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Register a new userThe halo mass function from the dark ages through the present day
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Darren Reed
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We use an array of high-resolution N-body simulations to determine the mass function of dark matter haloes at redshifts 10-30. We develop a new method for compensating for the effects of finite simulation volume that allows us to find an approximation to the true ``global mass function. By simulating a wide range of volumes at different mass resolution, we calculate the abundance of haloes of mass 10^{5-12} Msun/h. This enables us to predict accurately the abundance of the haloes that host the sources that reionize the universe. In particular, we focus on the small mass haloes (>~10^{5.5-6} Msun/h) likely to harbour population III stars where gas cools by molecular hydrogen emission, early galaxies in which baryons cool by atomic hydrogen emission at a virial temperature of ~10^4K (10^{7.5-8} Msun/h), and massive galaxies that may be observable at redshift ~10. When we combine our data with simulations that include high mass halos at low redshift, we find that the best fit to the halo mass function depends not only on linear overdensity, as is commonly assumed in analytic models, but also upon the slope of the linear power spectrum at the scale of the halo mass. The Press-Schechter model gives a poor fit to the halo mass function in the simulations at all epochs; the Sheth-Tormen model gives a better match, but still overpredicts the abundance of rare objects at all times by up to 50%. Finally, we consider the consequences of the recently released WMAP 3-year cosmological parameters. These lead to much less structure at high redshift, reducing the number of z=10 ``mini-haloes by more than a factor of two and the number of z=30 galaxy hosts by more than four orders of magnitude. Code to generate our best-fit halo mass function may be downloaded from http://icc.dur.ac.uk/Research/PublicDownloads/genmf_readme.html
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In this paper we investigate how the halo mass function evolves with redshift, based on a suite of very large (with N_p = 3072^3 - 6000^3 particles) cosmological N-body simulations. Our halo catalogue data spans a redshift range of z = 0-30, allowing us to probe the mass function from the dark ages to the present. We utilise both the Friends-of-Friends (FOF) and Spherical Overdensity (SO) halofinding methods to directly compare the mass function derived using these commonly used halo definitions. The mass function from SO haloes exhibits a clear evolution with redshift, especially during the recent era of dark energy dominance (z < 1). We provide a redshift-parameterised fit for the SO mass function valid for the entire redshift range to within ~20% as well as a scheme to calculate the mass function for haloes with arbitrary overdensities. The FOF mass function displays a weaker evolution with redshift. We provide a `universal fit for the FOF mass function, fitted to data across the entire redshift range simultaneously, and observe redshift evolution in our data versus this fit. The relative evolution of the mass functions derived via the two methods is compared and we find that the mass functions most closely match at z=0. The disparity at z=0 between the FOF and SO mass functions resides in their high mass tails where the collapsed fraction of mass in SO haloes is ~80% of that in FOF haloes. This difference grows with redshift so that, by z>20, the SO algorithm finds a ~50-80% lower collapsed fraction in high mass haloes than does the FOF algorithm, due in part to the significant over-linking effects known to affect the FOF method.
The powerful combination of the cutting-edge multi-object spectrograph MOSAIC with the world largest telescope, the ELT, will allow us to probe deeper into the Universe than was possible. MOSAIC is an extremely efficient instrument in providing spectra for the numerous faint sources in the Universe, including the very first galaxies and sources of cosmic reionization. MOSAIC has a high multiplex in the NIR and in the VIS, in addition to multi-Integral Field Units (Multi-IFUs) in NIR. As such it is perfectly suited to carry out an inventory of dark matter (from rotation curves) and baryons in the cool-warm gas phases in galactic haloes at z=3-4. MOSAIC will enable detailed maps of the intergalactic medium at z=3, the evolutionary history of dwarf galaxies during a Hubble time, the chemistry directly measured from stars up to several Mpc. Finally, it will measure all faint features seen in cluster gravitational lenses or in streams surrounding nearby galactic halos, providing MOSAIC to be a powerful instrument with an extremely large space of discoveries. The preliminary design of MOSAIC is expected to begin next year, and its level of readiness is already high, given the instrumental studies made by the team.
Utilising optical and near-infrared broadband photometry covering $> 5,{rm deg}^2$ in two of the most well-studied extragalactic legacy fields (COSMOS and XMM-LSS), we measure the galaxy stellar mass function (GSMF) between $0.1 < z < 2.0$. We explore in detail the effect of two source extraction methods (SExtractor and ProFound) in addition to the inclusion/exclusion of Spitzer IRAC 3.6 and 4.5$mu$m photometry when measuring the GSMF. We find that including IRAC data reduces the number of massive ($log_{10}(M/M_odot) > 11.25$) galaxies found due to improved photometric redshift accuracy, but has little effect on the more numerous lower-mass galaxies. We fit the resultant GSMFs with double Schechter functions down to $log_{10}(M/M_odot)$ = 7.75 (9.75) at z = 0.1 (2.0) and find that the choice of source extraction software has no significant effect on the derived best-fit parameters. However, the choice of methodology used to correct for the Eddington bias has a larger impact on the high-mass end of the GSMF, which can partly explain the spread in derived $M^*$ values from previous studies. Using an empirical correction to model the intrinsic GSMF, we find evidence for an evolving characteristic stellar mass with $delta log_{10}(M^*/M_odot)/delta z$ = $-0.16pm0.05 , (-0.11pm0.05)$, when using SExtractor (ProFound). We argue that with widely quenched star formation rates in massive galaxies at low redshift ($z<0.5$), additional growth via mergers is required in order to sustain such an evolution to a higher characteristic mass.
The claimed detection of large amounts of substructure in lensing flux anomalies, and in Milky Way stellar stream gaps statistics, has lead to a step change in constraints on simple warm dark matter models. In this study we compute predictions for the halo mass function both for these simple models and also for comprehensive particle physics models of sterile neutrinos and dark acoustic oscillations. We show that the mass function fit of Lovell et al. underestimates the number of haloes less massive than the half-mode mass, $M_mathrm{hm}$ by a factor of 2, relative to the extended Press-Schechter (EPS) method. The alternative approach of applying EPS to the Viel et al. matter power spectrum fit instead suggests good agreement at $M_mathrm{hm}$ relative to the comprehensive model matter power spectra results, although the number of haloes with mass $<M_mathrm{hm}$ is still suppressed due to the absence of small scale power in the fitting function. Overall, we find that the number of dark matter haloes with masses $<10^{8}M_{odot}$ predicted by competitive particle physics models is underestimated by a factor of $sim2$ when applying popular fitting functions, although careful studies that follow the stripping and destruction of subhaloes will be required in order to draw robust conclusions.
Studies of flux anomalies statistics and perturbations in stellar streams have the potential to constrain models of warm dark matter (WDM), including sterile neutrinos. Producing these constraints requires a parametrization of the WDM mass function relative to that of the cold dark matter (CDM) equivalent. We use five WDM models with half-mode masses, $M_mathrm{hm}=[1.3,35]times10^{8}$~$M_{odot}$, spread across simulations of the Local Group, lensing ellipticals and the $z=2$ universe, to generate such a parametrization: we fit parameters to a functional form for the WDM-to-CDM halo mass function ratio, $n_mathrm{WDM}(M_{X})/n_mathrm{CDM}(M_{X})$, of ($1+(alpha M_mathrm{hm}/M_{X})^{beta})^{gamma}$. For $M_{X}equiv$ virial mass of central halos we obtain $alpha=2.3$, $beta=0.8$, and $gamma=-1.0$, and this fit is steeper than the extended Press-Schechter formalism predicts. For $M_{X}equiv$ mass of subhalos we instead obtain $alpha=4.2$, $beta=2.5$ and $gamma=-0.2$; in both mass definitions the scatter is $sim20$~per~cent. The second fit typically underestimates the relative abundance of $z=2$ WDM subhaloes at the tens of per cent level. We caution that robust constraints will require bespoke simulations and a careful definition of halo mass, particularly for subhalos of mass $<10^{8}M_{odot}$.
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