A circular statistical method for extracting rotation measures

We propose a new method for the extraction of rotation measures from spectral polarization data. The method is based on maximum likelihood analysis and takes into account the circular nature of the polarization data. The method is unbiased and statistically more efficient than the standard χ ² procedure. We also find that the method is computationally much more convenient than the standard χ ² procedure if the number of data points is very large. We find that for most sources the method gives results very close to the standard χ ² minimization procedure. We give results for all the cases for which the method gives significantly different results from χ ² minimization. We also make a λ ³ fit to the data in order to extract non-Faraday rotation behaviour for those sources for which a large number of data points are available.     

Multi-Conjugate Adaptive Optics with laser guide stars: performance in the infrared and visible

The assumption of the Gaussianity of primordial perturbations plays an important role in modern cosmology. The most direct test of this hypothesis consists of testing the Gaussianity of cosmic microwave background (CMB) maps. Counting the pixels with the temperatures in given ranges and thus estimating the one-point probability function of the field is the simplest of all the tests. Other usually more complex tests of Gaussianity generally use a great deal of the information already contained in the probability function. However, the most interesting outcome of such a test would be the signal of non-Gaussianity independent of the probability function. It is shown that the independent information has purely morphological character i.e. it depends on the geometry and topology of the level contours only. As an example we discuss in detail the quadratic model   v = u + α ( u ²-1)  ( u is a Gaussian field with   u¯ =0  and  〈 u ²〉=1  , α is a parameter) that may arise in slow-roll or two-field inflation models. We show that in the limit of small amplitude α the full information about the non-Gaussianity is contained in the probability function. If other tests are performed on this model they simply recycle the same information. A simple procedure allowing us to assess the sensitivity of any statistics to the morphological information is suggested. We provide an analytic estimate of the statistical limit for detecting the quadratic non-Gaussianity α _c as a function of the map size in the ideal situation when the scale of the field is resolved. This estimate is in a good agreement with the results of the Monte Carlo simulations of 256² and 1024² maps. The effect of resolution on the detection quadratic non-Gaussianity is also briefly discussed.     

A modified χ2-test for cosmic microwave background analyses

We present a new general procedure for determining a given set of quantities. To this end, we define a certain statistic, which we call 'modified  χ²' (χ²_M)  , because of its similarity to the standard  χ²  . The terms of this  χ²_M  are made up of the fluctuations of an unbiased estimator of some statistical quantities and certain weights. Only the diagonal terms of the covariance matrix appear explicitly in our statistic, while the full covariance matrix (and not its inverse) is included implicitly in the calculation of the weights. Choosing these weights, we may obtain, through minimizing  χ²_M  , the estimator that provides the minimum rms, either for those quantities or for the parameters on which these quantities depend. In this paper, we describe our method in the context of cosmic microwave background experiments, in order to obtain either the statistical properties of the maps or the cosmological parameters. The test here is constructed out of some estimator of the two-point correlation function at different angles. For the problem of one-parameter estimation, we show that our method has the same power as the maximum-likelihood method. We have also applied this method to Monte Carlo simulations of the COBE -DMR data, as well as to the actual 4-yr data, obtaining consistent results with previous analyses. We also provide a very good analytical approximation to the distribution function of our statistic, which could also be useful in other contexts.     

On a time-symmetric Hermite integrator for planetary N-body simulation

We describe a P(EC) ⁿ Hermite scheme for planetary N -body simulation. The fourth-order implicit Hermite scheme is a time-symmetric integrator that has no secular energy error for the integration of periodic orbits with time-symmetric time-steps. In general N -body problems, however, this advantage is of little practical significance, since it is difficult to achieve time-symmetry with individual variable time-steps. However, we can easily enjoy the benefit of the time-symmetric Hermite integrator in planetary N -body systems, where all bodies spend most of the time on nearly circular orbits. These orbits are integrated with almost constant time-steps even if we adopt the individual time-step scheme. The P(EC) ⁿ Hermite scheme and almost constant time-steps reduce the integration error greatly. For example, the energy error of the P(EC)² Hermite scheme is two orders of magnitude smaller than that of the standard PEC Hermite scheme in the case of an N  = 100,  m  = 10²⁵ g planetesimal system with the rms eccentricity 〈 e ²〉^1/2 ≲0.03.     

On the comoving distance as an arc-length in four dimensions

The inner product provides a conceptually and algorithmically simple method for calculating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The key to this is that just as a distance between two points 'on' the surface of the ordinary 2-sphere ² is simply an arc-length (angle multiplied by radius) in ordinary Euclidean 3-space ℰ³, the distance between two points 'on' a 3-sphere ³ (a 3-hyperboloid ℋ³) is simply an 'arc-length' in Euclidean 4-space ℰ⁴ (Minkowski 4-space ℳ⁴), i.e. an 'hyper-angle' multiplied by the curvature radius of the 3-sphere (3-hyperboloid).     

Microlensing in dark matter haloes

Using eight dark matter haloes extracted from fully self-consistent cosmological N -body simulations, we perform microlensing experiments. A hypothetical observer is placed at a distance of 8.5 kpc from the centre of the halo measuring optical depths, event durations and event rates towards the direction of the Large Magellanic Cloud. We simulate 1600 microlensing experiments for each halo. Assuming that the whole halo consists of massive astronomical compact halo objects (MACHOs),   f = 1.0  , and a single MACHO mass is   m _M= 1.0 M_⊙  , the simulations yield mean values of  τ= 4.7^+5.0_−2.2× 10⁻⁷  and  Γ= 1.6^+1.3_−0.6× 10⁻⁶  events star⁻¹ yr⁻¹. We find that triaxiality and substructure can have major effects on the measured values so that τ and Γ values of up to three times the mean can be found. If we fit our values of τ and Γ to the MACHO collaboration observations, we find   f = 0.23^+0.15_−0.13  and   m _M= 0.44^+0.24_−0.16  . Five out of the eight haloes under investigation produce f and m _M values mainly concentrated within these bounds.     

Radiative decay data for highly excited Zr i levels

Radiative lifetimes of 17 excited levels in Zr  i , in the energy interval 29 000–40 974 cm⁻¹, have been investigated using the time-resolved laser-induced fluorescence method. The levels belong to the 4d²5s5p, 4d³5p and 4d5s²5p electronic configurations and were excited in a single-step process from either the ground term, 4d²5s² a ³F, or from the low-lying 4d²5s² a ³P and a ⁵F terms. For three levels, we confirm previous measurements while for 14 of the levels the lifetimes have been measured for the first time. The experimental results are compared to theoretical calculations performed with a multiconfiguration relativistic Hartree–Fock method including core-polarization effects. Theoretical transition probabilities of astrophysical interest, scaled by the experimental lifetimes, for the depopulating channels of the investigated levels are also presented.     

Detection of an H92α recombination line in the starburst galaxy NGC 660

We have used the Very Large Array (VLA) to search for the H92α radio recombination line (RRL) in four starburst galaxies. In NGC 660, the line was detected over a 17Å‐8 arcsec² region near its starburst nucleus. The line and continuum emission indicate that the RRL-emitting gas is most likely in the form of a cluster of H ii regions with a small filling factor. Using a simple model we find that the total ionized mass in the nuclear region is in the range 2–8Å‐10⁴ M⊙ and the rate of production of UV photons N _Lyc∼1–3Å‐10⁵³ s⁻¹. The ratio of H92α and Brγ line intensities in NGC 660 indicates that extinction is significant even at λ=2 μm. The velocity field of the ionized gas is consistent with a rotating disc with an average velocity gradient of ∼15 km s⁻¹ arcsec⁻¹. The dynamical mass within the central 500 pc is ∼4Å‐10⁸ M⊙ and may be about ∼6Å‐10⁷ M⊙ within the central 120 pc. No line was detected in the other galaxies (NGC 520, NGC 1614 and NGC 6946) to a 3σ limit of 300 μJy. In the starburst galaxies in which RRLs have been detected, we find that there is a rough correlation between the integrated H92α line flux density and both the total far-infrared flux density and the radio continuum emission from the central region.     

Do binaries in clusters form in the same way as in the field?

We examine the dynamical destruction of binary systems in star clusters of different densities. We find that at high densities  (10⁴– 10⁵ M_⊙ pc⁻³)  almost all binaries with separations  >10³  au are destroyed after a few crossing times. At low densities [     ], many binaries with separations  >10³  au are destroyed, and no binaries with separations  >10⁴  au survive after a few crossing times. Therefore, the binary separations in clusters can be used as a tracer of the dynamical age and past density of a cluster.
We argue that the central region of the Orion nebula cluster was ∼100 times denser in the past with a half-mass radius of only 0.1–0.2 pc as (i) it is expanding, (ii) it has very few binaries with separations  >10³  au and (iii) it is well mixed and therefore dynamically old.
We also examine the origin of the field binary population. Binaries with separations  <10²  au are not significantly modified in any cluster, therefore at these separations the field reflects the sum of all star formation. Binaries with separations in the range  10²– 10⁴  au are progressively more and more heavily affected by dynamical disruption in increasingly dense clusters. If most star formation is clustered, these binaries must be overproduced relative to the field. Finally, no binary with a separation  >10⁴  au can survive in any cluster and so must be produced by isolated star formation, but only if all isolated star formation produces extremely wide binaries.     

Calculated spectra for HeH+ and its effect on the opacity of cool metal-poor stars

The wavelength and Einstein A coefficient are calculated for all rotation–vibration transitions of  ⁴He¹H⁺, ³He¹H⁺, ⁴He²H⁺  and  ³ He²H⁺  , giving a complete line list and the partition function for  ⁴HeH⁺  and its isotopologues. This opacity is included in the calculation of the total opacity of low-metallicity stars and its effect is analysed for different conditions of temperature, density and hydrogen number fraction. For a low helium number fraction (as in the Sun), it is found that HeH⁺ has a visible but small effect for very low densities  (ρ≤ 10⁻¹⁰ g cm⁻³)  , at temperatures around 3500 K. However, for high helium number fraction, the effect of HeH⁺ becomes important for higher densities  (ρ≤ 10⁻⁶ g cm⁻³)  , its effect being most important for a temperature around 3500 K. Synthetic spectra for a variety of different conditions are presented.     

The gamma-ray conversion efficiency of rotation-powered pulsars

We use a new self-consistent model to derive the conversion efficiency from rotation power to γ-ray power for pulsars (ε_th). Our result indicates that ε_th∝τ^6/7 P ², where τ and P are the characteristic age and period of the pulsar, which shows that although the efficiency increases with the characteristic age of the pulsar, it also depends on the pulsar period. We test our model results with the survey of high-energy γ-rays from pulsars by EGRET. Our model not only successfully explains the efficiency of the confirmed γ-ray pulsars but also explains why the γ-ray efficiency of millisecond pulsars is so low.     

The alignment of clusters using large-scale simulations

The alignment of clusters of galaxies with their nearest neighbours and between clusters within a supercluster is investigated using simulations of 512³ dark matter particles for ΛCDM and τ CDM cosmological models. Strongly significant alignments are found for separations of up to 15  h ⁻¹ Mpc in both cosmologies, but for the ΛCDM model the alignments extend up to separations of 30  h ⁻¹ Mpc. The effect is strongest for nearest neighbours, but is not significant enough to be useful as an observational discriminant between cosmologies. As a check of whether this difference in alignments is present in other cosmologies, smaller simulations with 256³ particles are investigated for four different cosmological models. Because of poor number statistics, only the standard CDM model shows indications of having different alignments from the other models.     

The WARPS survey – IV. The X-ray luminosity–temperature relation of high-redshift galaxy clusters

We present a measurement of the cluster X-ray luminosity–temperature ( L – T ) relation out to high redshift ( z ∼0.8). Combined ROSAT PSPC spectra of 91 galaxy clusters detected in the Wide Angle ROSAT Pointed Survey (WARPS) are simultaneously fitted in redshift and luminosity bins. The resulting temperature and luminosity measurements of these bins, which occupy a region of the high-redshift L – T relation not previously sampled, are compared with existing measurements at low redshift in order to constrain the evolution of the L – T relation. We find the best fit to low-redshift ( z <0.2) cluster data, at T >1 keV, to be L ∝ T ^3.15±0.06. Our data are consistent with no evolution in the normalization of the L – T relation up to z ∼0.8. Combining our results with ASCA measurements taken from the literature, we find η =0.19±0.38 (for Ω₀=1, with 1 σ errors) where L _Bol∝(1+ z ) ^η T ^3.15, or η =0.60±0.38 for Ω₀=0.3. This lack of evolution is considered in terms of the entropy-driven evolution of clusters. Further implications for cosmological constraints are also discussed.     

On invisible plasma content in radio-loud AGNs: the case of TeV blazar Markarian 421

Invisible plasma content in blazar jets such as protons and/or thermal electron–positron ( e ^±) pairs is explored through combined arguments of dynamical and radiative processes. By comparing physical quantities required by the internal shock model with those obtained through the observed broad-band spectra for Mrk 421, we obtain that the ratio of the Lorentz factors of a pair of cold shells resides in about 2 ∼ 20, which implies that the shocks are at most mildly relativistic. Using the obtained Lorentz factors, the total mass density ρ in the shocked shells is investigated. The upper limit of ρ is obtained from the condition that thermal bremsstrahlung emission should not exceed the observed γ-ray luminosity, whilst the lower limit is constrained from the condition that the energy density of non-thermal electrons is smaller than that of the total plasma. Then, we find ρ is 10²–10³ times heavier than that of non-thermal electrons for pure   e ^±  pairs, while 10²–10⁶ times heavier for pure electron–proton ( e / p ) content, implying the existence of a large amount of invisible plasma. The origin of the continuous blazar sequence is briefly discussed and we speculate that the total mass density and/or the blending ratio of e ^± pairs and e / p plasma could be new key quantities for the origin of the sequence.     

Molecular hydrogen emission in Cygnus A

We present J , H and K -band spectroscopy of Cygnus A, spanning 1.0–2.4 μm in the rest-frame and hence several rovibrational H₂, H recombination and [Fe  ii ] emission lines. The lines are spatially extended by up to 6 kpc from the nucleus, but their distinct kinematics indicate that the three groups (H, H₂ and [Fe  ii ]) are not wholly produced in the same gas. The broadest line, [Fe  ii ] λ 1.644, exhibits a non-Gaussian profile with a broad base (FWHM≃1040 km s⁻¹), perhaps because of the interaction with the radio source. Extinctions to the line-emitting regions substantially exceed earlier measurements based on optical H recombination lines.
Hard X-rays from the quasar nucleus are likely to dominate the excitation of the H₂ emission. The results of Maloney, Hollenbach & Tielens are thus used to infer the total mass of gas in H₂ v=1–0 S(1)-emitting clouds as a function of radius, for gas densities of 10³ and 10⁵ cm⁻³, and stopping column densities N _H=10²²–10²⁴ cm⁻². Assuming azimuthal symmetry, at least 2.3×10⁸ M_⊙ of such material is present within 5 kpc of the nucleus, if the line-emitting clouds see an unobscured quasar spectrum. Alternatively, if the bulk of the X-ray absorption to the nucleus inferred by Ueno et al. actually arises in a circumnuclear torus, the implied gas mass rises to ∼10¹⁰ M_⊙. The latter plausibly accounts for 10⁹ yr of mass deposition from the cluster cooling flow, for which within this radius.     

Heavy-element abundances in seven SC stars and several related stars

We employ spectra of resolution 20–35000 of seven SC stars, four S stars, two Ba stars and two K–M stars to derive abundances of a variety of elements from Sr to Eu relative to iron. Special attention is paid to Rb and Tc, and to the ratio of the heavy s-process species to the light s-process elements. Abundances are derived in LTE, both by using model atmospheres in which the carbon and oxygen abundances are nearly equal and by using curves of growth. Spectrum synthesis is used for critical lines such as the 5924-Å line of Tc and the 7800-Å line of Rb. For most of the heavy-element stars the enhancement of the s-process elements is about a factor of 10. The ratio of the heavy to light s-process species is not far from solar, except for RR Her for which the same ratio is +0.45 dex. For Tc the blending by other lines is severe. While we have probably detected the 5924-Å line, we can only present abundances in the less-than-or-equal-to category. For Rb, whose abundance is sensitive to the ⁸⁵Rb/⁸⁷Rb ratio and hence to the neutron density during s-process production, we find a considerable range of abundances, indicating a neutron density from 10⁶ to ≳10⁸ cm⁻³ for the SC stars. For the four S stars the range is from 10⁷ to ≳10⁸ cm⁻³. Recent calculations by Gallino et al. show that neutron densities near 10⁷ cm⁻³ favour the ¹³C source for neutrons, while densities greater than 10⁸ cm⁻³ may be associated with neutrons from the ²²Ne source.     

ASCA observations of deep ROSAT fields — III. The discovery of an obscured Type 2 AGN at z = 0.67

We report on the discovery of a narrow-emission-line object at z  = 0.672 detected in a deep ASCA survey. The object, AXJ 0341.4–4453, has a flux in the 2–10 keV band of 1.1 ± 0.27 × 10⁻¹³ erg s⁻¹ cm⁻², corresponding to a luminosity of 1.8 × 10⁴⁴ erg s⁻¹ ( q ₀ = 0.5, H ₀ = 50 km s⁻¹ Mpc⁻¹). It is also marginally detected in the ROSAT 0.5–2 keV band with a flux 5.8 × 10⁻¹⁵ erg s⁻¹ cm⁻². Both the ASCA data alone and the combined ROSAT/ASCA data show a very hard X-ray spectrum, consistent with either a flat power law (α < 0.1) or photoelectric absorption with a column of n _H > 4 × 10²² cm⁻² (α = 1). The optical spectrum shows the high-ionization, narrow emission lines typical of a Seyfert 2 galaxy. We suggest that this object may be typical of the hard sources required to explain the remainder of the X-ray background at hard energies.     

A deep Giant Metre-wave Radio Telescope 610-MHz survey of the 1HXMM–Newton/Chandra survey field

We present the results of a deep 610-MHz survey of the 1 ^H XMM–Newton / Chandra survey area with the Giant Metre-wave Radio Telescope. The resulting maps have a resolution of ∼7 arcsec and an rms noise limit of 60 μJy. To a 5σ detection limit of 300 μJy, we detect 223 sources within a survey area of 64 arcmin in diameter. We compute the 610-MHz source counts and compare them to those measured at other radio wavelengths. The well-known flattening of the Euclidean-normalized 1.4-GHz source counts below ∼2 mJy, usually explained by a population of starburst galaxies undergoing luminosity evolution, is seen at 610 MHz. The 610-MHz source counts can be modelled by the same populations that explain the 1.4-GHz source counts, assuming a spectral index of −0.7 for the starburst galaxies and the steep spectrum active galactic nucleus (AGN) population. We find a similar dependence of luminosity evolution on redshift for the starburst galaxies at 610 MHz as is found at 1.4 GHz (i.e.  ' Q '= 2.45^+0.3_−0.4  ).     

The SCUBA HAlf Degree Extragalactic Survey – VI. 350-μm mapping of submillimetre galaxies

A follow-up survey using the Submillimetre High-Angular Resolution Camera (SHARC-II) at 350 μm has been carried out to map the regions around several 850-μm-selected sources from the Submillimetre HAlf Degree Extragalactic Survey (SHADES). These observations probe the infrared (IR) luminosities and hence star formation rates in the largest existing, most robust sample of submillimetre galaxies (SMGs). We measure 350-μm flux densities for 24 850-μm sources, seven of which are detected at ≥2.5σ within a 10 arcsec search radius of the 850-μm positions. When results from the literature are included the total number of 350-μm flux density constraints of SHADES SMGs is 31, with 15 detections. We fit a modified blackbody to the far-IR (FIR) photometry of each SMG, and confirm that typical SMGs are dust-rich  ( M _dust≃ 9 × 10⁸ M_⊙)  , luminous  ( L _FIR≃ 2 × 10¹² L_⊙)  star-forming galaxies with intrinsic dust temperatures of ≃35 K and star formation rates of  ≃400 M_⊙ yr⁻¹  . We have measured the temperature distribution of SMGs and find that the underlying distribution is slightly broader than implied by the error bars, and that most SMGs are at 28 K with a few hotter. We also place new constraints on the 350-μm source counts, N ₃₅₀(>25 mJy) ∼ 200–500 deg⁻².     

Star formation triggered by supernova explosions in young galaxies

We study the evolution of supernova remnants in a low-metallicity medium   Z /Z_⊙= 10⁻⁴ to 10⁻²  in the early universe, using one-dimensional hydrodynamics with non-equilibrium chemistry. Once a post-shock layer is able to cool radiatively, a dense shell forms behind the shock. If this shell becomes gravitationally unstable and fragments into pieces, next-generation stars are expected to form from these fragments. To explore the possibility of this triggered star formation, we apply a linear perturbation analysis of an expanding shell to our results and constrain the parameter range of ambient density, explosion energy and metallicity where fragmentation of the shell occurs. For the explosion energy of  10⁵¹ erg (10⁵² erg)  , the shell fragmentation occurs for ambient densities higher than  ≳10² cm⁻³ (10 cm⁻³  ), respectively. This condition depends little on the metallicity in the ranges we examined. We find that the mode of star formation triggered occurs only in massive  (≳10⁸ M_⊙)  haloes.