Observational evidence has accumulated in recent years, showing that the Galactic bulge includes two populations, a metal-poor one and a metal-rich one, which in addition to having different metallicities show different alpha over iron abundances, spatial distribution, and kinematics. While the metal-rich, barred component has been fairly well characterized, the metal-poor, spheroidal component has been more elusive and harder to describe. RR Lyrae variables are clean tracers of the old bulge component, and they are, on average, more metal-poor than red clump stars. In the present paper, we provide a new catalog of 16488 ab-type RR Lyrae variables in the bulge region within |l|$ and |b|$ extracted from multi-epoch Point Spread Function photometry performed on VISTA Variable in the V\' a L\'actea survey data. We used the catalog to constrain the shape of the old, metal-poor, bulge stellar population. The identification of ab-type RR Lyrae among a large sample of candidate variables of different types has been performed via a combination of a Random Forest classifier and visual inspection. We optimized this process in such a way to extract a clean catalog with high purity, although for this reason its completeness, close to the midplane, is lower compared to a few other near-infrared catalogs covering the same region of the sky. We used the present catalog to derive the shape of their distribution around the Galactic center, resulting in an elongated spheroid with projected axis ratio of b/asim 0.7 and an inclination angle of phi sim 20 degrees. We discuss how observational biases, such as errors on the distances
and a nonuniform sampling in longitude, affect both the present measurements and previous ones, especially those based on red clump stars. Because the latter have not been taken into account before, we refrain from a quantitative comparison between these shape parameters and those derived for the main Galactic bar. Nonetheless, qualitatively, taking into account observational biases would lower the estimated ellipticity of the bar derived from red clump stars, and hence reduce the difference with the present results. We publish a high-purity RRab sample for future studies of the oldest Galactic bulge population, close to the midplane. We explore different choices for the period-luminosity-metallicity relation, highlighting how some of them introduce spurious trends of distance with either the period or the metallicity, or both.
We provide evidence that they trace a structure that is less elongated than the main bar, though we also highlight some biases of these kind of studies not discussed before.
