On the possibility of observing the Shapiro effect for pulsars in globular clusters

Abstract

For pulsars in globular clusters, we suggest using observations of the relativistic time delay of their radiation in the gravitational field of a massive body (the Shapiro effect) located close to the line of sight to detect and identify invisible compact objects and to study the distribution of both visible and dark matter in globular clusters and different components of the Galaxy. We have derived the dependences of the event probability on the Galactic latitude and longitude of sources for two models of the mass distribution in the Galaxy: the “classical” Bahcall—Soneira model and the more recent Dehnen—Binney model. Using three globular clusters (M15, 47 Tuc, Terzan 5) as an example, we show that the ratios of the probability of the events due to the passages of massive Galactic objects close to the line of sight to the parameter f 2 for pulsars in the globular clusters 47 Tuc and M 15 are comparable to those for close passages of massive objects in the clusters themselves and are considerably higher than those for the cluster Terzan 5. We have estimated the rates of such events. We have determined the number of objects near the line of sight toward the pulsar that can produce a modulation of its pulse arrival times characteristic of the effect under consideration; the population of brown dwarfs in the Galactic disk, whose concentration is comparable to that of the disk stars, has been taken into account for the first time.