Spectral lags caused by the curvature effect of fireballs

Recently, Shen et al. have studied the contributions of the curvature effect of fireballs to the spectral lag and have shown that the observed lags can be accounted for by the effect. Here, we check their results by performing a more precise calculation with both formulae presented by Shen et al. and Qin et al. Several other aspects which were not considered by Shen et al. are investigated. We find that in the case of ultrarelativistic motions, both formulae are identical as long as the whole fireball surface is concerned. In our analysis, the previous conclusion that the detected spectral lags can be accounted for by the curvature effect is confirmed, while the conclusion that the lag has no dependence on the radius of fireballs is not true. We find that introducing extreme physical parameters is not the only outlet to explain these observed large lags. Even for the larger lags (∼5 s), a wider local pulse  (Δ t _θ,FWHM= 10⁷ s)  can account for it. Some conclusions not presented in Shen et al. or those modified in our analysis are listed below: (i)  lag ∝Γ^−ε  with  ε > 2  ; (ii) lag is proportional to the local pulse width and the full width at half-maximum of the observed light curves; (iii) a large lag requires a large α₀ and a small β₀ as well as a large   E _0,p  ; (iv) when the rest-frame spectrum varies with time, the lag would become larger; (v) lag decreases with the increase of   R_c   ; (vi) lag ∝ E within the certain energy range for a given Lorentz factor; (vii) lag is proportional to the opening angle of uniform jets when  θ_j < 0.6Γ⁻¹  .     

Gamma-ray burst afterglows: effects of radiative corrections and non-uniformity of the surrounding medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be the result of continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, i.e. n _ext ∝  R ^{− k} , we study the effects of the first-order radiative correction and the non-uniformity of the medium on a GRB afterglow analytically. We first derive a new relation among the observed time, the shock radius and the Lorentz factor of the fireball: t _⊕ =  R /4(4− k ) γ²c, and also derive a new relation among the comoving time, the shock radius and the Lorentz factor of the fireball: t _co = 2 R /(5− k ) γc. We next study the evolution of the fireball by using the analytic solution of Blandford &38; McKee. The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is p  = 2.5, implied from the spectra of GRBs, the X-ray afterglow of GRB 970616 is well fitted by assuming k  = 2.     

Spectral variability of ultraluminous X-ray sources

We study spectral variability of 11 ultraluminous X-ray sources (ULX) using archived XMM–Newton and Chandra observations. We use three models to describe the observed spectra: a power law, a multicolour disc (MCD) and a combination of these two models. We find that seven ULXs show a correlation between the luminosity L _X and the photon index Γ. Furthermore, four out of these seven ULXs also show spectral pivoting in the observed energy band. We also find that two ULXs show an   L _X–Γ  anticorrelation. The spectra of four ULXs in the sample can be adequately fitted with a MCD model. We compare these sources to known black hole binaries (BHB) and find that they follow similar paths in their luminosity–temperature diagrams. Finally, we show that the 'soft excess' reported for many of these ULXs at ∼0.2 keV seems to roughly follow a trend   L _soft∝ T ^−3.5  when modelled with a power law plus a 'cool' MCD model. This is contrary to the   L ∝ T ⁴  relation that is expected from theory and what is seen for many accreting BHBs. The observed trend could instead arise from disc emission beamed by an outflowing wind around a  ∼10 M_⊙  black hole.     

A survey of hard spectrum ROSAT sources – I. X-ray source catalogue

We present a catalogue of 147 serendipitous X-ray sources selected to have hard spectra ( α <0.5) from a survey of 188 ROSAT fields. Such sources must be the dominant contributors to the X-ray background at faint fluxes. We have used Monte Carlo simulations to verify that our technique is very efficient at selecting hard sources: the survey has 10 times as much effective area for hard sources as it has for soft sources above a 0.5–2 keV flux level of 10⁻¹⁴ erg cm⁻² s⁻¹. The distribution of best-fitting spectral slopes of the hard sources suggests that a typical ROSAT hard source in our survey has a spectral slope α ∼0. The hard sources have a steep number flux relation (d N /d S ∝ S ^{− γ} with a best-fitting value of γ =2.72±0.12) and make up about 15 per cent of all 0.5–2 keV sources with S >10⁻¹⁴ erg cm⁻² s⁻¹. If their N ( S ) continues to fainter fluxes, the hard sources will comprise ∼40 per cent of sources with 5×10⁻¹⁵< S <10⁻¹⁴ erg cm⁻² s⁻¹. The population of hard sources can therefore account for the harder average spectra of ROSAT sources with S <10⁻¹⁴ erg cm⁻² s⁻¹. They probably make a strong contribution to the X-ray background at faint fluxes and could be the solution to the X-ray background spectral paradox.     

Millimetre and submillimetre continuum observations of the core and hotspots of Cygnus A

We present millimetre photometry and submillimetre imaging of the central core and two hotspots in the radio lobes of the galaxy Cygnus A. For both hotspots and the central core, the synchrotron spectrum continues smoothly from the radio to a frequency of 677 GHz. The spectral index of the hotspots is constant over our frequency range, with a spectral index of α ≈ −1.0 ( S _ν ∝ ν^α), which is steeper than at lower frequencies and represents the emission from an aged population of electrons. The core is significantly flatter, with α = −0.6 ± 0.1, suggestive of an injected spectrum with no ageing, but some evidence for steepening exists at our highest observing frequency. Although IRAS data suggest the presence of dust in Cygnus A, our 450-μm data show no evidence of cold dust, therefore the dust component must have a temperature lying between 85 and 37 K, corresponding to dust masses of 1.4 × 10⁶ and 1.0 × 10⁸ M_⊙ respectively.     

X-ray variability of the Seyfert 1 Markarian 335: power spectrum and time lags

To investigate further the comparison between active galactic nuclei (AGN) and black hole X-ray binaries, we have studied the main X-ray variability properties of the Seyfert 1 galaxy Mrk 335. We put particular emphasis on the X-ray time lags, which is a potentially important diagnostic of physical models. From a 100 ks observation by XMM–Newton , we show that the power spectrum of this source is well fitted by a bending power-law model, and the bend time-scale T _b is precisely at the value predicted by the T _b versus Hβ linewidth relation of McHardy et al. Variations in different energy bands show time-scale-dependent time lags, where higher energy bands lag lower ones. The lag, τ, varies as a function of the Fourier frequency, f , of the variability component in the light curves as  τ∝ f ⁻¹  at low frequencies, but there is a sharp cut-off in the lags at a frequency close to the bend frequency in the power spectrum. Similar behaviour is seen in black hole X-ray binary systems. The length of the time lags increases continuously with energy separation, in an almost loglinear relation. We show that the lag spectra can be produced by fluctuations propagating through the accretion flow as long as the energy spectrum of the X-ray emitting region hardens towards the centre.     

AMI limits on 15-GHz excess emission in northern H ii regions

We present observations between 14.2 and 17.9 GHz of 16 Galactic H  ii regions made with the Arcminute Microkelvin Imager. In conjunction with data from the literature at lower radio frequencies we investigate the possibility of a spinning dust component in the spectra of these objects. We conclude that there is no significant evidence for spinning dust towards these sources and measure an average spectral index of  α= 0.15 ± 0.07  (where   S ∝ν^−α  ) between 1.4 and 17.9 GHz for the sample.     

Non-linear evolution of suppressed dark matter primordial power spectra

We address the degree and rapidity of generation of small-scale power over the course of structure formation in cosmologies where the primordial power spectrum is strongly suppressed beyond a given wavenumber. We first summarize the situations where one expects such suppressed power spectra and point out their diversity. We then employ an exponential cut-off, which characterizes warm dark matter (WDM) models, as a template for the shape of the cut-off and focus on damping scales ranging from 10⁶ to  10⁹  h ⁻¹ M_⊙  . Using high-resolution simulations, we show that the suppressed part of the power spectrum is quickly (re)generated and catches up with both the linear and the non-linear evolution of the unsuppressed power spectrum. From   z = 2  onwards, a power spectrum with a primordial cut-off at  10⁹  h ⁻¹ M_⊙  becomes virtually indistinguishable from an evolved cold dark matter (CDM) power spectrum. An attractor such as that described in Zaldarriaga, Scoccimarro & Hui for power spectra with different spectral indices also emerges in the case of truncated power spectra. Measurements of   z ∼ 0  non-linear power spectra at  ∼100  h ⁻¹ kpc  cannot rule out the possibility of linear power spectra damped below  ∼10⁹  h ⁻¹ M_⊙  . Therefore, WDM or scenarios with similar features should be difficult to exclude in this way.     

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.     

Parameters of core collapse

This paper considers the phenomenon of deep core collapse in collisional stellar systems, with stars of equal mass. The collapse takes place on some multiple,  ξ⁻¹  , of the central relaxation time, and produces a density profile in which  ρ∝ r ^−α  , where α is a constant. The parameters α and ξ have usually been determined from simplified models, such as gas and Fokker–Planck models, often with the simplification of isotropy. Here we determine the parameters directly from N -body simulations carried out using the newly completed GRAPE-6.     

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.     

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.     

Sakurai's Object: characterizing the near-infrared CO ejecta between 2003 and 2007

We present observations of Sakurai's Object obtained at 1–5 μm between 2003 and 2007. By fitting a radiative transfer model to an echelle spectrum of CO fundamental absorption features around  4.7 μm  , we determine the excitation conditions in the line-forming region. We find  ¹²C/¹³C = 3.5^+2.0_−1.5  , consistent with CO originating in ejecta processed by the very late thermal pulse, rather than in the pre-existing planetary nebula. We demonstrate the existence of  2.2 × 10⁻⁶≤ M _CO≤ 2.7 × 10⁻⁶ M_⊙  of CO ejecta outside the dust, forming a high-velocity wind of  500 ± 80 km s⁻¹  . We find evidence for significant weakening of the CO band and cooling of the dust around the central star between 2003 and 2005. The gas and dust temperatures are implausibly high for stellar radiation to be the sole contributor.     

Cygnus X-3 with ISO: investigating the wind

We have observed the energetic binary Cygnus X-3 in both quiescent and flaring states between 4 and 16 μm using the ISO satellite. We find that the quiescent source shows the thermal free–free spectrum typical of a hot, fast stellar wind, such as from a massive helium star. The quiescent mass-loss rate arising from a spherically symmetric, non-accelerating wind is found to be in the range (0.4–2.9)×10⁻⁴ M_⊙ yr⁻¹, consistent with other infrared and radio observations, but considerably larger than the 10⁻⁵ M_⊙ yr⁻¹ deduced from both the orbital change and the X-ray column density. There is rapid, large-amplitude flaring at 4.5 and 11.5 μm at the same time as enhanced radio and X-ray activity, with the infrared spectrum apparently becoming flatter in the flaring state. We believe that non-thermal processes are operating, perhaps along with enhanced thermal emission.     

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.     

Long-term variability of the low-luminosity active galactic nucleus of M81

Long-term X-ray variability of the low-luminosity active galactic nucleus of M81 was studied, using 16 ASCA observations spanning 5.5 yr. The object exhibits a factor of 3 variation over the 5.5 yr. The source intensity was relatively constant within each observation which lasted typically for one day, but intra-day variability by 30 per cent was detected on the 15th observation. The power-spectral density (PSD) was estimated in a 'forward' manner, over a frequency range of 10^−8.2–10^−4.3 Hz (period range of 0.25 d–5.5 yr), by utilizing the structure function and extensive Monte Carlo simulations in order to overcome the very sparse and uneven data samplings. When the PSD is assumed to be white below a 'break frequency' f _b and falls off as ∝  f ^{− α} above f _b, where f is frequency and α is a positive parameter, the M81 light curve is well described with 1/ f _b≥800 d and α =1.4±0.2.     

Optimal filters for the construction of the ensemble pulsar time

An algorithm of the ensemble pulsar time based on the optimal Wiener filtration method has been constructed. This algorithm allows the separation of the contributions to the post-fit pulsar timing residuals of the atomic clock and the pulsar itself. Filters were designed using the cross- and auto-covariance functions of the timing residuals. The method has been applied to the timing data of millisecond pulsars PSR B1855+09 and B1937+21 and allowed the filtering out of the atomic-scale component from the pulsar data. Direct comparison of the terrestrial time TT(BIPM06) and the ensemble pulsar time PT_ens revealed that the fractional instability of TT(BIPM06)−PT_ens is equal to  σ _z = (0.8 ± 1.9) × 10⁻¹⁵  . Based on the  σ _z   statistics of TT(BIPM06)−PT_ens, a new limit of the energy density of the gravitational wave background was calculated to be equal to  Ω_g h ²∼ 3 × 10⁻⁹  .     

The local star formation rate and radio luminosity density

We present a new determination of the local volume-averaged star formation rate from the 1.4-GHz luminosity function of star forming galaxies. Our sample, taken from the   B ≤12  Revised Shapley–Ames catalogue (231 normal spiral galaxies over an effective area of 7.1 sr) has ≃100 per cent complete radio detections and is insensitive to dust obscuration and cirrus contamination. After removal of known active galaxies, the best-fitting Schechter function has a faint-end slope of  −1.27±0.07  in agreement with the local H α luminosity function, characteristic luminosity   L ∗=(2.6±0.7)×10²² W Hz⁻¹  and density   φ ∗=(4.8±1.1)×10⁻⁴ Mpc⁻³.  The inferred local radio luminosity density of  (1.73±0.37±0.03)×10¹⁹ W Hz⁻¹ Mpc⁻³  (Poisson noise, large-scale structure fluctuations) implies a volume-averaged star formation rate ∼2 times larger than the Gallego et al. H α estimate, i.e.   ρ _1.4 GHz=(2.10±0.45±0.04)×10⁻² M_⊙ yr⁻¹ Mpc⁻³  for a Salpeter initial mass function from  0.1–125 M_⊙  and Hubble constant of 50 km s⁻¹ Mpc⁻¹. We demonstrate that the Balmer decrement is a highly unreliable extinction estimator, and argue that optical–ultraviolet (UV) star formation rates (SFRs) are easily underestimated, particularly at high redshift.     

A Chandra observation of the distant radio galaxy B2 0902+343: a powerful obscured active galaxy

We report a Chandra observation of the   z =3.395  radio galaxy B2 0902+343. The unresolved X-ray source is centred on the active nucleus. The spectrum is well fitted by a flat power law of photon index of  Γ∼1.1  with intrinsic absorption of  8×10²² cm^-2  , and an intrinsic  2–10 keV  luminosity of  3.3×10⁴⁵ erg s^-1  . More complex models that allow for a steeper spectral index cause the column density and intrinsic luminosity to increase. The data limit any thermal luminosity of the hot magnetized medium, assumed responsible for high Faraday rotation measures seen in the radio source, to less than ∼10⁴⁵ erg s⁻¹.