GMCs and Star Formation in the Galaxy: I. Effects of an HII region on a GMC

TL;DR

This work addresses how ionizing radiation from off-center OB associations destroys GMCs by driving HII regions that photoevaporate gas and eject neutral shells. It combines a semi-analytic off-center, spherical-cloud model with detailed numerical simulations to track mass loss across a wide parameter space spanning ${M}$, ${Σ}$, ${S}$, and association placement ${ξ_{c0}}$, while neglecting radiation pressure, winds, and supernovae to focus on EUV effects. The authors derive analytic approximations that capture the key dynamics, including a modified Spitzer expansion, stalls due to cloud pressure, and transitions between embedded, blister, and cometary stages, and they provide parametric fits for the final cloud mass loss ${M_{loss,f}}$ as a function of the input parameters. They show that low-mass clouds tend to lose more mass via neutral-shell ejection, while higher-mass clouds experience evaporation-dominated destruction, and that cometary remnants arise only for certain combinations of ${M}$, ${Σ}$, and ${S}$, with a critical surviving mass ${M_{survive}}$ separating regimes. The results yield practical insights into GMC lifetimes and star-formation efficiency in galaxies, enabling rapid estimates of EUV-induced cloud destruction across diverse galactic environments.

Abstract

The destruction of Giant Molecular Clouds is a key component in galaxy evolution. We theoretically model the destruction of GMCs by HII regions, which evaporate ionized gas and eject neutral gas during their expansion. HII regions follow one of three tracks, depending on the EUV luminosity, $S$, of the ionizing OB association: the expansion can stall inside the cloud; it can break out, forming a blister (champagne) flow; or, for $S>S_{\rm com}$, it can result in the formation of a cometary cloud. We present results for the accumulated mass loss, $M_{\rm loss}(t)$, and the final mass loss, $M_{{\rm loss},f}$, by evaporation and ejection for a range of cloud masses ($10^4<M<10^{7}$ M$_\odot$), cloud surface densities ($50<Σ<1000$ M$_\odot$ pc$^{-2}$), OB association luminosities ($10^{44}<S<10^{52}$ s$^{-1}$), and off-center position of the association. We do not consider starbursts; our neglect of radiation pressure restricts our treatment to $S<10^{52} [(M/10^6$ M$_\odot)^{0.3})/(Σ/100$ M$_\odot$ pc$^{-2}$)] s$^{-1}$, and our neglect of gravity restricts $(M/10^6$ M$_\odot$)($Σ/ 100$ M$_\odot$ pc$^{-2}) < 10$. We find that $M_{{\rm loss},f}$ for the range $0.1 < M_{{\rm loss},f}/M < 0.7$ , is proportional to $S^p$, where $p\sim 0.45-0.75$ depends on $M$, $Σ$, and association position. We find analytic fits to $S_{\rm com}$ as a function of $Σ$, $M$, and association position. $S> S_{\rm com}$ associations destroy at least 70% of the initial cloud. We find a critical cloud mass $M_{\rm survive}$ above which clouds never become cometary and lose $<$ 70% of their mass via a single association. Low mass clouds mostly lose mass via ejection of neutral gas.

Figures (10)

• Figure 1: The GMC is assumed spherical with radius ${R_c}$; the normalized distance from the association to the cloud surface is $\xi_c=r_c/R_c$. The number density of H nuclei in the cloud (HII region) is $n_{\rm 0}$ ($n_{\rm II}$) and the mass density is $\rho_0$ ($\rho_{\rm II}$). In our numerical work, $n_{\rm II}$ and $\rho_{\rm II}$ are functions of $\theta$, but in our analytic work we take them to be independent of $\theta$. Similarly, the shell is spherical (as pictured above) in our analytic work, but non-spherical in our numerical work. The association is located at a normalized distance ${\xi_{c0}}=r_{c0}/ R_c$ from the nearest cloud surface and at a normalized distance $\xi_{\rm cen}=r_{\rm cen}/R_c=R_a/R_c$ from the cloud center. Ionizing radiation from the association creates an HII region that drives a shell of neutral gas into the cloud with a normalized radius $\xi_s=r_s/R_c$ and velocity $v_s$. Once the HII region transitions from fully embedded to a blister (pictured), the shell intersects the cloud surface at a dimensionless distance ${\xi_{cs}}\equiv {r_{cs}}/{R_c}$ from the association, and the angle this ray makes with the line going through the association and cloud center is $\theta_{cs}$. $A_o$ is the area of the opening to the ISM. The partially enclosed HII region lies between $A_o$ and the internal shell surface (area $A_s$), and has a mass $M_{\rm ion,os}$. Gas is ejected and evaporated from the cloud out of the opening $A_o$. We assume the cloud transitions to cometary cloud when ${\theta_{cs}}=150^\circ$.
• Figure 3: Evolution of the EUV luminosity per unit stellar mass, $S_{49}(t)/M_a$, for three associations with initial masses of 100 M$_\odot$ (blue, green, and red dashed lines), one association of 1000 M$_\odot$ (orange), one association of 10000 M$_\odot$ (violet), and one association of 100000 M$_\odot$ (black), which most fully samples the IMF. The most massive star in the 100 M$_\odot$ associations are 74 M$_\odot$ (blue), 12 M$_\odot$ (green) and 5 M$_\odot$ (red). The arrow indicates the initial EUV luminosity per unit stellar mass in a fully sampled IMF (see text).
• Figure 4: The EUV lifetime of an association as a function of ${S_{49}}$. The blue dots correspond to 1000 associations with masses between 40 and $10^5$$\hbox{M}_\odot$ following a power-law association mass distribution of index $-1$. Each association is created using the pg07 method for creating a stellar mass distribution for an association of given mass. The red points and dashed curve show $t_{{\rm ion}}(S_{49})$ for single stars. The diagonal black line is the fit $t_{{\rm ion}}= 6.05\, S_{49}^{-0.18}$ Myr to the average value of $t_{{\rm ion}}$ of associations with $S_{49} < 10$. The horizontal black segment is the fit $t_{{\rm ion}}= 4$ Myr for associations with $S_{49} > 10$.
• Figure 5: The six top panels show the evolution of a shell around an association of ionizing luminosity $S_{49}$ at a depth $\xi_{c0}=0.3$ inside a cloud of mass $M_6=1, 0.1$ and $0.01$. The three left-hand panels, (a), (b) and (c), have luminosities that produce a fractional mass loss $\sim 0.1$, whereas the three right-hand panels, (d), (e) and (f), have luminosities that produce a fractional mass loss $\sim 0.5$. We assume the Galactic surface density, $\Sigma_2=1.05 M_6^{0.08}$. The shell position is marked every $\Delta t=0.5$ Myr from $t=0$ to $t_{\rm ion}$. The red curve marks the position at $t=1$ Myr and the green curve at $t_{\rm ion}$ (4, 11.4, 23.5, 4, 5.9 and 15.5 Myr in the panels, respectively). The blue circle is the initial cloud surface. When a curve in the region outside the initial cloud surface terminates, all the mass in the shell at that time and position has been evaporated. The black curves in the second row panels show the evolution of the contact radius, $r_{cs}$, where the shell intersects the cloud surface. The red, orange, green and blue curves show respectively the evolution of $r_s$ in the $\theta=0$, $\theta=60^\circ$, $\theta=120$ and $\theta=180^\circ$ directions. The colored diagonal arrows indicate the time when the shell in the corresponding direction crosses the cloud surface. If the shell in a given direction $\theta$ stalls and the shell gets completely ionized, the line representing $r_s(\theta)$ changes from solid to dotted and goes from horizontal to rising. The increase of $r_s(\theta)$ after the shell gets completely ionized shows the advance of the ionization front into the ambient gas of the cloud; in the figure this only occurs in the 180° direction in case b, in the 120° and 180° directions in case c, and in the 180° direction in case f. The dash-gray horizontal lines in the second row show where $r=r_{c0}$; the red arrows show when the shell breaks out at $\theta=0$, so they originate at $r=r_{c0}$. The third row panels show the evolution of the shell velocity in the four directions displayed in the second row panels. The bottom panels show the evolution of the accumulated total mass loss ($M_{\rm loss}$, black curve, Eq. \ref{['eq:mloss2']}), the neutral shell mass ejected from the cloud ($M_{\rm ej}$, brown curve), the ionized mass lost (evaporated) from the cloud ($M_{\rm evap}$, orange curve) and the mass of embedded ionized gas ($M_{\rm ion,os}$, green curve).
• Figure 6: Same as Figure \ref{['fig:shell']} but for $S_{49}=S_{{\max},49}=440 M_6$. The shells do not stall. The center and right columns show cases where the final state is cometary. The dash-gray lines drawn in the top row at $\theta=150^\circ$ show the portion of the shell after ejection from a cloud that is considered cometary. The cometary stage is not attained in the case $M_6=1$ and $S=S_{\max}$, nor is it achieved in any of the cases shown in Figure \ref{['fig:shell']}. The black and salmon triangles in the bottom panels indicate the times $t_{\rm com}$ and $t_{\rm com,max}$, respectively (see text).