On the Interpretation of the Age Distribution of Star Clusters in the Small Magellanic Cloud

We re-analyze the age distribution (dN/dt) of star clusters in the Small Magellanic Cloud (SMC) using age determinations based on the Magellanic Cloud Photometric Survey. For ages younger than 3x10^9 yr the dN/dt distribution can be approximated by a power-law distribution, dN/dt propto t^-beta, with -beta=-0.70+/-0.05 or -beta=-0.84+/-0.04, depending on the model used to derive the ages. Predictions for a cluster population without dissolution limited by a V-band detection result in a power-law dN/dt distribution with an index of ~-0.7. This is because the limiting cluster mass increases with age, due to evolutionary fading of clusters, reducing the number of observed clusters at old ages. When a mass cut well above the limiting cluster mass is applied, the dN/dt distribution is flat up to 1 Gyr. We conclude that cluster dissolution is of small importance in shaping the dN/dt distribution and incompleteness causes dN/dt to decline. The reason that no (mass independent) infant mortality of star clusters in the first ~10-20 Myr is found is explained by a detection bias towards clusters without nebular emission, i.e. cluster that have survived the infant mortality phase. The reason we find no evidence for tidal (mass dependent) cluster dissolution in the first Gyr is explained by the weak tidal field of the SMC. Our results are in sharp contrast to the interpretation of Chandar et al. (2006), who interpret the declining dN/dt distribution as rapid cluster dissolution. This is due to their erroneous assumption that the sample is limited by cluster mass, rather than luminosity.Comment: 8 pages, 4 figures, accepted for publication in Ap

Runaway Merging of Black Holes: Analytical Constraint on the Timescale

Following the discovery of a black hole (BH) with a mass of 10^3-10^6 M(sun) in a starburst galaxy M82, we study formation of such a BH via successive merging of stellar-mass BHs within a star cluster. The merging has a runaway characteristic. This is because massive BHs sink into the cluster core and have a high number density, and because the merging probability is higher for more massive BHs. We use the Smoluchowski equation to study analytically the evolution of the BH mass distribution. Under favorable conditions, which are expected for some star clusters in starburst galaxies, the timescale of the runaway merging is at most of order 10^7 yr. This is short enough to account for the presence of a BH heavier than 10^3 M(sun) in an ongoing starburst region.Comment: 10 pages, no figures, to appear in The Astrophysical Journal (Letters

A New Formation Channel for Double Neutron Stars Without Recycling: Implications for Gravitational Wave Detection

We report on a new evolutionary path leading to the formation of close double neutron stars (NS), with the unique characteristic that none of the two NS ever had the chance to be recycled by accretion. The existence of this channel stems from the evolution of helium-rich stars (cores of massive NS progenitors), which has been neglected in most previous studies of double compact object formation. We find that these non-recycled NS-NS binaries are formed from bare carbon-oxygen cores in tight orbits, with formation rates comparable to or maybe even higher than those of recycled NS-NS binaries. On the other hand, their detection probability as binary pulsars is greatly reduced (by about 1000) relative to recycled pulsars, because of their short lifetimes. We conclude that, in the context of gravitational-wave detection of NS-NS inspiral events, this new type of binaries calls for an increase of the rate estimates derived from the observed NS-NS with recycled pulsars, typically by factors of 1.5-3 or even higher.Comment: Accepted for publication in ApJ Letters; 5 pages, 1 figure, 2 tables. Two new paragraphs and one formula adde

Controllability and stability of 3D heat conduction equation in a submicroscale thin film

We obtain a closed form analytic solution for the Dual Phase Lagging equation. This equation is a linear, time-independent partial differential equation modeling the heat distribution in a thin film. The spatial domain is of micrometer and nanometer geometries. We show that the solution is described by a semigroup, and obtain a basis of eigenfunctions. The closure of the set of eigenvalues contains an interval, and so the theory on Riesz spectral operator of Curtain and Zwart cannot be applied directly. The exponential stability and the approximate controllability is shown

Studies of the Relativistic Binary Pulsar PSR B1534+12. II. Origin and Evolution

We have recently measured the angle between the spin and orbital angular momenta of PSR B1534+12 to be either 25+/-4 deg or 155+/-4 deg. This misalignment was almost certainly caused by an asymmetry in the supernova explosion that formed its companion neutron star. Here we combine the misalignment measurement with measurements of the pulsar and companion masses, the orbital elements, proper motion, and interstellar scintillation. We show that the orbit of the binary in the Galaxy is inconsistent with a velocity kick large enough to produce a nearly antialigned spin axis, so the true misalignment must be ~25 deg. Similar arguments lead to bounds on the mass of the companion star immediately before its supernova: 3+/-1 Msun. The result is a coherent scenario for the formation of the observed binary. After the first supernova explosion, the neutron star that would eventually become the observed pulsar was in a Be/X-ray type binary system with a companion of at least 10--12 Msun. During hydrogen (or possibly helium) shell burning, mass transfer occurred in a common envelope phase, leaving the neutron star in a roughly half-day orbit with a helium star with mass above ~3.3 Msun. A second phase of mass transfer was then initiated by Roche lobe overflow during shell helium burning, further reducing both the helium star mass and orbital period before the second supernova. Scenarios that avoid Roche lobe overflow by the helium star require larger helium star masses and predict space velocities inconsistent with our measurements. The companion neutron star experienced a velocity kick of 230+/-60 km/s at birth, leading to a systemic kick to the binary of 180+/-60 km/s.Comment: 9 pages, submitted to ApJ. Abstract shortened. Version with high-resolution figures available at http://www.astro.ubc.ca/people/stairs/papers/tds04_orig.ps.g

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 due to fallback. For massive progenitors above 20 solar masses, 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 solar masses 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.Comment: 15 pages total, 4 figures, Modifications in Conclusion, accepted by Ap