### CASCA 2010 compact objects session 1

Orbital eccentricity in numerical simulations of binary black holes (Harald P. Pfeiffer)

Eccentricity in black-hole binaries is radiated away faster than the semi-major axis, so that they become circular fairly rapidly. Thus, for example, when a binary makes its way into the LIGO band the eccentricity is down around 10^-6. For numerical GR this means you have to be able to measure - for that matter, define - eccentricity, and you need to be able to produce near-zero eccentricities. To define it, you often construct some function that measures deviation from a circular inspiral, but this is difficult because of (among other things) coordinate dependence. It turns out it works better to define eccentricity in terms of its  gravitational wave effects. You also have to work on periastron advance (for which third-order post-Newtonian models are not good enough). How is very low eccentricity achieved? The problem is in constructing your initial data: coordinate location, sizes, velocities; these need to satisfy complicated PDEs to satisfy the constraints, and it's not clear what goal values you should choose to get circular orbits. The approach is to simulate a few orbits, then fix the initial condition as if it were Newtonian; this roughly works, so you iterate the process until you get a nice low eccentricity. When you go to precessing binaries (i.e. rotating black holes) spin-orbit coupling complicates your life, but you can still extract an eccentricity measurement and initial condition corrections.

Rayachaudhuri's Equation in Regge Calculus (Parandis Khavari)

These equations are important in the proof of singularity theorems, lensing, collapse, and cracking under self-gravity. They concern expansion and shear of fluids in self-gravitation. Absent vorticity they imply collapse into a singularity in a finite amount of time. Regge calculus is finite-element GR that fixes flat geometry within simplices; curvature is concentrated on n-2-dimensional sub-simplices ("bones") and can be described by the deficit angle. Geodesics in the Regge calculus are straight lines within simplices; where they meet faces, the angle on the entrance edge matches the angle on the exit edge, but it's a little tricky since there's no unique way to assign the deficit angle to the n-1 simplices around a particular bone. This work is about expansion of geodesics in (2+1)-dimensions. She obtains expressions for shear and expansion of lensing. Remaining problems include that Rayachaudhuri's equation has no unique discrete representation.

Numerical simulations of precessing binary black holes (Abdul Mroue)

Gravitational wave detection will only be possible if we have accurate banks of template gravitational waveforms. The three main categories are inspiral, merger, and ringdown. To build these templates we need some combination of post-Newtonian models and numerical relativity. We expect an event in the LIGO range at a rate <1/year, but advanced LIGO should have ~0.5/day. So building a template bank is crucial. The parameter space (for zero eccentricity) is given by the mass ratio and the two spins. A 15-orbit binary takes ~10^5 CPU-hours (plus a great number of grad student-hours). Less than 100 waveforms are available from all groups worldwide. So far very little work has been done on systems with generic spins. The spin has very significant effects on the system evolution. This work has two major approaches: make BBH runs easier (i.e. reduce the person-hours) by automating the initial setup and transition between regimes, and make BBH runs faster, primarily by making their simulation code run on GPU supercomputers (possibly an order of magnitude speedup). Currently running on his desktop's GPU.

Questions: Do we expect spin-orbit alignment? Maybe; what happens in the final orbits is totally unclear. [No comment on whether binary evolution is likely to produce aligned binary systems.]

Modelling Gravitational Lens Systems with Genetic Algorithms and Particle Swarm Methods (Adam Rogers)

Lensing has been observed on many cosmological structures; it's interesting because on the one hand it depends on the mass of the lens, and on the other hand it provides an important magnification effect. The goal of this research is to try to reconstruct the un-lensed image of the source. They assume a thin lens. The lensing equation is clearly nonlinear, as shown by multiple lensing. Rather than solve a complicated nonlinear equation, one can simply raytrace past a lens shape. One can combine this information into a mapping matrix; in this formalism, finding the source pixel intensities is a linear least-squares problem. Unfortunately the matrix sizes are comparable to the number of pixels [so you need sparsity], so you need to use a small PSF, i.e. optical data. With some cleverness one can reformulate the problem into a deconvolution problem that never needs to construct the huge matrices. On simulated data it's quite effective at recovering even highly distorted images when you know the lens parameters. Finding the lens parameters requires a fitting procedure, for which he's using genetic algorithms and particle swarms. Particle swarm optimizers attract each particle to its local best and the global best according to a spring force. Of the two the particle swarm optimizer is a little faster, while the GA is much more thorough in searching the parameter space (e.g. local loses one of the two 180-degree options for ellipse orientation).

Questions: Have you applied your models to real data? Yes, but it's old data that's already been partially processed. What is he optimizing? "chi-squared between the model and the data"

New properties od teh 35-day cycle of Hercules X-1 (Denis Leahy)

RXTE ASM data of Her X-1, plus PCA data when available. Her X-1 is 6.6 kpc and high galactic latitude; it's a neutron star with a 2.5 Msun A7 companion. Over 35 days (many binary orbits) you get brightness variations. One model is a twisted disk that occults the NS; its shadow on the companion star changes on the same cycle, which explains the optical variations. ASM data shows that the cycle length varies substantially - 34-38 days - and this variation is correlated with the flux. The turn-on appears to occur uniformly in orbital phase. They have 1.58 Ms of PCA data in total. One idea for explaining some of the irregularities is that the impact point on the disk is not the outer edge, since it's not flat; other models include an uneven disk surface or blobs in the accretion stream, but these don't match the data well.

Questions: Why is the disk twisted? Heating by the central source  produces a torque that increases as the disk gets out-of-plane up to the point where it starts shadowing itself.