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Astron. Astrophys. 349, 605-618 (1999)

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4. Discussion

4.1. Previous studies of the DR 18 region

Despite the lack of near infrared observations of DR 18 in the literature, a number of surveys in the far infrared and radio domains have included it. The HII region has been observed in several hydrogen radio recombination lines (Piepenbrink & Wendker 1988, Lockman 1989). In the centimeter radio continuum, both single dish (Wendker 1984, Wendker et al. 1991) and aperture synthesis observations (Miralles et al. 1994) exist. At other wavelengths, studies have searched for emission by high density tracers such as H2O masers (Scalise et al. 1989, Palla 1991, Brand et al. 1994, Miralles et al. 1994), NH3 (Miralles et al. 1994, Molinari et al. 1996), HCO+ (Richards et al. 1987) and H2CO (Piepenbrink & Wendker 1988).

Many of the observations have been motivated by the presence in the region of IRAS 20333+4102, a point source in the IRAS catalog lying on a ridge of extended emission running from Southeast to Northwest. The IRAS colors of the point source are typical of a dense molecular core containing an embedded bright source (Wood & Churchwell 1989; Palla et al. 1993). Its fluxes in the (1,1) and (2,2) NH3 lines (Miralles et al. 1994, Molinari et al. 1996) indicate a high temperature of 20-30 K, supporting the existence of an embedded source in a core with density [FORMULA] cm-3. Such densities are confirmed by the detection of HCO+ (Richards et al. 1987). Even higher densities are revealed by the H2O maser emission detected by Scalise et al. 1989, with an intensity of 5 Jy. Likely variability of the H2O emission explains its non detection in other epochs, as reported in Brand et al. 1994 and Miralles et al. 1994, despite detection limits as low as 1.3 Jy rms. Nearly all the line measurements are coincident in assigning a velocity [FORMULA] km s-1, including the NH3, HCO+, H2CO, and hydrogen recombination lines. The exception is the H2O observation of Scalise et al. 1989, who found [FORMULA] km s-1. This discrepancy is interpreted by Miralles et al. 1994 as being indicative of the existence of an outflow associated to the central object.

The precise position of IRAS 20333+4102 in our images is not known, as the beam sizes of IRAS and of the radio telescopes used for the observations of high density tracers are typically of a few arcminutes. However, a direct relation between the central star and IRAS 20333+4102 seems clearly discarded. The central star lies outside the IRAS error ellipse of that source, and all the high density tracers suggest its identification with a protostellar core, rather than with an emerged star. If the IRAS position is taken at face value, IRAS 20333+4102 lies [FORMULA] east of the central star, on the bright rim seen in the nebulosity in the K band. No obvious near-infrared counterpart of this source is identified, although a few very red sources with [FORMULA] exist within the IRAS error ellipse. The presence of IRAS 20333+4102 and the significant background emission prevents an estimate of the emission characteristics of the arc nebula at IRAS wavelengths.

The compact HII radio continuum emission detected in the VLA observations of Miralles et al. 1994 nicely matches in both position and appearance the crescent-shaped bright spot seen next to the central star in our Br[FORMULA] image, which seems clearly related to the central star. This, together with the evolutionary scenario that we propose for DR 18 (see Sect. 4.3) naturally explains the offset between the IRAS position and the radio continuum peak remarked by Miralles et al., at least for the present case (such offsets have been observed by those same authors in a few other instances, but it is doubtful that the present cause applies to them as well). In this context, IRAS 20333+4102 may thus be an embedded source, perhaps an intermediate mass protostar (Molinari et al. 1996), embedded in the molecular cloud that is being eroded by the central star, bearing no direct relevance to the structures that are seen in the near infrared. Therefore, we will not include it in our further discussion of the region.

4.2. The central star and the distance to DR 18

Kinematic distances in the Cygnus region are very poorly constrained. The observed positive [FORMULA] of the material associated to the HII region and to IRAS 20333+4102 clearly places DR 18 in the Cygnus arm, rather than in the background Perseus arm where strongly negative velocities are observed. However, kinematic distances are meaningless for distances below [FORMULA] kpc, due to the small value of [FORMULA]. Using optical tracers, several authors have discussed distances to individual structures in the direction of Cygnus, finding in general values between 0.7 and 2.5 kpc for objects in the local arm (see e.g. Odenwald & Schwartz 1993). Discussing distances to OB associations possibly related to the Cygnus Superbubble, Comerón et al. 1993, 1998 adopt 1.25 kpc for the bulk of the massive stellar population, although a large scatter is certainly allowed by the available data.

A more precise determination of the distance is possible using the available VJHK photometry of the central star and its spectral type, that we estimated to be between B0 and B1 as discussed in Sect. 3.2. The input photometry, and the estimated parameters that we discuss in this section, are presented in Table 1. As a starting point, we have estimated the foreground extinction using the [FORMULA] color, assuming that the flux at both bands is purely photospheric. This is a doubtful assumption for a young hot star at J, as circumstellar emission may be noticeable at this band. However, the moderately red [FORMULA] and [FORMULA] colors lead us to think that this is a reasonable approach. The extinction is then calculated as


where [FORMULA] is the intrinsic color index, and [FORMULA] is given by the interstellar extinction law. Intrinsic color indexes for main sequence stars of spectral types B and later are compiled by Kenyon & Hartmann 1995. The [FORMULA] color changes from -0.70 to -0.61 between types B0V and B1V. As to [FORMULA], Rieke & Lebofsky 1985 give a value of 0.282 for the standard extinction law. Steenman & Thé 1989 have modelled the grain size distribution to account for anomalous extinction laws, and by increasing the maximum grain size to account for a total to selective extinction ratio [FORMULA] they predict [FORMULA]. As discussed in Sect. 3.3, the extinction towards DR 18 may be expected to lie between these two cases. Considering all the possible values that can be obtained in Eq. (1) by varying [FORMULA] and [FORMULA] between the quoted limits, we obtain that [FORMULA] most probably lies between 7.6 and 8.6. This source of uncertainty on the distance can be considered to be small, as we will estimate the latter using the J band flux, where the extinction (and its uncertainty) are reduced by a factor of 3. The luminosity of the star should lie between [FORMULA] for type B0V and [FORMULA] for type B1V (Schmidt-Kaler 1982) which, using the intrinsic color indexes and bolometric corrections of Kenyon & Hartmann 1995, translates into an absolute magnitude [FORMULA] between -3.28 (B0V) and -2.55 (B1V). In this way, we obtain for the distance r:



Table 1. Observed and derived parameters of the central star

4.3. The nebula

4.3.1. Overall structure

The most remarkable feature of DR 18 in the near infrared is its distinct arc shape, and the changing appearance of the nebula in the different filters as seen in Fig. 3 is essential to understand the nature of the emission. The brightness of the arc relative to the rest of the nebula is highest in the K band, and especially in the filters containing H2 transitions (2.122 µm, 2.248 µm, and 2.260 µm). On the other hand, such a contrast is hardly seen in the J and 2.166 µm filters, where hydrogen recombination lines are expected to dominate (Pa[FORMULA] in the J band, and Br[FORMULA] in 2.166 µm). The overall appearance of the nebula, even excluding the prominent knot of emission near the central star, is rather centrally peaked in those bands. This suggests that the brightness enhancement in the arc is not directly related to the HII region, although the arc can still be traced in the J and 2.166 µm filters all the way out to nearly its outer rim. In the H band image (Fig. 2) the situation is intermediate: the bright rim can still be discerned, although it is not as prominent as in the K band. The H window is expected to contain abundant hydrogen recombination lines, corresponding to transitions of the Brackett series from levels higher than 10.

4.3.2. The photodissociation region

Additional information on the nature of the emission from the arc can be obtained from the fact, already noted in Sect. 3.1, that the intensity ratios between the 2.248 µm and the 2.260 µm images are approximately the same for the stars as for the nebula, suggesting that, like in the stars, the nebular emission is mostly in the form of a continuum, at least at those wavelengths. Such continuum emission must provide a nonzero background in all the narrow band filters, including Br[FORMULA], to be taken into account when considering the spatial distribution of the ionized gas. Near infrared continuum emission is frequently seen in reflection nebulae illuminated by early B stars (Sellgren 1984, Sellgren et al. 1992, Giard et al. 1994, Field et al. 1998), as well as in planetary nebulae (Likkel et al. 1994, Hora et al. 1993, Luhman & Rieke 1996). Several possible origins for it have been proposed. Models based on the transient heating of very small grains [FORMULA] Å in size by the ultraviolet emission from the star (Sellgren 1984) successfully account for the spectral energy distribution of this continuum emission, characterized by a color temperature of [FORMULA] K. Other sources of continuum can be macromolecules such as polycyclic aromatic hydrocarbons (PAHs; Giard et al. 1994). Black & van Dishoeck 1987 also note that the blending of the very numerous fluorescence lines arising in radiatively excited H2 produces a pseudo-continuum when observed at low spectral resolution. However, the latter explanation seems unlikely in the present case, as an intense pseudo-continuum would be accompanied by even more intense emission in the main fluorescence lines, what is not supported by the comparison between the 2.248 µm and the 2.260 µm images as noted above. Moreover, the pseudocontinuum should be more intense at J, while the arc is actually almost inobservable in that band. The increasing prominence of the arc towards longer wavelengths also argues against scattered starlight as the origin of the luminosity (Sellgren et al. 1992). An explanation for the continuum emission based on either small grains or PAHs thus seems the most likely one.

The inner edge of the arc can then be explained as due to either a front of destruction of the emitting particles, or to a density discontinuity. The latter is expected to take place in the transition layer from cold neutral gas to an HII region as a consequence of the large difference in temperature, provided that the ionized gas is allowed to expand rapidly. Moreover, if the emitting particles are PAHs, the first cause would be present too: as shown by Giard et al. 1994, PAHs are destroyed in a very short timescale after crossing the ionization front. Both explanations thus place the ionization front at the inner edge of the arc shaped nebula. The fact that a peak is observed in the 2.248 µm and 2.260 µm images, and more faintly in the 2.122 µm image, near the position of the central star (although by far not as prominent as the 2.166 µm peak) suggests that the particles responsible for the continuum emission do survive in the HII region environment. Thus, we tentatively ascribe the continuum emission to small heated grains. The absence of the PAH 3.3 µm feature in future spectroscopic observations of the crescent-shaped peak would confirm this hypothesis.

If the continuum emission of the arc nebula is mostly due to small grains or large molecules in the zone inmediately outside the HII region, such emission can thus be considered as a tracer of the PDR that constitutes the interface between it and the unperturbed molecular gas that the central star is eroding. The remarkable regularity of the PDR suggests that the molecular gas belongs to a single clump with a well defined structure, rather than to a complex of clumps; in the latter case, the ultraviolet radiation would be expected to penetrate to widely varying depths, resulting in a more extended and irregular emission, as is observed in other regions (Schneider et al. 1998). Models of PDR emission in the near infrared have concentrated on the predicted spectrum of fluorescent emission by H2 (Black & van Dishoeck 1987, Abgrall et al. 1992, Draine & Bertoldi 1996; see also the comprehensive review on H2 infrared emission mechanisms by Sternberg 1989, and references therein). Our images do not allow the direct observation of H2 emission or the measurement of line ratios, but some theoretical results concerning the thickness of the PDR can provide useful insights on its physical conditions.

We use for this purpose the extensive set of models calculated by Black & van Dishoeck 1987. We are mainly interested in the ratio of the derived column density of photodissociated gas to the input volume density of the models. This ratio should provide an estimate of the geometrical depth of the PDR, which can be directly measured in our images and, for a given density, it depends primarily on the intensity of the incident ultraviolet radiation at [FORMULA] Å. Realistic limits on the radiation field thus constrain the volume density in the PDR. To estimate the incident flux per unit surface of the arc nebula, we have used the ultraviolet spectrophotometry of Holberg et al. 1982 for [FORMULA] Per, a star commonly classified as B0.5V (e.g. Murphy 1969). The distance has been taken as 165 pc from the Hipparcos parallax. From the ultraviolet spectrum of Holberg et al. 1982, we take the flux at 1000 Å as 700 photons cm-2 s- 1 Å-1. This corresponds to [FORMULA] photons cm-2 s- 1 Å-1 at the estimated distance of 0.2 pc between the star and the inner surface of the arc nebula, assuming a negligible absorption of photons with [FORMULA] Å in the HII region. At 1000 Å, this is [FORMULA] times the background ultraviolet field in the solar neighbourhood adopted by Black & van Dishoeck 1987. The thickness of the PDR at the adopted distance to DR 18, [FORMULA] pc, thus places rather strong constraints on the density: Model 13 of Black & van Dishoeck predicts that thickness for [FORMULA] cm-3 and an ultraviolet flux [FORMULA] greater than the interstellar average, while their Model 20, in which [FORMULA] cm-3, requires an ultraviolet flux 100 times higher to produce the same geometrical depth. Given the calculated ultraviolet flux of the central star as seen from the inner edge of the nebula, a crude estimate of the volume density in the arc nebula is [FORMULA] cm-3. As found by Black & van Dishoeck 1987, this estimate is fairly sensitive to the grain properties and the formation model of H2 molecules. Moreover, the inferred column density, of order [FORMULA] cm-2, is in the range where line overlap becomes important in the treatment of radiative transfer inside the PDR (Draine & Bertoldi 1996), and a more realistic treatment may result in a decrease of the estimated density. On the other hand, the model results depend little on the temperature of the PDR (Black & van Dishoeck 1987) and on the color temperature of the ultraviolet radiation field (Bertoldi & Draine 1996). Dynamical effects resulting from the presence of an ionization front propagating into the PDR are unlikely to be important in the case of moderate ultraviolet fields, like the one produced by the central star of DR 18 (Bertoldi & Draine 1996).

The dominance of the continuum emission prevents us from carrying out a more detailed analysis based on line ratios, and future K-band spectroscopy of DR 18 may be expected to substantially improve the assessment of its physical conditions on the basis of a detailed comparison to PDR models. Given the passbands of the narrow band filters used in our imaging (Sect. 2.1), the continuum would dominate over the emission in the (1,0) H2 S(1) line in other objects described in the literature, such as the Orion bar PDR (Luhman et al. 1998), the planetary nebula Hubble 12 (Luhman & Rieke 1996), and probably other planetary nebulae as well (Likkel et al. 1994). However, judging from Burton et al. 1998, narrow-band imaging at 2.122 µm of NGC 2023 may be dominated by line emission, although probably not everywhere (see Field et al. 1998). As to DR 18, the eastern outer rim of the arc nebula may be an exception to the overall dominance of the continuum emission. Figs. 2 and 3 show that this rim is brightened in the 2.122 µm images, a feature that is not seen in any other of the narrow band filters, including the one centered at 2.248 µm. We interpret this as due to the (1,0) H2 [FORMULA] line being much stronger with respect to the local continuum than in other parts of the nebula. This is what would be expected if the PDR is bounded in the side opposite to the central star by a shock that propagates into the molecular cloud. Collisional excitation may thus be the dominant mechanism of excitation of H2 in this region, while past the shock and closer to the star it would be ultraviolet pumping. If this is so, then the shock must be faster than [FORMULA] km s-1 in order to heat the gas to the [FORMULA] K required to populate the [FORMULA] level of the H2 molecules (Shull & Draine 1987, Sternberg 1989). The absence of enhanced (2,1) H2 [FORMULA] emission in the 2.248 µm filter is consistent with a non dissociative shock, rather than ultraviolet pumping, as the mechanism producing the H2 emission in that layer. Using the relation for the Alfvén velocity [FORMULA] (Genzel 1992) and the empirical scaling relationship for the magnetic field [FORMULA] (Troland & Heiles 1986), the quoted minimum velocity of 5 km s-1 would be weakly superalfvénic, although whether or not this is really so obviously depends on the actual values of the density and the magnetic field. A shock velocity of 5 km s-1 can thus be considered as a lower limit, while a velocity above [FORMULA] km s-1 would produce a dissociative shock increasing the [FORMULA] ratio to a value of order unity, which is not observed.

4.3.3. The ionized gas

The emission peak near the central star seen in the J and the 2.166 µm bands, as well as in the centimeter continuum as pointed out in Sect. 4.1, suggests the interaction of a flow of ionized gas streaming away from the arc nebula with the environment of the central star. This is supported by the crescent shape of the peak, and by its orientation facing the nebula. Such flow of ionized gas is expected to occur naturally when a molecular cloud is being ionized by a star located outside it (Tenorio-Tagle et al. 1979), and some actual examples of it have been observed (e.g. the HII region S 201; Felli et al. 1987). If the star has a considerable wind and is conveniently placed, it may act as an obstacle in the stream of ionized gas, which then forms a crescent-shaped density enhancement ahead of the star.

The erosion of a cloud by a star located outside it may be regarded as a particular case of the champagne phase of a HII region (Tenorio-Tagle & Bodenheimer 1988, and references therein). A common feature to the dynamical simulations of the classical champagne phase, in which the star lies within or near a cloud of uniform density, is the acceleration of gas to supersonic velocities in a transition zone, lying between the compact HII region contained in the volume initially occupied by the molecular cloud, and the extended component originated by the ionized material expanding in the intercloud medium. Therefore, in this scenario the ionizing star should be placed in the outskirts of this transition zone or in the extended component in order to develop a bow shock around it.

This does not seem to be the case for DR 18, where the star lies approximately on the major axis of an ellipse roughly delineating the arc nebula. This may be just an effect of perspective if the star happened to be projected in front or behind the arc, but physically far from the molecular cloud. However, in such case we should be seeing the bow shock nearly pole-on, approximately surrounding the star rather than beside it. Moreover, the supersonic region in the champagne model for a cloud of uniform density has a density much lower than that of the ionized gas in the compact component, and the bow shock would then produce just a very slight increase on the background emission caused by the compact component. The observations suggest that the acceleration of the gas to supersonic velocities thus takes place in the compact component.

To explore the conditions under which a bow shock like the observed one would develop, while being consistent with the observed morphology of the emission and the position of the central star, we have performed several gas dynamic numerical simulations suited to the specific conditions of DR 18. The methods used are based on those described by Comerón 1997 to study the erosion of a molecular cloud by an embedded star, taking into account the effects of both the ionizing radiation and the stellar wind. The 2-D computations have been carried out on an grid of [FORMULA] cells simulating the axial plane of a cylinder 0.5 pc in height and 0.5 pc in radius, with a linear resolution of 0.0013 pc, and assuming symmetry around the axis. Due to the complexity involved in modeling the physical conditions inside it, we have made no attempt at reproducing the PDR in the simulations.

We have carried out an initial set of simulations placing the star at different locations with respect to the boundary of a cloud of uniform density, both inside and outside it. The reference parameters used for the star are a mass loss rate [FORMULA] [FORMULA] yr-1 and a terminal wind velocity [FORMULA] km s-1. These are rather arbitrary choices, but our conclusions on the formation of a bow shock are unchanged when varying either of the two parameters even by a factor of 10. The ionizing flux of the star has been set to [FORMULA] photons s-1 (Schaerer & de Koter 1997); again, reasonable changes in this value do not affect our results. The density of the cloud has been varied between [FORMULA] and [FORMULA] cm-3. Our results confirm those of Tenorio-Tagle and collaborators in that the flow of gas around the star is very slow when it is placed inside the cloud, and no bow shock develops. On the other hand, placing the star in the region of supersonic flow does produce a bow shock as expected, but in a region where the ambient density of ionized gas is typically a factor of 4 or more smaller than in the compact component contained in the cloud. Since the geometrical depth of the compact component (roughly given in our case by the size of the ring nebula) is much greater than that of the bow shock, the latter would be indistinguishable in practice.

We have found a much better agreement with the observations when allowing the density of the cloud to increase with depth. This is expected to be closer to the reality, in agreement with observations of the structure of clumps within molecular clouds which typically have density profiles [FORMULA] (e.g. Williams et al. 1995). In the present case, IRAS 20333+4102 may be a protostar being formed at the high density center of the core. If the ionizing star is placed off-center, the density gradient inside the cloud becomes a pressure gradient when the gas is ionized, which produces supersonic motions of ionized gas inside the compact component.

This is illustrated by the results of the numerical simulation shown in Fig. 8. The input parameters of the simulation are as described above, but the molecular cloud is now modelled as a plane-parallel stratified slab with the density increasing from a value of [FORMULA] cm-3 at the surface of the cloud to infinity at the edge of the grid, following a [FORMULA] law (where z is the coordinate parallel to the axis). The star is initially placed near the edge of the cloud, 0.0125 pc below its surface. The upper panels in Fig. 8 depict the distribution and motions of the gas [FORMULA] years after the onset of the ionizing flux and the stellar wind, when a sizeable cavity has been already produced in the cloud. The density gradient makes the ionization front propagate faster in the direction parallel to the surface of the molecular cloud, thus giving the HII region a bowl shape. We note that the edge of the DR 18 HII region, as outlined by the PDR, is also elongated, rather than hemispherical as would be in the case of the erosion of a homogeneous molecular cloud. The growth in the parallel direction is however moderated by the dense stream of ionized gas flowing outwards from deeper into the cloud, which maintains a high density ([FORMULA] cm-3 in the example shown here) in the cavity. The upper right panel in Fig. 8, with the velocity map superimposed on the density contour plot, shows that the ionized gas is accelerated to supersonic velocities soon after being ionized. In the stage of evolution shown here, the gas moves at 15 km s-1 towards the star when it finds the bow shock caused by its interaction with the stellar wind. The structure produced by this interaction has been studied in detail by Comerón & Kaper 1998. The situation found here is comparable to the case of a low velocity runaway star described in that paper, giving rise to a stable bow shock.

[FIGURE] Fig. 8. Model structure of DR 18, using the input parameters described in the text, [FORMULA] years after the ionizing flux and the stellar wind are switched on. Upper left: Density structure of the ionized gas flow. To clearly show the formation of the bow shock, the greyscale on the left panel has been set so that the lighter grey represents densities above 3000 cm-3; the stratified molecular gas thus lies outside the greyscale used here. The density increase factor of the gas when crossing the bow shock is 2.15, and the maximum density in the bow shock is 700 cm-3. Upper right: The velocity vector of the gas at different points of the grid is plotted on a contour map of the density. The longest vector shown represents a velocity of 20.5 km s-1. Bottom: Distribution of the emission measure that would be observed along lines of sight forming an angle of [FORMULA] with respect to the axis of the simulation. A crescent shape appears just ahead of the star and facing the cloud, as observed in DR 18. The units are arbitrary; the ratio between the peak value and that at mid distance between the peak and the edge of the HII region is 1.7.

The lower panel in Fig. 8 simulates the spatial distribution of the emission measure, [FORMULA], where [FORMULA] is the electron density and l is the length along the line of sight. In a first approximation, this figure should thus be compared to the observed distribution of intensity. An angle of view of [FORMULA] formed by the visual and the axis of the computational grid has been assumed, being representative of the results found over a fairly wide range of observation geometries. In agreement with the observations, the intensity distribution peaks just ahead of the star. This is due to the local increase in density caused by the compression of the gas in the bow shock, but also to the fact that such peak is seen in projection against a broader peak of emission due to the compact component. Finally, we note that the crescent shape is rather due to the sharp cut in intensity behind the star, where the dense ionized flow is replaced by a much more tenuous, hot gas produced by the collision between the stellar wind and the HII region. The numerical simulation presented here yields a ratio of 1.7 between the peak intensity and the intensity midway between the peak and the edge of the HII region, comparable to the [FORMULA] that we estimate from our Br[FORMULA] images. It should be kept in mind however that the images also contain a contribution from heated dust. The intensity distribution produced by small dust grains in the HII region is expected to peak near the star too, due to the increase in density found at the bow shock, but also to the higher rate of absorption of ultraviolet photons per grain. This effect is not taken into account in the numerical simulations, what prevents a straightforward comparison between the Br[FORMULA] image and the simulated map of emision measure.

The description given here is mostly qualitative and does not intend to reproduce in detail the observed structure of the HII region. This is due to the many free input parameters of the simulations, to the limited constraints on the relevant quantities that can be derived from our observations, and to the entangling between the emission of small particles and of the ionized gas. However, the basic characteristics of the scenario described here remain valid when changing the input parameters (ionizing flux, stellar wind, cloud density and size) within a broad range.

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Online publication: September 2, 1999