ABSTRACT
We present radiation-magneto-hydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds, modelling the formation of individual massive stars, including their ...UV radiation feedback. The set of simulations have cloud masses between mgas = 103 M⊙ and 3 × 105 M⊙ and gas densities typical of clouds in the local Universe ($\overline{n}_{\rm gas} \sim 1.8\times 10^2$ cm−3) and 10× and 100× denser, expected to exist in high-redshift galaxies. The main results are as follows. (i) The observed Salpeter power-law slope and normalization of the stellar initial mass function at the high-mass end can be reproduced if we assume that each star-forming gas clump (sink particle) fragments into stars producing on average a maximum stellar mass about $40{{\ \rm per\ cent}}$ of the mass of the sink particle, while the remaining $60{{\ \rm per\ cent}}$ is distributed into smaller mass stars. Assuming that the sinks fragment according to a power-law mass function flatter than Salpeter, with log-slope 0.8, satisfy this empirical prescription. (ii) The star formation law that best describes our set of simulation is ${\rm d}\rho _*/{\rm d}t \propto \rho _{\rm gas}^{1.5}$ if $\overline{n}_{\rm gas}\lt n_{\rm cri}\approx 10^3$ cm−3, and ${\rm d}\rho _*/{\rm d}t \propto \rho _{\rm gas}^{2.5}$ otherwise. The duration of the star formation episode is roughly six cloud’s sound crossing times (with cs = 10 km s−1). (iii) The total star formation efficiency in the cloud is $f_*=2{{\ \rm per\ cent}} (m_{\rm gas}/10^4~\mathrm{M}_\odot)^{0.4}(1+\overline{n}_{\rm gas}/n_{\rm cri})^{0.91}$, for gas at solar metallicity, while for metallicity Z < 0.1 Z⊙, based on our limited sample, f* is reduced by a factor of ∼5. (iv) The most compact and massive clouds appear to form globular cluster progenitors, in the sense that star clusters remain gravitationally bound after the gas has been expelled.
Molecular cloud structure is regulated by stellar feedback in various forms. Two of the most important feedback processes are UV photoionization and supernovae from massive stars. However, the ...precise response of the cloud to these processes, and the interaction between them, remains an open question. In particular, we wish to know under which conditions the cloud can be dispersed by feedback, which, in turn, can give us hints as to how feedback regulates the star formation inside the cloud. We perform a suite of radiative magnetohydrodynamic simulations of a 10 super( 5) solar mass cloud with embedded sources of ionizing radiation and supernovae, including multiple supernovae and a hypernova model. A UV source corresponding to 10 per cent of the mass of the cloud is required to disperse the cloud, suggesting that the star formation efficiency should be of the order of 10 per cent. A single supernova is unable to significantly affect the evolution of the cloud. However, energetic hypernovae and multiple supernovae are able to add significant quantities of momentum to the cloud, approximately 10 super( 43) g cm s super( -1) of momentum per 10 super( 51) erg of supernova energy. We argue that supernovae alone are unable to regulate star formation in molecular clouds. We stress the importance of ram pressure from turbulence in regulating feedback in molecular clouds.
We present a new set of analytic models for the expansion of H ii regions powered by ultraviolet (UV) photoionization from massive stars and compare them to a new suite of radiative ...magnetohydrodynamic simulations of turbulent, self-gravitating molecular clouds. To perform these simulations, we use ramses-rt, a Eulerian adaptive mesh magnetohydrodynamics code with radiative transfer of UV photons. Our analytic models successfully predict the global behaviour of the H ii region provided the density and velocity structure of the cloud are known. We give estimates for the H ii region behaviour based on a power-law fit to the density field assuming that the system is virialized. We give a radius at which the ionization front should stop expanding (‘stall’). If this radius is smaller than the distance to the edge of the cloud, the H ii region will be trapped by the cloud. This effect is more severe in collapsing clouds than in virialized clouds, since the density in the former increases dramatically over time, with much larger photon emission rates needed for the H ii region to escape a collapsing cloud. We also measure the response of Jeans unstable gas to the H ii regions to predict the impact of UV radiation on star formation in the cloud. We find that the mass in unstable gas can be explained by a model in which the clouds are evaporated by UV photons, suggesting that the net feedback on star formation should be negative.
ABSTRACT
We calculate the hydrogen- and helium-ionizing radiation escaping star-forming molecular clouds, as a function of the star cluster mass and compactness, using a set of high-resolution ...radiation-magnetohydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds. In these simulations, presented in He et al., the formation of individual massive stars is well resolved, and their UV radiation feedback and lifetime on the main sequence are modelled self-consistently. We find that the escape fraction of ionizing radiation from molecular clouds, $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle$ , decreases with increasing mass of the star cluster and with decreasing compactness. Molecular clouds with densities typically found in the local Universe have negligible $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle$ , ranging between $0.5{{\ \rm per\ cent}}$ and $5{{\ \rm per\ cent}}$. 10 times denser molecular clouds have $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle$ $\approx 10{{\ \rm per\ cent}}{-}20{{\ \rm per\ cent}}$, while 100× denser clouds, which produce globular cluster progenitors, have $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle$ $\approx 20{{\ \rm per\ cent}}{-}60{{\ \rm per\ cent}}$. We find that $\langle f_{\rm esc}^{\scriptscriptstyle \rm MC}\rangle$ increases with decreasing gas metallicity, even when ignoring dust extinction, due to stronger radiation feedback. However, the total number of escaping ionizing photons decreases with decreasing metallicity because the star formation efficiency is reduced. We conclude that the sources of reionization at z > 6 must have been very compact star clusters forming in molecular clouds about 100× denser than in today’s Universe, which lead to a significant production of old globular clusters progenitors.
Molecular clouds are turbulent structures whose star formation efficiency (SFE) is strongly affected by internal stellar feedback processes. In this paper, we determine how sensitive the SFE of ...molecular clouds is to randomized inputs in the star formation feedback loop, and to what extent relationships between emergent cloud properties and the SFE can be recovered. We introduce the YULE suite of 26 radiative magnetohydrodynamic simulations of a 10 000 solar mass cloud similar to those in the solar neighbourhood. We use the same initial global properties in every simulation but vary the initial mass function sampling and initial cloud velocity structure. The final SFE lies between 6 and 23 per cent when either of these parameters are changed. We use Bayesian mixed-effects models to uncover trends in the SFE. The number of photons emitted early in the cluster's life and the length of the cloud provide the strongest predictors of the SFE. The H II regions evolve following an analytic model of expansion into a roughly isothermal density field. The more efficient feedback is at evaporating the cloud, the less the star cluster is dispersed. We argue that this is because if the gas is evaporated slowly, the stars are dragged outwards towards surviving gas clumps due to the gravitational attraction between the stars and gas. While star formation and feedback efficiencies are dependent on non-linear processes, statistical models describing cloud-scale processes can be constructed.
Context. Feedback processes and the galactic shear regulate star formation. Aims. We investigate the effects of differential galactic rotation and stellar feedback on the interstellar medium (ISM) ...and on the star formation rate (SFR). Methods. A numerical shearing box is used to perform three-dimensional simulations of a 1 kpc stratified cubic box of turbulent and self-gravitating interstellar medium (in a rotating frame) with supernovae and H II feedback. We vary the value of the velocity gradient induced by the shear and the initial value of the galactic magnetic field. Finally, the different star formation rates and the properties of the structures associated with this set of simulations are computed. Results. We first confirm that the feedback has a strong limiting effect on star formation. The galactic shear has also a great influence: the higher the shear, the lower the SFR. Taking the value of the velocity gradient in the solar neighbourhood, the SFR is too high compared to the observed Kennicutt law, by a factor approximately three to six. This discrepancy can be solved by arguing that the relevant value of the shear is not the one in the solar neighbourhood, and that in reality the star formation efficiency within clusters is not 100%. Taking into account the fact that star-forming clouds generally lie in spiral arms where the shear can be substantially higher (as probed by galaxy-scale simulations), the SFR is now close to the observed one. Different numerical recipes have been tested for the sink particles, giving a numerical incertitude of a factor of about two on the SFR. Finally, we have also estimated the velocity dispersions in our dense clouds and found that they lie below the observed Larson law by a factor of about two. Conclusions. In our simulations, magnetic field, shear, H II regions, and supernovae all contribute significantly to reduce the SFR. In this numerical setup with feedback from supernovae and H II regions and a relevant value of galactic shear, the SFRs are compatible with those observed, with a numerical incertitude factor of about two.
Context.
Understanding the conditions in which stars and stellar clusters form is of great importance. In particular, the role that stellar feedback may have is still hampered by large uncertainties.
...Aims.
We aim to investigate the role played by ionising radiation and protostellar outflows during the formation and evolution of a stellar cluster. To self-consistently take into account gas accretion, we start with clumps of tens of parsecs in size.
Methods.
Using an adaptive mesh refinement code, we ran magneto-hydrodynamical numerical simulations aimed at describing the collapse of massive clumps with either no stellar feedback or taking into account ionising radiation and/or protostellar jets.
Results.
Stellar feedback substantially modifies the protostellar cluster properties in several ways. We confirm that protostellar outflows reduce the star formation rate by a factor of a few, although the outflows do not stop accretion and, likely enough, do not modify the final cluster mass. On the other hand, once sufficiently massive stars have formed, ionising radiation efficiently expels the remaining gas and reduces the final cluster mass by a factor of several. We found that while HII radiation and jets barely change the distribution of high density gas, the latter increases the dense gas velocity dispersion again by a factor of several in a few places. As we are starting from a relatively large scale, we found that the clusters whose mass and size are, respectively, of the order of a few 1000
M
⊙
and a fraction of parsec, present a significant level of rotation. Moreover, we found that the sink particles that mimic the stars themselves tend to have rotation axes aligned with the cluster’s large-scale rotation. Finally, computing the classical
Q
parameter used to quantify stellar cluster structure, we infer that when jets are included in the calculation, the
Q
values are typical of observations, while when protostellar jets are not included, the
Q
values tend to be significantly lower. This is due to the presence of sub-clustering that is considerably reduced by the jets.
Conclusions.
Both large-scale gas accretion and stellar feedback, namely HII regions and protostellar jets, appear to significantly influence the formation and evolution of stellar clusters.
ABSTRACT
We explore to what extent simple algebraic models can be used to describe H ii regions when winds, radiation pressure, gravity, and photon breakout are included. We (a) develop algebraic ...models to describe the expansion of photoionized H ii regions under the influence of gravity and accretion in power-law density fields with ρ ∝ r−w, (b) determine when terms describing winds, radiation pressure, gravity, and photon breakout become significant enough to affect the dynamics of the H ii region where w = 2, and (c) solve these expressions for a set of physically motivated conditions. We find that photoionization feedback from massive stars is the principal mode of feedback on molecular cloud scales, driving accelerating outflows from molecular clouds in cases where the peaked density structure around young massive stars is considered at radii between ∼0.1 and 10–100 pc. Under a large range of conditions the effect of winds and radiation on the dynamics of H ii regions is around 10 per cent of the contribution from photoionization. The effect of winds and radiation pressure is most important at high densities, either close to the star or in very dense clouds such as those in the Central Molecular Zone of the Milky Way. Out to ∼0.1 pc they are the principal drivers of the H ii region. Lower metallicities make the relative effect of photoionization even stronger as the ionized gas temperature is higher.
ABSTRACT
Radiative feedback from massive Population III (Pop III) stars in the form of ionizing and photodissociating photons is widely believed to play a central role in shutting off accretion on to ...these stars. Understanding whether and how this occurs is vital for predicting the final masses reached by these stars and the form of the Pop III stellar initial mass function. To help us better understand the impact of UV radiation from massive Pop III stars on the gas surrounding them, we carry out high-resolution simulations of the formation and early evolution of these stars, using the arepo moving-mesh code coupled with the innovative radiative transfer module sprai. Contrary to most previous results, we find that the ionizing radiation from these stars is trapped in the dense accretion disc surrounding them. Consequently, the inclusion of radiative feedback has no significant impact on either the number or the total mass of protostars formed during the 20 kyr period that we simulate. We show that the reason that we obtain qualitatively different results from previous studies of Pop III stellar feedback lies in how the radiation is injected into the simulation. H ii region trapping only occurs if the photons are injected on scales smaller than the local scale height of the accretion disc, a criterion not fulfilled in previous 3D simulations of this process. Finally, we speculate as to whether outflows driven by the magnetic field or by Lyman-α radiation pressure may be able to clear enough gas away from the star to allow the H ii region to escape from the disc.
ABSTRACT
Winds from young massive stars contribute a large amount of energy to their host molecular clouds. This has consequences for the dynamics and observable structure of star-forming clouds. In ...this paper, we present radiative magnetohydrodynamic simulations of turbulent molecular clouds that form individual stars of 30, 60, and 120 solar masses emitting winds and ultraviolet radiation following realistic stellar evolution tracks. We find that winds contribute to the total radial momentum carried by the expanding nebula around the star at 10 per cent of the level of photoionization feedback, and have only a small effect on the radial expansion of the nebula. Radiation pressure is largely negligible in the systems studied here. The 3D geometry and evolution of wind bubbles is highly aspherical and chaotic, characterized by fast-moving ‘chimneys’ and thermally driven ‘plumes’. These plumes can sometimes become disconnected from the stellar source due to dense gas flows in the cloud. Our results compare favourably with the findings of relevant simulations, analytic models and observations in the literature while demonstrating the need for full 3D simulations including stellar winds. However, more targeted simulations are needed to better understand results from observational studies.
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