Propto Sigma Research Articles

Effective Roughness and Displaced Mean Flow over Complex Terrain

Via analysis of velocity and stress fields from Reynolds-Averaged Navier–Stokes simulations over diverse complex terrains spanning several continents, in neutral conditions we find displaced areal-mean logarithmic wind speed profiles. The corresponding effective roughness length (z_text {0,eff}), friction velocity (u _{*text {,eff}}), and displacement height (d_text {eff}) characterise the drag exerted by the terrain. Simulations and spectral analyses reveal that the terrain statistics—and consequently d_text {eff}, u _{*text {,eff}} and z_text {0,eff}—can change significantly with flow direction, including flow in opposite directions. Previous studies over scaled or simulated fractal surfaces reported z_text {0,eff} to depend on the standard deviation of terrain elevation (sigma _h), but over real terrains we find z_text {0,eff} varies with standard deviation of terrain slopes (sigma _{Delta h/Delta x}). Terrain spectra show the dominant scales contributing to sigma _{Delta h/Delta x} vary from sim 1–10 km, with power-law behaviour over smaller scales corresponding to fractal terrain used in earlier works. The dependence of z_text {0,eff} on sigma _{Delta h/Delta x} is consistent with fractal terrain having sigma _{Delta h/Delta x} propto sigma _h, as well as classic theory for individual hills. We obtain relationships for z_text {0,eff}, d_text {eff}, and u _{*text {,eff}} in terms of sigma _{Delta h/Delta x}, finding that d_text {eff} acts as a characteristic length scale within z_text {0,eff}. Considering flow in opposite directions, use of upslope statistics did not improve z_text {0,eff} predictions; sheltering effects likely require more sophisticated treatment. Our findings impact practical applications and research, including micrometeorological flow, computational fluid dynamics, atmospheric model coupling, and mesoscale and climate modelling. We discuss limitations of the z_text {0,eff} formulations developed herein, and provide recommendations for practical use.

Black hole wind speeds and the M − σ relation

We derive an M_bh-sigma relation between supermassive black hole mass and stellar velocity dispersion in galaxy bulges, that results from self-regulated, energy-conserving feedback. The relation is of the form M_bh v_w \propto sigma^5, where v_w is the velocity of the wind driven by the black hole. We take a sample of quiescent early-type galaxies and bulges with measured black hole masses and velocity dispersions and use our model to infer the wind speeds they would have had during an active phase. This approach, in effect, translates the scatter in the observed M_bh-sigma relation into a distribution of v_w. There are some remarkable similarities between the distribution of black hole wind speeds that we obtain and the distributions of outflow speeds observed in local AGN, including a comparable median of v_w = 0.035 c.

Diffuse Lyα haloes around Lyα emitters at z=3: do dark matter distributions determine the Lyα spatial extents?

Using stacks of Ly-a images of 2128 Ly-a emitters (LAEs) and 24 protocluster UV-selected galaxies (LBGs) at z=3.1, we examine the surface brightness profiles of Ly-a haloes around high-z galaxies as a function of environment and UV luminosity. We find that the slopes of the Ly-a radial profiles become flatter as the Mpc-scale LAE surface densities increase, but they are almost independent of the central UV luminosities. The characteristic exponential scale lengths of the Ly-a haloes appear to be proportional to the square of the LAE surface densities (r(Lya) \propto Sigma(LAE)^2). Including the diffuse, extended Ly-a haloes, the rest-frame Ly-a equivalent width of the LAEs in the densest regions approaches EW_0(Lya) ~ 200 A, the maximum value expected for young (< 10^7 yr) galaxies. This suggests that Ly-a photons formed via shock compression by gas outflows or cooling radiation by gravitational gas inflows may partly contribute to illuminate the Ly-a haloes; however, most of their Ly-a luminosity can be explained by photo-ionisation by ionising photons or scattering of Ly-a photons produced in HII regions in and around the central galaxies. Regardless of the source of Ly-a photons, if the Ly-a haloes trace the overall gaseous structure following the dark matter distributions, it is not surprising that the Ly-a spatial extents depend more strongly on the surrounding Mpc-scale environment than on the activities of the central galaxies.

Nature vs. nurture in the low-density environment: structure and evolution of early-type dwarf galaxies in poor groups

We present the stellar population properties of 13 dwarf galaxies residing in poor groups (low-density environment, LDE) observed with VIMOS@VLT. Ages, metallicities, and [alpha/Fe] ratios were derived from the Lick indices Hbeta, Mgb, Fe5270 and Fe5335 through comparison with our simple stellar population (SSP) models accounting for variable [alpha/Fe] ratios. For a fiducial subsample of 10 early-type dwarfs we derive median values and scatters around the medians of 5.7 \pm 4.4 Gyr, -0.26 \pm 0.28, and -0.04 \pm 0.33 for age, log Z/Zsun, and [alpha/Fe], respectively. For a selection of bright early-type galaxies (ETGs) from the Annibali et al.2007 sample residing in comparable environment we derive median values of 9.8 \pm 4.1 Gyr, 0.06 \pm 0.16, and 0.18 \pm 0.13 for the same stellar population parameters. It follows that dwarfs are on average younger, less metal rich, and less enhanced in the alpha-elements than giants, in agreement with the extrapolation to the low mass regime of the scaling relations derived for giant ETGs. From the total (dwarf + giant) sample we derive that age \propto sigma^{0.39 \pm 0.22}, Z \propto sigma^{0.80 \pm 0.16}, and alpha/Fe \propto sigma^{0.42 \pm 0.22}. We also find correlations with morphology, in the sense that the metallicity and the [alpha/Fe] ratio increase with the Sersic index n or with the bulge-to-total light fraction B/T. The presence of a strong morphology-[alpha/Fe] relation appears to be in contradiction to the possible evolution along the Hubble sequence from low B/T (low n) to high B/T (high n) galaxies. We also investigate the role played by environment comparing the properties of our LDE dwarfs with those of Coma red passive dwarfs from the literature. We find possible evidence that LDE dwarfs experienced more prolonged star formations than Coma dwarfs, however larger data samples are needed to draw more firm conclusions.

REGULATION OF STAR FORMATION RATES IN MULTIPHASE GALACTIC DISKS: A THERMAL/DYNAMICAL EQUILIBRIUM MODEL

We develop a model for regulation of galactic star formation rates Sigma_SFR in disk galaxies, in which ISM heating by stellar UV plays a key role. By requiring simultaneous thermal and (vertical) dynamical equilibrium in the diffuse gas, and star formation at a rate proportional to the mass of the self-gravitating component, we obtain a prediction for Sigma_SFR as a function of the total gaseous surface density Sigma and the density of stars + dark matter, rho_sd. The physical basis of this relationship is that thermal pressure in the diffuse ISM, which is proportional to the UV heating rate and therefore to Sigma_SFR, must adjust to match the midplane pressure set by the vertical gravitational field. Our model applies to regions where Sigma < 100 Msun/pc^2. In low-Sigma_SFR (outer-galaxy) regions where diffuse gas dominates, the theory predicts Sigma_SFR \propto Sigma (rho_sd)^1/2. The decrease of thermal equilibrium pressure when Sigma_SFR is low implies, consistent with observations, that star formation can extend (with declining efficiency) to large radii in galaxies, rather than having a sharp cutoff. The main parameters entering our model are the ratio of thermal pressure to total pressure in the diffuse ISM, the fraction of diffuse gas that is in the warm phase, and the star formation timescale in self-gravitating clouds; all of these are (in principle) direct observables. At low surface density, our model depends on the ratio of the mean midplane FUV intensity (or thermal pressure in the diffuse gas) to the star formation rate, which we set based on Solar neighborhood values. We compare our results to recent observations, showing good agreement overall for azimuthally-averaged data in a set of spiral galaxies. For the large flocculent spiral galaxies NGC 7331 and NGC 5055, the correspondence between theory and observation is remarkably close.

A deep AAOmega survey of low-luminosity galaxies in the Shapley supercluster: stellar population trends

We present new optical spectroscopy for 342 R<18 galaxies in the Shapley Supercluster obtained with the AAOmega facility at the Anglo-Australian Telescope. We describe the observations and measurements of central velocity dispersion, emission line equivalent widths and absorption line indices. The distinguishing characteristic of the survey is its coverage of a very wide baseline in velocity dispersion (30-300 km/s), while achieving high signal-to-noise ratio throughout (median 60 per Ang). Significant emission at H-alpha was detected in ~20 per cent of red-sequence Shapley members. Using line-ratio diagnostics, we find that the emission is LINER-like at high luminosity, but driven by star-formation in low-luminosity galaxies. We use Lick indices to characterise the absorption spectra. We define a subset of galaxies with very low emission contamination, and fit the index-sigma relations for this subset. Comparing the index-sigma slopes against predictions from single-burst stellar population models, we infer the scaling relations of age, total metallicity, [Z/H], and alpha-element abundance ratio, [a/Fe]. To reproduce the observed index-sigma slopes, all three parameters must increase with increasing velocity dispersion. Specifically, we recover: Age \propto sigma^0.52+/-0.10, Z/H \propto sigma^0.34+/-0.07, and a/Fe \propto sigma^0.23+/-0.06 (error reflects systematic effects), derived over a decade baseline in velocity dispersion. The recovered age-sigma relation is shown to be consistent with the observed evolution in the giant-to-dwarf galaxy ratio in clusters at redshifts z=0.4-0.8. A companion paper will analyse the distribution of age, [Z/H] and [a/Fe] for individual galaxies. (Abridged.)

The Sizes of Galaxy Halos in Galaxy Cluster Abell 1689

The multiple images observed in galaxy cluster Abell 1689 provide strong constraints not only on the mass distribution of the cluster but also on the ensemble properties of the cluster galaxies. Using parametric strong lensing models for the cluster, and by assuming well motivated scaling laws between the truncation radius s and the velocity dispersion sigma of a cluster galaxy we are able to derive sizes of the dark matter halos of cluster galaxies. For the scaling law expected for galaxies in the cluster environment (s propto sigma), we obtain s = 64^{+15}_{-14} (sigma / 220 km/s) kpc. For the scaling law used for galaxies in the field with s propto sigma^2 we find s = 66^{+18}_{-16} (sigma / 220 km/s)^2 kpc. Compared to halos of field galaxies, the cluster galaxy halos in Abell 1689 are strongly truncated.

Star Captures by Quasar Accretion Disks: A Possible Explanation of theM‐σ Relation

A new theory of quasars is presented in which the matter of thin accretion disks around black holes is supplied by stars that plunge through the disk. Stars in the central part of the host galaxy are randomly perturbed to highly radial orbits, and as they repeatedly cross the disk they lose orbital energy by drag, eventually merging into the disk. Requiring the rate of stellar mass capture to equal the mass accretion rate into the black hole, a relation between the black hole mass and the stellar velocity dispersion is predicted of the form M_{BH} \propto sigma_*^{30/7}. The normalization depends on various uncertain parameters such as the disk viscosity, but is consistent with observation for reasonable assumptions. We show that a seed central black hole in a newly formed stellar system can grow at the Eddington rate up to this predicted mass via stellar captures by the accretion disk. Once this mass is reached, star captures are insufficient to maintain an Eddington accretion rate, and the quasar may naturally turn off as the accretion switches to a low-efficiency advection mode. The model provides a mechanism to deliver mass to the accretion disk at small radius, probably solving the problem of gravitational instability to star formation in the disk at large radius. We note that the matter from stars that is incorporated to the disk has an average specific angular momentum that is very small or opposite to that of the disk, and discuss how a rotating disk may be maintained as it captures this matter if a small fraction of the accreted mass comes from stellar winds that form a disk extending to larger radius. We propose several observational tests and consequences of this theory.

On the estimation of galaxy structural parameters: the Sersic model

This paper addresses some questions which have arisen from the use of the S\'ersic r^{1/n} law in modelling the luminosity profiles of early type galaxies. The first issue deals with the trend between the half-light radius and the structural parameter n. We show that the correlation between these two parameters is not only real, but is a natural consequence from the previous relations found to exist between the model-independent parameters: total luminosity, effective radius and effective surface brightness. We also define a new galaxy concentration index which is largely independent of the image exposure depth, and monotonically related with n. The second question concerns the curious coincidence between the form of the Fundamental Plane and the coupling between _e and r_e when modelling a light profile. We explain, through a mathematical analysis of the S\'ersic law, why the quantity r_e_e^{0.7} appears almost constant for an individual galaxy, regardless of the value of n (over a large range) adopted in the fit to the light profile. Consequently, Fundamental Planes of the form r_e_e^{0.7} propto sigma_0^x (for any x, and where sigma_0 is the central galaxy velocity dispersion) are insensitive to galaxy structure. Finally, we address the problematic issue of the use of model-dependent galaxy light profile parameters versus model-independent quantities for the half-light radii, mean surface brightness and total galaxy magnitude. The former implicitly assume that the light profile model can be extrapolated to infinity, while the latter quantities, in general, are derived from a signal-to-noise truncated profile. We quantify (mathematically) how these parameters change as one reduces the outer radius of an r^{1/n} profile, and reveal how these can vary substantially when n>4.

Self-consistent theory of rupture by progressive diffuse damage.

We analyze a self-consistent theory of crack growth controlled by a cumulative damage variable d(t) dependent on stress history, in the quasistatic regime where the sound wave velocity is taken as infinite. Depending upon the damage exponent m, which controls the rate of damage dd/dt~sigma(m) as a function of local stress sigma, we find two regimes. For 0<m<2, the model predicts a finite-time singularity. This retrieves previous results by Zobnin for m=1 and by Bradley and Wu for 0<m<2. To improve on this self-consistent theory which neglects the dependence of stress on damage, we apply the functional renormalization method of Yukalov and Gluzman and find that divergences are replaced by singularities with exponents in agreement with those found in acoustic emission experiments. For m>/=2, the rupture dynamics is not defined without the introduction of a regularizing scheme. We investigate three regularization schemes involving, respectively, a saturation of damage, a minimum distance of approach to the crack tip, and a fixed stress maximum. In the first and third schemes, the finite-time singularity is replaced by a crack dynamics defined for all times but which is controlled by either the existence of a microscopic scale at which the stress is regularized or by the maximum sustainable stress. In the second scheme, a finite-time singularity is again found. In the first two schemes within this regime m>/=2, the theory has no continuous limit.

TheLX‐T,LX‐σ, and σ‐TRelations for Groups and Clusters of Galaxies

While in the hierarchical model of structure formation, groups of galaxies are believed to be the scaled-down version of clusters of galaxies, a similarity breaking in the fundamental laws may occur on the group scale, reflecting a transition between galaxy-dominated and intracluster medium dominated properties. In this paper, we present an extensive study of the relations between the X-ray luminosity (Lx), the temperature (T) of hot diffuse gas and the velocity dispersion (sigma) of galaxies for groups and clusters of galaxies, based on the largest sample of 66 groups and 274 clusters drawn from literature. Our best fit Lx-T and Lx-sigma relations for groups read Lx propto T^(5.57+-1.79) propto sigma^(2.35+-0.21), which deviates remarkably from those for clusters: Lx propto T^(2.79+-0.08) propto sigma^(5.30+-0.21). The significance of these correlations have been justified by both the co-consistency test and the Kendall's tau statistics. We have thus confirmed the existence of similarity breaking in the Lx-T and Lx-sigma relations between groups and clusters as claimed in previous work, although the best fit sigma-T relations remain roughly the same in both systems: sigma propto T^0.64. Alternatively, the significant disagreement between the observationally fitted Lx-T and Lx-sigma relations for groups and those expected from a perfect hydrostatic equilibrium hypothesis indicates that the X-ray emission of individual galaxies and the non-gravitational heating must play a potentially important role in the dynamical evolution of groups. Therefore, reasonable caution should be exercised in the cosmological applications of the dynamical properties of groups.