SOUTHAMPTON

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The first year of the European network for Gravitational wave sources has been an active one for the Southampton group. Combining the EU grant with several other grants, the group has four permanent members of staff and currently supports three postdocs and five research students.

The EU funded postdoc, Reinhard Prix, works with Nils Andersson and a PPARC funded postdoc Ian Jones on modelling various aspects of gravitational waves from neutron stars. The addition of Reinhard's expertise on relativistic superfluids has provided significant momentum in the direction towards more realistic models as most mature neutron stars are expected to have superfluid constituents. We were also strengthened by the fact that Greg Comer was able to visit from St Louis during two months of the summer. At the present time much of the foundation for understanding the dynamics of superfluid stars has been laid and we are moving towards studies of astrophysical problems. In a series of paper we have i) studied rotating two-fluid configurations in which the two fluids are allowed to rotate at different rates [1, 2] (recall that the standard model for neutron star glitches is based on transfer of angular momentum between two loosely coupled components), ii) investigated neutron star oscillation modes both qualitatively and in quantitative detail [3, 4]. So far the main new results concern the possible existence of two classes of r-modes (which may be unstable due to the emission of gravitational waves) in a superfluid star and progress in understanding the effect of entrainment (which couples the two fluids in a non-dissipative way) in relativistic oscillations. We are currently formulating the equations that describe inertial modes (of which the infamous r-modes is a subclass) in both a Newtonian and a relativistic context. We anticipate considerable progress in this area in the next year. Particularly fruitful may be a long-term visit of Reinhard to Toulouse and the group of Michel Rieutord, who has considerable expertise on the oscillations of rotating Newtonian stars. Reinhard is also involved in a collaboration with Jerome Novak (Meudon) and Greg Comer on developing a fully relativistic numerical code for determining rapidly rotating two-fluid configurations.

The groups work on the r-mode instability has continued apace. Results from the past year range from the first detailed study of the inertial modes of a relativistic star [5, 6] to phenomenological modelling of the astrophysical relevance of a strong instability in a newly born neutron star [7]. Together with Kokkotas, Andersson has written a major review article on the many aspects of the r-mode problem [8]. The groups main r-mode project is carried out by Ian Jones and is based on the idea of using perturbative time-evolutions to understand various aspects of a secular gravitational-wave instability. This programme was slightly delayed as papers on freely precessing neutron stars (an often mentioned, but rarely analysed in detail, source for gravitational waves) were written [9, 10] but good progress has still been made. In its current reincarnation, the numerical code preserves an r-mode oscillation for several hundred rotation periods of a rapidly spinning (and thus centrifugally deformed) Newtonian star. As one of the many code tests we have verified the mode frequencies calculated by Karino et al. This comparison shows that the numerical approach can provide results with excellent accuracy. In the near future we plan to extend the project in three important directions. First of all, Ian and Anna Watts will study the effect of differential rotation. Secondly, we will implement a local gravitational radiation reaction force according to the description of Blanchet, Damour and Schaefer. Here we will initially restrict the study to the mass multipole radiation (which although less important than the current multipole for r-modes is still significant), but the hope is that discussions with the Jena group will allow a definite prescription for including also current multipoles in a numerically accurate way. Finally, preliminary sketches have laid out a framework for extending the code to the weakly nonlinear regime. This would allow us to investigate the role of mode-coupling and perhaps also begin to probe mode saturation. All in all, it is anticipated that these steps will provide significant insight into the r-mode (and analogous) instabilities.

Together with Philippos Papadopoulos in Portsmouth (and to some extent Andersson), Uli Sperhake (who is due to defend his PhD thesis in October and then join the Thessaloniki group) has carried out detailed tests of a novel approach to nonlinear perturbation calculation. The idea is that one can in many quasistationary situations benefit from subtracting off a known ``background'' and focus attention of whatever is left -- the ``perturbations''. The early studies have demonstrated the great promise of this scheme, with applications to neutron star oscillations and shock formation.

In addition to these main projects, the group has made some progress on perturbations of rotating black holes. Andersson has worked with Kostas Glampedakis in Cardiff on the late-time behaviour of perturbations of near extreme Kerr [11, 12], and Rhiannon Williams is developing a 2+1 null-timelike perturbation code. The hope is that this will provide a useful tool that will allow us to study the late-time behaviour in further detail. It is also possible that the approach can be extended to study rapidly spinning stars. This would be an important application and we intend to pursue the problem in the next year or so.

The progress on the Cauchy-Characteristic Matching project has been fairly limited because of personnel problems. It did not prove possible to recruit either a Network postdoc or a postgraduate student to work on the project. This only leaves Ray d'Inverno involved in code development, although he has made two visits to Golm to work on the code with Denis Pollney. Unfortunately, Ray has limited time to devote to the project because of his major administrative responsibilities as Deputy Dean in the Mathematics Faculty. An upto-date review of the current status of the code can be found in [13]. There is now a considerable body of evidence that CCM has distinct advantages in one dimensional problems i.e. those possessing cylindrical or spherical symmetry. However, it has not as yet proved itself in two dimensional problems i.e. axisymmetric systems. A master CCM vacuum code has been constructed which consists of four modules: a Cauchy interior module, a characteristic exterior module, an interface injection module and an interface extraction module. To date the Cauchy module has been tested and gives good results for Schwarzschild (where it runs stably for times in excess of 1000M), so-called eta waves and l=2 and l=3 Teukolsky waves. Testing is currently focused on the characteristic module. The hope remains that if it proves possible to demonstrate that CCM still possesses advantages in two dimensions, then it will be a relatively easy process to extend the two dimensional code to three dimensions (where effectively the only difference is that the dependent variables will additionally become functions of the polar azimuthal coordinate .)

Carsten Gundlach and (EPSRC funded postdoc) José María Martín-García have informally joined the network to work on the perturbations of spherical stellar collapse. They have recently derived a general framework for evolving the non-spherical perturbations of a time-dependent spherical perfect fluid solution [14, 15]. It is similar to that of Ed Seidel's PhD thesis [16, 17], but formulated without reference to coordinates. We are now going to apply it to two types of gravitational wave source: the core collapse and bounce in a type II supernova, and the accretion-triggered collapse of a neutron star to a black hole. Originally, we are planning a free-standing code based on the Valencia collapse code, in collaboration with José Pons and Jerome Novak. Ed has also volunteered to put various background codes into Cactus, so that different background and perturbation codes can be combined. In preparation, we plan to write our code so that it accepts background data in any coordinate system. We would like input on interesting background physics and, even more importantly, suggestions for realistic initial data for the perturbations!

Outside the scope of the EU network, Carsten and José María are working on critical phenomena in gravitational collapse. Our current projects are collisionless matter and non-spherical perturbations of a perfect fluid. Is anyone looking for a nice 1D evolution warmup project for a graduate student? Carsten would like to test symmetry-seeking coordinates [18] in critical collapse, as a toy model for merging binaries, but lacks the time.

The network support has allowed us to increase our interaction with our European colleagues and exchange news and views in an unprecedented way. Particularly profitable has been the visits of several members of the SISSA and Meudon groups to Southampton, and the two network meetings in Golm and Thessaloniki. The fact that we could afford to bring most of our students to the latter two events was of major importance for the group. Several members of the group (Andersson, Jones and Sperhake) stayed in Thessaloniki after the June meeting and interacted actively with their group. In addition to this, the network funds enabled visits of Gundlach and d'Inverno to Golm and several visits of Prix to Paris.

We are currently planning a meeting in Paris during November or December 2001, in order to make further progress on the many aspects of stellar instabilities that are being investigated within the network. We are also looking forward to hosting the next network meeting in January or February 2002. Although we are unlikely to find a beach location that compares to Greece (and let's not even mention the food) we expect the meeting will still be an exciting event and we hope that all our network colleagues will enjoy a few rainy days on Britain's riviera.