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Photometric and spectroscopic studies of cool stars discovered in EXOSAT X-ray images. IV. The northern hemisphere sample We present high-precision photometry, high- and medium-resolutionspectroscopy for a sample of 32 stars likely to be the opticalcounterparts of X-ray sources serendipitously detected by the EXOSATsatellite. Using also recent results from the Hipparcos satellite, weinfer spectral types, compute X-ray luminosities and Li abundances andinvestigate the single or binary nature of the sample stars. We foundeleven new variable stars, whose photometric periods fall in the1.2-27.5 day range, for most of which the optical variability isconsistent with the presence of photospheric cool spots. For our sampleof X-ray selected stars we confirm the existence of a strong correlationbetween the stellar rotation rate and the level of activity, and alsobetween the X-ray and bolometric luminosities. Two stars in our sampleare likely to be pre-main sequence objects, one is likely to be apreviously unknown M-type star within 25 pc. Based on data collected atCatania Astrophysical Observatory (Mt. Etna, Italy), at ObservatorioAstronomico Nacional (UNAM, S. Pedro Martir, BC, Mexico) and at KittPeak National Observatory (Kitt Peak, AZ, USA) Table 1 is available inthe on-line version; Table 3 and the complete data set are available inelectronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr orvia http://cdsweb.u-strasbg.fr/Abstract.html}
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