Measuring the relative mass contributions of luminous and dark matter in spiral galaxies is important for understanding their formation and evolution .
The combination of a galaxy rotation curve and strong lensing is a powerful way to break the disk-halo degeneracy that is inherent in each of the methods individually .
We present an analysis of the 10-image radio spiral lens B1933 + 503 at z _ { l } = 0.755 , incorporating ( 1 ) new global VLBI observations , ( 2 ) new adaptive-optics assisted K-band imaging , ( 3 ) new spectroscopic observations for the lens galaxy rotation curve and the source redshift .
We construct a three-dimensionally axisymmetric mass distribution with 3 components : an exponential profile for the disk , a point mass for the bulge , and an NFW profile for the halo .
The mass model is simultaneously fitted to the kinematics and the lensing data .
The NFW halo needs to be oblate with a flattening of a / c = 0.33 ^ { +0.07 } _ { -0.05 } to be consistent with the radio data .
This suggests that baryons are effective at making the halos oblate near the center .
The lensing and kinematics analysis probe the inner \sim 10 kpc of the galaxy , and we obtain a lower limit on the halo scale radius of 16 kpc ( 95 % CI ) .
The dark matter mass fraction inside a sphere with a radius of 2.2 disk scale lengths is f _ { DM, 2.2 } = 0.43 ^ { +0.10 } _ { -0.09 } .
The contribution of the disk to the total circular velocity at 2.2 disk scale lengths is 0.76 ^ { +0.05 } _ { -0.06 } , suggesting that the disk is marginally submaximal .
The stellar mass of the disk from our modeling is \log _ { 10 } ( M _ { * } / { M } _ { \sun } ) = 11.06 ^ { +0.09 } _ { -0.11 } assuming that the cold gas contributes \sim 20 \% to the total disk mass .
In comparison to the stellar masses estimated from stellar population synthesis models , the stellar initial mass function of Chabrier is preferred to that of Salpeter by a probability factor of 7.2 .