 173, 729 Hurley, J.R., Pols, O.R., & Tout, C.A., 2000, MNRAS, 315, 543 Hut, P., 1981, A&A, 99, 126 Iben, I., Ritossa, C., García-Berro, E. , 1997, ApJ, 489, 772 Marigo, P., Bressan, A., Chiosi, C., 1996, A&A, 313, 545 Nelemans, G., Yungelson, L.R., Portergies Zwart, S.F., & Verbunt, F., 2001b, A&A, 365, 491 Nelemans, G., Tout, C.A., 2005, MNRAS, 365, 753 Poelarends, A.J.T., Herwing, F., Langer, N., Heger, A., 2007, ApJ, 675, 614 Scalo, J., 1988, in ‘’The Stellar Initial Mass function’’, E.d.: G. Gilmore and D. Howell, PASP Conf. Ser., 142, 201 Zahn, J.P., 1977, A&A, 57, 383 Zahn, J.P., 1989, A&A, 220, 112 6. Final mass ratio of the components q=mWD/M2finalversus 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 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 • Detached binaries: • White dwarf + giant. • White dwarf + core helium burning (CHeB).