Interstellar Extinction Law toward the Galactic Center IV: J, H, and Ks
  Bands from VVV Red Clump Stars
  We have determined the wavelength dependence of the extinction in the
near-infrared bands ($J$, $H$, $K_{\mathrm S}$) toward the Galactic center from
the VVV (VISTA Variables in the V\'ia L\'actea) aperture photometry of the
stars in the region $|l|\lesssim2^\circ.0$ and
$0^\circ.5\lesssim|b|\lesssim1^\circ.0$; this region consists of 12 VVV tiles.
We have found significant systematic discrepancy up to $\sim0.1$ mag between
the stellar magnitudes of the same stars in overlapping VVV tiles. However, by
carefully using the positions of red clump stars in color-magnitude diagrams as
a tracer of the extinction and reddening, we are able to determine the average
of the ratios of total to selective extinction to be $A(K_{\mathrm
S})/E(H-K_{\mathrm S})=1.44\pm0.04$, $A(K_{\mathrm S})/E(J-K_{\mathrm
S})=0.423\pm0.024$, $A(H)/E(J-H)=1.25\pm0.04$; from these ratios, a steep power
law $A(\lambda)\propto\lambda^{-\alpha}$ whose index $\alpha$ is $\sim2.0-2.3$
in the $J,H,K_{\mathrm S}$ wavelength range is estimated. The obtained
wavelength dependence is consistent with those obtained with the MKO
photometric system employed in SIRIUS camera attached to the IRSF telescope in
previous studies. Such a steep decline of extinction toward the longer
wavelengths is also in line with recent results based on deep imaging surveys.
The determined extinction law seems to be variable in the VVV tile to tile, and
it is not clear how much of this is due to real sight line variations and due
to observational systematic effects. Thus, there might be room for improvement
of the extinction law determination from the existing VVV data, but this steep
extinction law tends to locate heavily reddened objects in the Galactic plane
more distant from us when their distance moduli are calculated from the
observed reddening values.
