By adopting the extended Chaplygin equation-of-state, Ilidio Lopes and colleagues carried out study on the isotropic and slowly-rotating dark energy stars. They found that the moment of inertia increases with the mass of the star and in the case of non-rotating objects the moment of inertia grows faster. Their study recently appeared in Arxiv.
A dark-energy star is a hypothetical compact astrophysical object, which a minority of physicists think might constitute an alternative explanation for observations of astronomical black hole candidates. The concept was proposed by physicist George Chapline. The theory states that infalling matter is converted into vacuum energy or dark energy, as the matter falls through the event horizon. The space within the event horizon would end up with a large value for the cosmological constant and have negative pressure to exert against gravity.
Now, Ilidio Lopes and colleagues carried out study on the isotropic and slowly-rotating dark energy stars. They computed the moment of inertia as a function of the mass of the stars, both for rotating and non-rotating objects. They have also shown a solution for the non-diagonal metric component as a function of the radial coordinate for three different star masses: i) a light star (M ∼ 1.4 M), ii) a heavy star (M ∼ 2 M) and iii) an average star (M ∼ 1.75 M).
They found that, the moments of inertia increase with the mass of the star.
While, in the case of non-rotating objects the moment of inertia grows faster.
Finally, they found that the curve corresponding to rotation lies below the one corresponding to non-rotating stars. Therefore the deviation is smaller for light stars and larger for heavy stars.
Moreover, it has been found that, for a given mass, a rotating star has a lower moment of inertia than its non-rotating counterpart.
“The increase of observational data expected in the coming years will allow us to study the effect of rotation on the moments of inertia to validate or exclude this type of EoS models.”
— they concluded.
Reference: Grigoris Panotopoulos, Angel Rincon, Ilıdio Lopes, “Slowly rotating dark energy stars”, Arxiv, 2021. arXiv:2109.05619
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Shinchirou Yoshida & colleagues studied the effect of r-mode instability on the rotational frequency of dark stars.
Previous studies presented some alternative models against such standard compact object models as neutron stars and black holes. One such category is a compact object made of dark matter particles. Though nature of dark matter is still elusive, the most plausible candidates are elementary particles beyond the standard model, which interact very weakly (or do not interact) with the standard model particles. These dark matter particles may form a bound state by their self-gravity. One of the suggestions made is that these exotic objects may be an alternative to black hole candidates in compact X-ray binaries. However, these alternatives in accreting X-ray binaries is shown to exhibit thermonuclear flashes which is absent in observed black hole candidates.
Previous studies also considered objects with typical mass of neutron stars and made from dark matter. They are termed as dark stars and possibility of them to be alternatives to neutron stars is discussed. These dark stars are made of asymmetric dark matter (ADM) with self-interaction which is a candidate of cold dark matter & introduced to solve some cosmological and astrophysical problems.
Effects of rotation on these alternatives have not been fully investigated. One of the possible and important effects is appearance of instability related to stellar rotation. For relativistic stars, Chandrashekhar-Friedman-Schutz instability, where coupling of stellar oscillations with gravitational wave leads to secular instability for rotating stars, may be powerful enough to limit the stellar rotation speed by removing its angular momentum through gravitational wave emission. Especially the r-mode instability may be effective even for slowly rotating stars as far as the viscous damping of the oscillations are sufficiently weak.
Now, Shinchirou Yoshida & colleagues studied the effect of r-mode instability on the rotational frequency of dark stars, composed of asymmetric and self-interacting dark Fermions, which are alternatives of conventional neutron stars and black holes. They do not consider Bosonic dark star, since they may not resemble a fluid star, but rather a gigantic Bose-Einstein condensate, which require a totally different treatment.
The r-mode instability is driven by gravitational radiation via the Chandrasekhar-Friedman-Schutz(CFS) mechanism, which occurs in all rotating perfect fluid compact stars. The mode is generically unstable to the CFS instability, which leads to the rapid growth of the r-mode amplitude. In contrast, the growth of the mode is suppressed by the viscosity of the stellar matter (dark Fermion fluid). Also, by emitting gravitational wave this mode, affects thermal and spin evolution (i.e. it spins down a star) of compact stars. The mode have been identified as viable and promising targets for continuous gravitational wave searches, meanwhile, it would allow us to probe the interior of compact stars directly.
Shinchirou Yoshida & colleagues considered the critical angular frequency for which both mechanisms balances (which I shown in bold letters), which marks the final spin frequency of the star. By applying the conventional model of molecular viscosity to dark Fermions, they obtained weak shear viscosity and showed that the critical angular frequency is less than half of the break-up limit of the star.
They also found that the higher the mass, the lower the frequency becomes. For typical mass of millisecond pulsars (1.5M) to massive neutron stars (2M) the relative critical frequency to the Keplerian one is less than 20%, which may constrain the alternative models in the presence of the fastest spinning pulsars. For a stellar-mass black hole case (10M), it may be less than 10%, which may be a strong constraint to the existence of the alternative model to nearly extreme-Kerr black holes in X-ray binaries.