TY - JOUR

T1 - A ray-tracing algorithm for spinning compact object spacetimes with arbitrary quadrupole moments. II. Neutron stars

AU - Bauböck, Michi

AU - Psaltis, Dimitrios

AU - Özel, Feryal

AU - Johannsen, Tim

PY - 2012/7/10

Y1 - 2012/7/10

N2 - A moderately spinning neutron star acquires an oblate shape and a spacetime with a significant quadrupole moment. These two properties affect its apparent surface area for an observer at infinity, as well as the light curve arising from a hot spot on its surface. In this paper, we develop a ray-tracing algorithm to calculate the apparent surface areas of moderately spinning neutron stars making use of the Hartle-Thorne metric. This analytic metric allows us to calculate various observables of the neutron star in a way that depends only on its macroscopic properties and not on the details of its equation of state. We use this algorithm to calculate the changes in the apparent surface area, which could play a role in measurements of neutron-star radii and, therefore, in constraining their equation of state. We show that whether a spinning neutron star appears larger or smaller than its non-rotating counterpart depends primarily on its equatorial radius. For neutron stars with radii 10 km, the corrections to the Schwarzschild spacetime cause the apparent surface area to increase with spin frequency. In contrast, for neutron stars with radii 15 km, the oblateness of the star dominates the spacetime corrections and causes the apparent surface area to decrease with increasing spin frequency. In all cases, the change in the apparent geometric surface area for the range of observed spin frequencies is ≲5% and hence only a small source of error in the measurement of neutron-star radii.

AB - A moderately spinning neutron star acquires an oblate shape and a spacetime with a significant quadrupole moment. These two properties affect its apparent surface area for an observer at infinity, as well as the light curve arising from a hot spot on its surface. In this paper, we develop a ray-tracing algorithm to calculate the apparent surface areas of moderately spinning neutron stars making use of the Hartle-Thorne metric. This analytic metric allows us to calculate various observables of the neutron star in a way that depends only on its macroscopic properties and not on the details of its equation of state. We use this algorithm to calculate the changes in the apparent surface area, which could play a role in measurements of neutron-star radii and, therefore, in constraining their equation of state. We show that whether a spinning neutron star appears larger or smaller than its non-rotating counterpart depends primarily on its equatorial radius. For neutron stars with radii 10 km, the corrections to the Schwarzschild spacetime cause the apparent surface area to increase with spin frequency. In contrast, for neutron stars with radii 15 km, the oblateness of the star dominates the spacetime corrections and causes the apparent surface area to decrease with increasing spin frequency. In all cases, the change in the apparent geometric surface area for the range of observed spin frequencies is ≲5% and hence only a small source of error in the measurement of neutron-star radii.

KW - gravitation

KW - relativistic processes

KW - stars: neutron

KW - stars: rotation

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U2 - 10.1088/0004-637X/753/2/175

DO - 10.1088/0004-637X/753/2/175

M3 - Article

AN - SCOPUS:84863313939

SN - 0004-637X

VL - 753

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 2

M1 - 175

ER -