Very Old Isolated Compact Objects as Dark Matter Probes

Very old isolated neutron stars and white dwarfs have been suggested to be probes of dark matter. To play such a role, two requests should be fulfilled, i.e., the annihilation luminosity of the captured dark matter particles is above the thermal emission of the cooling compact objects (request-I) and also dominate over the energy output due to the accretion of normal matter onto the compact objects (request-II). Request-I calls for very dense dark matter medium and the critical density sensitively depends on the residual surface temperature of the very old compact objects. The accretion of interstellar/intracluster medium onto the compact objects is governed by the physical properties of the medium and by the magnetization and rotation of the stars and may outshine the signal of dark matter annihilation. Only in a few specific scenarios both requests are satisfied and the compact objects are dark matter burners. The observational challenges are discussed and a possible way to identify the dark matter burners is outlined.

💡 Research Summary

The paper investigates whether very old, isolated neutron stars (NS) and white dwarfs (WD) can serve as astrophysical detectors of dark matter (DM). Two necessary conditions are identified. (I) The luminosity generated by annihilation of DM particles captured inside the compact object must exceed the thermal emission that results from the star’s own cooling. (II) The same DM‑induced luminosity must also dominate over the energy released by the accretion of ordinary interstellar or intracluster gas onto the star.

The authors first calculate the capture rate of weakly interacting massive particles (WIMPs) by NS and WD. The rate depends on the local DM density ρχ, the WIMP mass mχ, the star’s mass and radius (through GM/R), the average WIMP speed v̄, and the scattering cross‑section σχ. For typical WIMP–nucleon cross sections (σχ≈10⁻⁴⁴ cm²) the capture efficiency factor f is of order unity; for smaller cross sections f scales linearly with σχ. Captured WIMPs quickly thermalize and settle into a dense core at the stellar centre. Assuming the canonical annihilation cross section ⟨σAv⟩≈3×10⁻²⁶ cm³ s⁻¹, equilibrium between capture and annihilation is reached on a timescale τeq≪10⁹ yr, so the annihilation luminosity is simply Lann≈½F, where F is the capture rate.

The surface temperature that would result from this heating, Tann∝ρχ¹⁄⁴R⁻¹⁄⁴M¹⁄⁴v̄⁻¹⁄⁴f¹⁄⁴, is compared with the temperatures expected from standard cooling models (≈10³–10⁴ K for NS and ≈10³ K for WD after ≳10⁸ yr). Solving for the minimum DM density required to make Lann larger than the cooling luminosity yields ρχ,crit≈38 GeV cm⁻³·(Tcool/10⁴ K)⁴·R_NS⁴·M_NS⁻¹·f⁻¹·v̄⁷⁄⁴ for neutron stars, and a similar expression for white dwarfs that is even more demanding (∼10 TeV cm⁻³ for typical parameters). These critical densities are orders of magnitude above the canonical Galactic halo value (≈0.3 GeV cm⁻³), implying that only objects residing in regions of very high DM concentration (e.g., the Galactic centre, dwarf spheroidal galaxies, or dense globular‑cluster cores) could satisfy condition I.

Condition II concerns the ordinary matter accretion luminosity. In the absence of magnetic fields the Bondi–Hoyle formula gives a mass‑inflow rate Ṁ∝ρ∞M²/(v∞²+V²)³⁄², where ρ∞ is the ambient gas density, v∞ its thermal speed, and V the star’s space velocity. The corresponding accretion luminosity Lacc≈GMṀ/R* is typically 10⁴–10⁶ times larger than Lann for the densities required by condition I, so in most Galactic environments condition II would be violated.

However, most NS and many WD possess strong magnetic fields (B∼10¹²–10¹⁴ G) and rotate rapidly (periods of seconds). The magnetic pressure balances the ram pressure of the inflowing gas at the Alfvén radius rA. If rA exceeds the gravitational capture radius racc, the inflow is channeled along field lines and the effective accretion rate is dramatically reduced. The authors derive a critical magnetic moment μcrit≈6×10³¹ G cm³·λ_s¹⁄²·M³·V⁻⁵⁄²·ρ∞¹⁄²; objects with μ>μcrit are in the “georotator” regime where accretion is essentially shut off. Additionally, rapid rotation creates a centrifugal barrier at the corotation radius rco; if rco>racc, the propeller effect ejects incoming material. The critical spin period for this suppression is Pcrit≈30 s·μ¹⁄²·λ_s⁻¹⁄⁴·M⁻¹⁄²·ρ∞⁻¹⁄⁴·V¹⁄². Consequently, a sufficiently magnetized, fast‑spinning neutron star can satisfy condition II even in a relatively dense ambient medium, making the DM heating the dominant energy source.

The paper discusses observational challenges. Detecting ultra‑cold NS (T≲10³ K) or WD (T≲10³ K) is difficult; the coolest known NS has an effective temperature ≈8×10⁴ K, and the coolest WD observed is ≈2000 K. Future deep infrared and optical surveys (e.g., JWST, LSST) are required to find candidates. Once identified, one must verify that the surrounding environment indeed has a high DM density and that the star’s magnetic field and spin are sufficient to suppress ordinary accretion. Complementary searches for annihilation by‑products (γ‑rays, neutrinos) could provide independent confirmation.

In summary, the authors conclude that “dark‑matter burners” – compact objects whose surface emission is powered primarily by captured DM annihilation – can exist only under a narrow set of circumstances: the object must reside in a region of very high DM density, and it must possess a strong magnetic field and/or rapid rotation to quench normal accretion. While the concept is theoretically sound, practical detection will require next‑generation surveys capable of identifying extremely cold, isolated neutron stars or white dwarfs and of characterizing their magnetic and rotational properties as well as their local astrophysical environment.