  We try to constrain the Equation-of-State (EoS) of supra-nuclear-density
matter in neutron stars (NSs) by observations of nearby NSs. There are seven
thermally emitting NSs known from X-ray and optical observations, the so-called
Magnificent Seven (M7), which are young (up to few Myrs), nearby (within a few
hundred pc), and radio-quiet with blackbody-like X-ray spectra, so that we can
observe their surfaces. As bright X-ray sources, we can determine their
rotational (pulse) period and their period derivative from X-ray timing. From
XMM and/or Chandra X-ray spectra, we can determine their temperature. With
precise astrometric observations using the Hubble Space Telescope, we can
determine their parallax (i.e. distance) and optical flux. From flux, distance,
and temperature, one can derive the emitting area - with assumptions about the
atmosphere and/or temperature distribution on the surface. This was recently
done by us for the two brightest M7 NSs RXJ1856 and RXJ0720. Then, from
identifying absorption lines in X-ray spectra, one can also try to determine
gravitational redshift. Also, from rotational phase-resolved spectroscopy, we
have for the first time determined the compactness (mass/radius) of the M7 NS
RBS1223. If also applied to RXJ1856, radius (from luminosity and temperature)
and compactness (from X-ray data) will yield the mass and radius - for the
first time for an isolated single neutron star. We will present our
observations and recent results.
