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Register a new userSimulating radiative feedback and star cluster formation in GMCs: I. Dependence on gravitational boundedness
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Radiative feedback is an important consequence of cluster formation in Giant Molecular Clouds (GMCs) in which newly formed clusters heat and ionize their surrounding gas. The process of cluster formation, and the role of radiative feedback, has not been fully explored in different GMC environments. We present a suite of simulations which explore how the initial gravitational boundedness, and radiative feedback, affect cluster formation. We model the early evolution ($<$ 5 Myr) of turbulent, 10$^6$ M$_{odot}$ clouds with virial parameters ranging from 0.5 to 5. To model cluster formation, we use cluster sink particles, coupled to a raytracing scheme, and a custom subgrid model which populates a cluster via sampling an IMF with an efficiency of 20% per freefall time. We find that radiative feedback only decreases the cluster particle formation efficiency by a few percent. The initial virial parameter plays a much stronger role in limiting cluster formation, with a spread of cluster formation efficiencies of 37% to 71% for the most unbound to the most bound model. The total number of clusters increases while the maximum mass cluster decreases with an increasing initial virial parameter, resulting in steeper mass distributions. The star formation rates in our cluster particles are initially consistent with observations but rise to higher values at late times. This suggests that radiative feedback alone is not responsible for dispersing a GMC over the first 5 Myr of cluster formation.
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The process of radiative feedback in Giant Molecular Clouds (GMCs) is an important mechanism for limiting star cluster formation through the heating and ionization of the surrounding gas. We explore the degree to which radiative feedback affects early ($lesssim$5 Myr) cluster formation in GMCs having masses that range from 10$^{4-6}$ M$_{odot}$ using the FLASH code. The inclusion of radiative feedback lowers the efficiency of cluster formation by 20-50% relative to hydrodynamic simulations. Two models in particular --- 5$times$10$^4$ and 10$^5$ M$_{odot}$ --- show the largest suppression of the cluster formation efficiency, corresponding to a factor of $sim$2. For these clouds only, the internal energy, a measure of the energy injected by radiative feedback, exceeds the gravitational potential for a significant amount of time. We find a clear relation between the maximum cluster mass, M$_{cl,max}$, formed in a GMC of mass M$_{GMC}$; M$_{cl,max}propto$ M$_{GMC}^{0.81}$. This scaling result suggests that young globular clusters at the necessary scale of $10^6 M_{odot}$ form within host GMCs of masses near $sim 5 times 10^7 M_{odot}$. We compare simulated cluster mass distributions to the observed embedded cluster mass function ($dlog(N)/dlog(M) propto M^{beta}$ where $beta$ = -1) and find good agreement ($beta$ = -0.99$pm$0.14) only for simulations including radiative feedback, indicating this process is important in controlling the growth of young clusters. However, the high star formation efficiencies, which range from 16-21%, and high star formation rates compared to locally observed regions suggest other feedback mechanisms are also important during the formation and growth of stellar clusters.
We study star cluster formation in various environments with different metallicities and column densities by performing a suite of three-dimensional radiation hydrodynamics simulations. We find that the photoionization feedback from massive stars controls the star formation efficiency (SFE) in a star-forming cloud, and its impact sensitively depends on the gas metallicity $Z$ and initial cloud surface density $Sigma$. At $Z=1~Z_{odot}$, SFE increases as a power law from 0.03 at $Sigma = 10~M_{odot}{rm pc^{-2}}$ to 0.3 at $Sigma = 300~M_{odot}{rm pc^{-2}}$. In low-metallicity cases $10^{-2}- 10^{-1} Z_{odot}$, star clusters form from atomic warm gases because the molecule formation time is not short enough with respect to the cooling or dynamical time. In addition, the whole cloud is disrupted more easily by expanding H{sc ii} bubbles which have higher temperature owing to less efficient cooling. With smaller dust attenuation, the ionizing radiation feedback from nearby massive stars is stronger and terminate star formation in dense clumps. These effects result in inefficient star formation in low-metallicity environments: the SFE drops by a factor of $sim 3$ at $Z=10^{-2}~Z_{odot}$ compared to the results for $Z=1~Z_{odot}$, regardless of $Sigma$. Newborn star clusters are also gravitationally less bound. We further develop a new semi-analytical model that can reproduce the simulation results well, particularly the observed dependencies of the SFEs on the cloud surface densities and metallicities.
Molecular clouds are supported by turbulence and magnetic fields, but quantifying their influence on cloud lifecycle and star formation efficiency (SFE) remains an open question. We perform radiation MHD simulations of star-forming giant molecular clouds (GMCs) with UV radiation feedback, in which the propagation of UV radiation via ray-tracing is coupled to hydrogen photochemistry. We consider 10 GMC models that vary in either initial virial parameter ($1lealpha_{v,0}le 5$) or dimensionless mass-to-magnetic flux ratio (0.5-8 and $infty$); the initial mass $10^5M_{odot}$ and radius 20pc are fixed. Each model is run with five different initial turbulence realizations. In most models, the duration of star formation and the timescale for molecular gas removal (primarily by photoevaporation) are 4-8Myr. Both the final SFE ($epsilon_*$) and time-averaged SFE per freefall time ($epsilon_{ff}$) are reduced by strong turbulence and magnetic fields. The median $epsilon_*$ ranges between 2.1% and 9.5%. The median $epsilon_{ff}$ ranges between 1.0% and 8.0% and anticorrelates with $alpha_{v,0}$, in qualitative agreement with previous analytic theory and simulations. However, the time-dependent $alpha_{v}(t)$ and $epsilon_{ff,obs}(t)$ based on instantaneous gas properties and cluster luminosity are positively correlated due to rapid evolution, making observational validation of star formation theory difficult. Our median $epsilon_{ff,obs}(t)approx$ 2% is similar to observed values. We show that the traditional virial parameter estimates the true gravitational boundedness within a factor of 2 on average, but neglect of magnetic support and velocity anisotropy can sometimes produce large departures. Magnetically subcritical GMCs are unlikely to represent sites of massive star formation given their unrealistic columnar outflows, prolonged lifetime, and low escape fraction of radiation.
Feedback from photoionisation may dominate on parsec scales in massive star-forming regions. Such feedback may inhibit or enhance the star formation efficiency and sustain or even drive turbulence in the parent molecular cloud. Photoionisation feedback may also provide a mechanism for the rapid expulsion of gas from young clusters potentials, often invoked as the main cause of infant mortality. There is currently no agreement, however, with regards to the efficiency of this process and how environment may affect the direction (positive or negative) in which it proceeds. The study of the photoionisation process as part of hydrodynamical simulations is key to understanding these issues, however, due to the computational demand of the problem, crude approximations for the radiation transfer are often employed. We will briefly review some of the most commonly used approximations and discuss their major drawbacks. We will then present the results of detailed tests carried out using the detailed photoionisation code MOCASSIN and the SPH+ionisation code iVINE code, aimed at understanding the error introduced by the simplified photoionisation algorithms. This is particularly relevant as a number of new codes have recently been developed along those lines. We will finally propose a new approach that should allow to efficiently and self-consistently treat the photoionisation problem for complex radiation and density fields.
It is speculated that the accretion of material onto young protostars is episodic. We present a computational method to include the effects of episodic accretion in radiation hydrodynamic simulations of star formation. We find that during accretion events protostars are switched on, heating and stabilising the discs around them. However, these events typically last only a few hundred years, whereas the intervals in between them may last for a few thousand years. During these intervals the protostars are effectively switched off, allowing gravitational instabilities to develop in their discs and induce fragmentation. Thus, episodic accretion promotes disc frag- mentation, enabling the formation of low-mass stars, brown dwarfs and planetary-mass objects. The frequency and the duration of episodic accretion events may be responsible for the low-mass end of the IMF, i.e. for more than 60% of all stars.
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