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Register a new userStellar mass spectrum within massive collapsing clumps III. Effects of temperature and magnetic field
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The stellar mass spectrum is an important property of the stellar cluster and a fundamental quantity to understand our Universe. The fragmentation of diffuse molecular cloud into stars is subject to physical processes such as gravity, turbulence, thermal pressure, and magnetic field. The final mass of a star is believed to be a combined outcome of a virially unstable reservoir and subsequent accretion. We aim to clarify the roles of different supporting energies, notably the thermal pressure and the magnetic field, in determining the stellar mass. Following previous studies by Lee & Hennebelle (2018a,b), we perform a series of numerical experiments of stellar cluster formation inside an isolated molecular clump. By changing the effective equation of state (EOS) of the diffuse gas (that is to say gas whose density is below the critical density at which dust becomes opaque to its radiation) and the strength of the magnetic field, we investigate whether any characteristic mass is introduced into the fragmentation processes. The EOS of the diffuse gas, including the bulk temperature and the polytropic index, does not affect significantly the shape of the stellar mass spectrum. The presence of magnetic field slightly modifies the shape of the mass spectrum only when extreme values are applied. This study confirms that the peak of the IMF is primarily determined by the adiabatic high-density end of the EOS that mimics the radiation inside the high-density gas. Furthermore, the shape of the mass spectrum is mostly sensitive to the density PDF, and the magnetic field has likely only a secondary role. In particular, we stress that the Jeans mass at the mean cloud density and at the critical density are not responsible of setting the peak.
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We investigate the dependence of the peak of the IMF on the physics of the so-called first Larson core, which corresponds to the point where the dust becomes opaque to its own radiation. We perform numerical simulations of collapsing clouds of $1000 M_odot$ for various gas equation of state (eos), paying great attention to the numerical resolution and convergence. The initial conditions of these numerical experiments are varied in the companion paper. We also develop analytical models that we confront to our numerical results. If an isothermal eos is used, we show that the peak of the IMF shifts to lower masses with improved numerical resolution. When an adiabatic eos is employed, numerical convergence is obtained. The peak position varies with the eos and we find that the peak position is about ten times the mass of the first Larson core. By analyzing the stability of non-linear density fluctuations in the vicinity of a point mass and then summing over a reasonable density distribution, we find that tidal forces exert a strong stabilizing effect and likely lead to a preferential mass several times larger than that of the first Larson core. We propose that in a sufficiently massive and cold cloud, the peak of the IMF is determined by the thermodynamics of the high density adiabatic gas as well as the stabilizing influence of tidal forces. The resulting characteristic mass is about ten times the mass of the first Larson core, which altogether leads to a few tenths of solar masses. Since these processes are not related to the large scale physical conditions and to the environment, our results suggest a possible explanation for the apparent universality of the peak of the IMF.
The connection between the pre-stellar core mass function (CMF) and the stellar initial mass function (IMF) lies at the heart of all star formation theories. In this paper, we study the earliest phases of star formation with a series of high-resolution numerical simulations that include the formation of sinks. In particular, we focus on the transition from cores to sinks within a massive molecular filament. We compare the CMF and IMF between magnetized and unmagnetized simulations, and between different resolutions. We find that selecting cores based on their kinematic virial parameter excludes collapsing objects because they host large velocity dispersions. Selecting only the thermally unstable magnetized cores, we observe that their mass-to-flux ratio spans almost two orders of magnitude for a given mass. We also see that, when magnetic fields are included, the CMF peaks at higher core mass values with respect to pure hydrodynamical simulations. Nonetheless, all models produce sink mass functions with a high-mass slope consistent with Salpeter. Finally, we examine the effects of resolution and find that, in isothermal simulations, even models with very high dynamical range fail to converge in the mass function. Our main conclusion is that, although the resulting CMFs and IMFs have similar slopes in all simulations, the cores have slightly different sizes and kinematical properties when a magnetic field is included. However, a core selection based on the mass-to-flux ratio alone is not enough to alter the shape of the CMF, if we do not take thermal stability into account. Finally, we conclude that extreme care should be given to resolution issues when studying sink formation with an isothermal equation of state.
We mapped the kinetic temperature structure of the Orion molecular cloud 1 with para-H2CO(303-202, 322-221, and 321-220) using the APEX 12m telescope. This is compared with the temperatures derived from the ratio of the NH3(2,2)/(1,1) inversion lines and the dust emission. Using the RADEX non-LTE model, we derive the gas kinetic temperature modeling the measured averaged line ratios of para-H2CO 322-221/303-202 and 321-220/303-202. The gas kinetic temperatures derived from the para-H2CO line ratios are warm, ranging from 30 to >200 K with an average of 62 K at a spatial density of 10$^5$ cm$^{-3}$. These temperatures are higher than those obtained from NH3(2,2)/(1,1) and CH3CCH(6-5) in the OMC-1 region. The gas kinetic temperatures derived from para-H2CO agree with those obtained from warm dust components measured in the mid infrared (MIR), which indicates that the para-H2CO(3-2) ratios trace dense and warm gas. The cold dust components measured in the far infrared (FIR) are consistent with those measured with NH3(2,2)/(1,1) and the CH3CCH(6-5) line series. With dust at MIR wavelengths and para-H2CO(3-2) on one side and dust at FIR wavelengths, NH3(2,2)/(1,1), and CH3CCH(6-5) on the other, dust and gas temperatures appear to be equivalent in the dense gas of the OMC-1 region, but provide a bimodal distribution, one more directly related to star formation than the other. The non-thermal velocity dispersions of para-H2CO are positively correlated with the gas kinetic temperatures in regions of strong non-thermal motion (Mach number >2.5) of the OMC-1, implying that the higher temperature traced by para-H2CO is related to turbulence on a 0.06 pc scale. Combining the temperature measurements with para-H2CO and NH3(2,2)/(1,1) line ratios, we find direct evidence for the dense gas along the northern part of the OMC-1 10 km s$^{-1}$ filament heated by radiation from the central Orion nebula.
For a general understanding of the physics involved in the star formation process, measurements of physical parameters such as temperature and density are indispensable. The chemical and physical properties of dense clumps of molecular clouds are strongly affected by the kinetic temperature. Therefore, this parameter is essential for a better understanding of the interstellar medium. Formaldehyde, a molecule which traces the entire dense molecular gas, appears to be the most reliable tracer to directly measure the gas kinetic temperature.We aim to determine the kinetic temperature with spectral lines from formaldehyde and to compare the results with those obtained from ammonia lines for a large number of massive clumps.Three 218 GHz transitions (JKAKC=303-202, 322-221, and 321-220) of para-H2CO were observed with the 15m James Clerk Maxwell Telescope (JCMT) toward 30 massive clumps of the Galactic disk at various stages of high-mass star formation. Using the RADEX non-LTE model, we derive the gas kinetic temperature modeling the measured para-H2CO 322-221/303-202and 321-220/303-202 ratios. The gas kinetic temperatures derived from the para-H2CO (321-220/303-202) line ratios range from 30 to 61 K with an average of 46 K. A comparison of kinetic temperature derived from para-H2CO, NH3, and the dust emission indicates that in many cases para-H2CO traces a similar kinetic temperature to the NH3 (2,2)/(1,1) transitions and the dust associated with the HII regions. Distinctly higher temperatures are probed by para-H2CO in the clumps associated with outflows/shocks. Kinetic temperatures obtained from para-H2CO trace turbulence to a higher degree than NH3 (2,2)/(1,1) in the massive clumps. The non-thermal velocity dispersions of para-H2CO lines are positively correlated with the gas kinetic temperature. The massive clumps are significantly influenced by supersonic non-thermal motions.
(Abridged) Aims: We aim to use the progressive heating of the gas caused by the feedback of high-mass young stellar objects (YSOs) to prove the statistical validity of the most common schemes used to define an evolutionary sequence for high-mass clumps, and characterise the sensitivity of different tracers to this process. Methods: From the spectroscopic follow-ups of the ATLASGAL TOP100 sample, we selected several multiplets of CH3CN, CH3CCH, and CH3OH emission lines to derive and compare the physical properties of the gas in the clumps along the evolutionary sequence. Our findings are compared with results obtained from CO isotopologues, dust, and NH3 from previous studies on the same sample. Results: The chemical properties of each species have a major role on the measured physical properties. Low temperatures are traced by NH3, CH3OH, and CO (in the early phases), the warm and dense envelope can be probed with CH3CN, CH3CCH, and, in evolved sources via CO isotopologues. CH3OH and CH3CN are also abundant in the hot cores, and their high-excitation transitions may be good tools to study the kinematics in the hot gas surrounding the YSOs that these clumps are hosting. All tracers show, to different degrees, progressive warming with evolution. The relation between gas temperature and L/M is reproduced by a toy model of a spherical, internally heated clump. Conclusions: The evolutionary sequence defined for the clumps is statistically valid and we could identify the processes dominating in different intervals of L/M. For L/M<2Lsun/Msun a large quantity of gas is still being accumulated and compressed at the bottom of the potential well. Between 2Lsun/Msun<L/M<40Lsun/Msun the YSOs gain mass and increase in L; the first hot cores appear around L/M=10Lsun/Msun. Finally, for L/M>40Lsun/Msun HII regions become common, showing that dissipation of the parental clump dominates.
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