Signatures of dark subhalos in dwarf spheroidal galaxies: I. Fluctuations in surface density

TL;DR

This work introduces a Fourier-based framework to detect dark matter subhalo imprints in the projected stellar density of dwarf spheroidal galaxies, leveraging controlled N-body toy models to reveal how subhalos induce out-of-equilibrium density fluctuations. The method constructs a Poisson-based fluctuation statistic, analyzes its azimuthally averaged power spectrum with a two-component Voigt fit, and isolates large-scale subhalo signatures via a low-pass filter, linking spectral features to the subhalo mass function. Across simulations, a characteristic low-frequency peak near $2\pi\kappa r_{\rm scale} \sim 0.4$ robustly traces subhalo interactions, with peak strength depending on halo mass and tracer count $N_{\star}$; higher $N_{\star}$ enhances detectability, enabling constraints down to subhalo masses $M_{\rm subhalo} \lesssim 10^{6}\ M_\odot$ in favorable cases. Application to Gaia and HST data suggests Fornax may host detectable subhalo-induced corrugations, while Sculptor remains consistent with equilibrium; forthcoming surveys (Euclid, Roman, Rubin) with $N_{\star}\sim10^{5}$ per dwarf are poised to substantially tighten constraints on the subhalo mass function in Local Group dwarfs.

Abstract

Dark matter (DM) subhalos offer critical tests of cosmological models through their abundance and properties, yet most remain undetectable due to their lack of stars. We investigate whether their presence leaves measurable imprints on the projected stellar density fields of dwarf spheroidal galaxies (dSphs). Building on literature $N$-body experiments, we show that subhalo interactions induce subtle out-of-equilibrium fluctuations appearing as density corrugations. In a CDM framework, these fluctuations are dominated by the most massive subhalos in the host halo. We develop a Fourier-based framework to quantify these features, identifying characteristic peaks in the spatial frequency spectrum that are well described by Voigt profiles. The peak parameters are sensitive to both the subhalo mass function and the number of stellar tracers. For the configurations tested, $N_{\star} \sim 10^5$ stars suffice to detect subhalo populations with $M_{\rm subhalo} \lesssim 10^6~\mathrm{M}_{\odot}$, while larger masses produce stronger and more complex signatures. We assess the feasibility of this technique by analyzing Gaia and HST data: in this context, the Fornax dwarf shows residual low-frequency structures resembling those in our controlled subhalo experiments, making it an interesting case for follow-up. Prospectively, wide-field surveys such as Euclid, the Nancy Grace Roman Space Telescope, and the Vera C. Rubin Observatory are expected to deliver stellar samples of $N_{\star} \sim 10^5$ per dwarf, offering compelling prospects for probing subhalo imprints. Our results introduce a novel pathway to constrain the subhalo mass function in dSphs, and motivate follow-up work that incorporates alternative DM models and additional dynamical perturbations.

Figures (14)

• Figure 1: Subhalo masses: Cumulative number of subhalo masses for the three DM halo models considered in this study, with $M_{\rm halo}~[\rm M_\odot] = \{ 3~\times~10^{8}, 10^{9}, 10^{10} \}$. The subhalo sampling procedure and its dependence on the host halo properties are described in section 2.3 of Penarrubia+25.
• Figure 2: Evolution of the Plummer distribution. Stellar density profiles illustrating the dynamical impact of subhalos on the stellar component of the dwarf galaxy, shown at intervals of 2 Gyr per column, for a fiducial model with $M_{\rm halo} = 10^{9}~\rm M_\odot$ and $N_{\star} = 10^{5}$ stellar particles. Top row: projected Cartesian density maps, where color and transparency scale with local relative stellar surface density; the red dashed ellipse marks the fitted projected half‐number ellipse; subhalos are plotted as white circles, their radii proportional to their log-masses and their transparency increasing with the distance from the dwarf's centre. Middle row: corresponding radial surface density profiles (green) versus projected distance from the galaxy centre (in unities of scale radii, defined in Eq. \ref{['eq: axi-sd-plummer']}), overlaid with the best‐fitting axisymmetric Plummer model (red). Bottom row: radial residuals of the fit (i.e. ratio of observed and fitted $\Sigma(R)$ profiles), revealing a faint, corrugated pattern. This figure illustrates that, to first order, an axisymmetric Plummer model provides an excellent fit to the numerical data at all stages of the dwarf's evolution.
• Figure 3: Evolution of the power spectrum: Azimuthally averaged power spectrum of the $\chi$ statistic (Eq. \ref{['eq: chi-measure-poisson']}) normalized by the high-frequency floor $\mathcal{C}$ (Eq. \ref{['eq: power-spectrum']}), plotted against the normalized radial spatial frequency, $2 \pi \, \kappa \, r_{\rm scale}$ (see Eq. \ref{['eq: axi-sd-plummer']} for the definition of $r_{\rm scale}$). Each column corresponds to a different evolutionary stage of the simulation. The top row shows equilibrium mock spectra based on the snapshot's best-fit Plummer profile, while the bottom row displays spectra from the corresponding run with subhalos. Transparent curves trace the raw signal, while solid lines show the Voigt fits using Eq. \ref{['eq: power-spectrum']}. Where a significant feature is present, the primary peak defines the fitted position $\mu_{1}$ and width $w_{1}$ of the main signal, while secondary peaks at lower frequencies are attributed to smoothing artifacts (see Appendix \ref{['app: chi-reconstruct']} for details and interpretation). The fiducial simulation contains $N_{\star}=10^{5}$ stellar particles in a halo of mass $M_{\rm halo}=10^{9}~\rm M_\odot$. The emergence of Voigt components at $\kappa < 1$ -- absent in the control runs -- is a robust signature of subhalo–dwarf spheroidal interactions, made possible by the controlled nature of the simulations, which exclude additional perturbations such as tidal forces or major mergers.
• Figure 4: Low-pass filter: Low-pass filtered $\chi$ fields for the same simulation snapshots shown in Figure \ref{['fig: power-spectrum']}, constructed using Eqs. \ref{['eq: low-pass']} and \ref{['eq: butterworth']}. The maps are projected in a rotated and centreed reference frame aligned with the galaxy’s photometric axes, and spatial coordinates are normalized by the instantaneous scale radii, $r_{\rm scale}$, as defined in Eq. \ref{['eq: axi-sd-plummer']}. When present, subhalos are plotted as white circles, their radii proportional to their log-masses and their transparency increasing with the distance from the dwarf's centre. All panels share a consistent color scale for visual clarity. These filtered maps highlight coherent structures resulting from subhalo interactions, including central stellar depletion and ring-like accumulations at larger radii. We display a dashed gray circle to mark the characteristic scale of such ring-like oscillations, located at $1/\mu_{1} \sim 2.5 \, r_{\rm scale}$. In some cases, localized overdensities also emerge, tracing stars temporarily captured by individual subhalos -- such as the feature near $((X - X_0)', (Y - Y_0)') \sim (4, 2) \, r_{\rm scale} \times r_{\rm scale}$, in the lower rightmost panel.
• Figure 5: Impact of halo mass on power spectrum: Similar to Figure \ref{['fig: power-spectrum']}, but here, the rows correspond to three halo–subhalo models, namely with $M_{\rm halo}~[\rm M_\odot] = \{ 3 \times 10^{8}, 10^{9}, 10^{10} \}$ (top to bottom). All runs contain $N_{\star}=10^{5}$ tracer stars. The panels trace the temporal evolution of the normalized power spectrum and demonstrate its systematic dependence on the underlying mass model.