Black holes from other black holes?

Transcription

1 Black holes from other black holes? Davide Gerosa NASA Einstein Fellow California Institute of Technology arxiv: with E. Berti January 22nd, 208 Valletta, Malta

2 Outline. The field/cluster debate 2. Multiple generations of black holes 3. Bayesian model selection 4. A generation gap

3 Have we been together for so long? Yes! I ve known you since you were a star Don t you remember? We just met in cluster

4 Do BHs remember how they formed? 4 Masses and rates? Easy to measure, but models overlap >00 events needed to distinguish populations Stevenson+ 205, Zevin+ 207 Eccentricities? Promising, especially for specific scenarios Nishizawa+ 207 Spins have secrets! What information can we extract from the events we have? And from many more detections? Higher SNR? Field binaries: evolve together. Tidal interactions and accretion tend to align the spins?? Cluster binaries: evolve separately and then meet. Isotropic spin distribution, more precession??

5 Black hole generations DG Berti 207 g BH g BH g BH g BH redshift z g BH g BH 2g BH redshift z 2 redshift z 2g BH g BH 2g BH g BH g BH redshift z redshift z redshift z g+g event g+2g event 2g+2g event Orthogonal, but complementary, direction to the usual field vs. cluster debate

6 Spins: the magic number DG Berti 207, Berti Volonteri 2008 Orbital hang-up n g + g g + 2g 2g + 2g Primary s spin S L S2 S S L S2 At merger, the binary s angular momentum has to be converted into spin More or less whatever you do when you merge two BHs, you get ~0.7! Spins remember previous mergers! S n Secondary s spin

7 r instabilities and ate the mass disthe redshift distribution of BH mergers in the three ltiple mergers and di erent populations should be di erent, because on ave. erage 2g mergers are expected to happen later than e spin magnitude g mergers. We can estimate the delay times between in all three cases the formation and merger of a BH binary using the nitudes,2 to be quadrupole formula m, m 2 [5M, 50M ] 2 heir directions to only interested in da 64 q M 3 G3 Uniform g =, () uniform in magnitude population. Since dt 5 ( + q) a c Flat opic under precesin log 2g from fitting formula on [5, 52], the aswith the result 2.5 Power law p(m ) / m Barausse Rezzolla 2009 the small separaˆ 0 dt 0 5 ( + q)2 a4 c5 r this reason there t= da =. (2) and 2g from fitting formula Barausse n evolutions of the 256 q M G a da es of the kind disif the binary initial separations a are drawn from a logflat distribution (i.e., dn/da / /a), the distribution of more massive the merger times is also log-flat (cf. [26]): Mock BH populations Masses More mergers means: Redshifts g uniform in coming volume tion 2g add lookback time ulation we use the tract two binaries these binaries, we f of the merger y fitting formulas 3 54]. These masses flat n Spins 2 dn dn da = / 4 /. dt da dt a t equal mass (3) closer higher spins The lookback time tl is given by [64] ˆ z dz p tl =, (4) H0 0 ( + z) M ( + z) g + g 2.0 g 0, + 2g where we assume k = M = 0.307, 0.6= and 2g From the lookback time we H0 = 67.7 kms [65]..5 Mpc 2g can compute the time tl (z ) tl (z2 ) necessary for the Universe to evolve from redshift z to redshift z field binaries should y BHs receive small rbit [49, 50], while the We distribute the g+g sources uniformly in comovstellar environments DG Berti 207 ing volume with populadetailed 0 investigation redshifts z < 2. For the g+2g tion, we that 0.2 2g at some redshift z nd binary BH30 formaassume BHs0.6formed s beyond the scope of M drawn from the same distribution q used for g+g bina- z ries. We then extract a delay time t from a flat distri eff

8 Introducing errors Binned analysis Errors are introduced spreading the source over multiple bins Barrett+ 207 Info kindly provided by Gosh+ 206 and scaled with SNR Ghosh et al. 206 Sampled M z/z 0.6 Figure 3. An illustration of how we include measurement errors in our analysis. A Gaussian is centred on each bin, with a standard deviation proportional to the value at the centre of that bin. That 0.8 bin s counts are then distributed to other bins according to the fraction of that Gaussian falling in each bin q/q M/M likelihood function. Performing volve a modification of the the analysis in this way would correctly account for correlations between bins, whereas 0.2 in the simplified approach bins are modified independently, losing information and slightly DG Berti 207 swelling the uncertainty q z Uncertainty quantification.5 2.0

9 Detectable populations flat LIGO g + g g + 2g 2g + 2g n 5 n M DG Berti q n n z e

10 Can we infer previous mergers happened? O Number of observations needed to distinguish two models at a given significance g+g vs. 2g+2g g+g true 2g+2g true DG Berti N obs g+g vs. g+2g g+g true g+2g true N obs flat LIGO g+2g vs. 2g+2g g+2g true 2g+2g true N obs Need only 0-60 observations to distinguish g+g vs 2g+2g at 5σ! Already! Using O events only: gg vs. 2g2g. Odds: 2 gg vs. g2g. Odds: 2 g2g vs. 2g2g. Odds: 6 2σ statement our BHs are not 2g+2g!

11 What if all three are there? flat LIGO N obs = 00 f g+g = 60% f g+2g = 0% f 2g+2g = 30% DG Berti 207 2g+2g log p Three models mixed, can we measure their mixing fraction? each pure model is on a corner assuming 00 BBH 90% and 50% confidence intervals 3.0 g+g g+2g Yes, but that s harder. Need O(00) observations and/or a better detector!

12 A generation gap? Pulsation instability? Upper BH mass cutoff Migration traps and accretion disks Heger Woolley 2002, Woolley 207 Bellovary+ 206, McKernan+ 207 Even in globulars if you re lucky (but kicks ) Rodriguez+ 207

13 Caltech and GWverse Not really in Europe, but now an International Partner institution Researchers from COST countries can visit Caltech

14 Outline. The field/cluster debate 2. Multiple generations of black holes 3. Bayesian model selection 4. A generation gap

15 Backup slides

16 N obs at 5 ggt/2g2g 2g2gT/gg ggt/g2g g2gt/gg g2gt/2g2g 2g2gT/g2g 5% 50% 95% 5% 50% 95% 5% 50% 95% 5% 50% 95% 5% 50% 95% 5% 50% 95% LIGO O flat log power law Ad. LIGO flat log power law A+ flat log power law Voyager flat log power law

17 Injection Test Preferred flat g+g flat g+g vs flat 2g+2g flat g+g 3T log g+g vs log 2g+2g not significant power law g+g vs power law 2g+2g power law g+g 3 flat 2g+2g flat g+g vs flat 2g+2g flat 2g+2g 3T log g+g vs log 2g+2g log 2g+2g 3 power law g+g vs power law 2g+2g power law g+g 7 log g+g flat g+g vs flat 2g+2g flat g+g 3 log g+g vs log 2g+2g log g+g 3T power law g+g vs power law 2g+2g power law g+g 3 log 2g+2g flat g+g vs flat 2g+2g flat g+g 7 log g+g vs log 2g+2g log 2g+2g 3 power law g+g vs power law 2g+2g power law g+g 7 power law g+g flat g+g vs flat 2g+2g flat g+g 3 log g+g vs log 2g+2g log g+g 3 power law g+g vs power law 2g+2g power law g+g 3T power law 2g+2g flat g+g vs flat 2g+2g flat g+g 7 log g+g vs log 2g+2g log g+g 7 power law g+g vs power law 2g+2g power law 2g+2g 3T