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Register a new userDo cooling and heating functions actually exist?
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Cooling and heating functions describe how radiative processes impact the thermal state of the gas as a function of its temperature and other physical properties. In a most general case they depend on the detailed distributions of level populations of numerous ionic species and on the radiation spectrum. Hence, these functions may vary on a very wide range of spatial and temporal scales. In this paper, we explore cooling and heating functions between $5leq z leq10$ in simulated galaxies from the Cosmic Reionization On Computers (CROC) project. We find that the actual cooling (heating) rates experienced by the gas at different temperatures in the simulations do not correspond to any single cooling (heating) function. Gas about $T gtrsim 10^{4}$ K has sufficiently different combinations of density, metallicity, and photoionization rates than colder gas such that, if the hot gas were suddenly cooler, it would still cool and heat more efficiently than $T lesssim 10^{4}$ K gas. In other words, the thermodynamics of the gas in the simulations cannot be described by a single set of a cooling plus a heating function that could be computed with common tools, such as Cloudy.
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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.
Galaxy merger histories correlate strongly with stellar mass, largely regardless of morphology. Thus, at fixed stellar mass, spheroids and discs share similar assembly histories, both in terms of the frequency of mergers and the distribution of their mass ratios. Since mergers are the principal drivers of disc-to-spheroid morphological transformation, and the most massive galaxies typically have the richest merger histories, it is surprising that discs exist at all at the highest stellar masses (e.g. beyond the knee of the mass function). Using Horizon-AGN, a cosmological hydro-dynamical simulation, we show that extremely massive (M*> 10^11.4 MSun) discs are created via two channels. In the primary channel (accounting for ~70% of these systems and ~8% of massive galaxies) the most recent, significant merger (stellar mass ratio > 1:10) between a massive spheroid and a gas-rich satellite `spins up the spheroid by creating a new rotational stellar component, leaving a massive disc as the remnant. In the secondary channel (accounting for ~30% of these systems and ~3% of massive galaxies), a system maintains a disc throughout its lifetime, due to an anomalously quiet merger history. Not unexpectedly, the fraction of massive discs is larger at higher redshift, due to the Universe being more gas-rich. The morphological mix of galaxies at the highest stellar masses is, therefore, a strong function of the gas fraction of the Universe. Finally, these massive discs have similar black-hole masses and accretion rates to massive spheroids, providing a natural explanation for why a minority of powerful AGN are surprisingly found in disc galaxies.
NGC 1097 is a nearby Seyfert 1 galaxy with a bright circumnuclear starburst ring, a strong large-scale bar and an active nucleus. We present a detailed study of the spatial variation of the far infrared (FIR) [CII]158um and [OI]63um lines and mid-infrared H2 emission lines as tracers of gas cooling, and of the polycyclic aromatic hydrocarbon (PAH) bands as tracers of the photoelectric heating, using Herschel-PACS, and Spitzer-IRS infrared spectral maps. We focus on the nucleus and the ring, and two star forming regions (Enuc N and Enuc S). We estimated a photoelectric gas heating efficiency ([CII]158um+[OI]63um)/PAH in the ring about 50% lower than in Enuc N and S. The average 11.3/7.7um PAH ratio is also lower in the ring, which may suggest a larger fraction of ionized PAHs, but no clear correlation with [CII]158{mu}m/PAH(5.5 - 14um) is found. PAHs in the ring are responsible for a factor of two more [CII]158um and [OI]63um emission per unit mass than PAHs in the Enuc S. SED modeling indicates that at most 25% of the FIR power in the ring and Enuc S can come from high intensity photodissociation regions (PDRs), in which case G0 ~ 10^2.3 and nH ~ 10^3.5 cm^-3 in the ring. For these values of G0 and nH PDR models cannot reproduce the observed H2 emission. Much of the the H2 emission in the starburst ring could come from warm regions in the diffuse ISM that are heated by turbulent dissipation or shocks.
Polynomials with coefficients in ${-1,1}$ are called Littlewood polynomials. Using special properties of the Rudin-Shapiro polynomials and classical results in approximation theory such as Jacksons Theorem, de la Vallee Poussin sums, Bernsteins inequality, Rieszs Lemma, divided differences, etc., we give a significantly simplified proof of a recent breakthrough result by Balister, Bollobas, Morris, Sahasrabudhe, and Tiba stating that there exist absolute constants $eta_2 > eta_1 > 0$ and a sequence $(P_n)$ of Littlewood polynomials $P_n$ of degree $n$ such that $$eta_1 sqrt{n} leq |P_n(z)| leq eta_2 sqrt{n},, qquad z in mathbb{C},, , , |z| = 1,,$$ confirming a conjecture of Littlewood from 1966. Moreover, the existence of a sequence $(P_n)$ of Littlewood polynomials $P_n$ is shown in a way that in addition to the above flatness properties a certain symmetry is satisfied by the coefficients of $P_n$ making the Littlewood polynomials $P_n$ close to skew-reciprocal.
Definitely, an affirmative answer to this question would have implications of fundamental importance for astrophysics (a new class of compact stars), and for the physics of strong interactions (deconfined phase of quark matter, and strange matter hypothesis). In the present work, we use observational data for the newly discovered millisecond X-ray pulsar SAX J1808.4-3658 and for the atoll source 4U 1728-34 to constrain the radius of the underlying compact stars. Comparing the mass-radius relation of these two compact stars with theoretical models for both neutron stars and strange stars, we argue that a strange star model is more consistent with SAX J1808.4-3658 and 4U 1728-34, and suggest that they are likely strange star candidates.
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