This paper describes outstanding issues in astrophysics and cosmology that can be solved by astronomical observations in a broad spectral range from far infrared to millimeter wavelengths. The discussed problems related to the formation of stars and planets, galaxies and the interstellar medium, studies of black holes and the development of the cosmological model can be addressed by the planned space observatory Millimetron (the "Spectr-M" project) equipped with a cooled 10-m mirror. Millimetron can operate both as a single-dish telescope and as a part of a space-ground interferometer with very long baseline.

The luminosity of accreting magnetised neutron stars can largely exceed the Eddington value due to appearance of accretion columns. The height of the columns can be comparable to the neutron star radius. The columns produce the X-rays detected by the observer directly and illuminate the stellar surface, which reprocesses the X-rays and causes additional component of the observed flux. The geometry of the column and the illuminated part of the surface determines the radiation beaming. Curved spacetime affects the angular flux distribution. We construct a simple model of the beam patterns formed by direct and reflected flux from the column. We take into account the possibility of appearance of accretion columns, whose height is comparable to the neutron star radius. We argue that depending on the compactness of the star the flux from the column can be either strongly amplified due to gravitational lensing, or significantly reduced due to column eclipse by the star. The eclipses of high accretion columns result in specific features in pulse profiles. Their detection can put constraints on the neutron star radius. We speculate that column eclipses are observed in X-ray pulsar V 0332+53, leading us to the conclusion of large neutron star radius in this system (∼ 15 km if M ∼ 1.4M ). We point out that the beam pattern can be strongly affected by scattering in the accretion channel at high luminosity, which has to be taken into account in the models reproducing the pulse profiles.

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