The animation above shows a schematic representation of a (non-radial) stellar oscillation for a non-rotating star and as viewed from the southern hemisphere. As any type of oscillation, the angular properties of the one shown above can be described in terms of its land m mode numbers (see here for a more detailed discussion of the mode description and classification). More precisely it refers to a l=m=2 mode and, because it deforms the star into a bar, it is commonly known as called a "bar-mode" oscillation.Einstein's theory of General Relativity predicts that a movement of matter deforms the spacetime in which the matter resides. This deformation of spacetime will then produce small ripples of the spacetime curvature that will reach infinity in the form of gravitational waves. The oscillations of relativistic stars (neutron stars, strange stars, etc.) will thus emit gravitational waves, and represent one of the most promising sources for up-coming gravitational wave detectors.
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In rotating relativistic stars, some of the oscillation modes might not be damped but actually have amplitudes that grow exponentially in time. In this case the oscillations are said to be "unstable" and one of the mechanism responsible for this is the so called CFS(Chandrasekhar-Friedman-Schutz) instabilitymechanism. The origin of this fascinating phenomena is the coupling between the loss of energy and angular momentum via radiation (graviational, electromagnetic, etc.) and the stellar oscillation modified by the rotation.
Because of the very large amplitudes that the oscillation modes can reach when driven unstable, the amount of gravitational radiation emitted can become considerable and these unstable stars are then promising sources of gravitational waves, detectable by the gravitational-wave observatories now working or being under construction.
The emission of gravitational waves carries to infinity a large amount of the stellar angular momentum and, as a consequence, these CFS unstable stars will be brought to a rapid spin-down. In this way the emission of gravitational waves via a CFS instability provides a simple explanation of how initially rapidly rotating stars can be brought to have the rather "long" rotation periods observed in young pulsars. The group in SISSA is interested in the detailed study of these modes using perturbative analyses under a number of different assumptions and approximations. Particular attention is paid to the investigation of the so-called r-modes and f-modes. A brief description of the different modes, their classification and their most important properties can be found here
Besides being good emitters of gravitational waves, the stellar oscillation modes carry important physical information about the structure of the star and the properties of the matter composing it. As a result, observations of these oscillation modes via the gravitational waves they produce can provide information of the most interior parts of the star which are not accessible through electromagnetic radiation. This line of thought has been applied with success to the study of the internal structure of closeby stars such as the Sun. This technique, which is usually referred to as helioseismology, has been fully developed in recent years and has yielded an unexpected wealth of information on the physical structure of the Sun and on the processes that take place in its deep interior.
The basic properties of modes observable via gravitational waves are essentially given by their frequency and their damping (or growth) time scales. From the knowledge of these quantities not only can the parameters of the stellar structure be determined, but also valuable information on the properties of matter at extremely high densities, which cannot be obtained in terrestrial laboratories.
In the course of the evolution of
unstable modes, the amplitude of the stellar oscillations is expected to
grow to very large values and produce nonlinear processes that cannot be
described adequately by linear perturbative analyses.
Similar nonlinear regimes are also
reached when a compact object is produced after the gravitational collapse
of a stellar core as the remnant of the coalescence of neutron star binary.
All of these astrophysical scenario are expected to be accompanied by large
amplitude perturbations and yield considerable amounts of gravitational
radiation. The only effective way to circumvent the limitations introduced
by perturbative approaches is to make use of numerical simulations that
solve Einstein equations without approximations and assumptions of symmetries.
The area of research that implements this approach is usually referred
to as "Numerical Relativity" which is focussed on the development and use
of three-dimensional codes that solve Einstein equations in full generality
and exploiting the numerical resources offered by the most powerful supercomputers.
The group in SISSA is actively involved in this line of research, developing
parallel codes such as the Cactus
code and its relativistic hydrodynamics counterpart Whisky.
People involved: