My work in structure formation is concerned with the evolution of dark matter halos, and the connection between this evolution and their density structure. My collaborators in this effort are Andrey Kravtsov and Surhud More. Below I describe some of our papers, in reverse chronological order.

### A universal model for halo concentrations

We present a numerical study of dark matter halo concentrations in ΛCDM and self-similar cosmologies. We show that the relation between concentration, c, and peak height, ν, exhibits the smallest deviations from universality if halo masses are defined with respect to the critical density of the universe.

These deviations can be explained by the residual dependence of concentration on the local slope of the matter power spectrum, n, which affects both the normalization and shape of the c–ν relation. In particular, there is no well-defined floor in the concentration values. Instead, the minimum concentration depends on redshift: at fixed ν, halos at higher z experience steeper slopes n, and thus have lower minimum concentrations.

We show that the concentrations in our simulations can be accurately described by a universal seven-parameter function of only ν and n. This model matches our ΛCDM results to ≲5% accuracy up to z=6, and matches scale-free Ωm=1 models to ≲15%. The model also reproduces the low concentration values of Earth-mass halos at z≈30, and thus correctly extrapolates over 16 orders of magnitude in halo mass. The predictions of our model differ significantly from all models previously proposed in the literature at high masses and redshifts. Our model is in excellent agreement with recent lensing measurements of cluster concentrations.

**Paper:** Diemer & Kravtsov, *A universal model for halo concentrations *[ads] [arXiv]

**Poster: **Diemer & Kravtsov, *Are halo profiles and concentrations universal? *[pdf]

### Dependence of the outer density profiles of halos on their mass accretion rate

We present a systematic study of the density profiles of LCDM halos, focusing on the outer regions, 0.1 < r / Rvir < 9. We show that the median and mean profiles of halo samples of a given peak height exhibit significant deviations from the universal analytic profiles discussed previously in the literature, such as the Navarro-Frenk-White and Einasto profiles, at radii r > 0.5 R200m. In particular, at these radii the logarithmic slope of the median density profiles of massive or rapidly accreting halos steepens more sharply than predicted. The steepest slope of the profiles occurs at r ~ R200m, and its absolute value increases with increasing peak height or mass accretion rate, reaching slopes of -4 and steeper.

Importantly, we find that the outermost density profiles at r > R200m are remarkably self-similar when radii are rescaled by R200m. This self-similarity indicates that radii defined with respect to the mean density are preferred for describing the structure and evolution of the outer profiles. However, the inner density profiles are most self-similar when radii are rescaled by R200c.

We propose a new fitting formula that describes the median and mean profiles of halo samples selected by their peak height or mass accretion rate with accuracy < 10% at all radii, redshifts and masses we studied, r < 9 Rvir, 0 < z < 6 and Mvir > 1.7E10 Msun/h. We discuss observational signatures of the profile features described above, and show that the steepening of the outer profile should be detectable in future weak-lensing analyses of massive clusters. Such observations could be used to estimate the mass accretion rate of cluster halos.

**Paper:** Diemer & Kravtsov; 2014, ApJ 789, 1 [ads] [arXiv]

**Poster:** Diemer & Kravtsov, *Non-universality of halo profiles and their scaling with the “virial” radius *[pdf]

### On the evolution of cluster scaling relations

In this follow-up to the pseudo-evolution project described below, we investigate whether the evolution of cluster scaling relations is affected by pseudo-evolution. We use the relation between mass, M, and velocity dispersion, sigma, as a test case.

We find that the deviation from the M-sigma relation due to pseudo-evolution is smaller than 10% for a wide range of mass definitions. The reason for this small impact is a tight relation between the velocity dispersion and mass profiles which holds across a large radial range. We show that such a relation is generically expected for a wide range of density profiles, as long as halos are in approximate Jeans equilibrium.

We consider the implications of these results for other cluster scaling relations, and argue that pseudo-evolution should have very small effects on most scaling relations, except for those which involve the stellar masses of galaxies. In particular, we show that the relation between stellar mass fraction and total mass is affected by pseudo-evolution, and is largely shaped by it for halo masses smaller than 1E14 Msun.

**Paper:** Diemer, Kravtsov, & More; 2013, ApJ 779, 159 [ads] [arXiv]

### The pseudo-evolution of halo mass

The observable properties of galaxies such as their stellar content, its growth with time, and their sizes, are shaped by the underlying mass of the extended dark matter halos surrounding them. Understanding how dark matter halos grow with time is important in order to understand the evolution of these galaxy properties. Unfortunately, dark matter halos do not have well-defined boundaries which makes it difficult to quantify their physical growth.

Often, boundaries are defined using the spherical overdensity definition; according to this definition, the halo radius encloses a fixed multiple (e.g. 200) of the critical or matter density of the universe (the reference density). We show that this definition leads to a spurious evolution in halo mass, which we call “pseudo-evolution”, because the reference density decreases with time as the universe expands. Thus, the halo radius and mass grow, even if the density profile of a halo remains static (see plot below).

Even though halo density profiles are not necessarily static, pseudo-evolution increases halo masses by about a factor of two since z=1. The majority of galaxy-sized halos barely accrete any matter after z=1, and grow almost exclusively through pseudo-evolution. Larger halos still accrete matter, meaning that pseudo-evolution accounts for a smaller fraction of their overall mass growth. Pseudo-evolution has some important consequences for the evolutions of the halo mass function, the concentration-mass relation, and the stellar mass-halo mass relation.

**Paper:** Diemer, More, & Kravtsov; 2013, ApJ 766, 25 [ads] [arXiv]

**Poster:** Diemer, More, & Kravtsov, *The pseudo-evolution of halo mass* [pdf]