Signatures of dark subhaloes in dwarf spheroidal galaxies – I. Fluctuations in surface density

ABSTRACT Dark matter (DM) subhaloes 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 cold dark matter (CDM) framework, these fluctuations are dominated by the most massive subhaloes 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 $M_{\rm subhalo} \lesssim 10^6\ \rm M_\odot$, while larger masses produce stronger and more complex signatures. We assess the feasibility of this technique by analysing Gaia and Hubble Space Telescope (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.