Chris L. Fryer

The Nuclear Spectroscopic Telescope Array (NuSTAR) High-Energy X-Ray Mission

The Nuclear Spectroscopic Telescope Array (NuSTAR) is a National Aeronautics and Space Administration (NASA) Small Explorer mission that carried the first focusing hard X-ray (6-79 keV) telescope into orbit. It was launched on a Pegasus rocket into a low-inclination Earth orbit on June 13, 2012, from Reagan Test Site, Kwajalein Atoll. NuSTAR will carry out a two-year primary science mission. The NuSTAR observatory is composed of the X-ray instrument and the spacecraft. The NuSTAR spacecraft is three-axis stabilized with a single articulating solar array based on Orbital Sciences Corporations LEOStar-2 design. The NuSTAR science instrument consists of two co-aligned grazing incidence optics focusing on to two shielded solid state CdZnTe pixel detectors. The instrument was launched in a compact, stowed configuration, and after launch, a 10-meter mast was deployed to achieve a focal length of 10.15 m. The NuSTAR instrument provides sub-arcminute imaging with excellent spectral resolution over a 12-arcminute field of view. The NuSTAR observatory will be operated out of the Mission Operations Center (MOC) at UC Berkeley. Most science targets will be viewed for a week or more. The science data will be transferred from the UC Berkeley MOC to a Science Operations Center (SOC) located at the California Institute of Technology (Caltech). In this paper, we will describe the mission architecture, the technical challenges during the development phase, and the post-launch activities.

Hyperaccreting black holes and gamma-ray bursts

A variety of current models of gamma-ray bursts (GRBs) suggest a common engine: a black hole of several solar masses accreting matter from a disk at a rate of 0.01 to 10 M☉ s-1. Using a numerical model for relativistic disk accretion, we have studied steady state accretion at these high rates. Outside about 108 cm, the disk is advection dominated; energy released by dissipation is carried in by the optically thick gas, and the disk does not cool. Inside this radius, for accretion rates greater than about 0.01 M☉ s-1 a global state of balanced power comes to exist between neutrino losses, chiefly pair capture on nucleons, and dissipation. As a result of these losses, the temperature is reduced, the density is raised, and the disk scale height is reduced compared to the advective solution. The sudden onset of neutrino losses (due to the high temperature dependence) and photodisintegration leads to an abrupt thinning of the disk that may provide a favorable geometry for jet production. The inner disk remains optically thin to neutrinos for accretion rates of up to about 1 M☉ s-1. The energy emitted in neutrinos is less, and in the case of low accretion rates, very much less, than the maximum efficiency factor for black hole accretion (0.057 for no rotation; 0.42 for extreme Kerr rotation) times the accretion rate, c2. Neutrino temperatures at the last stable orbit range from 2 MeV (no rotation, slow accretion) to 13 MeV (Kerr geometry, rapid accretion), and the density ranges from 109 to 1012 g cm-3. The efficiency for producing a pair fireball along the rotational axis by neutrino annihilation is calculated and found to be highly variable and very sensitive to the accretion rate. For some of the higher accretion rates studied, it can be several percent or more; for accretion rates less than 0.05 M☉ s-1, it is essentially zero. The efficiency of the Blandford-Znajek mechanism in extracting rotational energy from the black hole is also estimated. In light of these results, the viability of various gamma-ray burst models is discussed, and the sensitivity of the results to disk viscosity, black hole rotation rate, and black hole mass is explored. A diverse range of GRB energies seems unavoidable, and neutrino annihilation in hyperaccreting black hole systems can explain bursts of up to 1052 ergs. Larger energies can be inferred for beaming systems.

Inside the supernova: A powerful convective engine

Condensed Abstract: We present an extensive study of the inception of supernova explosions by following the evolution of the cores of two massive stars (15 Msun and 25 Msun) in two dimensions. Our calculations begin at the onset of core collapse and stop several 100 ms after the bounce, at which time successful explosions of the appropriate magnitude have been obtained. (...) Guided by our numerical results, we have developed a paradigm for the supernova explosion mechanism. We view a supernova as an open cycle thermodynamic engine in which a reservoir of low-entropy matter (the envelope) is thermally coupled and physically connected to a hot bath (the protoneutron star) by a neutrino flux, and by hydrodynamic instabilities. (...) In essence, a Carnot cycle is established in which convection allows out-of-equilibrium heat transfer mediated by neutrinos to drive low entropy matter to higher entropy and therefore extracts mechanical energy from the heat generated by gravitational collapse. We argue that supernova explosions are nearly guaranteed and self-regulated by the high efficiency of the thermodynamic engine. (...) Convection continues to accumulate energy exterior to the neutron star until a successful explosion has occurred. At this time, the envelope is expelled and therefore uncoupled from the heat source (the neutron star) and the energy input ceases. This paradigm does not invoke new or modified physics over previous treatments, but relies on compellingly straightforward thermodynamic arguments. It provides a robust and self-regulated explosion mechanism to power supernovae which is effective under a wide range of physical parameters.

Mass Limits For Black Hole Formation

We present a series of two-dimensional core-collapse supernova simulations for a range of progenitor masses and different input physics. These models predict a range of supernova energies and compact remnant masses. In particular, we study two mechanisms for black hole formation: prompt collapse and delayed collapse owing to fallback. For massive progenitors (greater than 20 M☉), after a hydrodynamic time for the helium core (a few minutes to a few hours), fallback drives the compact object beyond the maximum neutron star mass, causing it to collapse into a black hole. With the current accuracy of the models, progenitors more massive than 40 M☉ form black holes directly with no supernova explosion (if rotating, these black holes may be the progenitors of gamma-ray bursts). We calculate the mass distribution of black holes formed and compare these predictions to the observations, which represent a small biased subset of the black hole population. Uncertainties in these estimates are discussed.

Formation Rates of Black Hole Accretion Disk Gamma-Ray Bursts

The cosmological origin of at least an appreciable fraction of classical gamma-ray bursts (GRBs) is now supported by redshift measurements for a half-dozen faint host galaxies. Still, the nature of the central engine (or engines) that provide the burst energy remains unclear. While many models have been proposed, those currently favored are all based upon the formation of and/or rapid accretion into stellar-mass black holes. Here we discuss a variety of such scenarios and estimate the probability of each. Population synthesis calculations are carried out using a Monte Carlo approach in which the many uncertain parameters intrinsic to such calculations are varied. We estimate the event rate for each class of model as well as the propagation distances for those having significant delay between formation and burst production, i.e., double neutron star (DNS) mergers and black hole-neutron star (BH/NS) mergers. One conclusion is a 1-2 order of magnitude decrease in the rate of DNS and BH/NS mergers compared to that previously calculated using invalid assumptions about common envelope evolution. Other major uncertainties in the event rates and propagation distances include the history of star formation in the universe, the masses of the galaxies in which merging compact objects are born, and the radii of the hydrogen-stripped cores of massive stars. For reasonable assumptions regarding each, we calculate a daily event rate in the universe for (1) merging neutron stars: ~100 day-1; (2) neutron star-black hole mergers: ~450 day-1; (3) collapsars: ~104 day-1; (4) helium star black hole mergers: ~1000 day-1; and (5) white dwarf-black hole mergers: ~20 day-1. The range of uncertainty in these numbers, however, is very large, typically 2-3 orders of magnitude. These rates must additionally be multiplied by any relevant beaming factor (fΩ < 1) and sampling fraction (if the entire universal set of models is not being observed). Depending upon the mass of the host galaxy, one-half of the DNS mergers will happen within 60 kpc (for a galaxy with a mass comparable to that of the Milky Way) to 5 Mpc (for a galaxy with negligible mass) from the Galactic center. The same numbers characterize BH/NS mergers. Because of the delay time, neutron star and black hole mergers will happen at a redshift 0.5-0.8 times that of the other classes of models. Information is still lacking regarding the hosts of short, hard bursts, but we suggest that they are due to DNS and BH/NS mergers and thus will ultimately be determined to lie outside of galaxies and at a closer mean distance than long complex bursts (which we attribute to collapsars). In the absence of a galactic site, the distance to these bursts may be difficult to determine.

Theoretical Black Hole Mass Distributions

We derive the theoretical distribution function of black hole masses by studying the formation processes of black holes. We use the results of recent two-dimensional simulations of stellar core collapse to obtain the relation between remnant and progenitor masses and fold it with an initial mass function for the progenitors. Thus, we are able to derive the binary black hole mass distribution. We examine how the calculated black hole mass distributions are modified by (1) strong-wind mass loss at different evolutionary stages of the progenitors and (2) the presence of close binary companions to the black hole progenitors. The compact-remnant distribution is dominated by neutron stars in the mass range 1.2-1.6 M☉ and falls off exponentially at higher remnant masses. Our results are most sensitive to mass loss from stellar winds (particularly from Wolf-Rayet stars), and the effects of winds are even more important in close binaries. Wind mass loss leads to flatter black hole mass distributions and limits the maximum possible black hole mass (10-15 M☉). We also study the effects of the uncertainties in the explosion and unbinding energies for different progenitors. The distributions are continuous and extend over a broad range. We find no evidence for a gap at low values (3-5 M☉) or for a peak at higher values (~7 M☉) of black hole masses, but we argue that our black hole mass distribution for binaries is consistent with the current sample of measured black hole masses in X-ray transients. We discuss possible biases against the detection or formation of X-ray transients with low-mass black holes. We also comment on the possibility of black hole kicks and their effect on binaries.

Pair-Instability Supernovae, Gravity Waves, and Gamma-Ray Transients

Growing evidence suggests that the first generation of stars may have been quite massive (~100-300 M☉). If they retain their high mass until death, such stars will, after about 3 Myr, make pair-instability supernovae. Models for these explosions have been discussed in the literature for four decades, but very few included the effects of rotation and none employed a realistic model for neutrino trapping and transport. Both turn out to be very important, especially for those stars whose cores collapse into black holes (helium cores above about 133 M☉). We consider the complete evolution of two zero-metallicity stars of 250 and 300 M☉. Despite their large masses, we argue that the low metallicities of these stars imply negligible mass loss. Evolving the stars with no mass loss, but including angular momentum transport and rotationally induced mixing, the two stars produce helium cores of 130 and 180 M☉. Products of central helium burning (e.g., primary nitrogen) are mixed into the hydrogen envelope with dramatic effects on the radius, especially in the case of the 300 M☉ model. Explosive oxygen and silicon burning cause the 130 M☉ helium core (250 M☉ star) to explode, but explosive burning is unable to drive an explosion in the 180 M☉ helium core, and it collapses to a black hole. For this star, the calculated angular momentum in the presupernova model is sufficient to delay black hole formation, and the star initially forms an ~50 M☉, 1000 km core within which neutrinos are trapped. The calculated growth time for secular rotational instabilities in this core is shorter than the black hole formation time, and they may develop. If so, the estimated gravitational wave energy and wave amplitude are EGW ≈ 10-3 M☉ c2 and h+ ≈ 10-21/d(Gpc), but these estimates are very rough and depend sensitively on the nonlinear nature of the instabilities. After the black hole forms, accretion continues through a disk. The mass of the disk depends on the adopted viscosity but may be quite large, up to 30 M☉ when the black hole mass is 140 M☉. The accretion rate through the disk can be as large as 1-10 M☉ s-1. Although the disk is far too large and cool to transport energy efficiently to the rotational axis by neutrino annihilation, it has ample potential energy to produce a 1054 erg jet driven by magnetic fields. The interaction of this jet with surrounding circumstellar gas may produce an energetic gamma-ray transient, but given the probable redshift and the consequent timescale and spectrum, this model may have difficulty explaining typical gamma-ray bursts.

ON THE MAXIMUM MASS OF STELLAR BLACK HOLES

We present the spectrum of compact object masses: neutron stars and black holes (BHs) that originate from single stars in different environments. In particular, we calculate the dependence of maximum BH mass on metallicity and on some specific wind mass loss rates (e.g., Hurley et al. and Vink et al.). Our calculations show that the highest mass BHs observed in the Galaxy M bh ~ 15 M ☉ in the high metallicity environment (Z = Z ☉ = 0.02) can be explained with stellar models and the wind mass loss rates adopted here. To reach this result we had to set luminous blue variable mass loss rates at the level of ~10–4 M ☉ yr–1 and to employ metallicity-dependent Wolf-Rayet winds. With such winds, calibrated on Galactic BH mass measurements, the maximum BH mass obtained for moderate metallicity (Z = 0.3 Z ☉ = 0.006) is M bh,max = 30 M ☉. This is a rather striking finding as the mass of the most massive known stellar BH is M bh = 23-34 M ☉ and, in fact, it is located in a small star-forming galaxy with moderate metallicity. We find that in the very low (globular cluster-like) metallicity environment the maximum BH mass can be as high as M bh,max = 80 M ☉ (Z = 0.01 Z ☉ = 0.0002). It is interesting to note that X-ray luminosity from Eddington-limited accretion onto an 80 M ☉ BH is of the order of ~1040 erg s–1 and is comparable to luminosities of some known ultra-luminous X-ray sources. We emphasize that our results were obtained for single stars only and that binary interactions may alter these maximum BH masses (e.g., accretion from a close companion). This is strictly a proof-of-principle study which demonstrates that stellar models can naturally explain even the most massive known stellar BHs.

Compact Remnant Mass Function: Dependence on the Explosion Mechanism and Metallicity

The mass distribution of neutron stars and stellar-mass black holes provides vital clues into the nature of stellar core collapse and the physical engine responsible for supernova explosions. A number of supernova engines have been proposed: neutrino- or oscillation-driven explosions enhanced by early (developing in 10-50 ms) and late-time (developing in 200 ms) convection as well as magnetic field engines (in black hole accretion disks or neutron stars). Using our current understanding of supernova engines, we derive mass distributions of stellar compact remnants. We provide analytic prescriptions for both single-star models (as a function of initial star mass) and for binary-star models-prescriptions for compact object masses for major population synthesis codes. These prescriptions have implications for a range of observations: X-ray binary populations, supernova explosion energies, and gravitational wave sources. We show that advanced gravitational radiation detectors (like LIGO/VIRGO or the Einstein Telescope) will be able to further test the supernova explosion engine models once double black hole inspirals are detected.

Core-Collapse Simulations of Rotating Stars

We present the results from a series of two-dimensional core-collapse simulations using a rotating progenitor star. We find that the convection in these simulations is less vigorous because (1) rotation weakens the core bounce that seeds the neutrino-driven convection and (2) the angular momentum profile in the rotating core stabilizes against convection. The limited convection leads to explosions that occur later and are weaker than the explosions produced from the collapse of nonrotating cores. However, because the convection is constrained to the polar regions, when the explosion occurs it is stronger along the polar axis. This asymmetric explosion may explain the polarization measurements of core-collapse supernovae. These asymmetries also provide a natural mechanism to mix the products of nucleosynthesis out into the helium and hydrogen layers of the star. We also discuss the role the collapse of these rotating stars plays in the generation of magnetic fields and neutron star kicks. Given a range of progenitor rotation periods, we predict a range of supernova energies for the same progenitor mass. The critical mass for black hole formation also depends upon the rotation speed of the progenitor.