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.     

Direct observation of cosmic strings via their strong gravitational lensing effect – I. Predictions for high-resolution imaging surveys

We use present theoretical estimates for the density of long cosmic strings to predict the number of strong gravitational lensing events in astronomical imaging surveys as a function of the angular resolution and survey area. We show that angular resolution is the single most important factor, and that interesting limits on the dimensionless string tension   G μ/ c ²  can be obtained by existing and planned surveys. At the resolution of the Hubble Space Telescope ( HST ) (0.14 arcsec), it is sufficient to survey of the order of a few square degrees – well within reach of the current HST archive – to probe the regime   G μ/ c ²∼ 10⁻⁷  . If lensing by cosmic strings is not detected, such a survey would improve the limit on the string tension by a factor of two over that available from the cosmic microwave background. Future high resolution imaging surveys, covering a few hundred square degrees or more, either from space in the optical or from large-format radio telescopes on the ground, would be able to further lower this limit to   G μ/ c ²∼ 10⁻⁸  . These limits will not be improved significantly by increasing the solid angle of the survey.     

Deep galaxy counts, extragalactic background light and the stellar baryon budget

We assess the constraints imposed by the observed extragalactic background light (EBL) on the cosmic history of star formation and the stellar-mass density today. The logarithmic slope of the galaxy number–magnitude relation from the Southern Hubble Deep Field imaging survey is flatter than 0.4 in all seven UBVIJHK optical bandpasses, i.e. the light from resolved galaxies has converged from the UV to the near-IR. We find a lower limit to the surface brightness of the optical extragalactic sky of about 15 nW m⁻² sr⁻¹, comparable to the intensity of the far-IR background from COBE data. Assuming a Salpeter initial mass function with a lower cut-off consistent with observations of M subdwarf disc stars, we set a lower limit of Ω_g+s h ²>0.0013  I ₅₀ to the visible (processed gas + stars) mass density required to generate an EBL at a level of 50  I ₅₀ nW m⁻² sr⁻¹; our 'best-guess' value is Ω_g+s h ²≈0.0031  I ₅₀. Motivated by the recent microlensing results of the MACHO collaboration, we consider the possibility that massive dark haloes around spiral galaxies are composed of faint white dwarfs, and show that only a small fraction (≲5 per cent) of the nucleosynthetic baryons can be locked in the remnants of intermediate-mass stars forming at z _F≲5, as the bright early phases of such haloes would otherwise overproduce the observed EBL.     

Iron line profiles including emission from within the innermost stable orbit of a black hole accretion disc

We propose a model for the source of the X-ray background (XRB) in which low-luminosity active nuclei ( L  ∼ 10⁴³ erg s⁻¹) are obscured ( N  ∼ 10²³ cm⁻²) by nuclear starbursts within the inner ∼ 100 pc. The obscuring material covers most of the sky as seen from the central source, rather than being distributed in a toroidal structure, and hardens the averaged X-ray spectrum by photoelectric absorption. The gas is turbulent with velocity dispersion ∼ few × 100 km s⁻¹ and cloud–cloud collisions lead to copious star formation. Although supernovae tend to produce outflows, most of the gas is trapped in the gravity field of the star-forming cluster itself and the central black hole. A hot ( T  ∼ 10⁶ − 10⁷ K) virialized phase of this gas, comprising a few per cent of the total obscuring material, feeds the central engine of ∼ 10⁷ M⊙ through Bondi accretion, at a sub-Eddington rate appropriate for the luminosity of these objects. If starburst-obscured objects give rise to the residual XRB, then only 10 per cent of the accretion in active galaxies occurs close to the Eddington limit in unabsorbed objects.     

The contribution of faint active galactic nuclei to the hard X-ray background

Hard X-ray selection is the most efficient way to discriminate between accretion-powered sources, such as active galactic nuclei (AGN), and sources dominated by starlight. Hard X-rays are also less affected than other bands by obscuration. We have therefore carried out the BeppoSAX High Energy Large Area Survey (HELLAS) in the largely unexplored 5–10 keV band, finding 180 sources in ∼50 deg² of sky with flux≳5×10⁻¹⁴ erg cm⁻² s⁻¹. After correction for the non-uniform sky coverage this corresponds to resolving about 30 per cent of the hard cosmic X-ray background (XRB). Here we report on a first optical spectroscopic identification campaign, finding 12 AGN out of 14 X-ray error boxes studied. Seven AGN show evidence for obscuration in X-ray and optical bands, a fraction higher than in previous ROSAT or ASCA – ROSAT surveys (at 95–99 and 90 per cent confidence levels respectively), thus supporting the scenario in which a significant fraction of the XRB is created by obscured AGN.     

Measuring the power spectrum of density fluctuations at intermediate redshift with X-ray background observations

The precision of intensity measurements of the extragalactic X-ray background (XRB) on an angular scale of about a degree is dominated by spatial fluctuations caused by source confusion noise. X-ray source counts at the flux level responsible for these fluctuations, ∼10⁻¹² erg cm⁻² s⁻¹, will soon be accurately measured by new missions, and it will then be possible to detect the weaker fluctuations caused by the clustering of the fainter, more distant sources which produce the bulk of the XRB. We show here that measurements of these excess fluctuations at the level of (Δ I/I )∼2×10⁻³ are within reach, improving by an order of magnitude on present upper limits. Since it is likely that most (if not all) of the XRB will be resolved into sources by AXAF , subsequent optical identification of these sources will reveal the X-ray volume emissivity in the Universe as a function of redshift. With these ingredients, all-sky observations of the XRB can be used to measure the power spectrum (PS) of the density fluctuations in the Universe at comoving wavevectors k _c∼0.01–0.1 Mpc⁻¹ at redshifts where most of the XRB is likely to originate ( z ∼1–2) with a sensitivity similar to, or better than, the predictions from large-scale structure theories. A relatively simple X-ray experiment, carried out by a large-area proportional counter with a 0.5–2 deg² collimated field of view scanning the whole sky a few times, would be able to determine the PS of the density fluctuations near its expected peak in wavevector with an accuracy better than 10 per cent.     

The physical parameters of Markarian 501 during flaring activity

We analyse an N -body simulation of the Small Magellanic Cloud (SMC), that of Gardiner & Noguchi, to determine its microlensing statistics. We find that the optical depth owing to self-lensing in the simulation is low, 0.4×10⁻⁷, but still consistent (at the 90 per cent level) with that observed by the EROS and MACHO collaborations. This low optical depth is due to the relatively small line-of-sight thickness of the SMC produced in the simulation. The proper motions and time-scales of the simulation are consistent with those observed assuming a standard mass function for stars in the SMC. The time-scale distribution from the standard mass function generates a significant fraction of short time-scale events: future self-lensing events towards the SMC may have the same time-scales as events observed towards the Large Magellanic Cloud (LMC). Although some debris was stripped from the SMC during its collision with the LMC about 2×10⁸ yr ago, the optical depth of the LMC owing to this debris is low, a few ×10⁻⁹, and thus cannot explain the measured optical depth towards the LMC.     

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.     

Rotating haloes and the microlensing MACHO mass estimate

We investigate the implications of a bulk rotational component of the Galactic halo velocity distribution for MACHO mass estimates. We find that for a rotating halo to yield a MACHO mass estimate significantly below that of the standard spherical case, its microlensing must be highly concentrated close to the Sun. We examine two classes of models fitting this criterion: a highly flattened 1/ r ² halo, and a spheroid-like population the density of which falls off as 1/ r ^3.5. The highly flattened 1/ r ² models can decrease the implied average MACHO mass only marginally, and the spheroid models not at all. Generally, rotational models cannot bring the MACHO mass implied by the current microlensing data down to the substellar range.     

Searching for large-scale structure in deep radio surveys

We calculate the expected amplitude of the dipole and higher spherical harmonics in the angular distribution of radio galaxies. The median redshift of radio sources in existing catalogues is z  ∼ 1, which allows us to study large-scale structure on scales between those accessible to present optical and infrared surveys, and that of the cosmic microwave background (CMB). The dipole is a result of two effects which turn out to be of comparable magnitude: (i) our motion with respect to the CMB, and (ii) large-scale structure, parametrized here by a family of cold dark matter power-spectra. We make specific predictions for the Green Bank 1987 (87GB) and Parkes–MIT–NRAO (PMN) catalogues, which in our combined catalogue include ∼ 40 000 sources brighter than 50 mJy at 4.85 GHz, over about 70 per cent of the sky. For these relatively sparse catalogues both the motion and large-scale structure dipole effects are expected to be smaller than the Poisson shot noise. However, we detect dipole and higher harmonics in the combined 87GB–PMN_raw catalogue which are far larger than expected. We attribute this to a 2 per cent flux mismatch between the two catalogues. Ad hoc corrections made in an effort to match the catalogues may suggest a marginal detection of a dipole. To detect a dipole and higher harmonics unambiguously, a catalogue with full sky coverage and ∼ 10⁶ sources is required. We also investigate the existence and extent of the supergalactic plane in the above catalogues. In a strip of ± 10° of the standard supergalactic equator, we find a 3 σ detection in PMN_raw, but only 1 σ in 87 GB_raw. We briefly discuss the implications of ongoing surveys such as FIRST and NVSS and follow-up redshift surveys.     

Prompt optical emission and synchrotron self-absorption constraints on emission site of GRBs

We constrain the distance of the gamma-ray burst (GRB) prompt emission site from the explosion centre R , by determining the location of the electron's self-absorption frequency in the GRB prompt optical-to-X/γ-ray spectral energy distribution, assuming that the optical and the γ-ray emissions are among the same synchrotron radiation continuum of a group of hot electrons. All possible spectral regimes are considered in our analysis. The method has only two assumed parameters, namely the bulk Lorentz factor of the emitting source Γ and the magnetic field strength B in the emission region (with a weak dependence). We identify a small sample of four bursts that satisfy the following three criteria: (1) they all have simultaneous optical and γ-ray detections in multiple observational time intervals, (2) they all show temporal correlations between the optical and γ-ray light curves and (3) the optical emission is consistent with belonging to the same spectral component as the γ-ray emission. For all the time intervals of these four bursts, it is inferred that   R ≥ 10¹⁴  (Γ/300)^3/4 ( B /10⁵ G)^1/4  cm. For a small fraction of the sample, the constraint can be pinned down to   R ≈ 10¹⁴–10¹⁵ cm  for  Γ∼ 300  . For a second sample of bursts with prompt optical non-detections, only upper limits on R can be obtained. We find no inconsistency between the R -constraints for this non-detection sample and those for the detection sample.     

IRAM observations of JVAS/CLASS gravitational lenses

We have searched for molecular absorption lines at millimetre wavelengths in 11 gravitational lens systems discovered in the JVAS/CLASS surveys of flat spectrum radio sources. Spectra of only one source 1030+074 were obtained in the 3-, 2- and 1.3-mm bands at the frequencies corresponding to common molecular transitions of CO and HCO⁺ as continuum emission was not found in any of the other sources. We calculated upper limits to the column density in molecular absorption for 1030+074, using an excitation temperature of 15 K, to be N _CO<6.3×10¹³ cm⁻² and N _HCO+<1.3×10¹¹ cm⁻² , equivalent to hydrogen column density of the order N _H<10¹⁸ cm⁻² , assuming standard molecular abundances. We also present the best upper limits of the continuum at the lower frequency for the other 10 gravitational lenses.     

Using SCUBA to place upper limits on arcsecond-scale cosmic microwave background anisotropies at 850 m

The SCUBA instrument on the James Clerk Maxwell Telescope has already had an impact on cosmology by detecting relatively large numbers of dusty galaxies at high redshift. Apart from identifying well-detected sources, such data can also be mined for information about fainter sources and their correlations, as revealed through low-level fluctuations in SCUBA maps. As a first step in this direction, we analyse a small SCUBA data set as if it were obtained from a cosmic microwave background (CMB) differencing experiment. This enables us to place limits on CMB anisotropy at 850 m. Expressed as Q _flat, the quadrupole expectation value for a flat power spectrum, the limit is 152 K at 95 per cent confidence, corresponding to     (or T T <1410⁵) for a Gaussian autocorrelation function, with a coherence angle of about 2025 arcsec. These results could easily be reinterpreted in terms of any other fluctuating sky signal. This is currently the best limit for these scales at high frequency, and comparable to limits at similar angular scales in the radio. Even with such a modest data set, it is possible to put a constraint on the slope of the SCUBA counts at the faint end, since even randomly distributed sources would lead to fluctuations. Future analysis of sky correlations in more extensive data sets ought to yield detections, and hence additional information on source counts and clustering.     

Parallax microlensing events in the OGLE II data base toward the Galactic bulge

We present a systematic search for parallax microlensing events among a total of 512 microlensing candidates in the OGLE II data base for the  1997–1999  seasons. We fit each microlensing candidate with both the standard microlensing model and a parallax model that accounts for the Earth's motion around the Sun. We then search for the parallax signature by comparing the χ ² of the standard and parallax models. For the events which show a significant improvement, we further use the 'duration' of the event and the signal-to-noise ratio as criteria to separate true parallax events from other noisy microlensing events. We have discovered one convincing new candidate, sc33_4505, and seven other marginal cases. The convincing candidate (sc33_4505) is caused by a slow-moving, and likely low-mass, object, similar to other known parallax events. We found that irregular sampling and gaps between observing seasons hamper the recovery of parallax events. We have also searched for long-duration events that do not show parallax signatures. The lack of parallax effects in a microlensing event puts a lower limit on the Einstein radius projected on to the observer plane, which in turn imposes a lower limit on the lens mass divided by the relative lens–source parallax. Most of the constraints are however quite weak.     

Q2237+0305 source structure and dimensions from light-curve simulation

Assuming a two-component quasar structure model consisting of a central compact source and an extended outer feature, we produce microlensing simulations for a population of compact masses in the lensing galaxy of Q2237+0305. Such a model is a simplified version of that adopted to explain the brightness variations observed in Q0957. The microlensing light curves generated for a range of source parameters were compared to the light curves obtained in the framework of the Optical Gravitational Lensing Experiment program. With a large number of trials, we built, in the domain of the source structure parameters, probability distributions to find 'good' realizations of light curves. The values of the source parameters which provide the maximum of the joint probability distribution calculated for all the image components have been accepted as estimates for the source structure parameters. The results favour the two-component model of the quasar brightness structure over a single compact central source model, and in general the simulations confirm the Schild–Vakulik model that previously described successfully the microlensing and other properties of Q0957. Adopting 3300 km s⁻¹ for the transverse velocity of the source, the effective size of the central source was determined to be about  2 × 10¹⁵ cm  , and  ɛ≈ 2  was obtained for the ratio of the integral luminosity of the outer feature to that of the central source.     

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.     

An absorption event in the X-ray light curve of NGC 3227

We have monitored the Seyfert galaxy NGC 3227 with the Rossi X-ray Timing Explorer ( RXTE ) since 1999 January. During late 2000 and early 2001 we observed an unusual hardening of the 2–10 keV X-ray spectrum which lasted several months. The spectral hardening was not accompanied by any correlated variation in flux above 8 keV. We therefore interpret the spectral change as transient absorption by a gas cloud of column density 2.6 × 10²³ cm⁻² crossing the line of sight to the X-ray source. A spectrum obtained by XMM–Newton during an early phase of the hard-spectrum event confirms the obscuration model and shows that the absorbing cloud is only weakly ionized. The XMM–Newton spectrum also shows that ∼10 per cent of the X-ray flux is not obscured, but this unabsorbed component is not significantly variable and may be scattered radiation from a large-scale scattering medium. Applying the spectral constraints on the cloud ionization parameter and assuming that the cloud follows a Keplerian orbit, we constrain the location of the cloud to be   R ∼ 10–100  light-days from the central X-ray source, and its density to be   n _H∼ 10⁸ cm⁻³  , implying that we have witnessed the eclipse of the X-ray source by a broad line region cloud.     

The European Large Area ISO Survey – IV. The preliminary 90-μm luminosity function

We present the luminosity function of 90-μm-selected galaxies from the European Large Area ISO Survey (ELAIS), extending to z =0.3. Their luminosities are in the range 10⁹65⁻² L /L_⊙<10¹², i.e. non-ultraluminous. From our sample of 37 reliably detected galaxies in the ELAIS S1 region from the Efstathiou et al. S ₉₀100 mJy data base, we have found optical, 15-μm or 1.4-GHz identifications for 24 (65 per cent). We have obtained 2dF and UK Schmidt FLAIR spectroscopy of 89 per cent of identifications to rigid multivariate flux limits. We construct a luminosity function assuming that (i) our spectroscopic subset is an unbiased sparse sample, and (ii) there are no galaxies that would not be represented in our spectroscopic sample at any redshift. We argue that we can be confident of both assumptions. We find that the luminosity function is well described by the local 100-μm luminosity function of Rowan-Robinson, Helou & Walker. Assuming this local normalization, we derive luminosity evolution of (1+ z )^2.45±0.85 (95 per cent confidence). We argue that star formation dominates the bolometric luminosities of these galaxies, and we derive comoving star formation rates in broad agreement with the Flores et al. and Rowan-Robinson et al. mid-infrared-based estimates.     

Production of neutrons, neutrinos and gamma-rays by a very fast pulsar in the Galactic Centre region

We consider the possibility that the excess of cosmic rays near ∼10¹⁸ eV, reported by the AGASA and SUGAR groups from the direction of the Galactic Centre, is caused by a young, very fast pulsar in the high-density medium. The pulsar accelerates iron nuclei to energies ∼10²⁰ eV, as postulated by the Galactic models for the origin of the highest-energy cosmic rays. The iron nuclei, about 1 yr after pulsar formation, leave the supernova envelope without energy losses and diffuse through the dense central region of the Galaxy. Some of them collide with the background matter creating neutrons (from disintegration of Fe), neutrinos and gamma-rays (in inelastic collisions). We suggest that neutrons produced at a specific time after the pulsar formation are responsible for the observed excess of cosmic rays at ∼10¹⁸ eV. From normalization of the calculated neutron flux to the one observed in the cosmic ray excess, we predict the neutrino and gamma-ray fluxes. It has been found that the 1 km² neutrino detector of the IceCube type should detect from a few up to several events per year from the Galactic Centre, depending on the parameters of the considered model. Moreover, future systems of Cherenkov telescopes (CANGAROO III, HESS, VERITAS) should be able to observe  1–10 TeV  gamma-rays from the Galactic Centre if the pulsar was created inside a huge molecular cloud about  3–10×10³ yr  ago.     

A small source in Q2237+0305?

Microlensing in Q2237+0305 between 1985 and 1995 has been interpreted in two different ways. First, the observed variations can be explained through microlensing by stellar mass objects of a continuum source with dimensions significantly smaller than the microlens Einstein Radius ( ₀), but consistent with that expected for thermal accretion discs . However, other studies have shown that models having sources as large as 5 ₀ can reproduce the observed variation . In this paper we present evidence in favour of a small source. Our approach uses the distribution of microlensed light-curve derivatives to place statistical limits (as a function of source size) on the number of microlens Einstein radii crossed by the source during the monitoring period. In contrast with previous analyses, our results are therefore not dependent on an assumed time-scale. Limits on the source size are obtained from two separate light-curve features. First, recently published monitoring data show large variations (0.81.5 mag) between image brightnesses over a period of 700 d or 15 per cent of the monitoring period. Secondly, the 1988 peak in the image A light curve had a duration that is a small fraction (0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large, rapid variation limits the source size to be <0.2 ₀ (95 per cent confidence). The width of the light-curve peak provides a stronger constraint of <0.025 ₀ (99 per cent confidence). The Einstein radius (projected into the source plane) of the average microlens mass m in Q2237+0305 is The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.