Modeling the gravitational clustering in hierarchical scenarios of structure formation

[spa] En la tesis se presenta un método semianalítico para describir el crecimiento de objetos virializados en el escenario de inestabilidad gravitatoria. Se ha desarrollado el formalismo del sistema confluente de trayectorias, que permite seguir la evolución por filtrado de picos en un campo aleatorio gaussiano de perturbaciones de densidad. Este formalismo es aplicado para deducir la función de masas en el modelo de picos. Después de determinar el filtro (gaussiano) y las relaciones M(R) y SC(T) consistentes con la dinamica de colapso real, se ha encontrado una función de masas, corregida del efecto de nubes encajadas, muy próxima a la de Press y Schechter que ajusta bien los resultados de simulaciones a N-cuerpos. El formalismo del sistema confluente también permite calcular otras cantidades importantes relacionadas con la evolución de objetos virializados, con la ventaja de proporcionar una distinción práctica entre procesos de acreción y fusión. Esto conduce a una definición natural de los sucesos que indican la formación y destrucción de un objeto dado y, por lo tanto, a mejores estimaciones de los ritmos y tiempos típicos de crecimiento. En particular, se han deducido expresiones para los ritmos instantáneos de fusión, captura y formación, el ritmo de acreción de masa, la edad típica y el tiempo de supervivencia

Culminating the Peak Cusp to Descry the Dark Side of Halos

The ConflUent System of Peak trajectories (CUSP) is a rigorous formalism in the framework of the peak theory that allows one to derive from first principles andno free parameters the typical halo properties from the statistics of peaks in the filtered Gaussian random field of density perturbations. The predicted halo mass function, spherically averaged density, velocity dispersion, velocity anisotropy, ellipticity, prolateness and potential profiles, as well as the abundance and number density profiles of accreted and stripped subhalos and diffuse dark matter accurately recover the results of cosmological $N$-body simulations. CUSP is thus a powerful tool for the calculation, in any desired hierarchical cosmology with Gaussian perturbations, of halo properties beyond the mass, redshift and radial ranges covered by simulations. More importantly, CUSP unravels the origin of the characteristic features of those properties. In the present Paper we culminate its construction. We show that all halo properties but those related with subhalo stripping are independent of the assembly history of those objects, and that the Gaussian is the only smoothing window able to find the finite collapsing patches while properly accounting for the entropy increase produced in major mergers

An improved treatment of cosmological intergalactic medium evolution

The modeling of galaxy formation and reionization, two central issues of modern cosmology, relies on the accurate follow-up of the intergalactic medium (IGM). Unfortunately, owing to the complex nature of this medium, the differential equations governing its ionization state and temperature are only approximate. In this paper, we improve these master equations. We derive new expressions for the distinct composite inhomogeneous IGM phases, including all relevant ionizing/recombining and cooling/heating mechanisms, taking into account inflows/outflows into/from halos, and using more accurate recombination coefficients. Furthermore, to better compute the source functions in the equations we provide an analytic procedure for calculating the halo mass function in ionized environments, accounting for the bias due to the ionization state of their environment. Such an improved treatment of IGM evolution is part of a complete realistic model of galaxy formation presented elsewhere

Typical density profile for warm dark matter haloes

Using the model for (bottom-up) hierarchical halo growth recently developed by Salvador-Solé et al., we derive the typical spherically averaged density profile for haloes with several relevant masses in the concordant warm dark matter (ΛWDM) cosmology with non-thermal sterile neutrinos of two different masses. The predicted density profiles become flat at small radii, as expected from the effects of the spectrum cut-off. The core cannot be resolved, however, because the non-null particle velocity yields the fragmentation of minimum mass protohaloes in small nodes, which invalidates the model at the corresponding radii

An accurate comprehensive approach to substructure - I. Accreted subhaloes

This is the first of a series of three papers devoted to the study of halo substructure in hierarchical cosmologies by means of the CUSP formalism. In the present paper, we derive the properties of subhaloes and diffuse dark matter (dDM) accreted on to haloes and their progenitors. Specifically, we relate the dDM present at any time in the inter-halo medium of the real Universe or a cosmological simulation with the corresponding free-streaming mass or the halo resolution mass, respectively, and establish the link between subhaloes and their seeds in the initial density field. By monitoring the collapse and virialization of haloes, we derive from first principles and with no single free parameter the abundance and radial distribution of dDM and subhaloes accreted on to them. Our predictions are in excellent agreement with the results of simulations, but for the predicted fraction of accreted dDM, which is larger than reported in previous works as they only count the dDM accreted on to the final halo, not on to its progenitors. The derivation pursued here clarifies the origin of some key features of substructure. Overall, our results demonstrate that CUSP is a powerful tool for understanding halo substructure and extending the results of simulations to haloes with arbitrary masses, redshifts, and formation times in any hierarchical cosmology endowed with random Gaussian density perturbations

An accurate comprehensive approach to substructure - II. Stripped subhaloes

In Salvador-Solé, Manrique & Botella (Paper I), we used the ConflUent System of Peak trajectories (CUSP) formalism to derive from first principles and no single free parameter the accurate abundance and radial distribution of both diffuse dark matter (dDM) and subhaloes accreted on to haloes and their progenitors at all previous times. Here we use those results as initial conditions for the monitoring of the evolution of subhaloes and dDM within the host haloes. Specifically, neglecting dynamical friction, we accurately calculate the effects of repetitive tidal stripping and heating on subhaloes as they orbit inside the host halo and infer the amount of dDM and subsubhaloes they release into the intrahalo medium. We then calculate the expected abundance and radial distribution of stripped subhaloes and dDM. This derivation clarifies the role of halo concentration in substructure and unravels the origin of some key features found in simulations including the dependence of substructure on halo mass. In addition, it unveils the specific effects of dynamical friction on substructure. The results derived here are for purely accreting haloes. In Salvador-Solé et al. (Paper III), we complete the study by addressing the case of low-mass subhaloes, unaffected by dynamical friction, in ordinary haloes having suffered major mergers

Halo mass definition and multiplicity function

Comparing the excursion set and CUSP (confluent system of peak trajectories) formalisms for the derivation of the halo mass function, we investigate the role of the mass definition in the properties of the multiplicity function of cold dark matter (CDM) haloes. We show that the density profile for haloes formed from triaxial peaks that undergo ellipsoidal collapse and virialization is such that the ratio between the mean inner density and the outer local density is essentially independent of mass. This causes that, for suited values of the spherical overdensity (SO) Delta and the linking length b, SO and FoF masses are essentially equivalent to each other and the respective multiplicity functions are essentially the same. The overdensity for haloes having undergone ellipsoidal collapse is the same as if they had formed according to the spherical top-hat model, which leads to a value of b corresponding to the usual virial overdensity, Delta_vir , equal to ∼0.2. The multiplicity function resulting from such mass definitions, expressed as a function of the top-hat height for spherical collapse, is very approximately universal in all CDM cosmologies. The reason for this is that, for such mass definitions, the top-hat density contrast for ellipsoidal collapse and virialization is close to a universal value, equal to ∼0.9 times the usual top-hat density contrast for spherical collapse

Theoretical dark matter halo density profile

We derive the density profile for collisionless dissipationless dark matter haloes in hierarchical cosmologies making use of the secondary infall (SI) model. The novelties are (i) we deal with triaxial virialized objects, (ii) their seeds in the linear regime are peaks endowed with unconvolved spherically averaged density profiles according to the peak formalism, (iii) the initial peculiar velocities are taken into account and (iv) accreting haloes are assumed to develop from the inside out, keeping the instantaneous inner system unaltered. The validity of this latter assumption is accurately checked by comparing analytical predictions on such a growth with the results of numerical simulation. We show that the spherically averaged density profile of virialized objects can be inferred with no need to specify their shape. The typical spherically averaged halo density profile is inferred, down to arbitrarily small radii, from the power spectrum of density perturbations. The predicted profile in the Λ cold dark matter cosmology is approximately described by an Einasto profile, meaning that it does not have a cusp but rather a core, where the inner slope slowly converges to zero. Down to one-hundredth the total radius, the profile has the right NFW and Einasto forms, being close to the latter down to a radius of about four orders of magnitude less. The inner consistency of the model implies that the density profiles of haloes harbour no information on their past aggregation history. This would explain why major mergers do not alter the typical density profile of virialized objects formed by SI and do not invalidate the peak formalism based on such a formation

An accurate comprehensive approach to substructure: III. Masses and formation times of the host haloes

With this paper, we complete a comprehensive study of substructure in dark matter haloes. In Paper I, we derived the radial distribution and mass function (MF) of accreted subhaloes (scaled to the radius and mass of the host halo) and showed that they are essentially universal. This is not the case, however, for those of stripped subhaloes, which depend on halo mass and assembly history. In Paper II, we derived these latter properties in the simplest case of purely accreting haloes. Here, we extend the study to ordinary haloes having suffered major mergers. After showing that all the properties of substructure are encoded in the mean truncated-to-original subhalo mass ratio profile, we demonstrate that the dependence of the subhalo MF on halo mass arises from their mass-dependent concentration, while the shape of the subhalo radial distribution depends on the time of the last major merger of the host halo. In this sense, the latter property is a better probe of halo formation time than the former. Unfortunately, this is not the case for the radial distribution of satellites as this profile is essentially disconnected from subhalo stripping and the properties of accreted subhaloes are independent of the halo formation time

Fixing a rigorous formalism for the accurate analytic derivation of halo properties

We establish a one-to-one correspondence between virialized haloes and their seeds, namely peaks with a given density contrast at appropriate Gaussian-filtering radii, in the initial Gaussian random density field. This fixes a rigorous formalism for the analytic derivation of halo properties from the linear power spectrum of density perturbations in any hierarchical cosmology. The typical spherically averaged density profile and mass function of haloes so obtained match those found in numerical simulations