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Astron. Astrophys. 364, 712-722 (2000)

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3. Results

3.1. Photometric catalog of V and [FORMULA] for stars toward the Draco cloud

The results of the CCD photometry are presented below in Appendix A and B for nights 1 and 2, respectively. Appendix A presents coordinates of the stars and the V and [FORMULA] magnitudes from the night 1 photometry. All the coordinates in Appendix A have been checked against the Digital Sky Survey Images, and we have found that the accuracy of the coordinates is typically 3 arcseconds or better. This catalog contains 362 stars which appear toward the densest part of the Draco Cloud, in the selected areas indicated in Fig. 1 and Fig. 2.

The photometry for the second night includes values of V, [FORMULA], and [FORMULA], for the subset sample of 75 stars, and is presented in Appendix B. Many stars in Appendix B were not included in Appendix A, since the field centers of the second night did not coincide exactly with those of the first night. The stars in Appendix B were selected to have good quality U,[FORMULA], as well as B and V observations. Appendix B presents a comparison of the photometry between the two nights for V and [FORMULA], and coordinates of these 75 stars as measured against the field centers of the second night's data. The stars in Appendix B may include a mixture of early-type stars, and late-type stars with active chromospheres, as they were selected for high flux in U, B and H[FORMULA]. Further spectroscopic work is underway to test this possibility.

3.2. Photometric determination of the Draco cloud distance

We have attempted to derive the distance to the Draco Cloud using just the photometric observations, based on the assumption that the sample is deep enough to probe to very large distances. To give an overview of the depth of our program stars, Table 4 presents the expected line of sight distances for several main sequence stars of different spectral types, at a magnitude of V=18, and at two representative values of [FORMULA] for the foreground of the Draco Cloud.


Table 4. Line of sight distance for V=18.
a) Distances based on [FORMULA] values from Mihalas & Binney (1981).

It is clear from Table 4 that the magnitude limit of our sample, V=19, should be more than adequate to detect the Draco Nebula in absorption. In the following sections we present results that estimate the distance to the cloud using two methods. Sect. 3.3 presents the results of our tests of photometric classification of our program stars using a calibration of the index [FORMULA] to estimate [FORMULA]. Sect. 3.4 presents models of the counts in V magnitudes of the sample using a simulation of star numbers in the galaxy which includes realistic treatments of stellar populations, and stratification with [FORMULA]. Sect. 3.5 presents models of the expected color distributions of [FORMULA] resulting front the same model, which is capable of constraining both the distance to the cloud, and the ratio of total to selective extinction, RV. With the combination of methods we have detected the extinction arising from the Draco cloud. This gives a basis for a preliminary distance estimate, and by comparing the methods, we can derive and estimate for the uncertainty in this estimate.

3.3. The [FORMULA] index and photometric spectral classification

The narrow-band H[FORMULA] flux will depend strongly on MK spectral type for stars due to the decreasing Balmer hydrodgen line strengths for spectral types O-B-A, and less so for stars later than F. As such the index [FORMULA] could potentially be a useful tool for photometric spectral classification. The [FORMULA] index has been used previously to photometrically detect Be stars (Grebel et al. 1992) and was shown to be strongly correlated with [FORMULA], and highly sensitive to chromospheric activity. If a calibrated dependence between [FORMULA] and [FORMULA] can be shown for chromospherically inactive stars it is possible in principle to use just the measured values of [FORMULA] and [FORMULA] to derive values of [FORMULA] after correcting for the effects of reddening. We have performed a few experiments to test the feasibility of this technique for determining the distances to the stars in our sample.

To check the dependence between [FORMULA] and [FORMULA] we used the ten Landolt standard stars observed in the second night, which were assumed to be unreddened. Fig. 6 shows a plot of the very strong linear relation between [FORMULA] and [FORMULA] for these stars, which sampled a wide range of spectral types. The best fit line between these two indices corresponded to [FORMULA] = 1.5753 [FORMULA] [FORMULA] - 0.6607. We believe that these bright standard stars in our sample are unreddened and free from chromospheric activity, but must acknowledge that either effect would disrupt our calibration. We have performed some analysis of the effects of lumunosity class, using a library of stellar spectra, and an analysis of the [FORMULA] index with synthetic photometry. No significant differences in the [FORMULA] index were found as a function of luminosity class, and the fitted slope to the data in Fig. 7 was found to be mcalib=1.584 [FORMULA] 0.1, which is in excellent agreement with the calibration from our standard stars shown in Fig. 6.

[FIGURE] Fig. 6. Calibration of the photometric index [FORMULA] against the known values of [FORMULA] for the 10 standard stars with MK spectral types from the second night.

[FIGURE] Fig. 7. Calibration of the synthetic photometry indices [FORMULA] against the known values of [FORMULA] for 122 stars with unreddened digital spectra in the atlas of Jacoby et al. (1984). The luminosity class of the star is encoded by the plot symbol: crosses indicate class V, triangles indicate class III, and diamonds indicate class I. The slope of the relation for the stars was found to be mcalib = 1.584, in excellent agreement with the calibration photometry of our standard stars.

While we believe that the calibration of [FORMULA] and [FORMULA] has been determined for a sample of unreddened stars in the Fig. 6 and Fig. 7 above, a more difficult problem arises from the reddening of the [FORMULA] index. The [FORMULA] measurement is less susceptible to reddening than [FORMULA], and using a standard extinction curve (Cardelli 1989), one predicts that for [FORMULA] = 0.1, the [FORMULA] index is reddened by a value of [FORMULA] = 0.078. The result is a reddening vector in the [FORMULA],[FORMULA] plane with a slope of mred = 1.28, which is very close to the derived slope of mcalib = 1.58 in the [FORMULA] and [FORMULA] calibration. It is therefore very difficult to apply the [FORMULA] index for photometric spectral classification without extremely accurate photometry to enable dereddening of the observed [FORMULA],[FORMULA] colors. It is however possible in principle to solve for [FORMULA], using the observed [FORMULA],[FORMULA] colors and the reddening vector.

While in some respects the [FORMULA] index may be useful for photometric spectral classiciation, we conclude that for the stars in the present work, the combination of photometric uncertainties and variations in reddening (along with the possibility of chromospheric activity in the stars) makes the [FORMULA] unreliable for determining [FORMULA] and [FORMULA]. We have included this analysis to explore the applicability of this index for future photometric classification projects, where it may be useful for studying chromospherically inactive stars of uniform or little reddening. The [FORMULA] index could therefore be applied toward the photometric classification of early-type stars too faint for traditional uvby or UBV photometry which are unreddened, or in a cluster of known reddening.

3.4. Derivation of cloud extinction and distance from star count models

We have also used a model of the galaxy from Bahcall & Soneira (1980), which predicts observed star counts and colors at any galactic coordinates. We have modified this model to include the effects of a high latitude cloud, which is considered as a slab of gas at a given distance and extinction.

In our simulations we have included three populations of stars to model the galactic star counts at the galactic coordinates (l=90.0o,b=38.7o) near the center of the Draco nebula. We include stars from the disk, bulge and halo, with giant branch colors adopted from the globular cluster M13. Our models include an exponentially stratified HI layer of scale height [FORMULA] = 100 pc. Further details on the model can be found in Bahcall & Soneira (1980). We then compute the effects on the star counts with the addition of an interstellar cloud as a function of cloud distance, extinction [FORMULA], and total to selective extinction [FORMULA]. The modelled star counts were then compared with the observed star counts in our CCD fields.

Our CCD photometric sample for the star counts includes 465 stars with good V magnitudes, which is a superset of the stars included in Appendix A. The data in Figs. 8-12 include two binning modes in V magnitudes: a bin size of 0.5 in V (crosses) and bin size of 0.75 magnitudes in V (asterisks). Error bars for each bin were computed from the Poisson statistics of the sample size in each magnitude range. The smaller error bars for the 0.75 magnitude bins reflect the larger number of stars within each bin.

[FIGURE] Fig. 8. Results of star-count models at the coordinates of the Draco nebula, to test the effects of varying the scale height of HI and the giant branch colors used in the simulation. These models do not include the effects of an intervening interstellar cloud and show that the models are insensitive to the effects of the other variables. Included in the plots are the measured star counts from our samples; the star counts and uncertainties are indicated on the plot for two different binnings of V magnitudes - 0.5 magnitudes (crosses) and 0.75 magnitudes (stars).

[FIGURE] Fig. 9. Results of a star-count model, which includes the effects of an interstellar cloud at several distances ranging from distances of 500-2000 pc, and a total [FORMULA] of 0.5 magnitudes. The measured star counts and their uncertainties are indicated on the plot for two different binnings of V magnitudes - 0.5 magnitudes (crosses) and 0.75 magnitudes (stars).

[FIGURE] Fig. 10. Results of a star-count model, which includes the effects of a cloud at several distances ranging from distances of 500-2000 pc, and a total [FORMULA] of 1.0 magnitudes. The measured star counts and their uncertainties are indicated on the plot for two different binnings of V magnitudes - 0.5 magnitudes (crosses) and 0.75 magnitudes (stars).

[FIGURE] Fig. 11. Results of a star-count model, which includes the effects of a cloud at several distances ranging from distances of 500-2000 pc, and a total [FORMULA] of 2.0 magnitudes. The measured star counts and their uncertainties are indicated on the plot for two different binnings of V magnitudes.

[FIGURE] Fig. 12. Results of a star-count model, which includes the effects of a cloud at several distances ranging from distances of 500-2000 pc, and a total [FORMULA] of 3.0 magnitudes. The measured star counts and their uncertainties are indicated on the plot for two different binnings of V magnitudes.

In Fig. 8 we present the data from our star counts, and the modelled star counts without an intervening interstellar cloud, while varying some of the other parameters in the model (scale height and giant branch colors). Fig. 8 shows that the star count models are insensitive to these parameters, and that the models do not match the data well without including the effects of the absorbing interstellar cloud.

Fig. 9, Fig. 10, Fig. 11 and Fig. 12 show models which include the expected star counts with an intervening interstellar cloud at a range of distances from 500 [FORMULA] d [FORMULA] 2000 pc, at values of cloud extinction AV of 0.5, 1.0, 2.0, and 3.0 magnitudes, respectively.

It is possible to see from Figs. 8-12 that the effects of the cloud are detected in our star counts, and that the best fit models are found with clouds that have extinction in the range 1.0 [FORMULA] AV [FORMULA] 3.0 and distances in the range of 800 [FORMULA] d [FORMULA] 1500 pc. Of all the models considered, our star-counts are most consistent with the values of 2.0 [FORMULA] AV [FORMULA] 3.0 magnitudes, and d = 1100 pc. We have adopted the value of AV=2.5 [FORMULA] magnitudes to indicate the range of values for which the star counts provide acceptable fits to within our estimated uncertainties.

3.5. Theoretical [FORMULA] colors for stars and effects of distance, AV and RV

In addition to the counts of stars as a function of brightness, we also have modelled the theoretical colors of a sample of stars within this same region. Additional free parameters, such as the ratio of total to selective extinction, RV, and the magnitude limit of our sample in the B passband, need to be evaluated in order to estimate the colors in the sample.

The colors of the sample of stars were derived using the same modified Bahcall and Soneira model, with the additional free parameter of RV. A range of distances from 800 [FORMULA] d [FORMULA] 2000 pc was evaluated, over several values of extinction ranging from 1.0 [FORMULA] AV [FORMULA] 3.0, and values of RV ranging from 1.5 [FORMULA] RV [FORMULA] 9.0.

The variation of any of these parameters was found to have a significant effect on the predicted [FORMULA] colors, and for most values we tested, the colors predicted were bimodal, with a large peak in the histogram for values of [FORMULA] [FORMULA] 0.9, and a separate red peak for [FORMULA] [FORMULA] 1.5.

An examination of the observed [FORMULA] colors of our sample seen in Fig. 3 and Fig. 13 shows a similar, less pronounced bimodal distribution of colors than predicted in the models. This may be caused by our selection of stars which have both detectable B and V magnitudes, which may remove several of the reddest stars in the sightline if our B limiting magnitude is (as expected) brighter than the V magnitude. For this reason, we have emphasized the modelled colors of the bluer stars in comparing with our observed [FORMULA] distributions.

[FIGURE] Fig. 13. Modelled [FORMULA] colors for the sample using AV, superimposed on the observed colors from the Appendix A, for a fixed cloud extinction AV=2.5, and a range of values of cloud distance and RV. The default value of RV=3.0 was unable to duplicate the observed [FORMULA] colors (dashed line). The best fit is seen for d=1100 pc, AV=2.5, and RV=1.5 (solid line). The lack of a large number of observed stars at [FORMULA] [FORMULA] 1.5 probably results from a brighter limiting magnitude in B than in V, which would prevent inclusion of many of the faint, redder stars predicted in the model.

Suprisingly, only one set of the parameters d, AV, and RV matched the bluer peak in the color distribution well. We present in Fig. 13 a plot of a few of the models using the mean value of AV = 2.5 derived from the star-count analysis. Fig. 13 shows the observed [FORMULA] color histogram for the sample of Appendix A, and the modelled fit for AV = 2.5 and the default RV = 3.0 at the distance of d = 1100 pc. Additional lines in Fig. 13 show the modified fits using RV = 1.5, at a range of distances from 800 to 2000 pc. With the exception of the large peak in the number of red stars in our model, good agreement in the colors is seen for the AV=2.5 model with RV = 1.5 and d = 1100 pc.

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Online publication: January 29, 2001