Interstellar bubbles. II - Structure and evolution

“Alternately, the shock may be stronger and the shocked gas fully ionized, but radiative cooling in the dense swept-up shell may cause rapid recombination if the density is high enough (Weaver et al. 1977).”

“This idea has been suggested by a number of authors, (see e.g.Weaver et al. 1977; Heiles et al. 1980).”

“…increases gradually, while the wind velocity decreases slightly, which results in an almost constant mechanical luminosity Lw = 1 2 Ṁwv 2 w. (1) This behavior allows us to easily compute the time evolution of the main-sequence bubble using the analytical solutions given by Weaver et al. (1977).”

“Mostly formed in groups (Lada & Lada 2003), they create superbubbles up to kpc in size (Jaskot et al. 2011; Weaver et al. 1977), and drive large scale outflows (von Glasow et al. 2013).”

“Theoretical studies of the interaction of large OB associations with the interstellar medium (Weaver et al. 1977; McCray & Kafatos 1987; Mac Low & McCray 1988) predict that multiple SN events can create a large and low-density stellar wind bubble which pushes out a supershell of denser ionized…”

“We follow the formalism developed by Weaver et al. (1977) and Ostriker & McKee (1988) describing the hydrodynamic structure of a bubble.”

“…different “scaling relations”, or how the outflow properties (like mass outflow rate and outflow velocity) scale with host galaxy properties (Castor et al. 1975; McKee & Ostriker 1977; Weaver et al. 1977; Ferrara & Tolstoy 2000; Springel & Hernquist 2003; Murray et al. 2005; Hopkins et al. 2012).”

“In this depiction, we have calculated the expected kinetic energy of a stellar wind bubble using the analytical model developed by Weaver et al. (1977), Ekin ' 6 11 Lwt, (20) and the pressure-driven expansion of ionized gas (Spitzer 1978), Mshell ' 4π 3 R3S,0µn0 ( 1 + 7t 4ts )12/7 , (21) Ekin ' 1 2…”

“The evolutionary phases of an explosive wind are well understood analytically (Weaver et al. 1977), although we see additional substructure due to the complexity of the initial medium.”

“However, the equations of motion can be reduced to a straightforward numerical integration (Weaver et al. 1977) for the density and velocity profile in Region B.”

“3 of Weaver et al. 1977) and of moving stars (see fig.”

“After the first stars have formed, the gas surrounding the OCs is rapidly removed by stellar radiation (Krumholz & Matzner 2009; Dinnbier & Walch 2020), stellar winds (Weaver et al. 1977), or supernovae (McKee & Ostriker 1977).”

“The Bubbles as a Confined Galactic Wind We treat the bubbles in the framework of a continuous galactic outflow/superbubble with self-similar SedovTaylor solutions (e.g., Castor et al. 1975; Weaver et al. 1977; Mac Low & McCray 1988; Veilleux et al. 2005).”

“Under the assumption that 10-20% of the total energy goes into kinetic energy (e.g., Weaver et al. 1977; Walch & Naab 2015), the total kinetic power available is about 3− 6× 1039 erg s−1, a value similar to that found from the Hi clouds.”

“Following an approach similar to MNRAS 000, 1–6 (2017) Weaver et al. (1977) and Koo & McKee (1990), the set of equations giving the radius of the shell and the internal energy of the gas is { d dt (Mshell(R) ÛRR) = 2Eth + Mshell ÛR 2 + Egrav,t , Ein + Egrav,0 = Eth + 1 2 Mshell ÛR2 + Egrav,t ,…”

“The evolution of a wind expanding into a quasi-spherical density distribution is initially approximately adiabatic (e.g., Weaver et al. 1977), i.e. the combined thermal energy of the wind blown cavity and the kinetic energy of the swept up shell of shocked medium together increase at a rate set by…”

“…initially low-ionization gas being conductively evaporated, the Ovi column density may be increased by a factor of ∼ 3 from the equilibrium case (Weaver et al. 1977; Indebetouw & Shull 2004), as the region of Ovi ions extends into lower density and kinetically hotter material (the gas is…”

“Weaver et al. (1977) introduce two zones in this region – an inner shell of hot shocked wind and an outer shell of shocked ISM separated by a contact discontinuity.”

“Stellar winds and explosions are expected to create interacting gas shells (Weaver et al. 1977), merging of hot cavities may form superbubbles (Tenorio-Tagle & Bodenheimer 1988; Mac Low & McCray 1988; Cho & Kang 2008).”

“In principle, the evolution of main sequence and WolfRayet bubbles are influenced – although weakly – by various stellar and interstellar medium parameters (Weaver et al. 1977).”

“More details are provided in Weaver et al. (1977).”

“Both Weaver et al. (1977) and Capriotti & Kozminski (2001) derive criteria determining when a wind bubble can trap the H ii region, finding that strong winds (i.e. high mass stars) in dense gas are the most favourable scenario.”

“The mechanical luminosity of the star, Lw = 1 2 Ṁw V 2 w, (2) is a measure of the mechanical energy that the star puts into the CSM.”

“The superbubble pressure as a function of time, according to the adiabatic model of Weaver et al. (1977), is ∼ 34ρ3 2 sb, which at the end of cluster lifetime becomes psb, late kB ∼ 1.7 × 105 K cm−3N2/5OB,4η 2/5 mech,−2τ −6/5 OB,30n 3/5 g0,1, (20) where mechanical efficiency has been scaled to 0.01.”

“This situation is quite different from the Weaver et al. (1977) model, which applies to a nebula that has already settled into an energyconserving stage, with a strong reverse shock heating a bubble of high pressure that drives an outward expansion of a thin shell of swept-up ambient material.”

“Instead, if we combine the intensity measurements of Russell et al. (2007) with the shock wave models of Raymond et al. (1988) and the theory of interstellar bubbles blown by a continuous energy input (Castor et al. 1975; Weaver et al. 1977), we can get a tighter constraint on the power estimate.”

“6), indicating that these are consistent with the standard bubble model (Weaver et al. 1977).”

“However, the mass of X-ray-emitting gas is an order of magnitude less than the total mass of the swept-up interstellar medium, that is, the swept-up shell is not significantly depleted by evaporation into the hot region, in agreement with the self-similar approximation of Weaver et al. (1977).”

“For stationary stars, the wind-ISM interface is expected to be a spherical shell as shown, for example, by the analytic and hydrodynamic models of Weaver et al. (1977) and GarciaSegura et al. (1996), respectively.”

“…acts on only one side of a molecular cloud where as large-scale triggering describes the process by which a centralized source destroys the remainder of its parental molecular cloud, creating a void in the gas and a dense ridge of swept up material carried to large distances (Weaver et al. 1977).”

“The simplest model for the initial response of the interstellar gas to this feedback is based on stellar wind bubbles (Weaver et al. 1977; Shull & McKee 1979).”

“After a couple of 106 years, fast stellar winds start to play a major role in heating and shaping the medium, creating a low-density hot bubble (Weaver et al. 1977), probably even before the explosion of the first SN in the association.”

“The expansion radius r s,B of a wind-blown bubble from a constant stellar wind without heat transfer is given by (Weaver et al. 1977; Pittard 2013) r s,B(t) = ( 125 154π )1/5 ( Lω ρ 0,uni )1/5 t3/5 (22) where ρ 0,uni is the density of the initial homogeneous ambient medium with µ = 1.”

“7 of Weaver et al. (1977).”

“…bubbles which take into account the interaction of the expanding bubble with a surrounding confining medium were developed by Castor et al. (1975), Weaver et al. (1977), Shull (1980), Koo & McKee (1992a,b) and Cantó et al. (2000), and recently included in global molecular cloud simulations by…”

“From the interstellar bubble model of Weaver et al. (1977), we find that the age, t, of the bubble is related to its radius, Rs, in parsecs and its expansion velocity, Vs, in km s 1 by t ¼ 6 105Rs=Vs.”

“Assuming the ratio of ratio of kinetic energy of the H i clouds to the total input wind energy is ∼ 0.2 (Weaver et al. 1977), as often assumed for superbubbles, the required wind energy input was ∼ 8 × 1052 ergs over the past 106 yrs.”

“…mass-loss rate in units of 10 6 M yr 1, vw is the stellar wind velocity in units of 108 cm s 1, v is the motion of the star through the Northern Arm in units of 106 cm s 1, lH is the mean molecular weight, and nH is the gas density of the Northern Arm in units of cm s 1 (Weaver et al. 1977).”

“The snapshot clearly shows the structure of a standard stellar wind scenario (Weaver et al. 1977).”

“The less intense bulging of the emission seen to the ESE and WNW could be indicative of a bipolar outflow along the minor axis of the galaxy as would be expected from standard superbubble models (Weaver et al. 1977).”

“Such transitions typically lead to the formationof a wind-blown bubble (e.g., Weaver et al. 1977; Garcia-Segura et al. 1996a,b), and numerous researchers have explored the subsequent interaction between the complex CSM associated with a bubble and the SN blast wave (e.g., Chevalier & Liang 1989;…”

“Weaver et al. (1977) argued that the density in the hot interior of bubbles in uniform gas is dominated by conductive evaporation from the dense shell.”

“One can, therefore, expect to find some of the runaways via detection of their associated bow shocks – the natural attributes of supersonically moving stars (Baranov et al. 1971; Weaver et al. 1977).”

“According to Weaver et al. (1977), in the standard superbubble model, the time evolution of the radius of the dense shell of swept-up ambient material is given by R ¼ (65:9 pc)L0:238 n 0:20 t0:66 , where L38 is the mechanical luminosity injected by the starburst in units of 1038 ergs s 1, n0 is the…”

“In what follows I borrow liberally from a number of excellent treatments of spherical WBB theory (Pikel’ner 1968, Dyson & de Vries 1972, Weaver et al. 1977, Kwok et al. 1978, Dyson & Williams 1981, Kahn 1983, Koo & McKee 1992) When a stellar wind “turns on” it initially expands ballistically until…”

“For the Weaver et al. (1977) solution, we use wind luminosities of Lwind = 10 L , 100 L and 4000 L , which cover the measured range within G0.”

“As it expands, it sweeps up and shocks ambient material, creating an outflowing “superwind” (Castor et al. 1975; Weaver et al. 1977).”

“Indeed, Ugeom can easily be computed from the self-similar solutions of Koo & McKee (1992): using L = (1 + β)Sēi and evaluating for the case of a steady wind in a uniform medium (Weaver et al. 1977), Ugeom = 2Uem = 2.2kBTi 3(1 + β)ēi ṘIF fwvw .”

“If the ambient gas density9A.7, is 1 cm~3, a single massive star could easily blow a holen0this size in a few Myr (Weaver et al. 1977 ; McCray & Kafatos 1987), so there is no problem producing this shell with stars in clusters 4-2 or 4-1.”

“In the classical picture of an expanding superbubble, a dense, neutral shell will wrap around the 104 K region created by the reverse shock traced by bright Hα emission (Weaver et al. 1977).”

“One can see that (as in Weaver et al. 1977), the luminosity increases with time, in contrast to the model with dust cooling presented in Figure 12.”

“Therefore, a transition phase between the stratified to uniform medium is expected at a distance larger than & 10−2 pc (Weaver et al. 1977; Castor et al. 1975; Fryer et al. 2006).”

“…is tc = 3kTs/4n0Λ(Ts), with postshock electron number density 4n0 and shocked temperature Ts = (3µs/16k)v 2 shock, where µs is the mass per particle in the ionized ISM, and vshock is shock velocity given by a similarity solution of a bubble in a uniform density medium n0 by Weaver et al. (1977).”

“The resulting overpressure of this plasma leads to the formation of dense swept-up shells on the surfaces of surrounding clouds (Weaver et al. 1977).”

“According to the classical Weaver et al. (1977) model of expanding bubbles, v R t0.”

“In particular, massive stars are known to create large wind-blown bubbles of several tens of parsecs in size (Weaver et al. 1977; Chevalier 1999).”

“…of morphology observed in WR rings, analytic models and numerical simulations have been put forward for windblown bubbles in di†erent media : in a homogeneous ISM (e.g., Weaver et al. 1977), in a cloudy ISM (McKee, van Buren, & Lazare† 1984), and in a circumstellar medium & Mac Low 1995a, 1995b).”

“As a matter of fact, any of the four cavities in NGC 604 could have been created by the kinetic energy released into their surroundings by only one or a few massive stars (as opposed to the 200 here) in a period of 3 Myr if Weaver et al. (1977) models were applicable here.”

“The fast wind sweeps the ambient medium or slower wind into a dense shell, whose density can be extremely high if the wind shock is radiative (see Figure 1), and the swept-up mass collapses into a very thin dense shell bordered by a radiative shock (Weaver et al. 1977; Dwarkadas 2005).”

“16 in Weaver et al. 1977), which could be consistent with the suggestion that the SNR is evolving in a uniform medium (Badenes et al. 2007; Yamaguchi et al. 2014).”

“Before describing the interaction of the GC wind with the surrounding medium, we briefly summarize the evolution of a “standard” spherical bubble, that is, a bubble powered by a constant luminosity wind and expanding through a local uniform gas (Weaver et al. 1977).”

“The origin of these ISM features has long been attributed to stellar feedback from massive stars, i.e., stellar winds and Type II supernovae (SNe; Weaver et al. 1977; Cash et al. 1980; McCray & Kafatos 1987; Tenorio-Tagle & Bodenheimer 1988, and references therein).”

“The Interior TemperatureThe bubble temperature Tb is obtained from the model of Weaver et al. (1977).”

“This effect, which has been considered in the study of interstellar bubbles (e.g., Weaver et al. 1977), would be strongly suppressed if the magnetic field were strictly transverse to the flow direction, as is assumed in our model.”

“Furthermore, once a complete balance has been established between the ram pressures of the stellar wind and the ISM, the leading edge of the astropause remains a fixed distance ahead of the moving star (Weaver et al. 1977).”

“In the bubble model of Weaver et al. (1977), the fast stellar wind encounters an inner, stagnation shock and the shocked stellar wind provides the thermal pressure to drive the expansion of the nebular shell.”

“The model predicts that the interior pressure evolves as (e.g., Weaver et al. 1977), Pi/k = 1.83 × 10 5 L 2/5 38 n 3/5t −4/5 6 cm −3 K .”

“The dynamics of the wind-to-ISM transition phase was originally introduced by Weaver et al. (1977) and Castor et al. (1975).”

“The latter is tdyn = 0.6 Rshell/Vshell=13.7 Myr (Weaver et al. 1977).”