The TROY project

Use archival data from precise instruments (e.g., HARPS, SOPHIE, HIRES, etc.) to apply the technique proposed by Ford et al. (2006) to look for trojan planets.

1. Download list of planets with: mass, radius, period, stellar mass
2. Calculate the semi-amplitude of the RV.
3. Select those accomplishing all criteria stated in the "Targets" section below.
4. Search for archival RV data of the pre-selected targets in the papers published about them.
5. Among the targets with sufficient data, fit the RV assuming a single planet (leave eccentricity free).
6. Now fit the RV assuming a trojan planet.
7. Compare the likelihood of both fits.
8. Select those targets in which the fit with the trojan is statistically better ==> Probable detection.
9. Publish upper mass limits for those without statistical significance.
10. This should be included in the first publication of the project, describing TROY and methodologies (Lillo-Box et al., 2016, in prep.).
11. Optional: it would also be great to test the approach of Leleu et al. (2015) on the targets with small eccentricities.

Tarets should accomplish the following criteria:

• Planet host must transit its star: this is in order to have a reference time to compare with the time of null radial velocity.
• Planet host must be massive (Jupiter-like): This is in order to be able to detect the trojan body since the larger the planet is the deeper is the gravity well and so more massive trojans can be hosted.
• Period should not be too short (>5 days): According to Rodriguez et al. (2013), trojans hosted in short-period orbits are likely instable. However, I must note that this paper indicates that their work is valid for similar mass planet-trojan systems. By contrast, we are focusing our search in Jupiter+Earth systems.
• RV semi-amplitude should be large (>50 m/s) : this is necessary to be able to have a good S/N of the RV curve.

These criteria, leaves us with XX targets.

Our currently derived equations assume:

• Trojan body location is fixed at the Lagrangian point (i.e., no libration, dalpha/dt = 0, alpha = 60º). This probably forces the trojan body to be massive and formed in situ, since I would expect a less massive body (like an asteroid) to have been captured and so have a larger libration amplitude.

...

Use Kepler data and our dynamical expertise to explore the parameter space to look for transits at the Lagrangian points of KOIs (confirmed or validated).

1. This study must be performed in all the KOIs since all detected planet candidates will accomplish the mass criterion (mp + mt < 0.04*Ms) for the stability of the system.
2. Write the routine to automatically pre-process the Kepler light curve (download, detrending, co-adding, period splitting, etc.)
3. Look for transits. There are several options:
   • Brute force option: For each KOI, shift each individual period by a certain amount (whith a maximum of few hours, for instance) looking for maximizing the depth in L4/L5 phase. This can be really time consuming (one free parameter per period means around 300 free parameters for 5~days period planets). Additionally, if the inclination of the trojan libration is large, it could be that some periods the trojan does not transit at all, thus adding noise to the stacked curve. If possible, we can add some degrees of freedom by taking some periods out of the calculations. MCMC will be extremely time-consuming. We can apply my genetic algorithm (GAbox) to try this. I will do some simulations for ~20 periods and check for convergence.
   • Clever option: The ideal would be to use the equation of motion and just predict the position of the trojan and the location of its transit. Then shift the corresponding period appropriately to the rest frame and stack all of them to recover the transit with the maximum depth. This approaach would really reduce the number of free parameters and also will directly provide the solution for the orbital libration.
4. Determine the stability of the found systems.

• We could maybe focus on the confirmed KOIs with derived masses. This restricts the sample to around 300 cases, where most of the planets are gas giants. Also, in the case of the "Clever option" proposed above, we can better determine the position of the trojan, reducing even more the parameter space. Note that these cases might overlap with prject OP1 due to the target selection of that project. In those cases we will have extra information.

Use images of directly observed planets and look for trojan swarms at the Lagrnagian points.

1. Compile the planets with direct imaging observations.
2. Try to retrieve the public images
3. Look for co-orbital swarms at the Lagrangian points
4. Determine the stability of the found systems.
5. If something is found, request the private images to the different teams or request DDT time with another instrument.

• We already have one candidate, HD95086, where Jorge found a possible sign of a double bright spot exactly at 60 degrees from the known planet. The double spot seems to be both in the GPI and NACO images, which were taken in different epochs.

• 26/jun/2016: I have speaked with Anne-MArie LAgrange, the PI of the SPHERE GTO program that has observed this target to request all the data they have on it. Apparently, they have quite a large number of images and they were very positive in my request. So, they will send us and collaborate with us on this particular project OP3. I am waiting for the images. I will analyze them as soon as I get them and them send you the results.

Use images of directly observed planets and look for trojan swarms at the Lagrnagian points.

Use images of directly observed planets and look for trojan swarms at the Lagrnagian points.

Find the dependency on the available mass that can get trapped into the LPs of a single-planet system with the mass of the disk and the mass of the planet fromed. This is crucial to understand the kind of trojans that can be formed (i.e., do we have enough mass to form Earth-like trojans in situ?).

1. Run N-body simulations to check the amount of particules traped in a protoplanetary disk in the LPs.
2. Check and analyze the dependency with the different parameters of the simulation (disk density, particle size, planet and stellar mass, composition, etc.)