This section is the heart of your paper. It describes in detail just what you are planning to do with the data and evidence you have now accumulated. The reader has been very patient going through all of the previous sections, so you had better make this section 'sing'.
The Discussion section describes how you have interpreted the direct observations, and the derived quantities you presented in the previous section. This interpretation should lead the reader to some new insight to your particular research area, perhaps a re-determination of some critical constant used by astronomers, a new refinement to the theory of how stars are formed, or a proof that some previously-held understanding is incomplete or incorrect in some fundamental way.
Several mechanisms have been proposed to account for filamentary or comet-like morphologies among certain types of interstellar clouds. McKee and Cowie(1975), in their description of the interaction between a supernova blast wave and an HI cloud, describe the production of 'quasi-stationary flocculi' with convex shapes centered on the supernova remnant. A subsequent hydrodynamical study by Woodward(1976) showed that shock fronts may cause molecular clouds to break up into dense filaments of compressed gas due to Rayleigh-Taylor or Kelvin-Helmholtz instabilities. Reipurth(1983) has also proposed that some cometary clouds owe their shapes to passing ionization fronts from nearby OB stars that evaporate molecular clouds, exposing their dense cores as Bok globules. The 'tails' represent material left over from the original cloud that was shielded in the 'shadow zone' behind the cores.
A common feature of these models is that they involve the passage of a shock front through a pre-existing, quiescent cloud which is initially at rest relative to the pre-shock ISM. Although this mechanism may be effective for describing the origin of cometary clouds near supernova remnants or OB associations, most of the 15 clouds in this survey are not situated near supernova or OB associations. A particularly exceptional case is the Draco cloud located in an isolated region of the sky well above the plane of the Galaxy. The Draco cloud has a pronounced filamentary appearance with a nuclear, comet-like core. The cloud core is not known to be gravitationally bound (MBM), and material appears to be flowing from the core leaving behind filaments. Its morphology has been described by Odenwald and Rickard(1987) as the result of a high velocity molecular cloud apparently interacting with the ambient medium at low Reynolds number.
The generation of cometary or filamentary extensions as a result of the rapid motion of a cloud through the ISM has an obvious advantage over other sculpting mechanisms involving external shock fronts or ionization fronts. External sources for the shock fronts, such as OB associations or supernova remnants, are not required. Provided that the cloud is not gravitationally bound, and that the viscosity of the surrounding gas is high enough, ablation of gas from the cloud can be expected to occur. If the Reynolds number of cloud- ISM system is low enough, the ablation flow will be filamentary. For the Draco cloud, these conditions appear to be satisfied. For an ambient medium with a temperature near 1 million degrees K, and a density of about 0.02 cc, the viscosity of this fully-ionized gas will be high enough to insure that for a cloud with V = 35 km / s and length = 2 pc, Re = 15 as suggested by the morphology of the filamentary plumes. At higher Reynolds numbers, the flow will be highly turbulent and appear as a diffuse, featureless, plume. If the velocity of the cloud relative to the ambient medium is supersonic, the cloud may even develop a conical shape indicative of a 'Mach cone'.
We now consider the morphological consequences of a rapidly moving cloud interacting with the interstellar medium, and whether such a mechanism can explain the appearances of selected clouds in this survey. Attention will be focussed on 4 clouds: G110-13, G225- 66, G315+21 and G359-17 since they share features in common with the other clouds in this sample, or otherwise, have already been studied in detail at other wavelengths.
a) Cometary Clouds
G110-13 and G315+21, shown in Figs. 4(a) and 4(b), display a pronounced head-tail appearance with a relatively smooth and unstructured tail. The conical shape of the nuclear regions are similar to those of the clouds associated with the Gum Nebula. They are also reminiscent of the lobes of extragalactic radio sources where ram pressure confinement is believed to be the sculpting agent (deYoung and Axford, 1967).
In the deYoung-Axford model (see Pacholczyk, 1977) a gas cloud moves with velocity V through a medium with a density rho(ISM). For a thermal plasma with no entrained magnetic field, the hydrostatic pressure distribution within the cloud is given by P = P(0) exp(-z/h) where P(0) is the stagnation pressure at the head of the cloud, and z is the distance along the axis of the cloud. The quantity, h, is the scale height of the gas within the cloud given by h = rho(ISM) V^2 / Rho(0) g where Rho(0) is the density of the cloud at the stagnation point, V is the velocity of the cloud and g is the cloud deceleration. The cloud shape is given by Formula 4. Additional relations that may be derived for such a cloud are :
where N is the ambient medium density in cc, h is in parsecs, V is in km / s and n(0) is the cloud density in units of 1000 / cc.
Using the predicted shape of the cloud as a function of h, the optical images of G315+21 and G110-13 can be fitted by choosing h near 0.5 pc in the former case and h near 0.25 pc in the latter. The density of the ambient medium, N, can be estimated by using the parameters based on the HI data reviewed by Burton(1976). For an intercloud medium with an HI density of about 0.17 / cc in the galactic plane, a 125 pc exponential scale height, and a distance above the galactic plane for G315+21 of 300 pc, one obtains N = 0.17 exp(-300/125) = 0.07/ cc. A similar calculation for G110-13 yields N = 0.10 cc. The cloud density for G315+21 is n = 1000 / cc (n(0) = 1) based on the CO and far- IR column densities. Although CO data are not available for G110-13, it has a similar 100 micron optical depth and is assumed to have n ~ 1000 / cc (n(0) = 1) as well. The space velocities of these clouds through the ISM are difficult to determine. In the case of G315+21, VLSR = -6 km/s so that if the remaining two velocity components are also of this magnitude, the total space velocity is V = 10 km/s. The velocity for G110-13 is unknown so we will assume for the time being that it is similar to that for G315+21. From Eq. 4 we deduce for G315+21; M = 25 M(sun), the stopping time is 2 million years and the stopping distance is 5.3 kpc. Similar calculations for G110-13 imply that; M = 3 M(sun), t(stop) = 720,000 years and the stopping distance is about 1.8 kpc.
The cloud masses for G315+21 and G110-13 of 25 and 3 M(sun), derived using Eq. 4(a), can be reconciled with their masses derived from the far-IR data provided that new distances are assumed for the clouds. The mass determined by Eq. 4(a) scales as d^3 where d is the distance to the cloud. The mass determined from the far-IR column density scales as d^2. If the clouds were placed at 1 kpc and 850 pc respectively, Eq 4(a) and the far-IR data would yield mass estimates of 740 and 170 M(sun). It is also of particular interest that the luminosity of G315+21, at 1 kpc, would be 570 L(sun) comparable to that of a B5 V star (Allen, 1981) in agreement with the inferred spectral types of the embedded stars as determined by TLD. For G110-13, the adjusted far-IR luminosity would be 170 L(sun) which is similar to the expected luminosity from the embedded B9 V star ( 125 L(sun)). Based on the far-IR data, the viability of the deYoung-Axford model, and the estimated luminosities of the embedded stars, G315+21 and G110-13 are probably distant clouds with masses of 740 and 170 M(sun).
The appearances of G315+21 and G110-13 are also reminiscent of 'Mach cones' which form at the leading edges of objects moving supersonically through the ambient medium. The cone angle, Theta, defined as the angle formed by the edges of the cone projected to a convergent point ahead of the cloud, is related to the Mach number, M, via sin(Theta/2) = 1/M. For G315+21, Theta = 30 degrees so M ~ 3.8 while for G110-13, Theta = 10 degrees and M = 11. If the space velocity for each of the clouds is 10 km / s, the Mach numbers suggest that near G315+21, the sound speed Cs = 2.6 km / s and for G110-13, Cs = 0.9 km / s. Since Cs = 0.0928 T^0.5 km /s , one deduces that G315+21, located 105 pc above the galactic plane, is embedded in an ISM where T = 780 K so that M = 3.8, whereas the ambient medium near G110-13 , located 45 pc above the plane, is only T = 95 K so that for V = 10 km / s, M = 11. The temperature derived for the ambient medium near G110-13, is comparable to the temperature generally assumed for the intercloud HI in the galactic disk.
The apparently supersonic motion of the clouds through the local ISM not only accounts for their comet-like appearance as predicted by the deYoung-Axford model, but also explains why such low-mass clouds can be such efficient star forming regions. The shock front produced by the cloud's supersonic motion appears to have assisted in the triggering of star formation events in the cloud cores due to the shock-induced over-pressure. A related phenomenon has also been identified in hydrodynamic calculations by Sandford, Whitaker and Klein(1982). The Jeans mass is given by MJ = 1.2 T(gas)^0.666 n(0)^0.5 M(sun) where T(gas) is the gas temperature within the cloud and n(0) is the cloud gas density in units of 1000 / cc. For the two clouds in question, if T(gas) = 20 K, MJ = 11 M(sun). For each cloud, the Jeans masses are comparable to, or less than, the masses of the clouds deduced from the deYoung-Axford scenario when allowance is made for the masses of the stars already formed. This implies that a significant fraction of the mass in these clouds was originally unstable to gravitational collapse, requiring only an external compressive agency to initiate collapse. The shock produced through the cloud's supersonic motion may well be that agency.
b) Filamentary Clouds
G359-17, shown in Fig. 5, is similar to G315+21 in that both objects are associated with prominent optical emission nebulae and are near local maxima in the soft X-ray background. They differ, however, in that while the optical photograph of G315+21 has a relatively featureless tail, G359-17 has one that is filamentary and sinuous. The optical tail of G359-17 extends to the east of the R CrA region and is not coincident with the tail apparent in the far-IR image which extends southwest of R CrA. Unlike the other objects in this survey, the optical photograph of G359-17 shows a stronger and more elaborate filamentary structure at optical wavelengths than at 100 microns.
The general optical appearance of G359-17 is not unlike that observed in Type-1 solar system comets such as Morehouse 1908 III. In these comets, filamentary plumes or rays with a scalloped or sinuous shape trail the nucleus, and are composed of ions rather than dust grains. The pronounced optical filaments in G359-17 not correlated with 100 microns emission from dust grains, suggest that they may also be artifacts of a primarily ionized gas component of this cloud. Does the apparent similarity of G359-17 with Type-1 solar system comets belie a common dynamical origin for these filamentary structures, though at a scale 1 billion times greater? To explore this possibility, we need to provide answers to three questions: What are the mechanisms currently proposed to account for Type-1 tail morphology? Can they be scaled-up to the dimensions of G359-17? ,and, How do the known physical conditions in the environment of G359-17 compare with the scaled-up results?
Alfven(1957) suggested that the shape of the Type-1 comet tails may be due to magnetohydrodynamic waves generated near the comet's nucleus propagating through the ionized gas in the tail. Ip and Axford(1963) described the generation of plasma instabilities in a comet's bow shock due to sudden changes in the local solar wind. They showed that the growth of long wavelength flute instabilities, leading to filaments with a scalloped, sinuous appearance, will probably not occur in the presence of a quiescent wind. During high wind conditions, however, the growth time for the flute instability can be shorter than magneto-sonic crossing timescales, and the tail becomes unstable to the formation of sinuous or scalloped filaments. Ershkovich(1980) also investigated the evolution of MHD instabilities in Type-1 tails and concluded that for a likely range of solar wind and tail parameters, Type-1 tails are Kelvin-Helmholtz unstable. This implies that they can be expected to show wave-like morphologies due to plasma instabilities.
The growth time of flute instabilities is given by Ip and Axford(1963) as shown in Formula 5 where RBis the radius of curvature of the field lines, Te and Ti are the electron and ion temperatures, and L is the length scale of the density gradient. As an example, for comets in a quiescent solar wind, L = RB = 1000 km, mi = 20 m(proton) and k (Te + Ti ) ~ 1 ev so t ~ 300 sec. This is greater than the Alfven wave propagation time scale ( assuming B = 500 micro Gauss, N = 1000 / cc) or the sound speed crossing time, so the comet tail is stable against the formation of flutes. Under high wind conditions, however, solar wind compression can cause RB and L < 1000 km so that tf < 300 sec. The flute growth time is thereby shorter than Alfven or thermal timescales and the tail becomes unstable to the growth of flutes.
In the case of G359-17, a similar timescale calculation can be performed. For RB ~ L ~ 1 pc, Te ~ Ti ~ 10,000 K, and mi ~ m(proton), one obtains tf ~ 74,000 years. The thermal diffusion timescale is L/10 km /sec ~ 100,000 years and the Alfven timescale is 400,000 B^-1.0 n^0.5 yrs. Provided that the field strength within the filaments B < 6 micro Gauss, a flute instability in the tail of G359-17 may be able to grow faster than it can be damped out on thermal or Alfvenic timescales.
Does the structure in G359-17 represent a gas dynamical or magneto-hydrodynamical phenomenon at work? The distinction is, largely, one of the mean free path (mfp) of the particles in the ambient medium relative to the scale of the system. Assuming the ambient medium to be fully ionized, the mfp of ionized gas is given by Lang(1983) as Formula 6 where T is the ambient medium temperature, Z is the electronic charge, N is the particle density in cc^-1 and ln(S) is the coulomb logarithm term taken to be ~ 30. The mfp will be less than the ~ 2 pc scale of the cloud head for T^2 N^-1 < 6 x 10^13 , a constraint easily satisfied if N > 0.01 /cc and T < 10^6 K. This is also a very general result. Provided that the sizes of the clouds in the ISM are < 3 pc, the ISM will behave more or less as a fluid for nearly all combinations of T and N currently favored for the various components of the ISM.
The distinction between hydrodynamics and magnetohydrodynamics can be decided by comparing the thermal pressure of the gas in the filaments P = nkT with that of the pressure due to the magnetic fields within the cloud, P = B^2/8pi. The study by Vrba, Coyne and Tapia(1981) suggests that B < 150 micro Gauss so that the pressure normal to the field lines is P < 9 x 10^-10 dynes/cm^2. This will exceed the thermal pressure in the filaments for nT < 6.5 x 10^6. If the filaments are ionized, T~ 10,000 K and so n < 650 /cc. If the filaments are cold so that T ~ 20 K, then n < 3.2 x 10^5 /cc. In the latter instance, the filaments should be readily apparent at 100 microns which they are not observed to be in the IRAS images. No filaments are apparent with a contrast relative to the background greater than I(100 microns) ~ 1 MJy/str, so that their column density must be < 7 x 10^19 cm^2 with a corresponding volume density n < 250 /cc assuming a diameter of 0.1 pc. We conclude that the available far-IR and optical data are consistent with the filaments being ionized gas, and that this gas may be magnetically confined perpendicular to the filament major axis. Radio continuum observations could help to decide between the 'hot' and 'cold' filament models by detecting HII in the filaments if T(gas) > 10,000 K.
Another indicator of the stability of a fluid flow against the spontaneous growth of instabilities and turbulence is the Reynolds number. Systems with Re ~ 10 show very little turbulence and are characterized by laminar flows. The resulting appearance is that of long, uniform plumes trailing the object as it passes through a viscous medium. For Re ~ 50, vortices develop in the flow behind the object and propagate down the trailing plume in what are called 'vortex streets'. For Re >> 100, the flow becomes fully turbulent and the trailing material takes-on a very chaotic and complex morphology. The Reynolds number is given by Lang(1980) as, Formula 7a for fully ionized hydrogen gas without a magnetic field, and Formula 7b for ionized gas where the motion is perpendicular to the magnetic field. For a length 2 pc and V ~ 10 km/s, Re ~ 120 n T(6)^-5/2 where T(6) is the temperature of the ambient medium in units of 1 million K, n is the ambient gas density in cm^-3, and ln(S) ~ 30. For the case where the ionized gas moves transversly to the field axis, Re ~ 3 x 10^17 n T^0.5 B^2 where B is the field strength in micro Gauss and n is in the same units as before. Under these conditions, the flow will be completely turbulent and no organized, large-scale, filamentary structures would be expected. As a comparison to solar system Type-1 tails, the density of the ambient solar wind is ~ 5 /cc and T ~ 500,000 K so that from Eqn. 7(a), Re~ 700. In order to achieve the low Reynolds numbers implied by the filamentary and sinuous loops in G359-17, the motion of the gas in the cloud would have to be parallel to the local magnetic field so that the material is relatively free to move along the field lines.
In Fig. 6 is shown the N-T plane for a range likely to include those of the ISM in the vicinity of the cloud. Also shown are the loci of constant Re as determined from Eqn. 7(a). Evidently, the requirement that mfp < length scale is satisfied over much of the plane so that the relevant physics is, largely, that of hydrodynamics rather than gasdynamics. The condition that Re < 1000 based solely on filament morphology, implies that the ISM would have to be locally hot ( T > 20,000 K ). Such high temperatures may not be implausible in view of the coincidence between the position for G359-17 and a soft X-ray source (Odenwald and Rickard, 1987).
c) G225-66
This is one of the more intriguing cometary clouds in this survey due to its double-headed nucleus, and twin tails (Plate 1(c)) which are apparently intertwined as projected onto the sky. The appearance of this cloud is more similar to those of the other filamentary clouds in this survey than to G359-17, in that the filaments are nearly invisible, optically, while at 100 microns, they are prominent. This suggests a potentially different physical composition for the filaments, and possibly a different formation mechanism as well, than the MHD scenario used in G359-17.
In terms of its far-IR appearance, it shares much in common with the Draco cloud in terms of physical size and the extensiveness of its filamentary structure. Assuming a distance of 200 pc, this cloud has the longest tails of any in this survey extending ~ 14 pc. The nuclei have total masses ~ 5.2 M(sun) and show no evidence for star forming activity. Optically, the nuclei appear as very low surface brightness reflection nebulae similar to the Draco cloud. The luminosity, surface brightness and inferred dust temperatures are also consistent with such an interpretation. In view of its morphology, one may tentatively deduce that the two nuclei are shedding mass. Assuming a space velocity V ~ 10 km / s nearly perpendicular to the line-of-sight, the length of the tails suggest an age of t ~ 1.3 million years. During this time, a total mass of ~ 5 M(sun) has been shed corresponding to a mass loss rate of ~ 4 x 10^-6 M(sun) per year. This is similar to the mass loss rate estimated for the Draco cloud of 3 x 10^-6 M(sun) per year year.
If the two cloud cores in G225-66 represent a bound system, the tail morphology suggests that they have executed at most one orbit about their center-of-mass within the last ~ 1.3 million years. The resulting Keplerian orbital velocity at their current separation of R = 2 pc is v= 3.7 km /s , corresponding to a total gravitational mass R v^2/G ~ 3000 M(sun). Although this mass is comparable to that found in a small Giant Molecular Cloud, it substantially exceeds that of G225-66 ( ~ 10 M(sun) ).
A feature that G225-66 shares with several other clouds in this survey, notably G96-15 and G208-28, is that it is apparently attached to a large cloud-like feature several degrees away, via one or more twisted filamentary tails. The total masses of these accompanying clouds are shown in Table 4. The uncertainty in mass is large since the actual extent of each cloud can only be estimated on the basis of the lowest brightness contour at 100 microns and an assumed spherical shape. The total mass of G225-66, including the nuclei, tail and 'parent' cloud, does not appear to exceed ~ 60 M(sun), far less than the dynamical mass inferred from the presumed orbital motion of the two nuclei. Unless there exists a considerable amount of hidden mass in this system, it seems unlikely that the intertwined shape of the tails can be a result of two clouds losing mass while orbiting their center-of-mass.
Another possibility is that one or more small dense clouds collided with a more diffuse cloud and passed completely through it leaving behind the filaments. In this scenario, the two nuclei at the northern end of G225-66 would be the vestiges of the dense clouds, and are still coupled to the diffuse cloud that it collided with via the two filamentary tails. Other than morphology, there are no additional data available at this time that could substiantiate such a proposal, so it must remain highly speculative.
The remaining clouds in this survey have morphologies suggestive of mass-loss from small globules, but the details of the physical mechanisms involved in producing their morphologies are not recoverable from the IRAS images alone. Although G192-67, G208-28, G228-27, G239-15 and G354+24 might be analogous to the Draco cloud, such an interpretation does not seem relevant to G64-26, G206+24 and G213+26 which have a more complex morphology.
The Discussion section describes how you have interpreted the direct observations, and the derived quantities you presented in the previous section. This interpretation should lead the reader to some new insight to your particular research area, perhaps a re-determination of some critical constant used by astronomers, a new refinement to the theory of how stars are formed, or a proof that some previously-held understanding is incomplete or incorrect in some fundamental way.
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