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$omega$ Centauri (NGC 5139) hosts hundreds of pulsating variable stars of different types, thus representing a treasure trove for studies of their corresponding period-luminosity (PL) relations. Our goal in this study is to obtain the PL relations for RR Lyrae, and SX Phoenicis stars in the field of the cluster, based on high-quality, well-sampled light curves in the near-infrared (IR). $omega$ Centauri was observed using VIRCAM mounted on VISTA. A total of 42 epochs in $J$ and 100 epochs in $K_{rm S}$ were obtained, spanning 352 days. Point-spread function photometry was performed using DoPhot and DAOPHOT in the outer and inner regions of the cluster, respectively. Based on the comprehensive catalogue of near-IR light curves thus secured, PL relations were obtained for the different types of pulsators in the cluster, both in the $J$ and $K_{rm S}$ bands. This includes the first PL relations in the near-IR for fundamental-mode SX Phoenicis stars. The near-IR magnitudes and periods of Type II Cepheids and RR Lyrae stars were used to derive an updated true distance modulus to the cluster, with a resulting value of $(m-M)_0 = 13.708 pm 0.035 pm 0.10$ mag, where the error bars correspond to the adopted statistical and systematic errors, respectively. Adding the errors in quadrature, this is equivalent to a heliocentric distance of $5.52pm 0.27$ kpc.
$omega$ Centauri (NGC~5139) contains many variable stars of different types, including the pulsating type II Cepheids, RR Lyrae and SX Phoenicis stars. We carried out a deep, wide-field, near-infrared (IR) variability survey of $omega$ Cen, using the
The most massive and complex globular clusters in the Galaxy are thought to have originated as the nuclear cores of now tidally disrupted dwarf galaxies, but the connection between globular clusters and dwarf galaxies is tenuous with the M54/Sagittar
Asymptotic Giant Branch variables are found to obey period-luminosity relations in the mid-IR similar to those seen at K_S (2.14 microns), even at 24 microns where emission from circumstellar dust is expected to be dominant. Their loci in the M, logP
[ABRIDGED] $omega$ Centauri (NGC 5139) contains large numbers of variable stars of different types and, in particular, more than a hundred RR Lyrae stars. We have conducted a variability survey of $omega$ Cen in the NIR, using ESOs 4.1m Visible and I
We present new Near-Infrared (J,K) magnitudes for 114 RR Lyrae stars in the globular cluster Omega Cen (NGC 5139) which we combine with data from the literature to construct a sample of 180 RR Lyrae stars with J and K mean magnitudes on a common phot