The effects of a disc field on bulge surface brightness

Collisionless N -body simulations are used in an effort to reproduce the observed tendency of the surface brightness profile of bulges to change progressively from an R ^1/4 law to an exponential, going from early- to late-type spirals. A possible cause for this is the formation of the disc, later in the history of the galaxy, and this is simulated by applying on the N -body bulge the force field of an exponential disc the surface density of which increases with time. It is shown that n , the index of the Sersic law Σ _n  ( r ) ∝ exp [−( r / r ₀)^{1/ n} ] that best describes the surface brightness profile, does indeed decrease from 4 (de Vaucouleurs law) to smaller values; this decrease is larger for more massive and more compact discs. A large part of the observed trend of n with B/D ratio is explained, and many of the actual profiles can be matched exactly by the simulations. The correlation between the disc scalelength and bulge effective radius, used recently to support the 'secular evolution' origin for bulges, is also shown to arise naturally in a scenario like this. This mechanism, however, saturates at around n  = 2 and exponential bulges cannot be produced; as n gets closer to 1, the profile becomes increasingly robust against a disc field. These results provide strong support to the old-bulge hypothesis for the early-type bulges. The exponential bulges, however, remain essentially unexplained; the results here suggest that they did not begin their lives as R ^1/4 spheroids, and hence were probably formed, at least in part, by different processes from those of early-type spirals.     

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.     

Radial scalelengths of the galactic thin and thick disc with 2MASS data

This paper presents a global analysis of the 2MASS (Two Micron All Sky Survey) data as observed in seven fields at different galactic latitudes in our Galaxy. The data allow the preliminary determination of the scale parameters, which lead to strong constraints on the radial and vertical structure of the galactic thin and thick disc. The interpretation of star counts and colour distributions of stars in the near-infrared with the synthetic stellar population model gives strong evidence that the galactic thin disc density scalelength ( h _R ) is rather short (2.8±0.3 kpc). The galactic thick disc population is revisited in the light of new data. We find the thick disc to have a local density of 3.5±2.0 per cent of the thin disc, exponential scaleheight ( h _z ) of 860±200 pc and exponential scalelength ( h _R ) of 3.7±_0.5^0.8 kpc.     

Hypothesis testing for meagre data sets

Improved χ ² statistics are defined for both Poisson and multinomial data sets. Numerical experiments with the Nousek–Shue test problem from X-ray spectroscopy indicate that, in contrast to Pearson's statistic X ², these modified statistics remain approximately valid at the 2 σ level of significance even when the mean counts per bin is ≪1 provided that the total counts N ≳30. The simplest of the proposed statistics is formally equivalent to carrying out a goodness-of-fit test with Pearson's statistic but with modified confidence limits, and this procedure is recommended.     

The anomalous properties of Markarian 1460

We present and discuss optical, near-infrared and H  i measurements of the galaxy Markarian 1460 at a distance of 19 Mpc in the Ursa Major Cluster. This low-luminosity ( M _B =−14) galaxy is unusual because (i) it is blue ( B − R =0.8) and has the spectrum of an H  ii galaxy, (ii) it has a light profile that is smooth and well fitted by an r ^1/4 and not an exponential function at all radii larger than the seeing, and (iii) it has an observed central brightness of about μ _B =20 mag arcsec⁻² , intermediate between those of elliptical galaxies (on the bright μ _B side) and normal low-luminosity dwarf irregular (on the low μ _B side) galaxies. No other known galaxy exhibits all these properties in conjunction. On morphological grounds this galaxy looks like a normal distant luminous elliptical galaxy, since the Fundamental Plane tells us that higher luminosity normal elliptical galaxies tend to have lower surface-brightnesses. Markarian 1460 has 2×10⁷ M_⊙ of H  i and a ratio M (H  i )/ L _B of 0.2, which is low compared to the typical values for star-forming dwarf galaxies. From the high surface-brightness and r ^1/4 profile, we infer that the baryonic component of Markarian 1460 has become self-gravitating through dissipative processes. From the colours, radio continuum, H  i and optical emission line properties, and yet smooth texture, we infer that Markarian 1460 has had significant star formation as recently as ∼1 Gyr ago but not today.     

Mass models of the Milky Way

A parametrized model of the mass distribution within the Milky Way is fitted to the available observational constraints. The most important single parameter is the ratio of the scalelength R _d* of the stellar disc to R ₀. The disc and bulge dominate v _c( R ) at R ≲ R ₀ only for R _d,*/ R ₀≲0.3. Since the only knowledge we have of the halo derives from studies like the present one, we allow it to contribute to the density at all radii. When allowed this freedom, however, the halo causes changes in assumptions relating to R  ≪  R ₀ to affect profoundly the structure of the best-fitting model at R  ≫  R ₀. For example, changing the disc slightly from an exponential surface-density profile significantly changes the form of v _c( R ) at R  ≫  R ₀, where the disc makes a negligible contribution to v _c. Moreover, minor changes in the constraints can cause the halo to develop a deep hole at its centre that is not physically plausible. These problems call into question the proposition that flat rotation curves arise because galaxies have physically distinct haloes rather than outwards-increasing mass-to-light ratios.   The mass distribution of the Galaxy and the relative importance of its various components will remain very uncertain until more observational data can be used to constrain mass models. Data that constrain the Galactic force field at z ≳ R and at R  >  R ₀ are especially important.     

Single star scattering on an open cluster

We examine the scattering of single stars from an open star cluster. The probability of the capture of a star by a star cluster is dependent on the velocity and mass of the star, and the stars that are not captured experience a velocity change. For low-velocity stars there is an exponential decrease of the capture probability with the initial velocity, and the velocity change decreases almost linearly. For high-velocity stars there is a v ⁻⁶ dependence for the capture probability, and a v ⁻¹ dependence for the velocity change. Analytical estimations, Monte Carlo and full N -body simulations are all in good agreement.     

The alignment of clusters using large-scale simulations

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

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.     

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 early evolution of the star cluster mass function

Several recent studies have shown that the star cluster initial mass function (CIMF) can be well approximated by a power law, with indications for a steepening or truncation at high masses. This contribution considers the evolution of such a mass function due to cluster disruption, with emphasis on the part of the mass function that is observable in the first ∼1 Gyr. A Schechter type function is used for the CIMF, with a power-law index of −2 at low masses and an exponential truncation at M _*. Cluster disruption due to the tidal field of the host galaxy and encounters with giant molecular clouds flattens the low-mass end of the mass function, but there is always a part of the 'evolved Schechter function' that can be approximated by a power law with index −2. The mass range for which this holds depends on age, τ, and shifts to higher masses roughly as  τ^0.6  . Mean cluster masses derived from luminosity-limited samples increase with age very similarly due to the evolutionary fading of clusters. Empirical mass functions are, therefore, approximately power laws with index −2, or slightly steeper, at all ages. The results are illustrated by an application to the star cluster population of the interacting galaxy M51, which can be well described by a model with   M _*= (1.9 ± 0.5) × 10⁵ M_⊙  and a short (mass-dependent) disruption time destroying M _* clusters in roughly a Gyr.     

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  .     

Resolving cosmic structure formation with the Millennium-II Simulation

We present the Millennium-II Simulation (MS-II), a very large N -body simulation of dark matter evolution in the concordance Λ cold dark matter (ΛCDM) cosmology. The MS-II assumes the same cosmological parameters and uses the same particle number and output data structure as the original Millennium Simulation (MS), but was carried out in a periodic cube one-fifth the size  (100  h ⁻¹ Mpc)  with five times better spatial resolution (a Plummer equivalent softening of  1.0  h ⁻¹ kpc  ) and with 125 times better mass resolution (a particle mass of  6.9 × 10⁶  h ⁻¹ M_⊙  ). By comparing results at MS and MS-II resolution, we demonstrate excellent convergence in dark matter statistics such as the halo mass function, the subhalo abundance distribution, the mass dependence of halo formation times, the linear and non-linear autocorrelations and power spectra, and halo assembly bias. Together, the two simulations provide precise results for such statistics over an unprecedented range of scales, from haloes similar to those hosting Local Group dwarf spheroidal galaxies to haloes corresponding to the richest galaxy clusters. The 'Milky Way' haloes of the Aquarius Project were selected from a lower resolution version of the MS-II and were then resimulated at much higher resolution. As a result, they are present in the MS-II along with thousands of other similar mass haloes. A comparison of their assembly histories in the MS-II and in resimulations of 1000 times better resolution shows detailed agreement over a factor of 100 in mass growth. We publicly release halo catalogues and assembly trees for the MS-II in the same format within the same archive as those already released for the MS.     

ROSAT PSPC observations of the outer regions of the Perseus cluster of galaxies

We present an analysis of four off-axis ROSAT Position Sensitive Proportional Counter (PSPC) observations of the Perseus cluster of galaxies (Abell 426). We detect the surface brightness profile to a radius of 80 arcmin (∼2.4 h⁻¹₅₀ Mpc) from the X-ray peak. The profile is measured in various sectors and in three different energy bands. First, a colour analysis highlights a slight variation of N _H over the region, and cool components in the core and in the eastern sector. We apply the β-model to the profiles from different sectors and present a solution to the, so-called, β-problem. The residuals from an azimuthally-averaged profile highlight extended emission both in the east and in the west, with estimated luminosities of about 8 and 1 ×10⁴³ erg s⁻¹, respectively. We fit several models to the surface brightness profile, including the one obtained from the Navarro, Frenk &38; White potential. We obtain the best fit with the gas distribution described by a power law in the inner, cooling region and a β-model for the extended emission. Through the best-fitting results and the constraints from the deprojection of the surface brightness profiles, we define the radius where the overdensity inside the cluster is 200 times the critical value, r ₂₀₀, at 2.7 h⁻¹₅₀ Mpc. Within 2.3  h⁻¹₅₀ Mpc (0.85 r ₂₀₀), the total mass in the Perseus cluster is 1.2 × 10¹⁵ M_⊙ and its gas fraction is about 30 per cent.     

Statistical distribution of gravitational-lensing excursion angles: winding ways to us from the deep Universe

We investigate statistical distributions of differences in gravitational-lensing deflections between two light rays, the so-called lensing excursion angles. A probability distribution function of the lensing excursion angles, which plays a key role in estimates of lensing effects on angular clustering of objects (such as galaxies, quasi-stellar objects and also the cosmic microwave background temperature map), is known to consist of two components: a Gaussian core and an exponential tail. We use numerical gravitational-lensing experiments in a ΛCDM cosmology for quantifying these two components. We especially focus on the physical processes responsible for generating these two components. We develop a simple empirical model for the exponential tail which allows us to explore its origin. We find that the tail is generated by the coherent lensing scatter by massive haloes with   M > 10¹⁴  h ⁻¹ M_⊙  at   z < 1  and that its exponential shape arises due to the exponential cut-off of the halo mass function at that mass range. On scales larger than 1 arcmin, the tail does not have a practical influence on the lensing effects on the angular clustering. Our model predicts that the coherent scatter may have non-negligible effects on angular clustering at subarcminute scales.     

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.     

Two-Micron All-Sky Survey J01542930+0053266: a new eclipsing M dwarf binary system

We report on Two-Micron All-Sky Survey (2MASS) J01542930+0053266, a faint eclipsing system composed of two M dwarfs. The variability of this system was originally discovered during a pilot study of the 2MASS Calibration Point Source Working Data base. Additional photometry from the Sloan Digital Sky Survey yields an eight-passband light curve from which we derive an orbital period of  2.639 0157 ± 0.000 0016  d. Spectroscopic followup confirms our photometric classification of the system, which is likely composed of M0 and M1 dwarfs. Radial velocity measurements allow us to derive the masses  (M₁= 0.66 ± 0.03 M_⊙; M₂= 0.62 ± 0.03 M_⊙)  and radii  (R₁= 0.64 ± 0.08 R_⊙; R₂= 0.61 ± 0.09 R_⊙)  of the components, which are consistent with empirical mass–radius relationships for low-mass stars in binary systems. We perform Monte Carlo simulations of the light curves which allow us to uncover complicated degeneracies between the system parameters. Both stars show evidence of Hα emission, something not common in early-type M dwarfs. This suggests that binarity may influence the magnetic activity properties of low-mass stars; activity in the binary may persist long after the dynamos in their isolated counterparts have decayed, yielding a new potential foreground of flaring activity for next generation variability surveys.     

Mass transfer in eccentric binary stars

The concept of Roche lobe overflow is fundamental to the theory of interacting binaries. Based on potential theory, it is dependent on all the relevant material corotating in a single frame of reference. Therefore if the mass losing star is asynchronous with the orbital motion or the orbit is eccentric, the simple theory no longer applies and no exact analytical treatment has been found. We use an analytic approximation whose predictions are largely justified by smoothed particle hydrodynamic simulations (SPH). We present SPH simulations of binary systems with the same semi-major axis   a = 5.55 R_⊙  , masses   M ₁= 1 M_⊙, M ₂= 2 M_⊙  and radius   R ₁= 0.89 R_⊙  for the primary star but with different eccentricities   e = 0.4, 0.5, 0.6  and 0.7. In each case the secondary star is treated as a point mass. When   e = 0.4  no mass is lost from the primary while at   e = 0.7  catastrophic mass transfer, partly through the L₂ point, takes place near periastron. This would probably lead to common-envelope evolution if star 1 were a giant or to coalescence for a main-sequence star. In between, at   e ≥ 0.5  , some mass is lost through the L₁ point from the primary close to periastron. However, rather than being all accreted by the secondary, some of the stream appears to leave the system. Our results indicate that the radius of the Roche lobe is similar to circular binaries when calculated for the separation and angular velocity at periastron. Part of the mass loss occurs through the L₂ point.     

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.     

Outbursts of irradiated accretion discs

I solve analytically the viscous evolution of an irradiated accretion disc, as seen during outbursts of soft X-ray transients. The solutions predict steep power-law X-ray decays L _X ∼ (1 + t/t_visc)⁻⁴, changing to L _X ∼ (1 − t/t'_visc)⁴ at late times, where t _visc, t '_visc are viscous time-scales. These forms closely resemble the approximate exponential and linear decays inferred by King and Ritter in these two regimes. The decays are much steeper than for unirradiated discs because the viscosity is a function of the central accretion rate rather than of local conditions in the disc.