On Weyl group equivariant maps

We prove an equivariant analogue of Chevalley's isomorphism theorem for polynomial, C(infinity) or C(omega) maps

A Fatou- type theorem for harmonic functions on symmetric spaces

First published in the Bulletin of the American Mathematical Society in Vol.74, 1968, published by the American Mathematical Societ

Chandra and XMM-Newton X-ray observations of AWM 7 - I: Investigating X-ray surface brightness fluctuations

We investigate the levels of small scale structure in surface brightness images of the core of the X-ray bright cool-core galaxy cluster AWM 7. After subtraction of a model of the smooth cluster emission, we find a number of approximately radial surface brightness depressions which are not present in simulated images and are seen in both the Chandra and XMM-Newton data. The depressions are most strongly seen in the south of the cluster and have a magnitude of around 4 per cent in surface brightness. We see these features in both an energy band sensitive to the density (0.6 to 5 keV) and a band more sensitive to the pressure (3.5 to 7.5 keV). Histograms of surface brightness in the data, when compared to realisations of a smooth model, reveal stronger surface brightness variations. We use the Delta-variance technique to characterise the magnitude of the fluctuations as a function of length scale. We find that the spectrum in the 0.6 to 5 keV band is flatter than expected for Kolmogorov index fluctuations. If characterised by a power spectrum, on large scales it would have an index around -1.7, rather than -3.7. The implied 3D density fluctuations have a standard deviation of around 4 per cent. The implied 3D pressure variations are at most 4 per cent. Most of the longer-scale power in the density spectrum is contributed by the southern half of the cluster, where the depressions are seen. The density variations implied by the spectrum of the northern sector have a standard deviation of about 2 per cent.Comment: 17 pages, accepted by MNRAS, high resolution version available at http://www-xray.ast.cam.ac.uk/papers/awm7.pd

Testing the Hubble Law with the IRAS 1.2 Jy Redshift Survey

We test and reject the claim of Segal et al. (1993) that the correlation of redshifts and flux densities in a complete sample of IRAS galaxies favors a quadratic redshift-distance relation over the linear Hubble law. This is done, in effect, by treating the entire galaxy luminosity function as derived from the 60 micron 1.2 Jy IRAS redshift survey of Fisher et al. (1995) as a distance indicator; equivalently, we compare the flux density distribution of galaxies as a function of redshift with predictions under different redshift-distance cosmologies, under the assumption of a universal luminosity function. This method does not assume a uniform distribution of galaxies in space. We find that this test has rather weak discriminatory power, as argued by Petrosian (1993), and the differences between models are not as stark as one might expect a priori. Even so, we find that the Hubble law is indeed more strongly supported by the analysis than is the quadratic redshift-distance relation. We identify a bias in the the Segal et al. determination of the luminosity function, which could lead one to mistakenly favor the quadratic redshift-distance law. We also present several complementary analyses of the density field of the sample; the galaxy density field is found to be close to homogeneous on large scales if the Hubble law is assumed, while this is not the case with the quadratic redshift-distance relation.Comment: 27 pages Latex (w/figures), ApJ, in press. Uses AAS macros, postscript also available at http://www.astro.princeton.edu/~library/preprints/pop682.ps.g

A Photometric and Kinematic Study of AWM 7

We have measured redshifts and Kron-Cousins R-band magnitudes for a sample of galaxies in the poor cluster AWM 7. We have measured redshifts for 172 galaxies; 106 of these are cluster members. We determine the luminosity function from a photometric survey of the central 1.2 h^{-1} x 1.2 h^{-1} Mpc. The LF has a bump at the bright end and a faint-end slope of \alpha = -1.37+-0.16, populated almost exclusively by absorption-line galaxies. The cluster velocity dispersion is lower in the core (\sim 530 km/s) than at the outskirts (\sim 680 km/s), consistent with the cooling flow seen in the X-ray. The cold core extends \sim 150 h^{-1} kpc from the cluster center. The Kron-Cousins R-band mass-to-light ratio of the system is 650+-170 h M_\odot/L_\odot, substantially lower than previous optical determinations, but consistent with most previous X-ray determinations. We adopt H_0 = 100 h km/s/Mpc throughout this paper; at the mean cluster redshift, (5247+-76 km/s), 1 h^{-1} Mpc subtends 65\farcm5.Comment: 37 pages, LaTeX, including 12 Figures and 1 Table. Accepted for publication in the Astronomical Journa

Kinematics and Mass Profile of AWM 7

We have measured 492 redshifts (311 new) in the direction of the poor cluster AWM~7 and have identified 179 cluster members (73 new). We use two independent methods to derive a self-consistent mass profile, under the assumptions that the absorption-line galaxies are virialized and that they trace an underlying Navarro, Frenk & White (1997) dark matter profile: (1) we fit such an NFW profile to the radial distribution of galaxy positions and to the velocity dispersion profile; (2) we apply the virial mass estimator to the cluster. With these assumptions, the two independent mass estimates agree to \sim 15% within 1.7 h^{-1} Mpc, the radial extent of our data; we find an enclosed mass \sim (3+-0.5)\times 10^{14} h^{-1} M_\odot. The largest potential source of systematic error is the inclusion of young emission-line galaxies in the mass estimate. We investigate the behavior of the surface term correction to the virial mass estimator under several assumptions about the velocity anisotropy profile, still within the context of the NFW model, and remark on the sensitivity of derived mass profiles to outliers. We find that one must have data out to a large radius in order to determine the mass robustly, and that the surface term correction is unreliable at small radii.Comment: LaTeX, 5 tables, 7 figures, appeared as 2000 AJ 119 44; typos and Eq. 9 corrected; results are unaffecte

The 1.4 GHz light curve of GRB 970508

We report on Westerbork 1.4 GHz radio observations of the radio counterpart to $\gamma$-ray burst GRB~970508, between 0.80 and 138 days after this event. The 1.4 GHz light curve shows a transition from optically thick to thin emission between 39 and 54 days after the event. We derive the slope $p$ of the spectrum of injected electrons ($dN/d\gamma_{e}\propto\gamma_{e}^{-p}$) in two independent ways which yield values very close to $p=2.2$. This is in agreement with a relativistic dynamically near-adiabatic blast wave model whose emission is dominated by synchrotron radiation and in which a significant fraction of the electrons cool fast.Comment: Paper I. Accepted for publication in the Astrophysical Journal Letter

Surveying the Dynamic Radio Sky with the Long Wavelength Demonstrator Array

This paper presents a search for radio transients at a frequency of 73.8 MHz (4 m wavelength) using the all-sky imaging capabilities of the Long Wavelength Demonstrator Array (LWDA). The LWDA was a 16-dipole phased array telescope, located on the site of the Very Large Array in New Mexico. The field of view of the individual dipoles was essentially the entire sky, and the number of dipoles was sufficiently small that a simple software correlator could be used to make all-sky images. From 2006 October to 2007 February, we conducted an all-sky transient search program, acquiring a total of 106 hr of data; the time sampling varied, being 5 minutes at the start of the program and improving to 2 minutes by the end of the program. We were able to detect solar flares, and in a special-purpose mode, radio reflections from ionized meteor trails during the 2006 Leonid meteor shower. We detected no transients originating outside of the solar system above a flux density limit of 500 Jy, equivalent to a limit of no more than about 10^{-2} events/yr/deg^2, having a pulse energy density >~ 1.5 x 10^{-20} J/m^2/Hz at 73.8 MHz for pulse widths of about 300 s. This event rate is comparable to that determined from previous all-sky transient searches, but at a lower frequency than most previous all-sky searches. We believe that the LWDA illustrates how an all-sky imaging mode could be a useful operational model for low-frequency instruments such as the Low Frequency Array, the Long Wavelength Array station, the low-frequency component of the Square Kilometre Array, and potentially the Lunar Radio Array.Comment: 20 pages; accepted for publication in A

An XMM-Newton observation of the galaxy group MKW 4

We present an X-ray study of the galaxy group or poor cluster MKW 4. Working with XMM data we examine the distribution and properties of the hot gas which makes up the group halo. The inner halo shows some signs of structure, with circular or elliptical beta models providing a poor fit to the surface brightness profile. This may be evidence of large scale motion in the inner halo, but we do not find evidence of sharp fronts or edges in the emission. The temperature of the halo declines in the core, with deprojected spectral fits showing a central temperature of ~1.3 keV compared to ~3 keV at 100 kpc. In the central ~30 kpc of the group multi-temperature spectral models are required to fit the data, but they indicate a lack of gas at low temperatures. Steady state cooling flow models provide poor fits to the inner regions of the group and the estimated cooling time of the gas is long except within the central dominant galaxy, NGC 4073. Abundance profiles show a sharp increase in the core of the group, with mean abundance rising by a factor of two in the centre of NGC 4073. Fitting individual elements shows the same trend, with high values of Fe, Si and S in the core. We estimate that ~50% of the Fe in the central 40 kpc was injected by SNIa, in agreement with previous ASCA studies. Using our best fitting surface brightness and temperature models, we calculate the mass, gas fraction, entropy and mass-to-light ratio of the group. At 100 kpc (~0.1 virial radii) the total mass and gas entropy of the system (~2x10^13 Msol and ~300 keV cm^2) are quite comparable to those of other systems of similar temperature, but the gas fraction is rather low (~1%). We conclude that MKW 4 is a fairly relaxed group, which has developed a strong central temperature gradient but not a large-scale cooling flow.Comment: 17 pages, 9 postscript figures, accepted for publication in MNRA

The Dynamical Status of the Cluster of Galaxies 1E0657-56

We present the results of a new spectroscopic and photometric survey of the hot X-ray cluster 1E0657-56, at z=0.296. We determine the presence of a low velocity dispersion subcluster, which is offset from the main cluster position by 0.7 Mpc and about 600 km/s. We determine the virial masses and total luminosities of the cluster and its subcluster, and solve for the two-body dynamical model. With additional constraints from the results of the analysis of the cluster X-ray emission by Markevitch et al. (2001), we find that the subcluster passed through the cluster centre about 0.15 Gyr ago. Taken at face value the mass of the subcluster is typical of a loose group. It is however difficult to establish the pre-merger mass of the colliding system. We provide tentative evidence that the subcluster is in fact the remnant core of a moderately massive cluster, stripped by the collision with 1E0657-56. The main cluster dynamics does not seem to have suffered from this collision. On the contrary, the cluster X-ray properties seem to have been significantly affected. We also discuss the effect of the subcluster collision in relation to starburst events and the cluster radio halo.Comment: Accepted for publication on A&