On estimating redshift and luminosity distributions in photometric redshift surveys

The luminosity functions of galaxies and quasars provide invaluable information about galaxy and quasar formation. Estimating the luminosity function from magnitude limited samples is relatively straightforward, provided that the distances to the objects in the sample are known accurately; techniques for doing this have been available for about thirty years. However, distances are usually known accurately for only a small subset of the sample. This is true of the objects in the Sloan Digital Sky Survey, and will be increasingly true of the next generation of deep multi-color photometric surveys. Estimating the luminosity function when distances are only known approximately (e.g., photometric redshifts are available, but spectroscopic redshifts are not) is more difficult. I describe two algorithms which can handle this complication: one is a generalization of the V_max algorithm, and the other is a maximum likelihood approach. Because these methods account for uncertainties in the distance estimate, they impact a broader range of studies. For example, they are useful for studying the abundances of galaxies which are sufficiently nearby that the contribution of peculiar velocity to the spectroscopic redshift is not negligible, so only a noisy estimate of the true distance is available. In this respect, peculiar velocities and photometric redshift errors have similar effects. The methods developed here are also useful for estimating the stellar luminosity function in samples where accurate parallax distances are not available.Comment: 9 pages, 6 figures, submitted to MNRA

Black Mayors in Non-Majority Black (Medium Sized) Cities: Universalizing the Interests of Blacks

The nature of political representation of Black constituents\u27 interests from their elected Black representatives is changing in the twentyfirst century. Increasingly, African Americans are being elected to political offices where the majority of their constituents are not African American. Previous research on this question tended to characterize Black politicians\u27 efforts to represent their Black constituents\u27 interests in two frames: deracialized or racialized (McCormick and Jones 1993; Cruse 1990). However, the advent of the twenty-first century has exhausted the utility ofthat polarization. Black politicians no longer find explicit racial appeals appropriate for their electoral goals, given the changing demographic environment, and greater acceptance of African American politicians in highprofile positions of power. Black politicians also increasingly find that a lack of attention to racial disparities facing constituents within their political boundaries does not effectively address why certain groups like Blacks are disproportionately and negatively affected than others, across a range of issues. Rather than continue to make efforts to represent Black interests within those two frames, Black politicians have begun to universalize the interests of Blacks

Substructure in dark matter halos: Towards a model of the abundance and spatial distribution of subclumps

I develop a model for the abundance and spatial distribution of dark matter subclumps. The model shows that subclumps of massive parent halos formed at earlier times than subclumps of the same mass in lower mass parents; equivalently, halos in dense regions at a given time formed earlier than halos of the same mass in less dense regions. This may provide the basis for interpreting recent observations which indicate that the stellar populations of the most massive elliptical galaxies are also the oldest.Comment: 5 pages, 2 figures, submitted to MNRA

Black Lives Matter: Imagining and Realizing an Equitable Black Future

The idea for this special Ethnic Studies Review edition, Black Lives Matter: Imagining and Realizing an Equitable Black Future, germinated prior to the election of the 45th president of the United States. However, what this series of articles and commentaries contribute to the movement for Black lives is even more critically important

An excursion set model for the distribution of dark matter and dark matter haloes

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the dark matter itself, the model allows one to describe the evolution of the Eulerian space distribution of the haloes. It can also be used to describe density profiles, on scales larger than the virial radius, of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.Comment: 15 pages, 5 figures, submitted to MNRAS Sept. 199

The importance of stepping up in the excursion set approach

Recently, we provided a simple but accurate formula which closely approximates the first crossing distribution associated with random walks having correlated steps. The approximation is accurate for the wide range of barrier shapes of current interest and is based on the requirement that, in addition to having the right height, the walk must cross the barrier going upwards. Therefore, it only requires knowledge of the bivariate distribution of the walk height and slope, and is particularly useful for excursion set models of the massive end of the halo mass function. However, it diverges at lower masses. We show how to cure this divergence by using a formulation which requires knowledge of just one other variable. While our analysis is general, we use examples based on Gaussian initial conditions to illustrate our results. Our formulation, which is simple and fast, yields excellent agreement with the considerably more computationally expensive Monte-Carlo solution of the first crossing distribution, for a wide variety of moving barriers, even at very low masses.Comment: 10 pages, 5 figure

How unusual are the Shapley Supercluster and the Sloan Great Wall?

We use extreme value statistics to assess the significance of two of the most dramatic structures in the local Universe: the Shapley supercluster and the Sloan Great Wall. If we assume that Shapley (volume ~ 1.2 x 10^5 (Mpc/h)^3) evolved from an overdense region in the initial Gaussian fluctuation field, with currently popular choices for the background cosmological model and the shape and amplitude sigma8 of the initial power spectrum, we estimate that the total mass of the system is within 20 percent of 1.8 x 10^16 Msun/h. Extreme value statistics show that the existence of this massive concentration is not unexpected if the initial fluctuation field was Gaussian, provided there are no other similar objects within a sphere of radius 200 Mpc/h centred on our Galaxy. However, a similar analysis of the Sloan Great Wall, a more distant (z ~ 0.08) and extended concentration of structures (volume ~ 7.2 x 10^5 (Mpc/h)^3) suggests that it is more unusual. We estimate its total mass to be within 20 percent of 1.2 x 10^17 Msun/h; even if it is the densest such object of its volume within z=0.2, its existence is difficult to reconcile with Gaussian initial conditions if sigma8 < 0.9. This tension can be alleviated if this structure is the densest within the Hubble volume. Finally, we show how extreme value statistics can be used to address the likelihood that an object like Shapley exists in the same volume which contains the Great Wall, finding, again, that Shapley is not particularly unusual. It is straightforward to incorporate other models of the initial fluctuation field into our formalism.Comment: 13 pages, 8 figure