Trapped and excited w modes of stars with a phase transition and R>=5M

TL;DR

This paper investigates trapped and excited odd parity $w$-modes in stars with a phase transition, showing conditions for their existence, excitation, and stability, with implications for gravitational wave signals.

Contribution

It provides the first detailed analysis of trapped $w$-modes in stars with a phase transition, including excitation mechanisms and stability criteria.

Findings

Stars with $R/M extgreater 5$ can have multiple trapped $w$-modes.

Excitation of the least damped $w$-mode confirmed in some models.

Stars with phase transitions can have more trapped modes than homogeneous stars with same $R/M$.

Abstract

The trapped $w$-modes of stars with a first order phase transition (a density discontinuity) are computed and the excitation of some of the modes of these stars by a perturbing shell is investigated. Attention is restricted to odd parity (``axial'') $w$-modes. With $R$ the radius of the star, $M$ its mass, $R_{i}$ the radius of the inner core and $M_{i}$ the mass of such core, it is shown that stars with $R/M\geq 5$ can have several trapped $w$-modes, as long as $R_{i}/M_{i}<2.6$. Excitation of the least damped $w$-mode is confirmed for a few models. All of these stars can only exist however, for values of the ratio between the densities of the two phases, greater than $\sim 46$. We also show that stars with a phase transition and a given value of $R/M$ can have far more trapped modes than a homogeneous single density star with the same value of $R/M$, provided both $R/M$ and $R_{i}/M_{i}$ are smaller than 3. If the phase transition is very fast, most of the stars with trapped modes are unstable to radial oscillations. We compute the time of instability, and find it to be comparable to the damping of the $w$-mode excited in most cases where $w$-mode excitation is likely. If on the other hand the phase transition is slow, all the stars are stable to radial oscillations.