Astrophysical Lessons from LIGO/Virgo’s Black Holes M a y a Fishb a ch ICERM - St a tistic a l Methods for the Detection, Cl a ssi f ic a tion a nd Inference of Rel a tivistic Objects November 16 2020 1
World-wide network of gravitational-wave detectors LIGO Hanford Kagra (coming soon) LIGO India (coming ~2025) LIGO Livingston Virgo 2
LIGO and Virgo have observed gravitational waves from ~50 mergers Credit: Chris North & Stuart Lowe, 3 https://waveview.cardi ff gravity.org
LIGO and Virgo have observed gravitational waves from ~50 mergers GWTC-2 papers: Catalog: dcc.ligo.org/P2000061/public arXiv: 2010.14527 Population paper: dcc.ligo.org/LIGO-P2000077/public arXiv: 2010.14533 Tests of GR paper: dcc.ligo.org/LIGO-P2000091/public arXiv: 2010.14529 Credit: Chris North & Stuart Lowe, 4 https://waveview.cardi ff gravity.org
For each binary black hole merger, the gravitational-wave signal encodes: • The masses of the two components m 1 ≥ m 2 • The component spins a 1, a 2 • Distance d L , sky position ⍺ , 훿 , inclination 휄 , polarization Ψ Measuring these parameters for each event is known as parameter estimation 5
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Parameter estimation For individu a l events, me a surement uncert a inties a re l a rge, a nd our inferred posterior depends on the prior p ( m 1 , m 2 ∣ data) ∝ p (data ∣ m 1 , m 2 ) p 0 ( m 1 , m 2 ) Posterior Likelihood Prior LIGO/Virgo prior: flat in (detector-frame) masses 8
Measurements of individual events’ parameters Subset of events in GWTC - 2 9 Primary mass Secondary mass Mass ratio E ff ective inspiral spin Distance (redshift)
90% probability contours Mass ratio Total mass 10
From Single Events to a Population • Introduce a set of population hyper-parameters that describe the distributions of masses, spins, redshifts across multiple events • Example: Fit a power-law model to the mass distribution of black holes, p(mass | a) ∝ mass -a • Take into account measurement uncertainty and selection effects 11
Population analysis Find the “best” prior to use for individu a l events p ( m 1 , m 2 ∣ α ) Population model, common to all systems Parameter estimation likelihood for event i ∫ p (data i ∣ m 1 , m 2 ) p ( m 1 , m 2 ∣ α )d m 1 d m 2 p (data ∣ α ) = ∏ β ( α ) Likelihood given i Selection e ff ects: fraction of population detectable systems in the hyperparameters population 12 Mandel, Farr & Gair arXiv:1809.02063
Three Astrophysical Lessons The popul a tion properties of bin a ry bl a ck holes reve a l how these systems a re m a de 1. A feature in the mass distribution at ~40 solar masses 2. Misaligned black hole spins 3. Black hole merger rate across cosmic time 13
Three Challenges To a ccount for when recovering the popul a tion distribution of bin a ry bl a ck holes 1. The parameters of individual systems are uncertain 2. Some systems are easier to detect than others (selection effects) 3. Our models may not match the true population distribution (necessitates model checking) 14
Example of selection effects: Big black holes are louder than small black holes 10 1 V T ∝ 2 . 2 q = 1 q = 0 . 7 q = 0 . 5 V T (comoving Gpc 3 yr) Sensitive volume 10 0 q = 0 . 3 10 − 1 MF & Holz 2017 ApJL 851 L25 10 − 2 10 25 50 100 150 200 M tot ( M Ø ) Total mass 15
Astrophysical Lesson #1: De a rth of big bl a ck holes in the bl a ck hole popul a tion 10 1 V T ∝ 2 . 2 Where are LIGO’s big black q = 1 q = 0 . 7 holes? q = 0 . 5 V T (comoving Gpc 3 yr) 10 0 q = 0 . 3 Big black holes are very loud, In first two and yet we did not see any observing binary black holes with runs, lack of component masses above ~45 observations 10 − 1 in this mass solar masses in the fi rst two range observing runs. → These systems must be rare in MF & Holz 2017 ApJL 851 L25 10 − 2 the underlying population. 10 25 50 100 150 200 M tot ( M Ø ) 16
With the f irst 10 binary black holes, we measured the maximum black hole mass to be ~40 solar masses The bl a ck hole m a sses we observed were consistent with coming from a trunc a ted power l a w distribution Merger rate per mass Primary mass 17 Abbott+ arXiv:2010.14533
With the f irst 10 binary black holes, we measured the maximum black hole mass to be ~40 solar masses 0 . 200 M max = 42.0 +15.0 − 5.7 M ⊙ 0 . 175 0 . 150 probability density 0 . 125 Maximum mass posterior from GWTC-1 0 . 100 Primary mass measurements for the 10 GWTC-1 binary black holes 0 . 075 0 . 050 0 . 025 0 . 000 20 40 60 80 100 120 mass (solar masses) 18
We now know that ~40 solar masses is not a sharp limit: there are bigger black holes out there! Maximum mass measured with the second catalog, assuming a power law model Maximum mass measured with the fi rst catalog Maximum mass measurement with the second catalog, excluding the most massive event 19 Abbott+ arXiv:2010.14533
We now know that ~40 solar masses is not a sharp limit: there are bigger black holes out there! Example of challenge #3: we need to introduce additional mass distribution features in our model to adequately f it to the data Maximum mass measured with the second catalog, assuming a power law model Maximum mass measured with the fi rst catalog Maximum mass measurement with the second catalog, excluding the most massive event 20 Abbott+ arXiv:2010.14533
Nevertheless, there is a feature in the black hole mass distribution at ~40 solar masses With the third observing run, we know th a t big bl a ck holes a re not a bsent , but they a re r a re • A truncated power law with sharp cuto ff s fails to fi t the data • We must introduce additional features, like a Gaussian peak or a break in the power law • The black hole mass distribution steepens at ~40 solar masses 21 Abbott+ arXiv:2010.14533 arXiv:
Multiple observations allow us to resolve detailed features of the black hole mass distribution Power law + peak Broken power law Power law index above the break Power law index below the break Fraction of black holes in the Gaussian component Excludes 0 Excludes a single power law (equal indices) 22 Abbott+ arXiv:2010.14533
Astrophysical Implications: Feature at ~40 solar masses caused by pair-instability supernova? • (Pulsational) pair-instability supernovae predict an absence of black holes in the range ~40 - 120 solar masses • Applies to black holes formed from stellar collapse • Are black holes above this limit formed via a di ff erent channel? (E.g., from smaller black holes?) Or perhaps the limit is not as sharp as we thought? Further measurements will help us Credit: Gemini Observatory/NSF/AURA/ illustration by Joy Pollard resolve this question. 23
Astrophysical Lesson #2: Bl a ck hole spins a re not a lw a ys a ligned with the orbit a l a ngul a r momentum • The gravitational-wave signal can be parameterized by two “e ff ective” spins: • The e ff ective inspiral spin measures the total spin along the orbital angular momentum axis • The e ff ective precessing spin measures the spin in the orbital plane, perpendicular to Figure credit: Thomas Callister orbital angular momentum axis 24
For individual events, in-plane spins tend to be poorly constrained Individu a lly, no system shows strong evidence for in-pl a ne spins E ff ective precessing spin 25 Abbott+ a rXiv: 2010.14527
On a population level, we f ind that some systems have in-plane spins ( χ p > 0) χ p We me a sure the me a n a nd st a nd a rd devi a tion of the distribution of a cross a ll events, a ssuming a G a ussi a n distribution Std . dev χ p Excludes a delta- mean χ p function at 0 Abbott+ arXiv:2010.14533 26
On a population level, we f ind that some systems have in-plane spins ( χ p > 0) 12 10 8 p ( χ p ) 6 4 Gaussian Default 2 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 χ p 27 Abbott+ arXiv:2010.14533
Astrophysical Implications of Misaligned Spins Spin mis a lignments c a n be used to distinguish form a tion ch a nnels • Isolated fi eld formation: typically di ffi cult to get large misalignments, but depends on uncertain physics like black hole natal kicks, e ffi ciency of tides • Dynamical assembly: typically expect random spin orientations, but this can depend on whether the environment is gaseous (e.g. AGN disks) 28
Astrophysical Lesson #3: Me a suring the bl a ck hole merger r a te a cross cosmic time 1 . 0 dashed lines: O2 sensitivity 0 . 8 P ( § < z | detected) solid lines: design sensitivity cumulative 0 . 6 distribution in 10–10 M Ø redshift for detected binaries 20–20 M Ø 0 . 4 of a fixed mass 30–30 M Ø 40–40 M Ø 0 . 2 50–50 M Ø O2 sensitivity 0 . 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 z 29 MF , Holz, & Farr 2018 ApJL 863 L41
Merger rate of black hole mergers across cosmic time: Inference from the f irst 10 bin a ry bl a ck holes • Allowing the merger rate to evolve with redshift, GWTC-1 found: • Today (z = 0), the merger rate is between [4, 77] Gpc -3 yr -1 • 8 billion years ago (z = 1), the merger rate was higher, but uncertain by more than 4 orders of magnitude 30 Abbott+ 2019 ApJL 882 L24
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