Halo stars orbit within the potential of the Milky Way and hence their kinematics can be used to understand the underlying mass distribution .
However , the inferred mass distribution depends sensitively upon assumptions made on the density and the velocity anisotropy profiles of the tracer population .
Also , there is a degeneracy between the parameters of the halo and that of the disk or bulge .
Most previous attempts that use halo stars have made arbitrary assumptions about these .
In this paper , we decompose the Galaxy into 3 major components – a bulge , a Miyamoto-Nagai disk and an NFW dark matter halo and then model the kinematic data of the halo Blue Horizontal Branch and K-giant stars from the Sloan Extension for Galactic Understanding and Exploration ( SEGUE ) .
Additionally , we use the gas terminal velocity curve and the Sgr A ^ { * } proper motion .
With the distance of the Sun from the centre of Galaxy R _ { \odot } = 8.5 { kpc } , our kinematic analysis reveals that the density of the stellar halo has a break at 17.2 ^ { +1.1 } _ { -1.0 } { kpc } , and an exponential cut-off in the outer parts starting at 97.7 ^ { +15.6 } _ { -15.8 } { kpc } .
Also , we find the tracer velocity anisotropy is radially biased with \beta _ { s } = 0.4 \pm { 0.2 } in the outer halo .
We measure halo virial mass M _ { \text { vir } } to be 0.80 ^ { +0.31 } _ { -0.16 } \times 10 ^ { 12 } M _ { \sun } , concentration c to be 21.1 ^ { +14.8 } _ { -8.3 } , disk mass to be 0.95 ^ { +0.24 } _ { -0.30 } \times 10 ^ { 11 } M _ { \sun } , disk scale length to be 4.9 ^ { +0.4 } _ { -0.4 } { kpc } and bulge mass to be 0.91 ^ { +0.31 } _ { -0.38 } \times 10 ^ { 10 } M _ { \sun } .
The mass of halo is found to be small and this has important consequences .
The giant stars reveal that the outermost halo stars have low velocity dispersion but interestingly this suggests a truncation of the stellar halo density rather than a small overall mass of the Galaxy .
Our estimates of local escape velocity v _ { esc } = 550.9 ^ { +32.4 } _ { -22.1 } { kms ^ { -1 } } and dark matter density \rho ^ { DM } _ { \odot } = 0.0088 ^ { +0.0024 } _ { -0.0018 } M _ { \sun } { pc } ^ { -3 } ( 0.35 ^ { +0.08 } _ { -0.07 } GeV cm ^ { -3 } ) are in good agreement with recent estimates .
Some of the above estimates , in particular M _ { \text { vir } } , are depended on the adopted value of R _ { \odot } and also , on the choice of the outer power-law index of the tracer number density .