Neutron stars as dark matter probes

We examine whether the accretion of dark matter onto neutron stars could ever have any visible external effects. Captured dark matter which subsequently annihilates will heat the neutron stars, although it seems the effect will be too small to heat close neutron stars at an observable rate while those at the galactic center are obscured by dust. Nonannihilating dark matter would accumulate at the center of the neutron star. In a very dense region of dark matter such as that which may be found at the center of the galaxy, a neutron star might accrete enough to cause it to collapse within a period of time less than the age of the Universe. We calculate what value of the stable dark matter-nucleon cross section would cause this to occur for a large range of masses.

Figure 1

Einasto DM density profiles for four different sets of parameters: $(r_{-2},\alpha )=(10\mathrm{kpc},0.06)$, (12 kpc, 0.09), (16 kpc, 0.19), and (20 kpc, 0.53).

Figure 2

Dark matter accretion rates vs galactic radius for four different configurations of dark matter (cf. legend in figure) and with $(r_{-2},\alpha )=(16\mathrm{kpc},0.19)$. The merging of the two first cases is due to the fact that we take into account the limiting geometrical cross section of the neutron star surface.

Figure 3

Evolution of the internal (above) and surface temperatures of a $1.44M_{\odot }$ neutron star situated at various galactic radii. In the present case, $m_{\chi }=10\mathrm{GeV}$, ${\sigma }_0=1.5\times {10}^{-41}{\mathrm{cm}}^2$ and $(r_{-2},\alpha )=(16\mathrm{kpc},0.19)$.

Figure 4

Velocity dispersions with respect to the galactic radius for the four different Einasto DM density profiles considered in the present article.

Figure 5

Evolution of the surface temperature of a $1.44M_{\odot }$ neutron star situated at two different galactic radii. The plot is for dark matter with a mass $m_{\chi }=10\mathrm{GeV}$ and a scattering cross section of ${\sigma }_0=1.5\times {10}^{-41}{\mathrm{cm}}^2$. We compare here the approximate constant velocity dispersion ($\sigma \equiv \overline{v}=200\mathrm{km}/s$) with the effective velocity dispersion deduced from the static radial Jeans equation.

Figure 6

Final surface temperature of the neutron star (at late times) for different DM density distributions, with $m_{\chi }=10\mathrm{GeV}$ and ${\sigma }_0=1.5\times {10}^{-41}{\mathrm{cm}}^2$.

Figure 7

Evolution of the surface temperature of a $1.44M_{\odot }$ neutron star situated at various galactic radii (cf. legend in figure). The plot is for dark matter with a mass $m_{\chi }=10\mathrm{GeV}$ and a scattering cross section of ${\sigma }_0=1.5\times {10}^{-41}{\mathrm{cm}}^2$. The DM densities are deduced from two models: profiles obtained by Bertone and Merritt in [40] (BM) and Einasto profiles (E).

Figure 8

Neutron stars immersed for long enough in a high enough density of nonannihilating dark matter will eventually accumulate the amount of DM particles which correspond to the Chandrasekhar limit $M_{\mathrm{Ch}}$ and collapse. The red solid lines here correspond to the cross section ${\sigma }_0$ and mass $m_{\chi }$ required to cause collapse after ${10}^6\mathrm{years}$. The green longer dashed lines correspond to ${10}^8\mathrm{years}$ and the blue shorter dashed lines correspond to ${10}^{10}\mathrm{years}$. The thicker the line the higher the density—we plot two lines for each duration of time corresponding to ${10}^{11}$ and ${10}^5\mathrm{GeV}{\mathrm{cm}}^{-3}$. The upper right region of each line is excluded since the conditions in this region would give rise to a black hole. The curved line corresponds to the latest data from the CDMS experiment (assuming a velocity dispersion $\overline{v}=230\mathrm{km}/\mathrm{s}$ and ${\rho }_{\mathrm{DM}}=0.3\mathrm{GeV}/{\mathrm{cm}}^3$) to place the results in context. The change in the slope of the lines around ${10}^6\mathrm{GeV}$ is explained in the text.