Dark stars: Gravitational and electromagnetic observables

Theoretical models of self-interacting dark matter represent a promising answer to a series of open problems within the so-called collisionless cold dark matter paradigm. In case of asymmetric dark matter, self-interactions might facilitate gravitational collapse and potentially lead to the formation of compact objects predominantly made of dark matter. Considering both fermionic and bosonic (scalar ${\varphi }^4$) equations of state, we construct the equilibrium structure of rotating dark stars, focusing on their bulk properties and comparing them with baryonic neutron stars. We also show that these dark objects admit the $I$-Love-$Q$ universal relations, which link their moments of inertia, tidal deformabilities, and quadrupole moments. Finally, we prove that stars built with a dark matter equation of state are not compact enough to mimic black holes in general relativity, thus making them distinguishable in potential events of gravitational interferometers.

Figure 1

(Left) Mass-radius profiles for fermion stars with fixed $\alpha ={10}^{-3}$, dark particle mass $m_X=(1,2)\mathrm{GeV}$, and mediator mass $m_{\varphi }=(8,10,12)\mathrm{MeV}$. The standard EoS apr and ms1 are represented by the yellow solid and the dashed green curves, respectively. The shaded regions correspond to contour regions of constant surface redshift $z=0.35$ and $z=0.5$ with 10% of accuracy. (Center) Compactness $\mathcal{C}=M/R$ as a function of the stellar mass, for the models considered in the left panel. (Right) Minimum period, according to the Kepler frequency limit, $T=2\pi /{\mathrm{\Omega }}_{\mathrm{K}}$. The dashed horizontal line represents the fastest known pulsar with $f=716\mathrm{Hz}$.

Figure 2

Same as Fig. 1, but for boson stars with different values of the coupling constant $\beta =(0.5,1,1.5)\pi$ and boson mass $m_X=(300,400)\mathrm{MeV}$.

Figure 3

Moment of inertia for fermion (left) and boson (right) stars, for the various EoS considered in Figs. 1, 2. The yellow solid and green dashed curves correspond to the apr and ms1 EoS, respectively.

Figure 4

Same as Fig. 3 but for the tidal deformability $\lambda$.

Figure 5

Quadrupole moments as functions of the stellar mass $M$ for two values of the rotational frequency $f=(10,100)\mathrm{Hz}$. The data for fermion and boson stars are compared against the results derived for the standard EoS apr and ms1.

Figure 6

$I$-Love-$Q$ relations for fermion stars with a fixed coupling constant $\alpha ={10}^{-3}$ and different values for $m_{\varphi }$ and $m_X$. The bottom panels show the relative percentage errors between the numerical data and the universal relation (11) (dashed black curve).

Figure 7

Relative percentage errors between the universal relations (11) and the $(\overline{I},\overline{Q},\overline{\lambda })$ trio computed for the boson star models considered in this paper.