The Formation of Double Compact Objects as Gravitational

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啊 The Formation of Double Compact Objects as Gravitational Wave Sources 陈雪飞 云南天文台 2018.

啊 The Formation of Double Compact Objects as Gravitational Wave Sources 陈雪飞 云南天文台 2018. 05. 25 厦门 1

Outline • Stellar Remnants and Uncertainties • Mass Transfer in Binary Evolution • Formation

Outline • Stellar Remnants and Uncertainties • Mass Transfer in Binary Evolution • Formation of Double Compact Objects • Conclusion & Outlook

Stellar Remnants and Uncertainties 金 属 丰 度 Heger, 2003 ECSN SN kick PISN

Stellar Remnants and Uncertainties 金 属 丰 度 Heger, 2003 ECSN SN kick PISN 恒星质量 Stellar Wind, Rotation and Mixing

Stellar Wind Giacobbo et al. , 2018, MNRAS , 474, 2959 Z=0. 0002

Stellar Wind Giacobbo et al. , 2018, MNRAS , 474, 2959 Z=0. 0002

Rotation and Mixing Maeder, 1987, A&A, 178, 159 化学类均匀演化 Chemically homogeneous evolution Favored at

Rotation and Mixing Maeder, 1987, A&A, 178, 159 化学类均匀演化 Chemically homogeneous evolution Favored at low Z Yoon & Langer, 2005, A&A, 443, 643 Yoon & Langer, Norman, 2006, A&A, 460, 199 de Mink et al. , 2009, A&A, 497, 243 near contact binary systems

Massive Overcontact Binary VFTS 352 (29+29 Msun) vrot=330 km/s vrot=440 km/s Almeida et al.

Massive Overcontact Binary VFTS 352 (29+29 Msun) vrot=330 km/s vrot=440 km/s Almeida et al. 2015, Ap. J, 812, 102

Mass Transfer in Binary Evolution Roche lobe overflow Critical equipotential surface Primary L 1

Mass Transfer in Binary Evolution Roche lobe overflow Critical equipotential surface Primary L 1 Secondary M 2 M 1 Ø Expansion of the donor Ø Angular momentum loss Mass loss 、Gravitational radiation、Magnetic braking Wind Accretion Bondi-Holye-Like accretion Ph. Podsiadlowski Wind RLOF

Dynamical Mass Transfer & Common-Envelope Phase Mass transfer rate increases The star cannot keep

Dynamical Mass Transfer & Common-Envelope Phase Mass transfer rate increases The star cannot keep thermal equilibrium and expands Positive Feedback Dynamical mass transfer during which the donor is only restricted by hydrostatic equilibrium Q 1: When dynamical mass transfer starts? stable RLOF unstable RLOF Q 2: How dose common envelope evolve ? Ejection Merge Evolutionary Paths for a Binary with One Component Fulfilling its Roche Lobe

The Criterion for dynamical instability Critical equipotential surface L 1 Primary M 1 Response

The Criterion for dynamical instability Critical equipotential surface L 1 Primary M 1 Response of M 1 to mass loss Determined by stellar structure VS Secondary M 2 Response of Roche lobe Determined by mass and angular momentum loss Nuclear timescale(driven by nuclear reaction) Thermal timescale(recovery of thermal equilibrium) Dynamical timescale(recovery of hydrostatic equilibrium)

Criterion for dynamical instability Polytropic model Hjellming+ 1987 P and rho are pressure and

Criterion for dynamical instability Polytropic model Hjellming+ 1987 P and rho are pressure and density, n(=2/3) is polytropic index, and K is a constant. The critical mass ratio, qc=the donor/the accretor, is 2/3 for conservative mass transfer, and around 1 if other effects have been included. Nie+, 2012 common envelope Observations of Symbiotics Wind accretion

Common Envelope Evolution Standard Energy Budget orbital energy released Internal energy 抛射 Binding energy

Common Envelope Evolution Standard Energy Budget orbital energy released Internal energy 抛射 Binding energy of the CE Uncertainties in this scenario Ø What is the fraction of orbital energy contributing to the ejection of CE ? Ø Whether the internal energy plays a rule or not, and what’s the fraction if it works? Ø Where is the boundary between the core and envelope? Impact on numbers and separations of post-CE binaries, then merge rates particularly for double compact objects (a factor of ~3 -10 from BPS)

Searching for post-CE binaries to constrain the CEE process

Searching for post-CE binaries to constrain the CEE process

 • Significant uncertainty exists due to great uncertainty of the progenitors. • The

• Significant uncertainty exists due to great uncertainty of the progenitors. • The shortcoming cannot be resolved except for that we could know the properties of the progenitors exactly.

Short-orbital-period hot subdwarfs are excellent objects Kupfer+, 2015 He Blue:WD Red:MS Black:unknown Chen+, 2018,

Short-orbital-period hot subdwarfs are excellent objects Kupfer+, 2015 He Blue:WD Red:MS Black:unknown Chen+, 2018, in prep. Need samplers in globular clusters !

SPH simulation A NS+RG binary: time span~1010, space span~108 resolution : 1024 for 1010

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, Ap. J (Letters) Ricker, P. M. , & Taam, R. E. 2012, Ap. J USA De Marco, O. , Passy, J. -C. , Moe, M. , et al. 2011, MNRAS Passy, J. -C. , De Marco, O. , Fryer C. , et al. 2012, Ap. J USA, Australia Nandez, J. L. A. , Ivanova, N. , & Lombardi, J. C. , Jr. 2014, Ap. J Canada, Nandez, J. L. A. , Ivanova, N. , & Lombardi, J. C. 2015, MNRAS (Letters) University of Nandez, J. L. A. , & Ivanova, N. 2016, MNRAS Alberta Ivanova, N. , Justham, S. , & Podsiadlowski, P. 2015, MNRAS Ivanova, N. , & Nandez, J. L. A. 2016, MNRAS Ohlmann, S. T. , Roepke, F. K. , Pakmor, R. , & Springel, V. 2016 a, Ap. J (Letters) Ohlmann, S. T. , et al. 2016 b, MNRAS Germany Ohlmann, S. T. , Roepke, F. K. , Pakmor, R. , & Springel, V. 2017, A&A Mac. Leod, M. , & Ramirez-Ruiz, E. 2015 a, Ap. J (Letters), 798, L 19 USA, Mac. Leod, M. , & Ramirez-Ruiz, E. 2015 b, Ap. J, 803, 41 University of California Mac. Leod, M. , Macias, P. , Ramirez-Ruiz, E. , et al. 2017 a, Ap. J, 835, 282 Mac. Leod, M. , Antoni A. , Murguia-Berthier A. , et al. , 2017 b, Ap. J

Loss of corotation Han+, 1994, MN Nanz+, 2016, MN Plunge in Ø Only a

Loss of corotation Han+, 1994, MN Nanz+, 2016, MN Plunge in Ø Only a small fraction of envelope can be ejected if only orbital energy is included. Ø Recombination energy play a crucial role to eject the whole envelope, and alpha_th~1 Slow spiral-in Ø Red Luminous Novae are likely candidates for CEE At the end of plunge-in phase, only a part of CE has been ejected, the left part is outside the orbit of the inner binary with negative binding energy. During slow spiral-in phase, the orbital energy released is very little and cannot contribute to the CE ejection. But the CE expands and cools, and the gas recombination occurs and the energy stored in the gas begins to release and ejects the CE eventually.

双致密星的形成 • 基于恒星和双星演化理论提出形成图像(Idea) • 通过双星星族合成得到物理性质的统计特征(Method) • 与观测数据对比,解释并预言观测(Result) Binary Sample (more than 106) Uncertainties: IMF,

双致密星的形成 • 基于恒星和双星演化理论提出形成图像(Idea) • 通过双星星族合成得到物理性质的统计特征(Method) • 与观测数据对比,解释并预言观测(Result) Binary Sample (more than 106) Uncertainties: IMF, distributions of mass ratio, separation and eccentricity Population Synthesis (evolving the sample) Uncertainties: stellar wind, stability criterion, mass and angular momentum loss, common envelope evolution, supernovae and kick… Properties of Double Compact Objects numbers, masses, separation, eccentricity in cosmic time Frequency, Strain and Background

MS+MS Formation of Double Degenerates (Super)Giant +MS unstable RLOF Common envelope Algol, BSs gamma

MS+MS Formation of Double Degenerates (Super)Giant +MS unstable RLOF Common envelope Algol, BSs gamma description merger ejection CVs, SSS WD+MS ELM DDs MS+(Super)Giant SN Ia AM CVn ? Common envelope alpha description Single WD ejection non-degenerate He core merger ejection degenerate core WD+He star WD+WD CO+CO CO/He+He AM CVn Single WD SN Ia Chen+, 2018, Science China SN Ia Single WD after 2010

The Formation of DNSs, DBHs, BH-NS and NS-BH (standard mode merge disrupted Colpi &

The Formation of DNSs, DBHs, BH-NS and NS-BH (standard mode merge disrupted Colpi & Sesana 2016 rearranged from Tauris+, 2017, Ap. J, 846, 170

The Formation of DBHs and BH-NS (CHE) Mandel+, 2016, MNRAS Mass ratio q~1 Mtot~50

The Formation of DBHs and BH-NS (CHE) Mandel+, 2016, MNRAS Mass ratio q~1 Mtot~50 -110 Msun R: 10 Gpc-3 yr-1 Peak at z=0. 5 (twice tmerge=4 -10 Gyr of local) Marchant et al. 2017, A&A, 604, A 55

Kruckow et al. 2018, preprint (ax. Xiv: 1801. 05433) 偏 心 率 半长轴 银河系DNSs并合率:

Kruckow et al. 2018, preprint (ax. Xiv: 1801. 05433) 偏 心 率 半长轴 银河系DNSs并合率: 质量比 3. 0 Myr-1(上限 400 yr-1 Gpc-3)

Vigna-Gomez et al. 2018, preprint (ax. Xiv: 1805. 07974) 贝叶斯参数 • case BB MT

Vigna-Gomez et al. 2018, preprint (ax. Xiv: 1805. 07974) 贝叶斯参数 • case BB MT is probably stable • A natal kick distribution of two components is preferred

国内的研究情况: Liu, 2009, MNRAS/Liu+, 2010, Ap. J, e. LISA可探测的双白矮星 Liu+ 2014, Ap. J, e.

国内的研究情况: Liu, 2009, MNRAS/Liu+, 2010, Ap. J, e. LISA可探测的双白矮星 Liu+ 2014, Ap. J, e. LISA可探测的NS+WD, NS+NS, BH+BH Yu+ 2015, MNRAS, e. LISA可探测到的双中子星 Yu+ 2018, in prep, e. LISA可探测到的BH-WD Shao, Y. & Li, X. , 2018, MNRAS, BH+Pulsar(NS) binary 偏 心 率 轨道周期 Shao & Li, 2018, MNRAS