The matter power spectrum from the Lyα forest: an optical depth estimate

We measure the matter power spectrum from 31 Lyα spectra spanning the redshift range of 1.6–3.6. The optical depth, τ, for Lyα absorption of the intergalactic medium is obtained from the flux using the inversion method of Nusser & Haehnelt. The optical depth is converted to density by using a simple power-law relation,  τ∝ (1 +δ)^α  . The non-linear 1D power spectrum of the gas density is then inferred with a method that makes simultaneous use of the one- and two-point statistics of the flux and compared against theoretical models with a likelihood analysis. A cold dark matter model with standard cosmological parameters fits the data well. The power-spectrum amplitude is measured to be (assuming a flat Universe),  σ₈= (0.92 ± 0.09) × (Ω_m/0.3)^−0.3  , with α varying in the range of 1.56–1.8 with redshift. Enforcing the same cosmological parameters in all four redshift bins, the likelihood analysis suggests some evolution in the temperature–density relation and the thermal smoothing length of the gas. The inferred evolution is consistent with that expected if reionization of He  ii occurred at   z ∼ 3.2  . A joint analysis with the Wilkinson Microwave Anisotropy Probe results together with a prior on the Hubble constant as suggested by the Hubble Space Telescope key project data, yields values of Ω_m and σ₈ that are consistent with the cosmological concordance model. We also perform a further inversion to obtain the linear 3D power spectrum of the matter density fluctuations.     

On the distribution of haloes, galaxies and mass

The stochasticity in the distribution of dark haloes in the cosmic density field is reflected in the distribution function   P _V ( N _h| δ _m)  , which gives the probability of finding N _h haloes in a volume V with mass density contrast δ _m. We study the properties of this function using high-resolution N -body simulations, and find that   P _V ( N _h| δ _m)  is significantly non-Poisson. The ratio between the variance and the mean goes from ∼1 (Poisson) at  1+ δ _m≪1  to <1 (sub-Poisson) at  1+ δ _m∼1  to >1 (super-Poisson) at  1+ δ _m≫1  . The mean bias relation is found to be well described by halo bias models based on the Press–Schechter formalism. The sub-Poisson variance can be explained as a result of halo exclusion, while the super-Poisson variance at high δ _m may be explained as a result of halo clustering. A simple phenomenological model is proposed to describe the behaviour of the variance as a function of δ _m. Galaxy distribution in the cosmic density field predicted by semi-analytic models of galaxy formation shows similar stochastic behaviour. We discuss the implications of the stochasticity in halo bias to the modelling of higher order moments of dark haloes and of galaxies.     

The first high-amplitude δ Scuti star in an eclipsing binary system

Consider radar ranging of a distant galaxy in a Friedman–Lemaître cosmological model. In this model the comoving coordinate of the galaxy is constant; hence, the equations of null geodesics for photons travelling to the distant galaxy and back imply Here, τ_e, τ_r and τ_o are, respectively, the times of emission, reflection and observation of the reflected photons, and a (τ) is the scalefactor. Since the Universe is expanding, a (τ) is a monotonically increasing function, so the return traveltime, τ_o−τ_r, must be greater than the forward traveltime, τ_r−τ_e. Clearly, space expands, and on their way back, the photons must travel a longer distance! This paper explains why this argument for the Expansion of Space (EoS) is wrong. We argue that, unlike the expansion of the cosmic substratum, the EoS is unobservable. We therefore propose to apply to it – just like to the ether – Ockham's razor.     

Photoionized Hβ emission in NGC 5548: it breathes!

Emission-line regions in active galactic nuclei (AGNs) and other photoionized nebulae should become larger in size when the ionizing luminosity increases. This 'breathing' effect is observed for the Hβ emission in NGC 5548 by using Hβ and optical continuum light curves from the 13-yr (1989–2001) AGN Watch monitoring campaign. To model the breathing, we use two methods to fit the observed light curves in detail: (i) parametrized models and, (ii) the memecho reverberation-mapping code. Our models assume that optical continuum variations track the ionizing radiation, and that the Hβ variations respond with time-delays τ due to light travel-time. By fitting the data using a delay-map  Ψ(τ, F _c)  that is allowed to change with continuum flux F _c, we find that the strength of the Hβ response decreases and the time-delay increases with ionizing luminosity. The parametrized breathing models allow the time-delay and the Hβ flux to depend on the continuum flux so that,  τ∝ F ^β_c  and   F _Hβ∝ F ^α_c  . Our fits give  0.1 < β < 0.46  and  0.57 < α < 0.66. α  is consistent with previous work by Gilbert and Peterson, and Goad, Korista and Knigge. Although we find β to be flatter than previously determined by Peterson et al. using cross-correlation methods, it is closer to the predicted values from recent theoretical work by Korista and Goad.     

A shallow though extensive H2 2.122-μm imaging survey of Taurus–Auriga–Perseus – I. NGC 1333, L1455, L1448 and B1

We discuss wide-field near-infrared (near-IR) imaging of the NGC 1333, L1448, L1455 and B1 star-forming regions in Perseus. The observations have been extracted from a much larger narrow-band imaging survey of the Taurus–Auriga–Perseus complex. These H₂ 2.122-μm observations are complemented by broad-band K imaging, mid-IR imaging and photometry from the Spitzer Space Telescope , and published submillimetre CO   J = 3–2  maps of high-velocity molecular outflows. We detect and label 85 H₂ features and associate these with 26 molecular outflows. Three are parsec-scale flows, with a mean flow lobe length exceeding 11.5 arcmin. 37 (44 per cent) of the detected H₂ features are associated with a known Herbig–Haro object, while 72 (46 per cent) of catalogued HH objects are detected in H₂ emission. Embedded Spitzer sources are identified for all but two of the 26 molecular outflows. These candidate outflow sources all have high near-to-mid-IR spectral indices (mean value of  α∼ 1.4  ) as well as red IRAC 3.6–4.5 μm and IRAC/MIPS 4.5–24.0 μm colours: 80 per cent have [3.6]–[4.5] > 1.0 and [4.5]–[24] > 1.5. These criteria – high α and red [4.5]–[24] and [3.6]–[4.5] colours – are powerful discriminants when searching for molecular outflow sources. However, we find no correlation between α and flow length or opening angle, and the outflows appear randomly orientated in each region. The more massive clouds are associated with a greater number of outflows, which suggests that the star formation efficiency is roughly the same in each region.     

Mixed three-point correlation functions of the non-linear integrated Sachs–Wolfe effect and their detectability

In this paper, I investigate the family of mixed three-point correlation functions  〈τ ^q γ^{3− q} 〉, q = 0, 1, 2  , between the integrated Sachs–Wolfe (iSW) temperature perturbation τ and the galaxy overdensity γ as a tool for detecting the gravitational interaction of cosmic microwave background (CMB) photons with the potentials of non-linearly evolving cosmological structures. Both the iSW-effect and the galaxy overdensity are derived in hyperextended perturbation theory to second order and I emphasize the different parameter sensitivities of the linear and non-linear iSW-effect. I examine the configuration dependence of the relevant bispectra, quantify their sensitivities and discuss their degeneracies with respect to the cosmological parameters  Ω_m, σ₈, h   and the dark energy equation of state parameter w . I give detection significances for combining Planck CMB data and galaxy sample of a survey like Dark UNiverse Explorer (DUNE) by using a quadratic approximation for the likelihood with Λ cold dark matter (ΛCDM) as the fiducial cosmology: the combination of Planck with DUNE should be able to reach a cumulative signal-to-noise ratio of ≃0.6 for the bispectrum  〈τγ²〉  up to ℓ= 2000, which is too weak to be detected. The most important noise source is the primary CMB fluctuations as the Poisson noise in the galaxy number density is almost negligible for a survey like DUNE.     

Microwave polarization in the direction of galaxy clusters induced by the CMB quadrupole anisotropy

Electron scattering induces a polarization in the cosmic microwave background (CMB) signal measured in the direction of a galaxy cluster owing to the presence of a quadrupole component in the CMB temperature distribution. Measuring the polarization towards distant clusters provides the unique opportunity to observe the evolution of the CMB quadrupole at moderate redshifts, z ∼0.5–3. We demonstrate that for the local cluster population the polarization degree will depend on the cluster celestial position. There are two extended regions in the sky, which are opposite to each other, where the polarization is maximal, ∼0.1( τ /0.02) μK in the Rayleigh–Jeans part of the CMB spectrum ( τ being the Thomson optical depth across the cluster). This value exceeds the polarization introduced by the cluster transverse peculiar motion if v _t<1300 km s⁻¹. One can hope to detect this small signal by measuring a large number of clusters, thereby effectively removing the systematic contribution from other polarization components produced in clusters. These polarization effects, which are of the order of ( v _t c )² τ , ( v _t c ) τ ² and ( kT _e m _e c ²) τ ², as well as the polarization owing to the CMB quadrupole, were previously given by Sunyaev and Zel'dovich for the Rayleigh–Jeans part of the spectrum. We fully confirm their earlier results and present exact frequency dependences for all these effects. The polarization degree is considerably higher in the Wien region.     

Excitation of oscillation modes by tides in close binaries: constraints on stellar and orbital parameters

The parameter space favourable for the resonant excitation of free oscillation modes by dynamic tides in close binary components is explored using qualitative considerations to estimate the order of magnitude of the tidal force and the frequency range covered by the tidally induced oscillations. The investigation is valid for slowly rotating stars with masses in the interval between 2 and  20 M_⊙  , and an evolutionary stage ranging from the beginning to the end of the main sequence. Oscillation modes with eigenfrequencies of the order of five times the inverse of the dynamical time-scale  τ_dyn  of the star, i.e. the lowest-order p -modes, the f -mode and the lowest-order g ⁺-modes, are found to be outside the favourable parameter space since their resonant excitation requires orbital eccentricities that are too high for the binary to stay detached when the components pass through the periastron of their relative orbit. Resonances between dynamic tides and g ⁺-modes with frequencies of the order of half of the inverse of the dynamical time-scale of the star on the other hand are found to be favourable for orbital periods up to  ∼200τ_dyn  , provided that the binary mass ratio q is larger than 1/3, and the orbital eccentricity e is larger than ∼0.25. This favourable range comes down to orbital periods of up to 5–12 d in the case of  2–20 M_⊙  zero-age main-sequence binary components, and orbital periods of up to 21–70 d in the case of terminal main-sequence binary components.     

Observation of multiple sausage oscillations in cool post-flare loop

Using simultaneous high spatial (1.3 arcsec) and temporal (5 and 10 s) resolution Hα observations from the 15 cm Solar Tower Telescope at Aryabhatta Research Institute of Observational Sciences (ARIES), we study the oscillations in the relative intensity to explore the possibility of sausage oscillations in the chromospheric cool post-flare loop. We use the standard wavelet tool, and find the oscillation period of ≈587 s near the loop apex, and ≈349 s near the footpoint. We suggest that the oscillations represent the fundamental and the first harmonics of the fast-sausage waves in the cool post-flare loop. Based on the period ratio   P ₁/ P ₂∼1.68  , we estimate the density scaleheight in the loop as ∼17 Mm. This value is much higher than the equilibrium scaleheight corresponding to Hα temperature, which probably indicates that the cool post-flare loop is not in hydrostatic equilibrium. Seismologically estimated Alfvén speed outside the loop is  ∼300–330  km s⁻¹  . The observation of multiple oscillations may play a crucial role in understanding the dynamics of lower solar atmosphere, complementing such oscillations already reported in the upper solar atmosphere (e.g. hot flaring loops).     

Revisiting the baryon fractions of galaxy clusters: a comparison with WMAP 3-yr results

The universal baryonic mass fraction  (Ω_b/Ω_m)  can be sensitively constrained using X-ray observations of galaxy clusters. In this paper, we compare the baryonic mass fraction inferred from measurements of the cosmic microwave background with the gas mass fractions ( f _gas) of a large sample of clusters taken from the recent literature. In systems cooler than 4 keV, f _gas declines as the system temperature decreases. However, in higher temperature systems, f _gas( r ₅₀₀) converges to  ≈(0.12 ± 0.02)( h /0.72)^−1.5  , where the uncertainty reflects the systematic variations between clusters at r ₅₀₀. This is significantly lower than the maximum-likelihood value of the baryon fraction from the recently released Wilkinson Microwave Anisotropy Probe ( WMAP ) 3-yr results. We investigate possible reasons for this discrepancy, including the effects of radiative cooling and non-gravitational heating, and conclude that the most likely solution is that Ω_m is higher than the best-fitting WMAP value (we find  Ω_m= 0.36^+0.11_−0.08  ), but consistent at the 2σ level. Degeneracies within the WMAP data require that σ₈ must also be greater than the maximum likelihood value for consistency between the data sets.     

Probing the evolution of early-type galaxies using multicolour number counts and redshift distributions

We investigate pure luminosity evolution models for early-type (elliptical and S0) galaxies (i.e. no number density change or morphological transition), and examine whether these models are consistent with observed number counts in the B , I and K bands, and redshift distributions of two samples of faint galaxies selected in the I and K bands. The models are characterized by the star formation time-scale τ _SF and the time t _gw when the galactic wind starts to blow, in addition to several other conventional parameters. We find that the single-burst model ( τ _SF=0.1 Gyr and t _gw=0.353 Gyr), which is known to reproduce the photometric properties of early-type galaxies in clusters, is inconsistent with the redshift distributions of early-type galaxies in the field environment, owing to overpredictions of the number of galaxies at z ≳1.4 even with strong extinction which is at work until t _gw. In order for dust extinction to be more effective, we treat τ _SF and t _gw as free parameters, and find that models with τ _SF≳0.5 Gyr and t _gw>1.0 Gyr can be made consistent with both the observed redshift distributions and the number counts, if we introduce strong extinction [ E ( B − V )≥1 as a peak value]. These results suggest that early-type galaxies in the field environment do not have the same evolutionary history as described by the single-burst model.     

Self-similar solutions for the dynamical condensation of a radiative gas layer

A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow with a net cooling rate per unit volume and time  ∝ρ² T ^α  , where  ρ,  T   and α are the density, temperature and a free parameter, respectively. Given α, a family of self-similar solutions with one parameter η is found in which the central density and pressure evolve as follows:  ρ( x = 0, t ) ∝ ( t _c− t )^{−η/(2−α)}  and   P ( x = 0, t ) ∝ ( t _c− t )^{(1−η)/(1−α)}  , where t _c is the epoch at which the central density becomes infinite. For  η∼ 0  the solution describes the isochoric mode, whereas for  η∼ 1  the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for  0 < η < 1  . No self-similar solution is found for  α > 1  . We compare the obtained self-similar solutions with the results of one-dimensional hydrodynamical simulations. In a converging flow, the results of the numerical simulations agree well with the self-similar solutions in the high-density limit. Our self-similar solutions are applicable to the formation of interstellar clouds (H  i clouds and molecular clouds) by thermal instability.     

Variability associated with α accretion disc theory for standard and advection-dominated discs

The α turbulent viscosity formalism for accretion discs must be interpreted as a mean field theory, modelling a steady state only on spatial or time-scales greater than those of the turbulence. The extent of the scale separation determines the relative precision error (RPE) of the predicted luminosity L _ν. Turbulence and the use of α implies that (1) field line stretching gives a magnetic pressure  α²/6 of the total pressure generally, and a one-to-one relation between α and the pressure ratio for thin discs, and (2) large turbulent scales in advection-dominated accretion flows (ADAFs) predict a lower L _ν precision than thin discs for a given observation duration and central mass. The allowed variability (or RPE) at frequency ν increases with the size of the contributing region. For X-ray binary ADAFs, the RPE ∼ 5 per cent at R  ≤ 1000 Schwarzchild radii ( R _s) for averages over  1000 s. However, current data for galaxies like NGC 4258 and M87 give RPEs in L _ν of 50–100 per cent even at R  ≤ 100  R _S. More data are required, but systematic deviations from ADAF predictions are more significant than random deviations, and may constrain properties of the turbulence, the accretion mode, the assumption of a steady state or the accretion rate.     

Detection of OH and wide H i absorption toward B0218+357

Large-scale polarization of the cosmic microwave background measured by the WMAP satellite requires a mean optical depth to Thomson scattering,  τ_e∼ 0.17  . The reionization of the Universe must therefore have begun at relatively high redshift. We have studied the reionization process using supercomputer simulations of a large and representative region of a universe which has cosmological parameters consistent with the WMAP results (  Ω_m= 0.3, Ω_Λ= 0.7, h = 0.7, Ω_b= 0.04, n = 1  and  σ₈= 0.9  ). Our simulations follow both the radiative transfer of ionizing photons and the formation and evolution of the galaxy population which produces them. A previously published model with ionizing photon production as expected for zero-metallicity stars distributed according to a standard stellar initial mass function (IMF) (10⁶¹ photons per unit solar mass of formed stars) and with a moderate photon escape fraction from galaxies (5 per cent), produces  τ_e= 0.104  , which is within 1.0 to  1.5σ  of the 'best' WMAP value. Values of up to 0.16 can be produced by taking larger escape fractions or a top-heavy IMF. The data do not require a separate populations of 'miniquasars' or of stars forming in objects with total masses below  10⁹ M_⊙  . Reconciling such early reionization with the observed Gunn–Peterson troughs in   z > 6  quasars may be challenging. Possible resolutions of this problem are discussed.     

A numerical comparison of theories of violent relaxation

Using N -body simulations with a large set of massless test particles, we compare the predictions of two theories of violent relaxation, the well-known Lynden-Bell theory and the more recent theory by Nakamura. We derive 'weakened' versions of both the theories in which we use the whole equilibrium coarse-grained distribution function     as a constraint instead of the total energy constraint. We use these weakened theories to construct expressions for the conditional probability   K_i (τ)  that a test particle initially at the phase-space coordinate τ would end-up in the i th macro-cell at equilibrium. We show that the logarithm of the ratio   R_ij (τ) ≡ K_i (τ)/ K_j (τ)  is directly proportional to the initial phase-space density   f ₀(τ)  for the Lynden-Bell theory and inversely proportional to   f ₀(τ)  for the Nakamura theory. We then measure   R_ij (τ)  using a set of N -body simulations of a system undergoing a gravitational collapse to check the validity of the two theories of violent relaxation. We find that both the theories are at odds with the numerical results, both qualitatively and quantitatively.     

On the measurement precision of solar p-mode eigenfrequencies

We make use of 3456 d of observations of the low-ℓ p-mode oscillations of the Sun in order to study the evolution over time of the measurement precision of the radial eigenfrequencies. These data were collected by the ground-based Birmingham Solar-Oscillations Network (BiSON) between 1991 January and 2000 June. When the power spectrum of the complete time series is fitted, the analysis yields frequency uncertainties that are close to those expected from the returned coherence times of the modes. The slightly elevated levels compared with the prediction appear to be consistent with a degradation of the signal-to-noise ratio in the spectrum that is the result of the influence of the window function of the observations (duty cycle 71 per cent). The fractional frequency precision reaches levels of a several parts in 10⁶ for many of the modes. The corresponding errors reported from observations made by the GOLF instrument on board the ESA/NASA SOHO satellite, when extrapolated to the length of the BiSON data set, are shown to be (on average) about ∼25 per cent smaller than their BiSON counterparts owing to the uninterrupted nature of the data from which they were derived.
An analysis of the BiSON data in contiguous segments of different lengths, T , demonstrates that the frequency uncertainties scale as T ^−1/2. This is to be expected in the regime where the coherence (life) times of the modes, τ _{n ℓ}, are smaller than the observing time T (the 'oversampled' regime). We show that mode detections are only now beginning to encroach on the 'undersampled' regime (where   T < τ _{n ℓ})  .     

Towards a precision cosmology from starburst galaxies at z > 2

This work investigates the use of a well-known empirical correlation between the velocity dispersion, metallicity and luminosity in Hβ of nearby H  ii galaxies to measure the distances to H  ii -like starburst galaxies at high redshifts. This correlation is applied to a sample of 15 starburst galaxies with redshifts between   z = 2.17  and   z = 3.39  to constrain  Ω_m  , using data available from the literature. A best-fitting value of  Ω_m= 0.21^+0.30_−0.12  in a Λ-dominated universe and of  Ω_m= 0.11^+0.37_−0.19  in an open universe is obtained. A detailed analysis of systematic errors, their causes and their effects on the values derived for the distance moduli and  Ω_m  is carried out. A discussion of how future work will improve constraints on  Ω_m  by reducing the errors is also presented.     

A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric  α²– Ω  dynamo model is derived to explore the characteristics of the axisymmetric  ( m = 0)  and the first non-axisymmetric  ( m = 1)  modes and to provide a theoretical basis with which to explain the 'active longitude', 'flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the  α²–Ω  and the  α–Ω  models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.     

Principal components in active galactic nuclei variability data and the estimation of the flux contributions from different components

It has been found that the near-infrared flux variations of Seyfert galaxies satisfy relations of the form   F_i ≈α _{i j} +β _{i j} F_j   , where F_i , F_j are the fluxes in filters i and j ; and  α _{i , j} , β _{i , j}   are constants. These relations have been used to estimate the constant contributions of the non-variable underlying galaxies. The paper attempts a formal treatment of the estimation procedure, allowing for the possible presence of a third component, namely non-variable hot dust. In an analysis of a sample of 38 Seyfert galaxies, inclusion of the hot dust component improves the model fit in approximately half the cases. All derived dust temperatures are below 300 K, in the range 540–860 K or above 1300 K. A noteworthy feature is the estimation of confidence intervals for the component contributions: this is achieved by bootstrapping. It is also pointed out that the model implies that such data could be fruitfully analysed in terms of principal components.