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Register a new userRadiative cooling, heating and thermal conduction in M87
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The crisis of the standard cooling flow model brought about by Chandra and XMM-Newton observations of galaxy clusters, has led to the development of several models which explore different heating processes in order to assess if they can quench the cooling flow. Among the most appealing mechanisms are thermal conduction and heating through buoyant gas deposited in the ICM by AGNs. We combine Virgo/M87 observations of three satellites (Chandra, XMM-Newton and Beppo-SAX) to inspect the dynamics of the ICM in the center of the cluster. Using the spectral deprojection technique, we derive the physical quantities describing the ICM and determine the extra-heating needed to balance the cooling flow assuming that thermal conduction operates at a fixed fraction of the Spitzer value. We assume that the extra-heating is due to buoyant gas and we fit the data using the model developed by Ruszkowski and Begelman (2002). We derive a scale radius for the model of $sim 5$ kpc, which is comparable with the M87 AGN jet extension, and a required luminosity of the AGN of a $few times 10^{42}$ erg s$^{-1}$, which is comparable to the observed AGN luminosity. We discuss a scenario where the buoyant bubbles are filled of relativistic particles and magnetic field responsible for the radio emission in M87. The AGN is supposed to be intermittent and to inject populations of buoyant bubbles through a succession of outbursts. We also study the X-ray cool component detected in the radio lobes and suggest that it is structured in blobs which are tied to the radio buoyant bubbles.
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Context. The radiative energy balance in the solar chromosphere is dominated by strong spectral lines that are formed out of LTE. It is computationally prohibitive to solve the full equations of radiative transfer and statistical equilibrium in 3D time dependent MHD simulations. Aims. To find simple recipes to compute the radiative energy balance in the dominant lines under solar chromospheric conditions. Methods. We use detailed calculations in time-dependent and 2D MHD snapshots to derive empirical formulae for the radiative cooling and heating. Results. The radiative cooling in neutral hydrogen lines and the Lyman continuum, the H and K and intrared triplet lines of singly ionized calcium and the h and k lines of singly ionized magnesium can be written as a product of an optically thin emission (dependent on temperature), an escape probability (dependent on column mass) and an ionization fraction (dependent on temperature). In the cool pockets of the chromosphere the same transitions contribute to the heating of the gas and similar formulae can be derived for these processes. We finally derive a simple recipe for the radiative heating of the chromosphere from incoming coronal radiation. We compare our recipes with the detailed results and comment on the accuracy and applicability of the recipes.
Acoustic and magnetoacoustic waves are among the possible candidate mechanisms that heat the upper layers of solar atmosphere. A weak chromospheric plage near a large solar pore NOAA 11005 was observed on October 15, 2008 in the lines Fe I 617.3 nm and Ca II 853.2 nm with the Interferometric Bidimemsional Spectrometer (IBIS) attached to the Dunn Solar Telescope. Analyzing the Ca II observations with spatial and temporal resolutions of 0.4 and 52 s, the energy deposited by acoustic waves is compared with that released by radiative losses. The deposited acoustic flux is estimated from power spectra of Doppler oscillations measured in the Ca II line core. The radiative losses are calculated using a grid of seven 1D hydrostatic semi-empirical model atmospheres. The comparison shows that the spatial correlation of maps of radiative losses and acoustic flux is 72 %. In quiet chromosphere, the contribution of acoustic energy flux to radiative losses is small, only of about 15 %. In active areas with photospheric magnetic field strength between 300 G and 1300 G and inclination of 20-60 degrees, the contribution increases from 23 % (chromospheric network) to 54 % (a plage). However, these values have to be considered as lower limits and it might be possible that the acoustic energy flux is the main contributor to the heating of bright chromospheric network and plages.
We study phase shifts of the propagating slow waves in coronal loops invoking the effects of thermal conductivity, compressive viscosity, radiative losses and heating-cooling imbalance. We derive a general dispersion relation and solve it to determine phase shifts of density and temperature perturbations relative to the velocity and their dependence on equilibrium parameters ($rho_0$, $T_0$). We estimate phase difference ($Delta phi$) between density and temperature perturbations and its dependence on $rho_0$ and $T_0$. The effect of viscosity on the phase shifts was found negligible. The role of radiative losses along with h/c imbalance for chosen specific heating function ($H(rho, T) propto rho^{-0.5} T^{-3}$) in determining phase shifts, is found to be significant for the high density and low temperature loops. The h/c imbalance can increase the phase difference ($Delta phi approx 140^circ$) for low temperature loops compared to the constant heating case ($Delta phi approx 30^circ$). We derive a general expression for the polytropic index. We find that in the presence of thermal conduction alone, the polytropic index remains close to its classical value for all the considered $rho_0$ and $T_0$. However, it reduces to a value $1.2$ when loop density is decreased by an order of magnitude compared to its normal coronal value. We find that the inclusion of radiative losses, with or without h/c imbalance, cannot explain the observed polytropic index. The thermal ratio ($d$) needs to be enhanced by an order of magnitude, in order to explain its observed value $1.1 pm 0.02$ in the solar loops. We also explore the role of different heating functions for typical coronal parameters and found that although the polytropic index remains close to its classical value, the phase difference is highly dependent on the form of heating function (The abstract is restructured for arxiv).
We present a detailed investigation of the X-ray luminosity (Lx)-gas temperature (Tvir) relation of the complete X-ray flux-limited sample of the 64 brightest galaxy clusters in the sky (HIFLUGCS). We study the influence of two astrophysical processes, active galactic nuclei (AGN) heating and intracluster medium (ICM) cooling, on the Lx-Tvir relation, simultaneously for the first time. We determine best-fit relations for different subsamples using the cool-core strength and the presence of central radio activity as selection criteria. We find the strong cool-core clusters (SCCs) with short cooling times (< 1Gyr)to display the steepest relation (Lx ~ Tvir^{3.33}) and the non-cool-core clusters (NCCs) with long cooling times (> 7.7Gyr) to display the shallowest (Lx ~ Tvir^{2.42}). This has the simple implication that on the high-mass scale (Tvir > 2.5keV) the steepening of the Lx-Tvir relation is mainly due to the cooling of the intracluster medium gas. We propose that ICM cooling and AGN heating are both important in shaping the Lx-Tvir relation but on different length-scales. While our study indicates that ICM cooling dominates on cluster scales (Tvir > 2.5keV), we speculate that AGN heating dominates the scaling relation in poor clusters and groups (Tvir < 2.5keV). The intrinsic scatter about the Lx-Tvir relation in X-ray luminosity for the whole sample is 45.4% and varies from a minimum of 34.8% for weak cool-core clusters to a maximum of 59.4% for clusters with no central radio source. We find that after excising the cooling region, the scatter in the Lx-Tvir relation drops from 45.4% to 39.1%, implying that the cooling region contributes ~ 27% to the overall scatter. Lastly, we find the true SCC fraction to be 25% lower than the observed one and the true normalizations of the Lx-Tvir relations to be lower by 12%, 7%, and 17% for SCC, WCC, and NCC clusters, respectively. [abridged]
The discrepancy between expected and observed cooling rates of X-ray emitting gas has led to the {it cooling flow problem} at the cores of clusters of galaxies. A variety of models have been proposed to model the observed X-ray spectra and resolve the cooling flow problem, which involves heating the cold gas through different mechanisms. As a result, realistic models of X-ray spectra of galaxy clusters need to involve both heating {it and} cooling mechanisms. In this paper, we argue that the heating time-scale is set by the magnetohydrodynamic (MHD) turbulent viscous heating for the Intracluster plasma, parametrised by the Shakura-Sunyaev viscosity parameter, $alpha$. Using a cooling+heating flow model, we show that a value of $alphasimeq 0.05$ (with 10% scatter) provides improved fits to the X-ray spectra of cooling flow, while at the same time, predicting reasonable cooling efficiency, $epsilon_{cool} = 0.33^{+0.63}_{-0.15}$. Our inferred values for $alpha$ based on X-ray spectra are also in line with direct measurements of turbulent pressure in simulations and observations of galaxy clusters. This simple picture unifies astrophysical accretion, as a balance of MHD turbulent heating and cooling, across more than 16 orders of magnitudes in scale, from neutron stars to galaxy clusters.
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