Clustering of X-ray selected active galactic nuclei

A total of 235 active galactic nuclei (AGN) from two different soft X-ray surveys [the ROSAT Deep Survey (DRS) and the ROSAT International X-ray Optical Survey (RIXOS)] with redshifts between 0 and 3.5 are used to study the clustering of X-ray selected AGN and its evolution. A 2σ significant detection of clustering of such objects is found on scales < 40–80 h ⁻¹ Mpc in the RIXOS sample, while no clustering is detected on any scales in the DRS sample. Assuming a single power-law model for the spatial correlation function (SCF), quantitative limits on the AGN clustering have been obtained: a comoving correlation length 1.5 ≲  r ₀ ≲ 3.3  h ⁻¹ Mpc is implied for comoving evolution, while 1.9 ≲  r ₀ ≲ 4.8 for stable clustering and 2.2 ≲  r ₀ ≲ 5.5 for linear evolution. These values are consistent with the correlation lengths and evolutions obtained for galaxy samples, but imply smaller amplitude or faster evolution than recent ultraviolet and optically selected AGN samples. We also constrain the ratio of bias parameters between X-ray selected AGN and IRAS galaxies to be ≲ 1.7 on scales ≲ 10  h ⁻¹ Mpc, a somewhat smaller value than is inferred from local large-scale dynamical studies.     

Clustering of luminous red galaxies – II. Small-scale redshift-space distortions

This is the second paper of a series where we study the clustering of luminous red galaxies (LRG) in the recent spectroscopic Sloan Digital Sky Survey (SDSS) data release, DR6, which has 75 000 LRG covering over  1 Gpc³  h ⁻³  for  0.15 < z < 0.47  . Here, we focus on modelling redshift-space distortions in  ξ(σ, π)  , the two-point correlation in separate line-of-sight and perpendicular directions, at small scales and in the line-of-sight. We show that a simple Kaiser model for the anisotropic two-point correlation function in redshift space, convolved with a distribution of random peculiar velocities with an exponential form, can describe well the correlation of LRG on all scales. We show that to describe with accuracy the so-called 'fingers-of-God' (FOG) elongations in the radial direction, it is necessary to model the scale dependence of both bias b and the pairwise rms peculiar velocity σ₁₂ with the distance. We show how both quantities can be inferred from the  ξ(σ, π)  data. From   r ≃ 10 Mpc  h ⁻¹  to   r ≃ 1 Mpc  h ⁻¹  , both the bias and σ₁₂ are shown to increase by a factor of 2: from   b = 2  to 4 and from  σ₁₂= 400  to  800 km s⁻¹  . The latter is in good agreement, within a 5 per cent accuracy in the recovered velocities, with direct velocity measurements in dark matter simulations with  Ω_m= 0.25  and  σ₈= 0.85  .     

Non-linear redshift distortions: the two-point correlation function

We consider a situation where the density and peculiar velocities in real space are linear, and we calculate ξ _s , the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of the map from real to redshift space. Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space. We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of ξ _s . While the deviations are insignificant for the monopole ξ ₀, the hexadecapole ξ ₄ exhibits large deviations from the linear predictions. For a COBE normalized     ,     cold dark matter (CDM) power spectrum, our results for ξ ₄ deviate from the linear predictions by a factor of two on the scale of ∼10  h ⁻¹ Mpc. The deviations from the linear predictions depend separately on f (Ω) and b . This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only     .
We also show that the commonly used phenomenological model, where the non-linear redshift two-point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function, is a limiting case of our result.     

A measurement of the faint source correlation function in the GOODS and UDF surveys

We present a stable procedure for defining and measuring the two point angular autocorrelation function,   w (θ) =[θ/θ₀( V )]^−Γ  , of faint  (25 < V < 29)  , barely resolved and unresolved sources in the Hubble Space Telescope Great Observatories Origins Deep Survey and Ultra Deep Field data sets. We construct catalogues that include close pairs and faint detections. We show, for the first time, that, on subarcsec scales, the correlation function exceeds unity. This correlation function is well fit by a power law with index  Γ≈ 2.5  and a  θ₀= 10^{−0.1( V −25.8)} arcsec  . This is very different from the values of  Γ≈ 0.7  and  θ₀( r ) = 10^{−0.4( r −21.5)} arcsec  associated with the gravitational clustering of brighter galaxies. This observed clustering probably reflects the presence of giant star-forming regions within galactic-scale potential wells. Its measurement enables a new approach to measuring the redshift distribution of the faintest sources in the sky.     

Spatial clustering of Ultra Steep Spectrum sources and galaxies

We present measurements of the clustering properties of galaxies in the field of redshift range 0.5 ≲ z ≲ 1.5 Ultra Steep Spectrum radio sources selected from the Sydney University Molonglo Sky Survey and the National Radio Astronomy Observatories Very Large Array Sky Survey. Galaxies in these USS fields were identified in deep near-infrared observations, complete down to   K _s= 20  , using the IRIS2 instrument at the Anglo-Australian Telescope. We used the redshift distribution of   K _s < 20  galaxies taken from Cimatti et al. (2002) to constrain the correlation length r ₀. We find a strong correlation signal of galaxies with   K _s < 20  around our USS sample. A comoving correlation length   r ₀= 14.0 ± 2.8  h ⁻¹ Mpc  and γ= 1.98 ± 0.15 are derived in a flat cosmological model universe.
We compare our findings with those obtained in a cosmological N -body simulation populated with galform semi-analytic galaxies. We find that clusters of galaxies with masses in the range   M = 10^13.4–14.2  h ⁻¹ M_⊙  have a cluster–galaxy cross-correlation amplitude comparable to those found between the USS hosts and galaxies. These results suggest that distant radio galaxies are excellent tracers of galaxy overdensities and pinpoint the progenitors of present day rich clusters of galaxies.     

The redshift evolution of clustering in the Hubble Deep Field

We present a correlation function analysis for the catalogue of photometric redshifts obtained from the Hubble Deep Field image by Fernandez-Soto, Lanzetta & Yahil. By dividing the catalogue into redshift bins of width Δ z =0.4 we measured the angular correlation function w ( θ ) as a function of redshift up to z ∼4.8. From these measurements we derive the trend of the correlation length r ₀. We find that r ₀( z ) is roughly constant with look-back time up to z ≃2, and then increases to higher values at z ≳2.4. We estimate the values of r ₀, assuming ξ ( r , z )=[ r r ₀( z )]^{− γ} , γ =1.8 and various geometries. For Ω₀=1 we find r ₀( z =3)≃7.00±4.87  h ⁻¹ Mpc, in good agreement with the values obtained from analysis of the Lyman break galaxies.     

The three-point function in large-scale structure – I. The weakly non-linear regime in N-body simulations

This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, ξ and ζ , in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10  h ⁻¹ Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function   Q ₃∼ ζ / ξ ²  . For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ≃20 Mpc  h ⁻¹. On larger scales ξ goes to zero and the results are dominated by sampling errors. In more realistic models (such as the ΛCDM cosmology) deviations from the leading-order PT become important at smaller scales   r ≃10 Mpc  h ^-1  , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.     

The clustering of hot and cold IRAS galaxies: the redshift-space correlation function

We measure the autocorrelation function, ξ , of galaxies in the IRAS Point Source Catalogue galaxy redshift (PSC z ) survey and investigate its dependence on the far-infrared colour and absolute luminosity of the galaxies. We find that the PSC z survey correlation function can be modelled out to a scale of 10  h ⁻¹ Mpc as a power law of slope 1.30±0.04 and correlation length 4.77±0.20 . At a scale of 75  h ⁻¹ Mpc we find the value of J ₃ to be 1500±400 .
We also find that galaxies with higher 100 μm/60 μm flux ratio, corresponding to cooler dust temperatures, are more strongly clustered than warmer galaxies. Splitting the survey into three colour subsamples, we find that, between 1 and 10  h ⁻¹ Mpc, the ratio of ξ is a factor of 1.5 higher for the cooler galaxies compared with the hotter galaxies. This is consistent with the suggestion that hotter galaxies have higher star formation rates, and correspond to later-type galaxies which are less clustered than earlier types.
Using volume-limited subsamples, we find a weak variation of ξ as a function of absolute luminosity, in the sense that more luminous galaxies are less clustered than fainter galaxies. The trend is consistent with the colour dependence of ξ and the observed colour–luminosity correlation, but the large uncertainties mean that it has a low statistical significance.     

Variance and skewness in the FIRST survey

We investigate the large-scale clustering of radio sources in the FIRST 1.4-GHz survey by analysing the distribution function ( counts in cells ). We select a reliable sample from the the FIRST catalogue, paying particular attention to the problem of how to define single radio sources from the multiple components listed. We also consider the incompleteness of the catalogue. We estimate the angular two-point correlation function w (θ), the variance Ψ₂ and skewness Ψ₃ of the distribution for the various subsamples chosen on different criteria. Both w (θ) and Ψ₂ show power-law behaviour with an amplitude corresponding to a spatial correlation length of r ₀ ∼ 10  h ⁻¹Mpc. We detect significant skewness in the distribution, the first such detection in radio surveys. This skewness is found to be related to the variance through Ψ₃ =  S ₃(Ψ₂)^α, with α = 1.9 ± 0.1, consistent with the non-linear gravitational growth of perturbations from primordial Gaussian initial conditions. We show that the amplitude of variance and the skewness are consistent with realistic models of galaxy clustering.     

Continuous frequency spectrum of the global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star

We compute the continuous part of the ideal-magnetohydrodynamic (ideal-MHD) frequency spectrum of a polar mountain produced by magnetic burial on an accreting neutron star. Applying the formalism developed by Hellsten & Spies, extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfvén part and a cusp part. The eigenfunctions are chirped and anharmonic with an exponential envelope, and the eigenfrequencies cover the whole spectrum above a minimum ω_low. For equilibria with accreted mass  1.2 × 10⁻⁶≲ M _a/M_⊙≲ 1.7 × 10⁻⁴  and surface magnetic fields  10¹¹≲ B _*/G ≲ 10¹³, ω_low  is approximately independent of   B _*  , and increases with M _a. The results are consistent with the Alfvén spectrum excited in numerical simulations with the zeus-mp solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than ∼100 Hz. The implications for gravitational-wave searches for low-mass X-ray binaries are considered briefly.     

The angular correlation function of the ROSAT All-Sky Survey Bright Source Catalogue

We have derived the angular correlation function of a sample of 2096 sources detected in the ROSAT All-Sky Survey (RASS) Bright Source Catalogue, in order to investigate the clustering properties of active galactic nuclei (AGN) in the local Universe. Our sample is constructed by rejecting all known stars, as well as extended X-ray sources. Areas with | b |<30° and declination δ <−30° are also rejected owing to the high or uncertain neutral hydrogen absorption. Cross-correlation of our sample with the Hamburg/RASS optical identification catalogue suggests that the vast majority of our sources are indeed AGN. A 4.1 σ correlation signal between 0° and 8° was detected with w ( θ <8°)=2.5±0.6×10⁻². Assuming a two-point correlation function of the form w ( θ )=( θ θ ₀)^−0.8, we find θ ₀=0062. Deprojection on three dimensions, using Limber's equation, yields a spatial correlation length of r ₀≈6.0±1.6  h ⁻¹ Mpc. This is consistent with the AGN clustering results derived at higher redshifts in optical surveys and suggests a comoving model for the clustering evolution.     

Large-scale magnetic fields: galaxy two-point correlation function

We study the effect of large-scale tangled magnetic fields on the galaxy two-point correlation function in the redshift space. We show that (i) the magnetic field effects can be comparable to the gravity-induced clustering for present magnetic field strength   B ₀≃ 5 × 10⁻⁸ G  , (ii) the absence of this signal from the present data gives an upper bound   B ₀≲ 3 × 10⁻⁸ G  and (iii) the future data can probe the magnetic fields of  ≃10⁻⁸ G  . A comparison with other constraints on the present magnetic field shows that they are marginally compatible. However, if the magnetic fields corresponding to   B ₀≃ 10⁻⁸ G  existed at the last scattering surface, they will cause unacceptably large cosmic microwave background radiation anisotropies.     

On the transfer of radiation at asteroidal surfaces in relation to their orbit deflection – I

One of the methods discussed in deflecting the orbit of an Earth-colliding asteroid is the use of nuclear explosives. In assessing its feasibility, apart from political considerations, it is important to quantify how effective it is in orbit deflection. The transfer of radiation incident at the surface is governed by a non-linear diffusion equation. For low-yield explosions with a slab geometry ( S ₀≃10⁸ kJ μs⁻¹), the temperature at depth x and time t is well approximated by a similarity solution of the form T ( x , t )= T ₀ f (ξ), ξ= x/ ( T ⁿ ₀ t )^1/2, with T ₀ given by ( S ₀/σ)^1/4, where σ is the Stefan–Boltzmann constant, n is an index that specifies the radiation transfer and f (ξ) is the solution of a non-linear differential equation subject to the condition f (0)=1 and lim_ξ→∞ f (ξ)=0. For high-yield explosions ( S ₀≃10¹⁰ kJ μs⁻¹), numerical solutions to the non-linear diffusion equation can be obtained. These solutions have properties similar to the case of low-yield explosions. If the duration of the explosion is d ×10⁻⁸ s, where d is close to 3, the fraction of energy absorbed by the surface is found to be 7, 12 and 23 per cent for S ₀=10⁸, 10⁹ and 10¹⁰ kJ μs⁻¹ respectively.     

The cluster abundance in cosmic string models for structure formation

We use the present observed number density of large X-ray clusters to constrain the amplitude of matter density perturbations induced by cosmic strings on the scale of 8  h ⁻¹ Mpc ( σ ₈), in both open cosmologies and flat models with a non-zero cosmological constant. We find a slightly lower value of σ ₈ than that obtained in the context of primordial Gaussian fluctuations generated during inflation. This lower normalization of σ ₈ results from the mild non-Gaussianity on cluster scales, where the one-point probability distribution function is well approximated by a χ ² distribution and thus has a longer tail than a Gaussian distribution. We also show that σ ₈ normalized using cluster abundance is consistent with the COBE normalization.     

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.     

Seismological studies of ZZ Ceti stars – II. Application to the ZZ Ceti class

We used the detected pulsation modes and adiabatic pulsation models to do seismology of the class of ZZ Ceti stars and measure the H layer mass for 83 stars. We found the surface hydrogen layer to be within the range  10^−9.5≥ M _H/ M _*≥ 10⁻⁴  , with an average of   M _H/ M _*= 10^−6.3  , which is thinner than the predicted value of   M _H/ M _*= 10⁻⁴  , indicating that the stars lose more mass during their evolution than previously expected. These results are preliminary and do not include the possible effects of realistic C/O profiles on the fits.     

Molecular hydrogen in damped Lyα systems: clues to interstellar physics at high redshift

In order to interpret H₂ quasar absorption-line observations of damped Lyα systems (DLAs) and subDLAs, we model their H₂ abundance as a function of dust-to-gas ratio, including H₂ self-shielding and dust extinction against dissociating photons. Then, we constrain the physical state of the gas by using H₂ data. Using H₂ excitation data for DLAs with H₂ detections, we derive a gas density  1.5 ≲ log n (cm⁻³) ≲ 2.5  , temperature  1.5 ≲ log T (K) ≲ 3  , and an internal ultraviolet (UV) radiation field (in units of the Galactic value)  0.5 ≲ log χ≲ 1.5  . We then find that the observed relation between the molecular fraction and the dust-to-gas ratio of the sample is naturally explained by the above conditions. However, it is still possible that H₂ deficient DLAs and subDLAs with H₂ fractions less than  ∼10⁻⁶  are in a more diffuse and warmer state. The efficient photodissociation by the internal UV radiation field explains the extremely small H₂ fraction  (≲10⁻⁶)  observed for  κ≲ 1/30  (κ is the dust-to-gas ratio in units of the Galactic value); H₂ self-shielding causes a rapid increase in, and large variations of, H₂ abundance for  κ≳ 1/30  . We finally propose an independent method to estimate the star formation rates of DLAs from H₂ abundances; such rates are then critically compared with those derived from other proposed methods. The implications for the contribution of DLAs to the cosmic star formation history are briefly discussed.     

Cosmic microwave background anisotropies resulting from feedback-regulated inhomogeneous reionization

We calculate the secondary anisotropies in the cosmic microwave background (CMB) produced by inhomogeneous reionization from simulations in which the effects of radiative and stellar feedback effects on galaxy formation have been included. This allows us to determine self-consistently the beginning ( z _i≈30), the duration ( δz ≈20) and the (non-linear) evolution of the reionization process for a critical density cold dark matter (CDM) model. In addition, from the simulated spatial distribution of ionized regions, we are able to calculate the evolution of the two-point ionization correlation function, C _χ , and obtain the power spectrum of the anisotropies, C _ℓ, in the range 5000<ℓ<10⁶. The power spectrum has a broad maximum around ℓ≈30 000, where it reaches the value 2×10⁻¹². We also show that the ionization correlation function C _χ is not Gaussian, but at separation angles θ ≲10⁻⁴ rad it can be approximated by a modified Lorentzian shape; at larger separations an anticorrelation signal is predicted for both C _χ and C ( θ ). Detection of signals as above will be possible with future millimetre-wavelength interferometers like the Atacama Large Millimeter Array (ALMA) , which appears as an optimum instrument to search for signatures of inhomogeneous reionization.