R-mode Frequency Research Articles

Universal relations to measure neutron star properties from targeted r-mode searches

ABSTRACT R-mode oscillations of rotating neutron stars (NS) are promising candidates for continuous gravitational wave (GW) observations. In our recent work, we derived universal relations between the NS parameters compactness and dimensionless tidal deformability with the r-mode frequency. In this work, we investigate how these universal relations can be used to infer various NS intrinsic parameters following a successful detection of the r-modes. In particular, we show that for targeted r-mode searches, these universal relations along with the ‘I–Love–Q’ relation can be used to estimate both the moment of inertia and the distance of the NS, thus breaking the degeneracy of distance measurement for continuous gravitational wave (CGW) observations. We also discuss that, with a prior knowledge of the distance of the NS from electromagnetic observations, these universal relations can also be used to constrain the dense matter equation of state (EOS) inside the NS. We quantify the accuracy to which such measurements can be done using the Fisher information matrix for a broad range of possible, unknown parameters for both the a-LIGO and Einstein Telescope (ET) sensitivities.

Relativistic Correction to the r-mode Frequency in Light of Multimessenger Constraints

The r-mode oscillations of rotating neutron stars are promising candidates for continuous gravitational-wave (GW) observations. The r-mode frequencies for slowly rotating Newtonian stars are well known and independent of the equation of state (EOS), but for neutron stars several mechanisms can alter the r-mode frequency for which the relativistic correction is dominant and relevant for most of the neutron stars. The most sensitive searches for continuous GWs are those for known pulsars for which GW frequencies are in targeted narrow frequency bands of a few hertz. In this study, we investigate the effect of several state-of-the-art multimessenger constraints on the r-mode frequency for relativistic, slowly rotating, barotropic stars. Imposing these recent constraints on the EOS, we find that the r-mode frequency range is slightly higher than that from the previous study and the narrowband frequency range can increase by up to 25% for the most promising candidate PSR J0537−6910 depending on the range of compactness. We also derive universal relations between r-mode frequency and dimensionless tidal deformability that can be used to estimate the dynamical tide of the r-mode resonant excitation during the inspiral signal. These results can be used to construct the parameter space for r-mode searches in GW data and also constrain the nuclear EOS following a successful r-mode detection.

R-mode oscillations in accreting white dwarfs in cataclysmic variables

Some cataclysmic variables show short-period ($\sim$200 to $\sim$2000 s) light variations, which are attributable to nonradial pulsations of the accreting primary white dwarf. We regard these periodic variations as r-mode (global Rossby-wave) oscillations which are presumably excited mechanically and confined into hydrogen-rich layers in the white dwarf. Often observed modulations in amplitudes and frequencies even during an observing season may be interpreted as beatings among densely distributed r-mode frequencies. Making the r-mode frequency distribution of a model to be consistent (by adjusting the rotation frequency) with the observed pulsation frequencies, we obtain the best-fit rotation rate for each case. The rotation periods thus obtained for 17 accreting white dwarfs lie between 4 and 10 minutes. Pulsation frequencies observed sometime after a dwarf-nova outburst tend to be higher than the pre-outburst values, so that the best-fit rotation rate for the post-outburst frequencies is also higher. This indicates a spin-up of the hydrogen-rich layers to occur by an enhanced accretion at the outburst. We also discuss the relation between the rotation frequencies of pulsating accreting white dwarfs and the orbital periods.

M/R estimates for two neutron stars in LMXBs with possible r-mode frequencies detected

The puzzling existence of a number of neutron stars that appear to be in the r-mode instability window supports further investigations of the r-mode frequencies, damping times and saturation amplitudes, especially now in light of the much anticipated and exciting results from LIGO and NICER. It has been suggested by Mahmoodifar and Strohmayer that coherent frequencies found in the RXTE data of the accreting millisecond pulsar XTE J1751-305 and during the 2001 superburst of 4U 1636-536 (one of the accreting sources to be observed by NICER) could, in fact, be r-modes. Based on these observations, we expand here the results of a previous work on relativistic, rotational and differential rotation corrections to the r-mode frequency in order to provide more accurate estimates of the $M-R$ relation for these neutron stars. Finally, we compare our results with predictions from a few realistic tabulated equations of state, providing further constraints that favor more compact models. We find that, if the observed frequencies indeed correspond to r-modes, then the masses of XTE J1751-305 and 4U 1636-536 should lie in the approximate ranges $1.48 - 1.56 M_{\odot}$ and $1.60 - 1.68 M_{\odot}$, respectively.

Theory and evidence of global Rossby waves in upper main-sequence stars: r-mode oscillations in many Kepler stars

Asteroseismic inference from pressure modes (p modes) and buoyancy, or gravity, modes (g modes) is ubiquitous for stars across the Hertzsprung--Russell diagram. Until now, however, discussion of r modes (global Rossby waves) has been rare. Here we derive the expected frequency ranges of r modes in the observational frame by considering the visibility of these modes. We find that the frequencies of r modes of azimuthal order $m$ appear as groups at slightly lower frequency than $m$ times the rotation frequency. Comparing the visibility curves for r modes with Fourier amplitude spectra of Kepler light curves of upper main-sequence B, A and F stars, we find that r modes are present in many $\gamma$ Dor stars (as first discovered by Van Reeth et al. 2016), spotted stars, and so-called Heartbeat stars, which are highly eccentric binary stars. We also find a signature of r modes in a frequently bursting Be star observed by Kepler. In the amplitude spectra of moderately to rapidly rotating $\gamma$ Dor stars, r-mode frequency groups appear at lower frequency than prograde g-mode frequency groups, while in the amplitude spectra of spotted early A to B stars, groups of symmetric (with respect to the equator) r-mode frequencies appear just below the frequency of a structured peak that we suggest represents an approximate stellar rotation rate. In many Heartbeat stars, a group of frequencies can be fitted with symmetric $m=1$ r modes, which can be used to obtain rotation frequencies of these stars.

R -mode frequencies of rapidly and differentially rotating relativistic neutron stars

R-modes of neutron stars could be a source of gravitational waves for ground based detectors. If the precise frequency $\sigma$ is known, guided gravitational wave searches with enhanced detectability are possible. Because of its physical importance many authors have calculated the r-mode frequency. For the dominant mode, the associated gravitational wave frequency is 4/3 times the angular velocity of the star $\Omega$, subject to various corrections of which relativistic and rotational corrections are the most important. This has led several authors to investigate the dependence of the r-mode frequency on factors such as the relativistic compactness parameter ($M/R$) and the angular velocity of stars with different equations of state. The results found so far, however, are almost independent of the equation of state. Here we investigate the effect of rapid rotation and differential rotation on $\sigma$. We evolve the perturbation equations using the Cowling approximation by applying finite differencing methods to compute the r-mode frequency for a series of rotating neutron stars with polytropic equations of state. We find that rotational effects in the r-mode frequency can be larger than relativistic effects for rapidly spinning stars with low compactness, reducing the observed frequency. Differential rotation also acts to decrease $\sigma$, but its effect inscreases with the compactness. The results presented here are relevant to the design of gravitational wave and electromagnetic r-mode searches.

R-mode frequencies of slowly rotating relativistic neutron stars with realistic equations of state

The frequencies of r-mode oscillations of rotating neutron stars can be useful for guiding and interpreting gravitational wave and electromagnetic observations. The frequencies of slowly rotating, barotropic, and non-magnetic Newtonian stars are well known, but subject to various corrections. After making simple estimates of the relative strengths of these corrections we conclude that relativistic corrections are likely to be the most important. For this reason we extend the formalism of K. H. Lockitch, J. L. Friedman, and N. Andersson [Phys. Rev. D 68, 124010 (2003)], who consider relativistic polytropes, to the case of realistic equations of state. This formulation results in perturbation equations which are solved using a spectral method. We find that for realistic equations of state the r-mode frequency ranges from 1.39 to 1.57 times the spin frequency of the star when the relativistic compactness parameter (M/R) is varied over the astrophysically motivated interval 0.11 to 0.31. The results presented here are relevant to the design of gravitational wave and electromagnetic r-mode searches, and following a successful r-mode detection could help constrain the high density equation of state.

Prospects for transient gravitational waves at r-mode frequencies associated with pulsar glitches

t Glitches in pulsars are likely to trigger oscillation modes in the fluid interior of neutron stars. We examined these oscillations specifically at r-mode frequencies. The excited r-modes will emit gravitational waves and can have long damping time scales \U0001d4aa(minutes - days). We use simple estimates of how much energy the glitch might put into the r-mode and assess the detectability of the emitted gravitational waves with future interferometers.

Generation of whistler mode in a relativistic plasma

This paper contains the plasma maser interaction between high frequency nonresonant whistler R-mode and low frequency resonant ion acoustic mode in a relativistic plasma. It shows that the whistler R-mode grows through the plasma maser interaction between the relativistic electrons and the ion acoustic fluctuation.

Free vibration of multiwall carbon nanotubes

A multiple-elastic shell model is applied to systematically study free vibration of multiwall carbon nanotubes (MWNTs). Using Flugge [Stresses in Shells (Springer, Berlin, 1960)] equations of elastic shells, vibrational frequencies and associated modes are calculated for MWNTs of innermost radii 5 and 0.65 nm, respectively. The emphasis is placed on the effect of interlayer van der Waals (vdW) interaction on free vibration of MWNTs. Our results show that the interlayer vdW interaction has a crucial effect on radial (R) modes of large-radius MWNTs (e.g., of the innermost radius 5 nm), but is less pronounced for R modes of small-radius MWNTs (e.g., of the innermost radius 0.65 nm), and usually negligible for torsional (T) and longitudinal (L) modes of MWNTs. This is attributed to the fact that the interlayer vdW interaction, characterized by a radius-independent vdW interaction coefficient, depends on radial deflections only, and is dominant only for large-radius MWNTs of lower radial rigidity but less pronounced for small-radius MWNTs of much higher radial rigidity. As a result, the R modes of large-radius MWNTs are typically collective motions of almost all nested tubes, and the R modes of small-radius MWNTs, as well as the T and L modes of MWNTs, are basically vibrations of individual tubes. In particular, an approximate single-shell model is suggested to replace the multiple-shell model in calculating the lowest frequency of R mode of thin MWNTs (defined by the innermost radius-to-thickness ratio not less than 4) with relative errors less than 10%. In addition, the simplified Flugge single equation is adopted to substitute the exact Flugge equations in determining the R-mode frequencies of MWNTs with relative errors less than 10%.

R‐Mode Oscillations and Spin‐down of Young Rotating Magnetic Neutron Stars

Recent work has shown that a young, rapidly rotating neutron star loses angular momentum to gravitational waves generated by unstable r-mode oscillations. We study the spin evolution of a young, magnetic neutron star including the effects of both gravitational radiation and magnetic braking (modeled as magnetic dipole radiation). Our phenomenological description of nonlinear r-modes is similar to, but distinct from, that given by Owen and colleagues in 1998, in that our treatment is consistent with the principle of adiabatic invariance in the limit when direct driving and damping of the mode are absent. We show that while magnetic braking tends to increase the r-mode amplitude by spinning down the neutron star, it nevertheless reduces the efficiency of gravitational wave emission from the star. For B 1014(νs/300 Hz)2 G, where νs is the spin frequency, the spin-down rate and the gravitational waveforms are significantly modified by the effect of magnetic braking. We also estimate the growth rate of the r-mode due to electromagnetic (fast magnetosonic) wave emission and due to Alfven wave emission in the neutron star magnetosphere. The Alfven wave driving of the r-mode becomes more important than the gravitational radiation driving when B 1013(νs/150 Hz)3 G; the electromagnetic wave driving of the r-mode is much weaker. Finally, we study the properties of local Rossby-Alfven waves inside the neutron star and show that the fractional change of the r-mode frequency due to the magnetic field is of order 0.5(B/1016 G)2(νs/100 Hz)-2.

Gravitational-Wave Driven Instability of Rotating Relativistic Stars

A series of recent surprises appear dramatically to have improved the likelihood that the spin of rapidly rotating, newly formed neutron stars is limited by a nonaxisymmetric instability driven by gravitational waves — and that the emitted waves may be detectable. The first of these was the discovery that the r-modes, rotationally restored modes that have axial parity for spherical models, are unstable in perfect fluid models with arbitrarily slow rotation. First indicated in numerical work by Andersson, 1) the instability is implied in a nearly newtonian context by the newtonian expression for the r-mode frequency (3.1), and a computation by Friedman and Morsink 19) of the canonical energy of initial data showed (independent of assumptions on the existence of discrete modes) that the instability is a generic feature of axial-parity perturbations of relativistic stars. Studies of the viscous and radiative timescales associated with the rmodes, 38), 43), 2), 29), 37) have revealed a second surprising result: The growth time of r-modes driven by current-multipole gravitational radiation is significantly shorter than had been expected, so short, in fact, that the instability to gravitational radiation reaction easily dominates viscous damping in hot, newly formed neutron stars (see Fig. 1 below). As a result, a neutron star that is rapidly rotating at birth now appears likely to spin down by radiating most of its angular momentum in gravitational waves. (See, however, the caveats below.) Nearly simultaneous with these theoretical surprises was the discovery by Marshall et al. 41) of a fast (16ms) pulsar in a supernova remnant (N157B) in the Large Magellanic Cloud. Estimates of the initial period put it in the 6-9ms range, implying the existence of a class of neutron stars that are rapidly rotating at birth. Hence,