Formation of low-mass X-ray Binaries with a BH accretor: challenging the paradigm Semyon Chaichenets (UofA) Stephen Justham (KIAA, Beijing) John Fregeau (KITP, UCSB) Craig Heinke (UofA) Jamie Lombardi (Allegheny) Philipp Podsiadlowski (Oxford) Saul Rappaport (MIT) Tyrone Woods (UofA) Natasha Ivanova (UofA) CCRG, RIT, 31 March 2010
Low-mass X-ray binaries Compact accretors - NS or BH RLOF Donors - MS, RG, WD/degenerate low-mass, < 1M Binary Periods: 10 minutes to ~100 days Ages: ~ 0.1-10 Gyr MT timescale 10 7-10 9 yr Lx: can appear as a persistent or as a transient source. GRO J1655-40 Credit: NASA/CXC/A.Hobart ~10 32 erg/s(in quiescence) to ~10 39 erg/s (and may be more in outbursts) Can be detected in distant Galaxies in X-ray. Soft X-ray spectra (kt < 10 kev). Faint, L opt /L x <<0.1 Often have X-ray
X-ray binaries: why do we care? BH Most of observational confirmations for the physics of stellar mass BHs come from the studies of X- ray binaries with BH companions; BHs are the key test of general relativity in the strong-field regime. SN LMXBs and HMXBs give strong constraints on how SNe explode; constraints on how SN explode are critical for understanding how black holes form, how the heavy elements are created. GRB To understand the nature of γ-ray bursters, one needs a good model of their progenitors, which will most likely include interacting massive stars, where one of the influential evolutionary phases in the past was an X-ray binary. LIGO/LISA One of the needs of GW astrophysics is the prediction of what and how many events have hope of being observed. Best evolutionary constraints on the formation of different compact binaries comes from studies of X-ray binaries. IMBH Our knowledge of LMXBs helps us understand and interpret observations of ULXs.
Dynamically confirmed BH X-ray binaries 20 X-ray binaries with a BH candidate 17 LMXBs and 3 high mass X-ray binaries J. Orosz
LMXBs: standard paradigm Bhattacharya & van der Heuvel (1991) common envelope (CE) phase, during which the low-mass star spirals inward through the extended envelope of the massive primary star, and the phase is terminated upon ejection of the common envelope - the ejection uses the orbital energy as an energy source and the final binary is much more compact Further orbit shrinkage due to tides, magnetic braking and gravitational waves in, likely, an eccentric binary and may be a second episode of CE event magnetic braking (MB) is the process of the angular momentum loss for late type stars by magnetically coupled wind. The efficiency of the braking is proportional to the mass loss rate with stellar wind and magnetic field strength. Binary shrinks and mass transfer occurs again. Stable mass transfer reveals the system as an X-ray source.
LMXBs: standard paradigm it is not that simple! What can go wrong? Everything! We can be wrong about how a CE occurs, what is a donor that we see and, at the end, the whole formation path could be totally different Let s start from CE
Common envelope: standard paradigm common envelope (CE) - phase, during which the low-mass star spirals inward through the extended envelope of the massive primary star The phase is terminated upon ejection of the common envelope or merger α CE E orb <E bind env = GMM core R RL λ ce E orb = GMM d 2a f GM corem d 2a i standard: α CE λ ce =1 (Livio 1988)
Problem: formation rates of short-period BH LMXBs Observed formation rate: 1 per mln yr per MIlky Way (Romani 1998) (10-6 per gal per yr) Kalogera (1999): unrealistically high values of α ce λ ce are required for agreement with the observationally inferred BH-LMXB birthrate. Theoretical formation rate is at least 100 times less Podsiadlowski et al. 2003: BHs with low mass secondaries can only form with apparently unrealistic assumption. Realistic λ ce is only ~0.01! (Dewi & Tauris 2001, Podsiadlowski et al. 2003) a likely answer - IMXBs! Ivanova & Kalogera (2006): While it is hard to make a BH LMXB with a MS companion, it is 100-1000 times easier to have a WD companion! Question - Where are they?
short-period BH LMXBs from IMXBs: spectral type test Justham et al. (2006): magnetic braking can operate with Ap/Bp companions. The magnetic field is not generated by a dynamo like in low-mass MS stars, but is preserved from pre-ms stage (fossil MF). Orbital periods, donor masses, lifetimes & production rates are in agreement with the observations But not the effective temperatures! 8 known LMXBs with black-hole candidate companions, measured periods and Teff Evolutionary tracks shown as locations at the RL overflow of binaries assuming that a companion is 7 M BH (Justham et al 2006) Here are shown the hottest possible Teff assumption on irradiation does not help Systems with Li overabundance by 20-200 of a solar value. Note that Li over-abundance has been found NOT in the systems with smallest periods among non-giant donors, but with larger periods and therefore can not be explained by the tidal locking that enhances Li as the period decreases as in Maccarone et al. 2005 CNO Li
Observations and evolutionary tracks: MS and post-ms MS lifetime of 0.8 M star (of solar metallicity) is twice the Hubble time! Only 0.95 M will leave MS by Hubble time at Z=0.02 For Z=0.001, ZAMS shifts upwards and stars are hotter by about 1000K at the same period avoidance zone
Observations and evolutionary tracks: pre-ms?! A BH is created in 6-8 mln yr In ~10 mln yr only stars more massive than 2 M will reach their MS! Pre-MS star HAVE Li! They do not need to create it, they did not destroy it yet!
Observations: Westerlund 1 most masssive young cluster in MW X-ray pulsar (Muno et al. 2005) Stars below 3M are still pre-ms (Brandner et al 2008)
Observations and evolutionary tracks: pre-ms?! A pre-ms star CONTRACTS! How to maintain Roche lobe overflow? We need VERY strong AM loss! Ivanova 2006
Observations and evolutionary tracks: pre-ms?! Observations: B on the Sun : 2 G B in T Tauri 1-10 kg e.g., TW Hyd: 2.5 kg, age 2 10 7 yr By plugging-in strong MF, we find that it is possible to start and proceed the MT in a binary with a star that contracts very fast on its thermal time-scale! Ivanova 2006 Shown tracks are for different initial MF strength.
CE efficiency: further ideas? Consider: slow mergers. Ivanova (2002), Ivanova & Podsiadlowski (2003), did systematic studies of common envelope events that should result in mergers Nucleosynthesis ~10 10 cm CE evolution ~10 14 cm Stream hydrodynamics ~10 12 cm
CE efficiency: further ideas? Consider: slow mergers. It features a steady hydrogen stream onto the core! Ivanova 2002
CE efficiency: further ideas? Consider: slow mergers. It features a steady hydrogen stream onto the core! It has been found that one of the possible outcomes leads to the explosion of the He shell: Hydrogen Nuclear driven CE ejection! Helium Luminosity Ivanova 2002 Radius
Explosive CE ejection Podsiadlowski, Ivanova, Justham & Rappaport (2010, MNRAS accepted): The birth rate for short-period BH LMXBs is as in observations, 10-6 per yr per gal Ic type SN connection for long GRBs - both H and He layers are ejected, no Wolf-Rayet phase is required The formation rate for GRBs about 10-6 per yr per gal - can provide most of long GRBs
BH-WD: observations NGC 4472 (Zepf et al. 2008) L X 4 10 39 ergs s 1 strong variability strong, broad (2000 km/s) O III emission lines low Hα/[O III] ratio Could be a BH of 5-20 M, most likely 15 M (Gnedin et al. 2009)
BH-WD: observations CXO J033831.8-352604 (Irwin et al. 2009) L X 2 10 39 ergs s 1 strong, less broad (70 km/s) O III emission lines little or no hydrogen emission Suggested a tidal disruption of a WD by IMBH
BH-WD: observations How frequent are ULXs ( Lx > 10 39 ergs/s) in GCs? Kim et al. 2006: 8 in 6173 GCs 2.0 +1.5 1.0 10 9 per M Humphrey&Buote 2008: 2 in 3782 7 +15 6 10 10 per M Sivakoff 2010: 7 in 6776 GCs 2.2 +1.9 1.2 10 9 per M Kalogera et al 2004: BH X-ray binaries with non-degenerate companions are NOT expected to be detected in GCs!
How many BHs can be in a GC? Stellar evolution: each 150 200 M of currently remaining stellar mass produced a BH in the past half of these BHs have masses above 10M retention fraction after SN kicks 30 40% for v ecs = 50 km/s (Belczynski et al. 2006) Dynamics: Spitzer instability + quick evaporation through interactions inside formed BHs subcluster only one or two BHs could remain per cluster at the current epoch (Kalogera et al. 2004) Detailed numerical calculations of BH subcluster: in massive clusters, up to 20% of the BHs may remain; and these clusters do not reach equipartition (o Leary et al. 2006) Monte Carlo of a whole GC: up to 25% of initial BHs remained & participated in interaction with other stars (Downing et al. 2009). the number of BHs (> 10M ) retained, and available for interactions with core stars, could be from one per GC to 10% of all initially formed massive BHs (125-200 BHs per average massive GCs of 6 10 5 M or 4000-6000 BHs per each observed sample).
Observationally inferred formation rates τ X 2 10 5 yr persistent mass transfer at the Eddington level ( 4 10 39 ergs s 1 ) from a WD to a massive BH; 3 times longer for ULX luminosities L X > 10 39 ergs s 1 if all but one BH is evaporated, the formation rate of BH-WD binaries is about one X-ray binary formation per BH per Gyr. the minimum required formation rate is about 4 10 3 /f BH,0.1 per BH per Gyr. f BH,0.1 =0.1f BH,tot is the fraction of BHs that is retained in the cluster and not detached in the BH subcluster, and is normalized to 10% of all initially formed massive BHs (> 10M ).
To analyze the dynamical formation, we will proceed in reverse order: first, we will consider which BH-WD binaries, once formed, can become X-ray binaries second, we will consider at what rates these BH-WD binaries can be formed via different dynamical channels.
Time-scales The cross section for a strong encounter: σ =2π G k a m tot v 2 The time-scale to experience a strong encounter: τ =(σnv ) 1 The rate of strong encounters: Γ BS 0.1k m BH 15M n c 10km s 1 10 5 pc 3 v a R per Gyr Initial a/r and e of a 15+0.6 M BH-WD binary. τ gw constant gravitational merger time τ BS encounter time a sep is such that τ gw = τ BS
Encounters with single MS stars: mergers Fregeau et al. (2004): σ coll σ = 1 4k ( ) 0.65 215R, a k the ratio of the maximum pericenter considered as an encounter to a. σ coll = σ for BH-WD binaries a<15r with k 1. most BH-WD binaries that are able to start MT within 10 Gyr will experience a merger if a binary-single encounter with a MS star occurs
Encounters with single WD stars: exchanges f WD 0.2 of the total core population, Γ BS,WD = f WD Γ BS PC would occur only in BH-WD binaries with a<0.1r ( short-living, a a sep (e)). A more likely outcome would be preservation or a companion exchange. Exchanges: preferentially occur IF the incoming star is more massive than pre-encounter companion the post-encounter binary separation will be increased by the ratio of new companion mass to the old companion mass a BH-WD binary has a(e) >a sep (e) the resulting binary will most likely never be able to reach MT, as its binary separation will exceed a sep (e). Preservation: A binary will most likely then experience a consequent encounter with a single star and this consequent encounter has high probability to have a MS star as a participant and therefore to result in a merger.
Encounters with single stars Strong encounters with single stars will NOT create BH-WD binaries with a(e)<a sep (e) and therefore will not lead to a direct formation of a BH-WD X-ray binary.
Triples (hs) formation rate Fraction of encounters, for k = 20, that result in a hierarchically stable triple formation. BH-WD 15M +0.6M with a 1 = 15, 35, and 80R (green, red and blue). 0.6M +0.6M binary with a 2. The efficiency of triple formation is 20 30% with k = 20. Γ triples (a 1,a 2 ) Γ BS (a 1 ) 3 ( 2f wb 1+ a ) 2. a 1 With f wb = 5% a BH-WD binary of a = 20R can form a triple about 30 times per Gyr. This exceeds the interaction rate with single stars.
Triple induced mass transfer We define triple induced mass transfer (TIMT) systems to be those binaries that are brought into MT via the the Kozai mechanism. The maximum separation TIMT system can have is about 80 R The fraction of TIMT systems is a function of emax induced by Kozai mechanism and ranges between 0.07 (for a=15 R ) and 0.01 (for most separations, a> 40 R ). Combining it with the triple formation rate, we find that : A conservative level: all BH-WD binaries a<35 R have 100% chance to become TIMT system within 1 Gyr. An optimistic level: all BH-WD binaries with a <80 R can become a TIMT system at least once during several Gyr. This TIMT system formation will be successful only if the time between subsequent encounters is longer than the time necessary to achieve emax. τ Koz τ BB 4 10 14 0.42 ln(1/e f i ) b sin 2 (i 0 ) 0.4 ( a 2 2 a 1 R ) 5/2 ( triples with 15 R <a1 <80 R and a2 <10 5 R have their Kozai time significantly shorter than their collision time with either binary or single stars. m BH 15M ) 3/2 M m o ( 1 e 2 o ) 3/2 n c 10 5 pc 3 10km/s v
Triple induced mass transfer Once a potential TIMT system is formed, it will succeed in bringing its inner BH-WD to the mass transfer before its next encounter. all BH-WD binaries with a<35 R (conservatively) or with a<80 R (optimistically) will become X-ray binaries via TIMT mechanism.
Multiple encounters: Hardening Through multiple fly-by encounters hard binaries get harder (Hut 1983): N hard log(f change )/ log(1 + δ) δ m 3 /m bh 0.04 - the relative change in the binary's binding energy caused by an encounter. the hardening of a 1000 R BH-WD binary to 35 R should take about 100 encounters and this should take a few Gyr. However, this is an idealistic picture: there are plenty of strong encounters that this binary would have. Some of the encounters would result in exchanges, mergers, or even binary ionizations, reducing therefore the chance for a binary to harden to the separation we are interested in.
Hardening a i Hardened fraction [per cent] Average time [Gyr] Black hole fraction in the total core population [per cent] 0.4 0.04 0.004 0 0.4 0.04 0.004 0 Corresponding f BH,0.1 10 1 0.1 0 10 1 0.1 0 Hardening to 35 R Original binary survival only 100R 4.6 12.9 14.8 14.9 0.86 1.38 1.48 1.52 250R 0.53 2.5 3.4 3.4 1.07 1.9 1.9 1.9 500R 0. 0.8 1.0 1.3-1.9 2.1 2.3 Exchanges are allowed 100R 9.4 30.4 38.1 38.9 1.06 1.50 1.58 1.60 250R 1.3 9.8 13.9 13.3 1.17 1.85 2.00 2.07 500R 0. 3.2 4.8 5.9-1.78 2.15 2.09 Hardening to 80 R Original binary survival only 100R 37.9 56.0 58.2 60.6 0.22 0.29 0.30 0.31 150R 12.7 27.5 30.0 30.9 0.35 0.52 0.57 0.57 200R 6.5 16.9 19.1 20.7 0.41 0.64 0.68 0.70 250R 3.5 11.3 14.4 14.4 0.46 0.73 0.77 0. 77 500R 1.1 3.1 3.8 3.8 0.37 0.90 0.98 0.98 fhard <<1 Γ hard f BH,0.1 f hard the highest formation rate is in unlikely case f BH,0.1 = 10
Formation: exchanges a post a pre m BH /m c To create a BH-WD binary with a post < 35R, only encounters with WD-WD binaries are relevant. Γ exch,1 2 10 3 per Gyr per BH. Relatively wide hard BH-WD binaries (a 80 1000R ) can be formed through encounters with both MS-WD and WD-WD binaries. Γ exch,2 0.06f hard 2 10 3 per Gyr per BH. In the optimistic case (in all binaries with a post < 80R TIMT works): Γ exch,1 =6 10 3 and Γ exch,2 =1.5 10 2 per Gyr per BH.
Formation: BH-RG collisions
Formation: BH-RG collisions Γ BHRG 0.1f RG r p R RG m BH 15M n c 10 5 pc 3 RRG R 10km/s v per Gyr r p R RG is the border line between these collision that lead to the formation of BH-WD binary able to start MT in isolation, and these that could not r p 5R RG is the maximum distance when a bound binary is formed non-timt channel is 4x10-4 per BH per Gyr TIMT channel is 1.5x10-2 per BH per Gyr
Results Channel Conservative Optimistic EX + TIMT 2 10 3 6 10 3 EX + HARD + TIMT 2 10 3 1.5 10 2 PC 4 10 4 PC +TIMT 1.5 10 2 The most important mechanism is exchange+timt. The second most important is exchange + hardening + TIMT. Physical collisions without TIMT do not play a significant role. TIMT is very effective for BH-WD binaries and is not expected to be effective at all for BH-MS binaries.
BH population in GCs conservative estimate we can explain the formation rate inferred from observations only if f BH ~1: 10% of all formed BHs remain in the cluster and interact with the core's stellar populations. optimistic scenario all the channels have comparable formation rates and each of the channels can explain the observed formation rate of BH-WD X-ray binaries. The combined rate of all the channels is ~4x10-2 per BH per Gyr. f BH =0.1 is the minimum value to explain the formation rates inferred from the observations. even in the most optimistic case, we require that at least 1% of all initially formed BHs should be both not evaporated from the cluster and not dynamically detached from the core's stellar population to BH subcluster it also means that it will be continuos formation of BH-BH binaries in GCs at our epoch as well Ivanova et al. 2010
Conclusions we are still discovering how can X-ray binaries be formed and what are they now significant progress has been made in understanding of BH X-ray binaries with low-mass companions with both degenerate and non-degenerate donors, though a puzzle why BH-WD X-ray binaries are absent in the field remains Detection of BH-WD binaries in GCs gives new constraints on the dynamical evolution of BH population in GCs ECEE is a completely new and exciting way to evolve through the common envelope that removes the energetic problem and helps to make short-period LMXBs as well as explain long GRBs and Ic connection and their rates.