Expanding,homogeneous, ellipsoidal density perturbations. III. A simple theory for the acquisition of angular momentum by tidal torques with the effects of the spin growth on the expansion included

The effects of the acquisition of angular momentum on the expansion of homogeneous, ellipsoidal density perturbations is investigated by generalizing the theory of previous papers of this series, where spin grows to the first order in overdensity. A small difference is found to be between the two cases, except for the fact that the body under consideration becomes unbound earlier in the current approach. A comparison is also made with the results of a different theory, where spin grows to the second order in overdensity. Quasi-oblate triaxial configurations turn out to gain less angular momentum in respect to both oblate and more elongated configurations with same minor to major axis ratio. In all cases of physical interest, the spin growth from the beginning to the maximum ellipsoidal volume exceeds the spin growth from the maximum ellipsoidal volume to the turnaround of the major axis, by a factor of at least 3. It is also inferred that the spin growth from the turnaround of the major axis on, probably does not exceed about one third the angular momentum previously gained.     

Expanding,homogeneous, ellipsoidal density perturbations. I. The effect of the initial shape at some special stages of evolution

This paper investigates the effect of the initial shape of expanding, homogeneous, ellipsoidal density perturbations, at some special stages of evolution, namely at the occurrence of: (i) turn-around along the axes, (ii) maximum volume, (iii) strong decoupling from the Hubble flow, assumed to take place at overdensities equal to unity. To this aim, previous theory is reviewed and extended involving – among others – a deep analysis on the gravitational force induced on the unit mass at the top axes of the ellipsoid, an explicit expression of the overdensity, and a detailed investigation on the limiting cases of flat (two-dimensional) and oblong (one-dimensional) configurations. Then some physical parameters related to the above mentioned stages of evolution are computed for a wide range of initial shapes, in connection with an Einstein-de Sitter universe and an initial overdensity, which is typical for inhomogeneities with galactic masses in a classical CDM scenario. If the gain of spin by tidal torques grows in proportion to time until either the stage of evolution (i) or (ii), or (iii) is attained, it is found a difference in angular momentum related to the initial shape, which never exeeds a factor of about 3.6, 2.0, 1.4, respectively.     

The angular momentum content of dwarf galaxies: new challenges for the theory of galaxy formation

We compute the specific angular momentum distributions for a sample of low-mass disc galaxies observed by Swaters. We compare these distributions to those of dark matter haloes obtained by Bullock et al. from high-resolution N -body simulations of structure formation in a ΛCDM universe. We find that although the disc mass fractions are significantly smaller than the universal baryon fraction, the total specific angular momenta of the discs are in good agreement with those of dark matter haloes. This suggests that discs form out of only a small fraction of the available baryons, but yet manage to draw most of the available angular momentum. In addition we find that the angular momentum distributions of discs are clearly distinct from those of the dark matter; discs lack predominantly both low and high specific angular momenta. Understanding these findings in terms of a coherent picture for disc formation is challenging. Cooling, feedback and stripping, which are the main mechanisms to explain the small disc mass fractions found, seem unable to simultaneously explain the angular momentum distributions of the discs. In fact, it seems that the baryons that make up the discs must have been born out of angular momentum distributions that are clearly distinct from those of ΛCDM haloes. However, the dark and baryonic mass components experience the same tidal forces, and it is therefore expected that they should have similar angular momentum distributions. Therefore, understanding the angular momentum content of disc galaxies remains an important challenge for our picture of galaxy formation.     

Bulges versus discs: the evolution of angular momentum in cosmological simulations of galaxy formation

We investigate the evolution of angular momentum in simulations of galaxy formation in a cold dark matter universe. We analyse two model galaxies generated in the N -body/hydrodynamic simulations of Okamoto et al. Starting from identical initial conditions, but using different assumptions for the baryonic physics, one of the simulations produced a bulge-dominated galaxy and the other one a disc-dominated galaxy. The main difference is the treatment of star formation and feedback, both of which were designed to be more efficient in the disc-dominated object. We find that the specific angular momentum of the disc-dominated galaxy tracks the evolution of the angular momentum of the dark matter halo very closely: the angular momentum grows as predicted by linear theory until the epoch of maximum expansion and remains constant thereafter. By contrast, the evolution of the angular momentum of the bulge-dominated galaxy resembles that of the central, most bound halo material: it also grows at first according to linear theory, but 90 per cent of it is rapidly lost as pre-galactic fragments, into which gas had cooled efficiently, merge, transferring their orbital angular momentum to the outer halo by tidal effects. The disc-dominated galaxy avoids this fate because the strong feedback reheats the gas, which accumulates in an extended hot reservoir and only begins to cool once the merging activity has subsided. Our analysis lends strong support to the classical theory of disc formation whereby tidally torqued gas is accreted into the centre of the halo conserving its angular momentum.     

Effects of merging histories on angular momentum distribution of dark matter haloes

The effects of merging histories of proto-objects on the angular momentum distributions of the present-time dark matter haloes are analysed. An analytical approach to the analysis of the angular momentum distributions assumes that the haloes are initially homogeneous ellipsoids and that the growth of the angular momentum of the haloes halts at their maximum expansion time. However, the maximum expansion time cannot be determined uniquely, because in the hierarchical clustering scenario each progenitor, or subunit, of the halo has its own maximum expansion time. Therefore the merging history of the halo may be important in estimating its angular momentum. Using the merger tree model by Rodrigues &38; Thomas, which takes into account the spatial correlations of the density fluctuations, we have investigated the effects of the merging histories on the angular momentum distributions of dark matter haloes. It was found that the merger effects, that is, the effects of the inhomogeneity of the maximum expansion times of the progenitors which finally merge together into a halo, do not strongly affect the final angular momentum distributions, so that the homogeneous ellipsoid approximation happens to be good for the estimation of the angular momentum distribution of dark matter haloes. This is because the effect of the different directions of the angular momenta of the progenitors cancels out the effect of the inhomogeneity of the maximum expansion times of the progenitors.   The contribution of the orbital angular momentum to the total angular momentum when two or more pre-existing haloes merge together was also investigated. It is shown that this contribution is more important than that of the angular momentum of diffuse accreting matter to the total angular momentum, especially when the mergers occur many times.     

A simple model for the relationship between star formation and surface density

We investigate the relationship between the star formation rate per unit area and the surface density of the interstellar medium (ISM; the local Kennicutt–Schmitt law) using a simplified model of the ISM and a simple estimate of the star formation rate based on the mass of gas in bound clumps, the local dynamical time-scales of the clumps and an efficiency parameter of around  ε≈ 5  per cent. Despite the simplicity of the approach, we are able to reproduce the observed linear relation between star formation rate and surface density of dense (molecular) gas. We use a simple model for the dependence of H₂ fraction on total surface density to argue why neither total surface density nor the H  i surface density is a good local indicator of star formation rate. We also investigate the dependence of the star formation rate on the depth of the spiral potential. Our model indicates that the mean star formation rate does not depend significantly on the strength of the spiral potential, but that a stronger spiral potential, for a given mean surface density, does result in more of the star formation occurring close to the spiral arms. This agrees with the observation that grand design galaxies do not appear to show a larger degree of star formation compared to their flocculent counterparts.     

Specific angular momentum of disc merger remnants and the λR-parameter

We use two-dimensional kinematic maps of simulated binary disc mergers to investigate the  λ_R  -parameter, which is a luminosity-weighted measure of projected angular momentum per unit mass. This parameter was introduced to subdivide the SAURON sample of early-type galaxies in so-called fast  λ_R > 0.1  and slow rotators  λ_R < 0.1  . Tests on merger remnants reveal that  λ_R  is a robust indicator of the true angular momentum content in elliptical galaxies. We find the same range of  λ_R  values in our merger remnants as in the SAURON galaxies. The merger mass ratio is decisive in transforming fast rotators into slow rotators in a single binary merger, the latter being created mostly in an equal-mass merger. Slow rotators have a  λ_R  which does not vary with projection. The confusion rate with face-on fast rotators is very small. Mergers with a gas component form slow rotators with smaller ellipticities than collisionless merger remnants have, and are in much better agreement with the SAURON slow rotators. Remergers of merger remnants are slow rotators, but tend to have too high ellipticities. Fast rotators maintain the angular momentum content from the progenitor disc galaxy if merger mass ratio is high. Some SAURON galaxies have values of  λ _R   as high as our progenitor disc galaxies.     

Galaxy formation: Warm dark matter, missing satellites, and the angular momentum problem

We present warm dark matter (WDM) as a possible solution to the missing satellites and angular momentum problem in galaxy formation and introduce improved initial conditions for numerical simulations of WDM models, which avoid the formation of unphysical haloes found in earlier simulations. There is a hint, that because of that the mass function of satellite haloes has been overestimated so far, pointing to higher values for the WDM particle mass. This revised version was published online in August 2006 with corrections to the Cover Date.     

The G-dwarf problem in the solar neighbourhood: a Lagrangian picture. II

The current paper investigates how the empirical, G-dwarf metallicity distribution constrains simple, comoving models of chemical evolution. In doing this, the application of the models to a data sample, performed in a previous paper, is refined and extended. The key idea is that (i) different star formation rates with different mass spectra take place in different phases of evolution, i.e. contraction and equilibrium, and (ii) disk formation begins at a time t = T_d and ends at t = T_c, which marks the transition from contraction to equilibrium. In this view, the lowest-metallicity point of the empirical, differential distribution, consistent with a linear fit, is related to the beginning of disk formation, and an apparent discontinuity point to the transition from contraction to equilibrium. In addition, different linear fits hold on the left (early distribution) and on the right (late distribution) of the discontinuity point. Models consistent with the empirical, G-dwarf metallicity distribution are related to linear fits on the early and late side. Homologous solutions during the equilibrium phase are analysed in detail with respect to changes in T_c and T_a, the age of the Galaxy. Then we are left with a single free parameter which is relevant to the chemical evolution, i.e. the mass spectrum exponent during the equilibrium phase. The allowed values for the other parameters, thought as a function of the above mentioned one, are plotted for each case. A Salpeter mass spectrum exponent, p = −2.35, is ruled out by the theoretical, lower stellar mass limit, contrary to a Scalo mass spectrum exponent, p = −2.90, in contrast with previous literature. The reasons for this discrepancy are discussed. Our results are marginally consistent with a same initial mass function during the contraction and equilibrium phase, but in this case the disk mass fraction is of the is same order, or less, than the halo mass fraction. It is also investigated how the empirical age-metallicity relation constrains the duration of the contraction phase, for a reasonable upper limit of T_a. Keeping in mind that the empirical, G-dwarf metallicity distribution has not been corrected for the large cosmic scatter shown by the empirical, age-metallicity relation, we find a duration of disk formation, T_c — T_d = 1.07–1.5 Gyr, by a factor 3–5 less than it is found by use of simple infall models. The reasons of this difference are explained. The idea of a massive, white dwarf halo, which seems to be indicated by microlensing experiments, is ruled out by the empirical, G-dwarf metallicity distribution, in the light of the current model and provided the solar neighbourhood is a typical region of the Galaxy. More refined models involving e.g., the relax of instantaneous recycling would change our results, but the trend is expected to be only slightly altered.     

Photochemical evolution of elliptical galaxies – II. The impact of merging-induced starbursts

The effects of late gas accretion episodes and subsequent merger-induced starbursts on the photochemical evolution of elliptical galaxies are studied and compared to the picture of galaxy formation occurring at high redshift with a unique and intense starburst modulated by a very short infall, as suggested by Pipino and Matteucci in Paper I. By means of the comparison with the colour–magnitude relations (CMRs) and the  [〈Mg/Fe〉 _V ]–σ  relation observed in ellipticals, we conclude that either bursts involving a gas mass comparable to the mass already transformed into stars during the first episode of star formation (SF) and occurring at any redshift, or bursts occurring at low redshift (i.e. z ≤ 0.2) and with a large range of accreted mass, are ruled out. These models fail in matching the above relations even if the initial infalling hypothesis is relaxed, and the galaxies form either by means of more complicated SF histories or by means of the classical monolithic model. On the other hand, galaxies accreting a small amount of gas at high redshift (i.e. z ≥ 3) produce a spread in the model results, with respect to the best model of Paper I, which is consistent with the observational scatter of the CMRs, although there is only marginal agreement with the  [〈Mg/Fe〉 _V ]–σ  relation. Therefore, only small perturbations to the standard scenario seem to be allowed. We stress that the strongest constraints to galaxy-formation mechanisms are represented by the chemical abundances, whereas the colours can be reproduced under several different hypotheses.     

The G‐dwarf problem in the solar neighbourhood: II. Halo subdwarfs

The oxygen abundance distribution in solar neighbourhood halo subdwarfs is deduced, using two alternative, known empirical relationships, involving the presence or the absence of [O/Fe] plateau for low [Fe/H] values, from a sample of 372 kinematically selected halo stars, for which the iron abundance distribution has been determined by Ryan & Norris (1991). The data are interpreted by a simple, either homogeneous or inhomogeneous model of chemical evolution, using an updated value of the solar oxygen abundance. The effect of changing the solar oxygen abundance, the power‐law exponent in the initial mass function, and the rate of oxygen nucleosyntesis, keeping the remaining input parameters unchanged, is investigated, and a theorem is stated. In all cases, part of the gas must necessarily be inhibited from forming stars, and no disk contamination has to be advocated for fitting the empirical oxygen abundance distribution in halo subdwarfs of the solar neighbourhood (EGD). Then a theorem is stated, which allows a one‐to‐one correspondence between simple, homogeneous models with and without inhibited gas, related to same independent parameters of chemical evolution, except lower stellar mass limit, real yield, and inhibition parameter. The mutual correlations between the latter parameters are also specified. In addition the starting point, and the point related to the first step, of the theoretical distribution of oxygen abundance (TGD) predicted by simple, inhomogeneous models, is calculated analytically. The mean oxygen abundance of the total and only inhibited gas, respectively, are also determined. Following the idea of a universal, initial mass function (IMF), a power‐law with both an exponent p = 2.9, which is acceptably close to Scalo IMF for m ≳ m_⊙, and an exponent p = 2.35, i.e. Salpeter IMF, have been considered. In general, both the age‐metallicity relationship and the empirical distribution of oxygen abundance in G dwarfs of the disk solar neighbourhood, are fitted by power‐law IMF exponents in the range 2.35 ≤ p ≤ 2.9. Acceptable models predict about 15% of the total mass in form of long‐lived stars and remnants, at the end of halo evolution, with a mean gas oxygen abundance which is substantially lower than the mean bulge and initial disk oxygen abundance. To avoid this discrepancy, either the existence of a still undetected, baryonic dark halo with about 15% of the total mass, or an equal amount of gas loss during bulge and disk formation, is necessary. The latter alternative implies a lower stellar mass limit close to 0.2 m_⊙, which is related to a power‐law IMF exponent close to 2.77. Acceptable models also imply a rapid halo formation, mainly during the first step, Δt = 0.5 Gyr, followed by a period (three steps) where small changes occur. Accordingly, statistical fluctuations are found to produce only minor effects on the evolution.     

Testing tidal-torque theory – II. Alignment of inertia and shear and the characteristics of protohaloes

We investigate the cross-talk between the two key components of tidal-torque theory, the inertia ( I ) and shear ( T ) tensors, using a cosmological N -body simulation with thousands of well-resolved haloes. We find that the principal axes of I and T are strongly aligned , even though I characterizes the protohalo locally while T is determined by the large-scale structure. Thus, the resultant galactic spin, which plays a key role in galaxy formation, is only a residual due to ∼10 per cent deviations from the perfect alignment of T and I . The   T – I   correlation induces a weak tendency for the protohalo spin to be perpendicular to the major axes of T and I , but this correlation is erased by non-linear effects at late times, making the observed spins poor indicators of the initial shear field.
However, the   T – I   correlation implies that the shear tensor can be used for identifying the positions and boundaries of protohaloes in cosmological initial conditions – a missing piece in galaxy formation theory. The typical configuration is of a prolate protohalo lying perpendicular to a large-scale high-density ridge, with the surrounding voids inducing compression along the major and intermediate inertia axes of the protohalo. This leads to a transient sub-halo filament along the large-scale ridge, whose subclumps then flow along the filament and merge into the final halo.
The centres of protohaloes tend to lie in ∼1 σ overdensity regions, but their association with linear density maxima smoothed on galactic scales is vague: only ∼40 per cent of the protohaloes contain peaks. Several other characteristics distinguish protohaloes from density peaks, e.g. they tend to compress along two principal axes while many peaks compress along three axes.