We present very sensitive polarimetry of 55 Cnc and \tau Boo in an attempt to detect the partially polarised reflected light from the planets orbiting these two stars .
55 Cnc is orbited by a hot Neptune planet ( 55 Cnc e ) at 0.038 AU , a hot Jupiter planet ( 55 Cnc b ) at 0.11 AU , and at least 3 more distant planets .
The polarisation of this system is very stable , showing no sign of the periodic variations that would be expected if a short period planet were detected .
The measured standard deviation of the nightly averaged Stokes Q/I and U/I parameters is 2.2 \times 10 ^ { -6 } .
We derive upper limits on the geometric albedo , A _ { G } and planetary radius using Monte Carlo multiple scattering simulations of a simple model atmosphere .
We assume Rayleigh-like scattering and polarisation behaviour ( scaled by the maximum polarisation , p _ { m } at 90 ^ { \circ } ) and pressure insensitive extinction .
Atmospheres in which multiple scattering plays only a small role have an almost linear relation between polarisation and A _ { G } .
In this case , the 4 \sigma upper limit is A _ { G } < 0.13 ( R / 1.2 R _ { Jup } ) ^ { -2 } p _ { m } ^ { -1 } for 55 Cnc e. This is most easily explained if 55 Cnc e is relatively small , like GJ436b , and therefore not a pure H-He planet .
The data do not provide a useful upper limit for 55 Cnc b . \tau Boo is orbited by an unusually massive hot Jupiter planet .
The data show a standard deviation in the night to night average Stokes Q/I and U/I polarisation parameters of 5.1 \times 10 ^ { -6 } .
The 4 \sigma upper limit is A _ { G } < 0.37 ( R / 1.2 R _ { Jup } ) ^ { -2 } p _ { m } ^ { -1 } for \tau Boo b , adopting the fairly well established orbital inclination i \sim 40 ^ { \circ } .
This extends the similar upper limits reported previously for this planet to longer wavelengths .
The fact that the \tau Boo data show more scatter , despite the smaller photon noise for this bright star , may be due to the spot activity detected photometrically by the MOST satellite .
These results contrast markedly with the recent claim of a 3 \sigma detection of a periodic polarisation signal from HD189733 with amplitude P = 2 \times 10 ^ { -4 } , attributed to the planet HD189733 b .