J. Drake, C. Pfrommer, C. Reynolds, M. Ruszkowski, M. Swisdak, A. Einarsson, T. Thomas, A. Hassam, G. Roberg-Clark
{"title":"Whistler-regulated MHD: Transport equations for electron thermal conduction in the high $β$ intracluster medium of galaxy clusters","authors":"J. Drake, C. Pfrommer, C. Reynolds, M. Ruszkowski, M. Swisdak, A. Einarsson, T. Thomas, A. Hassam, G. Roberg-Clark","doi":"10.17863/CAM.74522","DOIUrl":"https://doi.org/10.17863/CAM.74522","url":null,"abstract":"Transport equations for electron thermal energy in the high $beta_e$ intracluster medium (ICM) are developed that include scattering from both classical collisions and self-generated whistler waves. The calculation employs an expansion of the kinetic electron equation along the ambient magnetic field in the limit of strong scattering and assumes whistler waves with low phase speeds $V_wsim{v}_{te}/beta_ell{v}_{te}$ dominate the turbulent spectrum, with $v_{te}$ the electron thermal speed and $beta_egg1$ the ratio of electron thermal to magnetic pressure. We find: (1) temperature-gradient-driven whistlers dominate classical scattering when $L_c>L/beta_e$, with $L_c$ the classical electron mean-free-path and $L$ the electron temperature scale length, and (2) in the whistler dominated regime the electron thermal flux is controlled by both advection at $V_w$ and a comparable diffusive term. The findings suggest whistlers limit electron heat flux over large regions of the ICM, including locations unstable to isobaric condensation. Consequences include: (1) the Field length decreases, extending the domain of thermal instability to smaller length-scales, (2) the heat flux temperature dependence changes from $T_e^{7/2}/L$ to $V_wnT_esim{T}_e^{1/2}$, (3) the magneto-thermal and heat-flux driven buoyancy instabilities are impaired or completely inhibited, and (4) sound waves in the ICM propagate greater distances, as inferred from observations. This description of thermal transport can be used in macroscale ICM models.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79018775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. Mountrichas, V. Buat, I. Georgantopoulos, G. Yang, V. Masoura, M. Boquien, D. Burgarella
{"title":"Galaxy properties of type 1 and 2 X-ray selected AGN and a comparison among different classification criteria","authors":"G. Mountrichas, V. Buat, I. Georgantopoulos, G. Yang, V. Masoura, M. Boquien, D. Burgarella","doi":"10.1051/0004-6361/202141273","DOIUrl":"https://doi.org/10.1051/0004-6361/202141273","url":null,"abstract":"We present analyses of host galaxy properties of type 1 and type 2 X-ray selected AGNs in the XMM-XXL field, which have available optical spectroscopic classification. We model their optical to far-infrared spectral energy distributions (SEDs) using the X-CIGALE code. X-CIGALE allows the fitting of X-ray flux and accounts for the viewing angle of dusty torus and the attenuation from polar dust. By selecting matched type 1 and 2 subsamples in the X-ray luminosity and redshift parameter space, we find that both types live in galaxies with similar star formation. However, type 2 AGN tend to reside in more massive systems ($10.87^{+0.06}_{-0.12},rm M_odot$) compared to their type 1 counterparts ($10.57^{+0.20}_{-0.12},rm M_odot$). In the second part of our analysis, we compare the spectroscopic classification with that from the SED fitting. X-CIGALE successfully identifies all spectroscopic type 2 sources either by estimating an inclination angle that corresponds to edge on viewing of the source or by measuring increased polar dust in these systems. $sim 85%$ of spectroscopic type 1 AGN are also identified as such, based on the SED fitting analysis. There is a small number of sources ($sim 15%$ of the sample), that present broad lines in their spectra, but show strong indications of obscuration, based on SED analysis. These, could be systems that are viewed face on and have an extended dust component along the polar direction. The performance of X-CIGALE in classifying AGN is similar at low and high redshifts, under the condition that there is sufficient photometric coverage. Finally, usage of optical/mid-IR colour criteria to identify optical red AGN (${it{u}}-rm W3$), suggests that these criteria are better suited for IR selected AGN and their efficiency drops for the low to moderate luminosity sources included in X-ray samples.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76935065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yao Wang, F. Du, D. Semenov, Hongchi Wang, Juan Li
{"title":"Chemical modeling of the complex organic molecules in the extended region around Sagittarius B2","authors":"Yao Wang, F. Du, D. Semenov, Hongchi Wang, Juan Li","doi":"10.1051/0004-6361/202140411","DOIUrl":"https://doi.org/10.1051/0004-6361/202140411","url":null,"abstract":"The chemical differentiation of seven COMs in the extended region around Sgr B2 has been observed: CH$_2$OHCHO, CH$_3$OCHO, t-HCOOH, C$_2$H$_5$OH, and CH$_3$NH$_2$ were detected both in the extended region and near the hot cores Sgr B2(N) and Sgr B2(M), while CH$_3$OCH$_3$ and C$_2$H$_5$CN were only detected near the hot cores. The density and temperature in the extended region are relatively low. Different desorption mechanisms have been proposed to explain the observed COMs in cold regions but fail to explain the deficiency of CH$_3$OCH$_3$ and C$_2$H$_5$CN. We explored under what physical conditions the chemical simulations can fit the observations and explain the different spatial distribution of these species. We used the Monte Carlo method to perform a detailed parameter space study. We investigated how different mechanisms affect the results. All gas-grain chemical models based on static physics cannot fit the observations. The results based on evolving physical conditions can fit six COMs when $Tsim30-60$ K, but the best-fit temperature is still higher than the observed dust temperature of 20 K. The best agreement at $Tsim27$ K is achieved by considering a short-duration $sim 10^2$ yr X-ray burst with $zeta_{mathrm{CR}}=1.3times10^{-13}$ s$^{-1}$ when the temperature is 20 K. The reactive desorption is the key mechanism for producing these COMs and inducing the low abundances of CH$_3$OCH$_3$ and C$_2$H$_5$CN. The evolution of the extended region around Sgr~B2 may have begun with a cold, $Tle10$ K phase followed by a warm-up phase. When its temperature reached $Tsim20$ K, an X-ray flare from Sgr A* with a short duration of no more than 100 years was acquired, affecting strongly the Sgr B2 chemistry. The observed COMs retain their observed abundances only several hundred years after such a flare, which could imply that such short-term X-ray flares occur relatively often.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80112028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Explaining the scatter in the galaxy mass–metallicity relation with gas flows","authors":"Maria L van Loon, P. Mitchell, J. Schaye","doi":"10.1093/mnras/stab1254","DOIUrl":"https://doi.org/10.1093/mnras/stab1254","url":null,"abstract":"The physical origin of the scatter in the relation between galaxy stellar mass and the metallicity of the interstellar medium, i.e. the Mass-Metallicity Relation (MZR), reflects the relative importance of key processes in galaxy evolution. The eagle cosmological hydrodynamical simulation is used to investigate the correlations between the residuals of the MZR and the residuals of the relations between stellar mass and, respectively, specific inflow, outflow and star formation rate as well as the gas fraction for central galaxies. At low redshift, all these residuals are found to be anti-correlated with the residuals of the MZR for $M_star/mathrm{M}_odot lesssim 10^{10}$. The correlations between the residuals of the MZR and the residuals of the other relations with mass are interrelated, but we find that gas fraction, specific inflow rate and specific outflow rate all have at least some independent influence on the scatter of the MZR. We find that, while for $M_star/mathrm{M}_odot > 10^{10.4}$ the specific mass of the nuclear black hole is most important, for $M_star/mathrm{M}_odot lesssim 10^{10.3}$ gas fraction and specific inflow rate are the variables that correlate most strongly with the MZR scatter. The timescales involved in the residual correlations and the time that galaxies stay above the MZR are revealed to be a few Gyr. However, most galaxies that are below the MZR at $z=0$ have been below the MZR throughout their lifetimes.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89626349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Roman-Duval, E. Jenkins, K. Tchernyshyov, B. Williams, C. Clark, K. Gordon, M. Meixner, L. Hagen, J. Peek, K. Sandstrom, J. Werk, Petia Yanchulova Merica-Jones
{"title":"METAL: The Metal Evolution, Transport, and Abundance in the Large Magellanic Cloud Hubble program. II. Variations of interstellar depletions and dust-to-gas ratio within the LMC.","authors":"J. Roman-Duval, E. Jenkins, K. Tchernyshyov, B. Williams, C. Clark, K. Gordon, M. Meixner, L. Hagen, J. Peek, K. Sandstrom, J. Werk, Petia Yanchulova Merica-Jones","doi":"10.17909/t9-g6d9-rj76","DOIUrl":"https://doi.org/10.17909/t9-g6d9-rj76","url":null,"abstract":"A key component of the baryon cycle in galaxies is the depletion of metals from the gas to the dust phase in the neutral ISM. The METAL (Metal Evolution, Transport and Abundance in the Large Magellanic Cloud) program on the Hubble Space Telescope acquired UV spectra toward 32 sightlines in the half-solar metallicity LMC, from which we derive interstellar depletions (gas-phase fractions) of Mg, Si, Fe, Ni, S, Zn, Cr, and Cu. The depletions of different elements are tightly correlated, indicating a common origin. Hydrogen column density is the main driver for depletion variations. Correlations are weaker with volume density, probed by CI fine structure lines, and distance to the LMC center. The latter correlation results from an East-West variation of the gas-phase metallicity. Gas in the East, compressed side of the LMC encompassing 30 Doradus and the Southeast HI over-density is enriched by up to +0.3dex, while gas in the West side is metal-deficient by up to -0.5dex. Within the parameter space probed by METAL, no correlation with molecular fraction or radiation field intensity are found. We confirm the factor 3-4 increase in dust-to-metal and dust-to-gas ratios between the diffuse (logN(H)~20 cm-2) and molecular (logN(H)~22 cm-2) ISM observed from far-infrared, 21 cm, and CO observations. The variations of dust-to-metal and dust-to-gas ratios with column density have important implications for the sub-grid physics of chemical evolution, gas and dust mass estimates throughout cosmic times, and for the chemical enrichment of the Universe measured via spectroscopy of damped Lyman-alpha systems.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75535741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jae Yeon Mun, H. Hwang, M. Lee, A. Chung, H. Yoon, Jong Chul Lee
{"title":"Star Formation Activity of Galaxies Undergoing Ram Pressure Stripping in the Virgo Cluster.","authors":"Jae Yeon Mun, H. Hwang, M. Lee, A. Chung, H. Yoon, Jong Chul Lee","doi":"10.5303/JKAS.2021.54.1.17","DOIUrl":"https://doi.org/10.5303/JKAS.2021.54.1.17","url":null,"abstract":"We study galaxies undergoing ram pressure stripping in the Virgo cluster to examine whether we can identify any discernible trend in their star formation activity. We first use 48 galaxies undergoing different stages of stripping based on HI morphology, HI deficiency, and relative extent to the stellar disk, from the VIVA survey. We then employ a new scheme for galaxy classification which combines HI mass fractions and locations in projected phase space, resulting in a new sample of 365 galaxies. We utilize a variety of star formation tracers, which include g - r, WISE [3.4] - [12] colors, and starburstiness that are defined by stellar mass and star formation rates to compare the star formation activity of galaxies at different stripping stages. We find no clear evidence for enhancement in the integrated star formation activity of galaxies undergoing early to active stripping. We are instead able to capture the overall quenching of star formation activity with increasing degree of ram pressure stripping, in agreement with previous studies. Our results suggest that if there is any ram pressure stripping induced enhancement, it is at best locally modest, and galaxies undergoing enhancement make up a small fraction of the total sample. Our results also indicate that it is possible to trace galaxies at different stages of stripping with the combination of HI gas content and location in projected phase space, which can be extended to other galaxy clusters that lack high-resolution HI imaging.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86117438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Sp'erone-Longin, P. Jablonka, F. Combes, G. Castignani, M. Krips, G. Rudnick, D. Zaritsky, R. Finn, G. Lucia, V. Desai
{"title":"SEEDisCS I. Molecular gas in galaxy clusters and their large scale structure: the case of CL1411.1$-$1148 at $zsim0.5$","authors":"D. Sp'erone-Longin, P. Jablonka, F. Combes, G. Castignani, M. Krips, G. Rudnick, D. Zaritsky, R. Finn, G. Lucia, V. Desai","doi":"10.1051/0004-6361/202038904","DOIUrl":"https://doi.org/10.1051/0004-6361/202038904","url":null,"abstract":"We investigate how the galaxy reservoirs of molecular gas fuelling star formation are transformed while the host galaxies infall onto galaxy cluster cores. As part of the Spatially Extended ESO Distant Cluster Survey (SEEDisCS), we present CO(3-2) observations of 27 star-forming galaxies obtained with the Atacama Large Millimeter Array (ALMA). These sources are located inside and around CL1411.1$-$1148 at $z=0.5195$, within five times the cluster virial radius. These targets were selected to have stellar masses M$_{rm star}$), colours, and magnitudes similar to those of a field comparison sample at similar redshift drawn from the Plateau de Bure high-$z$ Blue Sequence Survey (PHIBSS2). We compare the cold gas fraction ($mu_{rm H_2}=$ M$_{rm H_2}$/M$_{rm star}$), specific star formation rates (SFR/M$_{rm star}$) and depletion timescales ($t_{rm depl}=$ M$_{rm H_2}$/SFR) of our main-sequence galaxies to the PHIBSS2 subsample. While the most of our galaxies (63%) are consistent with PHIBSS2, the remainder fall below the relation between $mu_mathrm{H_2}$ and M$_{rm star}$ of the PHIBSS2 galaxies at $zsim0.5$. These low-$mu_mathrm{H_2}$ galaxies are not compatible with the tail of a Gaussian distribution, hence they correspond to a new population of galaxies with normal SFRs but low gas content and low depletion times ($lesssim 1$ Gyr), absent from previous surveys. We suggest that the star formation activity of these galaxies has not yet been diminished by their low fraction of cold molecular gas.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77572937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T. Ruiz-Lara, C. Gallart, M. Monelli, T. Fritz, G. Battaglia, S. Cassisi, M. L. Aznar, A. V. R. Cabrera, I. Rodr'iguez-Mart'in, Juan José SALAZAR-GONZÁLEZ
{"title":"Dissecting the stellar content of Leo I: a dwarf irregular caught in transition","authors":"T. Ruiz-Lara, C. Gallart, M. Monelli, T. Fritz, G. Battaglia, S. Cassisi, M. L. Aznar, A. V. R. Cabrera, I. Rodr'iguez-Mart'in, Juan José SALAZAR-GONZÁLEZ","doi":"10.1093/mnras/staa3871","DOIUrl":"https://doi.org/10.1093/mnras/staa3871","url":null,"abstract":"Leo I is considered one of the youngest dwarf spheroidals (dSph) in the Local Group. Its isolation, extended star formation history (SFH), and recent perigalacticon passage (~1 Gyr ago) make Leo~I one of the most interesting nearby stellar systems. Here, we analyse deep photometric Hubble Space Telescope data via colour-magnitude diagram fitting techniques to study its global and radially-resolved SFH. We find global star formation enhancements in Leo I ~13, 5.5, 2.0, and 1.0 Gyr ago, after which it was substantially quenched. Within the context of previous works focused on Leo I, we interpret the most ancient and the youngest ones as being linked to an early formation (surviving reionisation) and the latest perigalacticon passage (transition from dIrr to dSph), respectively. We clearly identify the presence of very metal poor stars ([Fe/H]~-2) ageing ~5-6 and ~13 Gyr old. We speculate with the possibility that this metal-poor population in Leo I is related to the merging with a low mass system (possibly an ultra-faint dwarf). This event would have triggered star formation (peak of star formation ~5.5 Gyr ago) and accumulated old, metal poor stars from the accreted system in LeoI. Some of the stars born during this event would also form from accreted gas of low-metallicity (giving rise to the 5-6 Gyr low-metallicity tail). Given the intensity and extension of the 2.0 Gyr burst, we hypothesise that this enhancement could also have an external origin. Despite the quenching of star formation around 1 Gyr ago (most probably induced by ram pressure stripping with the Milky Way halo at pericentre), we report the existence of stars as young as 300-500 Myr. We also distinguish two clear spatial regions: the inner ~190 pc presents an homogeneous stellar content (size of the gaseous star forming disc in LeoI from ~4.5 to 1 Gyr ago), whereas the outer regions display a clear positive age gradient.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85212872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spatially resolved properties of galaxies with a kinematically distinct core","authors":"K. Omori, T. Takeuchi","doi":"10.1051/0004-6361/202038244","DOIUrl":"https://doi.org/10.1051/0004-6361/202038244","url":null,"abstract":"Aims. Interacting galaxies show unique irregularities in their kinematic structure. By investigating the spatially resolved kinematics and stellar population properties of galaxies that show irregularities, we can paint a detailed picture of the formation and evolutionary processes that took place during its lifetimes. Methods. In this work, we focus on galaxies with a specific kinematic irregularity, a kinematically distinct stellar core (KDC), in particular, counter-rotating galaxies where the core and main body of the galaxy are rotating in opposite directions. We visually identify eleven MaNGA galaxies with a KDC from their stellar kinematics, and investigate their spatially resolved stellar and gaseous kinematic properties, namely the two-dimensional stellar and gaseous velocity and velocity dispersion ({sigma}) maps. Additionally, we examine the stellar population properties, as well as spatially resolved recent star formation histories using the Dn4000 and H{delta} gradients. Results. The galaxies display multiple off-centred, symmetrical peaks in the stellar {sigma} maps. The gaseous velocity and {sigma} maps display regular properties. The stellar population properties and their respective gradients show differing properties depending on the results of the spatially resolved emission line diagnostics of the galaxies, with some galaxies showing inside-out quenching but others not. The star formation histories also largely differ based on the spatially resolved emission line diagnostics, but most galaxies show indications of recent star formation either in their outskirts or core. Conclusions. We find a distinct difference in kinematic and stellar population properties in galaxies with a counter-rotating stellar core, depending on its classification using spatially resolved emission line diagnostics.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76492722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Density profile of a self-gravitating polytropic turbulent fluid in the context of ensembles of molecular clouds","authors":"S. Donkov, I. Stefanov, T. Veltchev, R. Klessen","doi":"10.1093/mnras/stab1572","DOIUrl":"https://doi.org/10.1093/mnras/stab1572","url":null,"abstract":"We obtain an equation for the density profile in a self-gravitating polytropic spherically symmetric turbulent fluid with an equation of state $p_{rm gas}propto rho^Gamma$. This is done in the framework of ensembles of molecular clouds represented by single abstract objects as introduced by Donkov et al. (2017). The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state changes from isothermal (in the outer cloud layers) with $Gamma=1$ to one of `hard polytrope' with exponent $Gamma>1$. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation reproduces the Bernoulli equation for the proposed model and describes the balance of the kinetic, thermal and gravitational energy of a fluid element. We propose as well a method to obtain approximate solutions in a power-law form which yields four solutions corresponding to different density profiles, polytropic exponents and energy balance equations for a fluid element. Only one of them, a density profile with slope $-3$ and polytropic exponent $Gamma=4/3$, matches with observations and numerical works. In particular, it yields a second power-law tail of the density distribution function in dense cloud regions.","PeriodicalId":8452,"journal":{"name":"arXiv: Astrophysics of Galaxies","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91139374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}