Salpeter Mass Research Articles

Dynamics of intermediate mass black holes in globular clusters

Context. We recently introduced a new method for simulating collisional gravitational N-body systems with approximately linear time scaling with N. Our method is based on the multi-particle collision (MPC) scheme, previously applied in fluid dynamics and plasma physics. We were able to simulate globular clusters with a realistic number of stellar particles (at least up to several times 106) on a standard workstation. Aims. We simulated clusters hosting an intermediate mass black hole (IMBH), probing a broad range of BH-cluster and BH–average-star mass ratios, unrestricted by the computational constraints that affect direct N-body codes. Methods. We set up a grid of hybrid particle-in-cell-MPC N-body simulations using our implementation of the MPC method, MPCDSS. We used either single mass models or models with a Salpeter mass function (a single power law with an exponent of −2.35), with the IMBH initially sitting at the centre. The force exerted by and on the IMBH was evaluated with a direct sum scheme with or without softening. For all simulations we measured the evolution of the Lagrangian radii and core density and velocity dispersion over time. In addition, we also measured the evolution of the velocity anisotropy profiles. Results. We find that models with an IMBH undergo core collapse at earlier times, the larger the IMBH mass the shallower they are, with an approximately constant central density at core collapse. The presence of an IMBH tends to lower the central velocity dispersion. These results hold independently of the mass function of the model. For the models with Salpeter MF, we observed that equipartition of kinetic energies is never achieved, even long after core collapse. Orbital anisotropy at large radii appears to be driven by energetic escapers on radial orbits, triggered by strong collisions with the IMBH in the core. We measured the wander radius, that is the distance of the IMBH from the centre of mass of the parent system over time, finding that its distribution has positive kurtosis. Conclusions. Among the results we obtained, which mostly confirm or extend previously known trends that had been established over the range of parameters accessible to direct N-body simulations, we underline that the leptokurtic nature of the IMBH wander radius distribution might lead to IMBHs presenting as off-centre more frequently than expected, with implications on observational IMBH detection.

GMC collisions as triggers of star formation – VIII. The core mass function

ABSTRACTCompression in giant molecular cloud (GMC) collisions is a promising mechanism to trigger the formation of massive star clusters and OB associations. We simulate colliding and non-colliding magnetized GMCs and examine the properties of pre-stellar cores, selected from projected mass surface density maps, including after synthetic ALMA observations. We then examine core properties, including mass, size, density, velocity, velocity dispersion, temperature, and magnetic field strength. After 4 Myr, ∼1000 cores have formed in the GMC collision, and the high-mass end of the core mass function (CMF) can be fit by a power-law dN/dlogM ∝ M−α with α ≃ 0.7, i.e. relatively top heavy compared to a Salpeter mass function. Depending on how cores are identified, a break in the power law can appear around a few $\times 10\, \mathrm{M}_\odot$. The non-colliding GMCs form fewer cores with a CMF with α ≃ 0.8–1.2, i.e. closer to the Salpeter index. We compare the properties of these CMFs to those of several observed samples of cores. Considering other properties, cores formed from colliding clouds are typically warmer, have more disturbed internal kinematics, and are more likely to be gravitational unbound, than cores formed from non-colliding GMCs. The dynamical state of the protocluster of cores formed in the GMC–GMC collision is intrinsically subvirial but can appear to be supervirial if the total mass measurement is affected by observations that miss mass on large scales or at low densities.

Gaia DR3 in 6D: the search for fast hypervelocity stars and constraints on the galactic centre environment

ABSTRACT The third data release (DR3) of the European Space Agency satellite Gaia provides coordinates, parallaxes, proper motions, and radial velocities for a sample of ∼34 million stars. We use the combined 6D phase space information to search for hypervelocity stars (HVSs), unbound stars accelerated by dynamical processes happening in the Galactic Centre. By looking at the kinematics of Gaia DR3 stars in Galactocentric coordinates and by integrating their orbits in the Galactic potential, we do not identify any HVS candidates with a velocity higher than 700 km s−1 and robustly observed kinematics. Assuming a scenario wherein the interaction between a stellar binary and the massive black hole Sgr A* is responsible for HVS ejections from the Galactic Centre, we derive degenerate limits on the ejection rate of HVSs and the slope of the initial mass function of the primary star among binaries in the Galactic Centre. Our results indicate that the HVS ejection rate is ≲8 × 10−5 yr−1 assuming a Salpeter mass function, and this upper limit becomes progressively smaller for an increasingly top-heavy mass distribution. A fiducial HVS ejection rate of 10−4 yr−1 prefers a mass function slope ≲−2.35, disfavouring previously claimed top-heavy initial mass functions among stars in the Galactic Centre.

Dark matter annihilation in the most luminous and the most massive ultra-compact dwarf galaxies (UCD)

In this paper, we explore the potential astrophysical signatures of dark matter (DM) annihilations in ultra-compact dwarf galaxies (UCDs) considering two of the richest known galaxy clusters within 100 million light-years, nominally, Virgo and Fornax. Fornax UCD3 is the most luminous known UCD and M59 UCD3 is the most massive known UCD. With the detection of a 3.5 million solar mass black hole (BH) in Fornax UCD3, we carefully model several dark matter (DM) enhanced profile scenarios, considering the presence of both a supermassive black hole (SMBH) and DM. For Fornax UCD3, the comparison of the stellar and dynamical masses suggests that there is little content of DM in UCDs. M59 UCD3 did not receive the same attention in simulations as Fornax UCD3, however deep radio imaging and X-ray observations were performed for M59 UCD3 and can be used to place limits in DM content of these UCDs. We take an average estimate of dark matter content and used the Salpeter and Kroupa mass functions. We model Fornax UCD3 and M59 UCD3 to have a DM content that is the average of these mass functions. We then analyze the constraints for Fornax and M59 UCD3 coming from γ-ray and radio sources, considering a dark matter particle with a mass between 10 and 34 GeV in our simulations. In the absence of a strong γ-ray signature, we show that the synchrotron emission from electrons and positrons produced by DM annihilations can be very sensitive to indirect DM search. We find that DM parameters can be significantly constrained at radio frequencies and that the spike profiles play an interesting role in the deep study of the enhancements of DM & BH interactions in ultra-compact galaxies.

Random fragmentation of turbulent molecular clouds lying in the central region of giant galaxies

A stochastic model of fragmentation of molecular clouds has been developed for studying the resulting Initial Mass Function (IMF) where the number of fragments, inter-occurrence time of fragmentation, masses and velocities of the fragments are random variables. Here two turbulent patterns of the velocities of the fragments have been considered, namely, Gaussian and Gamma distributions. It is found that for Gaussian distribution of the turbulent velocity, the IMFs are shallower in general compared to Salpeter mass function. On the contrary, a skewed distribution for turbulent velocity leads to an IMF which is much closer to Salpeter mass function. The above result might be due to the fact that strong driving mechanisms e.g. shocks, arising out of a big explosion occurring at the centre of the galaxy or due to big number of supernova explosions occurring simultaneously in massive parent clouds during the evolution of star clusters embedded into them are responsible for stripping out most of the gas from the clouds. This inhibits formation of massive stars in large numbers making the mass function a steeper one.

Statistical study of visual binaries

In this paper, some statistical distributions of wide pairs included in Double Star Catalogue are investigated. Frequency distributions and testing hypothesis are derived for some basic parameters of visual binaries. The results reached indicate that, it was found that the magnitude difference is distributed exponentially, which means that the majority of the component of the selected systems is of the same spectral type. The distribution of the mass ratios is concentrated about 0.7 which agree with Salpeter mass function. The distribution of the linear separation appears to be exponentially, which contradict with previous studies for close binaries.

Hubble–Lemaître fragmentation and the path to equilibrium of merger-driven cluster formation

This paper discusses a new method to generate self-coherent initial conditions for young substructured stellar cluster. The expansion of a uniform system allows stellar sub-structures (clumps) to grow from fragmentation modes by adiabatic cooling. We treat the system mass elements as stars, chosen according to a Salpeter mass function, and the time-evolution is performed with a collisional N-body integrator. This procedure allows to create a fully-coherent relation between the clumps' spatial distribution and the underlying velocity field. The cooling is driven by the gravitational field, as in a cosmological Hubble-Lema\^itre flow. The fragmented configuration has a `fractal'-like geometry but with a self-grown velocity field and mass profile. We compare the characteristics of the stellar population in clumps with that obtained from hydrodynamical simulations and find a remarkable correspondence between the two in terms of the stellar content and the degree of spatial mass-segregation. In the fragmented configuration, the IMF power index is ~0.3 lower in clumps in comparison to the field stellar population, in agreement with observations in the Milky Way. We follow in time the dynamical evolution of fully fragmented and sub-virial configurations, and find a soft collapse, leading rapidly to equilibrium (timescale of 1 Myr for a ~ 10^4 Msun system). The low-concentration equilibrium implies that the dynamical evolution including massive stars is less likely to induce direct collisions and the formation of exotic objects. Low-mass stars already ejected from merging clumps are depleted in the end-result stellar clusters, which harbour a top-heavy stellar mass function.

Statistics of light curves of a distant source microlensed by a system of point and extended masses

Gravitational microlensing of a distant source by a stochastic system of point masses (stars) and extended masses that model dark-matter clumps is analyzed. The size of each clump is set to be equal to 5 or 10 Einstein radii. A total of 100 realizations of the magnification map are generated under the assumption of a spatially homogeneous distribution of lenses with the Salpeter mass function for each set of parameters (optical microlensing depth and the clump size). Autocorrelation functions of light curves for different relative contributions of clumps to the total microlensing optical depth σtot = 0.3 are calculated on this basis. It is demonstrated that the dependence of autocorrelation functions on the optical depth of clumps is nonmonotonous.

Probing the stellar initial mass function with high-z supernovae

The first supernovae will soon be visible at the edge of the observable universe, revealing the birthplaces of Population III stars. With upcoming near-infrared missions, a broad analysis of the detectability of high-$z$ supernovae is paramount. We combine cosmological and radiation transport simulations, instrument specifications, and survey strategies to create synthetic observations of primeval core-collapse, Type IIn and pair-instability supernovae with the James Webb Space Telescope ($JWST$). We show that a dedicated observational campaign with the $JWST$ can detect up to $\sim 15$ pair-instability explosions, $\sim 300$ core-collapse supernovae, but less than one Type IIn explosion per year, depending on the Population III star formation history. Our synthetic survey also shows that $\approx 1-2 \times10^2$ supernovae detections, depending on the accuracy of the classification, are sufficient to discriminate between a Salpeter and flat mass distribution for high redshift stars with a confidence level greater than 99.5 per cent. We discuss how the purity of the sample affects our results and how supervised learning methods may help to discriminate between CC and PI SNe.

Monte Carlo simulations of star clusters - VII. The globular cluster 47 Tuc

We describe Monte Carlo models for the dynamical evolution of the massive globular cluster 47 Tuc (NGC 104). The code includes treatments of two-body relaxation, most kinds of three- and four-body interactions involving primordial binaries and those formed dynamically, the Galactic tide, and the internal evolution of both single and binary stars. We arrive at a set of initial parameters for the cluster which, after 12Gyr of evolution, gives a model with a fairly satisfactory match to surface brightness and density profiles, the velocity dispersion profile, the luminosity function in two fields, and the acceleration of pulsars. Our models appear to require a relatively steep initial mass function for stars above about turnoff, with an index of about 2.8 (where the Salpeter mass function has an index of 2.35), and a relatively flat initial mass function (index about 0.4) for the lower main sequence. According to the model, the current mass is estimated at 0.9 million solar masses, of which about 34% consists of remnants. We find that primordial binaries are gradually taking over from mass loss by stellar evolution as the main dynamical driver of the core. Despite the high concentration of the cluster, core collapse will take at least another 20Gyr.

The sequence of low- and high-mass star formation in the young stellar cluster IRAS 19343+2026

BVRIJHK photometry, Spitzer-GLIMPSE photometry and HK band spectroscopy were used to study the stellar content of IRAS 19343+2026, a (proto)star/cluster candidate, located close to the Galactic plane. The data suggest that IRAS 19343+2026 is a rich cluster associated with a massive protostar of 7.6 Msol with an age of ~ 10^5 yr. Three point sources in the vicinity of the far-infrared (FIR) peak are also found to be early B type stars. The remaining (predominantly low mass) members of the cluster are best represented by a 1 - 3 Myr pre-main-sequence (PMS) population. HK band spectra of two bright and five faint point sources in the cluster confirm that the results obtained from the photometry are good representations of their young stellar object (YSO) nature. Thus, IRAS 19343+2026 is a young cluster with at least four early B-type stars classified as young (10^4 - 10^5 yr), that are surrounded by a somewhat older (1 - 3 Myr) population of low mass YSOs. Together, these results argue for a scenario in which low mass stars form prior to massive stars in a cluster forming environment. We compute the Initial Mass Function (IMF) for this cluster using the K-band luminosity function; the slope of the IMF is shallower than predicted by the Salpeter's mass function. The cluster mass, Mtot, is estimated to be in the range ~ 307 Msol (from the data completeness limit) - 585 Msol (extrapolated down to the brown dwarf limit, assuming a certain IMF).

Analysis of the stellar population in the central area of the HII region Sh 2-284 ,

There is a lack of state-of-the-art information on very young open clusters, with implications for determining the structure of the Galaxy. Our main objective is to study the timing and location of the star formation processes which yielded the generation of the giant HII region Sh 2-284. The analysis is based on UBVRcIc CCD measurements and JHKs photometry in the central part of the HII region, where the cluster Dolidze 25 is located.The determination of cluster distance, reddening and age is carried out through comparison with ZAMS, post-MS and PMS isochrones. Reference lines for metallicity Z=0.004 are used, in agreement with spectroscopic metallicity determination published for several cluster members. The results are: E(B-V)=0.78+-0.02, M=12.8+-0.2, LogAge(yr)=6.51+-0.07. A PMS member sequence is proposed, coeval within the errors with the post-MS cluster age (LogAge(yr)=6.7+-0.2). The mass function for this PMS population in the mass range above 1.3-3.5 Msun is well fitted by a Salpeter mass function.The presence of a different star generation in the cluster with a distinctly older age, around 40 Myr, is suggested. The NIR results indicate a large number of sources with H-Ks excess, practically distinct from the optical PMS candidate members. The distance determined for the cluster is distinctly lower than previously published values. This result originates in the consistent use of low metallicity models for ZAMS fitting, applying published metallicity values for the cluster.

Very massive stars in high-redshift galaxies

A significant fraction of Lyα-emitting galaxies (LAEs) at z ≥ 5.7 have rest-frame equivalent widths (EWs) greater than ∼100 A. However, only a small fraction of the Lyα flux produced by a galaxy is transmitted through the intergalactic medium, which implies intrinsic Lyα EWs that are in excess of the maximum allowed for a Population II stellar population having a Salpeter mass function. In this paper, we study characteristics of the sources powering Lyα emission in high-redshift galaxies. We propose a simple model for Lyα emitters in which galaxies undergo a burst of very massive star formation that results in a large intrinsic EW, followed by a phase of Population II star formation with a lower EW. We confront this model with a range of high-redshift observations and find that the model is able to simultaneously describe the following eight properties of the high-redshift galaxy population with plausible values for parameters like the efficiency and duration of star formation: (i)-(iv) the ultraviolet and Lyα luminosity functions of LAEs at z = 5.7 and 6.5, (v)-(vi) the mean and variance of the EW distribution of Lyα-selected galaxies at z = 5.7, (vii) the EW distribution of i-drop galaxies at z ∼ 6, and (viii) the observed correlation of stellar age with EW. Our modelling suggests that the observed anomalously large intrinsic EWs require a burst of very massive star formation lasting no more than a few to 10 per cent of the galaxy's star-forming lifetime. This very massive star formation may indicate the presence of Population III star formation in a few per cent of i-drop galaxies, and in about half of the Lyα-selected galaxies. © 2007 RAS.

Constraints on the Stellar Mass Function from Stellar Dynamics at the Galactic Center

We consider the dynamical evolution of a disk of stars orbiting a central black hole. In particular, we focus on the effect of the stellar mass function on the evolution of the disk, using both analytic arguments and numerical simulations. We apply our model to the ring of massive stars at ~0.1pc from the Galactic Center, assuming that the stars formed in a cold, circular disk, and find that our model requires the presence of a significant population of massive (>100Msun) stars in order to explain the the observed eccentricities of 0.2-0.3. Moreover, in order to limit the damping of the heavier stars' eccentricities, we also require fewer low-mass stars than expected from a Salpeter mass function, giving strong evidence for a significantly ``top-heavy'' mass function in the rings of stars seen near to the Galactic Center. We also note that the maximum possible eccentricities attainable from circular initial conditions at ages of <10Myr are around 0.4-0.5, and suggest that any rings of stars found with higher eccentricities were probably not formed from circular disks.

Star cluster ecology - VII. The evolution of young dense star clusters containing primordial binaries

We study the first ∼100 Myr of the evolution of isolated star clusters initially containing 144 179 stars, including 13 107 (10 per cent) primordial hard binaries. Our calculations include the effects of both stellar and binary evolution. Gravitational interactions among the stars are computed by direct N-body integration using high-precision GRAPE-6 hardware. The evolution of the core radii and central concentrations of our simulated clusters are compared with the observed sample of young (≤100 Myr) star clusters in the large Magellanic Cloud. Even though our simulations start with a rich population of primordial binaries, core collapse during the early phase of the cluster evolution is not prevented. Throughout the simulations, the fraction of binaries remains roughly constant (∼10 per cent). Due to the effects of mass segregation the mass function of intermediate-mass main-sequence stars becomes as flat as a = - 1.8 in the central part of the cluster (where the initial Salpeter mass function had a = -2.35). About 6-12 per cent of the neutron stars were retained in our simulations; the fraction of retained black holes is 40-70 per cent. In each simulation about three neutron stars become members of close binaries with a main-sequence companion. Such a binary will eventually become an X-ray binary, when the main-sequence star starts to fill its Roche lobe. Black holes are found more frequently in binaries; in each simulated cluster we find ∼11 potential X-ray binaries containing a black hole. Binaries consisting of two white dwarfs are quite common, but few (20-30) are sufficiently close that they will merge within a Hubble time due to the emission of gravitational radiation. Clusters with shorter relaxation times tend to produce fewer merging white dwarf binaries. The white dwarf binaries that do merge are all sufficiently massive to produce a Type Ia supernova. The densest cluster produces about twice as many blue stragglers as a field population containing the same number of binaries, and these blue stragglers are more massive, bluer and brighter than in less dense clusters.

Tracing the Dynamical History of the Globular Cluster 47 Tucanae

We use two stellar populations in the globular cluster 47 Tucanae to trace its dynamical history: blue stragglers and low mass main sequence stars. We assumed that the blue stragglers were formed through stellar collisions in all regions of the cluster. We find that in the core of the cluster, models of collisional blue stragglers agree well with the observations as long as blue stragglers are still continuing to form and the mass function in the cluster is extremely biased towards massive stars (x=-8 where a Salpeter mass function has x=+1.35). We show that such an extreme mass function is supported by direct measurements of the luminosity function of main sequence stars in the centre of the cluster. In the middle region of our dataset (25'' to 130'' from the cluster centre), blue straggler formation seems to have stopped about half a Gyr ago. In the outskirts of the cluster, our models are least successful at reproducing the blue straggler data. Taken at face value, they indicate that blue straggler formation has been insignificant over the past billion years, and that a Salpeter mass function applies. However, it is more likely that the dominant formation mechanism in this part of the cluster is not the collisional one, and that our models are not appropriate for this region of the cluster. We conclude that blue stragglers can be used as tracers of dynamics in globular clusters, despite our incomplete understanding of how and where they were formed.

Spatial dependence of 2MASS luminosity and mass functions in the old open cluster NGC 188

Luminosity and mass functions in the old open cluster NGC 188 are analysed by means of J and H 2MASS pho- tometry, which provides uniformity and spatial coverage for a proper background subtraction. With an age of about 6-8 Gyr, NGC 188 is expected to be suffering the effects of advanced dynamical evolution. Indeed, previous works in optical bands have suggested the presence of mass segregation. Within the uncertainties, the observed projected radial density profile of NGC 188 departs from the two-parameter King model in two inner regions, which reflects the non-virialized dynamical state and possibly, some degree of non-sphericity in the spatial shape of this old open cluster. Fits with two and three-parameter King models to the radial distribution of stars resulted in a core radius Rcore = 1.3 ± 0.1 pc and a tidal radius Rtidal = 21 ± 4 pc, about twice as large as the visual limiting radius. The concentration parameter c = 1.2 ± 0.1 of NGC 188 makes this open cluster structurally comparable to the loose globular clusters. The present 2MASS analysis resulted in significant slope variations with distance in the mass function φ(m) ∝ m −(1+χ) , being flat in the central parts (χ = 0.6 ± 0.7) and steep in the cluster outskirts (χ = 7.2 ± 0.6). The overall mass function has a slope χ = 1.9 ± 0.7, slightly steeper than a standard Salpeter mass function. In this context, NGC 188 is similar to the 3.2 Gyr, dynamically evolved open cluster M 67. Solar metallicity Padova isochrone fits to the near- infrared colour-magnitude diagram of NGC 188 resulted in an age of 7.0 ± 1.0 Gyr. The best fit, obtained with the 7.1 Gyr isochrone, produced a distance modulus (m − M)0 = 11.1 ± 0.1, E(B − V) = 0.0, and a distance to the Sun d� = 1.66 ± 0.08 kpc. The observed stellar mass (in the range 0.98 M� −1.08 M� ) in NGC 188 is mobs = 380 ± 12 M� . A simple extrapolation of the observed overall mass function to stars with 0.08 Mresulted in a total present mass of mtot ∼ (1.8 ± 0.7) × 10 4 M� .O n the other hand, for a more realistic initial mass function which flattens in the low-mass range, the total mass in NGC 188 drops to mtot ∼ (3.8 ± 1.6) × 10 3 M� . Since mass-loss processes such as evaporation and tidal stripping have been occurring in this old open cluster for about 7 Gyr, the primordial mass in NGC 188 must have been significantly larger than ∼4 × 10 3 M� .W e also examined the consequences of the presence of unresolved binaries and concluded that, even if dominant in the CMD, binaries alone are not responsible for the flat central mass function, which supports the mass-segregation scenario.

Parameter properties and stellar population of the old open cluster NGC 3960

We present a $BVI$ photometric and astrometric catalogue of the open cluster NGC 3960, down to limiting magnitude $V\sim22$, obtained from observations taken with the Wide Field Imager camera at the MPG/ESO 2.2 m Telescope at La Silla. The photometry of all the stars detected in our field of view has been used to estimate a map of the strong differential reddening affecting this area. Our results indicate that, within the region where the cluster dominates, the $E(V-I)$ values range from 0.21 up to 0.78, with $E(V-I)=0.36$ ($E(B-V)=0.29$) at the nominal cluster centroid position; color excesses $E(V-I)$ up to 1 mag have been measured in the external regions of the field of view where field stars dominate. The reddening corrected color-magnitude diagram (CMD) allows us to conclude that the cluster has an age between 0.9 and 1.4 Gyr and a distance modulus of $(V-M_V)_0=11.35$. In order to minimize field star contamination, their number has been statistically subtracted based on the surface density map. The empirical cluster main sequence has been recovered in the $V$ vs. $V-I$ and in the $J$ vs. $J-K_S$ planes, using optical and infrared data, respectively. From these empirical cluster main sequences, two samples of candidate cluster members were derived in order to obtain the luminosity distributions as a function of the $V$ and $J$ magnitudes. The Luminosity Functions have been transformed into the corresponding Mass Functions; for $M>1 M_\odot$, the two distributions have been fitted with a power law of index $\alpha_V=2.95\pm0.53$ and $\alpha_J=2.81\pm0.84$ in $V$ and in $J$, respectively, while the Salpeter Mass Function in this notation has index $\alpha=2.35$.

Quantitative Interpretation of Quasar Microlensing Light Curves

We develop a general method for analyzing the light curves of microlensed quasars and apply it to the OGLE light curves of the four-image lens Q2237+0305. We simultaneously estimate the effective source velocity, the average stellar mass, the stellar mass function, and the size and structure of the quasar accretion disk. The light curves imply an effective source-plane velocity of 10,200 km s-1 ≲ veh⟨M/M☉⟩-1/2 ≲ 39,600 km s-1 (68% confidence). Given an independent estimate for the source velocity, found by combining estimates for the peculiar velocity of the lens galaxy with its measured stellar velocity dispersion, we obtain a mean stellar mass of ⟨M⟩ ≃ 0.037 h2 M☉ (0.0059 h2 M☉ ≲ ⟨M⟩ ≲ 0.20 h2 M☉). We were unable to distinguish a Salpeter mass function from one in which all stars had the same mass, but we do find a strong lower bound of κ*/κ ≳ 0.5 on the fraction of the surface mass density represented by the microlenses. Our models favor a standard thin accretion disk model as the source structure over a simple Gaussian source. For a face-on, thin disk radiating as a blackbody with temperature profile Ts ∝ R-3/4, the radius rs where the temperature matches the filter pass band [2000 Å or Ts(rs) ≃ 7 × 104 K] is 1.4 × 1015 h-1 cm ≲ rs ≲ 4.5 × 1015 h-1 cm. The flux predicted by the disk model agrees with the observed flux of the quasar, so nonthermal or optically thin emission processes are not required. From the disk structure we estimate a black hole mass of MBH ≃ 1.1 × 109 h-3/2η(L/LE)-1/2 M☉, consistent with the mass estimated under the assumption that the quasar is radiating at the Eddington luminosity (L/LE = 1).

Evolution, Explosion, and Nucleosynthesis of Core‐Collapse Supernovae

We present a new set of presupernova evolutions and explosive yields of massive stars of initial solar composition (Y = 0.285, Z = 0.02) in the mass range 13-35 M?. All the models have been computed with the latest version (4.97) of the FRANEC code that now includes a nuclear network extending from neutrons to 98Mo. The explosive nucleosynthesis has been computed twice: a first one with a hydro code and a second one following the simpler radiation-dominated shock approximation (RDA). The main results concerning the models and the associated explosions are as follows: (1) the inclusion of the latest available input physics does not alter significantly the main properties of the presupernova models with respect to our previous ones; (2) the differences between the old and new explosive yields computed with the RDA remain confined within a factor of 2 for most of the nuclei; (3) the differences between the elemental RDA yields and those computed with a hydro code do not exceed 0.1 dex, with the exceptions of the elements produced mainly by the complete explosive Si burning: in this case the variations are anyway less than a factor of 3; (4) the relation between the final kinetic energy and the 56Ni ejected weakens as the mass of the progenitor star increases; (5) the yields corresponding to the ejection of a given amount of 56Ni are in fair agreement with those obtained by a more energetic explosion in which the mass cut is chosen in order to give the same 56Ni. The production factors (integrated over a Salpeter mass function between 13 and 35 M?) of the majority of the isotopes show an almost scaled solar distribution relative to oxygen. The few exceptions are discussed in detail. We also find that the present integrated yields allow a fraction of the order of 10%-20% of Type Ia supernovae if their latest available yields are adopted.