Constraining Dark Acoustic Oscillations with the High-Redshift UV Luminosity Function

The gist The work uses measurements of galactic UV luminosity function (UVLF) at high redshifts to constrain the dark acoustic oscillation feature at small scales in a model-agnostic way.

Introduction and Motivation

Evidence from astrophysical and cosmological observations suggests that most of the matter in the Universe is in the form of dark matter, which is mostly invisible, cold, and collisionless [1]. A common feature of many dark sector models beyond ΛCDM is modification of the growth of density perturbations in the early universe, leading to deviations from the expected scaling behavior of the matter power spectrum P(k) ∝ k −3 at scales k > keq [2]. One such class of modifications, which can naturally arise in many well-motivated darksector models, is known as dark acoustic oscillations (DAOs), characterized by suppression and damped oscillations in the matter power spectrum at small length scales [2]. The presence of interactions in the dark sector between some or all of the dark matter (DM) and a dark radiation (DR) species in the early Universe, such as in the atomic dark matter (aDM) model, is a natural way to generate DAOs [3–6].

Transfer Function Model

The authors introduce a new phenomenological model of the modified linear matter power spectrum relative to ΛCDM, so that P(k, z) = T 2 (k)PΛCDM(k, z) [5]. This model has four free parameters that captures the DAO signature of suppression and damped oscillations at small scales [5]. The transfer function is modeled as a sum of two parts, T = Tαβγδ+Tosc [6]. The term Tαβγδ accounts for the suppression of the matter power spectrum by a mixed WDM/CDM-like function, which is identical to the αβγδ model of [106] with the replacement f ≡ 1 − δ: Tαβγδ(k) ≡ f(1 + (αk) β) γ + (1 − f) [6]. The oscillations are captured by Tosc, modeled as sinusoidal oscillations which have a maximum at a wave number kpeak and have a fixed angular frequency ω = 2.083π, determined by fitting to aDM power spectra [6].

Extended Press-Schechter Formalism

To predict the UVLF for arbitrary DAO transfer function parameters and compare to data, the authors use the Extended Press-Schechter formalism to compute the halo mass function dnh dMh from the linear matter power spectrum [7]. This formalism makes use of the statistics of first-crossing distributions in order to predict the fraction of matter that has collapsed into halos of a given mass at a particular time [7]. The halo mass function is calculated using dnh dMh = ρ¯m Mh d ln σ −1 Mh dMh fST(σMh) [8].

Simulations and Calibration

The authors perform N-body simulations to calibrate a semi-analytic formalism for predicting the HMF given an initial linear matter power spectrum [4]. The GIZMO multi-physics code is used to perform these simulations, running them for interacting dark matter fractions of 0.1, 0.5, and 1, and kDAO of 5, 20, 66, and 190 h/Mpc [4]. These simulations are run down to z = 4 from initial conditions generated using the CLASS-aDM code at z = 99 [4]. The halo mass function for each simulation is extracted with the aid of the halo-finder code Rockstar [8]. A least-squares regression fit for the EPS window-function parameters (c, β, q) is performed to compare semi-analytic HMFs to those obtained from all simulations at redshifts from 4 to 12 [8].

Halo-Galaxy Connection and Results

The authors model the halo-galaxy connection using the GALLUMI code [97], which relates the mass of a host halo to the absolute magnitude MUV of the galaxy it contains [5]. The UV luminosity function is computed as ΦUV ≡ dnh dMUV = dnh dMh × dMh dMUV [1]. The results show that constraints on the DAO transfer function parameters f and kpeak are obtained by running Markov Chain Monte Carlo (MCMC) scans to estimate the posterior distribution of the model parameters given data [6]. The Bayesian MCMC analysis finds that the transfer function parameter f is constrained to be less than ≈ 0.07 unless the wave number kpeak at which the DAOs appear is larger than ≈ 50 h/Mpc [21].

Conclusion

The constraints obtained by comparing with UVLF data are complementary to existing work using Lyman-α forest measurements to constrain non-standard dark matter interactions in many different models [80–84]. The results improve on the large-scale cosmological constraints by over an order of magnitude for fractional abundances over ≈ 10% [21]. The bound on f ≲ 0.07 can be straightforwardly interpreted as an upper limit on the fraction of dark matter that is atomic for kDAO ≲ 5 h/Mpc [21].

How it works

)& How it works The paper introduces a phenomenological model for the linear transfer function T2(k) relative to ΛCDM, which has four free parameters capturing the DAO signature of suppression and damped oscillations at small scales [5]. This model is constructed as a sum of two parts: T = Tαβγδ+Tosc [6]. The term Tosc models the oscillations with a maximum at kpeak and Gaussian damping, while Tαβγδ accounts for suppression by a mixed WDM/CDM-like function [6].

)& How it works The halo mass function dnh dMh is predicted semi-analytically from the linear matter power spectrum through the extended Press-Schechter formalism [7]. This formalism uses first-crossing distributions to predict the fraction of matter that has collapsed into halos of a given mass at a particular time [8].

)& How it works The halo-galaxy connection is modeled using the GALLUMI code, which relates the mass of a host halo to the absolute magnitude MUV of the galaxy it contains [5]. The UVLF is computed as ΦUV ≡ dnh dMUV = dnh dMh × dMh dMUV [1].

)& How it works Constraints are obtained by running Markov Chain Monte Carlo (MCMC) scans to estimate the posterior distribution of the model parameters given data [6]. The analysis uses measurements of the UVLF ranging over redshifts 3 to 9 from several different telescopes [6].

The paper provides novel constraints on dark matter models that exhibit dark acoustic oscillations at small scales by comparing with observations of the UV luminosity function at high redshifts.

How it works

The authors employ a highly flexible model of the halo-galaxy connection to predict the UV luminosity function while marginalizing over uncertainty in the details of galaxy and star formation at high redshift [4]. The combination of sensitivity to small scales, high redshift origin, and dependence on the HMF makes this observable well-suited to probing the DAO signature [4].

How it works

The constraints are derived from a Bayesian MCMC analysis allowing all parameters of the model to vary [6]. The data used include measurements from the Hubble Space Telescope using both blank and lensed fields, the James Webb Space Telescope, the Subaru Telescope, and Canada-France-Hawaii Telescope [6].

How it works

The frequentist profile likelihood analysis shows that if kpeak > 66 h/Mpc, then strong DAOs with f = 1 are consistent with UVLF observations at the 95% confidence level [20]. This suggests that for a given observable, sensitive to a limited range of scales, kpeak can be sufficiently large that even for f = 1 the DAOs have no effect [20].

How it works

The constraints on the DAO amplitude A or damping scale kdamp/kpeak are flat posteriors when marginalized over all other model parameters [15]. This suggests that these parameters are not significantly constrained by the UVLF data alone [15].

The paper demonstrates the utility of observables derived from higher redshift sources. As more data are collected with new and upcoming telescopes and our understanding of early galaxy formation evolves, we can expect that our ability to distinguish the more detailed features of the matter power spectrum will improve.

The final results show that for kpeak ≳ 50 h/Mpc, f up to 1 is permitted, with the bound on kpeak gradually strengthening for larger f [21]. Smaller values of kpeak are ruled out unless f ≲ 0.07 [21]. If there are any effects on the galaxy-halo connection independent of the halo mass function, as long as they can be captured by the functional form of the SFR in GALLUMI, we marginalize over them [5]. The constraints from CMB anisotropies are shown in gray, translated from constraints on atomic dark matter [141] [8].

The study concludes that for a given observable, sensitive to a limited range of scales, kpeak can be sufficiently large that even for f = 1 the DAOs have no effect [20]. The results are complementary to existing work using Lyman-α forest measurements to constrain non-standard dark matter interactions in many different models [80–84].

The study provides new meaningful bounds on the DAO parameter space, demonstrating the utility of observables derived from higher redshift sources.

The paper is structured as follows.

1. A model-agnostic constraint system can be developed to identify dark sector models exhibiting dark acoustic oscillations by analyzing high-redshift UV luminosity function (UVLF) data, as described in the abstract: In this work we use measurements of the galactic UV luminosity function (UVLF) at high redshifts to constrain the dark acoustic oscillation feature at small scales in a model-agnostic way.

2. The system can perform parameter space exploration for dark sector models by integrating constraints derived from multiple cosmological probes, such as CMB anisotropies, Lyman-alpha forest data, and UVLF measurements across various redshifts (z = 3–9), using the Bayesian MCMC analysis described in Section 6.

3. The AI can predict the suppression and oscillation of the halo mass function (HMF) at low halo mass scales by mapping a phenomenological transfer function model, such as T(k) ≡ P(k)/P(kΛCDM), to an HMF using the Extended Press-Schechter formalism (Section 3).

4. The system can constrain the fraction of dark matter undergoing DAOs by comparing results from Bayesian MCMC scans with frequentist profile likelihoods, specifically identifying that for a given observable, the transfer function parameter f is constrained to be less than ≈ 0.07 unless the wave number kpeak at which the DAOs appear is larger than ≈ 50 h/Mpc.

5. The system can re-cast constraints on specific particle physics models by relating phenomenological parameters to physical quantities, such as setting bounds on the fraction of dark matter that is atomic for kDAO ≲ 5 h/Mpc or restricting the kpeak wave number based on the confidence level of the UVLF data.

Dark acoustic oscillations (DAOs) in the matter power spectrum can arise in many different dark sector models, and can imprint on a variety of cosmological observables. In this work we use measurements of the galactic UV luminosity function (UVLF) at high redshifts to constrain the dark acoustic oscillation feature at small scales in a model-agnostic way. We introduce a phenomenological transfer function model for a dark sector with a species undergoing DAOs which can accommodate sub-dominant dark matter abundances, and obtain constraints on its parameters. In order to predict the UVLF, we employ an Extended Press-Schechter formalism which we calibrate using N-body simulations with initial conditions featuring DAOs. Using measurements from the Hubble Space Telescope, James Webb Space Telescope, Subaru Telescope, and Canada-France-Hawaii Telescope, we constrain the wave number of the first DAO peak to be at k 50 h/Mpc, unless the fraction of dark matter undergoing DAOs is less than 0.07.