Mass Limit on Nemesis
  We assume that if the sun has a companion, it has a period of 27 Myr corresponding to the periodicity seen in cometary impacts on earth. Based on this assumption, it is seen that the inner Lagrengian point of the interaction between the Sun and its companion is in the Oort cloud. From this we calculate the mass -- distance relation for the companion. We then compute the expected apparent magnitude (visible and J band) for the companion using the models of Burrows (1993). We then compare this with the catalogue completeness of optical and infrared catalogues to show that the sun cannot have a companion of mass greater than 44 M_jup (0.042 M_sun) 
Varun Bhalerao (1) and M. N. Vahia (2) ((1) Indian Institute of   Technology Bombay, (2) TIFR)