The scatter, residual correlations and curvature of the SPARC baryonic Tully-Fisher relation

In recent work, Lelli et al. (2016) argue that the tightness of the baryonic Tully-Fisher relation (BTFR) of the SPARC galaxy sample, and the weakness of the correlation of its residuals with effective radius, pose challenges to LCDM cosmology. In this Letter we calculate the statistical significance of these results in the framework of halo abundance matching, which imposes a canonical galaxy-halo connection. Taking full account of sample variance among SPARC-like realisations of the parent halo population, we find the scatter in the predicted BTFR to be 3.6 sigma too high, but the correlation of its residuals with galaxy size to be naturally weak. Further, we find abundance matching to generate BTFR curvature in 3.0 sigma disagreement with the data, and a fraction of galaxies with non-flat rotation curves somewhat larger than observed.Comment: 5 pages, 2 figures; revised to match MNRAS Letters accepted versio

Screened fifth forces in parity-breaking correlation functions

Cross-correlating two different types of galaxy gives rise to parity breaking in the correlation function that derives from differences in the galaxies' properties and environments. This is typically associated with a difference in galaxy bias, describing the relation between galaxy number density and dark matter density, although observational effects such as magnification bias also play a role. In this paper we show that the presence of a screened fifth force adds additional degrees of freedom to the correlation function, describing the effective coupling of the force to the two galaxy populations. These are also properties of the galaxies' environments, but with different dependence in general to galaxy bias. We derive the parity-breaking correlation function analytically as a function of fifth-force strength and the two populations' fifth-force charges, and explore the result numerically using Hu-Sawicki $f(R)$ as a toy model of chameleon screening. We find that screening gives rise to an octopole, which, in the absence of magnification bias, is not present in any gravity theory without screening and thus is a qualitatively distinct signature. The modification to the dipole and octopole can be $\mathcal{O}(10\%)$ and $\mathcal{O}(100\%)$ respectively at redshift $z \gtrsim 0.5$ due to screening, but decreases towards lower redshift. The change in the background power spectrum in $f(R)$ theories induces a change in the dipole of roughly the same size, but dominant to the effect of screening at low $z$. While current data is insufficient to measure the parity-breaking dipole or octopole to the precision required to test these models, future surveys such as DESI, Euclid and SKA have the potential to probe screened fifth forces through the dipole.Comment: Matches published versio

The Tully-Fisher and mass-size relations from halo abundance matching

The Tully-Fisher relation (TFR) expresses the connection between rotating galaxies and the dark matter haloes they inhabit, and therefore contains a wealth of information about galaxy formation. We construct a general framework to investigate whether models based on halo abundance matching are able to reproduce the observed stellar mass TFR and mass-size relation (MSR), and use the data to constrain galaxy formation parameters. Our model tests a range of plausible scenarios, differing in the response of haloes to disc formation, the relative angular momentum of baryons and dark matter, the impact of selection effects, and the abundance matching parameters. We show that agreement with the observed TFR puts an upper limit on the scatter between galaxy and halo properties, requires weak or reversed halo contraction, and favours selection effects that preferentially eliminate fast-rotating galaxies. The MSR constrains the ratio of the disc to halo specific angular momentum to be approximately in the range 0.6-1.2. We identify and quantify two problems that models of this nature face. (1) They predict too large an intrinsic scatter for the MSR, and (2) they predict too strong an anticorrelation between the TFR and MSR residuals. We argue that resolving these problems requires introducing a correlation between stellar surface density and enclosed dark matter mass. Finally, we explore the expected difference between the TFRs of central and satellite galaxies, finding that in the favoured models this difference should be detectable in a sample of ~700 galaxies.Comment: 27 pages, 10 figures; revised to match published MNRAS versio

Uncorrelated velocity and size residuals across galaxy rotation curves

The mass--velocity--size relation of late-type galaxies decouples into independent correlations between mass and velocity (the Tully-Fisher relation), and between mass and size. This behaviour is different to early-type galaxies which lie on a Fundamental Plane. We study the coupling of the Tully-Fisher and mass-size relations in observations (the SPARC sample) and in empirical galaxy formation models based on halo abundance matching, and rotation curve fits with a hydrodynamically motivated halo profile. We systematically investigate the correlation coefficient between the Tully-Fisher residuals $\Delta V_r$ and mass-size residuals $\Delta R$ as a function of the radius $r$ at which the velocity is measured, and thus present the $\Delta V_r-\Delta R$ relation across rotation curves. We find no significant correlation in either the data or models for any $r$, aside from $r \ll R_\text{eff}$ where baryonic mass dominates. We show that this implies an anticorrelation between galaxy size and halo concentration (or halo mass) at fixed baryonic mass, and provides evidence against the hypothesis that galaxy and halo specific angular momentum are proportional. Finally, we study the $\Delta V_r-\Delta R$ relations produced by the baryons and dark matter separately by fitting halo profiles to the rotation curves. The balance between these components illustrates the "disk-halo conspiracy" required for no overall correlation.Comment: 7 pages, 4 figures; revised to match MNRAS published versio

The Tight Empirical Relation between Dark Matter Halo Mass and Flat Rotation Velocity for Late-Type Galaxies

We present a new empirical relation between galaxy dark matter halo mass (${\rm M_{halo}}$) and the velocity along the flat portion of the rotation curve (${\rm V_{flat}}$), derived from 120 late-type galaxies from the SPARC database. The orthogonal scatter in this relation is comparable to the observed scatter in the baryonic Tully-Fisher relation (BTFR), indicating a tight coupling between total halo mass and galaxy kinematics at $r\ll R_{\rm vir}$. The small vertical scatter in the relation makes it an extremely competitive estimator of total halo mass. We demonstrate that this conclusion holds true for different priors on $M_*/L_{[3.6\mu]}$ that give a tight BTFR, but requires that the halo density profile follows DC14 rather than NFW. We provide additional relations between ${\rm M_{halo}}$ and other velocity definitions at smaller galactic radii (i.e. ${\rm V_{2.2}}$, ${\rm V_{eff}}$, and ${\rm V_{max}}$) which can be useful for estimating halo masses from kinematic surveys, providing an alternative to abundance matching. Furthermore, we constrain the dark matter analog of the Radial Acceleration Relation and also find its scatter to be small, demonstrating the fine balance between baryons and dark matter in their contribution to galaxy kinematics.Comment: 6 pages, 4 figures, Accepted to MNRAS Letter

Reconstructing the gravitational field of the local universe

Tests of gravity at the galaxy scale are in their infancy. As a first step to systematically uncovering the gravitational significance of galaxies, we map three fundamental gravitational variables -- the Newtonian potential, acceleration and curvature -- over the galaxy environments of the local universe to a distance of approximately 200 Mpc. Our method combines the contributions from galaxies in an all-sky redshift survey, halos from an N-body simulation hosting low-luminosity objects, and linear and quasi-linear modes of the density field. We use the ranges of these variables to determine the extent to which galaxies expand the scope of generic tests of gravity and are capable of constraining specific classes of model for which they have special significance. Finally, we investigate the improvements afforded by upcoming galaxy surveys.Comment: 12 pages, 4 figures; revised to match MNRAS accepted versio

On the fundamentality of the radial acceleration relation for late-type galaxy dynamics

Galaxies have been observed to exhibit a level of simplicity unexpected in the complex galaxy formation scenario posited by standard cosmology. This is particularly apparent in their dynamics, where scaling relations display much regularity and little intrinsic scatter. However, the parameters responsible for this simplicity have not been identified. Using the Spitzer Photometry & Accurate Rotation Curves galaxy catalogue, we argue that the radial acceleration relation (RAR) between galaxies' baryonic and total dynamical accelerations is the fundamental $1$-dimensional correlation governing the radial (in-disk) dynamics of late-type galaxies. In particular, we show that the RAR cannot be tightened by the inclusion of any other available galaxy property, that it is the strongest projection of galaxies' radial dynamical parameter space, and that all other statistical radial dynamical correlations stem from the RAR plus the non-dynamical correlations present in our sample. We further provide evidence that the RAR's fundamentality is unique in that the second most significant dynamical relation does not possess any of these features. Our analysis reveals the root cause of the correlations present in galaxies' radial dynamics: they are nothing but facets of the RAR. These results have important ramifications for galaxy formation theory because they imply that to explain statistically late-type galaxy dynamics within the disk it is necessary and sufficient to explain the RAR and lack of any significant, partially independent correlation. While simple in some modified dynamics models, this poses a challenge to standard cosmology.Comment: 17 pages, 9 figures. Accepted in MNRA

Marginalised Normal Regression: Unbiased curve fitting in the presence of x-errors

The history of the seemingly simple problem of straight line fitting in the presence of both $x$ and $y$ errors has been fraught with misadventure, with statistically ad hoc and poorly tested methods abounding in the literature. The problem stems from the emergence of latent variables describing the "true" values of the independent variables, the priors on which have a significant impact on the regression result. By analytic calculation of maximum a posteriori values and biases, and comprehensive numerical mock tests, we assess the quality of possible priors. In the presence of intrinsic scatter, the only prior that we find to give reliably unbiased results in general is a mixture of one or more Gaussians with means and variances determined as part of the inference. We find that a single Gaussian is typically sufficient and dub this model Marginalised Normal Regression (MNR). We illustrate the necessity for MNR by comparing it to alternative methods on an important linear relation in cosmology, and extend it to nonlinear regression and an arbitrary covariance matrix linking $x$ and $y$. We publicly release a Python/Jax implementation of MNR and its Gaussian mixture model extension that is coupled to Hamiltonian Monte Carlo for efficient sampling, which we call ROXY (Regression and Optimisation with X and Y errors).Comment: 14+6 pages, 9 figures; submitted to the Open Journal of Astrophysic