Structure and kinematics of Type II Cepheids in the Galactic bulge based on near-infrared VVV data

Context. Type II Cepheids (T2Cs) are radially pulsating variables that trace old stellar populations and provide distance estimates through their period-luminosity (PL) relation. Aims. We trace the structure of old stellar population in the Galactic bulge using new distance estimates and kinematic properties of T2Cs. Methods. We present new near-infrared photometry of T2Cs in the bulge from the VISTA Variables in the Via Lactea survey (VVV). We provide the largest sample (894 stars) of T2Cs with JHK(s) observations that have accurate periods from the Optical Gravitational Lensing Experiment (OGLE) catalog. Our analysis makes use of the K-s-band time-series observations to estimate mean magnitudes and individual distances by means of the PL relation. To constrain the kinematic properties of our targets, we complement our analysis with proper motions based on both the VVV and Gaia Data Release 2. Results. We derive an empirical K-s-band PL relation that depends on Galactic longitude and latitude: K-s0 = (10.66 +/- 0.02) (2.21 +/- 0.03).(log P-1.2) (0.020 +/- 0.003).l + (0.050 +/- 0.008) .vertical bar b vertical bar mag; individual extinction corrections are based on a 3D reddening map. Our targets display a centrally concentrated distribution, with solid evidence of ellipsoidal symmetry - similar to the RR Lyrae ellipsoid - and a few halo outliers up to >= 100 kpc. We obtain a distance from the Galactic center of R-0 = 8.46 +/- 0.03(stat.) +/- 0.11(syst.) kpc. We also find evidence that the bulge T2Cs belong to a kinematically hot population, as the tangential velocity components (sigma(vl*) = 104.2 +/- 3.0 km s(-1) and sigma(vb) = 96.8 +/- 5.5 km s(-1)) agree within 1.2 sigma. Moreover, the difference between absolute and relative proper motion is in good agreement with the proper motion of Sgr A* from VLBA measures. Conclusions. We conclude that bulge T2Cs display an ellipsoidal spatial distribution and have kinematics similar to RR Lyrae stars, which are other tracers of the old, low-mass stellar population. T2Cs also provide an estimate of R-0 that agrees excellently well with the literature, taking account of the reddening law.