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Astronomy & Astrophysics manuscript no. 1324 (DOI: will be inserted by hand later)

August 10, 2005

Numerical simulations of expanding sup ershells in dwarf irregular galaxies I I. Formation of giant HI rings
E. I. Vorobyov
1 2

1 ,2

and Shantanu Basu

2

Institute of Physics, Stachki 194, Rostov-on-Don, Russia e-mail: eduard vorobev@mail.ru Department of Physics and Astronomy, University of Western Ontario, London, Ontario, N6A 3K7, Canada e-mail: basu@astro.uwo.ca

Abstract. We perform numerical hydrodynamic modeling of various physical processes that can form an HI ring as is observed in Holmberg I (Ho I). Three energetic mechanisms are considered: multiple supernova explosions (SNe), a hypernova explosion associated with a gamma ray burst (GRB), and the vertical impact of a high velocity cloud (HVC). The total released energy has an upper limit of 1054 ergs. We find that multiple SNe are in general more effective in producing shells that break out of the disk than a hypernova explosion of the same total energy. As a consequence, multiple SNe form rings with a high ring-to-center contrast K < 100 in the HI column density, whereas single hypernova explosions form rings with K < 10. Only multiple SNe can reproduce both the size (diameter 1.7 kpc) and the ring-to-center contrast (K 15 - 20) of the HI ring in Ho I. High velocity clouds create HI rings that are much smaller in size ( < 0.8 kpc) and contrast (K < 4.5) than seen in Ho I. We construct model position-velocity (pV) diagrams and find that they can be used to distinguish among different HI ring formation mechanisms. The observed pV-diagrams of Ho I (Ott et al. 2001) are best reproduced by multiple SNe. We conclude that the giant HI ring in Ho I is most probably formed by multiple SNe. We also find that the appearance of the SNe-driven shell in the integrated HI image depends on the inclination angle of the galaxy. In nearly face-on galaxies, the integrated HI image shows a ring of roughly constant HI column density surrounding a deep central depression, whereas in considerably inclined galaxies ( i > 45 ) the HI image is characterized by two kidney-shaped density enhancements and a mild central depression. Key words. galaxies: dwarf, individual ­ Holmberg I=DDO 63 ­ ISM: bubbles

1. Introduction
There are a few nearby low-mass dwarf irregular galaxies (dIrr's) such as Holmberg I (Tully et al. 1978, Ott et al. 2001), M81 dwA (Sargent et al. 1983, Westpfahl & Puche 1993), Sagittarius DIG (Young & Lo 1997), Sextans A (Skillman et al. 1988, Stewart 1998), the HI morphology of which is totally dominated by a single ring structure of size comparable to or bigger than their optical extent. The integrated HI image of these dIrr's shows a central HI hole surrounded by a denser HI ring. The contrast in the azimuthally averaged HI column density between the central hole and the ring varies from 3 - 4 in Sextans A and M81 dwA to 15 - 20 in Holmberg I. HI rings that do not dominate the overall HI extent of a galaxy, yet occupy a considerable region (kpc scale), have also been found in other dIrr's such as DDO 47 (shell 13, according to Walter
Send offprint requests to : E. I. Vorobyov

& Brinks 2001) and Holmberg II (shell 21, according to Puche et al. 1992). There are a number of scenarios that could create HI holes in galactic disks (see S´ hez-Salcedo 2002), anc which can loosely be divided into two groups comprising the energetic and non-energetic mechanisms. The energetic mechanisms assume a deposition of vast amount of energy into the interstellar medium and include multiple supernova explosions (Mac Low & McCray 1988, De Young & Heckman 1994, Mac Low & Ferrara 1999, Silich et al. 2001), impact of high velocity clouds (TenorioTagle et al. 1987, Comer´ & Torra 1992, Rand & Stone on 1996), and gamma ray bursts (Efremov et al. 1998, Loeb & Perna 1998). The non-energetic mechanisms include a combined action of thermal and gravitational instabilities in the gas disk (Wada et al. 2000), turbulent clearing (Elmegreen 1997, Walter & Brinks 1999), and ultra-violet erosion of the HI disk (Vorobyov & Shchekinov 2004). It appears however very unlikely that a central HI depres-


2

E. I. Vorobyov, S. Basu: Formation of giant HI rings

sion surrounded by a denser HI ring with size comparable to the galaxy's optical extent could be produced by a non-energetic mechanism. Indeed, Vorobyov et al. (2004) have recently shown that the HI ring-like morphology of Holmberg I (Ho I) can be produced by multiple supernova explosions (SNe). In this paper, we consider two other energetic mechanisms of HI ring formation, namely the impact of high velocity clouds (HVCs) and gamma ray bursts (GRBs), and show that they cannot explain the formation of the observed giant HI ring in Ho I. We generate the positionvelocity diagrams and show that they can be used to distinguish between the rings created by different energetic mechanisms. We find that the appearance of HI rings created by multiple SNe is sensitive to the inclination angle of the galaxy. In considerably inclined galaxies, the HI ring would rather appear as two kidney-shaped density enhancements similar to those observed in Sectans A. The paper is organized as follows. In Sect. 2 the numerical hydrodynamic model for simulating multiple SNe, GRBs, and the impact of HVCs is formulated. A comparative study of multiple SNe and GRBs of the same total energy is performed in Sect. 4. The collision of HVCs with the galactic gas disk is considered in Sect. 5. The main results are summarized in Sect. 7.

2. Numerical model
Our model galaxy consists of a rotating gas disk, stellar disk, and a spherically symmetric dark matter halo. The density profile of the stellar component is chosen as: = s0 sech2 (z /zs ) exp(-r/rs ), (1)

where s0 is the stellar density in the center of the galaxy, and zs and rs are the vertical scale height and radial scale length of the stellar component, respectively. We assume that the density profile of the dark matter (DM) halo can be approximated by a modified isothermal sphere (Binney & Tremaine 1987) h = h0 , 1 + (r/rh )2 (2)

where the central density h0 and the characteristic scale length rh were given by Mac Low & Ferrara (1999) and Silich & Tenorio-Tagle (2001) based on the study of the dark-to-visible mass ratios by Persic, Salucci, & Stel (1996):
h0

= 6.3 â 10

10

M M

h

- 1 /3

h-

1 /3

M

kpc

-3

,

(3)

rh = 0.89 â 10-

5

M M

h

1 /2

h

1 /2

kpc.

(4)

Here, h is the Hubble constant in units of 100 km s-1 Mpc-1 and Mh is the total halo mass. We adopt h = 0.65 throughout the paper.

Our model galaxy is meant to represent Ho I and we use the observations of Ott et al. (2001) to constrain the parameters of our model. We note that Mh in Eqs. (3) and (4) is, in fact, the total mass of the halo. We vary Mh until the actual halo mass confined within the HI diameter of Ho I (5.8 kpc, Ott et al. 2001) agrees with the observed value, 3.1 â 108 M . This fit yields a value of Mh = 6.0 â 109 M for Ho I. Once the total halo mass is fixed, we derive the parameters of the halo density distribution using Eqs. (3) and (4), which are further used to compute the gravitational potential of the halo as described in Vorobyov et al. (2004). We have adopted a value of zs = 300 pc, which is typical for dwarf irregular galaxies. The radial scale length rs = 1.7 kpc of the stellar disk is estimated from the Ic -band radial surface brightness profile of Ho I. With rs and zs being fixed, the stellar density 0 in Eq.( 1) is varied so as to obtain the meas sured luminous stellar mass of Ms = 1.0 â 108 M . This results in 0 0.02 M pc-3 . The adopted parameters s of the stellar disk are further used to compute the stellar gravitational potential by solving the Poisson equation. Once the stellar and DM halo gravitational potentials are fixed, we obtain the initial gas density distribution by solving the steady-state momentum equation as described in Vorobyov et al. (2004). We set the gas velocity dispersion = (RT /µ)1/2 to be 9 km s-1 (Ott et al. 2001). We vary the rotation curve until the initial gas surface density distribution becomes exponential, which is in agreement with observations of the HI radial distribution in many dIrr's (Taylor et al. 1994). The observed rotation curve (RC) of Ho I is known to the accuracy of the inclination angle, which in turn is poorly determined (Ott et al. 2001) due to Ho I's small inclination. We have chosen the initial RC in our model so that the initial radial gas surface density distribution well reproduces the observed profile at r > 1 kpc, i.e. at radii which are not affected by the subsequent ring expansion. We do not expect our initial RC to match the currently observed RC, since the latter is already affected by ring formation. Furthermore, accurately modeling the observed RC (for an assumed inclination angle) requires non-axisymmetric simulations, since the dynamical center of Ho I is 0.7 kpc offset from the morphological center of the ring. This offset may complicate the shape of the observed RC, because it is measured around the dynamical center. This task is beyond the scope of our paper. The resulting radial gas surface density profile, as well as the Gaussian vertical scale height h of the gas distribution and initial gas rotation curve, are plotted in Fig. 1 by the solid, dotted, and dashed lines, respectively. The total gas mass within the computational domain is Mgas = 1.0 â 108 M , of which 30% is contributed by He (MHI+He 1.4 MHI , µ = 1.27, Brinks 1990). This value of Mgas roughly agrees with that obtained by Ott et al. (2001). A usual set of hydrodynamical equations in cylindrical coordinates (with the assumption of axial symmetry) is solved using the method of finite-differences with a timeexplicit, operator-split solution procedure as used in the


E. I. Vorobyov, S. Basu: Formation of giant HI rings

3

3. Energetic mechanisms of HI ring formation
Here, we briefly review possible mechanisms of HI ring formation as observed in Ho I. Consecutive supernova explosions. The origin of the giant HI rings in dIrr's is traditionally thought to lie in the combined effect of stellar winds and supernova explosions produced by young stellar associations (see e.g. Ott et al. 2001). In our simulations, the energy of supernova explosions is released in the form of thermal energy in the central region with a radius of 30 pc filled with the hot (T 107 K ) and rarified (n 10-3 cm-3 ) gas, which is presumably formed by the previous action of stellar winds. We use a constant wind approximation, i.e. at each time step we add energy to the source region at a rate of E = L, where L is the mechanical luminosity defined as the total released energy of SNe divided by the duration of the energy input phase. We choose the energy input phase to last for 30 Myr, which corresponds roughly to the difference in the lifetimes of the most and least massive stars capable of producing SNe in a cluster of simultaneously born stars. Since in the present simulations we deal with large stellar clusters with hundreds of supernovae, the release of the energy of SNe in the form of thermal energy is justified (Mac Low & McCray 1988). Gamma ray bursts. The consecutive SN explosions may not be the only mechanism that could release 1053 - 1054 ergs of energy, enough to form giant HI rings. Another mechanism has been suggested by Efremov et al. (1998) and Loeb & Perna (1998), who argued that the GRB explosions are powerful enough to make kpc-size shells in the interstellar media of spiral and irregular galaxies. Although the physics of GRBs is still poorly understood, the general picture emerging is that they are highly en´ ergetic events ( 1054 ergs, see e.g. Paczynski 1998) that release energy in a short period of time (of the order of a few seconds). Consequently, we model the GRB explosion (hereafter, "hypernova" according to Paczynski 1998) ´ by an instantaneous release of thermal energy within a sphere of 30 pc, filled with hot (T 107 K ) and rarified (n 10-3 cm-3 ) gas. We have also explored the injection of hypernova energy in the form of kinetic energy and found that it does not noticeably influence the dynamics of the hypernova-driven shell. Impact of high velocity clouds. Another possible mechanism that could create HI holes in the galactic disks was proposed by Tenorio-Tagle et al. (1987), who argued that the infall of high velocity clouds could deposit 1052 to 1054 ergs per collision. The numerical simulations of TenorioTagle et al. (1987) have indeed shown that HVCs are capable of forming the giant curved arcs and cavities in the Galactic disk (see also Rand & Stone (1996) for numerical simulations of HVC impact in NGC 4631). Most previous numerical simulations have been concerned with the infall of HVCs in massive galaxies, because their collisional cross section is much larger than that of dwarf irregulars. Moreover, the gas disks in dwarf irregulars are in general thicker than those of massive spiral galaxies, which would

Fig. 1. The equilibrium radial distribution of gas surface density (the solid line), the initial rotation curve (the dashed line), and the Gaussian vertical scale height of gas distribution (the dotted line).

ZEUS-2D code described in detail in Stone & Norman (1992). The computational domain spans the range of 7.2 kpc â 2 kpc in the vertical and horizontal directions, respectively, with a resolution of 5 pc. We have implemented the optically thin cooling curve given in Wada & Norman (2001) for a metallicity of one tenth of solar, which is typical for dIrr's. The cooling processes taken into account are: (1) recombination of H, He, C, O, N, Si, and Fe; (2) collisional excitation of HI, CI-IV, and OI-IV; (3) hydrogen and helium bremsstrahlung; (4) vibrational and rotational excitation of H2 ; (5) atomic and molecular cooling due to fine-structure emission of C, C+, and O, and rotational line emission of CO and H2 . We use an empirical heating function tuned to balance the cooling in the background atmosphere so that it maintains the gas in hydrostatic and thermal equilibrium; it may be thought of as a crude model for the stellar energy input. However, heating is prohibited at Tgas > 2.0 â 104 K to avoid the effects of spurious heating of a bubble's interior by the time-independent heating function. This is physically justified since most of the heating in the warm interstellar medium comes from the photoelectric heating of polycyclic aromatic hydrocarbon molecules (PAHs) and small grains, which will be either evaporated or highly ionized in the bubble filled with hot supernova ejecta. Cooling and heating are treated numerically at the end of the time integration step using an implicit update to the energy equation. The implicit equation for energy density is solved by Newton-Raphson iteration, supplemented by a bisection algorithm for occasional zones where the Newton-Raphson method does not converge. In order to monitor accuracy, the total change in the internal energy density in one time step is kept below 15%. If this condition is not met, the time step is reduced and a solution is again sought. In the following we give a brief description on the mechanisms of energy injection used in our numerical simulation.


4

E. I. Vorobyov, S. Basu: Formation of giant HI rings

Fig. 2. Temporal evolution of the gas volume density distribution after the release of 2 â 1053 ergs of thermal energy at z = 0, r = 0 pc. The upper panels correspond to 200 consecutive SN explosions over 30 Myr, while the lower panels show the impact of a single hypernova of the same total energy of 2.0 â 1053 ergs. The scale bar is in gm cm-3 .

Fig. 4. The same as Fig. 2, but for the energy input of 1054 ergs.

4. Supernova explosions versus gamma ray bursts
We start by showing in Fig. 2 the temporal evolution of the distribution of the gas volume density produced by 200 consecutive SNe (the upper panels) and by a hypernova explosion of the same total energy of 2 â 1053 ergs (the lower panels). The overall gas dynamics is similar in both cases. However, there are minor differences seen not only in the dynamics of the hot gas but also in the shape of the blown-up shell. In the case of a hypernova explosion, there is no "blowout" observed (i.e. the shell breaking out of the disk and pumping the hot gas into the intergalactic medium). The hot gas is always confined inside the shell in the early expansion phase and it cools down at later times t > 40 Myr due to the radiative cooling. As a result, the shell collapses at t = 45 Myr, creating a mildly compressed central core, the gas density of which is however below the Jeans limit. In the case of multiple SNe, part of the hot gas is lifted to a higher altitude of z 1 kpc due to a buoyancy effect developing at t 45 Myr. It is also seen that in the early expansion phase the shell is on average thicker in the case of the hypernova explosion than in the case of multiple SN explosions. Since the numerical modeling of Vorobyov et al. (2004) suggested that the shell in Ho I has already blown out of the disk, we do not consider further the energy release of 2.0 â 1053 ergs. The difference in the shell dynamics between the multiple SN and hypernova becomes pronounced as one considers more energetic explosions. For instance, Fig. 3 shows the distribution of the gas volume density produced by 500 consecutive SN explosions (the upper panels) and by a single hypernova explosion of the same total energy 5.0â1053 ergs (the lower panels). Now, the dynamics of the SN-driven shell shows a clear blowout phase at t 45 Myr after the beginning of the energy input phase. On the contrary, the hypernova-driven shell never breaks out of the disk, though its energy is equal to the total energy released by multiple supernovae. This difference remains for presumably an upper limit energy release of 1054 ergs that a stellar cluster could produce in Holmberg I. As seen

Fig. 3. The same as Fig. 2, but for the energy input of 5 â 1053 ergs.

make it more difficult for an HVC to penetrate the disk. In summary, the formation of a giant HI hole surrounded by a denser HI ring (as is observed in Ho I and other dwarf irregulars) by the infall of HVCs is not obvious and requires further investigation. Taking into account the diameter of the HI ring in Ho I ( 1.7 kpc), we consider the most energetic HVCs, which cover a velocity range 200 km s-1 vHVC 300 km s-1 and have HI column density 1020 cm-3 NHI 1021 cm-3 . In our simulations the kinetic energies of HVCs range from 1.0 â 1053 to 2.5 â 1054 ergs, which corresponds to a variation in HVC masses of 2.5 â 105 M to 2.5 â 106 M . Such massive and energetic HVCs most probably have an extragalactic origin.


E. I. Vorobyov, S. Basu: Formation of giant HI rings

5

Fig. 5. The vertical cut through the distribution of the gas volume density produced by 500 consecutive SNe at t=27 Myr (the left panel) and single hypernova of the same total energy of 5.0 â 1053 ergs (the right panel). The gas velocity field is shown by the arrows.

in the upper panels of Fig. 4, the shell dynamics governed by 1000 consecutive SN explosions exhibits a violent blowout, whereas that governed by a hypernova of the same total energy of 1054 ergs shows almost no sign of blowout. This is in good agreement with the previous model of Efremov, Ehlerov´ & Palou (1999), who used a a s thin shell approximation to study the evolution of shells formed by a single hypernova and multiple SNe. These authors have also found that an abrupt energy input creates shells that do not blow out to the galactic halo for energies < 1054 ergs. Noticeably, the final fate of the gas distribu tion is similar in all cases: the hot bubble fills in and the gas disk mostly recovers its pre-explosion appearance after 160 Myr with a slightly more centrally condensed radial gas distribution. The occurrence of the blowout in the case of multiple supernova explosions and its absence in the case of a hypernova explosion can be understood if one considers the dynamics of the hot gas filling the shell interior. In Fig. 5 we plot the gas volume density distribution and velocity field produced by 500 consecutive SN explosions (the

left panel) and a hypernova of the same total energy of 5.0 â 1053 ergs (the right panel). An obvious difference is seen: the hot gas ejected by multiple SNe forms a "vortex" that acts to de-stabilize the swept-up shell of cold material via a Kelvin-Helmholtz instability. The shell loses its smooth elliptical form and develops "ripples" at its tops. The dynamical pressure of the hot gas (note that its velocity is much higher than in the case of a hypernova explosion) accelerates the "rippled" shell. As a consequence, the shell shows a strong Rayleigh-Taylor instability via the development of a characteristic `spike-and-bubble' morphology, as is seen in the left panel of Fig. 5. In the case of a hypernova explosion of the same total energy, the gas velocity field plotted in the right panel of Fig. 5 lacks any circular motion inside the shell. The smooth elliptical shell of cold material of roughly the same size as in the case of multiple SNe expands at roughly the sound speed. The shell has already started losing its pressure support (as implied by the thickening of the shell walls) due to radiative cooling of its hot interior. As a consequence, the decelerating shell does not develop a Rayleigh-Taylor instability and the blowout phase is not observed. We note here that a hypernova-driven shell expands out to a certain radius faster than a shell created by multiple SNe with the same total energy, as reported by Efremov et al. (1999). Our numerical simulations have shown that the difference in the dynamics of shells produced by multiple SNe and a single hypernova of the same total energy intensifies as one considers more flattened gas systems. The maximum difference is found in the strongly vertically stratified gas distributions assumed for massive spiral galaxies. The vortex forms since the shell becomes elongated in the vertical direction. Consider the simplified situation of hot gas ejected radially by SNe which is reflected from the cold dense walls of the elliptical shell. The gas will not be reflected along the local normal direction to the shell unless it is moving along z = 0 or r = 0. In general, a tangential component of the velocity of hot gas vt (with respect to the shell's walls) is generated. It is always directed upwards for gas above the midplane and downwards for gas below the midplane. Let us consider the upper hemisphere. The occurrence of vt = 0 near the shell walls and the axial symmetry of the shell makes the hot gas (streaming upwards along the shell walls) accumulate at the top of the shell, because it cannot pass through the symmetry axis. Both the growing pressure of this hot gas (due to its negligible cooling) and the downward pull of the z -component of the galactic gravitational field lead to a downward flow along the axis of symmetry. This completes the circle and generates a vortex structure as seen in the left panel of Fig. 5. The development of such vortices is also seen in the axially symmetric numerical simulations of Recchi et al. (2001). However, a strong non-axisymmetry of the SNe-driven shell may complicate the formation of the vortex. The driving force for the vortex is a continuous or quasi-continuous release of energy by SNe of a stellar cluster or a group of closely located stellar clusters. This is also


6

E. I. Vorobyov, S. Basu: Formation of giant HI rings

the reason why vortices do not form in a shell created by a single hypernova explosion. We have found that the vortex develops even when the number of SNe is quite moderate ( 20) and the release of energy is discrete. The length scale of the vortex is approximately equal to the shell's semi-minor axis and time scale is limited by the duration of energy input from SNe, i.e. < 30 Myr. In general, at least two vortices can co-exist within a single shell: one in the upper hemisphere and the other in the lower hemisphere of the shell. Hypernovae tend to form complete shells. Such shells would appear in nearly face-on dwarf galaxies as HI rings with a low ring-to-center contrast in the HI column density. For instance, in Fig. 6 we plot the contrast in the HI column density between the ring and the central depression, K = Nr (H I )/Nc (H I ), as a function of the ring radius R obtained for three different energy inputs. The ring column density Nr (H I ) is computed by azimuthally averaging N (H I ) around the ring. An inclination angle (i.e. the angle between the rotation axis of the galaxy and the line of sight) of i = 5 is assumed, which is appropriate for a nearly face-on galaxy. The solid lines give the contrast K for the multiple SN explosions, whereas the dashed lines do that for the hypernova explosion. As is seen, the ring-to-center contrast K produced by the hypernova explosion never exceeds 10 even for the upper limit energy of hypernova explosions of 1054 ergs. On the other hand, multiple SNe can form HI rings with a much higher ringto-center contrast K < 100. The latter takes place when the SN-driven shell is in the blowout phase. Note that the difference in K between the HI rings produced by multiple SNe and those produced by hypernovae smears out if the total released energy is 2 â 1053 ergs.

4.1. PV-diagrams
The position-velocity (pV) diagram is a powerful tool to search for coherent structures in the interstellar medium. In this section we compute model pV-diagrams in order to determine their utility for distinguishing between the SN-driven shells and those produced by a hypernova explosion of the same total energy. The HI flux density SHI is obtained using the following conversion formula (Binney & Merrifield 1998): M
HI

Fig. 6. The contrast in the HI column density between the ring and the central depression K = Nr (H I )/Nc (H I ) as a function of the ring radius. The solid lines show the contrast K produced by multiple SNe, whereas the dashed lines show that produced by a single hypernova of the same total energy. An inclination angle of 5 is assumed. The energy input is indicated in the right upper corner of each panel. The dashed-dotted and dotted lines in the lower panel give the contrast K for an inclination angle of 45 .

v

= 2.35 â 10

5

D Mpc

2

SHI Jy

M km s

-1

,

(5)

where for the distance D we take 3.5 Mpc, appropriate for Holmberg I. The position-velocity cuts are taken along the ma jor axis of the pro jected shell. The width of the cuts is 30 pc. We tried twice wider cuts (60 pc), but found little difference in the appearance of the resulting pV-diagrams as compared to those obtained with narrower cuts. The gas is assumed to be thermalized when constructing the model pV-diagrams, i.e. a Maxwellian velocity distribution is assumed for the gas in each computational cell, with the scale determined by the local gas temperature

(see Mashchenko & Silich 1995). No attempt was made to include the effects of turbulence. The model galaxy is assumed to have an inclination angle of 5 . The positionvelocity cuts along the minor axis of the pro jected shell have similar appearance for such low inclination angles. Figure 7 shows the model pV-diagrams of the shell produced by 500 consecutive SNe. The quantity SHI is plotted in all model pV-diagrams. Two bright blobs elongated in the vertical direction are apparent in each pV-diagram. They represent the dense walls of the shell expanding in the plane of the galaxy, i.e. perpendicular to the line of sight at the adopted inclination angle of 5 . If the shell has not yet broken out of the disk (t = 9 and 18 Myr), these two blobs appear to close at their tops and form a complete elliptical ring. The relative amplitude of SHI around the ring is however varying by roughly an order


E. I. Vorobyov, S. Basu: Formation of giant HI rings

7

ciple, be detectable. Hypernova explosions tend to form complete shel ls that are clearly visible in the pV-diagrams. This characteristic feature of a hypernova-driven shell is also present when one considers very energetic explosions. For instance, Fig. 9 shows the pV-diagrams of the shell produced by a hypernova of the total energy of 1054 ergs. The elliptical hole surrounded by the ring is clearly seen even when the shell has already started to collapse at t = 45 Myr, as implied by the presence of a vertical bar at zero radial offset (see the lower right panel in Fig. 9). Note the size of the shell in Figs. 8 and 9. It is twice the local Gaussian scale height h, which is 350 pc at a galactocentric radius of 0.5 kpc in our model galaxy. The comparison of Fig. 7 and Figs. 8, 9 indicates that the SNe-driven shell in its late expansion phase (when its radius exceeds 1.5 h) may be distinguished from that produced by the single hypernova explosion based on its appearance in the pV-diagrams. The pV-diagrams of the hypernova-driven shell show the characteristic elliptical ring in virtually any evolutionary phase of the shell, whereas the pV-diagrams of the SN-driven shell do that only in the early expansion phase, well before the blowout. The present numerical simulations (see also Vorobyov & Shchekinov 2004) show that the SN-driven shell breaks out of the disk when its radius exceeds 1.5 h. As a consequence of the blowout, the SN-driven shell transforms into an open cylinder and the pV-diagrams show two parallel blobs representing the walls of the expanding cylindrical shell. On the contrary, the hypernova-driven shell appears to survive the expansion even when its radius exceeds 2.0 h. As a result, the characteristic elliptical ring representing the complete expanding shell is clearly seen in the pV-diagrams. Thus, if the pV-diagrams show an elliptical hole surrounded by a denser ring, the radius of which is greater than 1.5 h (as in the lower frames of Fig 8 and 9), this may indirectly point to a hypernova origin of the shell.

Fig. 7. The pV-diagrams of the shell created by 500 consecutive SNe. The pV-cuts are taken along the ma jor axis of the model galaxy viewed at an angle of 5 . The evolutionary time of the shell is indicated in the right upper corner. The quantity SHI is plotted in all model pV-diagrams.

of magnitude, reflecting the difference in the HI column density along the ma jor axis of the pro jected shell ­ there is much less gas on the approaching and receding sides of the shell than on those expanding perpendicular to the line of sight. The elliptical ring is virtually absent in the later expansion phase at t = 36 and 45 Myr when the