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Excitation of a nonradial mode in a millisecond X-ray pulsar XTE J1751-305
High Energy Astrophysical Phenomena · Submitted 14 Mar 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Because of this significant amplification of the $r$-mode amplitudes in the surface fluid layer, we suggest that, when proper corrections to the $r$-mode frequency such as due to the general relativistic effects are taken into consideration, the core $r$-mode of $l^\prime=m=2$ can be a candidate for the detected frequency, without leading to serious contradictions to, for example, the spin evolution of the underlying neutron star.
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The abstract, sentence by sentence
We discuss candidates for non-radial modes excited in a mass accreting and rapidly rotating neutron star to explain the coherent frequency identified in the light curves of a millisecond X-ray pulsar XTE J1751-305. The spin frequency of the pulsar is $\nu_{\rm spin}\cong435$Hz and the identified coherent frequency is $\nu_{\rm osc}=0.5727595\times\nu_{\rm spin}$. Assuming the frequency identified is that observed in the corotating frame of the neutron star, we find that the surface $r$-modes of $l^\prime=m=1$ and 2 excited by $\epsilon$-mechanism due to helium burning in the thin shell can give the frequency ratio $\kappa=\nu_{\rm osc}/\nu_{\rm spin}\simeq0.57$ at $\nu_{\rm spin}=435$Hz. As another candidate for the observed ratio $\kappa$, we also suggest a toroidal crustal mode that has penetrating amplitudes in the fluid core and is destabilized by gravitational wave emission. Since the surface fluid layer is separated from the fluid core by a solid crust, the amplitudes of an $r$-mode in the core, which is destabilized by emitting gravitational waves, can be by a large factor different from those in the fluid ocean. We find that the amplification factor defined as $f_{\rm amp}=\alpha_{\rm surface}/\alpha_{\rm core}$ is as large as $f_{\rm amp}\sim 10^2$ for the $l^\prime=m=2$ $r$-mode at $\nu_{\rm spin}=435$Hz for a $M=1.4M_\odot$ neutron star model. Because of this significant amplification of the $r$-mode amplitudes in the surface fluid layer, we suggest that, when proper corrections to the $r$-mode frequency such as due to the general relativistic effects are taken into consideration, the core $r$-mode of $l^\prime=m=2$ can be a candidate for the detected frequency, without leading to serious contradictions to, for example, the spin evolution of the underlying neutron star.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss candidates for non-radial modes excited in a mass accreting and rapidly rotating neutron star to explain the coherent frequency identified in the light curves of a millisecond X-ray pulsar XTE J1751-305. | contribution 0.94 | 0.68 | 0.08 | hedged possibility 0.60 |
| s1 | The spin frequency of the pulsar is $\nu_{\rm spin}\cong435$Hz and the identified coherent frequency is $\nu_{\rm osc}=0.5727595\times\nu_{\rm spin}$. | background 0.51 | 0.33 | 0.03 | asserted 0.99 |
| s2 | Assuming the frequency identified is that observed in the corotating frame of the neutron star, we find that the surface $r$-modes of $l^\prime=m=1$ and 2 excited by $\epsilon$-mechanism due to helium burning in the thin shell can give the frequency ratio $\kappa=\nu_{\rm osc}/\nu_{\rm spin}\simeq0.57$ at $\nu_{\rm spin}=435$Hz. | result 0.94 | 0.90 | 0.29 | asserted 0.80 |
| s3 | As another candidate for the observed ratio $\kappa$, we also suggest a toroidal crustal mode that has penetrating amplitudes in the fluid core and is destabilized by gravitational wave emission. | contribution 0.95 | 0.73 | 0.09 | hedged possibility 0.96 |
| s4 | Since the surface fluid layer is separated from the fluid core by a solid crust, the amplitudes of an $r$-mode in the core, which is destabilized by emitting gravitational waves, can be by a large factor different from those in the fluid ocean. | background 0.70 | 0.21 | 0.04 | asserted 0.57 |
| s5 | We find that the amplification factor defined as $f_{\rm amp}=\alpha_{\rm surface}/\alpha_{\rm core}$ is as large as $f_{\rm amp}\sim 10^2$ for the $l^\prime=m=2$ $r$-mode at $\nu_{\rm spin}=435$Hz for a $M=1.4M_\odot$ neutron star model. | result 1.00 | 0.94 | 0.10 | asserted 1.00 |
| s6 | Because of this significant amplification of the $r$-mode amplitudes in the surface fluid layer, we suggest that, when proper corrections to the $r$-mode frequency such as due to the general relativistic effects are taken into consideration, the core $r$-mode of $l^\prime=m=2$ can be a candidate for the detected frequency, without leading to serious contradictions to, for example, the spin evolution of the underlying neutron star. | interpretation 0.99 | 0.60 | 0.69 | hedged possibility 1.00 |
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The paper
Original abstract
We discuss candidates for non-radial modes excited in a mass accreting and rapidly rotating neutron star to explain the coherent frequency identified in the light curves of a millisecond X-ray pulsar XTE J1751-305. The spin frequency of the pulsar is $\nu_{\rm spin}\cong435$Hz and the identified coherent frequency is $\nu_{\rm osc}=0.5727595\times\nu_{\rm spin}$. Assuming the frequency identified is that observed in the corotating frame of the neutron star, we find that the surface $r$-modes of $l^\prime=m=1$ and 2 excited by $\epsilon$-mechanism due to helium burning in the thin shell can give the frequency ratio $\kappa=\nu_{\rm osc}/\nu_{\rm spin}\simeq0.57$ at $\nu_{\rm spin}=435$Hz. As another candidate for the observed ratio $\kappa$, we also suggest a toroidal crustal mode that has penetrating amplitudes in the fluid core and is destabilized by gravitational wave emission. Since the surface fluid layer is separated from the fluid core by a solid crust, the amplitudes of an $r$-mode in the core, which is destabilized by emitting gravitational waves, can be by a large factor different from those in the fluid ocean. We find that the amplification factor defined as $f_{\rm amp}=\alpha_{\rm surface}/\alpha_{\rm core}$ is as large as $f_{\rm amp}\sim 10^2$ for the $l^\prime=m=2$ $r$-mode at $\nu_{\rm spin}=435$Hz for a $M=1.4M_\odot$ neutron star model. Because of this significant amplification of the $r$-mode amplitudes in the surface fluid layer, we suggest that, when proper corrections to the $r$-mode frequency such as due to the general relativistic effects are taken into consideration, the core $r$-mode of $l^\prime=m=2$ can be a candidate for the detected frequency, without leading to serious contradictions to, for example, the spin evolution of the underlying neutron star.
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We therefore conclude that the r-mode interpretation of the observed oscillation is not consistent with our current understanding of neutron star dynamics and must be considered unlikely.
Implications of an r-mode in XTE J1751-305: Mass, radius and spin evolution · 0.87
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