Mass Spectrum Of Black Holes Research Articles

Lepton flavor asymmetries and the mass spectrum of primordial black holes

We study the influence of lepton flavour asymmetries on the formation and the mass spectrum of primordial black holes. We estimate the detectability of their mergers with LIGO/Virgo and show that the currently published gravitational wave events may actually be described by a primordial black hole spectrum from non-zero asymmetries. We suggest to use gravitational-wave astronomy as a novel tool to probe how lepton flavour asymmetric the Universe has been before the onset of neutrino oscillations.

Closer look at white hole remnants

The idea that, after their evaporation, Planck-mass black holes might tunnel into metastable white holes has recently been intensively studied. Those relics have been considered as a dark matter candidate. We show that the model is severely constrained and underline some possible detection paths. We also investigate, in a more general setting, the way the initial black hole mass spectrum would be distorted by both the bouncing effect and the Hawking evaporation.

Intermediate-mass Black Holes from High Massive-star Binary Fractions in Young Star Clusters

Abstract Black holes formed in dense star clusters, where dynamical interactions are frequent, may have fundamentally different properties than those formed through isolated stellar evolution. Theoretical models for single-star evolution predict a gap in the black hole mass spectrum from roughly 40–120 M ⊙ caused by (pulsational) pair-instability supernovae. Motivated by the recent LIGO/Virgo event GW190521, we investigate whether black holes with masses within or in excess of this “upper-mass gap” can be formed dynamically in young star clusters through strong interactions of massive stars in binaries. We perform a set of N-body simulations using the CMC cluster-dynamics code to study the effects of the high-mass binary fraction on the formation and collision histories of the most massive stars and their remnants. We find that typical young star clusters with low metallicities and high binary fractions in massive stars can form several black holes in the upper-mass gap and often form at least one intermediate-mass black hole. These results provide strong evidence that dynamical interactions in young star clusters naturally lead to the formation of more massive black hole remnants.

Formation of GW190521 from stellar evolution: the impact of the hydrogen-rich envelope, dredge-up, and 12C(α, γ)16O rate on the pair-instability black hole mass gap

ABSTRACT Pair-instability (PI) is expected to open a gap in the mass spectrum of black holes (BHs) between ≈40–65 and ≈120 M⊙. The existence of the mass gap is currently being challenged by the detection of GW190521, with a primary component mass of $85^{+21}_{-14}$ M⊙. Here, we investigate the main uncertainties on the PI mass gap: the 12C(α, γ)16O reaction rate and the H-rich envelope collapse. With the standard 12C(α, γ)16O rate, the lower edge of the mass gap can be 70 M⊙ if we allow for the collapse of the residual H-rich envelope at metallicity Z ≤ 0.0003. Adopting the uncertainties given by the starlib database, for models computed with the 12C(α, γ)16O rate $-1\, \sigma$, we find that the PI mass gap ranges between ≈80 and ≈150 M⊙. Stars with MZAMS > 110 M⊙ may experience a deep dredge-up episode during the core helium-burning phase, that extracts matter from the core enriching the envelope. As a consequence of the He-core mass reduction, a star with MZAMS = 160 M⊙ may avoid the PI and produce a BH of 150 M⊙. In the $-2\, {}\sigma {}$ case, the PI mass gap ranges from 92 to 110 M⊙. Finally, in models computed with 12C(α, γ)16O $-3\, {}\sigma {}$, the mass gap is completely removed by the dredge-up effect. The onset of this dredge-up is particularly sensitive to the assumed model for convection and mixing. The combined effect of H-rich envelope collapse and low 12C(α, γ)16O rate can lead to the formation of BHs with masses consistent with the primary component of GW190521.

Black Hole Genealogy: Identifying Hierarchical Mergers with Gravitational Waves

Abstract In dense stellar environments, the merger products of binary black hole mergers may undergo additional mergers. These hierarchical mergers are naturally expected to have higher masses than the first generation of black holes made from stars. The components of hierarchical mergers are expected to have significant characteristic spins, imprinted by the orbital angular momentum of the previous mergers. However, since the population properties of first-generation black holes are uncertain, it is difficult to know if any given merger is first-generation or hierarchical. We use observations of gravitational waves to reconstruct the binary black hole mass and spin spectrum of a population including the possibility of hierarchical mergers. We employ a phenomenological model that captures the properties of merging binary black holes from simulations of globular clusters. Inspired by recent work on the formation of low-spin black holes, we include a zero-spin subpopulation. We analyze binary black holes from LIGO and Virgo’s first two observing runs, and find that this catalog is consistent with having no hierarchical mergers. We find that the most massive system in this catalog, GW170729, is mostly likely a first-generation merger, having a 4% probability of being a hierarchical merger assuming a 5 × 105 M ⊙ globular cluster mass. Using our model, we find that 99% of first-generation black holes in coalescing binaries have masses below M ⊙, and the fraction of binaries with near-zero component spins is less than (90% probability). Upcoming observations will determine if hierarchical mergers are a common source of gravitational waves.

Connecting the Higgs potential and primordial black holes

It was recently demonstrated that small small black holes can act as seeds for nucleating decay of the metastable Higgs vacuum, dramatically increasing the tunneling probability. Any primordial black hole lighter than $4.5 \times 10^{14}$g at formation would have evaporated by now, and in the absence of new physics beyond the standard model, would therefore have entered the mass range in which seeded decay occurs, however, such true vacuum bubbles must percolate in order to completely destroy the false vacuum; this depends on the bubble number density and the rate of expansion of the universe. Here, we compute the fraction of the universe that has decayed to the true vacuum as a function of the formation temperature (or equivalently, mass) of the primordial black holes, and the spectral index of the fluctuations responsible for their formation. This allows us to constrain the mass spectrum of primordial black holes given a particular Higgs potential and conversely, should we discover primordial black holes of definite mass, we can constrain the Higgs potential parameters.

Search for Eccentric Binary Black Hole Mergers with Advanced LIGO and Advanced Virgo during Their First and Second Observing Runs

Abstract When formed through dynamical interactions, stellar-mass binary black holes (BBHs) may retain eccentric orbits (e > 0.1 at 10 Hz) detectable by ground-based gravitational-wave detectors. Eccentricity can therefore be used to differentiate dynamically formed binaries from isolated BBH mergers. Current template-based gravitational-wave searches do not use waveform models associated with eccentric orbits, rendering the search less efficient for eccentric binary systems. Here we present the results of a search for BBH mergers that inspiral in eccentric orbits using data from the first and second observing runs (O1 and O2) of Advanced LIGO and Advanced Virgo. We carried out the search with the coherent WaveBurst algorithm, which uses minimal assumptions on the signal morphology and does not rely on binary waveform templates. We show that it is sensitive to binary mergers with a detection range that is weakly dependent on eccentricity for all bound systems. Our search did not identify any new binary merger candidates. We interpret these results in light of eccentric binary formation models. We rule out formation channels with rates ≳100 Gpc−3 yr−1 for e > 0.1, assuming a black hole mass spectrum with a power-law index ≲2.

Primordial black holes from inflation with nonminimal derivative coupling

We propose a novel enhancement mechanism of the curvature perturbations in the nonminimal derivative coupling inflation model with a coupling parameter related to the inflaton field. By considering a special form of the coupling parameter as a function of the inflaton, a period of ultra-slow-roll inflation can be realized due to the gravitationally enhanced friction, and the resulting power spectrum of the curvature perturbations has a sharp peak, which is large enough to produce the primordial black holes. Under this mechanism, we can easily obtain a sharp mass spectrum of primordial black holes around specific masses such as $\mathcal{O}(10)M_\odot$, $\mathcal{O}(10^{-5})M_\odot$, and $\mathcal{O}(10^{-12})M_\odot$, which can explain the LIGO events, the ultrashort-timescale microlensing events in OGLE data, and the most of dark matter, respectively.

Binary Black Hole Population Properties Inferred from the First and Second Observing Runs of Advanced LIGO and Advanced Virgo

Abstract We present results on the mass, spin, and redshift distributions with phenomenological population models using the 10 binary black hole (BBH) mergers detected in the first and second observing runs completed by Advanced LIGO and Advanced Virgo. We constrain properties of the BBH mass spectrum using models with a range of parameterizations of the BBH mass and spin distributions. We find that the mass distribution of the more massive BH in such binaries is well approximated by models with no more than 1% of BHs more massive than 45 M ⊙ and a power-law index of α = 1.3 − 1.7 + 1.4 (90% credibility). We also show that BBHs are unlikely to be composed of BHs with large spins aligned to the orbital angular momentum. Modeling the evolution of the BBH merger rate with redshift, we show that it is flat or increasing with redshift with 93% probability. Marginalizing over uncertainties in the BBH population, we find robust estimates of the BBH merger rate density of R = 53.2 − 28.2 + 55.8 Gpc−3 yr−1 (90% credibility). As the BBH catalog grows in future observing runs, we expect that uncertainties in the population model parameters will shrink, potentially providing insights into the formation of BHs via supernovae, binary interactions of massive stars, stellar cluster dynamics, and the formation history of BHs across cosmic time.

Primordial density perturbation and primordial black holes

The black holes formed in the early universe are called primordial black holes. Primordial black holes provide a profound tool to detect the primordial cosmological structures and study nontrivial physics of the early Universe. By fitting the theoretical predictions about primordial black holes to the observational data, we can constrain the cosmological models. There exist several mechanisms about the formation of primordial black holes. In this review, we focus on the primordial black holes formed by the collapse of over-densed regions. This paper is organized as follows. The first section is the introduction. Then, in the second section, we introduce briefly several basic concepts on the primordial black holes formed by the collapse of the over-densed region, including the condition for an over-densed region to collapse into a primordial black hole, the mass, the formation time and the lifetime of a primordial black hole. About the primordial- black-hole mass, usually, in the over-densed-region-collapsing mechanism, the Carr-Hawking collapsing model is adopted to describe the formation. This collapsing model tells us that primordial black holes always form with the mass approximately equal to the mass contained by the Hubble horizon at the time when the over-densed regions enter the Hubble horizon. This is called the horizon-mass relation. But, recently, the numerical simulations show that the phenomenon of the critical collapse happens in the formation of primordial black holes. And primordial black holes with a range of masse are formed. The mass function of primordial black holes is given by a scaling relation. Here, both of the relations are introduced. Then, in the third section, based on the assumption that the primordial cosmological density perturbations obey the Gaussian distribution, we review the calculation of the mass spectrum of the primordial black holes. In this section, we, firstly, review the widely-used approximate expression of the initial mass spectrum of the primordial black holes. This approximate result is based on the horizon-mass relation that is implied by the Carr-Hawking collapsing model. Then by using the Press-Schechter method, we introduce the exact expression of the initial mass spectrum of the primordial black holes. This exact expression is based on the scaling relation that is implied by the critical collapse. Then by neglecting the effect of the Hawking radiation of primordial black holes, we express the present mass spectrum of the primordial black holes in terms of the initial mass spectrum of the primordial black holes. However, usually, the effect of the Hawking radiation of primordial black holes cannot be neglected. Then we also review how to calculate the mass spectrum of the primordial black holes by considering the effect of the Hawking radiation. Since the mainstream cosmologists believe that, up to now, inflation is the best mechanism to generate the primordial density perturbation, we assume that the initial over-densed regions also origin from inflation. Then in the subsection of the third section, we relate the primordial power spectrum generated by inflation to the initial mass spectrum of the primordial black holes. The fourth section is the summary and discussion.

Measuring the Binary Black Hole Mass Spectrum with an Astrophysically Motivated Parameterization

Abstract Gravitational-wave detections have revealed a previously unknown population of stellar mass black holes with masses above 20 M ⊙. These observations provide a new way to test models of stellar evolution for massive stars. By considering the astrophysical processes likely to determine the shape of the binary black hole mass spectrum, we construct a parameterized model to capture key spectral features that relate gravitational-wave data to theoretical stellar astrophysics. In particular, we model the signature of pulsational pair-instability supernovae, which are expected to cause all stars with initial mass 100 M ⊙ ≲ M ≲ 150 M ⊙ to form ∼40 M ⊙ black holes. This would cause a cutoff in the black hole mass spectrum along with an excess of black holes near 40 M ⊙. We carry out a simulated data study to illustrate some of the stellar physics that can be inferred using gravitational-wave measurements of binary black holes and demonstrate several such inferences that might be made in the near future. First, we measure the minimum and maximum stellar black hole mass. Second, we infer the presence of a peak due to pair-instability supernovae. Third, we measure the distribution of black hole mass ratios. Finally, we show how inadequate models of the black hole mass spectrum lead to biased estimates of the merger rate and the amplitude of the stochastic gravitational-wave background.

Fast radio bursts and the stochastic lifetime of black holes in quantum gravity

Nonperturbative quantum gravity effects might allow a black-to-white hole transition. We revisit this increasingly popular hypothesis by taking into account the fundamentally random nature of the bouncing time. We show that if the primordial mass spectrum of black holes is highly peaked, the expected signal can in fact match the wavelength of the observed fast radio bursts. On the other hand, if the primordial mass spectrum is wide and smooth, clear predictions are suggested and the sensitivity to the shape of the spectrum is studied.

Massive Primordial Black Holes as Dark Matter and their detection with Gravitational Waves

Massive Primordial Black Holes (MPBH) can be formed after inflation due to broad peaks in the primordial curvature power spectrum that collapse gravitationally during the radiation era, to form clusters of black holes that merge and increase in mass after recombination, generating today a broad mass-spectrum of black holes with masses ranging from 0.01 to 105 M⊙. These MPBH could act as seeds for galaxies and quick-start structure formation, initiating reionization, forming galaxies at redshift z > 10 and clusters at z > 1. They may also be the seeds on which SMBH and IMBH form, by accreting gas onto them and forming the centers of galaxies and quasars at high redshift. They form at rest with zero spin and have negligible cross-section with ordinary matter. If there are enough of these MPBH, they could constitute the bulk of the Dark Matter today. Such PBH could be responsible for the observed fluctuations in the CIB and X-ray backgrounds. MPBH could be directly detected by the gravitational waves emitted when they merge to form more massive black holes, as recently reported by LIGO. Their continuous merging since recombination could have generated a stochastic background of gravitational waves that could eventually be detected by LISA and PTA. MPBH may actually be responsible for the unidentified point sources seen by Fermi, Magic and Chandra. Furthermore, the ejection of stars from shallow potential wells like those of Dwarf Spheroidals (DSph), via the gravitational slingshot effect, could be due to MPBH, thus alleviating the substructure and too-big-to-fail problems of standard collisionless CDM. Their mass distribution peaks at a few tens of M⊙ today, and could therefore be detected also with long-duration microlensing events, as well as by the anomalous motion of stars in the field of GAIA. Their presence as CDM in the Universe could be seen in the time-dilation of strong-lensing images of quasars. The hierarchical large scale structure behaviour of MPBH does not differ from that of ordinary CDM.

Extended micro objects as dark matter particles

Models of various forms of composite dark matter (DM) predicted by particle theory and the DM constituents formed by gravity that are not reduced to new elementary particle candidates are discussed. Main attention is paid to a gravitational origin of the DM. The influence of extended mass spectrum of primordial black holes on observational limits is considered. It is shown that non-uniformly deformed extra space can be considered as point-like masses which possess only gravitational interaction with each other and with the ordinary particles. The recently discussed six-dimensional stable wormholes could contribute to the DM. The contribution of dark atoms is also considered.

Stellar-mass black holes in young massive and open stellar clusters and their role in gravitational-wave generation

The dynamical processes involving stellar-remnant black holes (BH) in stellar clusters has always drawn attention due to the BHs' potential in a number of astrophysical phenomena, especially the dynamical formation of binary black holes (BBH), which would potentially coalesce via radiation of gravitational waves (GW). This study presents a preliminary set of evolutionary models of compact stellar clusters with initial masses ranging over $1.0\times10^4M_\odot-5.0\times10^4M_\odot$, and half-mass radius of 2 pc or 1 pc, that is typical for young massive and starburst clusters. They have metallicities between $0.05Z_\odot-Z_\odot$. Including contemporary schemes for stellar wind and remnant-formation, such model clusters are evolved, for the first time, using the state-of-the-art direct N-body evolution program NBODY7, until their dissolution or at least for 10 Gyr. That way, a self-regulatory behaviour in the effects of dynamical interactions among the BHs, especially while heating and expanding the cluster and self-depleting the BHs, is demonstrated. The BBH mergers obtained here show a prominence in triple-mediated mergers while being bound to the clusters, compared to those occurring among the BBHs that are dynamically ejected from the clusters. This is in contrast with earlier N-body computations and also with recent Monte-Carlo method based ones. A broader mass spectrum of BHs and ejection of BBHs generally of wider orbits and in lower numbers, for the cluster masses explored here, might cause this which is yet to be fully understood. Among the BBH coalescences obtained here, there are ones that resemble the detected GW151226, LVT151012, and GW150914 events and also ones which are even more massive. A preliminary estimate suggests few 10s - 100s of BBH coalescences per year, originating due to dynamics in stellar clusters, that can be detected by the LIGO at its design sensitivity.

Accretion disk dynamics

Aims: We investigate the suitability of {\alpha}-viscosity in self-similar models for self-gravitating disks with a focus on active galactic nuclei (AGN) disks. Methods: We use a self-similar approach to simplify the partial differential equations arising from the evolution equation, which are then solved using numerical standard procedures. Results: We find a self-similar solution for the dynamical evolution of self-gravitating {\alpha}-disks and derive the significant quantities. In the Keplerian part of the disk our model is consistent with standard stationary {\alpha}-disk theory, and self-consistent throughout the self-gravitating regime. Positive accretion rates throughout the disk demand a high degree of self-gravitation. Combined with the temporal decline of the accretion rate and its low amount, the model prohibits the growth of large central masses. Conclusions: {\alpha}-viscosity cannot account for the evolution of the whole mass spectrum of super-massive black holes (SMBH) in AGN. However, considering the involved scales it seems suitable for modelling protoplanetary disks. Keywords: accretion, accretion disks, turbulence, hydrodynamics, methods: analytical

Effects of critical collapse on primordial black-hole mass spectra

Certain inflationary models as well as realisations of phase transitions in the early Universe predict the formation of primordial black holes. For most mass ranges, the fraction of matter in the form of primordial black holes is limited by many different observations on various scales. Primordial black holes are assumed to be formed when overdensities that cross the horizon have Schwarzschild radii larger than the horizon. Traditionally it was therefore assumed that primordial black-hole masses were equal to the horizon mass at their time of formation. However, detailed calculations of their collapse show that primordial black holes formed at each point in time should rather form a spectrum of different masses, obeying critical scaling. Though this has been known for more than fifteen years, the effect of this scaling behaviour is largely ignored when considering predictions for primordial black hole mass spectra. In this paper we consider the critical collapse scaling for a variety of models which produce primordial black holes, and find that it generally leads to a shift, broadening and an overall decrease of the mass contained in primordial black holes. This effect is model and parameter dependent and cannot be contained by a constant rescaling of the spectrum; it can become important and should be taken into account when comparing to observational constraints.

Black holes and the multiverse

Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive black holes. The mechanism of black hole formation described in this paper is very generic and has important implications for the global structure of the universe. Baby universes inside super-critical black holes inflate eternally and nucleate bubbles of all vacua allowed by the underlying particle physics. The resulting multiverse has a very non-trivial spacetime structure, with a multitude of eternally inflating regions connected by wormholes. If a black hole population with the predicted mass spectrum is discovered, it could be regarded as evidence for inflation and for the existence of a multiverse.

The quantum emission spectra of rapidly-rotating Kerr black holes: Discrete or continuous?

Bekenstein and Mukhanov (BM) have suggested that, in a quantum theory of gravity, black holes may have discrete emission spectra. Using the time-energy uncertainty principle they have also shown that, for a (non-rotating) Schwarzschild black hole, the natural broadening δω of the black-hole emission lines is expected to be small on the scale set by the characteristic frequency spacing Δω of the spectral lines: ζSch≡δω/Δω≪1. BM have therefore concluded that the expected discrete emission lines of the quantized Schwarzschild black hole are unlikely to overlap. In this paper we calculate the characteristic dimensionless ratio ζ(a¯)≡δω/Δω for the predicted BM emission spectra of rapidly-rotating Kerr black holes (here a¯≡J/M2 is the dimensionless angular momentum of the black hole). It is shown that ζ(a¯) is an increasing function of the black-hole angular momentum. In particular, we find that the quantum emission lines of Kerr black holes in the regime a¯≳0.9 are characterized by the dimensionless ratio ζ(a¯)≳1 and are therefore effectively blended together. Our results thus suggest that, even if the underlying mass (energy) spectrum of these rapidly-rotating Kerr black holes is fundamentally discrete as suggested by Bekenstein and Mukhanov, the natural broadening phenomenon (associated with the time-energy uncertainty principle) is expected to smear the black-hole radiation spectrum into a continuum.

The mass spectrum of compact remnants from the parsec stellar evolution tracks

The mass spectrum of stellar-mass black holes (BHs) is highly uncertain. Dynamical mass measurements are available only for few ( 10) BHs in X-ray binaries, while theoretical models strongly depend on the hydrodynamics of supernova (SN) explosions and on the evolution of massive stars. In this paper, we present and discuss the mass spectrum of compact remnants that we obtained with SEVN, a new public populationsynthesis code, which couples the PARSEC stellar evolution tracks with up-to-date recipes for SN explosion (depending on the Carbon-Oxygen mass of the progenitor, on the compactness of the stellar core at pre-SN stage, and on a recent two-parameter criterion based on the dimensionless entropy per nucleon at pre-SN stage). SEVN can be used both as a stand-alone code and in combination with direct-summation N-body codes (Starlab, HiGPUs). The PARSEC stellar evolution tracks currently implemented in SEVN predict signicantly larger values of the Carbon-Oxygen core mass with respect to previous models. For most of the SN recipes we adopt, this implies substantially larger BH masses at low metallicity (6 2 10 3 ), than other populationsynthesis codes. The maximum BH mass found with SEVN is 25, 60 and 130 M at metallicity Z = 2 10 2 , 2 10 3 and 2 10 4 , respectively. Mass loss by stellar winds plays a major role in determining the mass of BHs for very massive stars (> 90 M ), while the remnant mass spectrum depends mostly on the adopted SN recipe for lower progenitor masses. We discuss the implications of our results for the transition between NS and BH mass, and for the expected number of massive BHs (with mass > 25 M ) as a function of metallicity.