Stellar disruption of axion miniclusters in the Milky Way

Axion miniclusters are dense bound structures of dark matter axions that are predicted to form in the postinflationary Peccei-Quinn symmetry breaking scenario. Although dense, miniclusters can easily be perturbed or even become unbound by interactions with baryonic objects such as stars. Here, we characterize the spatial distribution and properties of miniclusters in the Milky Way (MW) today after undergoing these stellar interactions throughout their lifetime. We do this by performing a suite of Monte Carlo simulations which track the miniclusters’ structure and, in particular, accounts for partial disruption and mass loss through successive interactions. We consider two density profiles—Navarro-Frenk-White (NFW) and power-law (PL)—for the individual miniclusters in order to bracket the uncertainties on the minicluster population today due to their uncertain formation history. For our fiducial analysis at the solar position, we find a survival probability of 99% for miniclusters with PL profiles and 46% for those with NFW profiles. Our work extends previous estimates of this local survival probability to the entire MW. We find that towards the Galactic Center, the survival probabilities drop drastically. Although we present results for a particular initial halo mass function, our simulations can be easily recast to different models using the provided data and code (github.com/bradkav/axion-miniclusters). Finally, we comment on the impact of our results on lensing, direct, and indirect detection.

Figure 1

Models for the internal density profile of AMCs which we consider in this work: power-law, Eq. (9), and NFW, Eq. (8). Vertical dashed lines show the truncation radii $R_{\mathrm{AMC}}$. We fix the characteristic mass and density to $M_{\mathrm{AMC}}={10}^{-10}{M}_{\odot }$ and ${\rho }_{\mathrm{AMC}}={10}^6{M}_{\odot }{\mathrm{pc}}^{-3}$ $(\delta \approx 1.55)$ respectively. In the NFW case, the mean density is much lower and the AMC is much larger.

Figure 2

Illustration of an AMC-star encounter taking place at a distance $r$ from the Galactic Center. An AMC with radius $R_{\mathrm{AMC}}$ is passed by a star of mass $M_{\star }$ with impact parameter $b$ and relative velocity $V$. The energy $\mathrm{\Delta }E$ injected into the AMC is given in Eq. (16).

Figure 3

Fractional mass loss (solid lines) for AMCs with power-law and NFW profiles as a function of the size of the perturbation $\mathrm{\Delta }E$, in units of the binding energy $E_{\mathrm{bind}}$. Dashed lines show the fraction of the injected energy which is carried away by the ejected mass $f_{\mathrm{ej}}$, while dotted lines show the fraction of the initial AMC energy stored in particles which are eventually unbound in the interaction.

Figure 4

Fractional change in the minicluster properties $x=\{M,R,E_{\mathrm{bind}}\}$ under repeated perturbations for AMCs with power-law profiles (left panel) and NFW profiles (right panel). We fix the size of each perturbation to be 1000 times smaller than the initial binding energy, $\mathrm{\Delta }E={10}^{-3}{E}_{\mathrm{bind},i}$.

Figure 5

Top panel shows the eccentricity probability distribution for the orbits of AMCs taken from Ref. [102]. Bottom panel shows the joint probability that an AMC will have a particular semimajor axis and eccentricity given a particular galactocentric radius $r=8\mathrm{kpc}$.

Figure 6

The binned probability of finding an AMC at a particular radius $r$ with a fixed semimajor axis $a=1$. We show distributions for eccentricity values: $e=0.1$ (blue), $e=0.5$ (orange), and $e=0.9$ (green).

Figure 7

The top and central panels show the number of stellar interactions with AMCs on circular orbits at various galactocentric radii. Compared to AMCs with PL density profiles, miniclusters with NFW density profiles undergo significantly more interactions with $\mathrm{\Delta }E/E_{\mathrm{bind}}$ at a fixed galactocentric radius. For illustration, in the bottom panel we show the distribution of injected energies for PL profiles (which is approximately independent of galactocentric radii).

Figure 8

Example of AMC properties from our Monte Carlo simulations before (black dashed) and after (solid olive) disruption. We show the probability distributions of the mass $M_{\mathrm{AMC}}$, radius $R_{\mathrm{AMC}}$, and mean density $\overline{\rho }$. We assume these to have NFW internal density profiles and to be on circular orbits with a galactocentric radius of $r=6.96\mathrm{kpc}$, leading to a survival probability $p_{\mathrm{surv}}=0.91$. These probability distributions are obtained through the reconstruction procedure described in Sec. 5a. The grey shading indicates the regions of the parameter space that are removed by the AS cut. The white lines shows the smallest value of the corresponding parameter that passes the AS cut.

Figure 9

Survival probability of AMCs as a function of their galactocentric semimajor axes (left) and galactocentric radii (right). The vertical dashed line marks the position of the Solar System. In the right panel we show the survival probability for both circular (dotted) and eccentric (dashed) orbits. The eccentric orbits are smeared out according to the proportion of time they spend at a given galactocentric radius (as described in Sec. 5a). Finally, we show the survival probability for miniclusters with eccentric orbits that pass our AS cut (solid line) where we have normalized this to be one at large galactocentric radii.

Figure 10

Density of simulated AMCs before taking into account stellar interactions (solid gray), compared with the expected NFW profile for the DM halo (dotted gray). The spatial distribution of AMCs with PL and NFW internal density profiles are shown as blue and olive lines respectively. The density profiles are extracted from the Monte Carlo simulations according to the weighting procedure in Sec. 5. We also show the distribution of unperturbed and perturbed AMCs passing the AS cut (dot-dashed and solid lines respectively).

Figure 11

The number density of AMCs (in ${\mathrm{kpc}}^{-3}$) as a function of the distance of the lens $x=D_{\mathrm{L}}/D_{\mathrm{S}}$ for the unperturbed population (dot-dashed line) and for the total population of perturbed AMCs (solid lines). We show the results for target sources placed in the LMC (top), in the MW bulge (middle), and in M31 (bottom). For the both perturbed and unperturbed populations, we have applied to AS cut.

Figure 12

The enhancement in the local axion density due to the encounter of Earth with an AMC, in units of ${\rho }_{\odot }=0.45\mathrm{GeV}/{\mathrm{cm}}^3$, as a function of the duration of the encounter in days. We separately show the impact of a minicluster that follows a PL profile (top panel) and an NFW profile (bottom panel). We have considered an overdensity $\delta =1$ and masses $M={10}^{-10}{M}_{\odot }$ (red and black lines) and $M={10}^{-12}{M}_{\odot }$ (blue line), with an impact parameter $b=0.1R_{\mathrm{AMC}}$ (red and blue lines) and $b=0.5R_{\mathrm{AMC}}$ (black line). We have considered AMCs which have not been perturbed. As we show in the main text, these AMC encounters with Earth would be rare.

Figure 13

Tidal radius $R_t$ for AMCs in the Milky Way. We also show the AMC radii assumed in the main text for PL (blue dashed) and NFW (olive dashed) AMC density profiles, fixing $M_{\mathrm{AMC}}={10}^{-10}{M}_{\odot }$ and $\delta =1.0$.

Figure 14

Mass of NFW-profile AMCs after tidal stripping by the host halo $M_{\text{stripped}}$ (solid blue). For NFW AMCs, we apply this mass-loss fraction as a correction to the initial mass function in the main text. For comparison, we also show the mass loss expected by stripping an NFW halo from $c={10}^4$ to $c=100$.

Figure 15

Stellar density used in the Monte Carlo simulations as a function of the galactocentric radius $r$, averaged over the cylindrical Galactic height. We show the density of stars in the bulge (red line), in the disk (blue line), and the sum of the two (black line).

Figure 16

Examples of AMC density profiles. The NFW profile with truncation parameter $c=R_{\mathrm{AMC}}/r_s=100$ assumed in the main text can be compared with the more diffuse profile with $c={10}^4$ which we also consider here. In the case of $c=100$, we assume a total mass of $M_{\mathrm{AMC}}=0.44\times {10}^{-10}{M}_{\odot }$, to give the same central density as the $c={10}^4$ profile.

Figure 17

Response of NFW miniclusters with different truncation parameters $c$ to stellar perturbations, as a function of the injected energy $\mathrm{\Delta }E$. We plot the fractional mass loss (solid lines), the fraction of injected energy carried away by ejected particles (dashed lines) and the fraction of the initial AMC energy in particles which will eventually be unbound (dotted lines). See Sec. 3b for more details.

Figure 18

Comparison of final AMC properties for NFW profiles with different truncation parameters $c$. We assume an initial mass of $M_i={10}^{-10}{M}_{\odot }$ $(M_i=0.44\times {10}^{-10}{M}_{\odot })$ for the $c={10}^4$ ($c=100$) profile and an initial characteristic density of ${\rho }_{\mathrm{AMC}}={10}^6{M}_{\odot }{\mathrm{pc}}^{-3}$. We show the final probability distributions of the mass $M_{\mathrm{AMC}}$, radius $R_{\mathrm{AMC}}$, and mean density $\overline{\rho }$ (with the initial values shown as vertical dashed lines). In this toy sample, we assume AMCs on circular orbits at a galactocentric radius of 8 kpc. We list the fraction $p_{\mathrm{surv}}$ of AMCs which both survive and pass the AS cut (extrapolating to the full mass function), though we have not applied an AS cut to the final distributions.