Upsilon Andromedae - Non-coplanar multi-planet system

With the recent talk about hot Jupiters and Kozai oscillations, I'm forced to wonder what would be the effect on υ And Ad on υ And Ac, or even on υ And Ab, and perhaps even υ And B. How much does the possible existence of this fourth planet affect the interpretation of the astrometric motion of the star?

The paper's up here (behind paywall), and some of the parameters at EPE are updated.

Beautiful planetary system. Four massive planets and the second star - red dwarf in the Oort cloud.

This Rosetta stone for studying the dynamics of multi-planetary systems. First multi-planetary system discovery around simple stars. Also famous for the first temperature map of exoplanets.

In addition, it appears that all three outer planets are good targets for the photographic detection.

It's been argued based on the stellar inclination that the planets may have inclinations of 58°.

More info here.
Not sure how well this holds up to HST astrometric determination of their orbits (if at all). Though, HST astrometry doesn't seem to have always been reliable in all cases.

Similar arguments are made for the planets orbiting HD 10697, ε Eri, HD 130322, HD 3651, HD 69830, HD 89744, HD 154345, 51 Peg, and HD 92788.

I think this is related to the second paper linked in this thread.

Study of the dynamics of the system - concludes that planet-planet scattering was probably the cause of the misalignment, but it is not possible to determine whether the companion star was responsible for causing the scattering.

A&A forthcoming:

Quote :

A fourth planet orbiting upsilon Andromedae?
S. Curiel, J. Canto, L. Georgiev, C. Chavez, A. Poveda
Received: 03 September 2010 / Accepted: 07 November 2010
DOI: 10.1051/0004-6361/201015693

ArxiV seems offline, but A&A displays this as highlighted content

A fourth planet orbiting υ Andromedae

Quote :

We present a 4-planet Keplerian fit for the radial velocity curve of the F8V star υ Andromeda, indicating the presence of a fourth planet in the system. We detect an additional fifth coherent signal in the radial velocity curve which we attribute to stellar activity. The discovery of a new planet around υ Andromedae makes this system the fifth to contain, at least, four planets. These four planets have minimum masses of 0.69, 1.98, 4.13 and 1.06 MJup and orbital periods of 4.62, 241.26, 1276.46 and 3848.9 days, respectively. We have numerically integrated the orbital solution for these four planets and find that the system is stable for at least 10 Myr. The orbit of the fourth planet coincides with an island of stability reported by Rivera & Haghighipour (2007, MNRAS, 374, 599). We find that the characteristics of the new fourth planet are very similar to those of Jupiter and that the planets in this system have very strong interactions with each other. As previously found, υ And–b and υ And–c are in apsidal alignment, while the orbit of the new planet (υ And–e) is close to an external 3:1 resonance with υ And–c.

M4=1.059 Mj, a=5.24588 AUs, e=0.005. Quite Jupiter-like.

Also masses of inner planets seem not revised according to McArthur et al. (2010), giving c as 1.98 Mj and d as 4.13 Mj planets.

Detected also fifth signal (183 days), but likely due to stellar activity.

If you have signed up to the A&A EDPS service (which is free), you can download this article under the "latest articles free" service.

Interestingly enough, absolutely no reference is made to the astrometric results and it appears the system is being treated as coplanar with true masses being the minimum masses.

Dynamical Analysis of the 3:1 Resonance in the upsilon-Andromedae System
http://arxiv.org/abs/1108.2736

Quote :

We study the dynamics of the upsilon-Andromedae planetary system proposed by Curiel et al. (2011). We focus on the study of the 3:1 Mean Motion Resonance between upsilon-Andromedae-d and the recently discovered upsilon-Andromedae-e (hereafter upsilon-And-d and upsilon-And-e). Numerical simulations of the dynamics of the four planet system are conducted. The previously reported apsidal resonance between upsilon-And-c and upsilon-And-d is confirmed. In addition, we find that upsilon-And-d and upsilon-And-e are also in an apsidal resonance condition. Our results further indicate that the upsilon-Andromedae planetary system configuration is in the middle of a stability island in the semimajor axis-eccentricity domain. Additionally, we performed numerical integrations of the planetary configuration over 500 Myr and found it to be stable. We conclude that, within the uncertainties in the value of the orbital parameters, it is likely that upsilon-Andromedae planetary system will remain stable for a long timescale.

Resonances in a system that has evidence of scattering... hmm....

Not entirely sure what the point of this analysis is. The system is treated as coplanar with masses equal to the radial velocity minimum masses. The astrometric results from McArthur et al. (2011) are not mentioned, indeed that paper is not even in the references list.

Given the astrometric analysis gives much larger mass values for the planets, inverts the mass hierarchy of planets c and d, and alters the apsidal alignment, taking this into account would probably have a significant effect on the conclusions about the system dynamics.

Still waiting for an analysis of the four-planet system with the astrometry taken into account...

Wasn't sure whether to put this here or in the other Upsilon Andromedae thread...

Deitrick et al. "The 3-dimensional architecture of the Upsilon Andromedae planetary system"
http://arxiv.org/abs/1411.1059

Attempts to determine a stable orbit for Upsilon Andromedae b given the astrometric orbits for planets c and d.

Quote :

These solutions predict b’s mass is in the range 2 - 9 M_Jup and has an inclination angle from the sky plane of less than 25°. Combined with brightness variations in the combined star/planet light curve (“phase curve”), our results imply that planet b’s radius is ~1.8 RJup, relatively large for a planet of its age. However, the eccentricity of b in several of our stable solutions reaches > 0.1, generating upwards of 10¹⁹ watts in the interior of the planet via tidal dissipation, possibly inflating the radius to an amount consistent with phase curve observations.

There's also some interesting discussion about the evidence for the 4th planet, it does not look good for the Curiel et al. (2011) solution...

Quote :

While a longer period planet, indicated by a small slope in the radial velocities, may exist in this system, the 4th planet signal reported by Curiel et al. (2011) was a product of the earlier reduction of the Lick data, which did not account for an instrument change that caused a shift in the γ. For this reason, we do not include this planet in our study.

Now the inclination of the b planet has been measured.

Detection of Water Vapor in the Thermal Spectrum of the Non-Transiting Hot Jupiter upsilon Andromedae b
https://arxiv.org/abs/1707.01534

Quote :

The upsilon Andromedae system was the first multi-planet system discovered orbiting a main sequence star. We describe the detection of water vapor in the atmosphere of the innermost non-transiting gas giant ups~And~b by treating the star-planet system as a spectroscopic binary with high-resolution, ground-based spectroscopy. We resolve the signal of the planet's motion and break the mass-inclination degeneracy for this non-transiting planet via deep combined flux observations of the star and the planet. In total, seven epochs of Keck NIRSPEC L band observations, three epochs of Keck NIRSPEC short wavelength K band observations, and three epochs of Keck NIRSPEC long wavelength K band observations of the ups~And~system were obtained. We perform a multi-epoch cross correlation of the full data set with an atmospheric model. We measure the radial projection of the Keplerian velocity (KP = 55 ± 9 km/s), true mass (Mb = 1.7 +0.33−0.24 MJ), and orbital inclination \big(ib = 24 ± 4∘\big), and determine that the planet's opacity structure is dominated by water vapor at the probed wavelengths. Dynamical simulations of the planets in the ups~And~system with these orbital elements for ups~And~b show that stable, long-term (100 Myr) orbital configurations exist. These measurements will inform future studies of the stability and evolution of the ups~And~system, as well as the atmospheric structure and composition of the hot Jupiter.

That seems to favour the PRO2 solution from Dietrick et al. (2015), which has planet c as being the most massive planet, although PRO3 and PRO4 (both with planet d being more massive) aren't too far off. The dynamically-favoured PRO1 solution doesn't seem to work (not too surprising, given that they noted it leads to an inferred radius for planet b that is at odds with previous photometry). Unfortunately Dietrick et al. did not give any details of the scenarios with planet b in a retrograde orbit beyond the χ² values, so it is difficult to tell how well those match up.