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Register a new userNew class of g-modes and unexpected convection in neutron stars
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We suggest a specific new class of low-frequency g-modes in superfluid neutron stars. We determine the Brunt-Vaisala frequency for these modes and demonstrate that they can be unstable with respect to convection. The criterion for the instability onset (analogue of the well known Schwarzschild criterion) is derived. It is very sensitive to equation of state and a model of nucleon superfluidity. In particular, convection may occur for both positive and negative temperature gradients. Our results have interesting implications for neutron star cooling and seismology.
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We demonstrate a possibility of existence of a peculiar temperature-dependent composition $g$-modes in superfluid neutron stars. We calculate the Brunt-V$ddot{rm a}$is$ddot{rm a}$l$ddot{rm a}$ frequency for these modes, as well as their eigenfrequencies. The latter turn out to be rather large, up to $sim 500$ Hz for a chosen model of a neutron star. This result indicates, in particular, that use of the barotropic equation of state may be not a good approximation for calculation of inertial modes even in most rapidly rotating superfluid neutron stars.
We analyse the oscillations of general relativistic superfluid hyperon stars, following the approach suggested by Gusakov & Kantor and Gusakov et al. and generalizing it to the nucleon-hyperon matter. We show that the equations governing the oscillations can be split into two weakly coupled systems with the coupling parameters $s_{rm e}$, $s_{rm mu}$, and $s_{rm str}$. The approximation $s_{rm e} = s_{rm mu} = s_{rm str} = 0$ (decoupling approximation) allows one to drastically simplify the calculations of stellar oscillation spectra. An efficiency of the presented scheme is illustrated by the calculation of sound speeds in the nucleon-hyperon matter composed of neutrons (n), protons (p), electrons (e), muons ($mu$), as well as $rm Lambda$, ${rm Xi}^-$, and ${rm Xi}^0$-hyperons. However, the gravity oscillation modes (g-modes) cannot be treated within this approach, and we discuss them separately. For the first time we study the composition g-modes in superfluid hyperon stars with the $rm npemuLambda$ core and show that there are two types of g-modes (`muonic and `$Lambda$--hyperonic) in such stars. We also calculate the g-mode spectrum and find out that the eigenfrequencies $ u$ of the superfluid g-modes can be exceptionally large (up to $ u approx 742~{rm Hz}$ for a considered stellar model).
For the first time nonradial oscillations of superfluid nonrotating stars are self-consistently studied at finite stellar temperatures. We apply a realistic equation of state and realistic density dependent model of critical temperature of neutron and proton superfluidity. In particular, we discuss three-layer configurations of a star with no neutron superfluidity at the centre and in the outer region of the core but with superfluid intermediate region. We show, that oscillation spectra contain a set of modes whose frequencies can be very sensitive to temperature variations. Fast temporal evolution of the pulsation spectrum in the course of neutron star cooling is also analysed.
A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency $omega_a$ excites a pair of secondary waves of frequency $omega_b+omega_c simeq omega_a$. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that $omega_b+omega_c >>omega_a$. We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f_{gw} > 20 Hz and drive p-g pairs to significant energies on very short timescales (much less than the orbital decay time). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the instability and therefore cannot say precisely how it influences neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide: (i) induces significant orbital phase errors ($Delta phi$ > 1 radian) that accumulate primarily at low frequencies (f_{gw} < 50 Hz) and (ii) heats the neutron star core to T~10^{10} K. Since there are >100 unstable daughters, $Delta phi$ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from neutron star binaries at much larger orbital separations than previously thought.
We recently described an instability due to the nonlinear coupling of p-modes to g-modes and, as an application, we studied the stability of the tide in coalescing binary neutron stars. Although we found that the tide is p-g unstable early in the inspiral and rapidly drives modes to large energies, our analysis only accounted for three-mode interactions. Venumadhav, Zimmerman, and Hirata showed that four-mode interactions must also be accounted for as they enter into the analysis at the same order. They found a near-exact cancellation between three- and four-mode interactions and concluded that while the tide in binary neutron stars can be p-g unstable, the growth rates are not fast enough to impact the gravitational wave signal. Their analysis assumes that the linear tide is incompressible, which is true of the static linear tide (the m=0 harmonic) but not the non-static linear tide (m=+/- 2). Here we account for the compressibility of the non-static linear tide and find that the three- and four-mode interactions no longer cancel. As a result, we find that the instability can rapidly drive modes to significant energies (there is time for several dozen e-foldings of growth before the binary merges). We also show that linear damping interferes with the cancellation and may further enhance the p-g growth rates. The early onset of the instability (at gravitational wave frequencies near 50 Hz), the rapid growth rates, and the large number of unstable modes (> 10^3), suggest that the instability could impact the phase evolution of gravitational waves from binary neutron stars. Assessing its impact will require an understanding of how the instability saturates and is left to future work.
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