Mass Spectrum Of Black Holes Research Articles

Constraining the black hole mass spectrum with gravitational wave observations - II. Direct comparison of detailed models

A number of scenarios have been proposed for the origin of the supermassive black holes (SMBHs) that are found in the centres of most galaxies. Many such scenarios predict a high-redshift population of massive black holes (MBHs), with masses in the range 100 to 100000 times that of the Sun. When the Laser Interferometer Space Antenna (LISA) is finally operational, it is likely that it will detect on the order of 100 of these MBH binaries as they merge. The differences between proposed population models produce appreciable effects in the portion of the population which is detectable by LISA, so it is likely that the LISA observations will allow us to place constraints on them. However, gravitational wave detectors such as LISA will not be able to detect all such mergers nor assign precise black hole parameters to the merger, due to weak gravitational wave signal strengths. This paper explores LISA's ability to distinguish between several MBH population models. In this way, we go beyond predicting a LISA observed population and consider the extent to which LISA observations could inform astrophysical modellers. The errors in LISA parameter estimation are applied with a direct method which generates random sample parameters for each source in a population realisation. We consider how the distinguishability varies depending on the choice of source parameters (1 or 2 parameters chosen from masses, redshift or spins) used to characterise the model distributions, with confidence levels determined by 1 and 2-dimensional tests based on the Kolmogorov-Smirnov test.

Constraints on the induced gravitational wave background from primordial black holes

We perform a consistent calculation of primordial black hole (PBH) mass spectrum and second-order induced gravitational wave (GW) background produced from primordial scalar perturbations in radiation era of the early Universe. It is shown that the maximal amplitudes of the second order GW spectrum that can be approached without conflicting with the PBH data do not depend significantly on the shape of primordial perturbation spectrum. The constraints on the GW background obtained in previous works are extended to a wider GW frequency range. We discuss the applicability of the currently available pulsar timing limits for obtaining the constraints on scalar power spectrum and PBH abundance and show that they can be used for strongly constraining the PBH number density in the PBH mass range $\sim (0.03 - 10) M_{\odot}$.

A mechanism of supermassive primordial black hole formation

We discuss the mechanisms of supermassive primordial black hole formation in the period before the beginning of star formation. We study the dependence of the primordial black hole mass spectrum on the initial conditions at the inflationary stage.

Constraints on amplitudes of curvature perturbations from primordial black holes

We calculate the primordial black hole (PBH) mass spectrum produced from a collapse of the primordial density fluctuations in the early Universe using, as an input, several theoretical models giving the curvature perturbation power spectra ${\mathcal{P}}_{\mathcal{R}}(k)$ with large ($\ensuremath{\sim}{10}^{\ensuremath{-}2}\char21{}{10}^{\ensuremath{-}1}$) values at some scale of comoving wave numbers $k$. In the calculation we take into account the explicit dependence of gravitational (Bardeen) potential on time. Using the PBH mass spectra, we further calculate the neutrino and photon energy spectra in extragalactic space from evaporation of light PBHs, and the energy density fraction contained in PBHs today (for heavier PBHs). We obtain the constraints on the model parameters using available experimental data (including data on neutrino and photon cosmic backgrounds). We briefly discuss the possibility that the observed 511 keV line from the Galactic center is produced by annihilation of positrons evaporated by PBHs.

Mass spectrum of primordial black holes from inflationary perturbation in theRandall–Sundrum braneworld: a limit on blue spectra

The mass spectrum of the primordial black holes formed by density perturbation in theradiation-dominated era of the Randall–Sundrum type-2 cosmology is given. Thespectrum coincides with the standard four-dimensional one on large scales but thedeviation is apparent on smaller scales. The mass spectrum is initially softer than thestandard four-dimensional one, while after accretion during the earliest era itbecomes harder than that. We also show expected extragalactic diffuse photonbackground spectra varying the initial perturbation power-law power spectrum and giveconstraints on the blue spectra and/or the reheating temperature. The most recentobservations on the small scale density perturbation from WMAP, SDSS andLyman-α Forest are used. What we get are interpreted as constraints on thesmaller-scale inflation on the brane connected to the larger one at the scale ofLyman-α Forest. If we set the bulk curvature radius to be 0.1 mm and assume the reheating temperature is higherthan 106 GeV, the scalar spectral index from the smaller scale inflation is constrained to be . Typically, the constraints are tighter than the standard four-dimensional one, which isalso revised by us using the most recent observations.

The Brightest Point X‐Ray Sources in Elliptical Galaxies and the Mass Spectrum of Accreting Black Holes

We propose that the shape of the upper-end X-ray luminosity function (XLF) observed in elliptical galaxies for point sources carries valuable information about the black hole (BH) mass spectrum among old X-ray transients formed in the galaxies. Here we present the line of arguments and analysis that support this connection and the methodology for deriving the BH mass spectrum slope from the observed XLF slope. We show that this underlying BH mass spectrum is modified by a weighting factor that is related to the transient duty cycle, and it generally depends on the host galaxy age, the BH mass, and the X-ray binary (XRB) donor type (main-sequence, red giant, or white dwarf donors). We find that the observed XLF is dominated by transient BH systems in outburst (a prediction possibly testable by future observations) but that the assumption of a constant duty cycle for all systems leads to results inconsistent with current observations. We also find that the derived BH mass slope depends on the strength of the angular momentum loss due to magnetic braking for main-sequence donors. More specifically, we find that for standard magnetic braking, BH XRBs with red giant donors dominate the upper-end XLF but that for weaker magnetic braking prescriptions, main-sequence donors are found to be dominant. The methodology presented here can be used in the future as our understanding of the transient duty and its dependence on binary and mass transfer properties improves. Under certain assumptions for this dependence, we derive a differential BH mass spectrum slope of 2.5; an upper BH mass cutoff at 20 M☉ is needed to understand the very brightest of the BH XRBs in elliptical galaxies. We also show that our quantitative results are robust against expected variations by factors of a few of the outburst peak X-ray luminosities. We expect that our analysis will eventually help to constrain binary population synthesis models and the adopted relations between black holes and the masses of their progenitors.

Point X-ray Sources in Elliptical Galaxies

We analyze the upper-end X-ray luminosity function (XLF) observed in elliptical galaxies for point sources. We propose that the observed XLF is dominated by transient BH systems in outburst and the XLF shape reflects the black hole (BH) mass spectrum among old X-ray transients. The BH mass spectrum – XLF connection depends on a weighting factor that is related to the transient duty cycle and depends on the host-galaxy age, the BH mass and the donor type (main sequence, red giant, or white dwarf). We argue that the assumption of a constant duty cycle for all systems leads to results inconsistent with current observations. The type of dominant donors in the upper-end XLF depends on what type of magnetic braking operates: in the case of “standard” magnetic braking, BH X-ray binaries with red-giant donors dominate, and in the case of weaker magnetic braking prescriptions main sequence donors dominate.

Near extremal Schwarzschild-de Sitter black hole area spectrum from quasi-normal modes

Using the quasi-normal modes frequency of near extremal Schwar-zschild-de Sitter black holes, we obtain area and entropy spectrum for the black hole horizon. By using Bohr-Sommerfeld quantization for an adiabatic invariant I = ∫dEω(E), where E is the energy of the system and ω(E) is the vibrational frequency, we arrive at an equally spaced mass spectrum. In the other terms, we extend directly the Kunstatter’s approach kun [6] to determine mass and entropy spectrum of near extremal Schwarzschild-de Sitter black holes which are asymptotically de Sitter rather than asymptotically flat. We show the mass and area spectrum is equally spaced only for a fixed l. For different l there are multiplets with different values of spacing.

Supermassive black hole mass measurements for NGC 1300 and 2748 based on Hubble Space Telescope emission-line gas kinematics

We present Space Telescope Imaging Spectrograph emission-line spectra of the central regions of the spiral galaxies NGC 1300 and 2748. From the derived kinematics of the nuclear gas we have found evidence for central supermassive black holes in both galaxies. The estimated masses of the black holes in NGC 1300 and 2748 are (6.6 +6.3) × 10 7 and (4.4 +3.5) × 10 7 M� , respectively (both at the 95 per cent confidence level). These two black hole mass estimates contribute to the poorly sampled low-mass end of the nuclear black hole mass spectrum. Ke yw ords: black hole physics ‐ galaxies: individual: NGC 1300 ‐ galaxies: individual: NGC 2748 ‐ galaxies: kinematics and dynamics ‐ galaxies: nuclei ‐ galaxies: spiral.

Quantum Black Holes: the Event Horizon as a Fuzzy Sphere

Modeling the event horizon of a black hole by a fuzzy sphere it is shown that in the classical limit, for large astrophysical black-holes, the event horizon looks locally like a non-commutative plane with non-commutative parameter dictated by the Planck length. Some suggestions in the literature concerning black hole mass spectra are used to derive a formula for the mass spectrum of quantum black holes in terms of four integers which define the area, angular momentum, electric and magnetic charge of the black hole. We also suggest how the classical bounds on extremal black holes might be modified in the quantum theory.

The Mass Spectrum of Black Holes in Close Binary Systems

We present the results of population syntheses obtained using our "scenario machine." The mass spectra of black holes in X-ray binary systems before and after the stage of accretion from an optical companion are obtained for various evolutionary scenarios.The results of the model computations are compared to observational data.The observational data are used to estimate the fraction of a pre- supernova's mass that collapses into a black hole.This model can explain the formation of low-mass (2−4 M� ) black holes in binary systems with optical companions.We show that the number of low-mass black holes in the Galaxy is sufficiently high for them to be detected.The population-synthesis results suggest that the vast majority of low-mass black holes are formed via the accretion-induced collapse of neutron stars.The percentage of low-mass black holes in binary systems that form due to accretion- induced collapse is 2-15% of the total number of black holes in binaries, depending on the evolutionary scenario. c � 2005Pleiades Publishing, Inc.

CONCEPTUAL UNIFICATION OF ELEMENTARY PARTICLES, BLACK HOLES, QUANTUM DE SITTER AND ANTI-DE SITTER STRING STATES

We provide a conceptual unified description of the quantum properties of black holes (BH), elementary particles, de Sitter (dS) and Anti-de Sitter (AdS) string states.The conducting line of argument is the classical–quantum (de Broglie, Compton) duality here extended to the quantum gravity (string) regime (wave–particle–string duality). The semiclassical (QFT) and quantum (string) gravity regimes are respectively characterized and related: sizes, masses, accelerations and temperatures. The Hawking temperature, elementary particle and string temperatures are shown to be the same concept in different energy regimes and turn out the precise classical–quantum duals of each other; similarly, this result holds for the BH decay rate, heavy particle and string decay rates; BH evaporation ends as quantum string decay into pure (nonmixed) radiation. Microscopic density of states and entropies in the two (semiclassical and quantum) gravity regimes are derived and related, an unifying formula for BH, dS and AdS states is provided in the two regimes. A string phase transition towards the dS string temperature (which is shown to be the precise quantum dual of the semiclassical (Hawking–Gibbons) dS temperature) is found and characterized; such phase transition does not occurs in AdS alone. High string masses (temperatures) show a further (square root temperature behavior) sector in AdS. From the string mass spectrum and string density of states in curved backgrounds, quantum properties of the backgrounds themselves are extracted and the quantum mass spectrum of BH, dS and AdS radii obtained.

Universal canonical black hole entropy.

Nonrotating black holes in three and four dimensions are shown to possess a canonical entropy obeying the Bekenstein-Hawking area law together with a leading correction (for large horizon areas) given by the logarithm of the area with a universal finite negative coefficient, provided one assumes that the quantum black hole mass spectrum has a power-law relation with the quantum area spectrum found in nonperturbative canonical quantum general relativity. The thermal instability associated with asymptotically flat black holes appears in the appropriate domain for the index characterizing this power-law relation, where the canonical entropy (free energy) is seen to turn complex.

Varying constants, black holes, and quantum gravity

Tentative observations and theoretical considerations have recently led to renewed interest in models of fundamental physics in which certain ``constants'' vary in time. Assuming fixed black hole mass and the standard form of the Bekenstein-Hawking entropy, Davies, Davis and Lineweaver have argued that the laws of black hole thermodynamics disfavor models in which the fundamental electric charge $e$ changes. I show that with these assumptions, similar considerations severely constrain ``varying speed of light'' models, unless we are prepared to abandon cherished assumptions about quantum gravity. Relaxation of these assumptions permits sensible theories of quantum gravity with ``varying constants,'' but also eliminates the thermodynamic constraints, though the black hole mass spectrum may still provide some restrictions on the range of allowable models.

The Cosmic Density of Massive Black Holes from Galaxy Velocity Dispersions

Supermassive black holes are thought to be relics of quasars, and their numbers and masses are therefore related to the quasar luminosity function and its evolution with redshift. We have used the relationship between black hole mass and bulge velocity dispersion (the •-σ relation) to make an improved estimate of the mass density and mass spectrum of supermassive black holes. Uncertainties in the •-σ relation have little effect on the mass density. We find a mass density of (4.8 ± 1.6)h2 × 105 M⊙ Mpc-3. Some of the variance in published density estimates comes from the use of different values of the Hubble constant.

Cosmological constraints from evaporation of primordial black holes

A formula for the initial mass spectrum of primordial black holes (PBHs), which can be used for the general case of a scale dependent spectral index, and for a wide class of models of gravitational collapse, is derived. The derivation is based on the Press-Schechter formalism. A comparative analysis of different types of initial mass spectra used in concrete calculations is carried out. It is shown that densities of background radiation $(\ensuremath{\nu},$ $\ensuremath{\gamma})$ from PBH evaporation depend rather strongly on the type of gravitational collapse and on taking into account the spread of horizon masses at which PBHs can form. Constraints on the parameters of the primordial density perturbation amplitudes based on PBH evaporation processes and on atmospheric and solar neutrino data are obtained.

TOWARDS A THEORY OF QUANTUM BLACK HOLES

We describe some specific quantum black hole model. It is pointed out that the origin of a black hole entropy is the very process of quantum gravitational collapse. The quantum black hole mass spectrum is extracted from the mass spectrum of the gravitating source. The classical analog of quantum black hole is constructed.

Bounds from primordial black holes with a near critical collapse initial mass function

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational collapse. Assuming that these holes formed from the initial density perturbations seeded by inflation, we calculate model independent upper bounds on the mass variance at the reheating temperature by requiring that the mass density does not exceed the critical density and the photon emission does not exceed current diffuse gamma-ray measurements. We then translate these results into bounds on the spectral index n by utilizing the COBE data to normalize the mass variance at large scales, assuming a constant power law, and scale this result to the reheating temperature. We find that our bounds on n differ substantially $(\ensuremath{\delta}n>0.05)$ from those calculated using initial mass functions derived under the assumption that the black hole mass is proportional to the horizon mass at the collapse epoch. We also find a change in the shape of the diffuse gamma-ray spectrum which results from the Hawking radiation. Finally, we study the impact of a nonzero cosmological constant and find that the bounds on n are strengthened considerably if the universe is indeed vacuum-energy dominated today.

Initial mass spectrum of black holes in galactic nuclei

Within the framework of the cosmological model with cold dark matter we have calculated the initial mass function of supermassive black holes formed in galactic nuclei. The collapsing region is modeled by a homogeneous ellipsoid. It is assumed that the accumulation of angular momentum by the proto-object takes place under the action of external tidal forces, and that surmounting of the centrifugal barrier with subsequent gravitational collapse occurs as a result of turbulent viscosity. To determine the mass function, we first find the angular momentum distribution function of the nascent objects for an arbitrary spectrum of initial density perturbations. The initial mass function is compared with available observations, and some processes leading to its transformation are indicated.

Quantum properties of topological black holes

We examine quantum properties of topological black holes which are asymptotically anti--de Sitter. First, massless scalar fields and Weyl spinors which propagate in the background of an anti--de Sitter black hole are considered in an exactly soluble two--dimensional toy model. The Boulware--, Unruh--, and Hartle--Hawking vacua are defined. The latter results to coincide with the Unruh vacuum due to the boundary conditions necessary in asymptotically adS spacetimes. We show that the Hartle--Hawking vacuum represents a thermal equilibrium state with the temperature found in the Euclidean formulation. The renormalized stress tensor for this quantum state is well--defined everywhere, for any genus and for all solutions which do not have an inner Cauchy horizon, whereas in this last case it diverges on the inner horizon. The four--dimensional case is finally considered, the equilibrium states are discussed and a luminosity formula for the black hole of any genus is obtained. Since spacelike infinity in anti--de Sitter space acts like a mirror, it is pointed out how this would imply information loss in gravitational collapse. The black hole's mass spectrum according to Bekenstein's view is discussed and compared to that provided by string theory.