Using the photometric parallax method we estimate the distances to \sim 48 million stars detected by the Sloan Digital Sky Survey ( SDSS ) and map their three-dimensional number density distribution in the Galaxy .
The currently available data sample the distance range from 100 pc to 20 kpc and cover 6,500 deg ^ { 2 } of sky , mostly at high galactic latitudes ( |b| > 25 ) .
These stellar number density maps allow an investigation of the Galactic structure with no a priori assumptions about the functional form of its components .
The data show strong evidence for a Galaxy consisting of an oblate halo , a disk component , and a number of localized overdensities .
The number density distribution of stars as traced by M dwarfs in the Solar neighborhood ( D < 2 kpc ) is well fit by two exponential disks ( the thin and thick disk ) with scale heights and lengths , bias-corrected for an assumed 35 % binary fraction , of H _ { 1 } = 300 pc and L _ { 1 } = 2600 pc , and H _ { 2 } = 900 pc and L _ { 2 } = 3600 pc , and local thick-to-thin disk density normalization \rho _ { thick } ( R _ { \odot } ) / \rho _ { thin } ( R _ { \odot } ) = 12 % .
We use the stars near main-sequence turnoff to measure the shape of the Galactic halo .
We find a strong preference for oblate halo models , with best-fit axis ratio c / a = 0.64 , \rho _ { H } \propto r ^ { -2.8 } power-law profile , and the local halo-to-thin disk normalization of 0.5 % .
Based on a series of Monte-Carlo simulations , we estimate the errors of derived model parameters not to be larger than \sim 20 % for the disk scales and \sim 10 % for the density normalization , with largest contributions to error coming from the uncertainty in calibration of the photometric parallax relation and poorly constrained binary fraction .
While generally consistent with the above model , the measured density distribution shows a number of statistically significant localized deviations .
In addition to known features , such as the Monoceros stream , we detect two overdensities in the thick disk region at cylindrical galactocentric radii and heights ( R,Z ) \sim ( 6.5 , 1.5 ) kpc and ( R,Z ) \sim ( 9.5 , 0.8 ) kpc , and a remarkable density enhancement in the halo covering over a thousand square degrees of sky towards the constellation of Virgo , at distances of \sim 6-20 kpc .
Compared to counts in a region symmetric with respect to the l = 0 ^ { \circ } line and with the same Galactic latitude , the Virgo overdensity is responsible for a factor of 2 number density excess , and may be a nearby tidal stream or a low-surface brightness dwarf galaxy merging with the Milky Way .
The u - g color distribution of stars associated with it implies metallicity lower than that of thick disk stars , and consistent with the halo metallicity distribution .
After removal of the resolved overdensities , the remaining data are consistent with a smooth density distribution ; we detect no evidence of further unresolved clumpy substructure at scales ranging from \sim 50 pc in the disk , to \sim 1 - 2 kpc in the halo .