Thomas Tauris MPIfR / AIfA Uni. Bonn

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1 Thomas Tauris MPIfR / AIfA Uni. Bonn

2 1: Introduction Degenerate Fermi Gases Non-relativistic and extreme relativistic electron / (n,p,e - ) gases : White Dwarfs Structure, cooling models, observations 3: Neutron Stars Structure and Equation-of-state Radio Pulsars Characteristics, observations, spin evolution, magnetars 4: Binary Evolution and Interactions Accretion, X-ray Binaries, formation of millisecond pulsars Black Holes Observations, characteristics and spins 5: Testing Theories of Gravity Using Pulsars Gravitational Waves Sources and detection Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni.

circular orbit (ISCO) BH spin parameter BH spectra (BH mergers detected by LIGO not discussed)

3 Classification of BHs Masses, radii, spins Observations of BHs Persistent sources Transient sources BH spin measurements in X-ray binaries Continuum fitting model Innermost stable circular orbit (ISCO) BH spin parameter BH spectra (BH mergers detected by LIGO not discussed) BH spin and jets / mini-quasars BH mass determination Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 4

Black hole classifications Class Obs. evidence Mass Size Supermassive BH YES 10 5-10 10 M sun 0.

4 Black hole classifications Class Obs. evidence Mass Size Supermassive BH YES M sun AU Intermediate mass BH? 10 3 M sun 1000 km Stellar mass BH YES 10 M sun 30 km Micro BH NO M moon 0.1 mm 6

Reissner-Nordström black hole: Kerr black hole: Kerr-Newman black hole: no charge, no spin charge, no spin no charge, spin charge,

5 Only 3 externally observable parameters according to no hair theorem: mass spin (angular momenum) electric charge Four black hole solutions to the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity: Schwarzchild black hole: Reissner-Nordström black hole: Kerr black hole: Kerr-Newman black hole: no charge, no spin charge, no spin no charge, spin charge, spin It is likely that any initial BH change will be neutralized by surrounding medium Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 7

Mass: stellar mass black holes have masses in the interval: determined via Kepler s 3. law in binaries Radius: R sch GMBH c R 3 km ( M / M ) sch BH X-ray binaries: 4 M / M 16 BH cj Spin: 0.1 a* 0.

6 Mass: stellar mass black holes have masses in the interval: determined via Kepler s 3. law in binaries Radius: R sch GMBH c R 3 km ( M / M ) sch BH X-ray binaries: 4 M / M 16 BH cj Spin: 0.1 a* 0.99 a* GM Evidence for existence: (BH vs NS) mass of compact object above NS threshold features of X-ray emission (hard surface or not) warping of spacetime in khz QPOs gravitational waves detected by LIGO Bonn Summer 017 The Schwarzchild radius defines the event horizon 8

7 Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 9

in the Milky Way and local galaxies Uhuru X-ray

8 Observations: Cygnus X-1, beginning of 1970 s Today: ~4 accreting stellar mass black holes are identified in the Milky Way and local galaxies Uhuru X-ray emission!! Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 10

9 4 systems with wind-fed accretion Persistent sources 19 systems with Roche-lobe overflow accretion Transient sources Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 11

10 4 systems with wind-fed accretion Persistent sources Companion stars: Stellar wind mass loss: Cyg X-1, LMC X-1, LMC X-3 and M33 X-7 Characterised by large BH mass: P orb = days M 0 70 M M M yr and large spin: a O-stars and Wolf-Rayet stars MBH 1116 M Bonn Summer 017 1

19 systems with Roche-lobe overflow accretion Transient sources Companion stars: M (K-type dwarf / sub-giant) Soft-X-ray Transients (SXTs) (Four oddballs with M 6M including the mini-quasar GRS

11 19 systems with Roche-lobe overflow accretion Transient sources Companion stars: M (K-type dwarf / sub-giant) Soft-X-ray Transients (SXTs) (Four oddballs with M 6M including the mini-quasar GRS ) X-ray luminosity: M 1 Characterised by small BH mass: L 10 L L L 10 erg s quiescent outburst outburst Edd 4 10 M and small/medium/large spin: a P orb = days M BH Bonn Summer

12 Until 014, all ~80 Be/X-ray binaries had a NS companion! MWC 656 (Casares et al. (014), Nature 505, 378) Orbital period: Companion star: Porb 60 days M M Radial velocity measurements: (Be-star) q M / M BH Mass of BH: MBH M X-ray luminosity: inefficient accretion in quiescent state: L quiescent 10 7 L Edd Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 14

13 Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 15

An astrophysical BH is completely described by M and J (given that Q=0 via surrouding medium) a J c a* 0 (Schwarzchild BH ) a the dimensionless spin parameter * M GM a 1 (maximally rotating BH) The

14 An astrophysical BH is completely described by M and J (given that Q=0 via surrouding medium) a J c a* 0 (Schwarzchild BH ) a the dimensionless spin parameter * M GM a 1 (maximally rotating BH) The BH spin parameter provides information about: BH formation process (angular momentun of progenitor stars, GRBs) BH spin evolution (connection to accretion (spin-up?) and relativistic jets (spin-down?)) * = Kerr BH E Mc a spin 0.30 ( * 1) 16

15 Space around a spinning BH NASA Non-spinning BH Spinning BH (frame dragging) Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 17

16 Frame dragging and particle trajectories: Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 18

In principle, rotational energy of the BH can be extracted from the ergosphere by the Penrose (1969)

17 Killing Horizon No signal can escape the event horizon. lump of matter Inside the ergosphere spacetime is dragged along, causing matter being forced to corotate. In principle, rotational energy of the BH can be extracted from the ergosphere by the Penrose (1969) process. The Penrose process can extract rotational energy from a BH (see Shapiro & Teukolsky p.363). Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 19

The BH spin can be estimated in X-ray binaries via: 1. X-ray continuum spectrum (e.g. McClintock, Narayan & Steiner 013). Relativistically broadened iron line (e.g. Reynolds 013) 3.

18 The BH spin can be estimated in X-ray binaries via: 1. X-ray continuum spectrum (e.g. McClintock, Narayan & Steiner 013). Relativistically broadened iron line (e.g. Reynolds 013) 3. Quasi-periodic oscillations (e.g. Dokuchaev 013, Motta et al. 014) By measuring the radius of the innermost stable circular orbit, R ISCO one can obtain the spin parameter a * R ISCO 0

19 Risco GM c a 9 GM c a* 1 6 * 0 1 GM c a* 1 RH GM c a 1 GM c a* 1 * 0 1 GM c a* 1 The disk spectrum (peak emission and temperature) depends on R ISCO. Hence, R ISCO and thus a * can be determined from continuum fitting. 1

20 The solution to Einstein s equations for a rotating BH was discovered by Kerr (1963). Here shown in Boyer-Lindquist (1967) coordinates, in which the line element is given by (Shapiro & Teukolsky, Chap.1): M r 4aM r sin ds 1 dt dt d dr M ra sin d r a sin d (1.7.1) where the BH is spinning in the direction, and J a r M r a r a G c M a J c a* a* M GM,, cos, (note 1) Setting a=0 yields the Schwarzchild metric for a non-spinning BH. The dt d term shows the rotational frame-dragging properties of a spinning BH. Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni.

21 The event horizon, R H is found when the dr term in the line element becomes singular, i.e. when =0, or: R H M M a * * Note, only R H+ has an astrophysical meaning. The effective potential felt by particles orbiting a BH is given by: a 0 R M, R 0 H a 1 R R M H H V E r 3 a r Ma amel r M l m r H 4 ( ) (1.7.15) where E, l and m are the binding energy, ang. mom. and particle mass. non-radial motion of test particles (S&T Fig.1.). goes straight into BH (capture) 1. bounces off and escapes BH (unbound) 3. trapped orbit around BH (bound) B. Stable circular orbit C. Unstable circular orbit 3

22 For circular orbits, the specific energy and the specific ang. mom. are: E r M r a M r m r r 3 M r a M r l M r r a M r a m r r 3M r a (1.7.17) (1.7.18) The so-called photon radius is a singularity in the above equations (solving for the denominators being equal to zero): rph M a M 1 1 cos cos / (1.7.1) 3 a* 1, 0,1 rph 4 M,3 M,1M A photon sphere is a spherical region of space where gravity is strong enough that photons are forced to travel in orbits. Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 4

23 In GR, circular orbits can exist from r = to r = r ph, and these can be both bound or unbound. Furthermore, not all bound orbits are stable. Using the stability criterion: V/r =0 yields (after some algebra!): R M 3 Z (3 Z )(3 Z Z ) (1.7.4) isco / 1/3 1/3 1/3 Z1 1 1 a M 1 a M 1 a M, Z 3a M Z 1/ a* 1, 0,1 Risco 9 M, 6 M,1M Innermost Stable Circular Orbit (ISCO) Bardeen (197) Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 5

The binding energy at the ISCO is important for the accretion luminosity: a a m 4 1 ( E / m) / * * 3 3 1 ( E/ m) E m Thus the maximum energy release is: (1.7.

24 The binding energy at the ISCO is important for the accretion luminosity: a a m 4 1 ( E / m) / * * ( E/ m) E m Thus the maximum energy release is: (1.7.5) E m a* 1,0,1 / 5 / 7, 8 / 9, 1/ 3 1 1/ (For a non-spinning BH the energy release is: 1 8 / ) of rest-mass energy! *Defined to be zero at event horizon! (and not at infinity. Hence, max E release is 1-E) Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 7

25 Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 8

26 Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 9

27 Successful application of the continuum-fitting method requires spectra with a substantial thermal component and L/L Edd < 0.3. Otherwise, the thin disk model is invalidated. The constancy of R in suggests that this fitted parameter is indeed related to the R ISCO. Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 30

28 Notice, no retrograde spins observed S L in progenitor star (and BH kick is small). Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 31

29 The BH spin can be estimated from: 1. X-ray continuum spectrum (e.g. McClintock, Narayan & Steiner 013). Relativistically broadened iron line (e.g. Reynolds 013) 3. Quasi-periodic oscillations (?) (e.g. Dokuchaev 013, Motta et al. 014) Bonn Summer 017

30 Motta, Belloni et al. (014) a ( ) a ( M BH ) a( f orb ) Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 33

The spins of the persistent BHs must be natal: The accretion rate onto a BH is Eddington limited and the time interval of accretion is also limited by the

For Eddington-limited accretion this requires: spinup 31 Myr. However, the age of the system is only 47 Myr (Wong et al. 01).

31 The spins of the persistent BHs must be natal: The accretion rate onto a BH is Eddington limited and the time interval of accretion is also limited by the age of the companion star. Consider Cyg X-1: To acheive a 0.95 requires accretion of 7.3 M if the BH was born non-spinning (Bardeen 1970; King & Kolb 1999). For Eddington-limited accretion this requires: spinup 31 Myr. However, the age of the system is only 47 Myr (Wong et al. 01). Also for M33 X-7 and LMC X-1 is spinup nuc (factor 5-6) McClintock, Narayan & Steiner (013). Hence, these BH are born rapidly spinning. nuc Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 34

32 Connecting BH spin and their jets: Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 35

33 BHs may lose spin in jets Poloidal B-field are twisted by frame-dragging, thereby producing outgoing Poynting flux along twin jets. Ruffini & Wilson (1975); Blandford & Znajek (1977) Modern GRMHD simulations show that the power carried by the jet exceeded the total rest mass energy of accreted mass. Tchekhovskoy et al. (011) jet Ljet / Mc McClintock, Narayan & Steiner (013) jet H H 3 c a GM 1 1a * Angular velocity at the BH horizon Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 36

34 jet a * jet H However, see also critique by Fender et al. (010) and Russell et al. (013) Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 37

35 BHs may lose spin in jets Poloidal B-field are twisted by frame-dragging, thereby producing outgoing Poynting flux along twin jets. Ruffini & Wilson (1975); Blandford & Znajek (1977) Modern GRMHD simulations show that the power carried by the jet exceeded the total rest mass energy of accreted mass. Tchekhovskoy et al. (011) jet Ljet / Mc McClintock, Narayan & Steiner (013) jet H H 3 c a GM 1 1a * Angular velocity at the BH horizon For Cyg X-1: PH 1.3 ms Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 38

36 Accretion disk winds may eject a significant of the transfered material Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 39

Determination of BH masses via mass function f( M) 4 ( a sin i) M sin i 3 3 3 X G Porb ( M X M ) In practice, one measures the radial velocity amplitude: K X a X

37 Determination of BH masses via mass function f( M) 4 ( a sin i) M sin i X G Porb ( M X M ) In practice, one measures the radial velocity amplitude: K X a X 1 e sin i Hence, the estimated BH mass strongly depends on the (often) unknown orbital inclination angle, i. Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 41

38 obs i compact object Sometimes it is difficult to determine if the accreting object is a NS or a BH. Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 4

39 Ballistic jets and microquasars ASTRO 8504 Now in German! GRS Superluminal motion! Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 43

40 BH: radio/x-ray luminosity correlation GRS Superluminal motion! Gallo, Fender & Pooley (003), Coriat et al. (011), Meyer-Hoffmeister & Meyer (014) Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 44

41 Stellar mass BHs have spins: 0.1 a 0.99 a * * BH spins can be determined via the continuum-fitting model BH spins can also be measured in merging BH binaries (LIGO) The two classes of BHs (transient vs persistent) have different spins The fast spins of the persistent BHs are natal cj GM The BH spins seem to be correlated with the jet power Literature - Shapiro & Teukolsky (1983), Chapter 1 (14) - McClinck, Narayan & Steiner (013), Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets, arxiv: astro-ph: R. Shafee (008), Measuring Black Hole Spin, PhD Thesis, Chapter 1+ - LIGO consortium (016), Observations of Gravitational Waves Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 45

42 1: Introduction Degenerate Fermi Gases Non-relativistic and extreme relativistic electron / (n,p,e - ) gases : White Dwarfs Structure, cooling models, observations 3: Neutron Stars Structure and Equation-of-state Radio Pulsars Characteristics, observations, spin evolution, magnetars 4: Binary Evolution and Interactions Accretion, X-ray Binaries, formation of millisecond pulsars Black Holes Observations, characteristics and spins 5: Testing Theories of Gravity Using Pulsars Gravitational Waves Sources and detection Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 46

43 Bonn Summer 017 Thomas Tauris - MPIfR / Bonn Uni. 48

Measuring the Spin of the Accreting Black Hole In Cygnus X-1

Measuring the Masses and Spins of Stellar Black Holes Measuring the Spin of the Accreting Black Hole In Cygnus X-1 Lijun Gou Harvard-Smithsonian Center for Astrophysics Collaborators: Jeffrey McClintock,