The velocity function derived from large scale surveys can be compared with the predictions of LCDM cosmology, by matching the measured rotation velocities Vrot of galaxies to the maximum circular velocity of dark matter (DM) halos Vmax. For Vrot<50k
m/s, a major discrepancy arises between the observed and LCDM velocity functions. However, the manner in which different observational measures of Vrot are associated with Vmax is not straight forward in dwarf galaxies. We instead relate galaxies to DM halos using the empirical baryon- mass to halo-mass relation, and show that different observational measures of Vrot result in very different velocity functions. We show how the W50 velocity function, i.e. using the HI profile line width at 50% of peak HI flux to measure Vrot, can be reconciled with a LCDM cosmology. Our semi-empirical methodology allows us to determine the region of rotation curves that are probed by HI measurements (RHI), and shows that the Vrot of dwarfs are generally measured at a fraction of Rmax, explaining their tendency to have rising rotation curves. We provide fitting formulae for relating RHI and Reff (the effective radius) to the virial radius of DM halos. To continue to use velocity functions as a probe of LCDM cosmology, it is necessary to be precise about how the different measures of rotation velocity are probing the mass of the DM halos, dropping the assumption that any measure of rotational velocity can be equally used as a proxy for Vmax.
Rotation curves of galaxies show a wide range of shapes, which can be paramaterized as scatter in Vrot(1kpc)/Vmax i.e.the ratio of the rotation velocity measured at 1kpc and the maximum measured rotation velocity. We examine whether the observed scat
ter can be accounted for by combining scatters in disc scale-lengths, the concentration-halo mass relation, and the M*-Mhalo relation. We use these scatters to create model galaxy populations; when housed within dark matter halos that have universal, NFW density profiles, the model does not match the lowest observed values of Vrot(1kpc)/Vmax and has too little scatter in Vrot(1kpc)/Vmax compared to observations. By contrast, a model using a mass dependent dark matter profile, where the inner slope is determined by the ratio of M*/Mhalo, produces galaxies with low values of Vrot(1kpc)/Vmax and a much larger scatter, both in agreement with observation. We conclude that the large observed scatter in Vrot(1kpc)/Vmax favours density profiles that are significantly affected by baryonic processes. Alternative dark matter core formation models such as SIDM may also account for the observed variation in rotation curve shapes, but these observations may provide important constraints in terms of core sizes, and whether they vary with halo mass and/or merger history.
We contend that a single power law halo mass distribution is appropriate for direct matching to the stellar masses of observed Local Group dwarf galaxies, allowing the determination of the slope of the stellar mass-halo mass relation for low mass gal
axies. Errors in halo masses are well defined as the Poisson noise of simulated local group realisations, which we determine using constrained local universe simulations (CLUES). For the stellar mass range 10$^7$<M*<10$^8$M$_odot$, for which we likely have a complete census of observed galaxies, we find that the stellar mass-halo mass relation follows a power law with slope of 3.1, significantly steeper than most values in the literature. The steep relation between stellar and halo masses indicates that Local Group dwarf galaxies are hosted by dark matter halos with a small range of mass. Our methodology is robust down to the stellar mass to which the census of observed Local Group galaxies is complete, but the significant uncertainty in the currently measured slope of the stellar-to halo mass relation will decrease dramatically if the Local Group completeness limit was $10^{6.5}$M$odot$ or below, highlighting the importance of pushing such limit to lower masses and larger volumes.
Using cosmological galaxy formation simulations from the MaGICC project, spanning more than three magnitudes in stellar mass (~10^7-3x10^{10} Msun), we trace the baryonic cycle of infalling gas from the virial radius through to its participation in t
he star formation process. An emphasis is placed upon the temporal history of chemical enrichment during its passage through the corona and CGM. We derive the distributions of time between gas crossing the virial radius and being accreted to the star forming region (which allows mixing within the corona), as well as the time between gas being accreted to the star forming region and then forming stars (which allows mixing within the disc). Significant numbers of stars are formed from gas that cycles back through the hot halo after first accreting to the star forming region. Gas entering high mass galaxies is pre-enriched in low mass proto-galaxies prior to entering the virial radius of the central progenitor, with only small amounts of primordial gas accreted, even at high redshift (z~5). After entering the virial radius, significant further enrichment occurs prior to the accretion of the gas to the star forming region, with gas that is feeding the star forming region surpassing 0.1Z by z=0. Mixing with halo gas, itself enriched via galactic fountains, is thus crucial in determining the metallicity at which gas is accreted to the disc. The lowest mass simulation (Mvir~2x10^{10}Msun, with M*~10^7Msun), by contrast, accretes primordial gas through the virial radius and onto the disc at all times. Much like the classical analytical solutions to the `G-dwarf problem, overproduction of low-metallicity stars is ameliorated by the inefficiency of star formation. Finally, gas outflow/metal removal rates from star forming regions as a function of galactic mass are presented.
Using a cosmological hydrodynamical simulation of a galaxy of similar mass to the Large Magellanic Cloud (LMC), we examine the predicted characteristics of its lowest metallicity populations. In particular, we emphasise the spatial distributions of f
irst (Pop III) and second (polluted by only immediate Pop III ancestors) generation stars. We find that primordial composition stars form not only in the central galaxys progenitor, but also in locally collapsed sub-halos during the early phases of galaxy formation. The lowest metallicity stars in these sub-halos end up in a relatively extended distribution around the host, with these accreted stars possessing present-day galactocentric distances as great as ~40kpc. By contrast, the earliest stars formed within the central galaxy remain in the inner region, where the vast majority of star formation occurs, for the entirety of the simulation. Consequently, the fraction of stars that are from the earliest generation increases strongly with radius.
Within a cosmological hydrodynamical simulation, we form a disc galaxy with sub- components which can be assigned to a thin stellar disc, thick disk, and a low mass stellar halo via a chemical decomposition. The thin and thick disc populations so sel
ected are distinct in their ages, kinematics, and metallicities. Thin disc stars are young (<6.6 Gyr), possess low velocity dispersion ({sigma}U,V,W = 41, 31, 25 km/s), high [Fe/H], and low [O/Fe]. The thick disc stars are old (6.6<age<9.8 Gyrs), lag the thin disc by sim21 km/s, possess higher velocity dispersion ({sigma}U,V,W = 49, 44, 35 km/s), relatively low [Fe/H] and high [O/Fe]. The halo component comprises less than 4% of stars in the solar annulus of the simulation, has low metallicity, a velocity ellipsoid defined by ({sigma}U,V,W = 62, 46, 45 km/s) and is formed primarily in-situ during an early merger epoch. Gas-rich mergers during this epoch play a major role in fuelling the formation of the old disc stars (the thick disc). This is consistent with studies which show that cold accretion is the main source of a disc galaxys baryons. Our simulation initially forms a relatively short (scalelength sim1.7 kpc at z=1) and kinematically hot disc, primarily from gas accreted during the galaxys merger epoch. Far from being a competing formation scenario, migration is crucial for reconciling the short, hot, discs which form at high redshift in {Lambda}CDM, with the properties of the thick disc at z=0. The thick disc, as defined by its abundances maintains its relatively short scale-length at z = 0 (2.31 kpc) compared with the total disc scale-length of 2.73 kpc. The inside-out nature of disc growth is imprinted the evolution of abundances such that the metal poor {alpha}-young population has a larger scale-length (4.07 kpc) than the more chemically evolved metal rich {alpha}-young population (2.74 kpc).
We use the same physical model to simulate four galaxies that match the relation between stellar and total mass, over a mass range that includes the vast majority of disc galaxies. The resultant galaxies, part of the Making Galaxies in a Cosmological
Context (MaGICC) program, also match observed relations between luminosity, rotation velocity, size, colour, star formation rate, HI mass, baryonic mass, and metallicity. Radiation from massive stars and supernova energy regulate star formation and drive outflows, balancing the complex interplay between cooling gas, star formation, large scale outflows, and recycling of gas in a manner which correctly scales with the mass of the galaxy. Outflows also play a key role in simulating galaxies with exponential surface brightness profiles, flat rotation curves and dark matter cores. Our study implies that large scale outflows are the primary driver of the dependence of disc galaxy properties on mass. We show that the amount of outflows invoked in our model is required to meet the constraints provided by observations of OVI absorption lines in the circum-galactic-media of local galaxies.
