Star Formation, Supernovae and the Structure of Disk Galaxies

A physical model for bi-modal star formation and the structure of the interstellar medium and the self-regulating evolution of disk galaxies is presented. Stars heavier than about one solar mass are produced as a result of collisions of molecular clouds or in cloud crushing events whereas low-mass stars are produced at a steady rate in dense molecular clouds and the T-Tauri winds resulting maintain the support of these clouds against rapid collapse and fragmentation. Supernova explosions and stellar winds associated with the massive stars maintain the phase structure, and the scale height of the gas. The collective effects of these energetic processes may create a hole in the disk gas, and allow a galactic wind of metalenriched gas to develop. 1. Phase Structure of the ISM and the Collective Effects of Supernovae. The energetic processes (winds, ionising radiation and supernova explosions) associated with the young, massive stars exercise the fundamental control of the phase properties, pressure and distribution of the interstellar medium (ISM) in the plane of disk galaxies. This is the basis of the multi-phase models (Field.Goldsmith and Habing 1969; Cox and Smith 1974; McKee and Ostriker 1977; Cox 1979,1980), although these differ in the details of how such a multi-phase medium is set up and maintained. The local interstellar medium is perhaps not the best place to start to try to understand the phase structure of the ISM. We lie within a region of extensive recent star formation defined by the stars of the Gould's Belt, which extends over some 700pc, and encompasses the Sco-Cen, Taurus and Orion associations (Lindblad and Westin, 1985). Thus, the phase structure derived locally may not be generally applicable. The Magellanic Clouds, on the other hand, offer a convenient laboratory in which to study the phase structure of the ISM, and evidence for cloud, inter-cloud and coronal components may be found. It has become increasingly clear that Type Ilsupemovae interact with a highly modified ISM. However, Type I supernovae will tend to occur well separated in time and space from their star formation region, and are therefore much more useful in probing "normal" samples of the ISM. From a variety of lines of evidence, Tuohy et al. (1982) have shown that the Balmer dominated SNR are most likely to be the remnants of Type I SNR. For these, the Ha data suggest that the SNR is interacting with a phase of the ISM which has a density of about 0.1 cm", whereas the X-ray data gives 0.3 cm" for the same LMC remnants. This phase can be identified with an intercloud medium. The cloud medium, on the other hand has a density of about 10-30 cm" (Dopita, 1979; Wilson 1983), and is probably in stochastic pressure balance with the intercloud. The supernova rate in the LMC is about 1 per 200 years. This is insufficient to maintain a coronal medium with a large filling factor globally. However, in regions of http:/www.cambridge.org/core/terms. http://dx.doi.org/10.1017/S025292110010291X Downloaded from http:/www.cambridge.org/core. IP address: 54.186.46.42, on 01 Dec 2016 at 06:59:43, subject to the Cambridge Core terms of use, available at 494 Supernova Remnants and the Interstellar Medium local enhancement of the star formation rate, the collective effects of supernova explosions can be sufficient to strip out the disk HI, creating a bubble of coronal gas which eventually finds its way into an extended hot halo. This is graphically illustrated by the case of Shapley Constellation HI (Dopita, Mathewson and Ford, 1985). This region of very extensive star formation over the past 2xl0 year has produced a hole in the disk HI almost 2kpc across, and energetic processes such as stellar winds and SN explosions have pushed out a shell of HI at a velocity of 36 km.s". Such HI will take about 2xl0 years to return to the plane. Furthermore, once the disk HI is swept out, coronal gas produced by subsequent SN events is free to escape into a hot coronal medium which can pressurise the disk gas. Such coronal gas is undoubtedly present and has been observed directly in soft X-rays in Constellation III (see Helfand, Wu and Wang 1987, this conference, not published). For the Galaxy, it has become clear that a hot corona of shock-heated gas first suggested by Spitzer (1956) does indeed exist The presence of this gas is evident locally in the soft X-ray observations (Tanaka and Bleeker 1977; McCammon et al. 1983; Jakobsen and Kahn 1986), and in observations of OVI absorption (Jenkins 1978). As it cools, it gives rise to absorption in highly ionised species such as N V, C IV and Si IV which can be observed with the IUE Satellite (Savage and de Boer 1978,82; York et al. 1982; Pettini et al. 1982; de Boer and Savage 1983). From this work, it is evident that this gas has a (local) scale height for cooling of about 3-4 kpc, and is denser and more confined to the disk towards the inner parts of the Galaxy. If the gravitational binding energy of this hot gas is less than its thermal energy minus the radiative losses as it streams out into the halo, then a galactic wind, rather than a steady state "galactic fountain" will result. The conditions under which this will occur were discussed in an elegant paper by Chevalier and Oegerle (1979). In our local solar neighbourhood, and in the inner regions of the Galaxy, this condition does not appear to be met. However, the cooling timescale of this material at LMC and SMC abundances is very long, of order (0.3 3)xl0 years. Even if it cools, the height to which the hot gas rises is sufficiently distant above the plane to be very weakly bound to the system. It is likely that a galactic wind can be driven in this case. The pattern of elemental abundances (Dopita 1987) strongly suggests that this does indeed occur. The chemical yield of oxygen in the Magellanic Clouds is lower than that of the galaxy by a factor of two to three (e.g. Dufour, 1984). However, data from stellar atmospheres of young disk stars shows that both of [Fe/H] and [O/Fe] are lower in the Magellanic Clouds. This is in contradistinction with the Galaxy, for which old disk stars show a lower [Fe/H] is coupled with a higher [O/Fe] (Tomkin and Lambert, 1984; Tomkin, Sneden and Lambert, 1986; Sneden 1985; Nissen Edvardsson and Gustafsson 1985). Since O is made in massive stars, and Fe in lower mass stars, this difference could be taken to mean that the slopes of the IMFs are different. However, such observational evidence as we have does not support such a conclusion. The alternative hypothesis is that oxygen has been preferentially lost to the system. This could occur through the funnels opened out into the galactic halo by bursts of star formation. These will have filled by the time the Fe-producing Type I events occur, allowing the retention of this element. 2. Star-Formation Bimodal or Not? As Silk (1985), pointed out, the essential ingredients of a star formation theory are http:/www.cambridge.org/core/terms. http://dx.doi.org/10.1017/S025292110010291X Downloaded from http:/www.cambridge.org/core. IP address: 54.186.46.42, on 01 Dec 2016 at 06:59:43, subject to the Cambridge Core terms of use, available at Supernova Remnants and the interstellar Medium 495 the initial mass function (IMF), the star formation efficiency and the rate of star formation. Most models of galactic evolution (Audouze and Tinsley 1977; Vader and de Jong 1981) have tended to assume a constant IMF and to reduce the star formation problem to a simple "prescription" of the rate in terms of the local HI gas density (Schmidt 1959), or of HI surface density (Sanduleak 1969; Hamajima and Tosa 1975). The role of the IMF has been receiving increasing attention in recent papers. In our own Galaxy, star formation may well have a bimodal character, with high mass stars being preferentially formed in the vicinity of the spiral arms but low-mass stars being formed throughout the disk (Giisten and Mezger 1983). If the CO-emitting molecular clouds map star-formation regions, then their distribution in the Galaxy appears to offer convincing support of the bimodal hypothesis (Scoville and Good 1987). The CO clouds are clearly divided into two populations which reflect their kinetic temperatures. The warm molecular clouds are clustered, are associated with HII regions and form a spiral arm population. The cold core clouds are distributed throughout the disk. Scoville Sanders and Clemens (1986) argue that, since the star formation efficiency for massive stars appears to decrease as the mass of the parent cloud increases, the formation of these stars must be triggered by an external cause, such as cloud-cloud collisions, rather than internally as in the sequential star formation models. The apparent segregation of the high-mass and low-mass modes of star formation becomes even more pronounced in starburst regions. Here, several analyses suggest that, in these regions, only the high mass stars are being formed and that the low mass cutoff in the IMF is of order 3 solar masses (Rieke et al. 1980,1985; Olaffsson, Bergrall and Ekman 1984; Augarde andLequeux 1985). In an inspiring recent paper, Larson (1986) has presented convincing arguments that, provided that the global rate of star formation decreases with time, the IMF is a double peaked function. The division between the "high" and "low" mass sections of the IMF occurs at about one solar mass, so that, from the point of view of galactic chemical evolution, only the high mass mode of star formation is important Although, in our own Galaxy, the two modes of star formation appear to be spatially distinct, with the high-mass stars preferentially formed near spiral arms, it is not necessary, or even desirable, to associate this with a density wave trigger. Elmegreen (1985,86) has shown that galaxies of the same Hubble types with and without a density wave have effectively identical star formation rates. The role of the density wave is therefore one of spatial ordering of the star formation regions rather than one of enhancement of star formation rate. 3. The High-Mass Mode of Star Formation. Cloud-cloud collisions, or cloud crushing events generate a dense sheet of shock-compressed material. Let us assume that high-mass star formation results from the development of gravitational instabilities in such a shocked layer (Mouschovias, Shu and Woodward 1974; Elmegreen, 1979,1982; Cowie, 1981; Balbus and Cowie, 1985). Why should this preferentially produce high-mass stars? For an infinite isothermal sheet of surface density a M@ pc", the fastest growing mode of instability (Larson 1985; Field 1985) has a characteristic mass Mc given by Mc = 2 .4T 2 / a M 0 http:/www.cambridge.org/core/terms. http://dx.doi.org/10.1017/S025292110010291X Downloaded from http:/www.cambridge.org/core. IP address: 54.186.46.42, on 01 Dec 2016 at 06:59:43, subject to the Cambridge Core terms of use, available at 496 Supernova Remnants and the Interstellar Medium The typical cloud surface density is of order 100-200 M 0 pc . For low-mass star formation, cloud temperatures are 5-15 K so that Mc lies in the range 0.3-5 solar masses. However, in a shocked sheet, the surface density increases as the mean temperature of the post-shock gas falls towards its equilibrium level. Thus, the most massive modes of instability are triggered first, and fragmentation proceeds to smaller and smaller characteristic Jeans mass. However, this process is terminated when the massive stars reach the main sequence and ionise and break up the shocked layer. The characteristic Jeans mass of fragments is therefore determined by their characteristic temperature, given by the condition that the cooling timescale at this temperature should be comparable to the collapse timescale of the largest fragment Cloud-cloud collisions reduce the momentum, and therefore, the velocity dispersion of the gas in the vertical (w-plane). Thus, energetic processes associated with the high-mass mode of star formation must, in the steady state, feed as much momentum into the gas of the ISM as is being lost in cloud-cloud collisions. If da*/dt is the surface rate of star formation, and a„ is the surface density of gas, then: (da*/dt) = p ag / x^. (3.1) where the cloud-cloud collision timescale is xcc and where the constant of proportionality P is composed of both a "spontaneous" term and a "stimulated" term which accounts for the fact that a burst of star formation may induce a local overpressure leading to cloud crushing and induced star formation in its vicinity. These processes represent the justification for the model of stochastic self-propagating star formation (Gerola and Seiden 1978; Seiden and Gerola 1979; Feitzinger et al. 1981) which has enjoyed considerable success in reproducing the morphological features of both spiral and irregular disk galaxies. Here we assume that the coefficient of stimulated star formation is linearly related to the spontaneous term, so that p is not too sensitive to the galaxian environment. Since the cloud-cloud collisions are radiative, the physical parameter which is conserved in the collision is the momentum. In the steady state disk, therefore, the modulus of the sum of the momentum vectors of the individual gas clouds is maintained at a constant value. Thus, in steady-state; Y(da*/dt) = agvg/xcc (3.2) where v„ is the vertical w-velocity dispersion of the gaseous layer and y is a coupling constant To the extent that the IMF and the energy yield from the high mass stellar population does not depend on metallicity, y will be independent of galaxian environment. Equations (3.1) and (3.2) together imply an observational consequence;