We construct exhaustion and cut-off functions with controlled gradient and Laplacian on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the ...distance from a fixed reference point, without any assumptions on the topology or the injectivity radius. Along the way we prove a generalization of the Li-Yau gradient estimate which is of independent interest. We then apply our cut-offs to the study of the fast and porous media diffusion, of
L
q
-properties of the gradient and of the self-adjointness of Schrödinger-type operators.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Aims. Giant radio halos are diffuse, Mpc-scale, synchrotron sources located in the central regions of galaxy clusters and provide the most relevant example of cluster non-thermal activity. Radio and ...X-ray surveys allow to investigate the statistics of radio halos and may contribute to constrain the origin of these sources and their evolution. Methods. We investigate the distribution of clusters in the plane X-ray (thermal, ) vs. synchrotron (non-thermal, P sub(1.4)) luminosity, where clusters hosting giant radio halos trace the P sub(1.4)- correlation and clusters without radio halos populate a region that is well separated from that spanned by the above correlation. The connection between radio halos and cluster mergers suggests that the cluster Mpc-scale synchrotron emission is amplified during these mergers and then suppressed when clusters become more dynamically relaxed. Results. In this context, by analysing the distribution in the P sub(1.4)- plane of galaxy clusters from X-ray selected samples with adequate radio follow up, we constrain the typical time-scale of evolution of diffuse radio emission in clusters and discuss the implications for the origin of radio halos. Conclusions. We conclude that cluster synchrotron emission is suppressed (and amplified) in a time-scale significantly smaller than 1 Gyr. We show that this constraint appears difficult to reconcile with the hypothesis that the halo's radio power is suppressed due to dissipation of magnetic field in galaxy clusters. On the other hand, in agreement with models where turbulent acceleration plays a role, present constraints suggest that relativistic electrons are accelerated in Mpc-scale regions, in connection with cluster mergers and for a time-interval of about 1 Gyr, and then they cool in a relatively small time-scale, when the hosting cluster becomes more dynamically relaxed.
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Radio and far infrared luminosities of star-forming galaxies follow a tight linear relation. Making use of ASCA and BeppoSAX observations of a well-defined sample of nearby star-forming galaxies, we ...argue that tight linear relations hold between the X-ray, radio and far infrared luminosities. The effect of intrinsic absorption is investigated taking NGC 3256 as a test case. It is suggested that the hard X-ray emission is directly related to the Star Formation Rate. Star formation processes may also account for most of the 2–10 keV emission from LLAGNs of lower X-ray luminosities (for the same FIR and radio luminosity). Deep Chandra observations of a sample of radio-selected star-forming galaxies in the Hubble Deep Field North show that the same relation holds also at high ($0.2\la z\la 1.3$) redshift. The X-ray/radio relations also allow a derivation of X-ray number counts up to very faint fluxes from the radio Log N–Log S, which is consistent with current limits and models. Thus the contribution of star-forming galaxies to the X-ray background can be estimated.
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The most important evidence of non-thermal phenomena in galaxy clusters comes from giant radio haloes (GRHs), spectacular synchrotron radio sources extended over ≥Mpc scales, detected in the central ...regions of a growing number of massive galaxy clusters. A promising possibility to explain these sources is given by in situ stochastic reacceleration of relativistic electrons by turbulence generated in the cluster volume during merger events. Cassano and Brunetti have recently shown that the expected fraction of clusters with radio haloes and the increase of such a fraction with cluster mass can be reconciled with present observations provided that a fraction of 20-30 per cent of the turbulence in clusters is in the form of compressible modes.
In this work, we extend the above-mentioned analysis by including a scaling of the magnetic field strength with cluster mass. We show that, in the framework of the reacceleration model, the observed correlations between the synchrotron radio power of a sample of 17 GRHs and the X-ray properties of the hosting clusters are consistent with, and actually predicted by a magnetic field dependence on the virial mass of the form B∝M
b
v, with b≳ 0.5 and typical μG strengths of the average B intensity. The occurrence of GRHs as a function of both cluster mass and redshift is obtained: the evolution of such a probability depends on the interplay between synchrotron and inverse Compton losses in the emitting volume, and it is maximized in clusters for which the two losses are comparable.
The most relevant findings are that the predicted luminosity functions of GRHs are peaked around a power P
1.4 GHz∼ 1024 W Hz−1, and severely cut off at low radio powers due to the decrease of the electron reacceleration in smaller galaxy clusters, and that the occurrence of GRHs at 1.4 GHz beyond a redshift z∼ 0.7 appears to be negligible. As a related check, we also show that the predicted integral radio source counts within a limited volume (z≤ 0.2) are consistent with present observational constraints. Extending the source counts beyond z= 0.2, we estimate that the total number of GRHs to be discovered at ∼ mJy radio fluxes could be ∼100 at 1.4 GHz. Finally, the occurrence of GRHs and their number counts at 150 MHz are estimated in view of the forthcoming operation of low-frequency observatories (LOFAR, LWA) and compared with those at higher radio frequencies.
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We report on the lowest-frequency detection to date of three bursts from the fast radio burst FRB 180916.J0158+65, observed at 328 MHz with the Sardinia Radio Telescope (SRT). The SRT observed the ...periodic repeater FRB 180916.J0158+65 for five days from 2020 February 20 to 24 during a time interval of active radio bursting, and detected the three bursts during the first hour of observations; no more bursts were detected during the remaining ∼30 hr. Simultaneous SRT observations at 1548 MHz did not detect any bursts. Burst fluences are in the range 37 to 13 Jy ms. No relevant scattering is observed for these bursts. We also present the results of the multi-wavelength campaign we performed on FRB 180916.J0158+65, during the five days of the active window. Simultaneously with the SRT observations, others with different time spans were performed with the Northern Cross at 408 MHz, with XMM-Newton, NICER, INTEGRAL, AGILE, and with the TNG and two optical telescopes in Asiago, which are equipped with fast photometers. XMM-Newton obtained data simultaneously with the three bursts detected by the SRT, and determined a luminosity upper limit in the 0.3-10 keV energy range of ∼1045 erg s−1 for the burst emission. AGILE obtained data simultaneously with the first burst and determined a fluence upper limit in the MeV range for millisecond timescales of . Our results show that absorption from the circumburst medium does not significantly affect the emission from FRB 180916.J0158+65, thus limiting the possible presence of a superluminous supernova around the source, and indicate that a cutoff for the bursting mechanism, if present, must be at lower frequencies. Our multi-wavelength campaign sensitively constrains the broadband emission from FRB 180916.J0158+65, and provides the best limits so far for the electromagnetic response to the radio bursting of this remarkable source of fast radio bursts.
Aims. We present the results of the GMRT cluster radio halo survey. The main purposes of our observational project are to measure what fraction of massive galaxy clusters in the redshift range z ...=0.2-0.4 host a radio halo, and to constrain the expectations of the particle re-acceleration model for the origin of the non-thermal radio emission. Methods. We selected a complete sample of 50 clusters in the X-ray band from the REFLEX (27) and the eBCS (23) catalogues. We present Giant Metrewave Radio Telescope (GMRT) observations at 610 MHz for all clusters still lacking high sensitivity radio information, i.e. 16 eBCS and 7 REFLEX clusters, thus completing the radio information for the whole sample. The typical sensitivity in our images is in the range 1 sigma sim 35-100 similar to \muJy b super(-1). Results. We found a radio halo in A 697, a diffuse peripheral source of unclear nature in A 781, a core-halo source in Z 7160, a candidate radio halo in A 1682 and "suspect" central emission in Z 2661. Including the literature information, a total of 10 clusters in the sample host a radio halo. A very important result of our work is that 25 out of the 34 clusters observed with the GMRT do not host extended central emission at the sensitivity level of our observations, and for 20 of them firm upper limits to the radio power of a giant radio halo were derived. The GMRT Radio Halo Survey shows that radio halos are not common, and our findings on the fraction of giant radio halos in massive clusters are consistent with the statistical expectations based on the re-acceleration model. Our results favour primary to secondary electron models.
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The radio spectral index map of the Coma halo shows a progressive steepening of the spectral index with increasing radius. Such a steepening cannot be simply justified by models involving continuous ...injection of fresh particles in the Coma halo or by models involving diffusion of fresh electrons from the central regions. We propose a two-phase model in which the relativistic electrons injected in the Coma cluster by some processes (starbursts, AGNs, shocks, turbulence) during a first phase in the past are systematically reaccelerated during a second phase for a relatively long time (∼1Gyr) up to the present time. We show that for reacceleration time-scales of ∼0.1Gyr this hypothesis can well account for the radio properties of Coma C. For the same range of parameters which explain Coma C we have calculated the expected fluxes from the inverse Compton scattering of the Cosmic Microwave Background (CMB) photons, finding that the hard X-ray tail discovered by BeppoSAX may be accounted for by the stronger reacceleration allowed by the model. The possibility of extending the main model assumptions and findings to the case of the other radio haloes is also discussed, the basic predictions being consistent with the observations.
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Clusters of galaxies are sites of acceleration of charged particles and sources of nonthermal radiation. We report on new constraints on the population of cosmic rays in the intracluster medium (ICM) ...obtained via radio observations of a fairly large sample of massive, X-ray-luminous galaxy clusters In the redshift Interval 0.2-0.4. The bulk of the observed galaxy clusters does not show any hint of megaparsec-scale synchrotron radio emission at the cluster center (radio halo). We obtained solid upper limits to the diffuse radio emission and discuss their implications for the models for the origin of radio halos. Our measurements allow us to also derive a limit to the content of cosmic-ray protons in the ICM. Assuming spectral indices of these protons unk and mu G level magnetic fields, as from rotation measures, these limits are 1 order of magnitude deeper than present EGRET upper limits, while they are less stringent for steeper spectra and lower magnetic fields.
Aims. We present the first results of an ongoing project devoted to the search of giant radio halos in galaxy clusters located in the redshift range z =0.2-0.4. One of the main goals of our study is ...to measure the fraction of massive galaxy clusters in this redshift interval hosting a radio halo, and to constrain the expectations of the particle re-acceleration model for the origin of non-thermal radio emission in galaxy clusters. Methods. We selected 27 REFLEX clusters and here we present Giant Metrewave Radio Telescope (GMRT) observations at 610 MHz for 11 of them. The sensitivity (1\sigma) in our images is in the range 35-100 \muJy beam super(-1) for all clusters. Results. We found three new radio halos, doubling the number of halos known in the selected sample. In particular, giant radio halos were found in A 209 and RXCJ 2003.5-2323, and one halo (of smaller size) was found in RXCJ 1314.4-2515. Candidate extended emission on smaller scale was found around the central galaxy in A 3444 which deserves further investigation. Furthermore, a radio relic was found in A 521, and two relics were found in RXCJ 1314.5-2515. The remaining six clusters observed do not host extended emission of any kind.
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The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that ...can be successfully applied to nonlinear differential equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or for the Euclidean setting. The work is written in an easy style that makes it accessible even to non-specialists.After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by means of a concise but clear study of some aspects of the Yamabe problem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds.
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