The closest thing I found to describing the distribution functions for mass and period around intermediate mass stars was Bowler et al, which only said what the distribution function was not. Therefore, I decided to take matters into my own hands and examine the periods and masses for all stars with masses greater than 1.5 solar masses.
For the 39 data points, the first thing I saw was that mass was mostly a power law. Two lower mass planets at .6 and 1.2 Jupiter masses I ignored, since there were several 1.6 masses with it decaying from there. When I had 1.59 Jupiter masses as the xmin, it fit quite nicely, see figure. I would like to study this more and actually mathematically find the optimum xmin, not this guessing that I did.
Mass Distribution Function:
P(x)=1.3917*x^(-1.9118)
Now the semi-major axis (which translates to period) is more complicated and more sketchy approximation. I threw out the direct imaging stars (Beta Pic, Formalhaut, HR8799) since those were at massively larger semi-major axes and no doubt coming from different distributions. The planet desert less than 0.6 AU was definitely obvious, and planets also seemed to pile up right outside the 0.6 AU boundary. After taking out the 0.6 AU pile-up, the rest of the data points looked Gaussian to me, so I fit them with a Gaussian.
Non-Pile-Up Semi-Major Axis Parameters
Mean- 1.6772 AU
Standard Deviation:0.5149
No comments:
Post a Comment