Using the high resolution Ultraviolet and Visual Echelle Spectrograph ( UVES ) mounted on the Very Large Telescope ( VLT ) in combination with photometry from the high-speed CCD camera ULTRACAM , we derive precise system parameters for the pre-cataclysmic binary , NN Ser .
A model fit to the ULTRACAM light curves gives the orbital inclination as i = 89.6 ^ { \circ } \pm 0.2 ^ { \circ } and the scaled radii , R _ { \mathrm { WD } } / a and R _ { \mathrm { sec } } / a .
Analysis of the HeII 4686Å absorption line gives a radial velocity amplitude for the white dwarf of K _ { \mathrm { WD } } = 62.3 \pm 1.9 km s ^ { -1 } .
We find that the irradiation-induced emission lines from the surface of the secondary star give a range of observed radial velocity amplitudes due to differences in optical depths in the lines .
We correct these values to the centre of mass of the secondary star by computing line profiles from the irradiated face of the secondary star .
We determine a radial velocity of K _ { \mathrm { sec } } = 301 \pm 3 km s ^ { -1 } , with an error dominated by the systematic effects of the model .
This leads to a binary separation of a = 0.934 \pm 0.009 R _ { \sun } , radii of R _ { \mathrm { WD } } = 0.0211 \pm 0.0002 R _ { \sun } and R _ { \mathrm { sec } } = 0.149 \pm 0.002 R _ { \sun } and masses of M _ { \mathrm { WD } } = 0.535 \pm 0.012 M _ { \sun } and M _ { \mathrm { sec } } = 0.111 \pm 0.004 M _ { \sun } .
The masses and radii of both components of NN Ser were measured independently of any mass-radius relation .
For the white dwarf , the measured mass , radius and temperature show excellent agreement with a ‘ thick ’ hydrogen layer of fractional mass M _ { \mathrm { H } } / \mathrm { M } _ { \mathrm { WD } } = 10 ^ { -4 } .
The measured radius of the secondary star is 10 % larger than predicted by models , however , correcting for irradiation accounts for most of this inconsistency , hence the secondary star in NN Ser is one of the first precisely measured very low mass objects ( M \la 0.3 M _ { \sun } ) to show good agreement with models .
ULTRACAM r ’ , i ’ and z ’ photometry taken during the primary eclipse determines the colours of the secondary star as ( r ’ -i ’ ) _ { \mathrm { sec } } = 1.4 \pm 0.1 and ( i ’ -z ’ ) _ { \mathrm { sec } } = 0.8 \pm 0.1 which corresponds to a spectral type of M 4 \pm 0.5 .
This is consistent with the derived mass , demonstrating that there is no detectable heating of the unirradiated face , despite intercepting radiative energy from the white dwarf which exceeds its own luminosity by over a factor of 20 .