Ok so on investigating the parameters given in the HubbleSite version of the paper, it seems that to match the radial velocities and astrometric displacements (figures 9, 10 and 11), take the value of ? as being that for the reflex orbit (per normal conventions with spectroscopic binaries), and take the coordinate system as described in the link that Fridger provided
here: i.e. X points north, Z points away from Earth, Y completes the right-handed coordinate system (west). This then gives the same results as in figures 9 and 10, although the X and Y axes appear to have been mislabelled (as in figure 8, the orbit plot), with X pointing west and Y pointing north. I am therefore going to have to assume that X and Y as labelled on the graphs are arbitrary labels, and the thing to use is the orientation arrows in figure 8.
Unfortunately this then does not match the orbital diagram in figure 8. In fact, if we assume X and Y mean the same things in figures 8, 9 and 10, there is NO WAY to match the reflex orbit with the plotted planetary orbits. (In fact, figure 8 also appears to be inconsistent with the radial velocity orbits).
Therefore I am going to choose to ignore the plot in figure 8 and match the radial velocity and astrometric orbits. I have also chosen to take for planet b the inclination of 25 degrees suggested by dynamical stability arguments, and arbitrarily ?=0 (as this has not been constrained by the astrometry). This results in the following .ssc file:
Code: Select all
Modify "b" "HD 9826"
{
EllipticalOrbit {
Epoch 2450034.053
Period 0.01264096
SemiMajorAxis 0.0594
Eccentricity 0.012
Inclination 73.395
AscendingNode 152.209
ArgOfPericenter 13.306
}
UniformRotation {
Inclination 73.395 # to match orbit
AscendingNode 152.209 # to match orbit
}
}
Modify "c" "HD 9826"
{
Texture "exo-class3.*" # probably hot enough to be cloudless
Color [0.53 0.62 1]
EllipticalOrbit {
Epoch 2449922.532
Period 0.6596583
SemiMajorAxis 0.829
Eccentricity 0.245
Inclination 65.427
AscendingNode 121.246
ArgOfPericenter 13.306
}
UniformRotation {
Period 10 # plausible guess
Inclination 65.427 # to match orbit
AscendingNode 121.246 # to match orbit
}
}
Modify "d" "HD 9826"
{
Texture "exo-class3.*" # probably hot enough to be cloudless
Color [0.53 0.62 1]
EllipticalOrbit {
Epoch 2450059.382
Period 3.508574
SemiMajorAxis 2.53
Eccentricity 0.316
Inclination 71.312
AscendingNode 152.037
ArgOfPericenter 132.918
}
UniformRotation {
Period 10 # plausible guess
Inclination 71.312 # to match orbit
AscendingNode 152.037 # to match orbit
}
}