Reddening and Extinction Toward the Galactic Bulge from OGLE-III: The Inner Milky Way's Rv ~ 2.5 Extinction Curve

We combine VI photometry from OGLE-III with VVV and 2MASS measurements of E(J-K_{s}) to resolve the longstanding problem of the non-standard optical extinction toward the Galactic bulge. We show that the extinction is well-fit by the relation A_{I} = 0.7465*E(V-I) + 1.3700*E(J-K_{s}), or, equivalently, A_{I} = 1.217*E(V-I)(1+1.126*(E(J-K_{s})/E(V-I)-0.3433)). The optical and near-IR reddening law toward the inner Galaxy approximately follows an R_{V} \approx 2.5 extinction curve with a dispersion {\sigma}_{R_{V}} \approx 0.2, consistent with extragalactic investigations of the hosts of type Ia SNe. Differential reddening is shown to be significant on scales as small as as our mean field size of 6', with the 1{\sigma} dispersion in reddening averaging 9% of total reddening for our fields. The intrinsic luminosity parameters of the Galactic bulge red clump (RC) are derived to be (M_{I,RC}, \sigma_{I,RC,0}, (V-I)_{RC,0}, \sigma_{(V-I)_{RC}}, (J-K_{s})_{RC,0}) = (-0.12, 0.09, 1.06, 0.121, 0.66). Our measurements of the RC brightness, brightness dispersion and number counts allow us to estimate several Galactic bulge structural parameters. We estimate a distance to the Galactic center of 8.20 kpc, resolving previous discrepancies in distance determinations to the bulge based on I-band observations. We measure an upper bound on the tilt {\alpha} \approx 40{\deg}. between the bar's major axis and the Sun-Galactic center line of sight, though our brightness peaks are consistent with predictions of an N-body model oriented at {\alpha} \approx 25{\deg}. The number of RC stars suggests a total stellar mass for the Galactic bulge of 2.0*10^{10} M_{\odot}, if one assumes a Salpeter IMF.