First galaxy ultraviolet luminosity function limits on dark matter-proton scattering

1. Problem Statement

The nature of Dark Matter (DM) remains unknown, particularly regarding its potential non-gravitational interactions with Standard Model (SM) particles. While direct detection experiments constrain heavy DM (> GeV), they lose sensitivity for lighter DM masses due to kinematic thresholds.

This paper investigates Interacting Dark Matter (IDM) models where DM elastically scatters with protons. Such interactions transfer heat and momentum between the DM and baryon fluids, suppressing small-scale matter fluctuations in the early universe. The specific interaction cross-section is parametrized as:
$$\sigma = \sigma_0 \left(\frac{v}{c}\right)^n$$
where $n$ dictates the velocity dependence:

• $n=0$: Velocity-independent (contact interactions from heavy mediators).
• $n=2$: Velocity-dependent (pseudoscalar-mediated).
• $n=4$: Higher-order dipole interactions.

The goal is to constrain the interaction strength ($\sigma_0$) for DM masses ($m_\chi$) ranging from 10 keV to 10 GeV using high-redshift ($z \sim 4-10$) galaxy observations, which probe the small-scale matter power spectrum where these interactions leave an imprint.

2. Methodology

Data Sources

The authors utilize Ultraviolet Luminosity Functions (UVLFs) of galaxies observed by the Hubble Space Telescope (HST):

• Blank Fields: Standard deep fields providing data on brighter galaxies ($M_{UV} < -17$).
• Lensed Fields: "Frontier Fields" clusters magnify faint, high-redshift galaxies ($M_{UV} < -12$). These are crucial because they probe smaller dark matter halos and smaller physical scales, which are more sensitive to DM-proton scattering.
• Complementary Data: Planck CMB data (high-$\ell$ TT, TE, EE, low-$\ell$ EE, lensing) and the Pantheon Type-Ia supernova catalog are included in the Bayesian analysis to constrain cosmological parameters.

Modeling Framework

The authors employ a modified implementation of GALLUMI (a code for modeling galaxy luminosity functions) coupled with CLASS DMeff (a modified Boltzmann solver for interacting DM).

1. Halo Mass Function (HMF) & Filter Functions:

   • Standard cosmology often uses a "top-hat" filter, which is inadequate for models with a sharp cutoff in the matter power spectrum (like IDM, WDM, or FDM) because it overestimates low-mass halos.
   • The authors implement a smooth-$k$ filter ($W_{SMK}$) to better interpolate between the top-hat and sharp-$k$ filters. This accounts for Dark Acoustic Oscillations (DAOs)—oscillatory features in the matter power spectrum caused by DM-baryon scattering—which propagate into the HMF and subsequently the UVLF.
   • Parameters for the smooth-$k$ filter ($c=3.6, \beta=3.6$) are calibrated against ETHOS N-body simulations.

2. Halo-Galaxy Connection:

   • A probabilistic mapping relates halo mass ($M_h$) to UV magnitude ($M_{UV}$).
   • The stellar mass ($M_*$) is derived from $M_h$ using a double power-law relation with redshift-dependent parameters.
   • Star Formation Rate (SFR) is calculated from stellar mass and converted to UV luminosity.
   • A galaxy duty cycle ($f_{duty}$) is included to account for inefficient star formation in small halos due to feedback and photoionization.

3. Statistical Analysis:

   • A Markov Chain Monte Carlo (MCMC) analysis using MontePython is performed.
   • The analysis varies astrophysical parameters (e.g., star formation efficiency, duty cycle) and cosmological parameters while fixing $n$ and $m_\chi$ to derive posterior distributions for $\sigma_0$ at 95% confidence.

3. Key Contributions

• First UVLF Constraints on IDM: This is the first study to place limits on DM-proton scattering specifically using high-redshift UVLFs, extending previous constraints derived from CMB and Milky Way satellites.
• Inclusion of Lensed Fields: The paper demonstrates that including lensed UVLF data (probing fainter galaxies) significantly tightens constraints. Lensed fields access smaller scales ($k$-modes) that are more sensitive to the suppression caused by DM-proton scattering than blank fields alone.
• Improved Filter Implementation: By utilizing the smooth-$k$ filter instead of the standard top-hat, the authors provide a more physically accurate modeling of the Halo Mass Function in the presence of DAOs, avoiding non-physical oscillations that might arise from sharp cutoffs.
• Velocity-Dependent Scattering: The study provides the tightest constraints to date for velocity-dependent interactions ($n=2$ and $n=4$), which were previously less constrained than the velocity-independent ($n=0$) case.

4. Results

The study sets upper bounds on the interaction cross-section $\sigma_0$ for various DM masses ($m_\chi$) and velocity indices ($n$).

• Impact of Lensed Data: Including lensed fields improves constraints on $\sigma_0$ by a factor of $\sim 2$ compared to blank fields alone for $n > 0$.
• Specific Bounds (for $m_\chi = 1$ MeV):
  • $n=2$: $\sigma_0 < 1.1 \times 10^{-25} \text{ cm}^2$.
  • $n=4$: $\sigma_0 < 2.1 \times 10^{-22} \text{ cm}^2$.
  • $n=0$: The bound is within an order of magnitude of constraints from the Lyman-$\alpha$ forest and Milky Way satellites.
• Comparison with Other Probes:
  • For $n=2$ and $n=4$, the UVLF constraints (especially with lensed data) surpass existing bounds from Milky Way satellite abundance and CMB anisotropies.
  • For $n=0$, the results are competitive with Lyman-$\alpha$ forest constraints.
• DAO Signatures: The analysis notes that DM-proton scattering introduces "Dark Acoustic Oscillations" in the matter power spectrum, which translate into subtle oscillatory features in the UVLFs. While currently difficult to detect, these are a unique signature of IDM distinct from Warm Dark Matter (WDM) or Fuzzy Dark Matter (FDM).

5. Significance and Future Outlook

• New Window on Small Scales: This work establishes UVLFs, particularly from lensed fields, as a powerful probe for small-scale structure suppression, complementing and in some cases exceeding the sensitivity of traditional probes like satellite counts.
• Computational Efficiency: The UVLF-based pipeline is computationally cheaper than the heavy N-body simulations or Gaussian process emulators required for Milky Way satellite or Lyman-$\alpha$ analyses.
• Future Prospects with JWST:
  • While the current study relies on HST, the authors argue that JWST will be able to observe even fainter galaxies ($M_{UV} \approx -11$) at higher redshifts.
  • Future JWST UVLF data is expected to push constraints to even smaller scales, potentially matching or exceeding Lyman-$\alpha$ limits for $n=0$ and further tightening limits for $n=2, 4$.
  • The paper also highlights the potential of future 21-cm experiments (HERA, SKAO) to probe even smaller scales than galaxy surveys.

In conclusion, this paper demonstrates that high-redshift galaxy luminosity functions are a robust and competitive tool for constraining the microphysics of Dark Matter, specifically its scattering with baryons, and sets the stage for even more stringent tests with upcoming JWST observations.