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Astron. Astrophys. 346, 441-452 (1999)

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4. The reflection nebula

Fig. 3 shows a series of images of Holoea in 6 different bandpasses, V, R, I, J, H, and K. There is a clear variation of the morphology of the reflection nebula as a function of the filter central wavelength. We will now show that all of the morphology observed in these images can be understood in terms of a combination of scattering and obscuration. Furthermore, we can use the reflection nebula to probe the distribution of material near the central star.

[FIGURE] Fig. 3. V, R, I (top left to right) and J, H, K (bottom left to right) images of IRAS 05327+3404 (Holoea). The small inset box in the V image shows the region covered in Fig. 4. These images are each [FORMULA], with North up, East left.

4.1. Scattered light model

First, we make the assumption that the bulk of the light from the central source is coming to us directly from the central star, with some amount of extinction by intervening dust, but without scattering: i.e., we can see the central source directly. We will justify this assumption in more detail below. Thus, the observed flux from the central star is:

[EQUATION]

where [FORMULA] is the observed flux of the central star, [FORMULA] is the unextinguished flux of the central star, [FORMULA] is the extinction to the central star along the direct line of sight, and [FORMULA] is the extinction law. We assume the canonical extinction law, with [FORMULA] (i.e., Cardelli et al. 1989). Next, we assume that the light we observe from the reflection nebula is the result of scattered light from the central star. The flux we observe therefore has both the effects of extinction as well as scattering:

[EQUATION]

Where [FORMULA] is the observed flux from a point in the reflection nebula, [FORMULA] is the total extinction along a path from the central star, reflected off the nebula, and towards us, [FORMULA] is a normalization factor to determine how much light is scattered by the dust particles in the nebula, and [FORMULA] is the slope of the scattering function. For Rayleigh scattering, [FORMULA], and for most other types of scattering, [FORMULA] is still quite close to 4 (Whittet 1992). We do not include the effect of an anomalous extinction law for two reasons. First, as discussed above, the optical spectrum is most consistent with the nominal [FORMULA] value of 3.1. Second, and more importantly, changing the value of [FORMULA] has a more significant effect on the shape of the ultraviolet extinction, and only a small effect in the near IR. Any anomalous extinction behavior will make a small shift in the level of observed extinction, but should not significantly alter the derived morphology.

If we take the ratio of the flux from any location in the reflection nebula to that of the central star, we can remove the uncertainty in the intrinsic spectrum of the central star:

[EQUATION]

Expressing this in terms of logarithmic fluxes, we find:

[EQUATION]

Thus, by fitting to the flux ratios, we can determine the increased amount of extinction experienced by the light as it travels to different locations in the reflection nebula from the central star, [FORMULA].

4.2. Analysis of the images

To perform this measurement, we have rotated and scaled the images to match each other, so that the same pixel in each image represents the same point in the sky. We have also smoothed the images with Gaussian profiles to give them matching PSFs. Finally, we rebinned the images to a fairly large pixel scale (0:0069 per pixel) to increase the signal-to-noise in the nebulosity. The resulting images are shown in Fig. 4. For each of the resulting images, we have subtracted the sky level and converted the fluxes in each pixel to Janskys. We used the photometric calibrations to determine a relationship between pixel counts and magnitudes, and used the conversion factors listed in Landolt-Börenstein (1982) to go from magnitudes to flux units.

[FIGURE] Fig. 4. Map of [FORMULA] as a function position in the reflection nebula. The greyscale shows the V image, while the contours show the value of [FORMULA]. The values of the contours from thin to thick are 1.5, 3.0, 4.5 magnitudes. The line of sight with the lowest extinction is marked, along with the perpendicular, the assumed orientation of the circumstellar disk. A third line shows the direction towards [FORMULA], at roughly 33o.

The values of [FORMULA] and [FORMULA] at any location in the image are given by Eq. 4. We can solve for [FORMULA] and [FORMULA] as a function of position by performing a linear least-squares fit of this equation to the fluxes from any pixel in the six images. This fit is done on a pixel-by-pixel basis, fitting the model to the six spectral channels. For the values of [FORMULA], we used our photometric measurements (see Table 1). These flux measurements introduce one of our largest sources of error, the other large source being photon statistics, particularly for the V band image. Fig. 4 shows a contour map of [FORMULA] for the field of Holoea derived from these fits. This figure includes only the inner portion of the images in Fig. 3 ; a box in Fig. 3 shows the limits of Fig. 4. We have overlayed the contour plot of [FORMULA] on the V band image for comparison. The reduced [FORMULA] values are quite reasonable ([FORMULA]1) in the regions of significant emission from the reflection nebula. At the location of other stars, where our model for the flux is clearly inappropriate (since the dominant source of flux is another star), the [FORMULA] values are quite high. These [FORMULA] values imply that our model is a reasonable description for the flux observed from the reflection nebula.

The regions with the lowest extinction are found along the optical tail, and slightly to the west. The extinction increases gradually as the line of sight from the star to the nebula tilts towards the east and, at a lesser significance level, to the west. This pattern of extinction is consistent with our general picture of the system. We know from previous work (Paper I) that there is an ionized outflow which travels roughly towards the optical tail in the north, and which is evident in the P Cygni profile seen in the spectrum reflected by the tail. We also showed in Paper I that there is the suggestion of a circumstellar disk evident in the shape of the [OII ] lines, which exhibit extensive blue-shifted emission, but no redshifted emission. We expect the ionized outflow to be oriented perpendicular to the circumstellar disk. The extinction pattern is also suggestive of a circumstellar disk which causes the regions towards the east and west to view the star though an extensive amount of material, while the regions towards the north have a line of sight which is more nearly clear of material.

The map of extinction gives us some interesting details about the distribution of the circumstellar material. First of all, the angle between the region of lowest extinction and the region where the extinction climbs significantly tells us the opening angle of the hole in the circumstellar material. We have measured the angle to be [FORMULA]33o, between the axis of lowest extinction and the line shown in Fig. 4 where [FORMULA] rises to 4.0. We know from the high-resolution optical spectra discussed in Paper I that the angle between the reflected view of the ionized outflow (which is roughly down the path of the outflow) and the direct view is [FORMULA]o. The agreement between these measurements is reassuring. There are two other aspects of the jet and polar hole geometry to note. First, the angle between the region of lowest extinction and the region of reflection in which the outflow P Cygni profile is observed (Paper I) is [FORMULA]11o. This angle is a measurement of the collimation of the jet: if we assume the outflow is aligned with the region of lowest extinction, then 11o is roughly the half-width of the outflow cone. Finally, we note that even the region of lowest extinction has a positive value of [FORMULA]. This suggests that the direct image of the central source has the lowest extinction of any of the lines of sight evident in this image. However, this does not imply that the direct line of sight has the lowest extinction of all lines of sight. It is quite possible that the region directly above the pole, where the lowest extinction is naturally expected, also has very little dust to cause a reflection. Thus, the flux that we see in the region of lowest extinction in Fig. 4 comes from the front or back side of a conical distribution of reflecting dust.

An interesting result of these fits is that the asymmetry seen in the reflection nebula need not imply an asymmetric distribution of the circumstellar material. Rather, the asymmetry is due to variations in the amount of dust at a large distance from the star which is available for the scattering process. The extinction map represents the nearby amounts of circumstellar material, which appears to have general axial symmetry, with higher levels of extinction on both the sides of the direction of the outflow. The observed level of extinction on the West side of the star is somewhat lower than on the East, but the flux in this region is quite low, with a correspondingly higher level of uncertainty. We assume the dust causing the scattering is much further from the star than the material causing the extinction. At a distance of [FORMULA]10,000 AU ([FORMULA]10") from the star, it is perhaps left over from the original cloud.

4.3. Direct image or reflection?

One of the assumptions employed in the analysis above was that the central source represents light coming directly from the central star with some extinction, but without scattering. We will now present evidence to support this assumption.

First, the location of the stellar source does not change position with wavelength. In some other systems, such as L1551-IRS5, there is a bright stellar source which, on closer inspection, is found to be a bright reflection of a more embedded source (see e.g., Staude & Elsässer 1993, for an extensive review). However, in cases such as this, the location of the bright stellar source changes with wavelength as different portions of the reflection nebula are seen. The location of the stellar source seen at V though L are coincident to within 0:001, as discussed above. Second, the flux from the reflection nebula is well modeled as the flux of the central source adjusted for extinction along the line of sight and scattering towards us. It is not possible to model the stellar source and the nebula as having only different amounts of extinction. If the central source resulted from scattered light, then the reflection nebula would have to be the result of two scatterings to be consistent with the spectral fits. This seems to be quite implausible, and a very unusual geometry would be required to account not only for the observed distribution of nebulosity, but also for the H[FORMULA] line profiles observed in the high-resolution spectra reported in Paper I. Finally, the spectrum of the central source is well represented by a stellar spectrum modified by extinction. To incorporate a scattering term requires introducing a large extinction (8.5 mag) and an anomalous [FORMULA] value of 5.0. Occam's razor argues in favor of the simpler model: no scattering and no anomalous extinction. On the other hand, it is easier to explain the ratio of H[FORMULA] to H[FORMULA] with the level of extinction needed in the scattered light model. However, since the H[FORMULA] flux is not very well measured in our spectrum, and since the H[FORMULA] emission is clearly from a non-LTE source, this does not give strong support for the scattered light model. We conclude that the simplest model has a direct view of the central source as a result of a wide opening angle in the circumstellar material. The interpretation is consistent with the extinction pattern observed in Fig. 4 as well as the observed emission line profiles.

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© European Southern Observatory (ESO) 1999

Online publication: May 21, 1999
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