We investigated the magnitude–phase relation of ( 162173 ) 1999 JU3 , a target asteroid for the JAXA Hayabusa 2 sample return mission .
We initially employed the international Astronomical Union ’ s H – G formalism but found that it fits less well using a single set of parameters .
To improve the inadequate fit , we employed two photometric functions , the Shevchenko and Hapke functions .
With the Shevchenko function , we found that the magnitude–phase relation exhibits linear behavior in a wide phase angle range ( \alpha = 5–75° ) and shows weak nonlinear opposition brightening at \alpha < 5° , providing a more reliable absolute magnitude of H _ { \mathrm { V } } = 19.25 \pm 0.03 .
The phase slope ( 0.039 \pm 0.001 mag deg ^ { -1 } ) and opposition effect amplitude ( parameterized by the ratio of intensity at \alpha =0.3° to that at \alpha =5° , I ( 0.3 \arcdeg ) / I ( 5 \arcdeg ) =1.31 \pm 0.05 ) are consistent with those of typical C-type asteroids .
We also attempted to determine the parameters for the Hapke model , which are applicable for constructing the surface reflectance map with the Hayabusa 2 onboard cameras .
Although we could not constrain the full set of Hapke parameters , we obtained possible values , w =0.041 , g =-0.38 , B _ { 0 } =1.43 , and h =0.050 , assuming a surface roughness parameter \bar { \theta } =20° .
By combining our photometric study with a thermal model of the asteroid ( Müller et al .
in preparation ) , we obtained a geometric albedo of p _ { \mathrm { v } } = 0.047 \pm 0.003 , phase integral q = 0.32 \pm 0.03 , and Bond albedo A _ { \mathrm { B } } = 0.014 \pm 0.002 , which are commensurate with the values for common C-type asteroids .