1 What’s important here is the difference in chi-square for each subset of the data between the value at i=90 deg and the minimum value. Also, it’s important to address the significance of the dip (this is done by eye and from prior experience in the discussion below). [Note: Eugenio is using i=0 corresponds to the plane of the sky. In the post above, I would write this as I=90 -gL]

2 These are three-planet fits. Fourteen parameters are fit for each point on the plot, but the number of data points increases with time.

3 There is a major false assumption that goes into creating this figure: Prior observed velocities do not change as new velocities are added. [In reality, the measurement precision of all of the radial velocities in a given data set improves as more velocities are obtained. This is a consequence of the reduction method (see Butler et al. 1995) that is used. -gL]

4 Assuming that these curves are what they would have actually looked like in the past (see point 1), then:

a) After 1999, all we could have said is i >~40 and it was likely that i~40 and it was very likely that ii>60.

d) After 2002, the dip is significant (the change is comparable to the change after 2004, which was rigorously shown to be significant — it is also clearly deeper than the one after 2001); however, since the location of the minimum shifted, the (upper) constraint on i is weaker: 30>i>60.

e) After 2003, the dip is significant, with a minimum around 50, and 40>i>60. If the curve had actually looked like it does in the figure, it might have been possible to announce the i=50 solution. However, the actual curve after the 2003 season looked very different, and it would have been very unwise to make the announcement.

f) After 2004, (see Rivera et al 2005), i=50+-3 to 1 sigma and i=50+-10 to 3 sigma.

5 For all six curves, the minimum chisq value occurs for 40>i>60. This result is additional evidence that i is in this range (to 3 sigma).

– Eugenio