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.

     

Stellar velocity dispersion in narrow-line Seyfert 1 galaxies

Several authors have recently explored, for narrow-line Seyfert 1 galaxies (NLS1s), the relationship between black hole mass ( M _BH) and stellar velocity dispersion (σ_*). Their results are more or less in agreement and seem to indicate that NLS1s fill the region below the fit obtained by Tremaine et al., showing a range of σ_* similar to that of Seyfert 1 galaxies, and a lower M _BH. Until now, the [O  iii ] width has been used in place of the stellar velocity dispersion, but some indications have begun to arise against the effectiveness of the gaseous kinematics in representing the bulge potential, at least in NLS1s. Bian & Zhao have stressed the urgency of producing true σ_* measurements. Here, we present new stellar velocity dispersions obtained through direct measurements of the Ca  ii absorption triplet (∼8550 Å) in the nuclei of eight NLS1 galaxies. The resulting σ_* values and a comparison with σ_[O III] confirm our suspicion that [O  iii ] typically overestimates the stellar velocity dispersion. We demonstrate that NLS1s follow the   M _BH–σ_*  relation as Seyfert 1, quasars and non-active galaxies.     

Redshift and velocity dispersion of the cluster of galaxies around NGC 326

Redshifts of several galaxies thought to be associated with NGC 326 are determined. The results confirm the presence of a cluster and find a mean redshift of     and a line-of-sight velocity dispersion σ _z =599 (+230,−110) km s⁻¹. The velocity dispersion and previously measured X-ray gas temperature of kT ≃1.9 keV are consistent with the cluster σ _z kT relation, and NGC 326 is seen to be a slowly moving member of the cluster.     

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.     

The edge-on spiral gravitational lens B1600+434

We present new observations of the gravitational lens (GL) system B1600+434, strongly suggesting that the lens is an edge-on spiral galaxy. These observations are used to constrain the mass model of the system, in particular the oblateness and velocity dispersion of the dark matter halo around the lensing galaxy. From an analytical model we find a lower limit on the halo oblateness q _halo=( c/a )_ρ≳0.4; more detailed numerical models give a lower limit of q _halo≳0.5. We determine an average halo velocity dispersion of σ_halo=190±15 km s⁻¹ over all non-singular isothermal elliptical (NIE) halo models. Constraining the models to larger and more massive discs decreases this average by only 10 km s⁻¹. A lower limit of σ_halo≳150 km s⁻¹ is found, even for disc masses larger than the mass inside the Einstein radius. This lower limit indicates the need for a massive dark matter halo, contributing at least half of the mass inside the Einstein radius. Time-delay calculations give (54±3)/ h ₅₀ d for the NIE halo model and (70±4)/ h ₅₀ d for the modified Hubble profile (MHP) halo model. Although the time delay for both NIE and MHP halo models is well constrained on our parameter grid, it strongly depends on the halo surface density profile. We furthermore find that the presence of a flat luminous mass distribution can severely alter the statistical properties of the lens.     

The black hole mass–stellar velocity dispersion correlation: bulges versus pseudo-bulges

We investigate the correlation between the supermassive black holes (SMBHs) mass ( M _bh) and the stellar velocity dispersion  (σ_*)  in two types of host galaxies: the early-type bulges (disc galaxies with classical bulges or elliptical galaxies) and pseudo-bulges. In the form  log ( M _bh/M_⊙) =α+β log (σ_*/200 km s⁻¹)  , the best-fitting results for the 39 early-type bulges are the slope  β= 4.06 ± 0.28  and the normalization  α= 8.28 ± 0.05  ; the best-fitting results for the nine pseudo-bulges are  β= 4.5 ± 1.3  and  α= 7.50 ± 0.18  . Both relations have intrinsic scatter in  log  M _bh  of ≲0.27 dex. The   M _bh–σ_*  relation for pseudo-bulges is different from the relation in the early-type bulges over the 3σ significance level. The contrasting relations indicate the formation and growth histories of SMBHs depend on their host type. The discrepancy between the slope of the   M _bh–σ_*  relations using different definition of velocity dispersion vanishes in our sample, a uniform slope will constrain the coevolution theories of the SMBHs and their host galaxies more effectively. We also find the slope for the 'core' elliptical galaxies at the high-mass range of the relation appears steeper  (β≃ 5–6)  , which may be the imprint of their origin of dissipationless mergers.     

Kinematics and history of the solar neighbourhood revisited

We use proper motions and parallaxes from the new reduction of Hipparcos data and Geneva–Copenhagen radial velocities for a complete sample of  ∼15 000  main-sequence and subgiant stars, and new Padova isochrones to constrain the kinematics and star formation history of the solar neighbourhood. We rederive the solar motion and the structure of the local velocity ellipsoids. When the principal velocity dispersions are assumed to increase with time as   t ^β  , the index β is larger for  σ _W (β _W ≈ 0.45  ) than for  σ _U (β _U ≈ 0.31)  . For the three-dimensional velocity dispersion, we obtain  β= 0.35  . We exclude saturation of disc heating after  ∼3 Gyr  as proposed by Quillen & Garnett. Saturation after  ≳4 Gyr  combined with an abrupt increase in velocity dispersion for the oldest stars cannot be excluded. For all our models, the star formation rate (SFR) is declining, being a factor of 2–7 lower now than it was at the beginning. Models in which the SFR declines exponentially favour very high disc ages between 11.5 and 13 Gyr and exclude ages below  ∼10.5 Gyr  as they yield worse fits to the number density and velocity dispersion of red stars. Models in which the SFR is the sum of two declining exponentials representing the thin and thick discs favour ages between 10.5 and 12 Gyr with a lower limit of  ∼10.0 Gyr  . Although in our models the SFR peaked surprisingly early, the mean formation time of solar-neighbourhood stars is later than in ab initio models of galaxy formation, probably on account of weaknesses in such models.     

Streaming motions of galaxy clusters within 12 000 km s−1– I. New spectroscopic data

We present new spectroscopic data for 532 early-type galaxies, predominantly Abell cluster members with cz <12 000 km s⁻¹. We tabulate 919 individual measurements, from six observing runs, for recession velocity, cz , central velocity dispersion, σ , and magnesium line-strength indices, Mg₂ and Mg b . The median estimated error, per measurement, in σ is 5 per cent. The Mg₂ line-strength data have median errors of 0.009 mag. The observed scatter between repeat measurements is largely accounted for by photon-counting errors. These data will be employed in forthcoming papers, where they will form part of a merged and standardized catalogue of Fundamental Plane data for use in cluster distance estimates and peculiar velocity analyses.     

An XMM–Newton observation of the neutron star X-ray transient 2S 1803−245 in quiescence

We observed the neutron star X-ray transient 2S 1803−245 in quiescence with the X-ray satellite XMM–Newton , but did not detect it. An analysis of the X-ray bursts observed during the 1998 outburst of 2S 1803−245 gives an upper limit to the distance of ≤7.3 kpc, leading to an upper limit on the quiescent 0.5–10 keV X-ray luminosity of  ≤2.8 × 10³² erg s⁻¹  (3σ). Since the expected orbital period of 2S 1803−245 is several hours, this limit is not much higher than those observed for the quiescent black hole transients with similar orbital periods.     

Satellite kinematics – II. The halo mass–luminosity relation of central galaxies in SDSS

The kinematics of satellite galaxies reflect the masses of the extended dark matter haloes in which they orbit, and thus shed light on the mass–luminosity relation (MLR) of their corresponding central galaxies. In this paper, we select a large sample of centrals and satellites from the Sloan Digital Sky Survey and measure the kinematics (velocity dispersions) of the satellite galaxies as a function of the r -band luminosity of the central galaxies. Using the analytical framework presented in More, van den Bosch & Cacciato, we use these data to infer both the mean and the scatter of the MLR of central galaxies, carefully taking account of selection effects and biases introduced by the stacking procedure. As expected, brighter centrals on average reside in more massive haloes. In addition, we find that the scatter in halo masses for centrals of a given luminosity,  σ_{log  M}   , also increases with increasing luminosity. As we demonstrate, this is consistent with  σ_{log  L}   , which reflects the scatter in the conditional probability function   P ( L _c| M )  , being independent of halo mass. Our analysis of the satellite kinematics yields  σ_{log  L} = 0.16  ±  0.04  , in excellent agreement with constraints from clustering and group catalogues, and with predictions from a semi-analytical model of galaxy formation. We thus conclude that the amount of stochasticity in galaxy formation, which is characterized by  σ_{log  L}   , is well constrained, independent of halo mass and in a good agreement with current models of galaxy formation.     

Disc heating in NGC 2985

Various processes have been proposed to explain how galaxy discs acquire their thickness. A simple diagnostic for ascertaining this 'heating' mechanism is provided by the ratio of the vertical to radial velocity dispersion components. In a previous paper we have developed a technique for measuring this ratio, and demonstrated its viability on the Sb system NGC 488. Here we present follow-up observations of the morphologically similar Sab galaxy NGC 2985, still only the second galaxy for which this ratio has been determined outside the solar neighbourhood. The result is consistent with simple disc-heating models that predict ratios of σ _z σ _R less than one.     

Observable consequences of kinetic and thermal AGN feedback in elliptical galaxies and galaxy clusters

We have constructed an analytical model of active galactic nuclei (AGN) feedback and studied its implications for elliptical galaxies and galaxy clusters. The results show that momentum injection above a critical value will eject material from low-mass elliptical galaxies, and leads to an X-ray luminosity, L _X, that is  ∝σ⁸⁻¹⁰  , depending on the AGN fuelling mechanism, where σ is the velocity dispersion of the hot gas. This result agrees well with both observations and semi-analytic models. In more massive ellipticals and clusters, AGN outflows quickly become buoyancy dominated. This necessarily means that heating by a central cluster AGN redistributes the intracluster medium (ICM) such that the mass of hot gas, within the cooling radius, should be  ∝ L _X(< r _cool)/[ g ( r _cool)σ]  , where   g ( r _cool)  is the gravitational acceleration at the cooling radius. This prediction is confirmed using observations of seven clusters. The same mechanism also defines a critical ICM cooling time of  ∼0.5 Gyr  , which is in reasonable agreement with recent observations showing that star formation and AGN activity are triggered below a universal cooling time threshold.     

Kinematics of SDSS subdwarfs: structure and substructure of the Milky Way halo

We construct a new sample of ∼1700 solar neighbourhood halo subdwarfs from the Sloan Digital Sky Survey (SDSS), selected using a reduced proper-motion diagram. Radial velocities come from the SDSS spectra and proper motions from the light-motion curve catalogue of Bramich et al. Using a photometric parallax relation to estimate distances gives us the full phase-space coordinates. Typical velocity errors are in the range  30–50 km s⁻¹  . This halo sample is one of the largest constructed to date and the disc contamination is at a level of ≲1 per cent. This enables us to calculate the halo velocity dispersion to excellent accuracy. We find that the velocity dispersion tensor is aligned in spherical polar coordinates and that  (σ _r , σ_φ, σ_θ) = (143 ± 2, 82 ± 2, 77 ± 2) km s⁻¹  . The stellar halo exhibits no net rotation, although the distribution of   v _φ  shows tentative evidence for asymmetry. The kinematics are consistent with a mildly flattened stellar density falling with distance like   r ^−3.75  .
Using the full phase-space coordinates, we look for signs of kinematic substructure in the stellar halo. We find evidence for four discrete overdensities localized in angular momentum and suggest that they may be possible accretion remnants. The most prominent is the solar neighbourhood stream previously identified by Helmi et al., but the remaining three are new. One of these overdensities is potentially associated with a group of four globular clusters (NGC 5466, NGC 6934, M2 and M13) and raises the possibility that these could have been accreted as part of a much larger progenitor.     

Dynamics of the boxy elliptical galaxy NGC 1600

We use three-integral models to infer the distribution function (DF) of the boxy E3–E4 galaxy NGC 1600 from surface brightness and line-profile data on the minor and major axes. We assume axisymmetry and that the mass-to-light ratio is constant in the central ∼1 R _e. Stars in the resulting gravitational potential move mainly on regular orbits. We use an approximate third integral K from perturbation theory and write the DF as a sum of basis functions in the three integrals E , L _z and K . We then fit the projected moments of these basis functions to the kinematic observables and deprojected density, using a non-parametric algorithm. The deduced dynamical structure is radially anisotropic, with σ _θ σ _r ≈ σ _φ σ _r ≈0.7 on the major axis. Both on the minor axis and near the centre the velocity distribution is more isotropic; thus the model is flattened by equatorial radial orbits. The kinematic data are fitted without the need for a central black hole; the central mass determined previously from ground-based data therefore overestimates the actual black-hole mass. The mass-to-light ratio of the stars is M L _V =6  h ₅₀. The anisotropy structure of NGC 1600 with a radially anisotropic main body and more nearly isotropic centre is similar to that found recently in NGC 1399, 2434, 3379 and 6703, suggesting that this pattern may be common amongst massive elliptical galaxies. We discuss a possible merger origin of NGC 1600 in the light of these results.     

Kinematics of O-B5 giants

To study the kinematics of O-B5 giant stars (luminosity class III), 290 non-Gould belt stars with proper motions taken from the Hipparcos catalogue are used, of which 107 have radial velocities taken from other sources. Semidefinite programming solves for the kinematical parameters and the coefficients of the velocity ellipsoid. The condition that both solutions must yield the same solar velocity is enforced. The results obtained are reasonable: solar velocity of 13.83 ± 0.17 km s⁻¹; Oort's constants, in units of km s⁻¹ kpc⁻¹, A = 16.08 ± 0.72 and   B =−10.74 ± 0.65,  implying a rotational velocity of 228.0 ± 21.4 km s⁻¹ if we take the distance to the Galactic Centre as 8.5 ± 1.1 kpc; velocity dispersions, in units of km s⁻¹, of  σ _x = 32.44 ± 5.04, σ _y = 26.16 ± 2.75, σ _z = 18.71 ± 2.39  with a vertex deviation of         

A numerical algorithm for dissipative Keplerian particle discs

We present a numerical algorithm designed to study the evolution of a distribution of solid particles orbiting around the Sun that could be applied to similar systems in which f _c ≤ Ω/2π, where f _c is the frequency of collisions, and Ω is the orbital angular speed. A number of sample particles are used to represent the whole system. Binary collisions are treated in a novel way using a Monte Carlo method that works as follows. Orbits are locally sampled to compute the velocity dispersion. Then the velocity vectors of the sample particles are modified according to random collisions with virtual particles which have velocities taken from a normal distribution computed using the previously found local velocity dispersion. The energy and momentum taken up by the virtual particles are redistributed among the neighbours of the sample particle undergoing the collision, so that conservation laws are satisfied. Simulations using this model give an estimation of the final distribution of inclinations and the associated evolutionary time-scale.     

Clustering of luminous red galaxies – II. Small-scale redshift-space distortions

This is the second paper of a series where we study the clustering of luminous red galaxies (LRG) in the recent spectroscopic Sloan Digital Sky Survey (SDSS) data release, DR6, which has 75 000 LRG covering over  1 Gpc³  h ⁻³  for  0.15 < z < 0.47  . Here, we focus on modelling redshift-space distortions in  ξ(σ, π)  , the two-point correlation in separate line-of-sight and perpendicular directions, at small scales and in the line-of-sight. We show that a simple Kaiser model for the anisotropic two-point correlation function in redshift space, convolved with a distribution of random peculiar velocities with an exponential form, can describe well the correlation of LRG on all scales. We show that to describe with accuracy the so-called 'fingers-of-God' (FOG) elongations in the radial direction, it is necessary to model the scale dependence of both bias b and the pairwise rms peculiar velocity σ₁₂ with the distance. We show how both quantities can be inferred from the  ξ(σ, π)  data. From   r ≃ 10 Mpc  h ⁻¹  to   r ≃ 1 Mpc  h ⁻¹  , both the bias and σ₁₂ are shown to increase by a factor of 2: from   b = 2  to 4 and from  σ₁₂= 400  to  800 km s⁻¹  . The latter is in good agreement, within a 5 per cent accuracy in the recovered velocities, with direct velocity measurements in dark matter simulations with  Ω_m= 0.25  and  σ₈= 0.85  .     

The orbit and mass of the Sagittarius dwarf galaxy

Possible orbital histories of the Sgr dwarf galaxy are explored. A special-purpose N -body code is used to construct the first models of the Milky Way–Sgr dwarf system in which both the Milky Way and the Sgr dwarf are represented by full N -body systems and followed for a Hubble time. These models are used to calibrate a semi-analytic model of the Sgr dwarf's orbit that enables us to explore a wider parameter space than is accessible to the N -body models. We conclude that the extant data on the Sgr dwarf are compatible with a wide range of orbital histories. At one extreme the Sgr dwarf initially possesses ∼10¹¹ M_⊙ and starts from a Galactocentric distance R _D(0)≳200 kpc. At the other extreme the Sgr dwarf starts with ∼10⁹ M_⊙ and R _D(0)∼60 kpc, similar to its present apocentric distance. In all cases the Sgr dwarf is initially dark matter dominated and the current velocity dispersion of the Sgr dwarf's dark matter is tightly constrained to be 21±2 km s⁻¹. This number is probably compatible with the smaller measured dispersion of the Sgr dwarf's stars because of (i) the dynamical difference between dark and luminous matter, and (ii) velocity anisotropy.