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Astron. Astrophys. 364, 102-136 (2000)

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5. The interstellar reddening for the program stars

We have estimated the interstellar reddening for our BHB candidates by two direct and two indirect methods. The first direct method makes use of the whole sky map of the dust infrared emission and the second is based on the empirical calibration of the Strömgren colours. The indirect methods use model atmospheres to compare the observed and computed visible spectrophotometric data and the observed and computed UV colour indices.

5.1. The interstellar reddening for the program stars from whole-sky maps

The reddening in the direction of our program stars was estimated from the whole-sky maps of Schlegel et al. (1998, SFD) which give the total line-of-sight reddening ([FORMULA]) as a function of the galactocentric coordinates (l, b). The reddening between the stars and the observer (Table 6, Column 6) was derived by multiplying [FORMULA] by ([FORMULA] where z is the star's distance above the galactic plane. The value that was assumed for the scale height (h) was was taken to increase linearly from 50 pc for stars at a distance of 200 pc to 120 pc at a distance of 600 pc and to remain constant thereafter. The stellar distances (Table 6, Column 4) were computed assuming the [FORMULA] vs. ([FORMULA]) relation given by Preston et al. (1991) with the zero-point modified to give an [FORMULA] of +0.60 at ([FORMULA]) = 0.20 (the blue edge of the instability strip). The mean difference between the [FORMULA] found in this way from the SFD maps and those given by Harris (1996) for 16 high-latitude globular clusters is satisfactorily small (+0.004[FORMULA]0.003). At lower latitudes ([FORMULA] 30o), however, the extinction is too patchy for the simple exponential model to be reliable and the reddenings found in this way are much less certain. The least reliable values (Table 6, Column 6) are marked with a colon.


[TABLE]

Table 6. Galactic coordinates, distances, IUE colour [FORMULA] and a comparison of the extinctions for the program BHB stars by different methods.
Notes:
a) Derived from the whole sky map of Schlegel et al. (1998).
b) Derived from the energy distribution.
c) Derived from the Strömgren colours using the Moon (1985) code.
d) Derived from a comparison of the observed with the theoretical (ATLAS9) [FORMULA] colours ([FORMULA]).
e) Derived by comparing the observed [FORMULA] vs. [FORMULA] colours with the corresponding theoretical values ([FORMULA]).
f) The [M/H]/[FORMULA]/[FORMULA] that were used to obtain the reddenings that are given in Columns (9) and (10).


5.2. Reddening from the intrinsic colour calibration

We used the UVBYLIST code of Moon (1985) to derive the intrinsic Strömgren indices from the observed indices of our program BHB stars by means of empirical calibrations that are taken from the literature.

The stars are divided into eight photometric groups according to their spectral class and a different empirical calibration is used for each group. All our program stars except BD+32 2188 have 2.72[FORMULA]2.88 and belong to group 6 (stars of spectral type A3-F0 with luminosity class III-V). We placed BD+32 2188 in group 4 (B0-A0 bright giants).

A complete description of the dereddening procedures can be found in Moon (1985) and also Moon & Dworetsky (1985). Here we recall that for group 6, [FORMULA], and hence the reddening, is calculated from the equations given by Crawford (1979), which relate [FORMULA] to the [FORMULA], [FORMULA]c1, and [FORMULA]m1([FORMULA]) indices. For group 4, a dereddening equation was derived by coupling linear relations between the c0 and [FORMULA] colours, determined from Table IV of Zhang (1983), with the reddening ratios given by Crawford & Mandwewala (1976):

[EQUATION]

[EQUATION]

[EQUATION]

We emphasize, however, that the empirical calibrations used by this method are based on stars of spectral type B0 to M2 that lie on or near the main sequence . Hence, for the BHB stars, the reddening, the intrinsic indices, and results from them, should be compared with the corresponding quantities obtained with other methods in order to assess the reliability of this dereddening procedure. The reddening values derived from the UVBYLIST program are given in Column 8 of Table 6.

5.3. Reddening from spectrophotometric data

Spectrophotometric observations are available (Philip & Hayes 1983; Hayes & Philip 1983) for twelve of our candidate BHB stars. An estimate of the reddening was derived for these stars in the process of obtaining the stellar parameters (Sect. 7) by fitting the observed energy distributions to a grid of computed fluxes. For each star, we dereddened the observed energy distribution for a set of [FORMULA] values, sampled at steps of 0.005 mag and starting from 0.000 mag. The adopted reddening law A([FORMULA]) was taken from Table 1 in Mathis (1990) for [FORMULA] = 3.1. For each [FORMULA], the stellar parameters are those that give the minimum rms (Sect. 7.2). We assumed as the most probable [FORMULA], that which gave the minimum rms among those given by the fitting procedure. These [FORMULA] are listed in Column 7 of Table 6.

5.4. Reddening from IUE ultraviolet data

It has been shown (Huenemoerder et al. 1984) that far-UV spectra can be useful for classifying BHB stars and for determining their reddening. All of our candidate BHB stars (except HD 16456 and BD+25 2602) have UV IUE low-resolution (6 Å) spectra, that have been previously analysed and discussed (Huenemoerder et al. 1984; Cacciari 1985; Cacciari et al. 1987; de Boer et al. 1997 and references therein). We felt, however, that we should re-discuss the UV-spectra of these stars, especially the short-wavelength spectra (SWP, 1150-1980 Å), using the data that is in the IUE Final Archive 8. In this way we could extract all the UV-spectra in a homogeneous way using the final IUE flux calibration and image-processing techniques (Nichols & Linsky 1996; Bohlin 1996) and compare them to the latest model atmospheres for metal-poor stars computed by Castelli with the ATLAS9 code and the Opacity Distribution Functions (ODFs) from Kurucz (Castelli 1999).

The region of the UV spectrum that is best reproduced by the model atmospheres of stars with [FORMULA] between 7 500 K and 10 000 K seems to be that in the region of 1 800Å (Huenemoerder et al. 1984; Cacciari et al. 1987). The values of the observed fluxes at 1 800Å were obtained from the SWP spectra by averaging the flux over a rectangular bandpass 150 Å wide. The UV-colour [FORMULA] (given in Table 6, Column 5) is defined as

[EQUATION]

where [FORMULA] (Gray 1992). The UV-flux is strongly affected by interstellar extinction. Consequently, the reddening can be estimated from the [FORMULA] colour by comparing it with that predicted by a model atmosphere assuming that the temperature and/or gravity are known. We used corrections for reddening that were based on Seaton's (1979) reddening law, which gives

[EQUATION]

on the assumption that [FORMULA]. The recent reanalysis of the interstellar extinction by Fitzpatrick (1999) would give a somewhat higher value (4.85) for this ratio. We also estimated the [FORMULA]-colour, defined similarly to [FORMULA], as a check on the consistency of our results. The colours [FORMULA] and [FORMULA] sample contiguous parts of the energy distribution and so are highly correlated; [FORMULA] is closer to the 2 200Å feature and can be more noisy because it is near the edge of the energy distribution in the SWP spectra. We verified that both of these colours gave consistent results but only have used the more reliable [FORMULA] colour so as to avoid duplication.

We started with preliminary values of [FORMULA][FORMULA] and abundances that had been derived from the model atmosphere analysis. When it was available, we preferred the parameters derived from the H[FORMULA] profile because these are reddening-independent. These stellar parameters were used to calculate an intrinsic [FORMULA] colour and the difference between this and the observed [FORMULA] colour gives the reddening [FORMULA], called here [FORMULA]

The reddening [FORMULA] may also be estimated by comparing the observed [FORMULA] vs. [FORMULA] pairs with those predicted by the models at a given gravity, and is called here [FORMULA]. In Fig. 7 we show the program stars and theoretical relations for [M/H]=-1.5 and gravities 2.5, 3.0, 3.5 and 4.0 in the [FORMULA] vs. [FORMULA] plane. If these two estimates of the reddening were consistent within [FORMULA] 0.02 mag, then we assumed that our initial values of [FORMULA] and [FORMULA] were reasonably correct. If this was not the case, we repeated the analysis with different initial values. Our finally adopted values for [FORMULA] and [FORMULA] are given in Columns 9 and 10 of Table 6, where they are compared with the other reddening determinations. The finally adopted values for [M/H], [FORMULA] and [FORMULA] used to obtain these reddenings are given in Column 11 of Table 6. They generally agree with other determinations (Sect. 7). In the second method, the UV data essentially constrain the [FORMULA] that is permitted for a given reddening; in particular this strongly discriminates between FHB stars and main sequence stars of higher gravity. The internal accuracies of the parameters that are found by this way are estimated to be [FORMULA]0.1 in [FORMULA] and [FORMULA]100K in [FORMULA].

[FIGURE] Fig. 7. The theoretical (ATLAS9) colours [FORMULA] vs [FORMULA] for [m/H]=-1.5 and gravity from 2.5 to 4.0 in steps of 0.5. The arrow indicates the effect of reddening.

We estimate that the typical error in these reddenings that comes from photometric errors and the systematic errors to the absolute visual and UV photometric calibrations is [FORMULA] 0.03 mag. Using only the 20 higher latitude BHB stars where the SFD-derived reddenings (Table 6, Column 6) are reliable, the mean value of the SFD reddenings minus the mean of the two reddenings derived from the IUE data (Table 6, Columns 9 and 10) is +0.017[FORMULA]0.004. The mean difference between the reddenings derived by the intrinsic colour calibration (Sect. 5.2; Table 6, Column 11) and the mean of the two reddenings derived from the IUE data is -0.011[FORMULA]0.004 (28 stars).

A detailed comparison between the different reddening estimates is given in Table 6. Clearly systematic differences of the order of a few hundredths of a magnitude in [FORMULA] exist between the reddenings derived by the different methods even at high galactic latitudes. At lower latitudes, the differences are much larger because of the greater uncertainties in the reddenings derived from whole sky maps. It does not seem possible to resolve these differences without additional observations (e.g. mapping the extinction in the direction of the BHB stars using the Strömgren photometry of main sequence field stars).

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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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