A Statistically and Numerically Efficient Independence Test Based on Random Projections and Distance Covariance

Testing for independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation-based hypotheses testing for independence) have many advantages, compared with many other alternatives. A known limitation of the distance-based method is that its computational complexity can be high. In general, when the sample size is n, the order of computational complexity of a distance-based method, which typically requires computing of all pairwise distances, can be O(n2). Recent advances have discovered that in the univariate cases, a fast method with O(n log n) computational complexity and O(n) memory requirement exists. In this paper, we introduce a test of independence method based on random projection and distance correlation, which achieves nearly the same power as the state-of-the-art distance-based approach, works in the multivariate cases, and enjoys the O(nK log n) computational complexity and O( max{n, K}) memory requirement, where K is the number of random projections. Note that saving is achieved when K < n/ log n. We name our method a Randomly Projected Distance Covariance (RPDC). The statistical theoretical analysis takes advantage of some techniques on the random projection which are rooted in contemporary machine learning. Numerical experiments demonstrate the efficiency of the proposed method, relative to numerous competitors.

Supersonic Expansion of the Bipolar H ii Region Sh2-106: A 3500 Year Old Explosion?

Multi-epoch narrowband Hubble Space Telescope images of the bipolar H ii region Sh2-106 reveal highly supersonic nebular proper motions that increase with projected distance from the massive young stellar object S106 IR, reaching over ∼30 mas yr−1 (∼150 km s−1 at D = 1.09 kpc) at a projected separation of ∼1.′4 (0.44 pc) from S106 IR. We propose that S106 IR experienced a ∼1047 erg explosion ∼3500 yr ago. The explosion may be the result of a major accretion burst or a recent encounter with another star, or a consequence of the interaction of a companion with the bloated photosphere of S106 IR as it grew from ∼10 through ∼15 M ⊙ at a high accretion rate. Near-IR images reveal fingers of H2 emission pointing away from S106 IR and an asymmetric photon-dominated region surrounding the ionized nebula. Radio continuum and Brγ emission reveal a C-shaped bend in the plasma, indicating either the motion of S106 IR toward the east, or the deflection of plasma toward the west by the surrounding cloud. The H ii region bends around a ∼1′ diameter dark bay west of S106 IR that may be shielded from direct illumination by a dense molecular clump. Herbig–Haro and Molecular Hydrogen Objects tracing outflows powered by stars in the Sh2-106 protocluster such as the Class 0 source S106 FIR are discussed.

A Multiwavelength Study of ELAN Environments (AMUSE2). Detection of a Dusty Star-forming Galaxy within the Enormous Lyα Nebula at z=2.3 Sheds Light on its Origin

We present ALMA observations on and around the radio-quiet quasar UM 287 at z = 2.28. Together with a companion quasar, UM 287 is believed to play a major role in powering the surrounding enormous Lyα nebula (ELAN), dubbed the Slug ELAN, that has an end-to-end size of 450 physical kpc. In addition to the quasars, we detect a new dusty star-forming galaxy (DSFG), dubbed the Slug-DSFG, in 2 mm continuum with a single emission line consistent with CO(4−3). The Slug-DSFG sits at a projected distance of 100 kpc southeast from UM 287, with a systemic velocity difference of −360 ± 30 km s−1 with respect to UM 287, suggesting it is a possible contributor to the powering of the Slug ELAN. With careful modeling of the SED and dynamical analyses, it is found that the Slug-DSFG and UM 287 appear low in both gas fraction and gas-to-dust ratio, suggesting environmental effects due to the host’s massive halo. In addition, our Keck long-slit spectra reveal significant Lyα emissions from the Slug-DSFG, as well as a Lyα tail that starts at the location and velocity of the Slug-DSFG and extends toward the south, with a projected length of about 100 kpc. Supported by various analytical estimates we propose that the Lyα tail is a result of the Slug-DSFG experiencing ram pressure stripping. The gas mass stripped is estimated to be about 109 M ⊙, contributing to the dense warm/cool gas reservoir that is believed to help power the exceptional Lyα luminosity.

The obstructed jet in Mrk 231

Mrk 231 is the closest radio-quiet quasar known and one of the most luminous infrared galaxies in the local Universe. It is characterised by the co-existence of a radio jet and powerful multi-phase multi-scale outflows, making it an ideal laboratory to study active galactic nucleus (AGN) feedback. We analyse the multi-epoch very long baseline interferometry data of Mrk 231 and estimate the jet head advance speed to be ≲ 0.013 c, suggesting a sub-relativistic jet flow. The jet position angle changes from −113○ in the inner parsec to −172○ at a projected distance of 25 parsec. The jet structure change might result from either a jet bending following the rotation of the circum-nuclear disc or the projection of a helical jet on the plane of the sky. In the large opening angle (∼60○) cone, the curved jet interacts with the interstellar medium and creates wide-aperture-angle shocks which subsequently dissipate a large portion of the jet power through radiation and contribute to powering the large-scale outflows. The low power and bent structure of the Mrk 231 jet, as well as extensive radiation dissipation, are consistent with the obstruction of the short-length jet by the host galaxy’s environment.

Early Science from POSSUM: Shocks, turbulence, and a massive new reservoir of ionised gas in the Fornax cluster

We present the first Faraday rotation measure (RM) grid study of an individual low-mass cluster—the Fornax cluster—which is presently undergoing a series of mergers. Exploiting commissioning data for the POlarisation Sky Survey of the Universe’s Magnetism (POSSUM) covering a ${\sim}34$ square degree sky area using the Australian Square Kilometre Array Pathfinder (ASKAP), we achieve an RM grid density of ${\sim}25$ RMs per square degree from a 280-MHz band centred at 887 MHz, which is similar to expectations for forthcoming GHz-frequency ${\sim}3\pi$ -steradian sky surveys. These data allow us to probe the extended magnetoionic structure of the cluster and its surroundings in unprecedented detail. We find that the scatter in the Faraday RM of confirmed background sources is increased by $16.8\pm2.4$ rad m−2 within 1 $^\circ$ (360 kpc) projected distance to the cluster centre, which is 2–4 times larger than the spatial extent of the presently detectable X-ray-emitting intracluster medium (ICM). The mass of the Faraday-active plasma is larger than that of the X-ray-emitting ICM and exists in a density regime that broadly matches expectations for moderately dense components of the Warm-Hot Intergalactic Medium. We argue that forthcoming RM grids from both targeted and survey observations may be a singular probe of cosmic plasma in this regime. The morphology of the global Faraday depth enhancement is not uniform and isotropic but rather exhibits the classic morphology of an astrophysical bow shock on the southwest side of the main Fornax cluster, and an extended, swept-back wake on the northeastern side. Our favoured explanation for these phenomena is an ongoing merger between the main cluster and a subcluster to the southwest. The shock’s Mach angle and stand-off distance lead to a self-consistent transonic merger speed with Mach 1.06. The region hosting the Faraday depth enhancement also appears to show a decrement in both total and polarised radio emission compared to the broader field. We evaluate cosmic variance and free-free absorption by a pervasive cold dense gas surrounding NGC 1399 as possible causes but find both explanations unsatisfactory, warranting further observations. Generally, our study illustrates the scientific returns that can be expected from all-sky grids of discrete sources generated by forthcoming all-sky radio surveys.

Satellites and central galaxies in SDSS: the influence of interactions on their properties

ABSTRACT We use SDSS-DR14 to construct a sample of galaxy systems consisting of a central object and two satellites. We adopt projected distance and radial velocity difference criteria and impose an isolation criterion to avoid membership in larger structures. We also classify the interaction between the members of each system through a visual inspection of galaxy images, finding ${\sim}80{{\ \rm per\ cent}}$ of the systems lack evidence of interactions whilst the remaining ${\sim}20{{\ \rm per\ cent}}$ involve some kind of interaction, as inferred from their observed distorted morphology. We have considered separately, samples of satellites and central galaxies, and each of these samples were tested against suitable control sets to analyse the results. We find that central galaxies showing signs of interactions present evidence of enhanced star formation activity and younger stellar populations. As a counterpart, satellite samples show these galaxies presenting older stellar populations with a lower star formation rate than the control sample. The observed trends correlate with the stellar mass content of the galaxies and with the projected distance between the members involved in the interaction. The most massive systems are less affected since they show no star formation excess, possibly due to their more evolved stage and less gas available to form new stars. Our results suggest that it is arguably a transfer of material during interactions, with satellites acting as donors to the central galaxy. As a consequence of the interactions, satellite stellar population ages rapidly and new bursts of star formation may frequently occur in the central galaxy.

The weak imprint of environment on the stellar populations of galaxies

ABSTRACT We investigate the environmental dependence of the stellar populations of galaxies in Sloan Digital Sky Survey Data Release 7 (SDSS DR7). Echoing earlier works, we find that satellites are both more metal-rich (<0.1 dex) and older (<2 Gyr) than centrals of the same stellar mass. However, after separating star-forming, green valley, and passive galaxies, we find that the true environmental dependence of both stellar metallicity (<0.03 dex) and age (<0.5 Gyr) is in fact much weaker. We show that the strong environmental effects found when galaxies are not differentiated result from a combination of selection effects brought about by the environmental dependence of the quenched fraction of galaxies, and thus we strongly advocate for the separation of star-forming, green valley, and passive galaxies when the environmental dependence of galaxy properties are investigated. We also study further environmental trends separately for both central and satellite galaxies. We find that star-forming galaxies show no environmental effects, neither for centrals nor for satellites. In contrast, the stellar metallicities of passive and green valley satellites increase weakly (<0.05 and <0.08 dex, respectively) with increasing halo mass, increasing local overdensity and decreasing projected distance from their central; this effect is interpreted in terms of moderate environmental starvation (‘strangulation’) contributing to the quenching of satellite galaxies. Finally, we find a unique feature in the stellar mass–stellar metallicity relation for passive centrals, where galaxies in more massive haloes have larger stellar mass (∼0.1 dex) at constant stellar metallicity; this effect is interpreted in terms of dry merging of passive central galaxies and/or progenitor bias.

Going back to basics: accelerating exoplanet transit modelling using Taylor-series expansion of the orbital motion

ABSTRACT A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one. However, because the planet’s position and its time derivatives are constant for any specific point in orbital phase, the projected distance can be calculated rapidly and accurately in the vicinity of the transit by expanding the planet’s x and y positions in the sky plane into a Taylor series at mid-transit. Calculating the projected distance for an elliptical orbit using the four first time derivatives of the position vector (velocity, acceleration, jerk, and snap) is ∼100 times faster than calculating it using the Newton’s method, and also significantly faster than calculating z for a circular orbit because the approach does not use numerically expensive trigonometric functions. The speed gain in the projected distance calculation leads to 2–25 times faster transit model evaluation speed, depending on the transit model complexity and orbital eccentricity. Calculation of the four position derivatives using numerical differentiation takes $\sim 1\, \mu$s with a modern laptop and needs to be done only once for a given orbit, and the maximum error the approximation introduces to a transit light curve is below 1 ppm for the major part of the physically plausible orbital parameter space.

The Keck Baryonic Structure Survey: using foreground/background galaxy pairs to trace the structure and kinematics of circumgalactic neutral hydrogen at z ∼ 2

ABSTRACT We present new measurements of the spatial distribution and kinematics of neutral hydrogen in the circumgalactic and intergalactic medium surrounding star-forming galaxies at z ∼ 2. Using the spectra of ≃3000 galaxies with redshifts 〈z〉 = 2.3 ± 0.4 from the Keck Baryonic Structure Survey, we assemble a sample of more than 200 000 distinct foreground-background pairs with projected angular separations of 3–500 arcsec and spectroscopic redshifts, with 〈zfg〉 = 2.23 and 〈zbg〉 = 2.57 (foreground, background redshifts, respectively.) The ensemble of sightlines and foreground galaxies is used to construct a 2D map of the mean excess $\rm{H\,{\small I}}$$\rm Ly\,\alpha$ optical depth relative to the intergalactic mean as a function of projected galactocentric distance (20 ≲ Dtran/pkpc ≲ 4000) and line-of-sight velocity. We obtain accurate galaxy systemic redshifts, providing significant information on the line-of-sight kinematics of $\rm{H\,{\small I}}$ gas as a function of projected distance Dtran. We compare the map with cosmological zoom-in simulation, finding qualitative agreement between them. A simple two-component (accretion, outflow) analytical model generally reproduces the observed line-of-sight kinematics and projected spatial distribution of $\rm{H\,{\small I}}$. The best-fitting model suggests that galaxy-scale outflows with initial velocity vout ≃ 600 km s$^{-1}\,$ dominate the kinematics of circumgalactic $\rm{H\,{\small I}}$ out to Dtran ≃ 50 kpc, while $\rm{H\,{\small I}}$ at Dtran ≳ 100 kpc is dominated by infall with characteristic vin ≲ circular velocity. Over the impact parameter range 80 ≲ Dtran/pkpc ≲ 200, the $\rm{H\,{\small I}}$ line-of-sight velocity range reaches a minimum, with a corresponding flattening in the rest-frame $\rm Ly\,\alpha$ equivalent width. These observations can be naturally explained as the transition between outflow-dominated and accretion-dominated flows. Beyond Dtran ≃ 300 pkpc (∼1 cMpc), the line-of-sight kinematics are dominated by Hubble expansion.