It has been over 25 years since the discovery of the first millisecond radio pulsar in 1982. Since then powerful telescopes and observatories have revolutionized the field of observational astronomy and a large number of millisecond pulsars have been identified with the majority located in globular clusters. The first millisecond pulsar was found to be spinning at 642 Hz and its speed record held for 24 years. It was broken in 2006 by another radio pulsar spinning at 716 Hz. This 24 year gap between the two detections suggests that neutron stars spinning this fast are rare. Moreover, based on a Bayesian statistical analysis of the spin frequencies of 11 accretion powered millisecond pulsars whose spin periods are known from burst oscillations, Chakrabarty et al. (2003) claimed a cutoff limit of 760 Hz. Theoretically, the recycling model of pulsars allows for spins as high as 1.6 kHz depending on the equation of state. Instruments have no significant selection effects against detecting burst oscillations at frequencies well above 1 kHz. So, the question is "What limits the rotation rates?". The answer to this question depends on the internal neutron star physics such as internal dissipation and strength of magnetic fields.
One mechanism that has been proposed as an explanation for the sub-breakup spin rates of neutron stars in low mass x-ray binaries is the R-mode (Rossby wave) instability. This instability is driven by the gravitational radiation backreaction force and is active if this gravitational driving dominates the internal fluid dissipation of the star. My work at Cornell with Ph.D. advisors Ira Wasserman and Saul Teukolsky involves understanding and modeling this instability. We model the nonlinear interactions between near resonant modes together with basic neutron star physics including viscous heating, cooling and spin down of the star.
The nonlinear terms are included via three-mode couplings. In my Ph.D. work I have shown that a simple nonlinear model that uses the three-mode triplet at the lowest parametric instability threshold was sufficient to stop the linear growth of the R-mode in a variety of scenarios. The triplet is formed from the L=2, m=2 R-mode (referred to as the R-mode) and the two other near-resonant modes that are excited when the R-mode amplitude grows above its first parametric instability threshold, which is very low. We studied the possible outcomes for the evolution of the amplitudes of these three modes coupled to the temperature and spin evolution of the star. To explore all possible nonlinear behaviors we parameterized uncertain properties of neutron stars such as the rate at which it cools via neutrino emission and the rate at which the inertial modes dissipate energy via boundary layer effects and bulk viscosity. We found both bound evolutions (cyclic and steady state behavior) in which in the R-mode amplitude did not grow significantly above its first parametric instability threshold and unbound evolutions. In the latter case the R-mode amplitude grows above its second parametric instability threshold and excites more inertial modes.
I am currently working on modeling the R-mode instability in new born neutron stars and it's exciting! Preliminary results show that, depending on internal neutron star physics, the r-mode saturation amplitude can be two or three order of magnitude larger than in the case of neutron stars in LMXBs.2. Reshaping beam and mirror shapes in advanced gravitational waves interferometers
The dominant form of noise in the most sensitive frequency band of Advanced LIGO detectors is thermal noise in the substrate reflective coating of the mirrored test masses. Reshaping the beams to a flatter, wider profile that probes more of the mirror surface lowers this noise. Together with my brother (AEI/Caltech) and two other colleagues at Cornell, I worked on a project for optimizing currently proposed mirror shapes by taking into account finite mirror effects. To explore these effects for Mesa and hyperboloidal beam shapes we developed a pseudo-spectral code that calculates the diffraction loss directly from the propagator and found that the finite radius of the mirror causes beam shapes to deviate significantly from the infinite-mirror theoretical expectations. This causes previously unnoticed local minima in the diffraction loss that can be exploited to find a natural beam width for a given diffraction loss constraint. We also proposed new mirror and beam shapes that explicitly account for the finite mirror effects by reformulating the mirror surface to coincide with the phase front of the primary eigenmode. This lowered the diffraction loss by factors of 40-100 and allows for wider beams for the same diffraction loss constraint. The coating thermal noise is lowered by about 30% compared to previously considered Mesa shapes. While we are choosing advanced LIGO for definiteness, finite mirror effects should be important for any interferometric detector that needs to limit thermal noise. Our code could easily be generalized to work for other beam shapes. This project gave me the opportunity to broaden my interests and learn about instrumentation and optics and I have also learned to appreciate more the science behind building high precision observatories such as LIGO.
The Cornell side of our LIGO collaboration under a raibow (from left to right: Dave, me and Andy taking a break on top of the Space Sciences building to see the rainbow better before submitting the paper to PRD; Mihai - my brother - is the other person on the paper and was a postdoc at the AEI in Germany at the time; he joined us on a conference call on skype, but unfortunately was too far to climb on the roof with us). It's the first paper we wrote on our own as a collaboration among students (+ Mihai who had just graduated) with no senior person/advisor involved.
Together with Jayashree Balakrishna (Harris-Stowe U, St. Louis, MO), Gregory Daues (NCSA, Urbana, IL), my undergraduate advisor Edward Seidel and others, I worked on numerical relativity projects that involved studying Einstein's equations with simple matter sources such as boson stars (complex scalar field) and oscillating soliton stars (real scalar field). Scalar fields are important dark matter candidates. Recent evidence for the existence of dark matter was found with both the Hubble telescope and the Chandra Observatory. In principle, scalar particles could come together through some kind Jeans instability and form stars. We studied gravitational waveforms from single, nonradialy perturbed soliton and boson stars and compared the numerical waveforms to linear perturbation results for the boson star case. Working with Prof. Seidel gave me the opportunity to run large-scale numerical simulations on some of the world's largest supercomputers, to learn to handle large amounts of data and in general, to interact with a large research group. He also allowed me to engage in activities normally reserved for faculty members. I advised several students who are now working in his group and he supported my brother and I to organize a series of gravitational wave lectures at LSU that were based on Kip Thorne's Caltech course.