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Register a new userRadiation Transfer of Models of Massive Star Formation. III. The Evolutionary Sequence
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Yichen Zhang
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We present radiation transfer (RT) simulations of evolutionary sequences of massive protostars forming from massive dense cores in environments of high surface densities. The protostellar evolution is calculated with a detailed multi-zone model, with the accretion rate regulated by feedback from an evolving disk-wind outflow cavity. Disk and envelope evolutions are calculated self-consistently. In this framework, an evolutionary track is determined by three environmental initial conditions: the initial core mass M_c, the mean surface density of the ambient star-forming clump Sigma_cl, and the rotational-to-gravitational energy ratio of the initial core, beta_c. Evolutionary sequences with various M_c, Sigma_cl, beta_c are constructed. We find that in a fiducial model with M_c=60Msun, Sigma_cl=1 g/cm^2 and beta_c=0.02, the final star formation efficiency >~0.43. For each evolutionary track, RT simulations are performed at selected stages, with temperature profiles, SEDs, and images produced. At a given stage the envelope temperature is highly dependent on Sigma_cl, but only weakly dependent on M_c. The SED and MIR images depend sensitively on the evolving outflow cavity, which gradually wides as the protostar grows. The fluxes at <~100 microns increase dramatically, and the far-IR peaks move to shorter wavelengths. We find that, despite scatter caused by different M_c, Sigma_cl, beta, and inclinations, sources at a given evolutionary stage appear in similar regions on color-color diagrams, especially when using colors at >~ 70 microns, where the scatter due to the inclination is minimized, implying that such diagrams can be useful diagnostic tools of evolutionary stages of massive protostars. We discuss how intensity profiles along or perpendicular to the outflow axis are affected by environmental conditions and source evolution.
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We present a continuum radiative transfer model grid for fitting observed spectral energy distributions (SEDs) of massive protostars. The model grid is based on the paradigm of core accretion theory for massive star formation with pre-assembled gravitationally-bound cores as initial conditions. In particular, following the Turbulent Core Model, initial core properties are set primarily by their mass and the pressure of their ambient clump. We then model the evolution of the protostar and its surround structures in a self-consistent way. The model grid contains about 9000 SEDs with 4 free parameters: initial core mass, the mean surface density of the environment, the protostellar mass, and the inclination. The model grid is used to fit observed SEDs via chi^2 minimization, with the foreground extinction additionally estimated. We demonstrate the fitting process and results using the example of massive protostar G35.20- 0.74. Compared with other SED model grids currently used for massive star formation studies, in our model grid, the properties of the protostar and its surrounding structures are more physically connected, which reduces the dimensionality of the parameter spaces and the total number of models. This excludes possible fitting of models that are physically unrealistic or that are not internally self-consistent in the context of the Turbulent Core Model. Thus, this model grid serves not only as a fitting tool to estimate properties of massive protostars, but also as a test of core accretion theory. The SED model grid is publicly released with this paper.
(Abridged) Understanding the details of the formation process of massive (i.e. M<8-10M$_odot$) stars is a long-standing problem in astrophysics. [...] We present a method to derive accurate timescales of the different evolutionary phases of the high-mass star formation process. We model a representative number of massive clumps of the ATLASGAL-TOP100 sample which cover all the evolutionary stages. The models describe an isothermal collapse and the subsequent warm-up phase, for which we follow their chemical evolution. The timescale of each phase is derived by comparing the results of the models with the properties of the sources of the ATLASGAL-TOP100 sample, taking into account the mass and luminosity of the clumps, and the column densities of methyl acetylene (CH$_3$CCH), acetonitrile (CH$_3$CN), formaldehyde (H$_2$CO) and methanol (CH$_3$OH). We find that the chosen molecular tracers are affected by the thermal evolution of the clumps, showing steep ice evaporation gradients from 10$^3$ to 10$^5$ AU during the warm-up phase. We succeed in reproducing the observed column densities of CH$_3$CCH and CH$_3$CN, while H$_2$CO and CH$_3$OH show a poorer agreement with the observed values. The total (massive) star formation time is found to be $sim5.2times10^5$ yr, which is defined by the timescales of the individual evolutionary phases of the ATLASGAL-TOP100 sample: $sim5times10^4$ yr for 70-$mu$m weak, $sim1.2times10^5$ yr for mid-IR weak, $sim2.4times10^5$ yr for mid-IR bright and $sim1.1times10^5$ yr for HII-regions phases. Our models, with an appropriate selection of molecular tracers that can act as chemical clocks, allow to get robust estimates of the duration of the individual phases of the high-mass star formation process, with the advantage of being capable to include additional tracers aimed at increasing the accuracy of the estimated timescales.
Stars mostly form in groups consisting of a few dozen to several ten thousand members. For 30 years, theoretical models provide a basic concept of how such star clusters form and develop: they originate from the gas and dust of collapsing molecular clouds. The conversion from gas to stars being incomplete, the left over gas is expelled, leading to cluster expansion and stars becoming unbound. Observationally, a direct confirmation of this process has proved elusive, which is attributed to the diversity of the properties of forming clusters. Here we take into account that the true cluster masses and sizes are masked, initially by the surface density of the background and later by the still present unbound stars. Based on the recent observational finding that in a given star-forming region the star formation efficiency depends on the local density of the gas, we use an analytical approach combined with mbox{N-body simulations, to reveal} evolutionary tracks for young massive clusters covering the first 10 Myr. Just like the Hertzsprung-Russell diagram is a measure for the evolution of stars, these tracks provide equivalent information for clusters. Like stars, massive clusters form and develop faster than their lower-mass counterparts, explaining why so few massive cluster progenitors are found.
The evolutionary classification of massive clumps that are candidate progenitors of high-mass young stars and clusters relies on a variety of independent diagnostics based on observables from the near-infrared to the radio. A promising evolutionary indicator for massive and dense cluster-progenitor clumps is the L/M ratio between the bolometric luminosity and the mass of the clumps. With the aim of providing a quantitative calibration for this indicator we used SEPIA/APEX to obtain CH3C2H(12-11) observations, that is an excellent thermometer molecule probing densities > 10^5 cm^-3 , toward 51 dense clumps with M>1000 solar masses, and uniformly spanning -2 < Log(L/M) < 2.3. We identify three distinct ranges of L/M that can be associated to three distinct phases of star formation in massive clumps. For L/M <1 no clump is detected in CH3C2H , suggesting an inner envelope temperature below 30K. For 1< L/M < 10 we detect 58% of the clumps, with a temperature between 30 and 35 K independently from the exact value of L/M; such clumps are building up luminosity due to the formation of stars, but no star is yet able to significantly heat the inner clump regions. For L/M> 10 we detect all the clumps, with a gas temperature rising with Log(L/M), marking the appearance of a qualitatively different heating source within the clumps; such values are found towards clumps with UCHII counterparts, suggesting that the quantitative difference in T - L/M behaviour above L/M >10 is due to the first appearance of ZAMS stars in the clumps.
We present $sim10-40,mu$m SOFIA-FORCAST images of 14 intermediate-mass protostar candidates as part of the SOFIA Massive (SOMA) Star Formation Survey. We build spectral energy distributions (SEDs), also utilizing archival Spitzer, Herschel and IRAS data. We then fit the SEDs with radiative transfer (RT) models of Zhang & Tan (2018), based on Turbulent Core Accretion theory, to estimate key protostellar properties. With the addition of these intermediate-mass sources, SOMA protostars span luminosities from $sim10^{2}-10^{6}:L_{odot}$, current protostellar masses from $sim0.5-30:M_{odot}$ and ambient clump mass surface densities, $Sigma_{rm cl}$ from $0.1-3:{rm{g:cm}^{-2}}$. A wide range of evolutionary states of the individual protostars and of the protocluster environments are also probed. We have also considered about 50 protostars identified in Infrared Dark Clouds and expected to be at the earliest stages of their evolution. With this global sample, most of the evolutionary stages of high- and intermediate-mass protostars are probed. From the best fitting models, there is no evidence of a threshold value of protocluster clump mass surface density being needed to form protostars up to $sim25:M_odot$. However, to form more massive protostars, there is tentative evidence that $Sigma_{rm{cl}}$ needs to be $gtrsim1:{rm{g,cm}}^{-2}$. We discuss how this is consistent with expectations from core accretion models that include internal feedback from the forming massive star.
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