Azadeh Fattahi

Bent by baryons: the low mass galaxy-halo relation

The relation between galaxies and dark matter halos is of vital importance for evaluating theoretical predictions of structure formation and galaxy formation physics. We show that the widely used method of abundance matching based on dark matter only simulations fails at the low mass end because two of its underlying assumptions are broken: only a small fraction of low mass (< 109:5M�) halos host a visible galaxy, and halos grow at a lower rate due to the effect of baryons. In this regime, reliance on dark matter only simulations for abundance matching is neither accurate nor self-consistent. We find that the reported discrepancy between observational estimates of the halo masses of dwarf galaxies and the values predicted by abundance matching does not point to a failure of �CDM, but simply to a failure to account for baryonic effects. Our results also imply that the Local Group contains only a few hundred observable galaxies in contrast with the thousands of faint dwarfs that abundance matching would suggest. We show how relations derived from abundance matching can be corrected, so that they can be used self-consistently to calibrate models of galaxy formation. Key words: cosmology: theory, galaxies: formation, galaxies: evolution, galaxies: mass functions, methods: N-body simulations

The chosen few: the low-mass haloes that host faint galaxies

Since reionization prevents star formation in most halos below 3 x 10^9 solar masses, dwarf galaxies only populate a fraction of existing dark matter halos. We use hydrodynamic cosmological simulations of the Local Group to study the discriminating factors for galaxy formation in the early Universe and connect them to the present-day properties of galaxies and halos. A combination of selection effects related to reionization, and the subsequent evolution of halos in different environments, introduces strong biases between the population of halos that host dwarf galaxies, and the total halo population. Halos that host galaxies formed earlier and are more concentrated. In addition, halos more affected by tidal stripping are more likely to host a galaxy for a given mass or maximum circular velocity, vmax, today. Consequently, satellite halos are populated more frequently than field halos, and satellite halos of 10^8 - 10^9 solar masses or vmax of 12 - 20 km/s, similar to the Local Group dwarf spheroidals, have experienced a greater than average reduction in both mass and vmax after infall. They are on closer, more radial orbits with higher infall velocities and earlier infall times. Together, these effects make dwarf galaxies highly biased tracers of the underlying dark matter distribution.

The APOSTLE project: Local Group kinematic mass constraints and simulation candidate selection

We use a large sample of isolated dark matter halo pairs drawn from cosmological N-body simulations to identify candidate systems whose kinematics match that of the Local Group (LG) of galaxies. We find, in agreement with the ‘timing argument’ and earlier work, that the separation and approach velocity of the Milky Way (MW) and Andromeda (M31) galaxies favour a total mass for the pair of ∼5 × 1012M . A mass this large, however, is difficult to reconcile with the small relative tangential velocity of the pair, as well as with the small deceleration from the Hubble flow observed for the most distant LG members. Halo pairs that match these three criteria have average masses a factor of ∼2 times smaller than suggested by the timing argument, but with large dispersion. Guided by these results, we have selected 12 halo pairs with total mass in the range 1.6–3.6 × 1012M for the APOSTLE project (A Project Of Simulating The Local Environment), a suite of hydrodynamical resimulations at various numerical resolution levels (reaching up to ∼104M per gas particle) that use the subgrid physics developed for the EAGLE project. These simulations reproduce, by construction, the main kinematics of the MW–M31 pair, and produce satellite populations whose overall number, luminosities, and kinematics are in good agreement with observations of the MW and M31 companions. The APOSTLE candidate systems thus provide an excellent testbed to confront directly many of the predictions of the cold dark matter cosmology with observations of our local Universe.

The Orbital Ellipticity of Satellite Galaxies and the Mass of the Milky Way

We use simulations of Milky Way-sized dark matter haloes from the Aquarius Project to investigate the orbits of substructure haloes likely, according to a semi-analytic galaxy formation model, to host luminous satellites. These tend to populate the most massive subhaloes and are on more radial orbits than the majority of subhaloes found within the halo virial radius. One reason for this (mild) kinematic bias is that many low-mass subhaloes have apocentres that exceed the virial radius of the main host; they are thus excluded from subhalo samples identified within the virial boundary, reducing the number of subhaloes on radial orbits. Two other factors contributing to the difference in orbital shape between dark and luminous subhaloes are their dynamical evolution after infall, which affects more markedly low-mass (dark) subhaloes, and a weak dependence of ellipticity on the redshift of first infall. The ellipticity distribution of luminous satellites exhibits little halo-to-halo scatter and it may therefore be compared fruitfully with that of Milky Way satellites. Since the latter depends sensitively on the total mass of the Milky Way we can use the predicted distribution of satellite ellipticities to place constraints on this important parameter. Using the latest estimates of position and velocity of dwarfs compiled from the literature, we find that the most likely Milky Way mass lies in the range 6 × 10 11 M⊙ < M200 < 3.1 × 10 12 M⊙, with a best-fit value of M200 = 1.1 × 10 12 M⊙. This value is consistent with Milky Way mass estimates based on dynamical tracers or the timing argument.

Missing dark matter in dwarf galaxies

We use cosmological hydrodynamical simulations of the APOSTLE project to examine the fraction of baryons in CDM haloes that collect into galaxies. This ‘galaxy formation efficiency’ correlates strongly and with little scatter with halo mass, dropping steadily towards dwarf galaxies. The baryonic mass of a galaxy may thus be used to place a lower limit on total halo mass and, consequently, on its asymptotic maximum circular velocity. A number of dwarfs seem to violate this constraint, having baryonic masses up to ten times higher than expected from their rotation speeds, or, alternatively, rotating at only half the speed expected for their mass. Taking the data at face value, either these systems have formed galaxies with extraordinary efficiency ‐ highly unlikely given their shallow potential wells ‐ or they inhabit haloes with extreme deficits in their dark matter content. This ‘missing dark matter’ is reminiscent of the inner mass deficits of galaxies with slowly-rising rotation curves, but extends to regions larger than the luminous galaxies themselves, disfavouring explanations based on star formationinduced ‘cores’ in the dark matter. An alternative could be that galaxy inclination errors have been underestimated, and that these are just systems where inferred mass profiles have been compromised by systematic uncertainties in interpreting the velocity field. This should be investigated further, since it might provide a simple explanation not only for missing-dark-matter galaxies but also for other challenges to our understanding of the inner structure of cold dark matter haloes.

The low-mass end of the baryonic Tully–Fisher relation

The scaling of disc galaxy rotation velocity with baryonic mass (the ‘baryonic Tully–Fisher’ relation, BTF) has long confounded galaxy formation models. It is steeper than the M ∝ V3 scaling relating halo virial masses and circular velocities and its zero-point implies that galaxies comprise a very small fraction of available baryons. Such low galaxy formation efficiencies may, in principle, be explained by winds driven by evolving stars, but the tightness of the BTF relation argues against the substantial scatter expected from such a vigorous feedback mechanism. We use the APOSTLE/EAGLE simulations to show that the BTF relation is well reproduced in _cold dark matter (CDM) simulations that match the size and number of galaxies as a function of stellarmass. In such models, galaxy rotation velocities are proportional to halo virial velocity and the steep velocity-mass dependence results from the decline in galaxy formation efficiency with decreasing halo mass needed to reconcile the CDM halo mass function with the galaxy luminosity function. The scatter in the simulated BTF is smaller than observed, even when considering all simulated galaxies and not just rotationally supported ones. The simulations predict that the BTF should become increasingly steep at the faint end, although the velocity scatter at fixed mass should remain small. Observed galaxies with rotation speeds below ∼40 km s−1 seem to deviate from this prediction. We discuss observational biases and modelling uncertainties that may help to explain this disagreement in the context of _CDM models of dwarf galaxy formation.

Galaxy pairs in the Local Group

Current models of galaxy formation predict that galaxy pairs of comparable magnitudes should become increasingly rare with decreasing luminosity. This seems at odds with the relatively high frequency of pairings among dwarf galaxies in the Local Group. We use literature data to show that ~30% of all satellites of the Milky Way and Andromeda galaxies brighter than M_V=-8 are found in likely physical pairs of comparable luminosity. Besides the previously recognised pairings of the Magellanic Clouds and of NGC 147/NGC 185, other candidate pairs include the Ursa Minor and Draco dwarf spheroidals, as well as the And I/And III satellites of M31. These pairs are much closer than expected by chance if the radial and angular distributions of satellites were uncorrelated; in addition, they have very similar line-of-sight velocities and luminosities that differ by less than three magnitudes. In contrast, the same criteria pair fewer than 4% of satellites in N-body/semi-analytic models that match the radial distribution and luminosity function of Local Group satellites. If confirmed in studies of larger samples, the high frequency of dwarf galaxy pairings may provide interesting clues to the formation of faint galaxies in the current cosmological paradigm.

Knowing the unknowns: uncertainties in simple estimators of galactic dynamical masses

The observed stellar kinematics of dispersion-supported galaxies are often used to measure dynamical masses. Recently, several analytical relationships between the stellar line-of-sight velocity dispersion, the projected (2D) or deprojected (3D) half-light radius and the total mass enclosed within the half-light radius, relying on the spherical Jeans equation, have been proposed. Here, we use the APOSTLE cosmological hydrodynamical simulations of the Local Group to test the validity and accuracy of such mass estimators for both dispersion and rotation-supported galaxies, for field and satellite galaxies, and for galaxies of varying masses, shapes and velocity dispersion anisotropies. We find that the mass estimators of Walker et al. and Wolf et al. are able to recover the masses of dispersion-dominated systems with little systematic bias, but with a 1σ scatter of 25 and 23 per cent, respectively. The error on the estimated mass is dominated by the impact of the 3D shape of the stellar mass distribution, which is difficult to constrain observationally. This intrinsic scatter becomes the dominant source of uncertainty in the masses estimated for galaxies like the dwarf spheroidal (dSph) satellites of the Milky Way, where the observational errors in their sizes and velocity dispersions are small. Such scatter may also affect the inner density slopes of dSphs derived from multiple stellar populations, relaxing the significance with which Navarro–Frenk–White profiles may be excluded, depending on the degree to which the relevant properties of the different stellar populations are correlated. Finally, we derive a new optimal mass estimator that removes the residual biases and achieves a statistically significant reduction in the scatter to 20 per cent overall for dispersion-dominated galaxies, allowing more precise and accurate mass estimates.

The origin of the mass discrepancy-acceleration relation in ΛCDM.

We examine the origin of the mass discrepancy–radial acceleration relation (MDAR) of disc galaxies. This is a tight empirical correlation between the disc centripetal acceleration and that expected from the baryonic component. The MDAR holds for most radii probed by disc kinematic tracers, regardless of galaxy mass or surface brightness. The relation has two characteristic accelerations: a0, above which all galaxies are baryon dominated, and amin, an effective minimum acceleration probed by kinematic tracers in isolated galaxies. We use a simple model to show that these trends arise naturally in Λ cold dark matter (ΛCDM). This is because (i) disc galaxies in ΛCDM form at the centre of dark matter haloes spanning a relatively narrow range of virial mass; (ii) cold dark matter halo acceleration profiles are self-similar and have a broad maximum at the centre, reaching values bracketed precisely by amin and a0 in that mass range and (iii) halo mass and galaxy size scale relatively tightly with the baryonic mass of a galaxy in any successful ΛCDM galaxy formation model. Explaining the MDAR in ΛCDM does not require modifications to the cuspy inner mass profiles of dark haloes, although these may help to understand the detailed rotation curves of some dwarf galaxies and the origin of extreme outliers from the main relation. The MDAR is just a reflection of the self-similar nature of cold dark matter haloes and of the physical scales introduced by the galaxy formation process.

Mass-Discrepancy Acceleration Relation : A Natural Outcome of Galaxy Formation in Cold Dark Matter Halos

We analyze the total and baryonic acceleration profiles of a set of well-resolved galaxies identified in the eagle suite of hydrodynamic simulations. Our runs start from the same initial conditions but adopt different prescriptions for unresolved stellar and active galactic nuclei feedback, resulting in diverse populations of galaxies by the present day. Some of them reproduce observed galaxy scaling relations, while others do not. However, regardless of the feedback implementation, all of our galaxies follow closely a simple relationship between the total and baryonic acceleration profiles, consistent with recent observations of rotationally supported galaxies. The relation has small scatter: Different feedback implementations-which produce different galaxy populations-mainly shift galaxies along the relation rather than perpendicular to it. Furthermore, galaxies exhibit a characteristic acceleration g_{†}, above which baryons dominate the mass budget, as observed. These observations, consistent with simple modified Newtonian dynamics, can be accommodated within the standard cold dark matter paradigm.