Classification of tidal disruption events by the stellar orbits
KH et al. 2017 (submitted to ApJ)
Kimi Hayasaki (CBNU) In collaboration with Shiyan Zhong1 , Shuo Li1 , Peter Berczik1, and Rainer Spurzem1,2,3 1National Astronomical Observatory China / Chinese Academy Science 2Kavli Institute for Astronomy and Astrophysics 3Astronomisches Rechen-Institut, Zentrum fu r ̈ Astronomie, University of Heidelberg, Germany Outline
1. Introduction # Tidal disruption events（TDEs)
2. Classification of TDEs by the stellar orbits # Our hypothesis # Testing it by N-body experiments 3. Summary and Discussion 1. Introduction Scientific motivation for studying TDEs
1. Probe of quiescent supermassive black holes (SMBHs) 2. Contribution to SMBH growth 3. Laboratory for super-Eddington accretion and outflow physics 4. Gravitational wave source candidates
Good phenomena for multi-messenger astronomy Tidal Disruption of a star by a SMBH
Standard Picture 1. Spread in debris energy by tidal force Rees (1988) GMbh r ⇤ ~1pc 5 ✏ = 4 rt rt 3 2. Debris specific energy 2 Stellar debris flies if ε>=0 1 away from the black hole
Parabolic orbit Stellar debris is bounded by if ε< 0 the black hole’s gravity and falls back to black hole
3. Fallback time of most tightly bound debris
2/3 1 1/2 r m Mbh t 0.1yr ⇤ ⇤ Tidal disruption radius fb ⇠ R M 106 M (Tidal force=self-gravity force): ✓ ◆ ✓ ◆ ✓ ◆ 1/3 Mbh rt = r What is the rate of mass fallback? m ⇤ ✓ ⇤ ◆ Tidal disruption radius
rS : Schwarzschild radius 2/3 M r =1.1 r bh t S 108 M ✓ ◆ 1. The condition that TDE occurs
8 rS d 1 2/3 5/3 ✏ = (2 GM ) t dt 3 BH (by using Keplerian third law) Evans & Kochaneck (1989) Numerical SimulationsA half of stellar mass falls back to dM 5/3 black holes t dt Rees’s conjecture (1988) Comparison between analytical and simulated mass fallback rates 5/3 t Laguna et al. (1993); Ayal et al. (2001); Enrico&Rosswog (2009); Guillocheon et al.(2009,2013); Shiokawa et al.(2015); and the othersEvans & Kochaneck (1989)Massfallback rate(Log scale) Numerical SimulationsRees’s conjecture is consistent with numerical simulations TDE observations 1. How many TDE candidates (How frequently TDEs happen)2. What observable properties TDEs have Observed TDE candidates Komossa (2015) 1. 72 suspects (https:// tde.space) and 4~50 candidates (~20 are Soft-X-ray TDEs discovered during 2011-15 ) t-5/3 law 2. Three classes: soft-X-ray, optical-UV, and jetted (high- energy) TDEsSoft-X-ray TDE light curvesOptical-UV TDEsKomossa (2015) Deviation from t-5/3 law Optical-UV TDE light curveEarly-time deviations from the t−5/3 rate can be used to constrain the density profile of the disrupted star (Lodato et al. 2009; Gezari et al. 2012). Summary for TDE frequency Observation 10–4-10–5 per galaxy per year (Donley + 2002; van Velzen & Farrar 2014 ) 1-5 × 10–4 per galaxy per year (Auchettl et al. 2017) Jetted TDEs 3×10–9 per galaxy per year (Farrar & Piran 2014; Brown et al. 2015; Sun et al. 2015; Levan et al. 2016) Theory 10–4 -10–5 per galaxy per year (Magorrian & Tremaine 1999; Wang & Merritt 2004; Zhong et al. 2014; Stone & Mezer 2016) Recent progress of event rate estimation It depends on stellar types : Taras’s talk; Shuo’s talk Our questions d & 1pc Nuclear star cluster (Source of TDE stars ) SMBH or IMBH1. Stars fall to BH only on parabolic orbits?2. Can the stellar orbits change TDE characteristics? 2. Classification of TDEs by stellar orbits Type of stellar orbits εorb < 01. Type of stellar orbits εorb=0“Solar system dynamics” Murray & Dermot (1999) εorb>02. Specific orbital energy = rt/rp Specific energy of stellar debris1. Spread energy by the tidal disruptionGMbh r ✏ = ⇤ rt rt2. Energy distribution of stellar debris Condition for each TDE1. Eccentric TDEs ✏ + ✏orb 0 equality = rt/rp 2. Hyperbolic TDEs ✏ + ✏ 0 orb equality Five types of TDEsHyperbolic TDEs Marginally hyperbolic TDEsMarginally eccentric TDEs Eccentric TDEsStandard, Purely, Parabolic TDEs What is the rate of each TDE?We have examined it by N-body experiments for a spherical stellar cluster with a single SMBH Simulation models• N = 128K, 256K, and 512K (K=1024)• Simulation units: G = 1, Mc = 1, rc = 1, and Ec = −1/4 (H enon ́ units) -3 -4 -5 • Accretion radius: ξacc = racc / rc (10 , 10 , and 10 )• Plummer model for initial cluster density profile• Black hole mass: μ= Macc/Mc (0.01 and 0.05)• 15 models including the BH growth model(More detailed explanation in Shiyan’s talk) Five classes of TDEsHyperbolic TDEs Marginally hyperbolic TDEsMarginally eccentric TDEs Eccentric TDEsStandard, Purely, Parabolic TDEs = rt/rp Results of N-body experiments Summary1. Five types of TDEs, in which their bolometric light curves are different. The condition to categorize them is given by two critical eccentricities. 2. Only few eccentric and hyperbolic TDEs can occur in a spherical stellar system with a single IMBH to SMBH. 3. A substantial fraction of the stars approaching to the black hole would cause the marginally eccentric or marginally hyperbolic TDEs. Thank you for your attention
d 1 2/3 5/3 ✏ = (2 GM ) t dt 3 BH (by using Keplerian third law) Evans & Kochaneck (1989) Numerical Simulations
A half of stellar mass falls back to dM 5/3 black holes t dt Rees’s conjecture (1988) Comparison between analytical and simulated mass fallback rates
5/3 t Laguna et al. (1993); Ayal et al. (2001); Enrico&Rosswog (2009); Guillocheon et al.(2009,2013); Shiokawa et al.(2015); and the others
Evans & Kochaneck (1989)
Massfallback rate(Log scale) Numerical Simulations
Rees’s conjecture is consistent with numerical simulations TDE observations 1. How many TDE candidates (How frequently TDEs happen)
2. What observable properties TDEs have Observed TDE candidates Komossa (2015) 1. 72 suspects (https:// tde.space) and 4~50 candidates (~20 are Soft-X-ray TDEs discovered during 2011-15 ) t-5/3 law 2. Three classes: soft-X-ray, optical-UV, and jetted (high- energy) TDEs
Soft-X-ray TDE light curves
Optical-UV TDEs
Komossa (2015) Deviation from t-5/3 law Optical-UV TDE light curve
Early-time deviations from the t−5/3 rate can be used to constrain the density profile of the disrupted star (Lodato et al. 2009; Gezari et al. 2012). Summary for TDE frequency Observation 10–4-10–5 per galaxy per year (Donley + 2002; van Velzen & Farrar 2014 ) 1-5 × 10–4 per galaxy per year (Auchettl et al. 2017) Jetted TDEs 3×10–9 per galaxy per year (Farrar & Piran 2014; Brown et al. 2015; Sun et al. 2015; Levan et al. 2016) Theory 10–4 -10–5 per galaxy per year (Magorrian & Tremaine 1999; Wang & Merritt 2004; Zhong et al. 2014; Stone & Mezer 2016) Recent progress of event rate estimation It depends on stellar types : Taras’s talk; Shuo’s talk Our questions d & 1pc Nuclear star cluster (Source of TDE stars ) SMBH or IMBH
1. Stars fall to BH only on parabolic orbits?
2. Can the stellar orbits change TDE characteristics? 2. Classification of TDEs by stellar orbits Type of stellar orbits εorb < 0
1. Type of stellar orbits εorb=0
“Solar system dynamics” Murray & Dermot (1999) εorb>0
2. Specific orbital energy
= rt/rp Specific energy of stellar debris
1. Spread energy by the tidal disruption
GMbh r ✏ = ⇤ rt rt
2. Energy distribution of stellar debris Condition for each TDE
1. Eccentric TDEs
✏ + ✏orb 0 equality
= rt/rp 2. Hyperbolic TDEs
✏ + ✏ 0 orb equality Five types of TDEs
Hyperbolic TDEs Marginally hyperbolic TDEs
Marginally eccentric TDEs Eccentric TDEs
Standard, Purely, Parabolic TDEs What is the rate of each TDE?
We have examined it by N-body experiments for a spherical stellar cluster with a single SMBH Simulation models
• N = 128K, 256K, and 512K (K=1024)
• Simulation units: G = 1, Mc = 1, rc = 1, and Ec = −1/4 (H enon ́ units)
-3 -4 -5 • Accretion radius: ξacc = racc / rc (10 , 10 , and 10 )
• Plummer model for initial cluster density profile
• Black hole mass: μ= Macc/Mc (0.01 and 0.05)
• 15 models including the BH growth model
(More detailed explanation in Shiyan’s talk) Five classes of TDEs
Standard, Purely, Parabolic TDEs = rt/rp Results of N-body experiments Summary
1. Five types of TDEs, in which their bolometric light curves are different. The condition to categorize them is given by two critical eccentricities. 2. Only few eccentric and hyperbolic TDEs can occur in a spherical stellar system with a single IMBH to SMBH. 3. A substantial fraction of the stars approaching to the black hole would cause the marginally eccentric or marginally hyperbolic TDEs. Thank you for your attention