Interstellar bubbles. II - Structure and evolution

“These densities are such that the extent of a typical stellar wind would significantly overlap with that of its neighbor in less than 1Myr (e.g., Weaver et al. 1977).”

“Although many galactic WR stars possess a wind-blown bubble and theory suggests that shocked, hot gas should be present inside these bubbles (Weaver et al. 1977), only two of them are known to be X-ray emitters up to now.”

“The mechanical energy of the stellar winds and supernovae heats up the surrounding ISM and creates a large, so called super-bubble, filled with hot, X-ray emitting gas (Weaver et al. 1977).”

“Weaver et al. (1977) first discussed the structure of wind-driven bubbles produced by massive stars.”

“Indeed for decelerating self-similar flows, R1 grows with time slower than Rs (cf. Weaver et al. 1977), and so its evolution changes Pb negligibly, and hence the evolution of Rs.”

“…by the free streaming RSG wind, we have to check if the RSG shell is well outside the current shock radius.1 For this purpose we used equation (22) from Weaver et al. (1977), which gives the pressure inside the MS hot bubble, and the equation for the ram pressure of a stellar wind Pram = ρv2.”

“The theory of these bubbles has been considered by Castor et al. (1975) and Weaver et al. (1977), with further additions by Mac Low & McCray (1988) and Chu et al. (1995) amongst others.”

“It is thought that OB stars excavating an H II region may generate diffuse X-rays as fast winds shock the surrounding media (Weaver et al. 1977).”

“The emission is concentrated in a thin disk along the Galactic plane with visible cavities, so-called superbubbles (Weaver et al. 1977; Castor et al. 1975), that have been formed by massive star winds and supernovae (SNe) over Myr timescales.”

“The first condition specifies no transfer of heat from the shocked wind gas to the shocked nebular gas (Dyson & Williams 1980; Garcia-Segura et al. 1996) while the second allows for conductive heat flow across the contact surface (Weaver et al. 1977).”

“Dust bubbles blown by the stellar winds and/or radiation pressure from individual OB stars or massive star clusters (Weaver et al. 1977; Draine 2011) provide readilyidentifiable mid-infrared (IR) morphologies for Galactic H ii regions.”

“To catch the essence, some parameters are estimated according to canonical bubble relation (Castor et al. 1975; Weaver et al. 1977), as a crude approximation, as below.”

“This includes the LB’s outer shell, which was neglected in the preliminarily work by Feige (2010), but was later implemented as a Weaver et al. (1977) wind bubble for the improved analytical study contained in Breitschwerdt et al. (2016, hereafter BFS+).”

“The temperature and electron density profiles of such a bubble have been calculated by Weaver et al. (1977), and the X-ray luminosities of such bubbles can be determined using two methods outlined by Chu et al. (1995).”

“The motion of the cluster with respect to the shocked bubble, which is confined by either magnetic field or gas pressure, distorts the symmetry at the point of origin (Weaver et al. 1977).”

“Studies of superbubbles in the Large Magellanic Cloud by, e.g. Chu & Mac Low (1990) or Dunne et al. (2001) have shown that the X-ray luminosities of X-ray bright superbubbles is higher than what is predicted by theoretical models (e.g., the standard model by Weaver et al. 1977).”

“The size of the shock driven by the wind into the galactic ISM is (Weaver et al. 1977, Chevalier & Clegg 1985), Rwind ∼ 4 ( νsnǫ51t 3 7 n )1/5 Kpc More ionizing radiation will reach the galactic ISM as the fragmented shell expands and finally disperse.”

“We thus use the simple radius evolution law (Weaver et al. 1977): r ′sb = Atν .”

“…& Fabian 1990; Slavin et al. 1993; Esquivel et al. 2006; Kwak & Shelton 2010), wind-blown bubbles or supernovae remnants (SNRs, e.g., Castor et al. 1975; Weaver et al. 1977; Slavin & Cox 1992; Shelton 1998), photoionization by early-type stars or a hot cooling plasma (e.g., Knauth et al. 2003).”

“The morphology As well known from, say, the study of interaction between supernova remnant and ISM, the interaction between the supersonic wind and ISM will form four regions, namely unshocked wind, shocked wind, shocked ISM, and unshocked ISM (see Castor et al. 1975; Weaver et al. 1977).”

“They used an interacting wind model, following Weaver et al. (1977), in which the slow AGB wind is accelerated into a shock by the fast white dwarf wind.”

“The bulging of the diffuse emission seen to the NW and SE in the X-ray contours and XMM-Newton images, 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).”

“…stages, Chandra first enabled a detailed examination of diffuse X-ray emission in MSFRs. Theoretically, such a phenomenon had long been expected both around individual OB stars (Dyson and de Vries 1972; Castor et al. 1975; Weaver et al. 1977) as well as in MSFRs (Chevalier and Clegg 1985).”

“Once a bubble has formed, its structure is thought to be similar to the picture given in Weaver et al. (1977), Smith & Cox (2001), and Mac Low & McCray (1988).”

“The origin of these holes has long been attributed to stellar feedback by single-age new-born stellar clusters (Weaver et al. 1977; McCray & Kafatos 1987, and refer- ences therein).”

“The H region and wind bubble can become distorted if the star is moving (Weaver et al. 1977; Raga et al. 1997; Meyer et al. 2014), and if the star moves supersonically through the H region then the wind bubble drives a bow shock in the direction of motion (Baranov et al. 1971; Weaver et al. 1977;…”

“We also note that Weaver et al. (1977) refers to low velocity stellar winds but faster shocks with velocities > 1500 km s−1 are observed in narrow line regions of other nearby radio-bright Seyferts, similar to NGC 4151 (Axon et al. 1998; Capetti et al. 1999).”

“During this phase, the effects of gravity and radiation pressure are negligible, leaving one a relatively simple differential equation to solve for the shell motion (Weaver et al. 1977; Bisnovatyi-Kogan & Silich 1995; Rahner et al. 2017).”

“The interaction of the main-sequence wind with the surrounding (constant-density) interstellar medium gives rise to awindblown bubble (Weaver et al. 1977; Garcia-Segura et al. 1996; van Marle et al. 2005; Dwarkadas 2005, 2007; Toalá & Arthur 2011; Dwarkadas & Rosenberg 2012).”

“The relation between the shell age, its velocity and radius, for the case in which the radiative cooling of hot gas inside the shell can be neglected (readily applicable for multiple SN-blown bubbles), is given as tshell = 0.6 × R/Vshell (e.g., Weaver et al. 1977; Mac Low & McCray 1988).”

“The thermal pressure in the shocked wind bubble is not very different form the high metallicity case, since it depends on the mechanical luminosity of the wind to the power 0.4 (Weaver et al. 1977).”

“To estimate the radius reached by the structure at the end of the main-sequence phase we follow the evolution model of Weaver et al. (1977) which, for the constant wind momentum phase, gives R = 0.83 ( Ṁ Vw ρ0 )1/4 t1/2 (10) where ρ0 is the density of the ambient medium assumed uniform.”

“This mechanical energy feedback is responsible for the creation of superbubbles (Pikel’ner 1968; Weaver et al. 1977; see discussion in Oey et al. 2001).”

“Early work by Avedisova (1972), Castor et al. (1975) and Weaver et al. (1977) demonstrated that in the absence of radiative cooling, the cumulative energy emitted by a star over its lifetime can drive the expansion of hot bubbles around the host star(s).”

“This code numerically integrates the equations of motion for an adiabatic bubble with a thin shell (e.g., Weaver et al. 1977; Ostriker & McKee 1988), allowing variable input wind power.”

“In the absence of gas cooling, stellar winds can impart momentum into the surrounding material typically pr/M*≈ 50–65 km s −1 (Weaver et al. 1977), assuming a wind luminosity of 1034 erg s−1 (Starburst99; Leitherer et al. 1999), the ages of these clusters to be≈ 105 yr (Rico-Villas et al. 2020) and…”

“The interaction via winds and ionising radiation of a single massive star with its surroundings is usually referred to as “interstellar bubble” (Weaver et al. 1977): Strong winds are shocked close to the star and produce a hot overpressured bubble, which drives an ⋆ E-mail:…”

“Such an interaction can be described analytically (Weaver et al. 1977).”

“It is instead roughly constant with radius and then increases towards the edge5, as expected in individual supernova remnants (Vietri 2008) and bubbles blown by single stars (Weaver et al. 1977).”

“Below we show that the gravitational deceleration due to the galaxy and the central black hole can be safely neglected in our case, and thus the time evolution of the shell can be described by the classical formalism (Weaver et al. 1977, eq.”

“The evolution of such spherically symmetric outflows is governed by the following equations in the presence of cosmic rays and the hot gas (cf. Weaver et al. 1977; Ostriker & McKee 1988; Tegmark et al. 1993), d2Rs dt2 = 4πR2s [Pb + Pc − P0] ms(Rs) − ṁs(Rs) [ Ṙs − v0(Rs) ] ms(Rs) −GM(Rs) R2s ,…”

“As a result, when the winds shock against the dense accretion flow, their post-shock temperature can be > 107 K, well past the peak of the cooling curve (Castor et al. 1975; Weaver et al. 1977), and as a result the gas will stay hot rather than cooling radiatively.”

“The ratio Rf/H depends mostly on the internal sound speed, aside from the usual dependence on cext/(GL)0.2 that comes into the theoretical expression for the bubble expansion (Weaver et al. 1977).”

“Weaver model We modeled the central temperature and X-ray luminosity in the [0.3-2.0 keV] band for DEM L50 and DEM L152 using the similarity solutions of Weaver et al. (1977) as implemented by Oey & Massey (1995).”

“Thermal conduction was applied by Weaver et al. (1977) to stellar wind bubbles to produce a self-similar solution for the density and temperature structure in bubbles.”

“These arc-like structures of swept-up stellar wind material and ISM gasare the result ofthe distortion of their stellar wind bubble by the bulk motion of their central star (Weaver et al. 1977).”

“The effect of thermal conduction is to transfer thermal energy from a hotter to a colder medium, potentially leading warm gas to evaporate in the surrounding hotter material (e.g., Weaver et al. 1977; Cowie & McKee 1977; Brüggen & Scannapieco 2016; Armillotta et al. 2017).”

“In a realistic setting, this profile is expected to change at distances larger than the wind termination shock, Rw ≈ 9 pc A3/10? n −3/10 0 v 2/5 w,8(t/Myr) 2/5 (Weaver et al. 1977).”

“If thermal evaporation is not blocked by magnetic fields, the density and the temperature distributions in zone C are (Weaver et al. 1977; Mac Low & McCray 1988) n(x) ¼ n0(1 x) 2=5; T (x) ¼ T0(1 x)2=5; ð6Þ where x ¼ r /RCD is the fractional radius, RCD is the radius of the contact discontinuity, n0…”

“This implies a rapid hydrodynamic evolution that has caused the decay of the outer shock, inhibiting the formation of an outer shell of swept-up matter and the build-up of a superbubble (as otherwise described in Weaver et al. 1977).”

“A runaway wind-blowing (e.g. WR) star moving through the ISM creates a highly elongated bubble (Weaver et al. 1977; Brighenti & D’Ercole 1994), whose shape in the up-stream direction is determined by a ram pressure balance between the stellar wind and the ISM (Baranov, Krasnobaev & Kulikovskii…”

“This figure reproduces the classic features found in Weaver et al. (1977), which are labeled in Figure 1.”

“Following Weaver et al. (1977), the outer radius of an adiabetically expanding wind bubble (Rb) is proportional to: Rb ∝ (Lw/nism)1/5t3/5, where Lw the wind mechanical luminosity (Lw = 1/2Ṁu2w), nism the ISM density and t the age of the bubble.”

“Thermodynamical considerations provide the expansion law of the SB as (Castor et al. 1975; Weaver et al. 1977): 𝑅(𝑡) ≈ 68 ( 𝜉𝑏P 1038 erg/s )1/5 ( 𝑛0 cm−3 )−1/5 ( 𝑡 Myr )3/5 pc , (1) where P is the average mechanical power of the stellar cluster, 𝑛0 is the hydrogen number density of the…”

“In the standard picture (e.g., Weaver et al. 1977, McKee & Ostriker 1977, Chu et al. 1995), these structures are believed to be created by young star forming regions which supposedly eject a great amount of mechanical energy into the ambient ISM in terms of strong stellar winds and subsequent…”

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

“Theoretical models that invoke photo-ionization due to a classic HII region (Howk & Savage 1999) or a stellar wind-driven bubble (Weaver et al. 1977) can be presently discounted since they generally predict columnn density ratios that are incompatible with those we have determined for…”

“For example, de Geus (1992) considers bubbles created by stars in the Sco-Cen association, using the formulation of Weaver et al. (1977) and McCray & Kafatos (1987).”

“…the expan- sion velocity (V )of the Superbubble, the dynamical timescale (t) of the Superbubble can be estimated by t ≃ η D V −1 (Book et al. 2008), where η is 0.6 for an energy-conserved bubble (Castor et al. 1975; Weaver et al. 1977) and 0.4 for a momentum-conserved bubble (Steigman et al. 1975).”

“These plots contain numerous “superbubbles” driven by SNe from individual OB associations, as have been studied in several classic theoretical papers (Weaver et al. 1977; McCray & Snow 1979; Tomisaka & Ikeuchi 1986; Mac Low & McCray 1988; Tenorio-Tagle & Bodenheimer 1988; Mac Low et al. 1989).”

“Starting close to the star, the density in the MS bubble first follows a power-law in the stellar wind region; then it remains constant inside the long shocked wind region (nb ≈ 0.01 H cm−3); at the border of the MS bubble, ICM swept-up by the MS wind forms a MS bubble shell (Weaver et al. 1977).”

“Although theoretical work investigating the nature of the overlapping SN shock fronts is quite mature (e.g., Weaver et al. 1977; Tomisaka & Ikeuchi 1986; Mac Low & McCray 1988; Mac Low et al. 1989; Koo & McKee 1992), recent simulation work has significantly altered our understanding of the…”

“Considering that ∼10 – 20 % of the energy transmits from supernova explosions into the surrounding ISM (McCray & Kafatos 1987; Weaver et al. 1977; Larson 1974), 20,500 – 93,000 supernova explosions are required to account for the energy of SB1.”