Table 4.2.: Spectral type correlation to effective temperatures Spectral type Teff Spectral type Teff
[◦K] [◦K]
targets (85%) are identified among theStern et al.(1995) detections, where the limiting X-ray luminosity is 1−2×1028ergs s−1 (at the Hyades’ distance). Although the detection limit is lowered by about a magnitude (≈ 1.5×1027ergs s−1) by the deeper pointings, eg. Reid et al.(1995), only a small projected cluster area is covered, thus resulting in comparably few detected Hyades. We use the well established conversion factor of 6×10−12ergs s−1counts−1 to obtain X-ray fluxes from published ROSAT countrates.1 A number of objects are not detected, these are mostly among the latest spectral types. These stars are probably just too faint to produce an X-ray luminosity above the detection threshold, i.e. the irradiated X-ray flux is below the detection limit of ROSAT at the corresponding distance. For such non-detections, Table A.1lists upper limits based on the sensitivity of the RASS. Individual non-detections are discussed in Sec.5.2.2.
Bolometric luminosities are based on individualTeff and the corresponding luminosity from BCAH isochrones (650 Myr, solar metallicity). Because the (projected) size of the Hyades cluster extends over many square degrees, and the cluster diameter is of order 20 pc (Röser et al. 2011), the absolute distance to individual cluster stars can vary significantly, thus potentially overestimating the luminosity by a factor of up to 2.5. We try to minimize this effect by obtaining individual distances for all objects where available. Distances are preferentially taken from parallaxes inRöser et al.(2011), and subsequently fromStern et al.
(1995) and references therein. In a few cases, no distance information is available, and we assume for these stars a distance of 45 pc, eg. the approximate distance to the cluster center (46.34±0.27 pc, Perryman et al. 1998). Table 3.1 lists the individual distances and their origin for stars in the observed sample.
4.4. Rotational velocities
We determine the stellar projected rotational velocity2 vrotsini by measuring the spectral line broading. Rotation is degenerate in sini, where i is the inclination angle between the stellar rotation axis and the line-of-sight (i= 90◦ for pole-on). It can generally be assumed
1 This factor has been shown, eg. byFleming et al.(1993);Stern et al. (1994,1995);Reid et al.(1995), to well describe soft (≈0.1−1.8 keV) X-ray emission from stellar coronae.
2To ease readibility, we will use the shortenedvsinito refer to rotational velocity in the following text. This should not be mistaken as radial velocity.
thatiis randomly distributed, and hence does not pose a systematic bias on a large sample, albeit the rotational velocities of individual objects remain lower bounds of the true velocity.
We employ a cross-correlation technique to infer the line broadening similar to the methods used byBrowning et al.(2010) andWest & Basri(2009a) for cool, M-type stars. Our method cross-correlates each of the object spectra against a template spectrum of equal or very similar spectral type. The templates are constructed from slowly rotating stars observed with the same instrumental setup to minimize the effects of instrumental profile and spectral resolution changes. All of the templates have measured vsini≤ 3 km/s (cf. Table 4.3, and references therein) from high-resolution spectroscopy, which is at or below the detection limit for the R= 48 000 FEROS spectra, and a conservative estimate in case of UVES observations. This means that there are three categories of template and program stars owing to three different combinations of instrument and resolving power. The template stars were observed over a wide range in time, but were treated following the same steps as the object data in Sec.3.3.
We consider the template stars as non-rotating and their spectra as rotationally unbroadened, leaving them with an imprint of instrumental broadening only plus other physical broadening agents (which are negligible in templates and objects for our purposes). Categories of program and templates are thus always matched, i.e. program stars of a given instrument are always treated with template observations of the same instrument and with the same resolving power.
Table 4.3.: Template stars used for the cross-correlation analysis.
Name α(J2000) δ(J2000) SpT vsini Reference
[km s−1]
HD 162907 17 54 30.1 −26 37 55 K0V 1.0 Nordström et al. (2004) GL 559B 14 39 35.1 −60 50 13 K1V 1.1 Saar & Osten (1997) Gl 9251B 08 07 09.1 07 23 00 K7V 1.4 López-Santiago et al. (2010)
Gl 57 01 21 34.6 −41 39 23 K7V < 3.0 this work Notes.§ denotes template spectra available from both FEROS and UVES. All other template stars from either instrument.
4.4. Rotational velocities 27
4.4.1. Crosscorrelation procedure
Each template spectrum is artificially (rotationally) broadened employing a variable line-broadening kernel (Gray 2005) that corresponds to a series of rotational velocities from 0 to 50 km/s. As the broadening is non-linear, step sizes range from 0.5 km/s to 5 km/s at the lower and upper ends, respectively. These are then each cross-correlated with the original, unbroadened template. The resulting cross-correlation functions (XCFs) are a series of distinct gaussian-like peaks, where their width corresponds to the broadening applied to the template spectrum. We fit these peaks with gaussians and measure their FWHM. The correlation function’s width as a function of the underlying rotational velocities used in the broadening kernel yield a broadening “growth curve” that is specific for each combination of object and template spectra (and also depends on the wavelength range). This growth curve enables the computation of vsini inherent to a spectrum from the width of its cross-correlation profile. Cross-correlating the object spectrum with the unbroadened template (vsini ≈ 0 km/s) and measuring the corresponding width of the correlation function thus gives the rotational velocity vsini of the object. Note that template and object spectra have the same instrumental profiles, and are of very similar spectral type so that other line-broadening mechanisms thanvsiniare negliable and do, at most, alter the correlation profiles in a systematic way.
For each object-template combination,vsiniis measured from a set of pre-selected wavelength-ranges. These are typically 20-50 nm wide and exclude ranges with telluric features identified in the atlases ofKirkpatrick et al.(1991) andWallace et al.(2011). Cross-correlation is per-formed in about 20 ranges betweenλλ500−900 nm that contain moderately deep, unblended photospheric lines. We exclude overly broad and deep lines as these dominate and smear out the correlation profiles. Similarly, molecular band-heads are omitted, as these can produce a correlation profile with many peaks due to the many narrowly spaced lines in the spectrum.
Correlation profiles that do not resemble a gaussian are not taken into account. Each profile is assigned a quality flag, and only the best fits are considered in the further analysis. The shape of the correlation profile may also help to discriminate binary stars.
4.4.2. Template selection
Our template stars are field dwarfs, and thus probably considerably older than the interme-diate aged Hyades (625 Myr, Perryman et al. 1998). The latter have settled on the main sequence, but show quite some differences in their spectra when compared to the field stars of the same spectral type. This is likely due to loggcontraction effects, and results in subtle differences e.g. in linestrengths. The transition from K-type to M-type stars is particularly affected by a somewhat variable onset of dominating molecular features (TiO, FeH), which occurs in the open cluster stars at a spectral type that may be one or two sub-types earlier or later compared with the field stars. To account for the different spectral features present in early K to mid M-type stars, we use different sets of wavelength-ranges for K- and M-stars.
Furthermore, each cross-correlation analysis of an object is performed with at least three templates, where the additional templates are of neighbouring spectral types. We find that this scheme reduces the uncertainty in thevsinidetermination significantly, and gives us an additional measure of the suitability of a specific template for a given object.
Our sample of Hyades is comprised of the full range of K–mid M spectral types. This broad range makes the selection of suitable template stars a somewhat delicate issue, since the spectral shape and abundances drastically change over the course of K to M-types, rendering
a comparison of even close spectral types difficult. Other studies of rotation, mostly in field stars, avoid this issue by focussing solely on a narrow, more homogenous range of spectral classes, e.g. either a few adjacent spectral sub-classes in the M-type regime or earlier than mid K-type stars. The performance of the cross-correlation method to determine vsini to a certain degree depends on a good match between object and template spectrum. For our sample objects, it is obvious that a single template star cannot be employed for the entire set of object spectra. Our approach is to optimize the spectral difference between object and template, which in our experience provides the most robust results. We carefully constructed a set of template stars for both the FEROS and UVES subsamples independently, aiming at the slowest possible rotators among the range of spectral types covered. Only a few template stars are observed with both instruments. For the UVES subsample, an additional challenge is to match wavelength coverage and instrumental mode of object and template, since UVES observations were performed in a variety of resolving powers and wavelength settings. The resulting set of templates is listed in Table4.3.
4.4.3. Template matching
We were unable to follow our strict methodology for six program stars observed with UVES:
1. For 2M 03202921+0827161 (HIP 15563), 2M 04094935+0918197 (HIP 19441), and for 2M 05004888+0443591 (HIP 23312) the appropriate template spectra are only available at higher resolution compared to the targets. We degraded the corresponding tem-plates using a gaussian-like instrumental broadening kernel (Gray 2005) to match the resolution of the objects.
2. For 2M 04291234+1516259 (vA 529), the same procedure was applied, but degrading the object spectrum to match the available templates.
3. Observations of 2M 04033902+1927180 (RHy 44) and 2M 04322373+1745026 (RHy 308) were performed under conditions with the spectrograph‘s slit width larger than the seeing, so that the spectral resolution is not slit width but seeing dominated. In these cases, we degraded the resolution of the template spectra for each object-template combination following two steps: first, we measured the width of unblended telluric lines in the O2 band 6237–6350 Å in the objects by fitting gaussian profiles (these lines are free from stellar broadening agents). Then, we instrumentally broadened the corresponding template spectra (available in higher resolution) until the template’s telluric linewidths match those in the objects. In doing so, we assume that the intrinsic O2 linewidths of the program star’s observation are negligible compared to the effect of seeing (0.66′′ and 1.15′′for the two objects, respectively). The resulting object-template combinations then underwent the usual cross-correlation analysis.
4.4.4. Error estimation
The final (projected) rotational velocity for an object is then computed as follows: From the set ofvsinivalues obtained from the different wavelength-ranges for one template, those with a low quality flagged profile are discarded. For the remaining, the median and the standard deviation are taken. A typical spread is on the order of 1 km/s. From all template spectra employed for an object, a weighted average is computed from the individual median values, whose error we consider as the formalvsinierror, given in TableA.1. We note that this error