GK Workshop - J. Palous

Proceedings of the Workshop
"The Magellanic Clouds and Other Dwarf Galaxies"
of the Bonn/Bochum-Graduiertenkolleg

Holes and Shells in Galaxies:

Observations versus Theoretical Concepts

Jan Palous

Astronomical Institute, Academy of Sciences of the Czech Republic,
Bocní II 1401, 141 31 Prague 4, Czech Republic

Received 03rd April 1998

Abstract. Shells and holes discovered in the distribution of H I in the Milky Way and nearby galaxies within 10 Mpc are reviewed. To interpret the data, the hydrodynamical equations in 1D and 2D, and equations describing the expansion of infinitesimally thin shell in 2D and 3D, have been used. The abundance and distribution of holes and shells in the Milky Way, Magellanic Clouds, and other nearby galaxies are discussed and conditions for shell fragmentation and propagating star formation are evaluated.

1. Introduction

The H I distribution in spiral and dwarf galaxies shows coherent structures on scales from 10 pc up to 1-2 kpc. The lower limit is due to the limited angular resolution of radiotelescopes: the highest linear resolution below 10 pc can be achieved for H I in the Milky Way or nearby galaxies only with the largest single dish or synthetic telescopes.

The observed structures demonstrate the relation of stars to the interstellar medium. They are like footprints left in the interstellar medium after recent star formation. Particularly massive young stars strongly influence the ambient medium with stellar winds, ionizing radiation and supernova explosions. Single massive stars can be responsible for structures at scales of a few ×10 pc and expansion energies 10⁵⁰-10⁵¹ erg. At larger scales of a few ×100 pc and expansion energies 10⁵¹-10⁵³ erg an OB association composed of 10-100 stars may be the progenitor. However, even larger structures of 1 kpc or more in diameter involving expansion energies 10⁵³-10⁵⁶ erg or more can not be explained as due to a single OB association. The energy source can be a coeval group of several OB associations composed of 1000 or more massive young stars, called a star complex, or an encounter between the galactic H I plane and a high velocity cloud, or an infalling dwarf galaxy.

In this contribution we give a review of H I observations in the Milky Way and nearby galaxies up to 10 Mpc in distance, where the expanding shells, supershells and H I holes have been identified. Also the theoretical concepts and computer simulations interpreting the data are reviewed. Expanding shells may fragment and form new molecular clouds, which can be the seeds of new star formation. This cycle of propagating star formation is the mechanism connecting single star forming events to the large-scale structures in galaxies.

2. Discovery of H I Shells and Holes

The shells and supershells have been discovered in the Weaver and Williams (1973) H I survey of the Milky Way by Heiles (1979) as the filamentary arc-like structures appearing in successive radial velocity channels in the H I intensity maps. The expansion velocity of a shell is defined as 1/2 of the maximum radial velocity difference between the channels where the feature can be detected. The distinction between shells and supershells is given by the energy E₀, which Heiles (1979) estimated, using Chevalier's (1974) formula, to be necessary for their creation. The largest objects with E₀ > 3·10⁵² erg are designed as supershells. Later Heiles (1984, 1987, 1990, 1992), Koo et al. (1992) and Heiles et al. (1996) defined also narrow structures perpendicular to the galactic plane called chimneys or worms and related shells to OB stars and clustered supernovae.

The H I observations have been also extended to external galaxies and uncovered the depressions in the H I distribution called H I holes. They have been discovered in M31 (Brinks & Bajaja 1986), M33 (Deul & Hartog 1990), M101 (Kamphuis et al. 1991), Ho II (Puche et al. 1992), NGC 628, M81, NGC 4631, NGC 6996 (Kamphuis 1993), IC 10 (Shostak & Skillman 1989) and IC 2574 (Walter & Brinks 1998). The reviews on the H I observations are given by Brinks (1990) and van der Hulst (1996).

3. Sedov Approximation

Highly supersonic expansion of the shocked interstellar medium around an OB association is an example of an astrophysical blastwave (Ostriker & McKee 1988; Bisnovatyi-Kogan & Silich 1995). After an initial period dominated by stellar winds, radiation and supernovae, the thin and relatively cold shell surrounding a hot bubble develops. It expands while accumulating the ambient interstellar medium. The thickness of the shell is much less than its diameter, which gives an opportunity to apply the infinitesimally thin shell approximation invented by Sedov (1959) and Kompaneets (1960).

Using a dimensional analysis, Sedov (1959) derived the solution of the equation of motion of a strong shock propagating into the ambient medium: [Eq. (1)] where m and v are the mass and expansion velocity of the shell, S is its surface and P_int, P_ext are the pressures inside and outside of the shell. The adiabatic expansion with no external pressure, P_ext = 0, and an abrupt energy input gives in the case of spherical symmetry [Eq. (2)] where R is the radius of the shell, n₀ is the density of the ambient medium and t is the time since the beginning of expansion. For cylindrical symmetry the solution changes to [Eq. (3)] and for spherical symmetry and continuous energy input to [Eq. (4)] where [Formula] is the supernova rate and E_SN is the energy release per one supernova.

4. Computer Simulations: Chevalier's Formula and other Expansions

In the case of spherical symmetry, the one dimensional numerical solution of hydrodynamical equations has been achieved by Chevalier (1974). For adiabatic expansion in the homogeneous ambient medium with no external pressure and without cooling he confirms the analytical solution of Eq. (2). If the external pressure and cooling is considered, the expansion is slower: R∼t^0.31 and v∼t^-0.69. Eliminating the time between R(t) and v(t) Chevalier (1974) did obtain the formula [Eq. (5)]

which has been used later by Heiles (1979) and many others to estimate the initial energy E₀ necessary for the shell formation. We have to stress that the above formula Eq. (5) is derived from one-dimensional hydrodynamical simulations using the assumption of spherical symmetry. Therefore, any application to non-spherical situations such as blow-out bubbles, chimneys and worms does not give correct results.

Using the hydrodynamical ZEUS code in two dimensions, Mac Low & McCray (1988) and Mac Low et al. (1989) did confirm the applicability of the infinitesimally thin shell approximation. Also the large scale density gradients in the ambient medium have been introduced demonstrating the rôle of the stratification in the z-direction perpendicular to the plane of the galactic disk: in the stratified medium the blow-out of the shell to high z distances from the galactic plane may happen.

The computer simulations using the infinitesimally thin shell approximation in 2D, which are also called 1+1/2 dimensional, have been performed by Tenorio-Tagle & Palous (1987) and Palous et al. (1990). They include the galactic differential rotation. For abrupt energy input the results give [Eq. (6)] where r is the semi-minor axis of the elliptical shell, and t_ref is the reference time, which is inversely proportional to the epicyclic frequency at the galactocentric distance of the expansion center. In the beginning of expansion, when the shell is not substantially deformed by the galactic differential rotation, is the expansion similar to the Sedov analytical solution of Eq. (3) for cylindrical symmetry. This is due to the fact that in this 2D simulation the z-distribution of the ambient medium has been disregarded. Later, when the galactic differential rotation starts to be important, the expansion in r decelerates to zero, and even later, when t approaches to t_ref, r declines to zero and the shell degenerates to a line.

The thin shell approximation in 3D, which is called 2+1/2 dimensional, has been developed by Palous (1990, 1992) and Silich et al. (1996). Besides galactic differential rotation and z-stratification of the galactic ambient medium, also cooling and evaporation of small preexisting interstellar clouds is included. When a small (∼3 pc) cloud is engulfed by the shell, it is surrounded by the hot medium, and it starts to evaporate. Due to the evaporation the number of atoms inside of the shell growth, rising the importance of cooling, and increasing the X-ray luminosity of the bubble.

5. H I in Galaxies seen at high angular resolution

To achieve high angular resolution, the interferometric observations of the SMC have been performed with the Australian Compact Array by Staveley-Smith et al. (1997). If all the structures are real and not related to the interference patterns, an extremely complex sponge-like distribution composed of many interconnected holes and interacting shells has been discovered.

The abundance of holes in galaxies can be measured using a two or three dimensional porosity parameters Q_2D and Q_3D (Oey & Clarke 1997). For LMC, M31, and M33 these parameters are smaller than 1, which means that these galaxies are not strongly dominated by the hot medium of the bubbles. Another situation is in Holmberg II observed with the VLA by Puche et al. (1992), where Q_2D≥1. It means that this dwarf galaxy is hot medium dominated. Recent observation of the LMC by Kim et al. (1998) with the Australian Compact Array shows a jungle of H I tunnels, holes and expanding shells. The reality of these structures should be checked, and it would be interesting to get Q_2D and Q_3D parameters and compare LMC with SMC, Ho II and other galaxies.

A more complete statistics of H I holes and shells in the Milky Way is still missing. The angular resolution and sensitivity of Weaver & Williams (1973) and Leiden-Dwingeloo H I surveys (Burton & Hartmann 1994) are not high enough to see all the structures. Only selected fields along the galactic plane have been observed up to now with the Effelsberg 100 m radiotelescope: Braunsfurth & Reif (1984) did the Cassiopea - Perseus region and Ehlerová et al. (1998) a field of 4°×4° in Vulpecula. In the last region 8 new shells have been identified by Ehlerová (1998). Two of them are described by Ehlerová & Palous (1998) and another two are presented in Fig. 1 and 2.

The structure GS62.1+0.2-18 (Fig. 1) is quite complete elongated shell at the distance 9.6 kpc from the Sun, which transforms to the linear size of 170×110 pc². With the expansion velocity ∼13 km s^-1 and density of the ambient medium ∼0.3 cm^-3 we get from Chevalier's formula of Eq. (5) for the energy necessary for its formation E₀ = 1.3·10⁵¹ erg. This energy can originate in a few massive stars of an OB association. A comparison with the simulations shows an expansion age of the structure ∼10 Myr, which can explain why no massive stars remain visible inside of the shell.

The second shell, GS60.1-0.3+15, which is presented in Fig. 2, resides, taking a kinematical distance derived from the galactic rotation curve, either at the distance 1.4 or at the distance 7.9 kpc. Smaller distance seems to be more reasonable since a lot of small structures probably related to individual stars of Vul OB 1 association can be distinguished. In this case its size is ∼50 pc and the size of the substructures ∼10 pc. The overall expansion velocity ∼11 km s^-1 implies for the initial energy ∼1.3·10⁵⁰ erg corresponding to one single supernova only and the expansion time ≤3-5 Myr. A possible scenario can be that the shell is due to the first supernova of an OB association and the substructures correspond to energies released by stellar winds or supernovae by other members, which does not yet succeed to deliver their contributions to the main shell.

[Click here to see Fig. 1!]

[Click here to see Fig. 2!]

6. Shells in Spiral and Dwarf Galaxies

6.1. Distribution of Shells in the Milky Way

The distribution of shells and supershells identified in the Milky Way by Heiles (1979) has been discussed by Ehlerová & Palous (1996). The balance equation between the formation and extinction rates of shells at the galactocentric distance R_g is [Eq. (7)]

where σ(R_g) is the shell formation rate, n(R_g) is the number of shell in the galactocentric annulus of the width Δ R_g, and τ(R_g) is the typical age of shell at R_g. Assuming an equilibrium between shell formation and extinction we have [Eq. (8)]

Inserting Eq. (8) into Eq. (7) we get [Eq. (9)]

Substituting the values τ(R_g) derived from 3D computer simulations using the thin shell approximation, and values of n(R) derived from observations (Ehlerová & Palous 1996) to Eq. (9), we get the values of σ(R_g), which can be fitted with a formula [Eq. (10)]

We conclude that the radial scale length (4.2±0.3) kpc of the shell formation rate is close to the radial scale length of the stellar disk of the Milky Way indicating that the formation of the majority of shells in the Milky Way is related to the star formation rather than to the infall of HVCs.

6.2. Disc Halo Connection

The z-distribution of the ambient medium plays the key rôle: the bubbles can blow out to the galactic halo if the H I disk is sufficiently thin. With the same expansion energy, the thick disk confines a shell or supershell to |z| < 1 kpc. In a thin disk the shell blows out to large distances from the H I disk.

With a Gaussian z distribution [Eq. (11)] where σ_z is the disk thickness. The results of 3D simulations using the thin shell approximation after 60 Myr of expansion are given for the thick disk (σ_z = 500 pc) in Fig. 3. In this case is the hot medium of the bubble inside of an egg-like shell with walls, which are almost perpendicular to the plane of the galaxy. This type of bubbles and shells form in dwarf galaxies, which rotate only slowly, and where a typical disk thickness is ∼500 pc.

[Click here to see Fig. 3!]

The results for thin disk (σ_z = 200 pc) are given in Fig. 4. This case does not confine the hot medium to the galactic plane. Extended lobes at high z distances from the plane filled with hot gas are formed. The expansion can provide the hot coronal gas observed in the galactic halos, which may be enriched by heavy elements since the gas originates in star forming regions in the galactic plane. This type of bubbles and shells form in rapidly rotating spiral galaxies, with a thin H I disk of the thickness ∼200 pc or less.

[Click here to see Fig. 4!]

The high column density parts of the shells in spiral galaxies remain always near to the plane forming a conical shape as seen in Fig. 4. Similar shapes have been found in the Milky Way, e.g. Aquila supershell (Maciejewski et al. 1996) or the shell GS60.0-1.1-54 (Ehlerová & Palous 1998). Only a small fraction of the mass collected in a supershell is pushed to high z. The amount of gas in the high-z caps of the blow-out supershell is ≤ 1% of the total. From the distribution of the supershells in the Milky Way we found that in total there is ∼400 supershells pushing ≤ 0.5 M_sun yr^-1 to high z (Palous et al. 1995). This is an upper limit to the mass flow related to star formation in the disk of the Milky Way, which gives a restriction to the galactic fountain model of Norman & Ikeuchi (1989). We can conclude that only a small fraction of the high velocity clouds can be explained as due to the galactic fountain.

7. Propagating Star Formation

Conditions for the instability and the fragmentation of expanding and decelerating shells have been discussed by Ehlerová et al. (1997). The linear perturbations of transverse motions on a three-dimensional shell expanding into a uniform ambient medium have been discussed by Elmegreen (1994) and Vishniac (1994). The stretching of the perturbed region due to expansion may be compensated by the convergence of the flow due to own gravity of the shell if the maximum growth rate of a transverse perturbation ω > 0. [Eq. (12)]

where R is the radius of the shell with the mass column density Σ, v is its velocity of expansion relative to the ambient medium, c is the sound speed within the shell, and G is the constant of gravity.

ω can be evaluated in a 3D computer simulation using the thin shell approximation. In the beginning of expansion, when v is large and R is small ω is always negative, and the shell is stable. The stretching due to expansions is at early stages of rapid expansion much more important than own gravity of the shell. Later v decreases and R increases, so that the first negative term in Eq. (12) becomes less important, and at the same time Σ increases so that the second gravity term in Eq. (12), which is always positive, becomes more important. As soon as, at the expansion time t_b, ω starts to be positive we evaluate the fragmentation integral I_f(t): [Eq. (13)] At the time t = t_f when I_f(t) = 1 the fragments are well developed, so that star forming clouds may form at a later time.

The values of the fragmentation integral at 60 Myr of expansion in the thick and thin H I disk case are given in Fig. 5. In dwarf galaxies having a thick H I disk the fragmentation occurs in nearly whole shell while in spiral galaxies with thin H I disk it is restricted to a narrow belt at the galactic equator.

This is related to the conclusion of Theis et al. (1998) and Ehlerová et al. (1998) that the fragmentation can occur only when the shell expands into density gradient flatter than an isothermal profile. In the case of steeper density gradients the dilution due to expansion can not be compensated by gravity of the agglomerated mass and the shell becomes more and more stable.

Unstable fragments may become molecular and trigger the formation of molecular clouds where new stars are formed. We can conclude that in dwarf galaxies like Ho II, the star formation may propagate in all directions, so that the whole galaxy soon becomes hot medium dominated, and the system turns into a starburst. On the contrary in spiral galaxies, the star formation propagates only in some directions in the thin strip near the maximum H I density plane. Young stars form larger spiral-like structures several kpc in size, however, the galaxy does not increase the overall star formation rate dramatically, but keeps it constant for rather long time (Palous et al. 1994).

[Click here to see Fig. 5!]

8. Conclusions and what should be done in the future

The holes and shells in nearby galaxies have been discussed. They give an evidence for the recent star formation and energy input from young stars structuring the interstellar medium. The expanding shells may fragment and form new molecular clouds and propagate the star formation from one site in the galaxy to another site.

In the future, we need to verify the conclusions on shell fragmentation in a more detailed analysis taking into account the finite thickness of the expanding shell. This computation should be done with the hydrodynamical equations including the self-gravity of the shell. To mimic the complex network of holes and shells detected in galaxies (Staveley-Smith et al. 1997; Kim et al. 1998) also effects from cloud × cloud, cloud × shell and shell × shell collisions should be considered.

Star formation drives shells and supershells forming the fractal structure of the interstellar medium leading to further star formation. The propagating star formation cycle should be examined in a self-consistent way and compared with properties of nearby and distant galaxies. This may give us the chance to see the importance of star formation for the galactic evolution.

Acknowledgments. I like to thank Sona Ehlerová for preparation of figures. The author gratefully acknowledges financial support by the Grant Agency of the Czech Republic under grant No. 205/97/0699 and support by the grant project of the Academy of Sciences of the Czech Republic No. K1-003-601/4.

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