Final Black Hole Mass Research Articles

Super-critical accretion of medium-weight seed black holes in gaseous proto-galactic nuclei

ABSTRACT Accretion at sustained or episodic super-Eddington (SE) rates has been proposed as a pathway to grow efficiently light seeds produced by Pop-III stars. We investigate if SE accretion can be sustained onto a black hole (BH) with MBH ∼ 103 M⊙ in the centre of a gas-rich proto-galaxy at z = 15. We perform high-resolution smoothed-particle hydrodynamical simulations, including two different sub-grid models for SE accretion, one based on the slim disc paradigm, and one inspired by recent radiation-magnetohydrodynamical simulations by Jiang and collaborators. Radiative feedback has the form of a thermal dump to surrounding gas particles, with the radiative efficiency being set according to the different SE accretion models. We find that, in all simulations, star formation, BH feedback, and interactions between clumps and the BH rapidly quench accretion after ∼1 Myr, irrespective of the sub-grid model used for accretion. Quenching is stronger in the model based on the simulations of Jiang and collaborators relative to the slim disc model because of its higher radiative efficiency. The SE growth phase is always very brief, lasting a few 0.1 Myr. In the most optimistic case, the BH reaches a mass of ∼104 M⊙. We extrapolate the final BH masses from z = 15 to z ∼ 6, assuming subsequent galaxy mergers will replenish the gas reservoir and trigger new cycles of SE accretion. We find that at most BH seeds would grow to ∼106 M⊙, comparable to the mass of massive BHs in spiral galaxies such as the Milky Way, but falling short of the mass of the high-redshift quasars.

SN 1961V: A Pulsational Pair-instability Supernova

We explore a variety of models in which SN 1961V, one of the most enigmatic supernovae (SNe) ever observed, was a pulsational pair-instability supernova (PPISN). Successful models reproduce the bolometric light curve of the principal outburst and, in some cases, the emission 1 yr before and several years afterward. All models have helium-rich ejecta, bulk hydrogenic velocities near 2000 km s−1, and total kinetic energies of (4−8) × 1050 erg. Each eventually leaves behind a black hole remnant. Three subclasses of PPISN models are explored, each with two different choices of carbon abundance following helium burning. Carbon is an important parameter because shell carbon burning can weaken the explosion. The three subclasses correspond to situations where SN 1961V and its immediate afterglow were (a) a single event, (b) the first of two or more pulsational events separated by decades or centuries, or (c) the latter stages of a complex explosion that had already been going on for a year or more. For the low-carbon case, the main-sequence mass for SN 1961V’s progenitor would have been 100−115 M ⊙, its pre-SN helium core mass was 45−52 M ⊙, and the final black hole mass was 40−45 M ⊙. For the high-carbon case, these values are increased by roughly 20%−25%. In some PPISN models, a ∼1040 erg s−1 star-like object could still be shining at the site of SN 1961V, but it has more likely been replaced by a massive accreting black hole.

High-overtone fits to numerical relativity ringdowns: Beyond the dismissed n=8 special tone

In general relativity, the remnant object originating from an uncharged black hole merger is a Kerr black hole. The approach to this final state is reached through the emission of a late train of radiation known as the black hole ringdown. The ringdown morphology is described by a countably infinite set of damped sinusoids, whose complex frequencies are solely determined by the final black hole's mass and spin. Recent results advocate that ringdown waveforms from numerical relativity can be fully described from the peak of the strain onwards if quasi-normal mode models with $N_{max}=7$ overtones are used. In this work we extend this analysis to models with $N_{max}\geq 7$ up to $N_{max}=16$ overtones by exploring the parameter bias on the final mass and final spin obtained by fitting the nonprecessing binary black hole simulations from the SXS catalogue. To this aim, we have computed the spin weight $-2$ quasi-normal mode frequencies and angular separation constants for the special $(l=m=2, n=8,9)$ overtones for the Kerr spacetime. We find that a total of $N_{max}\sim 6$ overtones are on average sufficient to model the ringdown starting at the peak of the strain, although about $21\%$ of the cases studied require at least $N_{max}\sim 12$ overtones to reach a comparable accuracy on the final state parameters. Considering the waveforms from an earlier or later point in time, we find that a very similar maximum accuracy can be reached in each case, occurring at a different number of overtones $N_{max}$. We provide new error estimates for the SXS waveforms based on the extrapolation and the resolution uncertainties of the gravitational wave strain. Finally, we observe substantial instabilities on the values of the best-fit amplitudes of the tones beyond the fundamental mode and the first overtone, that, nevertheless, do not impact significantly the mass and spin estimates.

Mass Ejection in Failed Supernovae: Equation of State and Neutrino Loss Dependence

Abstract A failed core-collapse supernova from a nonrotating progenitor can eject mass due to a weakening of gravity associated with neutrino emission from the protoneutron star. This mechanism yields observable transients and sets an upper limit on the mass of the black hole (BH) remnant. Previous global simulations of this mechanism have included neutrino losses parametrically, however, with direct implications for the ejecta mass and energy. Here we evolve the inner supernova core with a spherically symmetric, general-relativistic neutrino radiation-hydrodynamic code until BH formation. We then use the result in a Newtonian code that follows the response of the outer layers of the star to the change in gravity and resolves the surface pressure scale height. We find that the dense-matter equation of state (EOS) can introduce a factor of ∼2 variation in gravitational mass lost to neutrinos, with a stiff EOS matching previous parametric results and a soft EOS yielding lower ejecta masses and energies by a factor of several. This difference is caused primarily by the longer time to BH formation in stiffer EOSs. With a soft EOS, our red and yellow supergiant progenitors fail to unbind mass if hydrogen recombination energy is not included. Using a linear ramp in time for mass-energy lost to neutrinos (with suitable parameters) yields a stellar response within ∼10% of that obtained using the detailed history of neutrino losses. Our results imply quantitative but not qualitative modifications to previous predictions for shock breakout, plateau emission, and final BH masses from these events.

Sensitivity of the lower edge of the pair-instability black hole mass gap to the treatment of time-dependent convection

ABSTRACT Gravitational-wave detections are now probing the black hole (BH) mass distribution, including the predicted pair-instability mass gap. These data require robust quantitative predictions, which are challenging to obtain. The most massive BH progenitors experience episodic mass ejections on time-scales shorter than the convective turnover time-scale. This invalidates the steady-state assumption on which the classic mixing length theory relies. We compare the final BH masses computed with two different versions of the stellar evolutionary code $\tt{MESA}$: (i) using the default implementation of Paxton et al. (2018) and (ii) solving an additional equation accounting for the time-scale for convective deceleration. In the second grid, where stronger convection develops during the pulses and carries part of the energy, we find weaker pulses. This leads to lower amounts of mass being ejected and thus higher final BH masses of up to ∼$5\, \mathrm{M}_\odot$. The differences are much smaller for the progenitors that determine the maximum mass of BHs below the gap. This prediction is robust at $M_{\rm BH, max}\simeq 48\, \mathrm{M}_\odot$, at least within the idealized context of this study. This is an encouraging indication that current models are robust enough for comparison with the present-day gravitational-wave detections. However, the large differences between individual models emphasize the importance of improving the treatment of convection in stellar models, especially in the light of the data anticipated from the third generation of gravitational-wave detectors.

Using final black hole spins and masses to infer the formation history of the observed population of gravitational wave sources

In this paper we propose a novel technique to constrain the progenitor binary black hole (BBH) formation history using the remnant masses and spins of merged black holes (BHs). Exploring different models, we found that dynamically formed BBHs are distributed differently in the mass-spin plane than those that have formed in isolation. Stellar evolution recipes crucially affect the remnant mass distribution, suggesting that future efforts should be devoted to finding a common way of modelling the evolutionary phases of single and binary stars. Our simple approach has allowed us to place weak constraints on the origin of the presently observed population of merged BHs, although with high uncertainties. Our results show that the fingerprints of different BBH formation channels will emerge as soon as LIGO detects more than $\sim 10^2$ merger events. This work provides a way of thinking that can be easily used both by people working on isolated and on dynamical BBH formation and evolution.

Multi-scale simulations of black hole accretion in barred galaxies

Due to the non-axisymmetric potential of the central bar, in addition to their characteristic arms and bar, barred spiral galaxies form a variety of structures within the thin gas disk, such as nuclear rings, inner spirals, and dust lanes. These structures in the inner kiloparsec are extremely important in order to explain and understand the rate of black hole feeding. The aim of this work is to investigate the influence of stellar bars in spiral galaxies on the thin self-gravitating gas disk. We focus on the accretion of gas onto the central supermassive black hole and its time-dependent evolution. We conducted multi-scale simulations simultaneously resolving the galactic disk and the accretion disk around the central black hole. In all the simulations we varied the initial gas disk mass. As an additional parameter we chose either the gas temperature for isothermal simulations or the cooling timescale for non-isothermal simulations. Accretion was either driven by a gravitationally unstable or clumpy accretion disk or by energy dissipation in strong shocks. Most of the simulations show a strong dependence of the accretion rate at the outer boundary of the central accretion disk (r< 300 pc) on the gas flow at kiloparsec scales. The final black hole masses reach up to ~109 M⊙after 1.6 Gyr. Our models show the expected influence of the Eddington limit and a decline in growth rate at the corresponding sub-Eddington limit.

Hangup effect in unequal mass binary black hole mergers and further studies of their gravitational radiation and remnant properties

We present the results of 74 new simulations of nonprecessing spinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/7\leq q\leq1$ and individual spins covering the parameter space $-0.95\leq\alpha_{1,2}\leq0.95$ with one runs with spins of $\pm0.95$. We supplement those runs with 107 previous simulations to study the hangup effect in black hole mergers, i.e. the delay or prompt merger of spinning holes with respect to non spinning binaries. We perform the numerical evolution for typically the last ten orbits before the merger and down to the formation of the final remnant black hole. This allows us to study the hangup effect for unequal mass binaries leading us to identify the spin variable that controls the number of orbits before merger as $\vec{S}_{hu}\cdot{\hat{L}},$ where $\vec{S}_{hu}=(1+\frac12\frac{m_2}{m_1})\vec{S}_1+(1+\frac12\frac{m_1}{m_2})\vec{S}_2$. We also combine the total results of those 181 simulations to obtain improved fitting formulae for the remnant final black hole mass, spin and recoil velocity as well as for the peak luminosity and peak frequency of the gravitational strain, and find new correlations among them. This accurate new set of simulations enhances the number of available numerical relativity waveforms available for parameter estimation of gravitational wave observations.

Turbulent gas accretion between supermassive black-holes and star-forming rings in the circumnuclear disk

While supermassive black holes are known to co-evolve with their host galaxy, the precise nature and origin of this co-evolution is not clear. We here explore the possible connection between star formation and black hole growth in the circumnuclear disk (CND) to probe this connection in the vicinity close to the black hole. We adopt here the circumnuclear disk model developed by Kawakatu & Wada (2008) and Wutschik et al. (2013), and explore both the dependence on the star formation recipe as well as the role of the gravitational field, which can be dominated by the central black hole, the CND itself or the host galaxy. A specific emphasis is put on the turbulence regulated star formation model by Krumholz et al. (2005) to explore the impact of a realistic star formation recipe. It is shown that this model helps to introduce realistic fluctuations in the black hole and star formation rate, without overestimating them. Consistent with previous works, we show that the final black hole masses are rather insensitive to the masses of the initial seeds, even for seed masses of up to 10^6 M_sol. In addition, we apply our model to the formation of high-redshift quasars, as well as to the nearby system NGC 6951, where a tentative comparison is made in spite of the presence of a bar in the galaxy. We show that our model can reproduce the high black hole masses of the high-redshift quasars within a sufficiently short time, provided a high mass supply rate from the host galaxy. In addition, it reproduces several of the properties observed in NGC 6951. With respect to the latter system, our analysis suggests that supernova feedback may be important to create the observed fluctuations in the star formation history as a result of negative feedback effects.

How AGN and SN Feedback Affect Mass Transport and Black Hole Growth in High-redshift Galaxies

Abstract Using cosmological hydrodynamical simulations, we study the effect of supernova (SN) and active galactic nucleus (AGN) feedback on the mass transport (MT) of gas onto galactic nuclei and the black hole (BH) growth down to redshift z ∼ 6 . We study the BH growth in relation to the MT processes associated with gravity and pressure torques and how they are modified by feedback. Cosmological gas funneled through cold flows reaches the galactic outer region close to freefall. Then torques associated with pressure triggered by gas turbulent motions produced in the circumgalactic medium by shocks and explosions from SNe are the main source of MT beyond the central ∼100 pc. Due to high concentrations of mass in the central galactic region, gravitational torques tend to be more important at high redshift. The combined effect of almost freefalling material and both gravity and pressure torques produces a mass accretion rate of order ∼ 1 M ⊙ yr−1 at approximately parsec scales. In the absence of SN feedback, AGN feedback alone does not affect significantly either star formation or BH growth until the BH reaches a sufficiently high mass of ∼ 10 6 M ⊙ to self-regulate. SN feedback alone, instead, decreases both stellar and BH growth. Finally, SN and AGN feedback in tandem efficiently quench the BH growth, while star formation remains at the levels set by SN feedback alone, due to the small final BH mass, ∼few times 10 5 M ⊙ . SNe create a more rarefied and hot environment where energy injection from the central AGN can accelerate the gas further.

Remnant of binary black-hole mergers: New simulations and peak luminosity studies

We present the results of 61 new simulations of nonprecessing spinning black hole binaries with mass ratios $q={m}_{1}/{m}_{2}$ in the range $1/3\ensuremath{\le}q\ensuremath{\le}1$ and individual spins covering the parameter space $\ensuremath{-}0.85\ensuremath{\le}{\ensuremath{\alpha}}_{1,2}\ensuremath{\le}0.85$. We additionally perform ten new simulations of nonspinning black hole binaries with mass ratios covering the range $1/6\ensuremath{\le}q<1$. We follow the evolution for typically the last ten orbits before merger down to the formation of the final remnant black hole. This allows for assessment of the accuracy of our previous empirical formulas for relating the binary parameters to the remnant final black hole mass, spin and recoil. We use the new simulation to improve the fit to the above remnant formulas and add a formula for the peak luminosity of gravitational waves, produced around the merger of the two horizons into one. We find excellent agreement (typical errors $\ensuremath{\sim}0.1%--0.2%$) for the mass and spin, and within $\ensuremath{\sim}5%$ for the recoil and peak luminosity. These formulas have direct application to parameter estimation techniques applied to LIGO observations of gravitational waves from binary black hole mergers.

GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence.

We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially identified within 70s by an online matched-filter search targeting binary coalescences. Subsequent off-line analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than 5σ. The signal persisted in the LIGO frequency band for approximately 1s, increasing in frequency and amplitude over about 55 cycles from 35 to 450Hz, and reached a peak gravitational strain of 3.4_{-0.9}^{+0.7}×10^{-22}. The inferred source-frame initial black hole masses are 14.2_{-3.7}^{+8.3}M_{⊙} and 7.5_{-2.3}^{+2.3}M_{⊙}, and the final black hole mass is 20.8_{-1.7}^{+6.1}M_{⊙}. We find that at least one of the component black holes has spin greater than 0.2. This source is located at a luminosity distance of 440_{-190}^{+180} Mpc corresponding to a redshift of 0.09_{-0.04}^{+0.03}. All uncertainties define a 90% credible interval. This second gravitational-wave observation provides improved constraints on stellar populations and on deviations from general relativity.

Global structure of exact scalar hairy dynamical black holes

We study the global structure of some exact scalar hairy dynamical black holes which were constructed in Einstein gravity either minimally or non-minimally coupled to a scalar field. We find that both the apparent horizon and the local event horizon (measured in luminosity coordinate) monotonically increase with the advanced time as well as the Vaidya mass. At late advanced times, the apparent horizon approaches the event horizon and gradually becomes future outer. Correspondingly, the space-time arrives at stationary black hole states with the relaxation time inversely proportional to the $1/(n-1)$ power of the final black hole mass, where $n$ is the space-time dimension. These results strongly support the solutions describing the formation of black holes with scalar hair. We also obtain new charged dynamical solutions in the non-minimal theory by introducing an Maxwell field which is non-minimally coupled to the scalar. The presence of the electric charge strongly modifies the dynamical evolution of the space-time.

Observation of Gravitational Waves from a Binary Black Hole Merger.

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160) Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

AGN feedback models: correlations with star formation and observational implications of time evolution

We examine the correlation between the star formation rate (SFR) and black hole accretion rate (BHAR) across a suite of different AGN feedback models, using the time evolution of a merger simulation. By considering three different stages of evolution, and a distinction between the nuclear and outer regions of star formation, we consider 63 different cases. Despite many of the feedback models fitting the M-\sigma\ relationship well, there are often distinct differences in the SFR-BHAR correlations, with close to linear trends only being present after the merger. Some of the models also show evolution in the SFR-BHAR parameter space that is at times directly across the long-term averaged SFR-BHAR correlation. This suggests that the observational SFR-BHAR correlation found for ensembles of galaxies is an approximate statistical trend, as suggested by Hickox et al. Decomposing the SFR into nuclear and outer components also highlights notable differences between models and there is only modest agreement with observational studies examining this in Seyfert galaxies. For the fraction of the black hole mass growth from the merger event relative to the final black hole mass, we find as much as a factor of three variation among models. This also translates into a similar variation in the post-starburst black hole mass growth. Overall, we find that while qualitative features are often similar amongst models, precise quantitative analysis shows there can be quite distinct differences.

Accretion disc particle accretion in major merger simulations

A recent approach to simulating localized feedback from active galactic nuclei by Power et al. (2011) uses an accretion disc particle to represent both the black hole and its accretion disc. We have extrapolated and adapted this approach to simulations of Milky Way-sized galaxy mergers containing black holes and explored the impact of the various parameters in this model as well as its resolution dependence. The two key parameters in the model are an effective accretion radius, which determines the radius within which gas particles are added to the accretion disc, and a viscous time-scale which determines how long it takes for material in the accretion disc to accrete on to the black hole itself. We find that there is a limited range of permitted accretion radii and viscous time-scales, with unphysical results produced outside this range. For permitted model parameters, the nuclear regions of simulations with the same resolution follow similar evolutionary paths, producing final black hole masses that are consistent within a factor of two. When comparing the resolution dependence of the model, there is a trend towards higher resolution producing slightly lower mass black holes, but values for the two resolutions studied again agree within a factor of two. We also compare these results to two other AGN feedback algorithms found in the literature. While the evolution of the systems vary, most notably the intermediate total black hole mass, the final black hole masses differ by less than a factor of five amongst all of our models, and the remnants exhibit similar structural parameters. The implication of this accretion model is that, unlike most accretion algorithms, a decoupling of the accretion rate on to the black hole and the local gas properties is permitted and obtained; this allows for black hole growth even after feedback has prevented additional accretion events on to the disc.

Remnant masses, spins and recoils from the merger of generic black hole binaries

We obtain empirical formulae for the final remnant black hole mass, spin, and recoil velocity from merging black hole binaries (BHBs) with arbitrary mass ratios and spins. Our formulae are based on the mass ratio and spin dependence of the post-Newtonian expressions for the instantaneous radiated energy, linear momentum, and angular momentum, as well as the ISCO binding energy and angular momentum. The relative weight between the different terms is fixed by amplitude parameters chosen through a least-squares fit of recently available fully nonlinear numerical simulations. These formulae can be used for statistical studies of N-body simulations of galaxy cores and clusters, and the cosmological growth of supermassive black holes. As an example, we use these formulae to obtain a universal spin magnitude distribution of merged black holes and recoil velocity distributions for dry and hot/cold wet mergers. We also revisit the long-term orbital precession and resonances and discuss how they affect spin distributions before the merging regime.

Approaching faithful templates for nonspinning binary black holes using the effective-one-body approach

We present an accurate approximation of the full gravitational radiation waveforms generated in the merger of noneccentric systems of two nonspinning black holes. Utilizing information from recent numerical relativity simulations and the natural flexibility of the effective-one-body (EOB) model, we extend the latter so that it can successfully match the numerical relativity waveforms during the last stages of inspiral, merger, and ringdown. By ``successfully'' here, we mean with phase differences $\ensuremath{\lesssim}8%$ of a gravitational-wave cycle accumulated by the end of the ringdown phase, maximizing only over time of arrival and initial phase. We obtain this result by simply adding a 4-post-Newtonian order correction in the EOB radial potential and determining the (constant) coefficient by imposing high-matching performances with numerical waveforms of mass ratios ${m}_{1}/{m}_{2}=1$, $3/2$, 2 and 4, ${m}_{1}$ and ${m}_{2}$ being the individual black-hole masses. The final black-hole mass and spin predicted by the numerical simulations are used to determine the ringdown frequency and decay time of three quasinormal-mode damped sinusoids that are attached to the EOB inspiral-(plunge) waveform at the EOB light ring. The EOB waveforms might be tested and further improved in the future by comparison with extremely long and accurate inspiral numerical relativity waveforms. They may be already employed for coherent searches and parameter estimation of gravitational waves emitted by nonspinning coalescing binary black holes with ground-based laser-interferometer detectors.

Mass Deficits, Stalling Radii, and the Merger Histories of Elliptical Galaxies

A binary supermassive black hole leaves an imprint on a galactic nucleus in the form of a "mass deficit," a decrease in the mass of the nucleus due to ejection of stars by the binary. The magnitude of the mass deficit is in principle related to the galaxy's merger history, but the relation has never been quantified. Here, high-accuracy N-body simulations are used to calibrate this relation. Mass deficits are shown to be approximately 0.5M_{12}, with M_{12} the total mass of the binary; the coefficient in this relation depends only weakly on the binary mass ratio or on the galaxy's pre-existing density profile. Hence, after N mergers, the mass deficit is ~0.5 N M_h with M_h the final (current) black hole mass. When compared with observed mass deficits, this result implies between 1 and 3 mergers for most galaxies, in accord with hierarchical galaxy formation models. Implications for binary stalling radii, the origin of hyper-velocity stars, and the distribution of dark matter at the centers of galaxies are discussed.

Explosion of very massive stars and the origin of intermediate mass black holes

AbstractWe calculate evolution, collapse, explosion, and nucleosynthesis of Population III very massive stars with 500 M⊙ and 1000 M⊙. It was found that both 500 M⊙ and 1000 M⊙ models enter the region of pair-instability but continue to undergo core collapse to black holes. For moderately aspherical explosions, the patterns of nucleosynthesis match the observational data of intergalactic and intercluster medium and hot gases in M82, better than models involving hypernovae and pair instability supernovae.Our results suggest that explosions of Population III core-collapse very massive stars contribute significantly to the chemical evolution of gases in clusters of galaxies. The final black hole masses are about 500 M⊙ for our most massive 1000 M⊙ models. This result may support the view that Population III very massive stars are responsible for the origin of intermediate mass black holes which were recently reported to be discovered.