Problems in Binary Evolution

Xuefei CHEN [email protected] Yunnan Observatories, Chinese Academy of Science

1 Outline

• Binary Evolution and Binary Population Synthesis

• Uncertainties in Modeling Binary Evolution

• Observation Constraints I. Binary evolution and binary population synthesis Roche Model for Binary Evolution Both components are assumed to be point masses or completely spherically symmetric.

2 GM GM ω 2 Φ = − 1 − 2 − s r1 r2 2

2 A Φ const ϕ ≡ − • = L1 1 + q GM 1

Equipotential surfaces in the co-rotating frame of a binary Mass transfer between the components

I. Roche lobe overflow (RLOF) R* >~ RL Critical equipotential surface Expansion of the donor Primary L1 Secondary Angular momentum loss M1 M2 Mass loss ,Gravitational wave radiation Magnetic braking

II. Wind mass transfer R* < RL Bondi-Holye-Like accretion Wind RLOF

Ph. Podsiadlowski Dynamical Mass Transfer & Common-Envelope Phase

• M The star loses thermal equilibrium and expands Positive Feedback

Dynamical mass transfer during which the donor is only restricted by hydrostatic equilibrium

Chen & Han,2008, MNRAS CEE

Ivanova Evolutionary Paths of a Binary when one of stars fulfills its Roche lobe

stable RLOF unstable RLOF period Orbital WD mass Common Envelope Evolution Li et al. 2019, ApJ CEE A long-period binary

Ejection Merge A short-period binary A single star Formation of Peculiar Stars

Cataclysmic variables ( CVs） Low/High mass X-ray binaries Millisecond pulsars Double Compact Binaries (DBHs, DNSs,DWDs, BH-NS, NS-WD, BH-WD) Supernovae (including SNe Ia) Planetary nebulae Barium/CH stars Subdwarf B stars Blue stragglers Symbiotic stars Extremely low-mass WDs ……

Binary Population Synthesis (BPS)

• To propose formation scenario(s) （Idea） • To obtain statistical properties via BPS（Method） • Comparing with and predicting observations （Result）

Binary Sample (more than 106) Uncertainties: IMF, distributions of mass ratio, separation and eccentricity

Population Synthesis (evolving the sample) Uncertainties: stability criterion, mass and angular momentum loss, common envelope evolution, stellar wind, supernovae and kick…

Properties of the Objects interested numbers,masses, mass ratio, separation etc and features special for certain stars e.g frequency, strain and background for gravitational wave sources,

II. Fundamental Problems in Binary Evolution Q1: Dynamical Mass Transfer stable RLOF unstable RLOF

Ejection Merge

Q2: Common Envelope Evolution The Criterion for dynamical instability critical equipotential surface

L1 Primary M1 Secondary M2

Response of M1 to mass loss VS Response of Roche lobe

∂lnR ∂lnR1 1 ∂lnRL ζ th= ∂lnM |th ζ ad= ∂lnM |ad ζ = | 1 1 L ∂lnM1 RLOF

Determined by stellar structure Determined by mass and angular momentum loss

(ζ ad ,ζ th ) > ζ L Nuclear timescale（driven by nuclear reaction）

ζ ad > ζ L > ζ th Thermal timescale（recovery of thermal equilibrium）

Dynamical timescale（recovery of hydrostatic equilibrium） ζ L >ζ ad Criterion for dynamical instability ζ L >ζ ad Polytropic model Hjellming+ 1987 P and rho are pressure and density, P = Kρ1+1/n n(=2/3) is polytropic index, and K is a constant.

The crical mass rao, qc=the donor/the accretor, is 2/3 for conservave mass transfer, and around 1 if other eﬀects have been included.

Nie+, 2012

common envelope Wind accreon

Observaons of Symbiocs Post –AGB binaries Barium/CH star, CEMP stars Criterion for dynamical instability ζ >ζ Detailed Binary Evolution Calculations L ad

Chen+, 2008

Han+, 2002

qc ~ 1.1-1.3, up to ~2.0 sometimes Long-period blue stragglers

The mass donors: AGB/FGB HST far UV Gosnell, 2015, ApJ Chen+, 2008, MNRAS, 387, 1416

case C NGC 188: 21 BSS Age：~7 Gyr

HST COS far-UV spectroscopy.

case B

Gosnell,2019, ApJ Criterion for dynamical instability ζ L >ζ ad Ge+ 2010, ApJ 717, 724 Adiabatic Mass Loss Model Ge+ 2015, ApJ 812, 40 Ge+ 2019, ApJ, in prep.

Energy transport

Entropy profile is fixed

Energy generation Chemical profile is fixed too Ge+, 2010, 2015, ApJ

Radius Log AGB

HG For FGB &AGB donors FGB MS Before: qc <~ 1, CEE only

Now: qc~1.4 – 5.0 some stable RLOF , some CEE

Log Mass Formation of double degenerates/type Ia supernovae

MS+MS

(Super)Giant +MS unstable

Common envelope （gamma-formalism）

Liu+, 2019, A&A WD+MS Tow different descriptions

MS+(Super)Giant stable Symbiotic stars Common envelope (alpha-formalism)

Ejection SN Ia Common Envelope Evolution

Standard Energy Budget 抛射

αCEΔEorb ≥ Ebind Internal Han+, 1994, MN energy GM1(M1 − Mc ) αCEΔEorb +αthEth ≥ Ebind = Egr = λR1 To determine merger or ejection, and the period after ejection

Impact on numbers and separations of post-CE binaries, then merge rates, for double compact objects, by a factor of ~3-10 from BPS Searching for post-CE binaries to constrain the CEE process

• WD+MS from SDSS and LAMOST and follow-up observations • Binary Central Stars in planetary nebulae • Cataclysmic variables • Subdwarfs in binaries • Double degenerates • ….

• Significant uncertainties due to great uncertainty of the progenitors.

• Cannot be resolved except for that we could know the properties of the progenitors exactly. SPH simulation A NS+RG binary: time span~1010, space span~108 resolution : 1024 for 1010 time steps 抛射

Ricker, P. M., & Taam, R. E. 2008, ApJ (Letters) Ricker, P. M., & Taam, R. E. 2012, ApJ USA

De Marco, O., Passy, J.-C., Moe, M., et al. 2011, MNRAS , Passy, J.-C., De Marco, O. , Fryer C., et al. 2012, ApJ USA Australia Nandez, J. L. A., Ivanova, N., & Lombardi, J. C., Jr. 2014, ApJ Canada， Nandez, J. L. A., Ivanova, N., & Lombardi, J. C. 2015, MNRAS (Letters) Nandez, J. L. A., & Ivanova, N. 2016, MNRAS University of Ivanova, N., Justham, S., & Podsiadlowski, P. 2015, MNRAS Alberta Ivanova, N., & Nandez, J. L. A. 2016, MNRAS Ohlmann, S. T., Roepke, F. K., Pakmor, R., & Springel, V. 2016a, ApJ (Letters) Ohlmann, S. T., et al. 2016b, MNRAS

Ohlmann, S. T., Roepke, F. K., Pakmor, R., & Springel, V. 2017, A&A Germany

MacLeod, M., & Ramirez-Ruiz, E. 2015a, ApJ (Letters), 798, L19 USA， MacLeod, M., & Ramirez-Ruiz, E. 2015b, ApJ, 803, 41 University of California MacLeod, M., Macias, P., Ramirez-Ruiz, E., et al. 2017a, ApJ, 835, 282 MacLeod, M., Antoni A., Murguia-Berthier A., et al., 2017b, ApJ GM1(M1 − Mc ) αCEΔEorb +αthEth ≥ Ebind = Egr = , Loss of corotation λR1 Han+, 1994, MN

Nanz+, 2016, MN Ø Only a small fraction of envelope can be ejected if only orbital energy is included. Plunge in Ø Recombination energy play a crucial role to eject the whole Slow spiral-in envelope, and alpha_th~1

Ø Red Luminous Novae are likely candidates for CEE

During slow spiral-in phase, the orbital energy released is very little and cannot contribute to the CE ejection. But the CE expands and At the end of plunge-in phase,only a part of CE cools,and the gas recombination occurs and has been ejected,the left part is outside the orbit the energy stored in the gas begins to release of the inner binary with negative binding energy. and ejects the CE eventually.

III. Observation constraints Hot subdwarf B stars

RHB

BHB L hot subdwarfs

EHB

T Extreme Horizontal Branch stars

⊙ M ≤ 0.02M⊙ He M ~ 0.5M env Observaons more than half are in binaries Allard et al. 1994, Thejll et al. 1999, Aznar Cuadrado & Jeffery 2001

>2/3 are in binaries, orbital periods from hours to days, masses around 0.5Ms some with WD companions • (Log P, Mcomp) • (Teff, log g) Maxted et al. 2001 • P • Log (g/Teff^4) • Mass function A binary model for sdB stars • Birthrate Han et al., 2002, 2003 • Number density • Fraction of sdB+MS • Fraction of close sdB binaries • …… sdB stars with short-orbital periods

Determined by He ignion

sdB+WD binaries sdB+MS binaries

Progenitors are at the tip of RGB and the properties are known sdB stars with short-orbital periods

Kupfer+, 2015 Blue：WD Red：MS Black：unknown

Chen+, 2019, in prep.

• alpha_CE seems dependent on the type of companions • Need samplers in globular clusters sdB stars with long-orbital periods

Han+, 2002,2003, MNRAS Chen+, 2013, MNRAS Observaons

23 sdB+DM binaries Vos+, 2019，MNRAS

Chen+, 2013, MNRAS Critical mass ratio for dynamical instability

Vos+, 2019，MNRAS Summary

Dynamical mass transfer and common envelope evolution are key processes in binary evolution, which determine the evolutionary destiny of binaries, the formation scenarios of peculiar stars, and the numbers and characteristics of post-CE binaries.

Progress has been achieved for both the processes in recent years.Preliminary applications of the progress have already shown significant improvement in the formation of some peculiar stars.

Non-conservative mass transfer is also important for binary evolution but there are no constraints on it yet.

Thanks for Your Attention sdB stars with short-orbital periods Determined by He ignition

sdB+MS binaries sdB+WD binaries Solid: gravitational Dashed: internal Ø Progenitors are at the tip of RGB Ø May trace the contribution of internal energy Kupfer+, 2015 Pop I

Black : αth = 0, αCE = 0.25, 0.50, 0.75, 1.0

Red : αCE = 0.5, αth = 0.25, 0.50, 0.75, 1.0

Blue : αCE = 0.75, αth = 0.25, 0.50, 0.75, 1.0

lpha_CE a lpha_CE a

2 2 log Pi M2/(r2 +rc )

For dM companions, there is some relationship between alpha-CE and initial orbital parameters/structures. But bot for WD companions. Roche Lobe Overflow Ge et al. 2015, ApJ Critical equipotential surface

Primary L1 Secondary

M1 M2

Ø Expansion of the donor

Ø Angular momentum loss Mass loss Gravitational wave radiation Magnetic braking Other Uncertainties in Modeling Binary Interactions

Non-conservative mass transfer Various studies on classes of particular binaries have shown that mass transfer must often be very non-conservative.

Ø How much mass lost from the system Ø The specific angular momentum taken away by the lost material

Different reasonable prescriptions can give very different evolutionary paths.

• Jeans mode (Fast wind) (M1)

• Isotropic re-emission (M2)

• L1 or L2 …… The Formation of Type Ia Supernovae

unstable RLOF stable RLOF CEE

ejection CO WD

Han+, 2004, MNRAS Meng+,2009, MNRAS Stable RLOF Li+, 1997,ApJ unstable RLOF Liu+,2019,A&A CEE

Wang+, 2009, MNRAS CO WD+CO/He WD He star Channel

Ivanova+, 2013, A&ARv