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Astron. Astrophys. 325, 1115-1124 (1997)

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3. Stellar surface flux densities

3.1. Ca II H&K flux densities

The surface flux density in the cores of the Ca II H&K lines, [FORMULA], has been derived from the S -values following Rutten (1984), using his `arbitrary' units:

[EQUATION]

where the conversion factor [FORMULA] depends on [FORMULA] and luminosity class (Rutten 1984), and [FORMULA] has been taken from Flower (1977) for giants with [FORMULA], and from Böhm-Vitense (1981) for all other stars.

The flux density in the Ca II line cores only partially originates in the active chromosphere. The other part, the so-called minimum flux, is of photospheric (line wings) and of basal (possibly acoustic) origin (see, e.g., Schrijver 1987). By subtracting this (colour-dependent) minimum flux component, we derive the excess flux density, which is listed in Table 2, column 2. For this minimum flux we have used the empirical minimum flux derived by Rutten (1987b), for a large sample of stars with luminosity classes between II-III and V. Rutten (1986) shows that this minimum flux is similar to the sum of two theoretically expected contributions: a line-wing contribution, and a minimum line-core contribution, both depending predominantly on effective temperature. Therefore, the minimum flux is taken the same for dwarfs and giants, in spite of the fact that the lowest observed fluxes for dwarfs with [FORMULA] are higher than this minimum flux.

The minimum flux is given for the 1Å passband, so we have converted the [FORMULA] -values to [FORMULA] -values using the relations [FORMULA], where [FORMULA] and [FORMULA] are given in Table 3 as a function of colour [FORMULA] and luminosity class LC. We have derived these relations from a sample of stars for which both [FORMULA] and [FORMULA] values have been measured (data listed by Rutten 1987a). The scatter [FORMULA] about the relationships is listed in Table 3; this scatter has been taken into account as an additional uncertainty in the [FORMULA] value, caused by the conversion. The conversion for stars with [FORMULA] is only slightly different from the conversion for cooler stars, but still results in a difference of about 20% at the lowest activity levels ([FORMULA]), and after subtraction of the minimum flux density this can lead to large differences in the excess flux density.


[TABLE]

Table 3. Conversion from the [FORMULA] value to the [FORMULA] value using the relation [FORMULA]. Listed are [FORMULA] (left) and [FORMULA] (middle) with their uncertainties (between parentheses). Also listed are the number of data-points n which define the relationship, and the scatter [FORMULA] around the relationship.


The conversion depends on the profile of the line core emission (basal and magnetic) and on the photospheric absorption profile. These profiles depend strongly on colour and luminosity class, so it is not surprising that we find different relations for the conversion of [FORMULA] to [FORMULA]. However, we do not find a significant difference between the conversion for giants (III) and dwarfs (V). In trying to understand the different relationships, we describe the S -value as a sum of two different parts: a minimum (photospheric and basal) component and a magnetic emission component. Two stars with different activity levels, but otherwise identical, will only show a difference in the amount of magnetic emission. Both stars have the same relative transmission of the magnetic emission component through the 1Å passband, as long as the width of the magnetic emission profile does not change with activity level (which is valid for active regions on the sun, Oranje 1983). The difference between the [FORMULA] -values of both stars is equal to the difference between the [FORMULA] -values scaled with the 1Å passband transmission factor and with the ratio of the (constant) normalisation factors of [FORMULA] and [FORMULA]. The slope [FORMULA] of the relations in Table 3 is the product of these two scaling factors, and not the transmission factor alone, as Schrijver et al. (1992) suggested. Wilson and Bappu (1957) showed that the width of the line core emission peak depends mainly on luminosity: about 0.5Å for dwarfs, 1Å for giants, and 2Å for supergiants. This means that the transmission through the 1Å passband is significantly smaller for bright giants than for giants, but the difference between the transmission for giants and dwarfs is not so pronounced, explaining the change in the slope of the conversion relationship around luminosity class II. It is remarkable that relatively cool stars ([FORMULA]) appear to have a larger transmission than relatively hot stars. This implies that the width of the line-core emission is much larger (about a factor 2 to 3) for stars with [FORMULA] than for cooler stars. This effect could partly be caused by rotational broadening in the (on average) faster rotating early type stars, which has the effect of moving part of the line-wing contribution to the line core. However, if we divide the sample of stars with colours [FORMULA] in two groups according to their rotational velocities, the change in slope  [FORMULA] is not very significant: the maximum difference in slope occurs between stars with [FORMULA] ([FORMULA]) and stars with [FORMULA] ([FORMULA]). Wilson and Bappu (1957) found that the width of the line core emission peak does not depend on effective temperature. However, the stars they used for their study are relatively cool: [FORMULA], so they could not have noticed the dependence we find here. For giants and dwarfs with [FORMULA] we do not find a change in the slope [FORMULA] with colour, either, consistent with the findings of Wilson and Bappu (1957).

3.2. X-ray flux densities

For each star detected in the ROSAT survey we derived the X-ray flux density at the stellar surface, [FORMULA], from the flux density on the detector, [FORMULA], following Oranje et al. (1982):

[EQUATION]

The intrinsic colour index [FORMULA] is from Fitzgerald (1970), bolometric corrections from Johnson (1966) for dwarfs and from Flower (1977) for giants. The surface flux densities [FORMULA] are listed in Table 2, column 5. The uncertainties in the surface flux densities are dominated by the uncertainties in the source count rate [FORMULA] and in the hydrogen column density [FORMULA], the latter being caused by the relatively large uncertainties in the distance and in [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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