Gravitational waves from scattering of stellar-mass black holes in galactic nuclei

Stellar-mass black holes (BHs) are expected to segregate and form a steep density cusp around supermassive black holes (SMBHs) in galactic nuclei. We follow the evolution of a multimass system of BHs and stars by numerically integrating the Fokker–Planck energy diffusion equations for a variety of BH mass distributions. We find that the BHs 'self-segregate', and that the rarest, most massive BHs dominate the scattering rate closest to the SMBH  (≲10⁻¹ pc)  . BH–BH binaries form out of gravitational wave emission during BH encounters. We find that the expected rate of BH coalescence events detectable by Advanced LIGO is  ∼1–10² yr⁻¹  , depending on the initial mass function of stars in galactic nuclei and the mass of the most massive BHs. We find that the actual merger rate is likely ∼10 times larger than this due to the intrinsic scatter of stellar densities in many different galaxies. The BH binaries that form this way in galactic nuclei have significant eccentricities as they enter the LIGO band (90 per cent with   e > 0.9  ), and are therefore distinguishable from other binaries, which circularize before becoming detectable. We also show that eccentric mergers can be detected to larger distances and greater BH masses than circular mergers, up to  ∼700 M_⊙  . Future ground-based gravitational wave observatories will be able to constrain both the mass function of BHs and stars in galactic nuclei.     

Star clusters around recoiled black holes in the Milky Way halo

Gravitational wave emission by coalescing black holes (BHs) kicks the remnant BH with a typical velocity of hundreds of  km s⁻¹  . This velocity is sufficiently large to remove the remnant BH from a low-mass galaxy but is below the escape velocity from the Milky Way (MW) galaxy. If central BHs were common in the galactic building blocks that merged to make the MW, then numerous BHs that were kicked out of low-mass galaxies should be freely floating in the MW halo today. We use a large statistical sample of possible merger tree histories for the MW to estimate the expected number of recoiled BH remnants present in the MW halo today. We find that hundreds of BHs should remain bound to the MW halo after leaving their parent low-mass galaxies. Each BH carries a compact cluster of old stars that populated the core of its original host galaxy. Using the time-dependent Fokker–Planck equation, we find that the present-day clusters are  ≲1 pc  in size, and their central bright regions should be unresolved in most existing sky surveys. These compact systems are distinguishable from globular clusters by their internal (Keplerian) velocity dispersion greater than 100 km s⁻¹ and their high mass-to-light ratio owing to the central BH. An observational discovery of this relic population of star clusters in the MW halo would constrain the formation history of the MW and the dynamics of BH mergers in the early Universe. A similar population should exist around other galaxies and may potentially be detectable in M31 and M33.     

The dynamical evolution of massive black hole binaries - II. Self-consistent N-body integrations

We use a hybrid N-body program to study the evolution of massive black hole binaries in the centers of galaxies, mainly to understand the factors affecting the binary eccentricity, the response of the galaxy to the binary merger, and the effect of loss-cone depletion on the merger time. The scattering experiments from paper I (Quinlan, 1996)[NewA, 1, 35] showed that the merger time is not sensitive to the eccentricity growth unless a binary forms with at least a moderate eccentricity. We find here that the eccentricity can become large under some conditions if a binary forms in a galaxy with a flat core or with a radial bias in its velocity distribution, especially if the dynamical friction is enhanced by resonances as suggested by Rauch & Tremaine (1996)[NewA, 1, 149]. But the necessary conditions seem unlikely, and our prediction from paper I remains unchanged: in most cases the eccentricity will start and remain small. The ejection of stars caused by the hardening of a binary may explain why large elliptical galaxies have weaker density cusps than smaller galaxies. If so, the central velocity distributions in those galaxies should have strong tangential anisotropies. The wandering of a binary from the center of a galaxy counteracts the effects of loss-cone depletion and helps the binary merge.     

The growth and assembly of a massive galaxy at z∼ 2

We study the stellar mass assembly of the Spiderweb galaxy  (MRC 1138−262)  , a massive   z = 2.2  radio galaxy in a protocluster and the probable progenitor of a brightest cluster galaxy. Nearby protocluster galaxies are identified and their properties are determined by fitting stellar population models to their rest-frame ultraviolet to optical spectral energy distributions. We find that within 150 kpc of the radio galaxy the stellar mass is centrally concentrated in the radio galaxy, yet most of the dust-uncorrected, instantaneous star formation occurs in the surrounding low-mass satellite galaxies. We predict that most of the galaxies within 150 kpc of the radio galaxy will merge with the central radio galaxy by   z = 0  , increasing its stellar mass by up to a factor of ≃2. However, it will take several hundred Myr for the first mergers to occur, by which time the large star formation rates are likely to have exhausted the gas reservoirs in the satellite galaxies. The tidal radii of the satellite galaxies are small, suggesting that stars and gas are being stripped and deposited at distances of tens of kpc from the central radio galaxy. These stripped stars may become intracluster stars or form an extended stellar halo around the radio galaxy, such as those observed around cD galaxies in cluster cores.     

Evolution of massive binary black holes

Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). In this paper we study the evolution of massive BBHs in realistic galaxy models, using a generalization of techniques used to study tidal disruption rates around massive BHs. The evolution of BBHs depends on BH mass ratio and host galaxy type. BBHs with very low mass ratios (say, ≲0.001) are hardly ever formed by mergers of galaxies, because the dynamical friction time-scale is too long for the smaller BH to sink into the galactic centre within a Hubble time. BBHs with moderate mass ratios are most likely to form and survive in spherical or nearly spherical galaxies and in high-luminosity or high-dispersion galaxies; they are most likely to have merged in low-dispersion galaxies (line-of-sight velocity dispersion ≲90 km s⁻¹) or in highly flattened or triaxial galaxies.
The semimajor axes and orbital periods of surviving BBHs are generally in the range  10^-3–10 pc  and  10–10⁵ yr;  they are also larger in high-dispersion galaxies than in low-dispersion galaxies, larger in nearly spherical galaxies than in highly flattened or triaxial galaxies, and larger for BBHs with equal masses than for BBHs with unequal masses. The orbital velocities of surviving BBHs are generally in the range  10²–10⁴ km s^-1  . The methods of detecting surviving BBHs are also discussed.
If no evidence of BBHs is found in AGNs, this may be either because gas plays a major role in BBH orbital decay or because nuclear activity switches on soon after a galaxy merger, and ends before the smaller BH has had time to spiral to the centre of the galaxy.     

Galaxy cores as relics of black hole mergers

We investigate the hypothesis that the cores of elliptical galaxies and bulges are created from the binding energy liberated by the coalescence of supermassive binary black holes during galaxy mergers. Assuming that the central density profiles of galaxies were initially steep power laws,   ρ ∼ r ^-2  , we define the 'mass deficit' as the mass in stars that had to be removed from the nucleus in order to produce the observed core. We use non-parametric deprojection to compute the mass deficit in a sample of 35 early-type galaxies with high-resolution imaging data. We find that the mass deficit correlates well with the mass of the nuclear black hole, consistent with the predictions of merger models. We argue that cores in haloes of non-interacting dark matter particles should be comparable in size to those observed in the stars.     

Imaging of the protoelliptical NGC 1700 and its globular cluster system

An excellent candidate for a young elliptical, or 'protoelliptical' galaxy is NGC 1700. Here we present new B -, V - and I -band imaging using the Keck telescope, and reanalyse existing V - and I -band images from the Hubble Space Telescope . After subtracting a model of the galaxy from the Keck images, NGC 1700 reveals two symmetric tidal tail-like structures. If this interpretation is correct, it suggests a past merger event involving two spiral galaxies. These tails are largely responsible for the 'boxiness' of the galaxy isophotes observed at a radius of ∼13 kpc.
We also show that the B − I colour distribution of the globular cluster system is bimodal. The mean colour of the blue population is consistent with that of old Galactic globular clusters. Relative to this old, metal-poor population, we find that the red population is younger and more metal-rich. This young population has an age and metallicity similar to that inferred for the central stars, suggesting that both populations are associated with an episode of star formation triggered by the merger that may have formed the galaxy. We find that, although they have large errors, the majority of the age estimates of NGC 1700 are reasonably consistent and we adopt a 'best estimate' for the age of 3.0±1.0 Gyr. This relatively low age places NGC 1700 within the age range where there is a notable lack of obvious candidates for protoellipticals. The total globular cluster specific frequency is rather low for a typical elliptical, even after taking into account the fading of the galaxy over the next 10 Gyr. We speculate that NGC 1700 will eventually form a relatively 'globular cluster poor' elliptical galaxy.     

Specific angular momentum of disc merger remnants and the λR-parameter

We use two-dimensional kinematic maps of simulated binary disc mergers to investigate the  λ_R  -parameter, which is a luminosity-weighted measure of projected angular momentum per unit mass. This parameter was introduced to subdivide the SAURON sample of early-type galaxies in so-called fast  λ_R > 0.1  and slow rotators  λ_R < 0.1  . Tests on merger remnants reveal that  λ_R  is a robust indicator of the true angular momentum content in elliptical galaxies. We find the same range of  λ_R  values in our merger remnants as in the SAURON galaxies. The merger mass ratio is decisive in transforming fast rotators into slow rotators in a single binary merger, the latter being created mostly in an equal-mass merger. Slow rotators have a  λ_R  which does not vary with projection. The confusion rate with face-on fast rotators is very small. Mergers with a gas component form slow rotators with smaller ellipticities than collisionless merger remnants have, and are in much better agreement with the SAURON slow rotators. Remergers of merger remnants are slow rotators, but tend to have too high ellipticities. Fast rotators maintain the angular momentum content from the progenitor disc galaxy if merger mass ratio is high. Some SAURON galaxies have values of  λ _R   as high as our progenitor disc galaxies.     

The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power-law cusp. We show that the bulk of stars with a small angular-momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so-called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement.
Our results show that for a primary black hole mass of  ∼10⁶–10⁷ M_⊙  , the black hole mass-ratio   q > 10⁻²  , cusp size ∼1 pc, the tidal disruption rate can be as large as  ∼10⁻²–1 M_⊙ yr⁻¹  . This is at least 10²–10⁴ times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical-friction time-scale, and it is rather short: ∼10⁵ yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.     

Stellar-mass black hole binaries as ultraluminous X-ray sources

Ultraluminous X-ray sources (ULXs) with   L _x > 10³⁹ erg s⁻¹  have been discovered in great numbers in external galaxies with ROSAT , Chandra and XMM-Newton . The central question regarding this important class of sources is whether they represent an extension in the luminosity function of binary X-ray sources containing neutron stars and stellar-mass black holes (BHs), or a new class of objects, e.g. systems containing intermediate-mass BHs  (100–1000 M_⊙)  . We have carried out a theoretical study to test whether a large fraction of the ULXs, especially those in galaxies with recent star formation activity, can be explained with binary systems containing stellar-mass BHs. To this end, we have applied a unique set of binary evolution models for BH X-ray binaries, coupled to a binary population synthesis code, to model the ULXs observed in external galaxies. We find that for donor stars with initial masses  ≳10 M_⊙  the mass transfer driven by the normal nuclear evolution of the donor star is sufficient to potentially power most ULXs. This is the case during core hydrogen burning and, to an even more pronounced degree, while the donor star ascends the giant branch, although the latter phases last only ∼5 per cent of the main-sequence phase. We show that with only a modest violation of the Eddington limit, e.g. a factor of ∼10, both the numbers and properties of the majority of the ULXs can be reproduced. One of our conclusions is that if stellar-mass BH binaries account for a significant fraction of ULXs in star-forming galaxies, then the rate of formation of such systems is  ∼3 × 10⁻⁷ yr⁻¹  normalized to a core-collapse supernova rate of 0.01 yr⁻¹.     

Multiwavelength observations of an evolved galaxy group: an end-point of galaxy merging?

The group of galaxies RXJ1340.6+4018 has approximately the same bolometric X-ray luminosity as other bright galaxy groups and poor clusters such as the Virgo cluster. However, 70 per cent of the optical luminosity of the group comes from a dominant giant elliptical galaxy, compared with 5 per cent from M87 in Virgo.The second brightest galaxy in RXJ1340.6+4018 is a factor of 10 fainter (Δ m ₁₂=2.5 mag) than the dominant elliptical, and the galaxy luminosity function has a gap at about L *.
We interpret the properties of the system as a result of galaxy merging within a galaxy group. We find that the central galaxy lies on the Fundamental Plane of ellipticals, has an undisturbed, non-cD morphology, and has no spectral features indicative of recent star formation, suggesting that the last major merger occurred ≳4 Gyr ago. The deviation of the system from the cluster L _X− T relation in the opposite sense to most groups may be caused by an early epoch of formation of the group or a strong cooling flow.
The unusual elongation of the X-ray isophotes and the similarity between the X-ray and optical ellipticities at large radii (∼230 kpc) suggest that both the X-ray gas and the outermost stars of the dominant galaxy are responding to an elongated dark matter distribution. RXJ1340.6+4018 may be part of a filamentary structure related to infall in the outskirts of the cluster A1774.     

The elliptical galaxy colour–magnitude relation as a discriminant between the monolithic and merger paradigms

The colour–magnitude relation (CMR) of cluster elliptical galaxies has been widely used to constrain their star formation histories (SFHs) and to discriminate between the monolithic collapse and merger paradigms of elliptical galaxy formation. We use a Λ cold dark matter hierarchical merger model of galaxy formation to investigate the existence and redshift evolution of the elliptical galaxy CMR in the merger paradigm. We show that the SFH of cluster ellipticals predicted by the model is quasi-monolithic , with only ∼10 per cent of the total stellar mass forming after   z ∼ 1  . The quasi-monolithic SFH results in a predicted CMR that agrees well with its observed counterpart in the redshift range  0 < z < 1.27  . We use our analysis to argue that the elliptical-only CMR can be used to constrain the SFHs of present-day cluster ellipticals only if we believe a priori in the monolithic collapse model. It is not a meaningful tool for constraining the SFH in the merger paradigm, since a progressively larger fraction of the progenitor set of present-day cluster ellipticals is contained in late-type star-forming systems at higher redshift, which cannot be ignored when deriving the SFHs. Hence, the elliptical-only CMR is not a useful discriminant between the two competing theories of elliptical galaxy evolution.     

Black hole spin and radio loudness in a Λ cold dark matter universe

We use a combination of a cosmological N -body simulation of the concordance Λ cold dark matter paradigm and a semi-analytic model of galaxy formation to investigate the spin development of central supermassive black holes (BHs) and its relation to the BH host galaxy properties. In order to compute BH spins, we use the α model of Shakura & Sunyaev and consider the King et al. warped disc alignment criterion. The orientation of the accretion disc is inferred from the angular momentum of the source of accreted material, which bears a close relationship to the large-scale structure in the simulation. We find that the final BH spin depends almost exclusively on the accretion history and only weakly on the warped disc alignment. The main mechanisms of BH spin-up are found to be gas cooling processes and disc instabilities, a result that is only partially compatible with Monte Carlo models where the main spin-up mechanisms are major mergers and disc instabilities; the latter results are reproduced when implementing randomly oriented accretion discs in our model. Regarding the BH population, we find that more massive BHs, which are hosted by massive ellipticals, have higher spin values than less massive BHs, hosted by spiral galaxies. We analyse whether gas accretion rates and BH spins can be used as tracers of the radio loudness of active galactic nuclei (AGN). We find that the current observational indications of an increasing trend of radio-loud AGN fractions with stellar and BH mass can be easily obtained when placing lower limits on the BH spin, with a minimum influence from limits on the accretion rates; a model with random accretion disc orientations is unable to reproduce this trend. Our results favour a scenario where the BH spin is a key parameter to separate the radio-loud and radio-quiet galaxy populations.     

The effect of dwarf galaxy disruption in semi-analytic models

We present results for a galaxy formation model that includes a simple treatment for the disruption of dwarf galaxies by gravitational forces and galaxy encounters within galaxy clusters. This is implemented a posteriori in a semi-analytic model by considering the stability of cluster dark matter subhaloes at   z = 0  . We assume that a galaxy whose dark matter substructure has been disrupted will itself disperse, while its stars become part of the population of intracluster stars responsible for the observed intracluster light. Despite the simplicity of this assumption, our results show a substantial improvement over previous models and indicate that the inclusion of galaxy disruption is indeed a necessary ingredient of galaxy formation models. We find that galaxy disruption suppresses the number density of dwarf galaxies by about a factor of 2. This makes the slope of the faint end of the galaxy luminosity function shallower, in agreement with observations. In particular, the abundance of faint, red galaxies is strongly suppressed. As a result, the luminosity function of red galaxies and the distinction between the red and the blue galaxy populations in colour–magnitude relationships are correctly predicted. Finally, we estimate a fraction of intracluster light comparable to that found in clusters of galaxies.     

Evolutionary history of the elliptical galaxy NGC 1052

We have obtained Keck spectra for 16 globular clusters (GCs) associated with the merger remnant elliptical NGC 1052, as well as a long-slit spectrum of the galaxy. We derive ages, metallicities and abundance ratios from simple stellar population models using the recently published methods of Proctor & Sansom , applied to extragalactic GCs for the first time. A number of GCs indicate the presence of strong blue horizontal branches that are not fully accounted for in the current stellar population models. We find all of the GCs to be ∼13 Gyr old according to simple stellar populations, with a large range of metallicities. From the galaxy spectrum we find NGC 1052 to have a luminosity-weighted central age of ∼2 Gyr and metallicity of  [Fe/H]∼+0.6  . No strong gradients in either age or metallicity were found to the maximum radius measured  (0.3  r _e≃ 1 kpc)  . However, we do find a strong radial gradient in α-element abundance, which reaches a very high central value. The young central starburst age is consistent with the age inferred from the H  i tidal tails and infalling gas of ∼1 Gyr. Thus, although NGC 1052 shows substantial evidence for a recent merger and an associated starburst, it appears that the merger did not induce the formation of new GCs, perhaps suggesting that little recent star formation occurred. This interpretation is consistent with 'frosting' models for early-type galaxy formation.     

Optical emission from massive donors in ultraluminous X-ray source binary systems

We present evolutionary tracks of binary systems with high-mass companion stars and stellar-through-intermediate mass black holes (BHs). Using Eggleton's stellar evolution code, we compute the luminosity produced by accretion from the donor during its entire evolution. We compute also the evolution of the optical luminosity and colours of the binary system taking the disc contribution and irradiation effects into account. The calculations presented here can be used to constrain the properties of the donor stars in ultraluminous X-ray sources by comparing their position on the Hertzsprung–Russell or colour–magnitude diagrams with the evolutionary tracks of massive BH binaries. This approach may actually provide interesting clues also on the properties of the binary system itself, including the BH mass. We found that, on the basis of their position on the colour–magnitude diagram, some of the candidate counterparts considered can be ruled out and more stringent constraints can be applied to the donor masses.     

贫金属富碳天琴RR变星的形成

贫金属富碳恒星(Carbon-Enhanced Metal-Poor, CEMP)是研究宇宙早期恒星性质和化学演化的极佳样本,通常认为来自双星.目前发现的贫金属富碳星中有9颗天琴RR变星(RR Lyrae star, RRL),其中至少7颗未表现出任何双星特征.传统双星物质转移模型不足以充分解释贫金属富碳天琴RR变星(CEMP-RR Lyrae)单星的形成.之前研究表明氦白矮星和赫氏空隙星(HG)的并合模型可以解释部分富碳红巨星单星的碳增丰现象,因此贫金属富碳星单星也可能来自氦白矮星和赫氏空隙星的并合模型渠道.通过详细计算的氦白矮星和赫氏空隙星并合模型来检验这一演化渠道,结果表明:该并合模型在后续的演化过程中,其重力加速度、温度、表面碳丰度均能与观测符合较好.由此,氦白矮星和赫氏空隙星并合模型极有可能是贫金属富碳天琴RR变星的形成渠道之一.     

Rates of tidal disruption of stars by massive central black holes

There is strong evidence for some kind of massive dark object in the centres of many galaxy bulges. The detection of flares from tidally disrupted stars could confirm that these objects are black holes (BHs). Here we present calculations of the stellar disruption rates in detailed dynamical models of real galaxies, taking into account the refilling of the loss cone of stars on disruptable orbits by two-body relaxation and tidal forces in non-spherical galaxies. The highest disruption rates (one star per 10⁴ yr) occur in faint ( L ≲10¹⁰ L_⊙) galaxies, which have steep central density cusps. More luminous galaxies are less dense and have much longer relaxation times and more massive BHs. Dwarf stars in such galaxies are swallowed whole by the BH and hence do not emit flares; giant stars could produce flares as often as every 10⁵ yr, although the rate depends sensitively on the shape of the stellar distribution function. We discuss the possibility of detecting disruption flares in current supernova searches. The total mass of stars consumed over the lifetime of the galaxy is of the order of 10⁶ M_⊙, independent of galaxy luminosity; thus, disrupted stars may contribute significantly to the present BH mass in galaxies fainter than ∼10⁹ L_⊙.     

Imprints of recoiling massive black holes on the hot gas of early-type galaxies

Anisotropic gravitational radiation from a coalescing black hole (BH) binary is known to impart recoil velocities of up to  ∼1000 km s⁻¹  to the remnant BH. In this context, we study the motion of a recoiling BH inside a galaxy modelled as a Hernquist sphere, and the signature that the hole imprints on the hot gas, using N -body/smoothed particle hydrodynamics simulations. Ejection of the BH results in a sudden expansion of the gas ending with the formation of a gaseous core, similarly to what is seen for the stars. A cometary tail of particles bound to the BH is initially released along its trail. As the BH moves on a return orbit, a nearly spherical swarm of hot gaseous particles forms at every apocentre: this feature can live up to ≈10⁸ years. If the recoil velocity exceeds the sound speed initially, the BH shocks the gas in the form of a Mach cone in density near each supersonic pericentric passage. We find that the X-ray fingerprint of a recoiling BH can be detected in Chandra X-ray maps out to a distance of Virgo. For exceptionally massive BHs, the Mach cone and the wakes can be observed out to a few hundred of milliparsec. The detection of the Mach cone is of twofold importance as it can be a probe of high-velocity recoils, and an assessment of the scatter of the   M _BH− M _bulge  relation at large BH masses.