Misaligned planetary system at Upsilon Andromedae

[ajtribick]

Upsilon Andromedae c and d apparently have a misalignment of about 30 degrees between their orbits, in contrast to our own solar system, PSR B1257+12 and Gliese 876 which all seem to be near-coplanar. Furthermore, planet c which has a lower minimum mass is closer to face-on and thus comes out with a higher true mass (although the uncertainties do overlap). Planet c also seems to come out with a mass above the deuterium fusion limit.

McArthur et al. (2010)

(Unfortunately the Extrasolar Planets Encyclopaedia does not list longitude of the node in its parameters, so I can't make a fully 3D model of this system for Celestia without access to the paper which is behind a paywall)

[ajtribick]

I managed to get a copy of the discovery paper from HubbleSite here, am currently trying to see if I can get this system into Celestia.

However as far as I can tell there are inconsistencies between the tabulated orbital elements and the displayed figures, so I'm going to hold off for awhile.

(The .ssc files I posted here briefly were consistent with some of the sky-projected orbit figure, but inconsistent with the radial velocity curves, hence I removed them)

[Hungry4info]

Thanks for the heads-up about the .pdf being on the HST site.

[ajtribick]

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
   }
}

[Hungry4info]

Very much appreciated.