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NGC 4631 is an interacting galaxy that exhibits one of the largest, gaseous halos observed among edge-on galaxies. We aim to examine the synchrotron and cosmic-ray propagation properties of its disk and halo emission with new radio continuum data. Radio continuum observations of NGC 4631 were performed with the Karl G. Jansky Very Large Array at C-band (5.99 GHz) in the C and D array configurations, and at L-band (1.57 GHz) in the B, C, and D array configurations. Complementary observations of NGC 4631 with the Effelsberg telescope were performed at 1.42 and 4.85 GHz. The interferometric total intensity data were combined with the single-dish Effelsberg data in order to recover the missing large-scale total power emission. The thermal and nonthermal components of the total radio emission were separated by estimating the thermal contribution through the extinction-corrected H$\alpha$ emission. The H$\alpha$ radiation was corrected for extinction using a linear combination of the observed H$\alpha$ and 24 $\mu$m data. NGC 4631 has a global thermal fraction at 5.99 (1.57) GHz of 14$\pm$3% (5.4$\pm$1.1%). The mean scale heights of the total emission in the radio halo (thick disk) at 5.99 (1.57) GHz are $1.79\pm0.54$ kpc ($1.75\pm0.27$ kpc) and have about the same values for the synchrotron emission. The total magnetic field of NGC 4631 has a mean strength of $\rm{\langle B_{eq}\rangle} \simeq 9 \rm{\mu G}$ in the disk, and a mean strength of $\rm{\langle B_{eq}\rangle}~\simeq 7~\rm{\mu G}$ in the halo. We also studied a double-lobed background radio galaxy southwest of NGC 4631, which is an FR~II radio galaxy according to the distribution of spectral index across the lobes. From the halo scale heights we estimated that the radio halo is escape-dominated with convective cosmic ray propagation, and conclude that there is a galactic wind in the halo of NGC 4631., Comment: 15 pages, 13 figures, accepted to be published in A&A

NGC 4631 is an interacting galaxy which exhibits one of the largest gaseous halos observed among edge-on galaxies. We aim to examine the synchrotron and polarization properties of its disk and halo emission with new radio continuum data. Radio continuum observations of NGC 4631 were performed with the Karl G. Jansky Very Large Array at C-band (5.99 GHz) in the C & D array configurations, and at L-band (1.57 GHz) in the B, C, & D array configurations. The Rotation Measure Synthesis algorithm was utilized to derive the polarization properties. We detected linearly polarized emission at C-band and L-band. The magnetic field in the halo is characterized by strong vertical components above and below the central region of the galaxy. The magnetic field in the disk is only clearly seen in the eastern side of NGC 4631, where it is parallel to the plane of the major axis of the galaxy. We detected for the first time a large-scale, smooth Faraday depth pattern in a halo of an external spiral galaxy, which implies the existence of a regular (coherent) magnetic field. A quasi-periodic pattern in Faraday depth with field reversals was found in the northern halo of the galaxy. The field reversals in the northern halo of NGC 4631, together with the observed polarization angles, indicate giant magnetic ropes (GMRs) with alternating directions. To our knowledge, this is the first time such reversals are observed in an external galaxy., 8 pages, 7 figures, accepted to be published in A&A

8 pages, 3 figures.-- En: Astronomy & Astrophysics manuscript no. AA_2009_13648v1 Dec 8, 2009, Aims: In this paper we study density cusps that may contain central black holes. The actual co-eval self-similar growth would not distinguish between the central object and the surroundings., Methods: To study the environment of a growing black hole we seek descriptions of steady 'cusps' that may contain a black hole and that retain at least a memory of self-similarity. We refer to the environment in brief as the 'bulge' and on smaller scales, the 'halo'., Results: We find simple descriptions of the simulations of collisionless matter by comparing predicted densities, velocity dispersions and distribution functions with the simulations. In some cases central point masses may be included by iteration. We emphasize that the co-eval self-similar growth allows an explanation of the black hole bulge mass correlation between approximately similar collisionless systems., Conclusions: We have derived our results from first principles assuming adiabatic self-similarity and either self-similar virialisation or normal steady virialisation. We conclude that distribution functions that retain a memory of self-similar evolution provide an understanding of collisionless systems. The implied energy relaxation of the collisionless matter is due to the time dependence. Phase mixing relaxation may be enhanced by clump-clump interactions., RNH acknowledges the support of an operating grant from the canadian Natural Sciences and Research Council. The work of MLeD is supported by CSIC (Spain) under the contract JAEDoc072,with partial support fromCICYT project FPA2006- 05807, at the IFT, Universidad Autonoma de Madrid, Spain

The density profiles established in the self-similar dynamical phase of dark matter haloes recollapse are all close to isothermal. This is steeper than the predictions of some n-body simulations for the central regions of the halo, which are in turn steeper than the profiles observed in the centre of some galaxies; particularly dwarfs and low surface brightness galaxies. The outer regions of galaxies both as observed and as simulated have density profiles steeper than the self-similar profile. Nevertheless there appears to be an intermediate region in most galaxies in which the inverse square behaviour is a good description. The outer deviations can be explained plausibly in terms of the transition from a self-gravitating extended halo to a Keplerian flow onto a dominant central mass (the isothermal distribution can not be complete), but the inner deviations are more problematic. Rather than attack this question directly, we use in this paper a novel coarse-graining technique combined with a shell code to establish both the distribution function associated with the self-similar density profile and the nature of the possible deviations in the central regions. In spherical symmetry we find that both in the case of purely radial orbits and in the case of orbits with non-zero angular momentum the self-similar density profile should flatten progressively near the centre of the system. The NFW limit of -1 seems possible. In a section aimed at demonstrating our technique for a spherically symmetric steady state, we argue that a Gaussian distribution function is the best approximation near the centre of the system., Comment: 21 pages, 4 eps figures, uses mn.cls, accepted for publication in M.N.R.A.S

In this article we give an account of a method of smoothing spatial inhomogeneous data sets by using wavelet reconstruction on a regular grid in an auxilliary space onto which the original data is mapped. In a previous paper by the present authors, we devised a method for inferring the velocity potential from the radial component of the cosmic velocity field assuming an ideal sampling. Unfortunately the sparseness of the real data as well as errors of measurement require us to first smooth the velocity field as observed on a 3-dimensional support (i.e. the galaxy positions) inhomogeneously distributed throughout the sampled volume. The wavelet formalism permits us to introduce a minimal smoothing procedure that is characterized by the variation in size of the smothing window function. Moreover the output smoothed radial velocity field can be shown to correspond to a well defined theoretical quantity as long as the spatial sampling support satisfies certain criteria. We argue also that one should be very cautious when comparing the velocity potential derived from such a smoothed radial component of the velocity field with related quantities derived from other studies (e.g : of the density field)., 19 pages, Latex file, figures are avaible under requests, published in Inverse Problems, 11 (1995) 765