Analytic solutions for coupled linear perturbations

Analytic solutions for the evolution of cosmological linear density perturbations in the baryonic gas and collisionless dark matter are derived. The solutions are expressed in a closed form in terms of elementary functions, for arbitrary baryonic mass fraction. They are obtained assuming =1 and a time-independent comoving Jeans wavenumber, k _J. By working with a time variable ln( t ^2/3), the evolution of the perturbations is described by linear differential equations with constant coefficients. The new equations are then solved by means of Laplace transformation, assuming that the gas and dark matter trace the same density field before a sudden heating epoch. In a dark matter-dominated Universe, the ratio of baryonic to dark matter density perturbation decays with time roughly as exp(5 /4) t ^5/6 to the limiting value 1/[1+( k k _J)²]. For wavenumbers the decay is accompanied by oscillations with a period in . In comparison, as increases in a baryonic matter-dominated Universe, the ratio approaches 1( k k _J)² for k k _J, and zero otherwise.     

Impact of cosmic rays on Population III star formation

We explore the implications of a possible cosmic-ray (CR) background generated during the first supernova explosions that end the brief lives of massive Population III stars. We show that such a CR background could have significantly influenced the cooling and collapse of primordial gas clouds in minihaloes around redshifts of   z ∼ 15–20  , provided the CR flux was sufficient to yield an ionization rate greater than about 10⁻¹⁹ s⁻¹ near the centre of the minihalo. The presence of CRs with energies  ≲10⁷  eV would indirectly enhance the molecular cooling in these regions, and we estimate that the resulting lower temperatures in these minihaloes would yield a characteristic stellar mass as low as  ∼10 M_⊙  . CRs have a less-pronounced effect on the cooling and collapse of primordial gas clouds inside more massive dark matter haloes with virial masses  ≳10⁸ M_⊙  at the later stages of cosmological structure formation around   z ∼ 10–15  . In these clouds, even without CR flux the molecular abundance is already sufficient to allow cooling to the floor set by the temperature of the cosmic microwave background.     

Collapse of low-mass clouds in the presence of a UV radiation field

The collapse of marginally Jeans-unstable primordial gas clouds in the presence of a UV radiation field is discussed. Assuming that the dynamical collapse proceeds approximately in an isothermal self-similar fashion, we investigate the thermal evolution of the collapsing central core until H₂ cooling dominates photoheating and the temperature drops to below 10⁴ K. Consequently, the mass of the cooled core is evaluated as M _cool=3.6×10⁶ M_⊙ ( I ₂₁/1)^−0.32. This scale depends only on the incident UV intensity, and provides a lower limit to the mass of collapsed objects in the UV radiation field.     

Collisional baryonic dark matter haloes

If dark haloes are composed of dense gas clouds, as has recently been inferred, then collisions between clouds lead to galaxy evolution. Collisions introduce a core in an initially singular dark matter distribution, and can thus help to reconcile scale-free initial conditions – such as are found in simulations – with observed haloes, which have cores. A pseudo-Tully–Fisher relation, between halo circular speed and visible mass (not luminosity), emerges naturally from the model: M _vis∝ V ^7/2.
Published data conform astonishingly well to this theoretical prediction. For our sample of galaxies, the mass–velocity relationship has much less scatter than the Tully–Fisher relation, and holds as well for dwarf galaxies (where diffuse gas makes a sizeable contribution to the total visible mass) as it does for giants. It seems very likely that this visible-mass/velocity relationship is the underlying physical basis for the Tully–Fisher relation, and this discovery in turn suggests that the dark matter is both baryonic and collisional.     

Wide triplets of galaxies: collapse on spatial scales of ∼1 Mpc

We study triple systems of galaxies with mean projected harmonic separation ≃0.6  h ⁻¹ Mpc     We call the systems 'wide triplets', in contrast to compact triplets with mean projected harmonic separation ≃0.04  h ⁻¹ Mpc, studied by Karachentsev et al. Data are taken for 108 wide triplets from a list compiled by Trofimov & Chernin; at least one-third of them are considered to be probably isolated physical systems. With typical crossing times of about the Hubble time, the wide triplets seem to be in a state of ongoing collapse. This is confirmed by a set of computer models which simulate well the observational characteristics of the ensemble of wide triplets. The simulations also give a statistical estimate of the total mass of a typical wide triplet: it proves to be ≃10¹³ M_⊙. This figure indicates that the dark matter mass is 15–30 times the mass of baryonic matter in the systems. The dynamics of wide triplets, as well as their dark matter content, provide new direct cosmological constraints by establishing that hierarchical evolution is occurring on a mass scale of ∼10¹³ M_⊙ and a spatial scale of ∼1 Mpc.     

Non-linear evolution of suppressed dark matter primordial power spectra

We address the degree and rapidity of generation of small-scale power over the course of structure formation in cosmologies where the primordial power spectrum is strongly suppressed beyond a given wavenumber. We first summarize the situations where one expects such suppressed power spectra and point out their diversity. We then employ an exponential cut-off, which characterizes warm dark matter (WDM) models, as a template for the shape of the cut-off and focus on damping scales ranging from 10⁶ to  10⁹  h ⁻¹ M_⊙  . Using high-resolution simulations, we show that the suppressed part of the power spectrum is quickly (re)generated and catches up with both the linear and the non-linear evolution of the unsuppressed power spectrum. From   z = 2  onwards, a power spectrum with a primordial cut-off at  10⁹  h ⁻¹ M_⊙  becomes virtually indistinguishable from an evolved cold dark matter (CDM) power spectrum. An attractor such as that described in Zaldarriaga, Scoccimarro & Hui for power spectra with different spectral indices also emerges in the case of truncated power spectra. Measurements of   z ∼ 0  non-linear power spectra at  ∼100  h ⁻¹ kpc  cannot rule out the possibility of linear power spectra damped below  ∼10⁹  h ⁻¹ M_⊙  . Therefore, WDM or scenarios with similar features should be difficult to exclude in this way.     

The Bullet Cluster 1E0657-558 evidence shows modified gravity in the absence of dark matter

A detailed analysis of the 2006 November 15 data release X-ray surface density Σ-map and the strong and weak gravitational lensing convergence κ-map for the Bullet Cluster 1E0657-558 is performed and the results are compared with the predictions of a modified gravity (MOG) and dark matter. Our surface density Σ-model is computed using a King β-model density, and a mass profile of the main cluster and an isothermal temperature profile are determined by the MOG. We find that the main cluster thermal profile is nearly isothermal. The MOG prediction of the isothermal temperature of the main cluster is   T = 15.5 ± 3.9 keV  , in good agreement with the experimental value   T = 14.8^+2.0_−1.7 keV  . Excellent fits to the 2D convergence κ-map data are obtained without non-baryonic dark matter, accounting for the 8σ spatial offset between the Σ-map and the κ-map reported in Clowe et al. The MOG prediction for the κ-map results in two baryonic components distributed across the Bullet Cluster 1E0657-558 with averaged mass fraction of 83 per cent intracluster medium (ICM) gas and 17 per cent galaxies. Conversely, the Newtonian dark matter κ-model has on average 76 per cent dark matter (neglecting the indeterminant contribution due to the galaxies) and 24 per cent ICM gas for a baryon to dark matter mass fraction of 0.32, a statistically significant result when compared to the predicted Λ-cold dark matter cosmological baryon mass fraction of 0.176^+0.019_−0.012.     

Separation of the visible and dark matter in the Einstein ring LBG J213512.73−010143

We model the mass distribution in the recently discovered Einstein ring LBG J213512.73−010143 (the 'Cosmic Eye') using archival Hubble Space Telescope imaging. We reconstruct the mass density profile of the z = 0.73 lens and the surface brightness distribution of the z = 3.07 source and find that the observed ring is best fitted with a dual-component lens model consisting of a baryonic Sersic component nested within a dark matter halo. The dark matter halo has an inner slope of 1.42^+0.24_−0.22, consistent with cold dark matter simulations after allowing for baryon contraction. The baryonic component has a mass-to-light ratio of  1.71^+0.28_−0.38 M_⊙/L _{B ⊙}  which when evolved to the present day is in agreement with local ellipticals. Within the Einstein radius of 0.77 arcsec (5.6 kpc), the baryons account for 46 ± 11 per cent of the projected lens mass. External shear from a nearby foreground cluster is accurately predicted by the model. The reconstructed surface brightness distribution in the source plane clearly shows two peaks. Through a generalization of our lens inversion method, we conclude that the redshifts of both peaks are consistent with each other, suggesting that we are seeing structure within a single galaxy.     

Universal gas density and temperature profile

We explore possibilities of collapse and star formation in Population III objects exposed to the external ultraviolet background (UVB) radiation. Assuming spherical symmetry, we solve self-consistently radiative transfer of photons, non-equilibrium H₂ chemistry and gas hydrodynamics. Although the UVB does suppress the formation of low-mass objects, the negative feedback turns out to be weaker than previously suggested. In particular, the cut-off scale of collapse drops significantly below the virial temperature T _vir∼10⁴ K at weak UV intensities ( J ₂₁≲10⁻²) , owing to both self-shielding of the gas and H₂ cooling. Clouds above this cut-off tend to contract highly dynamically, further promoting self-shielding and H₂ formation. For plausible radiation intensities and spectra, the collapsing gas can cool efficiently to temperatures well below 10⁴ K before rotationally supported and the final H₂ fraction reaches ∼ 10⁻³.
Our results imply that star formation can take place in low-mass objects collapsing in the UVB. The threshold baryon mass for star formation is ∼ 10⁹ M_⊙ for clouds collapsing at redshifts z ≲3 , but drops significantly at higher redshifts. In a conventional cold dark matter universe, the latter coincides roughly with that of the 1 σ density fluctuations. Objects near and above this threshold can thus constitute 'building blocks' of luminous structures, and we discuss their links to dwarf spheroidal/elliptical galaxies and faint blue objects. These results suggest that the UVB can play a key role in regulating the star formation history of the Universe.     

Formation of HD molecules in merging dark matter haloes

HD molecules can be an important cooling agent of the primordial gas behind the shock waves originated through merging of the dark matter haloes at epochs when the first luminous objects formed. We study the necessary conditions for the HD cooling to switch on in the low-temperature range   T < 200 K  . We show that these conditions are fulfilled in merging haloes with total (dark matter and baryon) mass in excess of   M _cr∼ 10⁷[(1 + z )/20]⁻² M_⊙  . Haloes with masses   M > M _cr  may be the sites of low-mass star formation.     

Dynamical response to supernova-induced gas removal in spiral galaxies with dark matter halo

We investigate the dynamical response, in terms of disc size and rotation velocity, to mass loss by supernovae in the evolution of spiral galaxies. A thin baryonic disc having the Kuzmin density profile embedded in a spherical dark matter halo having a density profile proposed by Navarro, Frenk & White is considered. For the purpose of comparison, we also consider the homogeneous and   r ⁻¹  profiles for dark matter in a truncated spherical halo. Assuming for simplicity that the dark matter distribution is not affected by mass-loss from discs and the change of baryonic disc matter distribution is homologous, we evaluate the effects of dynamical response in the resulting discs. We found that the dynamical response only for an adiabatic approximation of mass-loss can simultaneously account for the rotation velocity and disc size as observed particularly in dwarf spiral galaxies, thus reproducing the Tully–Fisher relation and the size versus magnitude relation over the full range of magnitude. Furthermore, we found that the mean specific angular momentum in discs after the mass-loss becomes larger than that before the mass-loss, suggesting that the mass-loss would most likely occur from the central disc region where the specific angular momentum is low.     

Interstellar CO towards X Persei (HD 24534) – II. Two-component model

The observations made by the Goddard High Resolution Spectrograph (GHRS) aboard the Hubble Space Telescope ( HST ) of molecular CO in absorbing gas towards X Persei are reported. The two-component statistical equilibrium model incorporating radiative excitation of CO by line emission at the same velocity that originates in nearby molecular clouds has been used to reproduce high-resolution GHRS spectra. Earlier analysis indicates that the cloud has a complex structure and at least a two-component model should be used to obtain accurate results. The spectra obtained from the International Ultraviolet Explorer ( IUE ) were used to complement GHRS data and constrain the space of possible solutions. The new oscillator strengths recommended by Eidelsberg et al. for A–X bands have been used. The results show that one of the components may be attributed to the Perseus OB2 molecular cloud, and the other component to an extension of the Taurus dark cloud. The total CO column density N (CO)=(1.0±0.2)×10¹⁶ cm⁻² has been determined. According to the results about 85 per cent of the observed CO belongs to an extension of the Taurus dark cloud. The CO radiation that originates in nearby molecular clouds may be the dominant excitation mechanism of the observed CO. The early results of ¹³CO line analysis indicate a ¹³CO/¹²CO ratio of about 40.     

Angular momentum and clustering properties of early dark matter haloes

In this paper, we study the angular momentum properties of simulated dark matter haloes at high redshifts that likely host the first stars in the Universe. Calculating the spin distributions of these  10⁶– 10⁷ M_⊙  haloes in redshift slices from   z = 15  to 6, we find that they are well fit by a lognormal distribution as is found for lower redshift and more massive haloes in earlier work. We find that both the mean value of the spin and dispersion are largely unchanged with redshift for all haloes. Our key result is that subsamples of low- and high-spin, 10⁶ and  10⁷ M_⊙  , haloes show difference in clustering strength. In both mass bins, higher spin haloes are more strongly clustered in concordance with a tidal torquing picture for the growth of angular momentum in dark matter haloes in the cold dark matter paradigm.     

A VAPID analysis of interstellar lithium in the ζ Oph sightline

We present observations of the Li  i 6708 Å doublet in the ζ Oph sightline, obtained at a resolution of ∼10⁶ and a signal-to-noise ratio of ∼1200, together with supplementary observations of K  i λ 7699 and the Na  i λ 3302 doublet. These observations marginally resolve the main '−15 km s⁻¹' system into its two principal clouds; we model the data using standard physical assumptions, but in a statistically rigorous manner, taking fully into account the hyperfine, doublet and isotopic structure for each species, in each cloud, using a new code, vapid . The average  ⁷Li/⁶Li  ratio determined in this sightline is  1.12±0.20 dex  (68 per cent confidence interval), in excellent agreement with the solar-system (meteoritic) value. The ratios in the individual clouds are determined with less precision, but are also consistent with the solar-system value, as is the total lithium abundance (with little evidence for depletion). The thermal and 'turbulent' broadening in the two clouds is discussed on the basis of observed line widths.     

Constraining the cosmological baryon density with X-ray clusters

We study the properties of X-ray galaxy clusters in four cold dark matter models with different baryon fractions Ω_BM, ranging from 5 to 20 per cent. By using an original three-dimensional hydrodynamic code based on the piecewise parabolic method, we run simulations on a box with a size of 64  h ⁻¹ Mpc and we identify the clusters by selecting the peaks in the X-ray luminosity field. We analyse these mock catalogues by computing the mass function, the luminosity function, the temperature distribution and the luminosity–temperature relation. By comparing the predictions of the different models to a series of recent observational results, we find that only the models with low baryonic content agree with the data, while models with larger baryon fraction are well outside the 1σ error bars. In particular, the analysis of the luminosity functions, both bolometric and in the energy band [0.5–2] keV, requires Ω_BM ≲ 0.05 when we fix the values h  = 0.5 and n  = 0.8 for the Hubble parameter and the primordial spectral index, respectively. Moreover we find that, independently of the cosmological scenario, all the considered quantities have very little redshift evolution, particularly between z  = 0.5 and 0.     

Implications of primordial black holes on the first stars and the origin of the super-massive black holes

If the cosmological dark matter has a component made of small primordial black holes (BHs), they may have a significant impact on the physics of the first stars and on the subsequent formation of massive BHs. Primordial BHs would be adiabatically contracted into these stars and then would sink to the stellar centre by dynamical friction, creating a larger BH which may quickly swallow the whole star. If these primordial BHs are heavier than  ∼10²² g  , the first stars would likely live only for a very short time and would not contribute much to the reionization of the Universe. They would instead become  10–10³ M_⊙  BHs which (depending on subsequent accretion) could serve as seeds for the super-massive BHs seen at high redshifts as well as those inside galaxies today.     

A ultraluminous X-ray source associated with a cloud collision in M 99

The Sc galaxy M 99 in the Virgo Cluster has been strongly affected by tidal interactions and recent close encounters, responsible for an asymmetric spiral pattern and a high star formation rate. Our XMM–Newton study shows that the inner disc is dominated by hot plasma at kT ≈ 0.30 keV, with a total X-ray luminosity of ≈10⁴¹ erg s⁻¹ in the 0.3–12 keV band. At the outskirts of the galaxy, away from the main star-forming regions, there is an ultraluminous X-ray source (ULX) with an X-ray luminosity of ≈2 × 10⁴⁰ erg s⁻¹ and a hard spectrum well fitted by a power law of photon index Γ≈ 1.7. This source is close to the location where a massive H  i cloud appears to be falling on to the M 99 disc at a relative speed of >100 km s⁻¹. We suggest that there may be a direct physical link between fast cloud collisions and the formation of bright ULXs, which may be powered by accreting black holes with masses ∼100 M_⊙. External collisions may trigger large-scale dynamical collapses of protoclusters, leading to the formation of very massive (≳200 M_⊙) stellar progenitors; we argue that such stars may later collapse into massive black holes if their metal abundance is sufficiently low.     

Are AGN broad emission lines formed by discrete clouds? Analysis of Keck high-resolution spectroscopy of NGC 4151

We search for a direct signature of discrete 'clouds' in the broad-line region (BLR) of the Seyfert galaxy NGC 4151. For this purpose we apply cross-correlation (CC) analysis to a high-resolution Keck spectrum of the galaxy. No such signature is found in the data. In order for cloud models to be compatible with this result, there must be at least ∼3×10⁷ emitting clouds in the BLR, where the limit is based on simulation of a homogeneous cloud population. More realistic distributions increase the lower limit to above 10⁸. These numbers are an order-of-magnitude improvement on our previous limit from Mrk 335, where the improvement comes from higher signal-to-noise ratio (S/N), broader lines and refined simulations. Combined with the predicted upper limit for the number of emitting clouds in NGC 4151 (10⁶–10⁷), the derived lower limit puts a strong constraint on the cloud scenario in the BLR of this object. Similar constraints can be placed on models where the emission originates in streams and sheets. Thus, this investigation suggests that the broad emission lines (BELs) in NGC 4151, and by extension in all AGNs, are not made of an ensemble of discrete independent emitters.     

Chemodynamical Modelling of Galaxy Formation and Evolution

We present our recently developed 3-dimensional chemodynamical code for galaxy evolution. This code follows the evolution of different galactic components like stars, dark matter and different components of the interstellar medium (ISM), i.e. a diffuse gaseous phase and the molecular clouds. Stars and dark matter are treated as collisionless N-body systems. The ISM is numerically described by a smoothed particle hydrodynamics (SPH) approach for the diffuse gas and a sticky particle scheme for the molecular clouds. Additionally, the galactic components are coupled by several phase transitions like star formation, stellar death or condensation and evaporation processes within the ISM. As an example we show the dynamical and chemical evolution of a star forming dwarf galaxy with a total baryonic mass of 2 ċ 10⁹ M_⊙. After a moderate collapse phase the stars and the molecular clouds follow an exponential radial distribution, whereas the diffuse gas shows a central depression as a result of stellar feedback. The metallicities of the galactic components behave quite differently with respect to their temporal evolution as well as their radial distribution. Especially, the ISM is at no stage well mixed. This revised version was published online in September 2006 with corrections to the Cover Date.     

The first generation of stars in the Λ cold dark matter cosmology

We have performed a large set of high-resolution cosmological simulations using smoothed particle hydrodynamics to study the formation of the first luminous objects in the Lambda cold dark matter cosmology. We follow the collapse of primordial gas clouds in eight early structures and document the scatter in the properties of the first star-forming clouds. Our first objects span formation redshifts from   z ∼ 10  to ∼50 and cover an order of magnitude in halo mass. We find that the physical properties of the central star-forming clouds are very similar in all of the simulated objects despite significant differences in formation redshift and environment. This suggests that the formation path of the first stars is largely independent of the collapse redshift; the physical properties of the clouds have little correlation with spin, mass or assembly history of the host halo. The collapse of protostellar objects at higher redshifts progresses much more rapidly due to the higher densities, which accelerates the formation of molecular hydrogen, enhances initial cooling and shortens the dynamical time-scales. The mass of the star-forming clouds cover a broad range, from a few hundred to a few thousand solar masses, and exhibit various morphologies: some have disc-like structures which are nearly rotational supported; others form flattened spheroids; still others form bars. All of them develop a single protostellar 'seed' which does not fragment into multiple objects up to the moment that the central gas becomes optically thick to H₂ cooling lines. At this time, the instantaneous mass accretion rate on to the centre varies significantly from object to object, with disc-like structures having the smallest mass accretion rates. The formation epoch and properties of the star-forming clouds are sensitive to the values of cosmological parameters.