Time evolution of orbital uncertainties for the impactor candidate 2004 AS1

We evaluate the asteroid impact risk from the discovery night onwards using six-dimensional statistical orbit computation techniques to examine the a posteriori probability density of the orbital elements. Close to the discovery moment the observational data of an object are typically exiguous: the number of observations is very small and/or the covered orbital arc is very short. For such data, the covariance matrices computed in the linear approximation (e.g., with the least-squares technique) are known to fail to describe the uncertainties in the orbital parameters. The technique of statistical ranging gives us rigorous means to assess the orbital uncertainties already on the discovery night. To examine the time evolution of orbital uncertainties, we make use of a new nonlinear Monte Carlo technique of phase-space sampling using volumes of variation, which complements the ranging technique for exiguous data and the least-squares technique for extensive observational data. We apply the statistical techniques to the near-Earth Asteroid 2004 AS₁, which grabbed the attention of asteroid scientists because, for one day, it posed the highest and most immediate impact risk so far recorded. We take this extreme case to illustrate the ambiguities in the impact risk assessment for short arcs. We confirm that the weighted fraction of the collision orbits at discovery was large but conclude that this was mostly due to the discordance of the discovery-night observations. This case study highlights the need to introduce a regularization in terms of an a priori probability density to secure the invariance of the probabilistic analysis especially in the nonlinear orbital inversion for short arcs. We remark that a predominant role of the a priori can give indications of the feasibility of the probabilistic interpretation, that is, how reliable the results derived from the a posteriori probability density are. Nevertheless, the strict mathematical definition of, e.g., the collision probability remains valid, and our nonlinear statistical techniques give us the means to always deduce, at the very least, order-of-magnitude-estimates for the collision probability.     

Kinematical studies of the low-mass X-ray binary GR Mus (XB 1254–690)

We present simultaneous high-resolution optical spectroscopy and X-ray data of the X-ray binary system GR Mus (XB 1254–690), obtained over a full range of orbital phases. The X-ray observations are used to re-establish the orbital ephemeris for this source. The optical data include the first spectroscopic detection of the donor star in this system through the use of the Doppler Tomography technique on the Bowen fluorescence blend (∼4630–4650 Å). In combination with an estimate for the orbital parameters of the compact object using the wings of the He  ii λ4686 emission line, dynamical mass constraints of  1.20 ≤ M _X /M_⊙≤ 2.64  for the neutron star and  0.45 ≤ M ₂/M_⊙≤ 0.85  for the companion are derived.     

How selection and weighting of astrometric observations influence the impact probability. The case of asteroid (99942) Apophis

The aim of this paper is to show that in the case of a low probability of asteroid collision with the Earth, the appropriate selection and weighting of the data are crucial for the impact investigation and for analysing the impact possibilities using extensive numerical simulations. By means of the Monte Carlo special method, a large number of 'clone' orbits have been generated. A full range of orbital elements in the six-dimensional parameter space, that is, in the entire confidence region allowed by the observational material, has been examined. On the basis of 1000 astrometric observations of (99942) Apophis, the best solutions for the geocentric encounter distance of  6.065 ± 0.081 R_⊕  (without perturbations by asteroids) or  6.064 ± 0.095 R_⊕  (including perturbations by the four largest asteroids) were derived for the close encounter with the Earth on 2029 April 13. The present uncertainties allow for special configurations ('keyholes') during this encounter that may lead to very close encounters in future approaches of Apophis. Two groups of keyholes are connected with the close encounter with the Earth in 2036 (within the minimal distance of  5.7736−5.7763 R_⊕  on 2029 April 13) and 2037 (within the minimal distance of  6.3359–6.3488 R_⊕  ). The nominal orbits for our most accurate models run almost exactly in the middle of these two impact keyhole groups. A very small keyhole for the impact in 2076 has been found between these groups at the minimal distance of 5.97347   R_⊕  . This keyhole is close to the nominal orbit. The present observations are not sufficiently accurate to eliminate definitely the possibility of impact with the Earth in 2036 and for many years after.     

The orbits of open clusters in the Galaxy

We present and analyse the kinematics and orbits for a sample of 488 open clusters (OCs) in the Galaxy. The velocity ellipsoid for our present sample is derived as  (σ _U , σ _V , σ _W ) = (28.7, 15.8, 11.0) km s⁻¹  which represents a young thin-disc population. We also confirm that the velocity dispersions increase with the age of a cluster subsample. The orbits of OCs are calculated with three Galactic gravitational potential models. The errors of orbital parameters are also calculated considering the intrinsic variation of the orbital parameters and the effects of observational uncertainties. The observational uncertainties dominate the errors of derived orbital parameters. The vertical motions of clusters calculated using different Galactic disc models are rather different. The observed radial metallicity gradient of clusters is derived with a slope of   b =−0.070 ± 0.011   dex kpc⁻¹. The radial metallicity gradient of clusters based on their apogalactic distances is also derived with a slope of   b =−0.082 ± 0.014   dex kpc⁻¹. The distribution of derived orbital eccentricities for OCs is very similar to that derived for the field population of dwarfs and giants in the thin disc.     

WIYN Open Cluster Study – XVI. Optical/infrared photometry and comparisons with theoretical isochrones

We present combined optical/near-infrared photometry ( BVIK ) for six open clusters – M35, M37, NGC 1817, NGC 2477, NGC 2420 and M67. The open clusters span an age range from 150 Myr to 4 Gyr and have metal abundances from  [Fe/H]=−0.27  to +0.09 dex. We have utilized these data to test the robustness of theoretical main sequences constructed by several groups as denoted by the following designations – Padova, Baraffe, Y², Geneva and Siess. The comparisons of the models with the observations have been performed in the  [ M_V , ( B − V )₀], [ M_V , ( V − I )₀]  and  [ M_V , ( V − K )₀]  colour–magnitude diagrams as well as the distance-independent  [( V − K )₀, ( B − V )₀]  and  [( V − K )₀, ( V − I )₀]  two-colour diagrams. We conclude that none of the theoretical models reproduces the observational data in a consistent manner over the magnitude and colour range of the unevolved main sequence. In particular, there are significant zero-point and shape differences between the models and the observations. We speculate that the crux of the problem lies in the precise mismatch between theoretical and observational colour–temperature relations. These results underscore the importance of pursuing the study of stellar structure and stellar modelling with even greater intensity.     

Limits on the 2.2-μm contrast ratio of the close-orbiting planet HD 189733b

We obtained 238 spectra of the close-orbiting extrasolar giant planet HD 189733b with resolution   R ∼ 15 000  during one night of observations with the Near-Infrared High-Resolution Spectrograph (NIRSPEC), at the Keck II Telescope. We have searched for planetary absorption signatures in the  2.0–2.4 μm  region where H₂O and CO are expected to be the dominant atmospheric opacities. We employ a phase-dependent orbital model and tomographic techniques to search for the planetary absorption signatures in the combined stellar and planetary spectra. Because potential absorption signatures are hidden in the noise of each single exposure, we use a model list of lines to apply a spectral deconvolution. The resulting mean profile possesses a signal-to-noise ratio (S/N) that is 20 times greater than that found in individual lines. Our spectral time series thus yields spectral signatures with a mean S/N = 2720. We are unable to detect a planetary signature at a contrast ratio of  log₁₀( F _p/ F _*) =−3.40  , with 63.8 per cent confidence. Our findings are not consistent with model predictions which nevertheless give a good fit to mid-infrared observations of HD 189733b. The 1σ result is a factor of 1.7 times less than the predicted 2.185-μm planet/star flux ratio of  log₁₀( F _p/ F _*) ∼−3.16  .     

Collision Probability for Earth-Crossing Asteroids Using Orbital Ranging

We introduce new techniques for the computation of the collision probability for Earth-crossing asteroids in the case of short observational arcs and/or small numbers of observations. The techniques rely on the orbital element probability density computed using statistical orbital ranging. We apply the techniques to the Earth-crossing asteroid 1998 OX₄with non-vanishing collision probability in numerous close approaches after the year 2012 (inclusive). We study the invariance of the collision probability in transformations between different orbital element sets, and develop a Spearman rank correlation measure for the validity of the linear approximation. We introduce an optimized, fast version of the statistical ranging method.     

The Hubble Deep Field North reveals a supernova at z∼0.95

We report the discovery of a variable object in the Hubble Deep Field North (HDF-N) which brightened, during the 8.5 d sampled by the data, by more than 0.9 mag in I ₈₁₄ and about 0.7 mag in V ₆₀₆, remaining stable in B ₄₅₀. Subsequent observations of the HDF-N show that two years later this object has dimmed to about its original brightness in I ₈₁₄. The colours of this object, its brightness, its time behaviour in the various filters and the evolution of its morphology are consistent with it being a Type Ib supernova in a faint galaxy at z .     

A new determination of the orbit and masses of the Be binary system δ Scorpii

The binary star δ Sco (HD143275) underwent remarkable brightening in the visible in 2000, and continues to be irregularly variable. The system was observed with the Sydney University Stellar Interferometer (SUSI) in 1999, 2000, 2001, 2006 and 2007. The 1999 observations were consistent with predictions based on the previously published orbital elements. The subsequent observations can only be explained by assuming that an optically bright emission region with an angular size of  ≳2 ± 1 mas  formed around the primary in 2000. By 2006/2007 the size of this region grew to an estimated ≳4 mas.
We have determined a consistent set of orbital elements by simultaneously fitting all the published interferometric and spectroscopic data as well as the SUSI data reported here. The resulting elements and the brightness ratio for the system measured prior to the outburst in 2000 have been used to estimate the masses of the components. We find   M_A = 15 ± 7 M_⊙  and   M_B = 8.0 ± 3.6 M_⊙  . The dynamical parallax is estimated to be  7.03 ± 0.15 mas  , which is in good agreement with the revised Hipparcos parallax.     

Primordial non-Gaussianity: local curvature method and statistical significance of constraints on fNL from WMAP data

We test the consistency of estimates of the non-linear coupling constant f _NL using non-Gaussian cosmic microwave background (CMB) maps generated by the method described in the work of Liguori, Matarrese & Moscardini. This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on the estimation of f _NL. Nevertheless, using spherical wavelets, we find results in very good agreement with Mukherjee & Wang, showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling constant from CMB observations by using the local curvature of the temperature fluctuation field. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on f _NL, and discuss the relation between the two approaches. The Bayesian approach tends to yield lower error bars than the frequentist approach, suggesting that a careful analysis of the different interpretations is needed. Using this method, we estimate   f _NL=−10⁺²⁷⁰₋₂₆₀  at the 2σ level (Bayesian) and   f _NL=−10⁺³¹⁰₋₂₇₀  (frequentist). Moreover, we find that the wavelet and the local curvature approaches, which provide similar error bars, yield approximately uncorrelated estimates of f _NL and therefore, as advocated in the work of Cabella et al., the estimates may be combined to reduce the error bars. In this way, we obtain   f _NL=−5 ± 85  and   f _NL=−5 ± 175  at the 1σ and 2σ level respectively using the frequentist approach.     

The Nyquist frequency for time series with slight deviations from regular spacing

The paper is based on the notion that the Nyquist frequency  ν_N  is a symmetry point of the periodogram of a time series: the power spectrum at frequencies above  ν_N  is a mirror image of that below  ν_N  . Koen showed that the sum     (where   t_k   and   t _ℓ  range over the time points of observation) is zero when the frequency  ν=ν_N  . This property is used to investigate the Nyquist frequency for data which are almost regularly spaced in time. For some configurations, there are deep minima of SS at frequencies  ν_P≪ν_N  ; such  ν_P  are dubbed 'pseudo-Nyquist' frequencies: the implication is that most of the information about the frequency content of the data is available in the spectrum over  (0, ν_P)  . Systematic simulation results are presented for two configurations – small random variations in respectively the time points of observation and the lengths of the intervals between successive observations. A few real examples of CCD time series photometry obtained over several hours are also discussed.     

Transit timing effects due to an exomoon

As the number of known exoplanets continues to grow, the question as to whether such bodies harbour satellite systems has become one of increasing interest. In this paper, we explore the transit timing effects that should be detectable due to an exomoon and predict a new observable. We first consider transit time variation (TTV), where we update the model to include the effects of orbital eccentricity. We draw two key conclusions.

• (i) 

  In order to maintain Hill stability, the orbital frequency of the exomoon will always be higher than the sampling frequency. Therefore, the period of the exomoon cannot be reliably determined from TTV, only a set of harmonic frequencies.
• (ii) 

  The TTV amplitude is  ∝ M _S a _S  where M _S is the exomoon mass and a _S is the semimajor axis of the moon's orbit. Therefore, M _S and a _S cannot be separately determined.

We go on to predict a new observable due to exomoons – transit duration variation (TDV). We derive the TDV amplitude and conclude that its amplitude is not only detectable, but the TDV signal will also provide two robust advantages.

• (i) 

  The TDV amplitude is  ∝ M _S a ^−1/2_S  and therefore the ratio of TDV to TTV allows for M _S and a _S to be separately determined.
• (ii) 

  TDV has a π/2 phase difference to the TTV signal, making it an excellent complementary technique.

     

A new method for determining physical parameters of fundamental mode RR Lyrae stars from multicolour light curves

We present a new method for determining physical parameters of RRab variables exclusively from multicolour light curves. Our method is an inverse photometric Baade–Wesselink analysis which, using a non-linear least-squares algorithm, searches for the effective temperature ( T _eff) and pulsational velocity ( V _p) curves and other physical parameters that best fit the observed light curves, utilizing synthetic colours and bolometric corrections from static atmosphere models. The T _eff and V _p curves are initially derived from empirical relations then they are varied by the fitting algorithm. The method yields the variations and the absolute values of the radius, the effective temperature, the visual brightness and the luminosity of individual objects. Distance and mass are also determined. The method is tested on nine RRab stars subjected to Baade–Wesselink analyses earlier by several authors. The physical parameters derived by our method using only the light-curve data of these stars are well within their possible ranges defined by direct Baade–Wesselink and other techniques. A new empirical relation between the I _C magnitude and the pulsational velocity is also presented, which allows to construct the V _p curve of an RRab star purely from photometric observations to an accuracy of about 3.5 km s⁻¹.     

The radial velocity of the companion star in the low-mass X-ray binary 2S 0921–630: limits on the mass of the compact object

In this paper we report on optical spectroscopic observations of the low-mass X-ray binary 2S 0921–630 obtained with the Very Large Telescope. We found sinusoidal radial velocity variations of the companion star with a semi-amplitude of  99.1 ± 3.1 km s⁻¹  modulated on a period of 9.006 ± 0.007 d, consistent with the orbital period found previously for this source, and a systemic velocity of  44.4 ± 2.4 km s⁻¹  . Owing to X-ray irradiation, the centre of light measured by the absorption lines from the companion star is probably shifted with respect to the centre of mass. We try to correct for this using the so-called K -correction. Conservatively applying the maximum correction possible and using the previously measured rotational velocity of the companion star, we find a lower limit to the mass of the compact object in 2S 0921–630 of   M_X sin³ i > 1.90 ± 0.25 M_⊙  (1σ errors). The inclination in this system is well constrained since partial eclipses have been observed in X-ray and optical bands. For inclinations in the range  60° < i < 90°  we find  1.90 ± 0.25 < M_X < 2.9 ± 0.4 M_⊙  . However, using this maximum K -correction we find that the ratio between the mass of the companion star and that of the compact object, q , is 1.32 ± 0.37, implying super-Eddington mass-transfer rates; however, evidence for that has not been found in 2S 0921–630. We conclude that the compact object in 2S 0921–630 is either a (massive) neutron star or a low-mass black hole.     

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

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

The optical spectrum of the planetary nebula NGC 6543

With the Hamilton echelle spectrograph at the Lick Observatory, emission-rich spectral lines of the planetary nebula NGC 6543 were secured in the wavelength range from 3550 to 10 100 Å. We chose two bright regions, ∼8 arcsec east and ∼13 arcsec north of the central star, the physical conditions and chemical abundances of which may differ as a result of the different physical characteristics involving the mass ejection of different epochs. By combining Hamilton echelle observations with archive UV data secured with the International Ultraviolet Explorer ( IUE ), we obtain improved diagnostics and chemical compositions for the two observed regions. The diagnostic diagram gives the average value of T _e=8000∼8300 K, and the electron number density near N _e∼5000 cm⁻³ for most ions, while some low-excitation lines indicate much higher temperatures, i.e. T _e∼10 000 K. With the construction of a photoionization model, we try to fit the observed spectra in a self-consistent way: thus, for most elements, we employ the same chemical abundances in the nebular shell; and we adopt an improved Sobolev approximation model atmosphere for the hydrogen-deficient Wolf–Rayet type central star. Within the observational errors, the chemical abundances do not seem to show any positional variation except for helium. The chemical abundances of NGC 6543 appear to be the same as in average planetary nebulae. The progenitor star may have been an object of one solar mass, most of the heavier elements of which were less plentiful than in the Sun.     

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.     

Expected planets in globular clusters

We argue that all transient searches for planets in globular clusters have a very low detection probability. Planets of low-metallicity stars typically do not reside at small orbital separations. The dependence of planetary system properties on metallicity is clearly seen when the quantity   I _e ≡ M _p[ a (1 − e )]²  is considered;   M _p, a   and e are the planet mass, semimajor axis and eccentricity, respectively. In high-metallicity systems, there is a concentration of systems at high and low values of I _e , with a low-populated gap near   I _e ∼ 0.3 M _J au²  , where M _J is Jupiter's mass. In low-metallicity systems, the concentration is only at the higher range of I _e , with a tail to low values of I _e . Therefore, it is still possible that planets exist around main-sequence stars in globular clusters, although at small numbers because of the low metallicity, and at orbital periods of ≳10 d. We discuss the implications of our conclusions on the role that companions can play in the evolution of their parent stars in globular clusters, for example, influencing the distribution of horizontal branch stars on the Hertzsprung–Russell diagram of some globular clusters, and in forming low-mass white dwarfs.     

The Parkes Multibeam Pulsar Survey: PSR J1811−1736, a pulsar in a highly eccentric binary system

We are undertaking a high-frequency survey of the Galactic plane for radio pulsars, using the 13-element multibeam receiver on the 64-m Parkes radio telescope. We describe briefly the survey system and some of the initial results. PSR J1811−1736, one of the first pulsars discovered with this system, has a rotation period of 104 ms. Subsequent timing observations using the 76-m radio telescope at Jodrell Bank show that it is in an 18.8-d, highly eccentric binary orbit. We have measured the rate of advance of periastron which indicates a total system mass of 2.6±0.9 M_⊙, and the minimum companion mass is about 0.7 M_⊙. This, the high orbital eccentricity and the recycled nature of the pulsar suggest that this system is composed of two neutron stars, only the fourth or fifth such system known in the disc of the Galaxy.     

Investigating the Andromeda stream – II. Orbital fits and properties of the progenitor

We construct test-particle orbits and simple N -body models that match the properties of the giant stellar stream observed to the south of M31, using the model of M31's potential derived in the companion paper by Geehan et al. We introduce a simple approximation to account for the difference in position between the stream and the orbit of the progenitor; this significantly affects the best-fitting orbits. The progenitor orbits we derive have orbital apocentre  ∼60 kpc  and pericentre  ∼3 kpc  , though these quantities vary somewhat with the current orbital phase of the progenitor which is as yet unknown. Our best combined fit to the stream and galaxy properties implies a mass within 125 kpc of M31 of  (7.4 ± 1.2) × 10¹¹ M_⊙  . Based on its length, width, luminosity, and velocity dispersion, we conclude that the stream originates from a progenitor satellite with mass   M _s∼ 10⁹ M_⊙  , and at most modest amounts of dark matter; the estimate of M _s is again correlated with the phase of the progenitor. M31 displays a large number of faint features in its inner halo which may be progenitors or continuations of the stream. While the orbital fits are not constrained enough for us to conclusively identify the progenitor, we can identify several plausible candidates, of which a feature in the planetary nebula distribution found by Merrett et al. is the most plausible, and rule out several others. We make predictions for the kinematic properties of the successful candidates. These may aid in observational identification of the progenitor object, which would greatly constrain the allowed models of the stream.