Unified Gas Heating Constraints on Extended Dark Matter Compact Objects

Abstract

We present the first unified constraints on a broad class of extended dark matter compact objects (EDCOs) from interstellar gas heating. These include axion stars, Q-balls, axion miniclusters, dark fermion stars and primordial black holes surrounded by dark matter halos, which arise in a wide range of theories beyond the Standard Model. As such massive objects traverse the interstellar medium, their gravitational influence generates wakes and, if sufficiently compact, drives accretion flows that heat gas in their vicinity. Our general framework extends standard dynamical friction treatments by incorporating finite-size effects, internal density profiles, gas penetration through objects, and criteria for accretion disk formation. We perform detailed numerical calculations of wake formation and gas heating and apply our results to the Leo T dwarf galaxy, establishing new constraints on the dark matter fraction in EDCOs heavier than a solar mass spanning several orders of magnitude in both mass and abundance.

Figures (11)

• Figure 1: Density wake $\alpha(\vec{x},t)$ generated by a spherically symmetric EDCO (white circle) with a uniform density profile moving in direction $\hat{z}$ subsonically with $\mathcal{M} = 0.67$ through a uniform gaseous medium, for $c_s t / R_{\rm obj}$ = 5 [Top left], 10 [Top right], 15 [Bottom left], 20 [Bottom right]. The perturbation forms a sonic sphere centered at the origin and peaked around the object. No Mach cone is present in the subsonic regime. The wake extends inside EDCO, in contrast to the point mass case, producing a smoother density profile and affecting Coulomb logarithm.
• Figure 2: Density wake $\alpha(\vec{x},t)$ generated by a spherically symmetric EDCO (white circle) with a uniform density profile moving in direction $\hat{z}$ supersonically with $\mathcal{M} = 1.50$ through a uniform gaseous medium, for $c_s t / R_{\rm obj}$ = 5 [Top left], 10 [Top right], 15 [Bottom left], 20 [Bottom right]. The perturbations consist of a sonic sphere and a pronounced Mach cone trailing the object, within which wavefronts from successive positions of the object overlap. The wake amplitude is enhanced inside the cone, as reflected by the factor of two in $\mathcal{S}(\vec{x},t)$ for $\mathcal{M} > 1$ in Eq. \ref{['eq:Spointmass']}. The wake extends inside EDCO, in contrast to the point mass case, producing a smoother density profile and affecting Coulomb logarithm.
• Figure 3: Zoomed-in wake profiles around a spherically symmetric EDCO with a uniform density distribution at $c_s t / R_{\rm obj} = 20$, for subsonic with $\mathcal{M} = 0.67$ [Left] and supersonic with $\mathcal{M} = 1.50$ [Right] motion. The white circle indicates the object radius $R_{\rm obj}$. In the subsonic case, the wake forms a smooth overdensity surrounding the object, while in the supersonic case, a sharp Mach cone intersects the object, leading to an enhanced and asymmetric wake structure. Since the wake in this regime depends only on the distance to the object as in Eq. \ref{['eq:S']}, the near-field profile shown here does not evolve with time.
• Figure 4: Time evolution of $I(\mathcal{M}, t)$ [Left] and $I_{\rm ext}(\mathcal{M}, t)$ [Right] for representative EDCO density distributions with uniform (black), NFW with concentration $\mathcal{C} = 200$ (red), Gaussian (blue) and dPBH (green) profiles at Mach numbers $\mathcal{M} = 1.25$ [Top] and $\mathcal{M} = 1.5$ [Bottom]. The total factor $I(\mathcal{M}, t)$ exhibits the expected logarithmic growth with time, while the correction term $I_{\rm ext}(\mathcal{M}, t)$ converges rapidly to its asymptotic value, highlighting the finite-size dependence of the dynamical friction force.
• Figure 5: Characteristic inner temperature $T_i$ of thin accretion disk as a function of EDCO $r_{\rm min}$. Parameters representative of Milky Way gas clouds (red, $n=0.4~\textrm{cm}^{-3}$ and $\tilde{v}=220~\textrm{km~s}^{-1}$), Leo T (green, $n=0.07~\textrm{cm}^{-3}$ and $\tilde{v}=10~\textrm{km~s}^{-1}$), and a dense gas cloud ($n=1~\textrm{cm}^{-3}$ and $\tilde{v}=1~\textrm{km~s}^{-1}$). As the object radius increases, the peak photon energy $\sim k_B T_i$ falls below the $13.6~\textrm{eV}$ ionization threshold of atomic hydrogen (gray shaded region), reducing absorption and the efficiency of gas heating. The exponentially suppressed high energy tail of the spectrum beyond the peak can still contribute appreciably to interstellar medium heating. We set $M_{\rm enc}=M$ throughout.