Cluster AgeS Experiment (CASE): RR Lyrae stars from the globular cluster ω Centauri as standard candles

New photometry of RRab and RRc stars in ω Centauri is used to calibrate their absolute magnitudes M_V as a function of (a) metallicity and (b) the Fourier parameters of light curves in the V band. The zero point of both calibrations relies on the distance modulus to the cluster derived earlier by the Cluster AgeS Experiment (CASE) project based on observations of the detached eclipsing binary OGLE GC17. For RRab variables, we obtained a relation of   M_V = (0.26 ± 0.08)[ Fe/H ] + (0.91 ± 0.13)  . A dereddened distance modulus to the Large Magellanic Cloud (LMC) based on that formula is  μ₀= 18.56 ± 0.14 mag  . The second calibration of M_V , which is based on Fourier coefficients of decomposed light curves, results in the LMC distance of  μ₀= 18.51 ± 0.07 mag  .     

On the mixing rules for astrophysical inhomogeneous grains

We present the computation of effective refractive coefficients for inhomogeneous two-component grains with three kinds of inclusions with   m _incl= 3.0 + 4.0i, 2.0 + 1.0i, 2.5 + 0.0001i  and a matrix with   m_m = 1.33 + 0.01i  for 11 volume fractions of inclusions from 0 to 50 per cent and wavelengths  λ= 0.5  , 1.0, 2.0 and 5.0 μm. The coefficients of extinction for these grains have been computed using a discrete dipole approximation. Computation of the extinction by the same method for grains composed of a matrix material with randomly embedded inclusions has been carried out for different volume fractions of inclusions. A comparison of extinction coefficients obtained for both models of grain material allows one to choose the best mixing rule for a mixture. In cases of inclusions with   m _incl= 2.0 + 1.0i  and 2.5 + 0.0001i the best fit for the whole wavelength range and volume fractions of inclusions from 0 to 50 per cent has been obtained for the Lichtenecker mixing rule. In the case of   m _incl= 3.0 + 4.0i  the fit for the whole wavelength range and volume fractions of inclusions from 0 to 50 per cent is not very significant but the best fit has been obtained for the Hanai rule. For volume fractions of inclusions from 0 to 15 per cent a very good fit has been obtained for the whole wavelength range for Rayleigh and Maxwell-Garnett mixing rules.     

Magnetic field, dust and axisymmetrical mass loss on the asymptotic giant branch

I propose a mechanism for axisymmetrical mass loss on the asymptotic giant branch (AGB) that may account for the axially symmetric structure of elliptical planetary nebulae. The proposed model operates for slowly rotating AGB stars, having angular velocities in the range of 10⁻⁴ω _Kep  ω  10⁻² ω_Kep, where ω_Kep is the equatorial Keplerian angular velocity. Such angular velocities could be gained from a planet companion of mass  0.1  M _Jupiter, which deposits its orbital angular momentum to the envelope at late stages, or even from single stars that are fast rotators on the main sequence. The model assumes that dynamo magnetic activity results in the formation of cool spots, above which dust forms much more easily. The enhanced magnetic activity towards the equator results in a higher dust formation rate there, and hence higher mass-loss rate. As the star ascends the AGB, both the mass-loss rate and magnetic activity increase rapidly, and hence the mass loss becomes more asymmetrical, with higher mass-loss rate closer to the equatorial plane.     

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.     

Theoretical calculations of the H i, He i and He ii free–bound continuous emission spectra

We present coefficients for the calculation of the continuous emission spectra of H  i , He  i and He  ii due to electron–ion recombination. Coefficients are given for photon energies from the first ionization threshold for each ion to the   n = 20  threshold of hydrogen  (36.5 μm)  , and for temperatures  100 ≤  T ≤ 10⁵ K  . The emission coefficients for He  i are derived from accurate ab initio photoionization data. The coefficients are scaled in such a way that they may be interpolated by a simple scheme with uncertainties less than 1 per cent in the whole temperature and wavelength domain. The data are suitable for incorporation into photoionization/plasma codes and should aid with the interpretation of spectra from the very cold ionized gas phase inferred to exist in a number of gaseous clouds.     

LO Pegasi: an investigation of multiband optical polarization

We present BVR polarimetric study of the cool active star LO Pegasi (LO Peg) for the first time. LO Peg was found to be highly polarized among the cool active stars. Our observations yield average values of polarization in LO Peg:   P_B = 0.387 ± 0.004 per cent, θ_B= 88°± 1°; P_V = 0.351 ± 0.004 per cent, θ_V= 91°± 1°  and   P_R = 0.335 ± 0.003 per cent, θ_R= 91°± 1°  . Both the degree of polarization and the position angle are found to be variable. The semi-amplitude of the polarization variability in B, V and R bands is found to be  0.18 ± 0.02, 0.13 ± 0.01  and  0.10 ± 0.02  per cent, respectively. We suggest that the levels of polarization observed in LO Peg could be the result of scattering of an anisotropic stellar radiation field by an optically thin circumstellar envelope or scattering of the stellar radiation by prominence-like structures.     

Anomalous mixing of the w2Po3/2 and x6Po3/2 levels in Fe ii

The neighbouring lines a ⁶D_5/2– x ⁶P^o_3/2 (1272.617 Å) and a ⁶D_5/2– w ²P^o_3/2 (1272.657 Å) have been observed in the UV spectrum of χ Lupi to be of comparable intensity. The latter, Δ S  = 2, transition would be expected to be very weak. The two upper states should display negligible mixing. We give a detailed, quantitative discussion of how the two upper states are in fact strongly mixed through their mixing with 3d⁶(³D)4p ⁴P^o_3/2, and hence we explain the relative strengths of the two UV lines.     

Wilkinson Microwave Anisotropy Probe 5-yr constraints on fnl with wavelets

We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr cosmic microwave background (CMB) temperature anisotropy data maps. We use several third-order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter f _nl using well-motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q , V , and W frequency bands. We use the KQ 75 mask recommended by the WMAP team which masks out 28 per cent of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients, we compute the third order estimators which are used to perform a  χ²  analysis. The  χ²  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f _nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f _nl parameter is constrained to  −8 < f _nl < +111  at 95 per cent confidence level (CL) for the combined   V + W   map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of  Δ f _nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.     

Principal-component analysis of the cosmic microwave background anisotropies: revealing the tensor degeneracy

A principal-component analysis of cosmic microwave background (CMB) anisotropy measurements is used to investigate degeneracies among cosmological parameters. The results show that a degeneracy with tensor modes – the 'tensor degeneracy'– dominates uncertainties in estimates of the baryon and cold dark matter densities,   ω _b=Ω_b  h ²  ,   ω _c=Ω_c  h ²  , ¹ from an analysis of CMB anisotropies alone. The principal-component analysis agrees well with a maximum-likelihood analysis of the observations, identifying the main degeneracy directions and providing an impression of the effective dimensionality of the parameter space.     

Consequences for some dark energy candidates from the type Ia supernova SN 1997ff

We examine the status of various dark energy models in light of the recently observed SN 1997ff at   z ≈1.7  . The modified data still fit a pure cosmological constant Λ or a quintessence with an equation of state similar to that of Λ. The kinematical Λ models,  Λ∼ S ^-2  and  Λ∼ H ²  , also fit the data reasonably well and require less dark energy density (hence more matter energy density) than is required by the constant Λ model. However, the model  Λ∼ S ^-2  with low energy density becomes unphysical as it cannot accommodate higher redshift objects.
We also examine an alternative explanation of the data, namely the absorption by the intervening whisker-like dust, and find that the quasi-steady state (QSS) model and the Friedmann–Robertson–Walker (FRW) model  Ω_m0=0.33  without any dark energy also fit the data reasonably well.
We notice that the addition of SN 1997ff to the old data has worsened the fit to most of the models, except a closed FRW model with a constant Λ and a closed quintessence model with   ω _φ =-0.82  , and the models have started departing from each other as we go above   z =1  . However, to make a clear discrimination possible, a few more supernovae with   z >1  are required.
We have also calculated the age of the Universe in these models and find that, in the models with a constant Λ, the expansion age is uncomfortably close to the age of the globular clusters. Quintessence models show even lower age. The kinematical Λ models are, however, interesting in this connection (especially the model  Λ∼ H ²)  , as they give a remarkably large age of the Universe.     

Structural parameters of Mayall II = G1 in M31

Mayall II = G1 is one of the most luminous globular clusters (GCs) known in M31. New deep, high-resolution observations with the Advanced Camera for Surveys on the Hubble Space Telescope are used to provide accurate photometric data to the smallest radii yet. In particular, we present the precise variation of ellipticity and position angle, and of surface brightness for the core of the object. Based on these accurate photometric data, we redetermine the structural parameters of G1 by fitting a single-mass isotropic King model. We derive a core radius,   r _c= 0.21 ± 0.01  arcsec (= 0.78 ± 0.04  pc)  , a tidal radius,   r _t= 21.8 ± 1.1  arcsec (= 80.7 ± 3.9  pc)  , and a concentration index   c = log ( r _t/ r _c) = 2.01 ± 0.02  . The central surface brightness is 13.510 mag arcsec⁻². We also calculate the half-light radius, at   r _h= 1.73 ± 0.07  arcsec (= 6.5 ± 0.3  pc)  . The results show that, within 10 core radii, a King model fits the surface brightness distribution well. We find that this object falls in the same region of the   M_V   versus  log   R _h  diagram as ω Centauri, M54 and NGC 2419 in the Milky Way. All three of these objects have been claimed to be the stripped cores of now defunct dwarf galaxies. We discuss in detail whether GCs, stripped cores of dwarf spheroidals and normal dwarf galaxies form a continuous distribution in the   M_V   versus  log   R _h  plane, or if GCs and dwarf spheroidals constitute distinct classes of objects; we present arguments in favour of this latter view.     

Gravitational lensing of anisotropic sources

In strong gravitational lensing, the multiple images we see correspond to light rays that leave the source in slightly different directions. If the source emission is anisotropic, the images may differ from conventional lensing predictions (which assume isotropy). To identify scales on which source anisotropy may be important, we study the angle δ between the light rays emerging from the source, for different lensing configurations. If the lens has a power-law profile   M ∝ R ^γ  , the angle δ initially increases with lens redshift and then either diverges (for a steep profile  γ < 1  ), remains constant (for an isothermal profile  γ= 1  ), or vanishes (for a shallow profile  γ > 1  ) as   z _l→ z _s  . The scaling with lens mass is roughly  δ∝ M ^1/(2−γ)  . The results for an Navarro–Frenk–White (NFW) profile are qualitatively similar to those for a shallow power law, with δ peaking at about half the redshift of the source (not half the distance). In practice, beaming could modify the statistics of beamed sources lensed by massive clusters: for an opening angle  θ_jet  , there is a probability as high as   P ∼ 0.02–0.07(θ_jet/0.5°)⁻¹  that one of the lensed images may be missed (for  2 ≲ z _s≲ 6  ). Differential absorption within active galactic nuclei (AGNs) could modify the flux ratios of AGNs lensed by clusters; a sample of AGNs lensed by clusters could provide further constraints on the sizes of absorbing regions. Source anisotropy is not likely to be a significant effect in galaxy-scale strong lensing.     

Experimental and theoretical radiative decay rates for highly excited ruthenium atomic levels and the solar abundance of ruthenium

The solar photospheric abundance of ruthenium is revised on the basis of a new set of oscillator strengths derived for Ru  i transitions with wavelengths in the spectral range 2250–4710 Å. The new abundance value (in the usual logarithmic scale where the solar hydrogen abundance is equal to 12.00),   A _Ru= 1.72 ± 0.10  , is in agreement with the most recent meteoritic result,   A _Ru= 1.76 ± 0.03  . The accuracy of the transition probabilities, obtained using a relativistic Hartree–Fock model including core-polarization effects, has been assessed by comparing the theoretical lifetimes with previous experimental results. A comparison is also made with new measurements performed in this work by the time-resolved laser-induced fluorescence spectroscopy for 10 highly excited odd-parity levels of Ru  i .     

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.     

New limits on the possible variation of physical constants

Recent detections of high-redshift absorption by both atomic hydrogen and molecular gas in the radio spectra of quasars have provided a powerful tool for measuring possible temporal and spatial variations of physical 'constants' in the universe.
We compare the frequency of high-redshift hydrogen 21-cm absorption with that of associated molecular absorption in two quasars to place new (1σ) upper limits on any variation in y≡g_pα² (where α is the fine-structure constant, and g_p is the proton g -factor of
   
at redshifts z = 0.25 and 0.68. These quasars are separated by a comoving distance of 3000 Mpc ( H ₀= 75 km s⁻¹ Mpc⁻¹ and q ₀). We also derive limits on the time rates of change
   
    between the present epoch and z = 0.68. These limits are more than an order of magnitude smaller than previous results derived from high-redshift measurements.     

Cosmological Perturbation Theory and the Spherical Collapse model — I. Gaussian initial conditions

We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, ξ_J, for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S _J  = ξ _J /ξ ^{J −1}₂. We compare our analytic results with N -body simulations, which turn out to be in very good agreement up to scales where σ ≈ 1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime.     

Constraining the cosmic equation of state from old galaxies at high redshift

New limits on the cosmic equation of state are derived from age measurements of three recently reported old high-redshift galaxies (OHRG). The results are based on a flat Friedmann–Robertson–Walker (FRW) type cosmological model driven by non-relativistic matter plus a smooth component parametrized by its equation of state p _x ωρ _x ( ω −1). The range of ω is strongly dependent on the matter density parameter. For Ω_M∼0.3, as indicated from dynamical measurements, the age estimates of the OHRG restrict the cosmic parameter to ω −0.27. However, if Ω_M is the one suggested by some studies of field galaxies, i.e., Ω_M≃0.5, only a cosmological constant ( ω =−1) may be compatible with these data.     

Could the Galactic disc heating be due to globular cluster impacts?

So far, six mechanisms have been proposed to account for the Galactic disc heating. Of these, the most important appear to be a combination of scattering of stars by molecular clouds and by spiral arms. We study a further mechanism, namely the repeated disc impact of the original Galactic globular cluster population up to the present. We find that globular clusters could have contributed at most a small fraction of the current vertical energy of the disc, as they could heat the whole disc to  σ _z = 5.5 km s⁻¹  (c.f. the observed 18 and 39 km s⁻¹ for the thick and thin discs, respectively). We find that the rate of rise of disc heat (  α= 0.22  in  σ _z ∼ t ^α  with t being time) is close to that found for scattering by molecular clouds.     

A Monte Carlo study of polarization structures in the Thomson-scattered line radiation

Thomson scattering is often invoked to explain broad wing features that are seen in various objects including active galactic nuclei and symbiotic stars. Despite the wavelength-independent scattering cross-section of Thomson scattering, the line flux may exhibit wavelength-dependent linear degree of polarization, because various parts of emission wings are contributed by photons with different scattering numbers. Specifically, more scattered and hence more weakly polarized photons tend to fill the farther wing parts from the line centre, while the neighbourhood of the line centre is dominated by less-scattered photons with higher degree of polarization. Using a Monte Carlo technique, we investigate the polarization structure of Thomson-scattered line radiation. A detailed analysis of polarization structure formation is conducted by investigating the dependence of the polarization and profile width on the scattering number for various finite electron scattering slabs. Significantly varying degree of polarization is obtained when the scattering medium has Thomson optical depth  τ_Th≥ 1  . We present our high-resolution spectrum of the symbiotic star V1016 Cyg obtained with the Bohyunsan Optical Echelle Spectrograph (BOES) in order to fit the broad profile around Hα by electron scattering wings adopting an oblate spheroidal geometry with Thomson optical depth  τ_Th= 0.5  and electron temperature   T _e= 6.2 × 10⁴  K  . Local maxima in the linear degree of polarization of Thomson-scattered line radiation are expected to appear in the spectral regions characterized by the average scattering number ≃1.     

Self-inhibiting heat flux

Heat transfer through weakly magnetized diffuse astrophysical plasmas excites whistlers. This leads to electron whistler resonant scattering, a reduction of the electron mean free path, and heat flux inhibition. However, only whistlers propagating at a finite angle to the magnetic field (off-axis) can scatter the heat flux carrying electrons. Thus the level of heat flux inhibition along the magnetic field lines depends on the presence of off-axis whistlers.   We obtain a solution of the Boltzmann equation with the whistler wave equation and show that if εthβe ≫ 10⁻⁴, where ε^th is the thermal collisional Knudsen number and β_e is the ratio of the electron pressure to the magnetic energy density, then scattering of heat flux carrying electrons by off-axis whistlers, which are shown to propagate at about 65δ, is efficient enough to lead to heat flux inhibition along field lines. The inhibition so obtained is proportional to (ε^thβ_e)⁻¹.