A Fundamental Plane for Gamma-Ray Pulsars. (arXiv:1904.01765v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Kalapotharakos_C/0/1/0/all/0/1">Constantinos Kalapotharakos</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Harding_A/0/1/0/all/0/1">Alice K. Harding</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Kazanas_D/0/1/0/all/0/1">Demosthenes Kazanas</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wadiasingh_Z/0/1/0/all/0/1">Zorawar Wadiasingh</a>
We show that the $gamma$-ray pulsar observables, i.e., their total
$gamma$-ray luminosity, $L_{gamma}$, spectrum cut-off energy, $epsilon_{rm
cut}$, stellar surface magnetic field, $B_{star}$, and spin-down power
$dot{mathcal{E}}$, obey a relation of the form $L_{gamma}=f(epsilon_{rm
cut},B_{star},dot{mathcal{E}})$, which represents a 3D plane in their 4D
log-space. Fitting the data of the 88 pulsars of the second Fermi pulsar
catalog, we show this relation to be $L_{gamma}propto epsilon_{rm
cut}^{1.18pm 0.24}B_{star}^{0.17pm 0.05}dot{mathcal{E}}^{0.41pm 0.08}$, a
pulsar fundamental plane (FP). We show that the observed FP is remarkably close
to the theoretical relation $L_{gamma}propto epsilon_{rm
cut}^{4/3}B_{star}^{1/6}dot{mathcal{E}}^{5/12}$ obtained assuming that the
pulsar $gamma$-ray emission is due to curvature radiation by particles
accelerated at the pulsar equatorial current sheet just outside the light
cylinder. Interestingly, this seems incompatible with emission by synchrotron
radiation. The corresponding scatter is $sim0.35$dex and can only partly be
explained by the observational errors while the rest is probably due to the
variation of the inclination and observer angles. We predict also that
$epsilon_{rm cut}propto dot{mathcal{E}}^{7/16}$ toward low
$dot{mathcal{E}}$ for both young and millisecond pulsars implying that the
observed death-line of $gamma$-ray pulsars is due to $epsilon_{rm cut}$
dropping below the Fermi-band. Our results provide a comprehensive
interpretation of the observations of $gamma$-ray pulsars, setting requirement
for successful theoretical modeling.
We show that the $gamma$-ray pulsar observables, i.e., their total
$gamma$-ray luminosity, $L_{gamma}$, spectrum cut-off energy, $epsilon_{rm
cut}$, stellar surface magnetic field, $B_{star}$, and spin-down power
$dot{mathcal{E}}$, obey a relation of the form $L_{gamma}=f(epsilon_{rm
cut},B_{star},dot{mathcal{E}})$, which represents a 3D plane in their 4D
log-space. Fitting the data of the 88 pulsars of the second Fermi pulsar
catalog, we show this relation to be $L_{gamma}propto epsilon_{rm
cut}^{1.18pm 0.24}B_{star}^{0.17pm 0.05}dot{mathcal{E}}^{0.41pm 0.08}$, a
pulsar fundamental plane (FP). We show that the observed FP is remarkably close
to the theoretical relation $L_{gamma}propto epsilon_{rm
cut}^{4/3}B_{star}^{1/6}dot{mathcal{E}}^{5/12}$ obtained assuming that the
pulsar $gamma$-ray emission is due to curvature radiation by particles
accelerated at the pulsar equatorial current sheet just outside the light
cylinder. Interestingly, this seems incompatible with emission by synchrotron
radiation. The corresponding scatter is $sim0.35$dex and can only partly be
explained by the observational errors while the rest is probably due to the
variation of the inclination and observer angles. We predict also that
$epsilon_{rm cut}propto dot{mathcal{E}}^{7/16}$ toward low
$dot{mathcal{E}}$ for both young and millisecond pulsars implying that the
observed death-line of $gamma$-ray pulsars is due to $epsilon_{rm cut}$
dropping below the Fermi-band. Our results provide a comprehensive
interpretation of the observations of $gamma$-ray pulsars, setting requirement
for successful theoretical modeling.
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