Abstract
Galaxy scaling laws, such as the Tully–Fisher, mass-size, and Fall relations, can provide extremely useful clues on our understanding of galaxy formation in a cosmological context. Some of these relations are extremely tight and well described by one single parameter (mass), despite the theoretical existence of secondary parameters such as spin and concentration, which are believed to impact these relations. In fact, the residuals of these scaling laws appear to be almost uncorrelated with each other, posing significant constraints on models where secondary parameters play an important role. Here, we show that a possible solution is that such secondary parameters are correlated amongst themselves, in a way that removes correlations in observable space. In particular, we focus on how the existence of an anti-correlation between the dark matter halo spin and its concentration, which is still debated in simulations, can weaken the correlation of the residuals of the Tully–Fisher and mass-size relations. Interestingly, in using simple analytic galaxy formation models, we find that this happens only for a relatively small portion of the parameter space that we explored, which suggests that this idea could be used to derive constraints on galaxy formation models that have yet to be explored.
Highlights
The fact that some of the most basic and fundamental dynamical properties of disc galaxies, such as mass, velocity, and angular momentum, are very correlated to one another is a crucial testimony of how galaxies assembled in our Universe
In particular, on the impact of two physical effects on the residuals of the TF, MS, and Fall relation: We allow (i) the halo spin to be anti-correlated with the halo concentration and (ii) the stellar-to-halo mass fraction to be correlated with the stellar-to-halo specific angular momentum fraction
We used a MonteCarlo method to sample the distributions of dark matter halo parameters, we generated a catalogue of model galaxies, and we fitted their scaling relations with power-laws
Summary
The fact that some of the most basic and fundamental dynamical properties of disc galaxies, such as mass, velocity, and angular momentum, are very correlated to one another is a crucial testimony of how galaxies assembled in our Universe. Dutton et al (2007, see Dutton & van den Bosch 2012) generated rather sophisticated semi-empirical models, based on the assumption that the angular momentum of the galaxy is proportional to that of the halo, and found that it was complicated to find a model that matched the observed scaling laws while having a negligible correlation in the TF residuals versus MS residuals (when calculated at a fixed mass, not luminosity, see e.g. Fig. 10 in Dutton et al 2007) This issue has later been used to argue that the observed absence of correlations in the TF and MS residuals provides evidence against the hypothesis that the galaxy’s and halo’s specific angular momenta are directly proportional, leaning towards an empirical, but less physically motivated, anti-correlation between galaxy size and halo concentration (Desmond et al 2019; Lelli et al 2019).
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