Masses, Beaming and Eddington Ratios in Ultraluminous X-ray Sources

I suggest that the beaming factor in bright ULXs varies as $b \propto \dot m^{-2}$, where $\dot m$ is the Eddington ratio for accretion. This is required by the observed universal $L_{\rm soft} \propto T^{-4}$ relation between soft--excess luminosity and temperature, and is reasonable on general physical grounds. The beam scaling means that all observable properties of bright ULXs depend essentially only on the Eddington ratio $\dot m$, and that these systems vary mainly because the beaming is sensitive to the Eddington ratio. This suggests that bright ULXs are stellar--mass systems accreting at Eddington ratios of order 10 -- 30, with beaming factors b \ga 0.1. Lower--luminosity ULXs follow bolometric (not soft--excess) $L \sim T^4$ correlations and probably represent {\it sub}--Eddington accretion on to black holes with masses \sim 10\msun. High--mass X-ray binaries containing black holes or neutron stars and undergoing rapid thermal-- or nuclear--timescale mass transfer are excellent candidates for explaining both types. If the $b \propto \dot m^{-2}$ scaling for bright ULXs can be extrapolated to the Eddington ratios found in SS433, some objects currently identified as AGN at modest redshifts might actually be ULXs (`pseudoblazars'). This may explain cases where the active source does not coincide with the centre of the host galaxy.Comment: MNRAS Letters, in pres

Relationships of Job and Family Involvement, Family Social Support, and Work–Family Conflict with Job and Life Satisfaction

A model of the relationship between work and family that incorporates variables from both the work-family conflict and social support literatures was developed and empirically tested. This model related bidirectional work-family conflict, family instrumental and emotional social support, and job and family involvement to job and life satisfaction. Data came from 163 workers who were living with at least 1 family member. Results suggested that relationships between work and family can have an important effect on job and life satisfaction and that the level of involvement the worker assigns to work and family roles is associated with this relationship. The results also suggested that the relationship between work and family can be simultaneously characterized by conflict and support. Higher levels of work interfering with family predicted lower levels of family emotional and instrumental support. Higher levels of family emotional and instrumental support were associated with lower levels of family interfering with work. (PsycINFO Database Record (c) 2013 APA, all rights reserved)

Black-Hole Transients and the Eddington Limit

I show that the Eddington limit implies a critical orbital period P_crit(BH) = 2d beyond which black-hole LMXBs cannot appear as persistent systems. The unusual behaviour of GRO J1655-40 may result from its location close to this critical period.Comment: 3 pages, no figures; to appear in MNRA

Magnetic Fields, Accretion, and the Central Engine of Gamma-Ray Bursts

I briefly review magnetic effects in accretion physics, and then go on to discuss a possible central engine for gamma-ray bursts. A rotating black hole immersed in a non-axisymmetric magnetic field experiences a torque trying to align spin and field. I suggest that gamma-ray burst hosts may provide conditions where this effect allows rapid extraction of a significant fraction of the hole's rotational energy. I argue that much of the electromagnetic emission is in two narrow beams parallel and antiparallel to the asymptotic field direction. This picture suggests that only a mass 10^-5 Msun is expelled in a relativistic outflow, as required by the fireball picture.Comment: 8 pages, Invited talk to appear in the Proceedings of Magnetic Fields in the Universe, Angra dos Reis, Brazil, November 28 - December 3 200

Minimal generating sets of non-modular invariant rings of finite groups

It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case. Apart from very few explicit computations of Groebner bases, the algorithm only involves very basic operations, and is thus rather fast. As a test bed for comparative benchmarks, we use transitive permutation groups on 7 and 8 variables. In most examples, our algorithm implemented in Singular works much faster than the one used in Magma, namely by factors between 50 and 1000. We also compute some further examples on more than 8 variables, including a minimal generating set for the natural action of the cyclic group of order 11 in characteristic 0 and of order 15 in characteristic 2. We also apply our algorithm to the computation of irreducible secondary invariants.Comment: 14 pages v3: Timings updated. One example adde