Interstellar bubbles. II - Structure and evolution

“Ring nebulae provide information on evolutionary links between WR stars and their precursors (Weaver et al. 1977).”

“The gist of their argument can be seen by considering a superbubble in a homogenous medium (Weaver et al. 1977), whose radius RP L1@5t3@5, but whose kinetic energy EP L t.”

“This picture is quite di†erent from the standard one of a simple expanding ““ superbubble ÏÏ in which the absorption is due to a thin layer of cooled postshock gas, and for which W > *v would be expected (e.g., Weaver et al. 1977).”

“…cooling processes (e.g., King 2003; Ciotti & Ostriker 1997, 2001 also emphasized the importance of Compton scattering 4 This is a simple approximation to more exact calculations; Weaver et al. (1977) show that for adiabatic bubbles in a uniform medium Eb ≈ (5/11)Lint. for AGN inflows and outflows).”

“Much of the literature on bubbles around massive stars and massive star clusters assumes that shocked stellar winds dominate the dynamics (e.g., Castor et al. 1975; Weaver et al. 1977; Chu & Mac Low 1990).”

“…of SNe (i.e., a sufficiently small mean interval tSN), the evolution of the SN bubble approaches the limit of continuous energy injection and an adiabatic interior, as in Weaver et al. (1977) (see also Tomisaka et al. 1981; McCray & Kafatos 1987; Ostriker & McKee 1988; Koo & McKee 1992a, 1992b).”

“From standard self-similar wind blown bubble theory (Weaver et al. 1977) the size of a pressure-driven bubble is only a weak function of the energy injection rate, R ∝ L1/5w , so we might expect model tbn 2 to be ∼ 60% the size of model tbn 1 at any given epoch.”

“…km s−1, characteristic age∼ 0.5–1 Myr, mechanical power∼ 1039–1040 erg s−1 (independently determined from the bubble expansion speed and from the Hβ luminosity; Weaver et al. 1977; Dopita & Sutherland 1995) and energy content∼ 1053 erg (Roberts et al. 2003; Grisé et al. 2006; Ramsey et al.…”

“…line represent the theoretical, self-similar, spherically symmetric evolution of the forward shock radius and contact discontinuity, respectively, of an energy-driven bubble (wind) in a uniform medium in Stage 1, as defined by Weaver et al. (1977) (see also Section 6 of Bicknell & Begelman 1996).”

“…hot superbubbles, potentially reducing the amount energy that is converted into turbulence at the midplane in favour of driving a galactic wind or a galactic fountain (Chevalier 1977; Weaver et al. 1977; Mac Low, McCray & Norman 1989; Mac Low & Ferrara 1999; Keller et al. 2014; Sharma et al. 2014).”

“…clouds (Whitworth 1979; Matzner 2002; Dale et al. 2012), fast stellar winds that shock-heat the ISM and produce expanding bubbles (Castor et al. 1975; Weaver et al. 1977; Chevalier & Clegg 1985), the pressure of both direct starlight and dust-reprocessed radiation (Krumholz & Matzner 2009; Murray…”

“Following blowout from the disk, their kinematics is no longer determined by the standard Weaver et al. (1977) wind-blown bubble model.”

“The canonical model for shell and hole formation is the evacuation of the cool ISM by the combined kinetic and radiation pressure stellar winds from massive stars and supernovae in H II and star-forming regions over a period of time (Weaver et al. 1977 ; McCray & Kafatos 1987).”

“…(5− β)3(3− β) 6π(7− 2β)(11− β) ](2−β)/(5−β) ×R−3β/(5−β)c ρ3/(5−β)c F (2−β)/(5−β) E t −(β+4)/(5−β) (A11) pB = 3(7− 2β) (3− β)(5− β)2 [ (3− β)(5− β)3 6π(7− 2β)(11− β) ]2/3 × ρ1/3c Rβ/3c F 2/3R −(β+4)/3 B (A12) For β = 0 the above equations reduce to the expressions derived in Weaver et al.…”

“Harper-Clark & Murray (2009) constructed one– dimensional models of the Carina nebula in which they pointed out that the model of Weaver et al. (1977) predicts a bubble too large for Carina’s estimated age.”

“In other cases such as LMC 2, the geometry is more complex and, although energy input by stellar winds and supernovae (Weaver et al. 1977) may dominate, the simple model of outward-propagating star formation requires modification (Points et al. 1999, 2000).”

“3 of Weaver et al. 1977).”

“After free expansion, the system develops distinct concentric zones from the centre moving outwards due to the strong shocks (Cooper et al 2008; Dopita & Sutherland 1996; Weaver et al. 1977).”

“Stellar winds might equally well counteract gravitational attraction due to the formation of hot low-density bubbles, found by theoretical estimates (Avedisova 1972; Castor, McCray & Weaver 1975; Weaver et al. 1977) as well as recent numerical simulations (Rogers & Pittard 2013; Dale et al. 2014).”

“The shell initially follows an energy-driven phase where rshell / t3=5 (Weaver et al. 1977).”

“Castor et al. (1975) and Weaver et al. (1977) derived analytic solutions for the expansion of stellar wind-blown bubbles into a uniform low-density medium.”

“Other processes, such as thermal conduction or turbulent mixing between cool dense gas and surrounding hot regions, can also lead to X-ray-emitting interface regions (Weaver et al. 1977).”

“…they can easily dominate the dynamics of the nebula by evacuating a hot cavity with characteristic temperatures ofT ∼ 107−108 K, and producing two-fluid shocks which lie within the ionization shocks in the coolerT ∼ 104 K HII region (e.g. Pikel’ner 1968; Dyson & de Vries 1972; Weaver et al. 1977).”

“Bubble evolution models predict that the ratio of swept-up ISM shell thickness to its radius should approach asymptotically to a ratio of 0.32 (see Weaver et al. 1977; Whitworth et al. 1994; Capriotti & Kozminski 2001).”

“‘Continuous’ feedback can, in principle, produce different scalings (see e.g. the discussion in Weaver et al. 1977; McKee, van Buren & Lazareff 1984; Freyer, Hensler & Yorke 2006; Faucher-Giguere & Quataert 2012; Gentry et al. 2017).”

“The structure of the shock pattern that ensues is analogous to that resulting from the interaction between a fast stellar wind and the surrounding interstellar gas (see e.g. Weaver et al. 1977; Dyson & Williams 1997).”

“The gas density in the undisturbed interstellar medium around the bubble is assumed to be equal to n0 = 1 cm −3 (physically, the value of n0 determines nb, see Weaver et al. 1977).”

“The evolution of the volume is slower than that of a freely expanding self-similar flow (Castor, McCray & Weaver 1975; Weaver et al. 1977) due to the complex interaction of the bubble with the multiphase ISM.”

“The models of Castor et al. (1975) and Weaver et al. (1977) assumes that the shock-heated gas is completely confined by a cool shell expanding into a uniform-density ISM.”

“22 of Weaver et al. (1977) gives Pbub = 1.6 × 10−10 dyn cm−2 assuming an ambient density of 9× 10−22 g cm−3 (roughly the average density of our GMC clump), and Pbub = 1.4× 10−12 dyn cm−2 assuming an ambient density of 3.33×10−25 g cm−3 (the density of the medium outside of our GMC clump).”

“Second, because superbubbles have both hot gas > 106 K and sharp temperature gradients, thermal conduction is significant (Weaver et al. 1977).”

“The interaction of a spherical outflow with external matter leads to the formation of a region of compressed material within two spherical boundaries (Weaver et al. 1977).”

“The entire M17 H ii region can be regarded as an energetic interstellar bubble blown into the surrounding interstellar medium (ISM) by the action of the combined winds of the OB stars (Weaver et al. 1977 ; Koo&McKee 1992; Capriotti &Kozminski 2001).”

“…from SN blast waves (Cox & Smith 1974; de Avillez & Breitschwerdt 2005b) or that reside within wind-blown bubbles around stars (Castor et al. 1975; Weaver et al. 1977), the thermal pressures of the ISM represent a small fraction (about one-tenth for T ∼ 100 K) of the total pressure (de Avillez &…”

“Weaver et al. (1977) assume that an equilibrium between the conductive energy flux and the mechanical energy flux due to evaporation of shell mass in the reverse direction is established.”

“Although in ideal adiabatic wind bubbles 20% of the wind luminosity is transferred to the expanding neutral shell (Weaver et al. 1977), more realistic numerical models suggest that no more than a few percent of the initial wind energy ends up as neutral gas kinetic energy (Arthur 2007).”

“This distinctive shape has previously been accounted for by the wind-blown model (Castor et al. 1975; Weaver et al. 1977), whereby stellar winds from central high mass star causes gas to be swept into a spherical shell.”

“15 16 For constant luminosity, the evolution of the shell radius in the radiative phase is given by (Castor, McCray & Weaver 1975; Weaver et al. 1977; Ostriker & McKee 1988) R(t) ≃ 66 ( L38 n0 )1/5 t 3/5 6 pc (25) whereL38 ≡ L/(1038 erg s−1) is the wind mechanical luminosity, n0 is the ambient gas…”

“ISM ““Ring ÏÏ Shock Except for the volume occupied by the superbubble Ðlaments, the concave bowl of a preblowout superbubble must be Ðlled largely with shocked wind (zone B in the nomenclature of Weaver et al. 1977).”

“…winds, and supernovae inject energy andmomentum into the surrounding gas, thermalizing some gas into a hot, 107 K, outflow and accelerating the residual gas out of the star-forming region (Weaver et al. 1977; Chevalier & Clegg 1985; Heckman et al. 2000; Cooper et al. 2008; Bustard et al. 2016).”

“A self-similar solution for the internal structure of the bubble determines the coefficient (∼0.88 for g = 5 3; see Weaver et al. 1977).”

“In the example presented in x IVof Weaver et al. (1977), which is based on an interstellar bubble very similar to our models, the conduction front behind the cool shell only spans a small fraction of the cavity radius.”

“Considering the stellar wind before the supernova explosion, the inner radius of the molecular cloud L1 is about a few tens of pc (Weaver et al. 1977).”

“Here we review analytically some of the expected properties of these bubbles (e.g., Weaver et al. 1977; McCray & Kafatos 1987; Koo & McKee 1992b), approximating the multiple SNe as a constant source of mass and energy.”

“We adoptKw = 0.02 (Leitherer et al. 1999; Veilleux et al. 2005; Harrison et al. 2014) and βout,∗ = 1/4 (Weaver et al. 1977).”

“In the classical model of a starburst-driven wind, the combined energy from multiple supernovae creates a Sedov–Taylor blast wave (Taylor 1950; Sedov 1959; McKee & Ostriker 1977; Weaver et al. 1977; Kim & Ostriker 2015).”

“If completely confined by an H ii shell expanding into a uniform density ISM, the hot gas pressure PX would be large (Castor et al. 1975; Weaver et al. 1977).”

“The evolution of supernova-driven superbubbles has been modeled by Mac Low & McCray (1988), assuming expansion into a homogeneous ISM, following the homologous solution of Weaver et al. (1977) for bubbles blown by stellar winds.”

“As shown by McKee et al. (1984) and Weaver et al. (1977), weak stellar winds (wind luminosity ≪ 1.26×1036×L49×n, where n is the ambient density) are likely to be confined by the H ii region pressure to a smaller bubble around the ionizing source, since gas that is evaporated from clumps of material…”

“A Simple Model The simplest physical model that can be compared to our data is an adiabatic expanding superbubble whose expansion is driven by the energy supplied by multiple supernovae (Weaver et al. 1977 ; Koo & McKee 1992).”

“In the standard picture of a stellar wind interacting with the interstellar medium, a four-zone structure (Castor et al. 1975,Weaver et al. 1977) settles very rapidly, consisting of: the innermost hypersonic stellar wind characterized by a density profile ρ ∝ r−2, a hot shocked stellar wind region,…”

“…3 – mentioned, stellar winds and supernovae from young massive stars in OB associations and Super Star Clusters (SSCs) are considered the main driving forces behind the creation of holes and shells whose radii can reach up to hundreds of parsecs (e.g., Weaver et al. 1977; McCray & Kafatos 1987).”

“The pressure-driven expanding Hii region (e.g., Weaver et al. 1977; Hosokawa & Inutsuka 2005) is usually discussed to explain the formation of the Spitzer bubbles (e.g., Deharveng et al. 2010), in which the expanding ionization front preceded by the shock front driven by the Hii region accumulates…”

“Such behaviour should mimic the result of continuous energy injection, where multiple overlapping SNe in the form of rarefactions or Sedov-Taylor blast waves (see e.g. Castor et al. 1975; Weaver et al. 1977; McCray & Kafatos 1987) drive a large-scale wind.”

“Using the wind bubble solution of Weaver et al. (1977), during the energy-conserving phase of expansion we expect that , wheret is the age of the1/5 3/5R p 0.76(L /r ) tw 0 bubble, is the wind luminosity of the central star, and isL rw 0 the density of the ambient medium.”

“The ages derived above and best-fit radii of the model give expansion velocities of 8 and 32 km s−1 for S1 and S2, respectively, using the standard model for the kinematic age of stellar wind bubbles with tkin = 0.6 R/vexp (Weaver et al. 1977).”

“Around young massive clusters, confined interacting winds produce hot (T ∼ 106−108 K) bubbles (Weaver et al. 1977, hereafter W77; Dunne et al. 2003).”