We establish an extragalactic , zero-motion frame of reference within the deepest optical image of a globular star cluster , a Hubble Space Telescope ( HST ) 123-orbit exposure of M4 ( GO 8679 , cycle 9 ) .
The line of sight beyond M4 ( l , b = 351 ^ { o } , 16 ^ { o } ) intersects the inner halo ( spheroid ) of our Galaxy at a tangent-point distance of 7.6 kpc ( for R _ { \circ } = 8 kpc ) .
The main sequence of this population can be clearly seen on the color-magnitude diagram ( CMD ) below the M4 main sequence .
We isolate these spheroid stars from the cluster on the basis of their proper motions over the 6-year baseline between these observations and others made at a previous epoch with HST ( GO 5461 , cycle 4 ) .
Distant background galaxies are also found on the same sight line by using image-morphology techniques .
This fixed reference frame allows us to determine an independent measurement of the fundamental Galactic constant , \Omega _ { \circ } = \Theta _ { \circ } / R _ { \circ } = 25.3 \pm 2.6 km/s/kpc , thus providing a velocity of the Local Standard of Rest v _ { LSR } = \Theta _ { \circ } = 202.7 \pm 24.7 km/s for R _ { \circ } = 8.0 \pm 0.5 kpc .
Secondly , the galaxies allow a direct measurement of M4 ’ s absolute proper motion , \mu _ { \alpha } \hat { \alpha } = - 12.26 \pm 0.54 mas/yr , \mu _ { \delta } \hat { \delta } = - 18.95 \pm 0.54 mas/yr , in excellent agreement with recent studies .
The clear separation of galaxies from stars in these deep data also allow us to search for inner-halo white dwarfs .
We model the conventional Galactic contributions of white dwarfs along our line of sight and predict 7.9 ( thin disk ) , 6.3 ( thick disk ) and 2.2 ( spheroid ) objects to the limiting magnitude at which we can clearly delineate stars from galaxies ( V \sim 29 ) .
An additional 2.5 objects are expected from a 20 % white dwarf dark halo consisting of 0.5 M _ { \odot } objects , 70 % of which are of the DA type .
After considering the kinematics and morphology of the objects in our data set , we find the number of white dwarfs to be consistent with the predictions for each of the conventional populations .
However , we do not find any evidence for dark halo white dwarfs .