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Astron. Astrophys. 333, 280-286 (1998)

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3. Discussion

3.1. Small scale structure in NGC 2023 and S(1)/S(2) line ratios

Evidence for small scale structure is based on marked spatial variations of S(1) and S(2) brightness within our images. For example the sharp-edged nature of the western side of the seahorse-shaped feature, to the north of HD 37903, shows that the scale-size of variations may be less than 1", that is, less than 0.002 pc. In this connection, we note that the observations are capable of yielding sharp features where such features are expected, that is, in shock-fronts in the Herbig-Haro objects in the south of the image, in harmony with the good seeing. The definition of the central image is somewhat poorer, possibly due to the 300 second exposure time used in F94. In Fig. 4a, we show a cut passing N-S through the seahorse region and in Fig. 4b another passing E-W. It is evident that very large changes in brightness occur over a physical size corresponding to less than 1" in the E-W direction, represented by a fall of the full height of the signal over 2 pixels, that is, 1". The minimum measurable scale, associated with a fall in signal to half-height, is limited by the seeing and is therefore 0.0017 pc (0.8 arcsec). In the N-S cut, the scale is of the order of 2", that is 0.004 to 0.005 pc. In other regions, for example to the south of HD 37903, features are less sharply defined than in the structure in the north. This is shown in the cuts in Fig. 5a and b, the first of which is a N-S cut 20 arcseconds east of star C, and the second a cut through the infrared cross E-W at a position 25 arcseconds north of star C. The smallest scale of structure associated with these regions is 0.004 pc. In the southern region as a whole, the scale over which large variations of intensity take place is considerably greater than in the central region. Turning to data for S(2), the ratio of S(1) and S(2) flux may be related (L96) to an effective rotational temperature, TR by


where [FORMULA] is the ratio of H2 molecules in ortho and para states created in the formation process at grain surfaces, and modified by any subsequent gas phase H atom exchange reactions (Burton et al. 1992; Chrysostomou et al. 1993) and [FORMULA] = the ratio of S(1) and S(2) flux. Values of [FORMULA] are shown in Table 1 for five different positions within the infrared cross. In principle, values of [FORMULA] might vary within the cross region. However, if for simplicity we assume that the value of [FORMULA] is constant within the infrared cross, then our data show that within the cross there are two distinct rotational temperatures. This arises because the values of S(1)/S(2) that is, [FORMULA], differ within the cross region. Draine and Bertoldi 1996 (DB96) calculate a value of TR [FORMULA] 1200K for NGC 2023. If we make the further assumption that this value applies for regions 11"W 39"N and 25"W 2"N of star C for which [FORMULA] = 1.6 (Table 1), then this implies values of TR = 600 to 700K in the other three regions of the cross in Table 1. Eq. 1, with [FORMULA] = 1.6 and TR = 1200K, gives [FORMULA] = 1.37. By way of contrast, Herbig-Haro objects should have [FORMULA] = 3, the equilibrium value appropriate for the high temperature thermalized gas encountered in shocks in these objects. An observed value of [FORMULA] = 2.7 shown in Table 1 for a HH object then yields a rotational temperature [FORMULA] 2000K as expected.

[FIGURE] Fig. 4. a  A cut passing N-S through the seahorse region (Fig. 1 and 3). b  As in a  but E-W.

[FIGURE] Fig. 5. a  A cut passing N-S 20" east of star C (Fig. 1 and 3). b  A cut passing E-W through the infrared cross 25" north of star C.


Table 1. Observed ratios, [FORMULA], of the intensities of H2 v=1-0 S(1) and S(2) emission lines for five regions within the infrared cross in NGC 2023 in the image shown in Fig. 1, with nomenclature given in Fig. 3. See text in Sect. 3.1 for the definition of [FORMULA], and for estimation of rotational temperatures.

3.2. H2 surface brightness

The observed brightness of the infrared triangle (= 9 x 10-8 Wm-2 sr-1) and of the infrared cross (=1.4 x 10-7 Wm-2 sr-1) may be reproduced using a PDR model, based upon a code described in Abgrall et al. 1992. The successful application of the model however depends critically on the intensity of the VUV field associated with HD 37903, the exciting star. DB96 have noted that there is some uncertainty associated with the VUV field associated with such a star. Here we use the field suggested by DB96, which is based upon the most recent stellar atmosphere models. A value of the intensity of the VUV field 5000 times that of the mean value in the interstellar medium (G0 = 5000) is given in DB96 for an angular distance of 78.5" from HD 37903 in the plane of the sky. The brightest region of the infrared triangle lies [FORMULA] 110 arcsec distant from HD 37903 and of the infrared cross [FORMULA] 80 arcsec, both in projection. If we assume (i) that the projected distance in the sky is the true distance and (ii) that there is negligible dust absorption between HD 37903 and the triangle or cross regions (DB96 and Fig. 2), we therefore estimate a (maximum) VUV field corresponding to G0 = 2000 to 2500 for the triangle region and 5000 for the cross region. We find that, using G0 = 2200 and a number density density (n(H) + n(H2)) of 105 cm-3, the surface brightness of the triangle region may be reproduced to within better than a few per cent, without any limb brightening contribution (F94, DB96). This is illustrated in Fig. 6, which shows the calculated brightness for a set of three number densities, 104, 105 and 106 cm-3, each for G0 = 2200. Thus high density material appears to extend far from HD 37903. Using G0 = 5000, for the cross region, we find that the surface brightness of this region is reproduced to within a few per cent, again for a number density of 105 cm-3.

[FIGURE] Fig. 6. The computed integrated surface brightness of the v=1-0 S(1) H2 emission line as a function of position within a plane parallel slab of gas irradiated by a VUV field of 2200 times the mean intensity in the ISM (G0 = 2200) for number densities (n(H) + n(H2)) of 104, 105 and 106 cm-3. The model used is based on that of Abgrall et al. (1992), but has been developed to include 250 rovibrational levels of H2 and improved values of collisional rate coefficients for H2.

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Online publication: April 15, 1998