Gas Density Profiles Research Articles

The Three Hundred project: the stellar and gas profiles

ABSTRACT Using the catalogues of galaxy clusters from The Three Hundred project, modelled with both hydrodynamic simulations (gadget-x and gadget-music), and semi-analytical models (SAMs), we study the scatter and self-similarity of the profiles and distributions of the baryonic components of the clusters: the stellar and gas mass, metallicity, the stellar age, gas temperature, and the (specific) star formation rate. Through comparisons with observational results, we find that the shape and the scatter of the gas density profiles matches well the observed trends including the reduced scatter at large radii which is a signature of self-similarity suggested in previous studies. One of our simulated sets, gadget-x, reproduces well the shape of the observed temperature profile, while gadget-music has a higher and flatter profile in the cluster centre and a lower and steeper profile at large radii. The gas metallicity profiles from both simulation sets, despite following the observed trend, have a relatively lower normalization. The cumulative stellar density profiles from SAMs are in better agreement with the observed result than both hydrodynamic simulations which show relatively higher profiles. The scatter in these physical profiles, especially in the cluster centre region, shows a dependence on the cluster dynamical state and on the cool-core/non-cool-core dichotomy. The stellar age, metallicity, and (s)SFR show very large scatter, which are then presented in 2D maps. We also do not find any clear radial dependence of these properties. However, the brightest central galaxies have distinguishable features compared to the properties of the satellite galaxies.

The chemical evolution of galaxy clusters: Dissecting the iron mass budget of the intracluster medium

Aims. We study the chemical evolution of galaxy clusters by measuring the iron mass in the ICM after dissecting the abundance profiles into different components. Methods. We used Chandra archival observations of 186 morphologically regular clusters in the redshift range of [0.04, 1.07]. For each cluster, we computed the azimuthally averaged iron abundance and gas density profiles. In particular, our aim is to identify a central peak in the iron distribution, which is associated with the central galaxy, and an approximately constant plateau reaching the largest observed radii, which is possibly associated with early enrichment that occurred before or shortly after achieving virialization within the cluster. We were able to firmly identify two components in the iron distribution in a significant fraction of the sample simply by relying on the fit of the iron abundance profile. From the abundance and ICM density profiles, we computed the iron mass included in the iron peak and iron plateau, and the gas mass-weighted iron abundance of the ICM out to an extraction radius of 0.4r500 and to r500 by extending the abundance profile as a constant. Results. We find that the iron plateau shows no evolution with redshift. On the other hand, we find a marginal (< 2σ c.l.) decrease with redshift in the iron mass included in the iron peak rescaled by the gas mass. We measure that the fraction of iron peak mass is typically a few percent (∼1%) of the total iron mass within r500. Therefore, since the total iron mass budget is dominated by the plateau, we find consistently that the global gas mass-weighted iron abundance does not evolve significantly across our sample. We were also able to reproduce past claims of evolution in the global iron abundance, which turn out to be due to the use of cluster samples with different selection methods combined with the use of emission-weighted, instead of gas mass-weighted, abundance values. Finally, while the intrinsic scatter in the iron plateau mass is consistent with zero, the iron peak mass exhibits a large scatter, in line with the fact that the peak is produced after the virialization of the halo and depends on the formation history of the hosting cool core and the strength of the associated feedback processes. Conclusions. We conclude that only a spatially resolved approach can resolve the issue of iron abundance evolution in the ICM, reconciling the contradictory results obtained in the last ten years. Evolutionary effects below z ∼ 1 are marginally measurable with present-day data, while at z > 1 the constraints are severely limited by poor knowledge of the high-z cluster population. The path towards a full and comprehensive chemical history of the ICM requires the application of high angular resolution X-ray bolometers and a dramatic increase in the number of faint, extended X-ray sources.

What Makes Lyα Nebulae Glow? Mapping the Polarization of LABd05

Abstract “Lyα nebulae” are giant (∼100 kpc), glowing gas clouds in the distant universe. The origin of their extended Lyα emission remains a mystery. Some models posit that Lyα emission is produced when the cloud is photoionized by UV emission from embedded or nearby sources, while others suggest that the Lyα photons originate from an embedded galaxy or active galactic nucleus (AGN) and are then resonantly scattered by the cloud. At least in the latter scenario, the observed Lyα emission will be polarized. To test these possibilities, we are conducting imaging polarimetric observations of seven Lyα nebulae. Here we present our results for LABd05, a cloud at z = 2.656 with an obscured, embedded AGN to the northeast of the peak of Lyα emission. We detect significant polarization. The highest polarization fractions P are ∼10%–20% at ∼20–40 kpc southeast of the Lyα peak, away from the AGN. The lowest P, including upper limits, are ∼5% and lie between the Lyα peak and AGN. In other words, the polarization map is lopsided, with P increasing from the Lyα peak to the southeast. The measured polarization angles θ are oriented northeast, roughly perpendicular to the P gradient. This unique polarization pattern suggests that (1) the spatially offset AGN is photoionizing nearby gas and (2) escaping Lyα photons are scattered by the nebula at larger radii and into our sightline, producing tangentially oriented, radially increasing polarization away from the photoionized region. Finally we conclude that the interplay between the gas density and ionization profiles produces the observed central peak in the Lyα emission. This also implies that the structure of LABd05 is more complex than assumed by current theoretical spherical or cylindrical models.

Mapping and characterization of cosmic filaments in galaxy cluster outskirts: strategies and forecasts for observations from simulations

ABSTRACT Upcoming wide-field surveys are well suited to studying the growth of galaxy clusters by tracing galaxy and gas accretion along cosmic filaments. We use hydrodynamic simulations of volumes surrounding 324 clusters from The ThreeHundred project to develop a framework for identifying and characterizing these filamentary structures and associating galaxies with them. We define three-dimensional reference filament networks reaching 5R200 based on the underlying gas distribution and quantify their recovery using mock galaxy samples mimicking observations such as those of the WEAVE Wide-Field Cluster Survey. Since massive galaxies trace filaments, they are best recovered by mass-weighting galaxies or imposing a bright limit (e.g. >L*) on their selection. We measure the transverse gas density profile of filaments, derive a characteristic filament radius of ≃ 0.7–1 h−1Mpc, and use this to assign galaxies to filaments. For different filament extraction methods, we find that at R > R200, ∼15–$20{{\ \rm per\ cent}}$ of galaxies with M* > 3 × 109M⊙ are in filaments, increasing to $\sim 60{{\ \rm per\ cent}}$ for galaxies more massive than the Milky Way. The fraction of galaxies in filaments is independent of cluster mass and dynamical state and is a function of cluster-centric distance, increasing from ∼13 per cent at 5R200 to ∼21 per cent at 1.5R200. As a bridge to the design of observational studies, we measure the purity and completeness of different filament galaxy selection strategies. Encouragingly, the overall three-dimensional filament networks and ∼67 per cent of the galaxies associated with them are recovered from two-dimensional galaxy positions.

Molecular Clumps Disguising Their Star Formation Efficiency per Free-fall Time: What We Can Do Not to Be Fooled

Abstract The presence of a volume-density gradient in molecular clumps allows them to raise their star formation rate compared with what they would experience if their gas were uniform in density. This higher value for the star formation rate yields in turn a higher star formation efficiency per free-fall time that we measure. The measured star formation efficiency per free-fall time, , of clumps is therefore plagued by a degeneracy, as two factors contribute to it: one is the density gradient of the clump gas, the other is the intrinsic star formation efficiency per free-fall time, , with which the clump would form stars should there be no gas-density gradient. This paper presents a method allowing one to recover the intrinsic efficiency of a centrally concentrated clump. It hinges on the relation between the surface densities in stars and gas measured locally from clump center to clump edge. Knowledge of the initial density profile of the clump gas is not required. A step-by-step description of the method is provided as a tool in hand for observers. Once has been estimated, it can be compared with its measured, clump-averaged, counterpart, , to quantify the impact that the initial gas-density profile of a clump has had on its star formation history.

SuperModel predictions in the outskirts of the galaxy cluster Zwicky 3146

ABSTRACT The relaxed galaxy cluster Zwicky 3146 is analysed via the SuperModel, a tool already tested on many clusters since 2009. In particular, this analysis is focused on the intracluster medium X-ray temperature data measured by XMM–Newton up to r500. A previous analysis was based on the temperature profile derived from the Sunyaev-Zeld′ovich effect pressure data. The gas mass fraction fgas is obtained from the resulting SuperModel temperature profile extrapolated up to the virial radius R, which turns out in agreement with the steep temperature profiles observed by Suzaku, and from the gas density profile observed by XMM–Newton. The comparison between fgas with the universal value indicates a non-thermal pressure component, pnth, in the cluster outskirts. The SuperModel analysis shows a ratio α(R) (${\simeq}50{{\ \rm per\ cent}}$) of pnth to the total pressure greater than the values found by simulations, highlighting the possible presence of accreting substructures and inhomogeneities in the gas density profile. Once that this profile is corrected for clumpiness, the level of pnth is considerably reduced. However, a significant turbulence ($\alpha (R)\simeq 20{{\ \rm per\ cent}}$) and entropy flattening are still present in the outskirts of the galaxy cluster Zwicky 3146.

Optimization of relativistic laser self-channeling in experimental Xenon gas jet target

Relativistic and ponderomotive self-channeling of intense ultrashort laser pulses in underdense plasmas is investigated numerically under more realistic experimental conditions. The optimization of the controlled power compression and stability of the channel can be realized with the use of appropriate incident laser power, beam focusing, and gas density profile conditions. The results of simulating the whole self-channeling are in good general agreement with the experimental observations for the self-channeling of TW-level 248 nm laser pulses in Xenon gas jets, capture the salient features of the relativistic self-channeling dynamics, and examine the root causes of experimental observations more accurately than before. The channel length is consistent with some transverse Xenon M-shell radiation measurements of the interaction region. The theoretically predicted ∼400 nm channel diameter indicates that the laser channel intensity could be an order of magnitude larger than previously anticipated.

Galaxy cluster hydrostatic masses using Tolman–Oppenheimer–Volkoff equation

Motivated by previous studies in literature about the potential importance of relativistic corrections to galaxy cluster hydrostatic masses, we calculate the masses of 12 relaxed clusters (with Chandra X-ray data) using the Tolman-Oppenheimer-Volkov (TOV) equation of hydrostatic equilibrium and the ideal gas equation of state. Analytical formulae for gas density and temperature profiles for these clusters, previously derived by Vikhlinin et al (astro-ph/0507092) were used to obtain these masses. We compare the TOV-based masses with those obtained using the corresponding Newtonian equation of hydrostatic equilibrium. We find that the fractional relative difference between the two masses are negligible, corresponding to $\sim \mathcal{O}(10^{-5})$.

The Three Hundred Project: Correcting for the hydrostatic-equilibrium mass bias in X-ray and SZ surveys

Accurate and precise measurement of the masses of galaxy clusters is key to deriving robust constraints on cosmological parameters. However, increasing evidence from observations confirms that X-ray masses obtained under the assumption of hydrostatic equilibrium might be underestimated, as previously predicted by cosmological simulations. We analyze more than 300 simulated massive clusters from the Three Hundred Project, and investigate the connection between mass bias and several diagnostics extracted from synthetic X-ray images of these simulated clusters. We find that the azimuthal scatter measured in 12 sectors of the X-ray flux maps is a statistically significant indication of the presence of an intrinsic (i.e., 3D) clumpy gas distribution. We verify that a robust correction to the hydrostatic mass bias can be inferred when estimates of the gas inhomogeneity from X-ray maps (such as the azimuthal scatter or the gas ellipticity) are combined with the asymptotic external slope of the gas density or pressure profiles, which can be respectively derived from X-ray and millimeter (Sunyaev-Zeldovich effect) observations. We also obtain that mass measurements based on either gas density and temperature or gas density and pressure result in similar distributions of the mass bias. In both cases, we provide corrections that help reduce both the dispersion and skewness of the mass bias distribution. These are effective even when irregular clusters are included leading to interesting implications for the modeling and correction of hydrostatic mass bias in cosmological analyses of current and future X-ray and SZ cluster surveys.

Density Profiles of Gases and Fluids in Gravitational Potentials from a Generalization of Hydrostatic Equilibrium

It is well-known that equilibrium density profiles of gases and fluids in gravitational potentials have an r−1 dependence, where r is the radius. This is found in both astronomical observations and detailed simulations in spherically-symmetric geometries. It is also well-known that the standard equation for hydrostatic equilibrium does not produce such solutions. This paper utilizes a Lagrangian formulation that produces a closed-form r−1 solution and identifies the needed terms to be added to the standard equation for hydrostatic equilibrium to obtain such a solution. Variants of the r−1 solution avoid a density singularity at the origin and a total-enclosed mass singularity at infinity. The resulting solutions are shown to be in good agreement with well-established density profiles of ordinary matter in galaxies, dark matter haloes, and the atmosphere of earth. Comparisons are made to solutions based on the standard hydrostatic equation, including solutions based on the Lane-Emden equation. The origins of differences are explained.

Simulation of the gas density distribution in the accelerator of the ELISE test facility.

In multiaperture electrostatic accelerators of negative ion sources, the plasma discharge is sustained by injecting gas in the plasma source, in a dynamic equilibrium with the gas flowing out through the accelerator. In this work, we present a three-dimensional numerical simulation of the gas flow inside the accelerator system of the large negative ion source ELISE at Max-Planck-Institut für Plasmaphysik Garching. ELISE has 640 apertures per electrode and lateral gaps between the electrode support structures that also contribute to the total gas conductance. Assuming molecular regime, we estimated the gas conductance, the gas density profile along the path of the ion beams from upstream of the plasma grid to downstream of the ground grid, and the transverse nonuniformities in the accelerator. The simulation included the most relevant geometrical features, while the results are compared to analytical results.

The impact of the observed baryon distribution in haloes on the total matter power spectrum

ABSTRACTThe interpretation of upcoming weak gravitational lensing surveys depends critically on our understanding of the matter power spectrum on scales $k \lt 10\, {h\, {\rm Mpc}^{-1}}$, where baryonic processes are important. We study the impact of galaxy formation processes on the matter power spectrum using a halo model that treats the stars and gas separately from the dark matter distribution. We use empirical constraints from X-ray observations (hot gas) and halo occupation distribution modelling (stars) for the baryons. Since X-ray observations cannot generally measure the hot gas content outside r500c, we vary the gas density profiles beyond this radius. Compared with dark matter only models, we find a total power suppression of $1\, {\mathrm{per\ cent}}$ ($5\, {\mathrm{per\ cent}}$) on scales $0.2\!-\!1\, {h\, {\rm Mpc}^{-1}}$ ($0.5\!-\!2\, {h\, {\rm Mpc}^{-1}}$), where lower baryon fractions result in stronger suppression. We show that groups of galaxies ($10^{13} \lt m_{\mathrm{500c}} / (h^{-1}\, \mathrm{M}_{\odot }) \lt 10^{14}$) dominate the total power at all scales $k \lesssim 10\, {h\, {\rm Mpc}^{-1}}$. We find that a halo mass bias of $30\, {\mathrm{per\ cent}}$ (similar to what is expected from the hydrostatic equilibrium assumption) results in an underestimation of the power suppression of up to $4\, {\mathrm{per\ cent}}$ at $k=1\, {h\, {\rm Mpc}^{-1}}$, illustrating the importance of measuring accurate halo masses. Contrary to work based on hydrodynamical simulations, our conclusion that baryonic effects can no longer be neglected is not subject to uncertainties associated with our poor understanding of feedback processes. Observationally, probing the outskirts of groups and clusters will provide the tightest constraints on the power suppression for $k \lesssim 1\, {h\, {\rm Mpc}^{-1}}$.

Diagnostics of the down-ramp gas and plasma density profiles in a gas jet and a capillary gas cell

Laser-aided plasma diagnostics is a very important tool for laser-driven plasma wakefield acceleration, where a gas jet or a gas cell is used to produce a plasma density of 1018∼1019/cm3. We developed special plasma sources based on a gas jet and a capillary gas cell with a sudden density down-ramp, which can induce easy self-injection of plasma electrons into the laser wakefield. In our research, the Mach-Zehnder laser interferometer with a Ti:sapphire laser of 40 fs pulse duration was used to diagnose the gas and laser-produced plasma densities in the gas jet and the capillary gas cell. The measurement results for the gas and plasma densities are reported in this paper.

Simulation and measurement of rarefied gas flow and neutral density profiles through a large multiaperture multigrid negative ion accelerator

In large multi-aperture, multi-grid negative-ion accelerator for fusion application, the background gas density in the electrostatic accelerator causes a loss of negative-ion current and the formation of dangerous stray particles. In addition, to sustain in dynamic equilibrium a sufficient gas pressure in the plasma ion-source, a very large pumping speed is typically necessary. This paper presents and compare simulations and measurements of gas flows and background pressure profiles, through the electrostatic accelerator of the SPIDER beam source, the full-size prototype source of the ITER neutral beam injectors. The gas pressure profiles through the ion accelerator were measured by multiple movable capacitive pressure gauges, mapping the uniformity of the profiles along nine beamlets at three different filling pressures. The gas flow simulations in molecular flow regime were performed with a large-scale view-factor model, and with a single-aperture periodic test particle Monte Carlo model. The models reproduced the measured pressure profiles but additionally, provided also the profiles of local gas density. The gas conductance and the profiles calculated with the full-scale gas flow model correctly reproduce the measured profiles, and the transversal non-uniformities over the 1.6 m × 0.6 m cross section. The calculated gas density profile is also verified by comparing the two different numerical approaches. The gas flow model validated at room temperature can be used to simulate the pressure profile during operation, in presence of gas heating and dissociation by the source plasma.

Runaway merger shocks in galaxy cluster outskirts and radio relics

ABSTRACT Moderately strong shocks arise naturally when two subclusters merge. For instance, when a smaller subcluster falls into the gravitational potential of a more massive cluster, a bow shock is formed and moves together with the subcluster. After pericentre passage, however, the subcluster is decelerated by the gravity of the main cluster, while the shock continues moving away from the cluster centre. These shocks are considered as promising candidates for powering radio relics found in many clusters. The aim of this paper is to explore the fate of such shocks when they travel to the cluster outskirts, far from the place where the shocks were initiated. In a uniform medium, such a ‘runaway’ shock should weaken with distance. However, as shocks move to large radii in galaxy clusters, the shock is moving down a steep density gradient that helps the shock to maintain its strength over a large distance. Observations and numerical simulations show that, beyond R500, gas density profiles are as steep as, or steeper than, ∼r−3, suggesting that there exists a ‘habitable zone’ for moderately strong shocks in cluster outskirts where the shock strength can be maintained or even amplified. A characteristic feature of runaway shocks is that the strong compression, relative to the initial state, is confined to a narrow region just behind the shock. Therefore, if such a shock runs over a region with a pre-existing population of relativistic particles, then the boost in radio emissivity, due to pure adiabatic compression, will also be confined to a narrow radial shell.

Automation of Reduction and Analysis of Chandra X-Ray Satellite Data for Studies of Clusters of Galaxies

In this work we developed a system to automate the processes of data reduction and analysis of galaxy clusters observed by Chandra X-ray satellite. This automation enables generation of temperature and gas density profiles from raw data of multiple observations, making data reduction and analysis easier and faster. The automation script uses a standard reducing data process from Chandra, extracts spectrum from data, and simultaneously fits the spectra of multiple observations while performing the deprojection process. We show some outputs of the reduction and analysis to demonstrate how the automation works.

Heating and ablation of high-Z cryogenic pellets in high temperature plasmas

A kinetic model is developed to determine the power deposition from energetic electrons into the neutral gas shield of an ablating high-Z pellet. For high-Z, the velocity distribution of the hot electrons is nearly isotropic, and we use this feature to develop solutions to the kinetic equation. In contrast to pre-existing models, we consider the effect of gyro-motion as well as elastic scattering of the hot electrons. Two limits are considered: when the gyro-frequency is much greater than the elastic collision frequency, the hot electrons diffuse longitudinally along the field lines as they slow down; but if the gyro-frequency is much less than the elastic collision frequency, the hot electrons diffuse radially. In both limits, it is possible to express the kinetic equation describing the hot electrons independently of the gas density profile, and therefore, the power deposition model is universal in this respect. The emphasis on elastic scattering yields an ablation rate which scales as Z−7/6 which is different than Z−2/3 shown in Sergeev et al (2006 Plasma Phys. Rep. 32 5). It is also shown that the sheath potential required to maintain ambipolarity in the cloud scales as Z−1/3. Fluid simulations yield ablation rates that scale with the four-thirds power of the pellet radius in agreement with [].

Cooling flow solutions for the circumgalactic medium

ABSTRACT In several models of galaxy formation feedback occurs in cycles or mainly at high redshift. At times and in regions where feedback heating is ineffective, hot gas in the galaxy halo is expected to form a cooling flow, where the gas advects inward on a cooling timescale. Cooling flow solutions can thus be used as a benchmark for observations and simulations to constrain the timing and extent of feedback heating. Using analytic calculations and idealized 3D hydrodynamic simulations, we show that for a given halo mass and cooling function, steady-state cooling flows form a single-parameter family of solutions, while initially hydrostatic gaseous haloes converge on one of these solutions within a cooling time. The solution is thus fully determined once either the mass inflow rate ${\dot{M}}$ or the total halo gas mass are known. In the Milky Way halo, a cooling flow with ${\dot{M}}$ equal to the star formation rate predicts a ratio of the cooling time to the free-fall time of ∼10, similar to some feedback-regulated models. This solution also correctly predicts observed $\rm{O\,{\small VII}}$ and $\rm{O\,{\small VIII}}$ absorption columns, and the gas density profile implied by $\rm{O\,{\small VII}}$ and $\rm{O\,{\small VIII}}$ emission. These results suggest ongoing heating by feedback may be negligible in the inner Milky-Way halo. Extending similar solutions out to the cooling radius however underpredicts observed $\rm{O\,{\small VI}}$ columns around the Milky-Way and around other low-redshift star-forming galaxies. This can be reconciled with the successes of the cooling flow model with either a mechanism which preferentially heats the $\rm{O\,{\small VI}}$-bearing outer halo, or alternatively if $\rm{O\,{\small VI}}$ traces cool photoionized gas beyond the accretion shock. We also demonstrate that the entropy profiles of some of the most relaxed clusters are reasonably well described by a cooling flow solution.

Polytropic state of the intracluster medium in the X-COP cluster sample

Aims. In this work, we have investigated the relation between the radially resolved thermodynamic quantities of the intracluster medium in the X-COP cluster sample, aiming to assess the stratification properties of the ICM. Methods. We modeled the relations between radius, gas temperature, density, and pressure using a combination of power-laws, also evaluating the intrinsic scatter in these relations. Results. We show that the gas pressure is remarkably well correlated to the density, with very small scatter. Also the temperature correlates with gas density with similar scatter. The slopes of these relations have values that show a clear transition from the inner cluster regions to the outskirts. This transition occurs at the radius rt = 0.19(±0.04) R500 and electron density nt = (1.91 ± 0.21) × 10−3 cm−3 E2(z). We find that above 0.2 R500 the radial thermodynamic profiles are accurately reproduced by a well defined and physically motivated framework, where the dark matter follows the NFW potential and the gas is represented by a polytropic equation of state. By modeling the gas temperature dependence upon both the gas density and radius, we propose a new method to reconstruct the hydrostatic mass profile based only on the relatively inexpensive measurement of the gas density profile.

Dust in and around galaxies: dust in cluster environments and its impact on gas cooling

Abstract Simulating the dust content of galaxies and their surrounding gas is challenging due to the wide range of physical processes affecting the dust evolution. Here we present cosmological hydrodynamical simulations of a cluster of galaxies, $M_\text{200,crit}=6 \times 10^{14}{\, \rm M_\odot }$, including a novel dust model for the moving mesh code arepo. This model includes dust production, growth, supernova-shock-driven destruction, ion-collision-driven thermal sputtering, and high-temperature dust cooling through far-infrared reradiation of collisionally deposited electron energies. Adopting a rather low thermal sputtering rate, we find, consistent with observations, a present-day overall dust-to-gas ratio of ∼2 × 10−5, a total dust mass of ${\sim } 2\times 10^9{\, \rm M_\odot }$, and a dust mass fraction of ∼3 × 10−6. The typical thermal sputtering time-scales within ${\sim } 100\, {\rm kpc}$ are around ${\sim } 10\, {\rm Myr}$, and increase towards the outer parts of the cluster to ${\sim } 10^3\, {\rm Myr}$ at a cluster-centric distance of $1\, {\rm Mpc}$. The condensation of gas-phase metals into dust grains reduces high-temperature metal-line cooling, but also leads to additional dust infrared cooling. The additional infrared cooling changes the overall cooling rate in the outer parts of the cluster, beyond ${\sim } 1\, {\rm Mpc}$, by factors of a few. This results in noticeable changes of the entropy, temperature, and density profiles of cluster gas once dust formation is included. The emitted dust infrared emission due to dust cooling is consistent with observational constraints.