Radiation pressure supported stars in Einstein gravity: eternally collapsing objects

Even when we consider Newtonian stars, that is, stars with surface gravitational redshift   z ≪ 1  , it is well known that, theoretically, it is possible to have stars supported against self-gravity almost entirely by radiation pressure. However, such Newtonian stars must necessarily be supermassive. We point out that this requirement for excessively large M in the Newtonian case is a consequence of the occurrence of low   z ≪ 1  . However, if we remove such restrictions, and allow for the possible occurrence of a highly general relativistic regime,   z ≫ 1  , we show that it is possible to have radiation pressure supported stars (RPSSs) at an arbitrary value of M . Since RPSSs necessarily radiate at the Eddington limit, in Einstein gravity, they are never in strict hydrodynamical equilibrium. Further, it is believed that sufficiently massive or dense objects undergo continued gravitational collapse to the black hole (BH) stage characterized by   z =∞  . Thus, late stages of BH formation, by definition, would have   z ≫ 1  , and hence would be examples of quasi-stable general relativistic RPSSs. It is shown that the observed duration of such Eddington limited radiation pressure dominated states is   t ≈ 5 × 10⁸ (1 + z ) yr  . Thus,   t →∞  as BH formation  ( z →∞)  takes place. Consequently, such radiation pressure dominated extreme general relativistic stars become eternally collapsing objects (ECOs) and the BH state is preceded by such an ECO phase. This result is also supported by our previous finding that trapped surfaces are not formed in gravitational collapse and the value of the integration constant in the vacuum Schwarzschild solution is zero. Hence the supposed observed BHs are actually ECOs.     

Glimpsing through the high-redshift neutral hydrogen fog

We analyse the transmitted flux in a sample of 17 QSOs spectra at 5.74 ≤ z _em≤ 6.42 to obtain tighter constraints on the volume-averaged neutral hydrogen fraction, x _{H  i} , at z ≈ 6. We study separately the narrow transmission windows (peaks) and the wide dark portions (gaps) in the observed absorption spectra. By comparing the statistics of these spectral features with a semi-analytical model of the Lyα forest, we conclude that x _{H  i} evolves smoothly from 10^−4.4 at   z = 5.3  to 10^−4.2 at   z = 5.6  , with a robust upper limit x _{H  i} < 0.36 at   z = 6.3  . The frequency and physical sizes of the peaks imply an origin in cosmic underdense regions and/or in H  ii regions around faint quasars or galaxies. In one case (the intervening H  ii region of the faint quasar RD J1148+5253 at   z = 5.70  along the line of sight of SDSS J1148+5251 at   z = 6.42  ) the increase of the peak spectral density is explained by the first-ever detected transverse proximity effect in the H  i Lyα forest; this indicates that at least some peaks result from a locally enhanced radiation field. We then obtain a strong lower limit on the foreground QSO lifetime of t _Q > 11 Myr. The observed widths of the peaks are found to be systematically larger than the simulated ones. Reasons for such discrepancy might reside either in the photoionization equilibrium assumption or in radiative transfer effects.     

The H i opacity of the intergalactic medium at redshifts 1.6 < z < 3.2

We use high-quality echelle spectra of 24 quasi-stellar objects to provide a calibrated measurement of the total amount of Lyα forest absorption (DA) over the redshift range  2.2 < z < 3.2  . Our measurement of DA excludes absorption from metal lines or the Lyα lines of Lyman-limit systems and damped Lyα systems. We use artificial spectra with realistic flux calibration errors to show that we are able to place continuum levels that are accurate to better than 1 per cent. When we combine our results with our previous results between  1.6 < z < 2.2  , we find that the redshift evolution of DA is well described over  1.6 < z < 3.2  as   A (1 + z )^γ  , where   A = 0.0062  and  γ= 2.75  . We detect no significant deviations from a smooth power-law evolution over the redshift range studied. We find less H  i absorption than expected at   z = 3  , implying that the ultraviolet background is  ∼40  per cent higher than expected. Our data appears to be consistent with an H  i ionization rate of  Γ∼ 1.4 × 10⁻¹² s⁻¹  .     

On the possibility of observing H2 emission from primordial molecular cloud kernels

We study the prospects for observing H₂ emission during the assembly of primordial molecular cloud kernels. The primordial molecular cloud cores, which resemble those at the present epoch, can emerge around  1+ z ∼20  according to recent numerical simulations. The kernels form inside the cores, and the first stars will appear inside the kernels. A kernel typically contracts to form one of the first generation stars with an accretion rate that is as large as ∼0.01 M_⊙ yr⁻¹. This occurs owing to the primordial abundances, which result in a kernel temperature of order 1000 K, and the collapsing kernel emits H₂ line radiation at a rate ∼10³⁵ erg s⁻¹. Predominantly   J =5-3   ( v =0)  rotational emission of H₂ is expected. At redshift  1+ z ∼20  , the expected flux is ∼0.01 μJy for a single kernel. While an individual object is not observable by any facilities available in the near future, the expected assembly of primordial star clusters on subgalactic scales can result in fluxes at the sub-mJy level. This is marginally observable with ASTRO-F and ALMA. We also examine the rotational   J =2-0   ( v =0)  and vibrational   δv =1  emission lines. The former may possibly be detectable with ALMA.     

The evolution of star formation in quasar host galaxies

We have used far-infrared data from IRAS , Infrared Space Observatory ( ISO ), Spitzer Wide-Area Infrared Extragalactic (SWIRE), Submillimetre Common User Bolometer Array (SCUBA) and Max-Planck Millimetre Bolometer (MAMBO) to constrain statistically the mean far-infrared luminosities of quasars. Our quasar compilation at redshifts  0 < z < 6.5  and I -band luminosities  −20 < I _AB < −32  is the first to distinguish evolution from quasar luminosity dependence in such a study. We carefully cross-calibrate IRAS against Spitzer and ISO , finding evidence that IRAS 100-μm fluxes at <1 Jy are overestimated by ∼30 per cent. We find evidence for a correlation between star formation in quasar hosts and the quasar optical luminosities, varying as star formation rate (SFR)  ∝ L ^0.44±0.07_opt  at any fixed redshift below   z = 2  . We also find evidence for evolution of the mean SFR in quasar host galaxies, scaling as  (1 + z )^1.6±0.3  at   z < 2  for any fixed quasar I -band absolute magnitude fainter than −28. We find no evidence for any correlation between SFR and black hole mass at  0.5 < z < 4  . Our data are consistent with feedback from black hole accretion regulating stellar mass assembly at all redshifts.     

Perturbations of ionization fractions at the cosmological recombination epoch

The development of perturbations of number densities of ions and electrons during the recombination epoch is analysed. The equations for relative perturbations of ionization fractions were derived from the system of equations for accurate computation of the ionization history of the early Universe. It is shown that strong dependence of ionization and recombination rates on the density and temperature of plasma provides the significant deviations of amplitudes of ionization fractions relative to perturbations from those of baryon matter density adiabatic perturbations. Such deviations are most prominent for cosmological adiabatic perturbations of scales larger than the sound horizon at the recombination epoch. The amplitudes of relative perturbations of number densities of electrons and protons at the last scattering surface exceed by a factor of ≃5 the amplitude of the relative perturbation of baryons total number density: for helium ions this ratio reaches a value of ≃18. For subhorizon cosmological perturbations, these ratios appear to be essentially smaller and depend on oscillation phase at the moment of decoupling. These perturbations of number densities of ions and electrons at the recombination epoch do not contribute to the intrinsic plasma temperature fluctuations but cause the 'corrugation' of the last scattering surface in optical depth,  δ z _dec/( z _dec+ 1) ≈−δ_b/3  , at scales larger than the sound horizon. It may result in notable changes of pre-calculated values of the cosmic microwave background polarization pattern at several degrees of angular scales.     

Neutralino annihilations and the gas temperature in the dark ages

Assuming that the dark matter is entirely made up of neutralinos, we re-visit the role of their annihilation on the temperature of diffuse gas in the high-redshift universe  ( z > 10)  , before the formation of luminous structures. We consider neutralinos of particle mass 36 and 100 GeV. The former is able to produce  ∼7  e ⁻ e ⁺  particles per annihilation through the fremionic channel, and the latter ∼53 particles assuming a purely bosonic channel. High-energy   e ⁻ e ⁺  particles up-scatter the cosmic microwave background (CMB) photons into higher energies via the inverse-Compton scattering. The process produces a power-law   e ⁻ e ⁺  energy spectrum of index −1 in the energy range of interest, independent of the initial energy distribution. The corresponding energy spectrum of the up-scattered photons is a power law of index −1/2, if absorption by the gas is not included. The scattered photons photoheat the gas by releasing electrons which deposit a fraction (14 per cent) of their energy as heat into the ambient medium. For uniformly distributed neutralinos, the heating is insignificant. The effect is greatly enhanced by the clumping of neutralinos into dense haloes. We use a time-dependent clumping model which takes into account the damping of density fluctuations on mass-scales smaller than  ∼10⁻⁶ M_⊙  . With this clumping model, the heating mechanism boosts the gas temperature above that of the CMB after a redshift of   z ∼ 30  . By   z ≈ 10  , the gas temperature is nearly 100 times its temperature when no heating is invoked. Similar increase is obtained for the two neutralino masses considered.     

Ultrasoft X-ray components in the high-temperature extreme

A search for high-redshift ( z  > 0.5) ultrasoft X-ray AGN in pointed ROSAT PSPC observations is made, using the wgacat catalogue. Evidence for a further three such objects is found, adding to three identified previously (E1346+266, EXO 1346.4+2637 and RX J0947.0+4721). The flux of one new object [1WGA J1342.4+2720; L (0.1–2 keV)∼ 2 × 10⁴⁵ erg s⁻¹)] was found to be variable (a factor of 1.7 over 2 d), and this object has relatively narrow permitted line emission. These properties, also seen in E1346+266 and EXO 1346.4+2637, are typical of ultrasoft AGN at all redshifts, in particular the narrow-line Seyfert 1s (NLS1s). The rarity of high- z ultrasoft AGN places limits on the 'temperature' of the soft X-ray component in the rest frame of AGN in general. It also provides an opportunity to investigate models for the soft component in the high-temperature extreme, e.g., for accretion disc models, testing the physics at the inner edge of the disc, and the effects of Comptonization in a hot, optically thin corona.     

Profiles of dark matter haloes at high redshift

I study the evolution of halo density profiles as a function of time in the SCDM and ΛCDM cosmologies. Following Del Popolo, I calculate the concentration parameter c = r _v / a and study its time evolution. For a given halo mass, I find that c ( z ) ∝ 1/(1+ z ) in both the ΛCDM and SCDM cosmology, in agreement with the analytic model of Bullock et al. and N -body simulations. In both models, a ( z ) is roughly constant. The present model predicts a stronger evolution of c ( z ) with respect to the Navarro, Frenk & White model. Finally I show some consequences of the results on galaxy modelling.     

On the evolution of the black hole: spheroid mass ratio

We present the results of a study which uses the 3C RR sample of radio-loud active galactic nuclei to investigate the evolution of the black hole:spheroid mass ratio in the most massive early-type galaxies from  0 < z < 2  . Radio-loud unification is exploited to obtain virial (linewidth) black hole mass estimates from the 3C RR quasars, and stellar mass estimates from the 3C RR radio galaxies, thereby providing black hole and stellar mass estimates for a single population of early-type galaxies. At low redshift  ( z ≲ 1)  , the 3C RR sample is consistent with a black hole:spheroid mass ratio of   M _bh/ M _sph≃ 0.002  , in good agreement with that observed locally for quiescent galaxies of similar stellar mass  ( M _sph≃ 5 × 10¹¹ M_⊙)  . However, over the redshift interval  0 < z < 2  the 3C RR black hole:spheroid mass ratio is found to evolve as   M _bh/ M _sph∝ (1 + z )^2.07±0.76  , reaching   M _bh/ M _sph≃ 0.008  by redshift   z ≃ 2  . This evolution is found to be inconsistent with the local black hole:spheroid mass ratio remaining constant at a moderately significant level (98 per cent). If confirmed, the detection of evolution in the 3C RR black hole:spheroid mass ratio further strengthens the evidence that, at least for massive early-type galaxies, the growth of the central supermassive black hole may be completed before that of the host spheroid.     

The Hα luminosity function and star formation rate up to z ∼ 1

We describe ISAAC/ESO-VLT observations of the Hαλ6563 Balmer line of 33 field galaxies from the Canada–France Redshift Survey (CFRS) with redshifts selected between 0.5 and 1.1. We detect Hα in emission in 30 galaxies and compare the properties of this sample with the low-redshift sample of CFRS galaxies at   z ∼ 0.2  . We find that the Hα luminosity,   L (Hα)  , is tightly correlated to   M ( B _AB)  in the same way for both the low- and high-redshift samples.   L (Hα)  is also correlated to L ([O  ii ]λ3727), and again the relation appears to be similar at low and high redshifts. The ratio L (lsqb;O  ii ])/   L (Hα)  decreases for brighter galaxies by as much as a factor of 2 on average. Derived from the Hα luminosity function, the comoving Hα luminosity density increases by a factor 12 from  〈 z 〉= 0.2  to  〈 z 〉= 1.3  . Our results confirm a strong rise of the star formation rate (SFR) at   z < 1.3  , proportional to  (1 + z )^4.1±0.3  (with   H ₀= 50 km s⁻¹ Mpc⁻¹, q ₀= 0.5  ). We find an average  SFR(2800 Å)/SFR (Hα)  ratio of 3.2 using the Kennicutt SFR transformations. This corresponds to the dust correction that is required to make the near-ultraviolet data consistent with the reddening-corrected Hα data within the self-contained, I -selected CFRS sample.     

The evolution of galactic discs

We use recent observations of high-redshift galaxies to study the evolution of galactic discs over the redshift range 0 <  z ≲1. The data are inconsistent with models in which discs were already assembled at z  = 1 and have evolved only in luminosity since that time. Assuming that disc properties change with redshift as powers of 1 +   z and analysing the observations assuming an Einstein–de Sitter universe, we find that for given rotation speed, disc scalelength decreases with z as ∼ (1 +  z )⁻¹, total B -band mass-to-light ratio decreases with z as ∼ (1 +  z )⁻¹, and disc luminosity (again in B ) depends only weakly on z . These scalings are consistent with current data on the evolution of disc galaxy abundance as a function of size and luminosity. Both the scalings and the abundance evolution are close to the predictions of hierarchical models for galaxy formation. If different cosmogonies are compared, the observed evolution in disc size and disc abundance favours a flat low-Ω₀ universe over an Einstein–de Sitter universe.     

Ly+ and ultraviolet emission from high-redshift gamma-ray burst hosts: to what extent do gamma-ray bursts trace star formation?

We report the result of a search for Lyα emission from the host galaxies of the gamma-ray bursts  (GRBs) 030226 ( z = 1.986), 021004 ( z = 2.335)  and  020124 ( z = 3.198)  . We find that the host galaxy of GRB 021004 is an extended (around 8 kpc) strong Lyα emitter with a rest-frame equivalent width (EW) of 68⁺¹²₋₁₁Å, and a star formation rate of  10.6 ± 2.0 M_⊙ yr⁻¹  . We do not detect the hosts of GRB 030226 and GRB 020124, but the upper limits on their Lyα fluxes do not rule out large rest-frame EWs. In the fields of GRB 021004 and GRB 030226 we find seven and five other galaxies, respectively, with excess emission in the narrow-band filter. These galaxies are candidate Lyα-emitting galaxies in the environment of the host galaxies. We have also compiled a list of all   z ≳ 2  GRB hosts, and demonstrate that a scenario where they trace star formation in an unbiased way is compatible with current observational constraints. Fitting the   z = 3  luminosity function (LF) under this assumption results in a characteristic luminosity of   R *= 24.6  and a faint-end slope of  α=−1.55  , consistent with the LF measured for Lyman-break galaxies.     

The redshift-space two-point correlation function of ELAIS-S1 galaxies

We investigate the clustering properties of galaxies in the recently completed ELAIS-S1 redshift survey through their spatial two-point autocorrelation function. We used a subsample of the ELAIS-S1 catalogue covering approximately 4 deg² and consisting of 148 objects selected at 15 μm with a flux >0.5 mJy and a redshift   z < 0.5  . We detected a positive signal in the correlation function that in the range of separations  1–10  h ⁻¹ Mpc  is well approximated by a power law with a slope  γ= 1.4 ± 0.25  and a correlation length   s ₀= 5.4 ± 1.2  h ⁻¹ Mpc  , at the 90 per cent significance level. This result is in good agreement with the redshift-space correlation function measured in more local samples of mid-infrared-selected galaxies such as the IRAS Point Source Catalog (PSC z ) redshift survey. This suggests a lack of significant clustering evolution of infrared-selected objects out to   z = 0.5  that is further confirmed by the consistency found between the correlation functions measured in a local  ( z < 0.2)  and a distant  (0.2 < z < 0.5)  subsample of ELAIS-S1 galaxies. We also confirm that optically selected galaxies in the local redshift surveys, especially those of the SDSS sample, are significantly more clustered than infrared objects.     

Downsizing of supermassive black holes from the SDSS quasar survey – II. Extension to z∼ 4

Starting from the quasar sample of the Sloan Digital Sky Survey (SDSS) for which the C  iv line is observed, we use an analysis scheme to derive the z -dependence of the maximum mass of active black holes, which overcomes the problems related to the Malmquist bias. The same procedure is applied to the low-redshift sample of SDSS quasars for which Hβ measurements are available. Combining with the results from the previously studied Mg  ii sample, we find that the maximum mass of the quasar population increases as  (1 + z )^1.64±0.04  in the redshift range  0.1 z 4  , which includes the epoch of maximum quasar activity.     

Hubble Space Telescope imaging of the CFRS and LDSS redshift surveys – IV. Influence of mergers in the evolution of faint field galaxies from z∼1

Hubble Space Telescope images of a sample of 285 galaxies with measured redshifts from the Canada–France Redshift Survey (CFRS) and Autofib–Low Dispersion Spectrograph Survey (LDSS) redshift surveys are analysed to derive the evolution of the merger fraction out to redshifts z ∼1. We have performed visual and machine-based merger identifications, as well as counts of bright pairs of galaxies with magnitude differences δm ≤1.5 mag. We find that the pair fraction increases with redshift, with up to ∼20 per cent of the galaxies being in physical pairs at z ∼0.75–1. We derive a merger fraction varying with redshift as ∝(1+ z )^3.2±0.6, after correction for line-of-sight contamination, in excellent agreement with the merger fraction derived from the visual classification of mergers for which m =3.4±0.6. After correcting for seeing effects on the ground-based selection of survey galaxies, we conclude that the pair fraction evolves as ∝(1+ z )^2.7±0.6. This implies that an average L * galaxy will have undergone 0.8–1.8 merger events from z =1 to z =0, with 0.5 to 1.2 merger events occuring in a 2-Gyr time-span at around z ∼0.9. This result is consistent with predictions from semi-analytical models of galaxy formation. From the simple coaddition of the observed luminosities of the galaxies in pairs, physical mergers are computed to lead to a brightening of 0.5 mag for each pair on average, and a boost in star formation rate of a factor of 2, as derived from the average [O  ii ] equivalent widths. Mergers of galaxies are therefore contributing significantly to the evolution of both the luminosity function and luminosity density of the Universe out to z ∼1.     

Recovering the initial conditions of our local Universe from NOG and PSCz catalogues

We apply the ztrace algorithm to the optical NOG and infrared PSC z galaxy catalogues to reconstruct the pattern of primordial fluctuations that have generated our local Universe. We check that the density fields traced by the two catalogues are well correlated, and consistent with a linear relation [either in δ or in  log (1 +δ)  ] with relative bias (of NOG with respect to PSC z )   b _rel= 1.1 ± 0.1  . The relative bias relation is used to fill the optical zone of avoidance at  | b | < 20°  using the PSC z galaxy density field.
We perform extensive testing on simulated galaxy catalogues to optimize the reconstruction. The quality of the reconstruction is predicted to be good at large scales, up to a limiting wavenumber   k _lim≃ 0.4 h Mpc⁻¹  beyond which all information is lost. We find that the improvement arising from the denser sampling of the optical catalogue is compensated by the uncertainties connected to the larger zone of avoidance.
The initial conditions reconstructed from the NOG catalogue are found (analogously to those from the PSC z ) to be consistent with a Gaussian paradigm. We use the reconstructions to produce sets of initial conditions ready to be used for constrained simulations of our local Universe.     

Radiation from early black holes – I. Effects on the neutral intergalactic medium

In the pre-reionization Universe, the regions of the intergalactic medium (IGM) which are far from luminous sources are the last to undergo reionization. Until then, they should be scarcely affected by stellar radiation; instead, the X-ray emission from an early black hole (BH) population can have much larger influence. We investigate the effects of such emission, looking at a number of BH model populations (differing for the cosmological density evolution of BHs, the BH properties, and the spectral energy distribution of the BH emission). We find that BH radiation can easily heat the IGM to  10³–10⁴ K  , while achieving partial ionization. The most interesting consequence of this heating is that BHs are expected to induce a 21-cm signal (  δ T _b∼ 20–30 mK  at   z ≲ 12  ) which should be observable with forthcoming experiments (e.g. LOFAR). We also find that at   z ≲ 10  BH emission strongly increases the critical mass separating star-forming and non-star-forming haloes.     

ΛCDM predictions for galaxy protoclusters – I. The relation between galaxies, protoclusters and quasars at z∼ 6

Motivated by recent observational studies of the environment of   z ∼ 6  QSOs, we have used the Millennium Run (MR) simulations to construct a very large  (∼4°× 4°)  mock redshift survey of star-forming galaxies at   z ∼ 6  . We use this simulated survey to study the relation between density enhancements in the distribution of i ₇₇₅-dropouts and Lyα emitters, and their relation to the most massive haloes and protocluster regions at   z ∼ 6  . Our simulation predicts significant variations in surface density across the sky with some voids and filaments extending over scales of 1°, much larger than probed by current surveys. Approximately one-third of all   z ∼ 6  haloes hosting i -dropouts brighter than   z = 26.5  mag  (≈ M *_{UV, z =6})  become part of   z = 0  galaxy clusters. i -dropouts associated with protocluster regions are found in regions where the surface density is enhanced on scales ranging from a few to several tens of arcminutes on the sky. We analyse two structures of i -dropouts and Lyα emitters observed with the Subaru Telescope and show that these structures must be the seeds of massive clusters in formation. In striking contrast, six   z ∼ 6  QSO fields observed with Hubble Space Telescope show no significant enhancements in their i ₇₇₅-dropout number counts. With the present data, we cannot rule out the QSOs being hosted by the most massive haloes. However, neither can we confirm this widely used assumption. We conclude by giving detailed recommendations for the interpretation and planning of observations by current and future ground- and space-based instruments that will shed new light on questions related to the large-scale structure at   z ∼ 6  .     

The evolution of the Lyα forest effective optical depth following He ii reionization

Three independent observational studies have now detected a narrow  (Δ z ≃ 0.5)  dip centred at   z = 3.2  in the otherwise smooth redshift evolution of the Lyα forest effective optical depth. This feature has previously been interpreted as an indirect signature of rapid photoheating in the intergalactic medium (IGM) during the epoch of He  ii reionization. We examine this interpretation using a semi-analytic model of inhomogeneous He  ii reionization and high-resolution hydrodynamical simulations of the Lyα forest. We instead find that a rapid  (Δ z ≃ 0.2)  boost to the IGM temperature  (Δ T ≃ 10⁴ K)  beginning at   z = 3.4  produces a well understood and generic evolution in the Lyα effective optical depth, where a sudden reduction in the opacity is followed by a gradual, monotonic recovery driven largely by adiabatic cooling in the low-density IGM. This behaviour is inconsistent with the narrow feature in the observational data. If photoheating during He  ii reionization is instead extended over several redshift units, as recent theoretical studies suggest, then the Lyα opacity will evolve smoothly with redshift. We conclude that the sharp dip observed in the Lyα forest effective optical depth is instead most likely due to a narrow peak in the hydrogen photoionization rate around   z = 3.2  , and suggest that it may arise from the modulation of either reprocessed radiation during He  ii reionization, or the opacity of Lyman limit systems.