Milky Way rotation curve from proper motions of red clump giants

We derive the stellar rotation curve of the Galaxy in the range of Galactocentric radii of R=4-16 kpc at different vertical heights from the Galactic plane of z between -2 and +2 kpc. We used the PPMXL survey, which contains the USNO-B1 proper motions catalog cross-correlated with the astrometry and near-infrared photometry of the 2MASS Point Source Catalog. To improve the accuracy of the proper motions, we calculated the average proper motions of quasars to know their systematic shift from zero in this PPMXL survey, and we applied the corresponding correction to the proper motions of the whole survey, which reduces the systematic error. We selected from the CM diagram K vs. (J-K) the red clump giants and used the information of their proper motions to build a map of the rotation speed of our Galaxy. We obtain an almost flat rotation curve with a slight decrease for higher values of R or |z|. The most puzzling result is obtained for the farthest removed and most off-plane regions, where a significant deviation from a null average proper motion (~4 mas/yr) in the Galactic longitude direction for the anticenter regions can be directly translated into a rotation speed much lower than in the solar Galactocentric radius: an average speed of 82+/-5(stat.)+/-58(syst.) km/s. A scenario with a rotation speed lower than 150 km/s in these regions of our explored zone is intriguing, and invites one to reconsider different possibilities for the dark matter distribution. However, given the high systematic errors, we cannot conclude about this. Hence, more measurements of the proper motions at high R and |z| are necessary to validate the exotic scenario that would arise if this low speed were confirmed.Comment: 10 pages, accepted for publication in A&A. v2: an erratum is correcte

Peaks in the CMBR power spectrum. I. Mathematical analysis of the associated real space features

The purpose of our study is to understand the mathematical origin in real space of modulated and damped sinusoidal peaks observed in cosmic microwave background radiation anisotropies. We use the theory of the Fourier transform to connect localized features of the two-point correlation function in real space to oscillations in the power spectrum. We also illustrate analytically and by means of Monte Carlo simulations the angular correlation function for distributions of filled disks with fixed or variable radii capable of generating oscillations in the power spectrum. While the power spectrum shows repeated information in the form of multiple peaks and oscillations, the angular correlation function offers a more compact presentation that condenses all the information of the multiple peaks into a localized real space feature. We have seen that oscillations in the power spectrum arise when there is a discontinuity in a given derivative of the angular correlation function at a given angular distance. These kinds of discontinuities do not need to be abrupt in an infinitesimal range of angular distances but may also be smooth, and can be generated by simply distributing excesses of antenna temperature in filled disks of fixed or variable radii on the sky, provided that there is a non-null minimum radius and/or the maximum radius is constrained.Comment: accepted to be published in Physica