Surface term effects on mass estimators

Context. We propose a way of estimating the mass contained in the volume occupied by a sample of galaxies in a virialized system. Aims. We analyze the influence of surface effects and the contribution of the cosmological constant terms on our mass estimations of galaxy systems. Methods. We propose two equations that contain surface terms to estimate galaxy sample masses. When the surface terms are neglected, these equations provide the so-called virial and projected masses. Both equations lead to a single equation that allows sample masses to be estimated without the need for calculating surface terms. Sample masses for some nearest galaxy groups are estimated and compared with virialized masses determined from turn-around radii and results of a spherical infall model. Results. Surface effects have a considerable effect on the mass estimations of the studied galaxy groups. According to our results, they lead sample masses of some groups to being less than half the virial mass estimations and even less than 10% of projected mass estimations. However, the contributions of cosmological constant terms to mass estimations are smaller than 2% for the majority of the virialized groups studied. Our estimations are in agreement with virialized masses calculated from turn-around radii. Virialized masses for complexes were found to be: (8.9 ± 2.8) × 10 11 M ⊙ for the Milky Way – M 31; (12.5 ± 2.5) × 10 11 M ⊙ for M 81 – NGC 2403; (21.5 ± 7.7) × 10 11 M ⊙ . for Cantaurs A – M 83; and (7.9 ± 2.6) × 10 11 M ⊙ . for IC 324 – Maffei. Conclusions. The nearest galaxy groups located inside a sphere of 5 Mpc have been addressed to explore the performance of our mass estimator. We have seen that surface effects make mass estimations of galaxy groups rather smaller than both virial and projected masses. In mass calculations, cosmological constant terms can be neglected; nevertheless, the collapse of cold dark matter leading to virialized structures is strongly affected by the cosmological constant. We have also seen that, if mass density were proportional to luminosity density on different scales in the Universe, the 5 Mpc sphere would have a mean density close to that of the sphere region containing galaxies and systems of galaxies; thus, the rest of the sphere could contain regions of low-mass dark halos with similar mass density. This mass density would be about 4.5 times greater than that of the matter background of the Universe at present.