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The Mass of CoRoT-7b

The Mass of CoRoT-7b. Artie P. Hatzes Thüringer Langessternwarte Tautenburg And members of the CEST. RV (m/s). JD. P rot = 23 d. The Challenge: Dealing with the Activity Signal. P rot = 23 d P planet = 0.85 d. 44. Just what is the mass of CoRoT 7b?.

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The Mass of CoRoT-7b

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  1. The Mass of CoRoT-7b Artie P. Hatzes Thüringer Langessternwarte Tautenburg And members of the CEST

  2. RV (m/s) JD Prot = 23 d The Challenge: Dealing with the Activity Signal Prot = 23 d Pplanet = 0.85 d 44

  3. Just what is the mass of CoRoT 7b? Is it 3.5 ± 0.6 MEarth (Queloz et al. 2009)? → Harmonic Filtering Is it 6.9 ± 1.43 MEarth (Hatzes et al. 2010)? → Fourier Pre-whitening Is it 8.0 ± 1.2 MEarth (Ferraz-Melo al. 2010)? → High pass filtering Is it 5.65 ± 1.6 MEarth (Boisse al. 2010)? → Harmonic Filtering Is it 2.26 ± 1.83 MEarth (Pont al. 2010)? → Activity modeling The mass you get depends on how you filter out the activity signal.

  4. Spots, long period planets, systematic errors K = 5 m/s Radial Velocity (m/s) Orbital Phase

  5. Poor fit at phase 0.8-0.1 Try K = 2 m/s Radial Velocity (m/s) Orbital Phase

  6. Try K = 8 m/s Radial Velocity (m/s) Orbital Phase Poor fit at phase 0-0.4

  7. Two simple and reasonable assumptions: • A 0.85 d period is present in the RV data • Reasonable given Leger, Rouan, Schneider et al. (2009) • RV Variations from other phenomena (activity, other planets, systematic errors) over DT < 4 hours is small. • Dfrot = 0.01, DRV < 0.5 m/s • DRVplanets = 0 ± 0.9 m/s

  8. Use a Subset of the 106 HARPS RV measurements (Less is More!) • 10 Nights with 3 measurements DT=4 hours (Dforbit = 0.2) • 17 Nights with 2 measurements DT=2 hours (Dforbit= 0.1) • Total 66 Measurements • Consider each night an „independent“ data set that has its own zero point offset caused by the contribution of activity jitter that should be constant for that night • Find the best fit sine curve with P = 0.85 d

  9. Best fit circular orbit: sO–C = 1.7 m/s sRV= 1.8 m/s K = 5.15 ± 0.94 m/s M = 7.29 ± 1.35 MEarth Zero point offsets and phase are the only free parameters. The RV phase agrees with transit phase to within 0.01 phase

  10. Input K-amplitude Output K-amplitude

  11. Sanity Check: Periodogram of the nightly offsets nrot (P=23 d) Amplitude of variations ≈ 10 m/s

  12. For 2) and 3) to hold the observed 0.85-d variations must be due to an alias of the fourth harmonic: 4nrot + 1 = 1.17 c/d ≈ nCoRoT-7b • This RV curve can be due to 3 possibilities: • It is due entirely to a planet • It is due entirely to activity • It is due to activity plus a planet

  13. Amplitude spectra of activity indicators No evidence for significant power at 4nrot Amplitude of FWHM @ 4nrot is 0.2 of main peak. This implies an RV amplitude < 1.7 m/s

  14. To produce small rms the variations of each RV curve must be small 10 To reproduce transit phase 0 one spot group must be located here Radial Velocity (m/s) -10 0.4 0.6 0 0.2 0.8 Rotation Phase To produce a 0.85 d (alias) variation you need 4 spot groups equally separated in longitude

  15. If Pont et al. K-amplitude of 1.6 m/s is correct, then 3.5 m/s is the activity contribution

  16. Each group has a filling factor of ≈0.25% s = 0.5 m/s (binned) Each group has a same area with 10% This spot coverage is constant over 80 days Estimating the RV amplitude due to Spots: • Saar & Donahue (1997) : ARV≈ 6.5 f0.9 vsini (m/s) • Hatzes (2002): ARV = (8.6 vsini -1.6)f0.9 The RV curve leaves little room for activity „jitter“

  17. For activity to contribute significantly to the RV curve the spot distribution must have a very special configuration: • Have 4 spot groups must be equally spaced in longitude, otherwise these would not add in phase to the 0.85-d period. • One spot group must located at transit phase 0, otherwise there will be large distortions to a sine wave in the RV curve. • The area (filling factor) of the 4 spot groups must be the same within about 10% otherwise this would introduce scatter in the RV curve. • The spot evolution in these groups must be small over the time span of the observations (≈ 80 days) otherwise this would introduce scatter above the measurement error. This is of course possible, but highly improbable

  18. Kepler-10b versus CoRoT-7b: Inactive versus Active Inactive Active s = 3.07 m/s s = 1.68 m/s cred2 = 4.3 cred2 = 1.5 Mstar = 0.895 ± 0.06 Msun Rstar = 1.056 ±0.02 Rsun MPl = 4.56 ±1.23 MEarth RPl = 1.416 ±0.025 REarth rPl = 8.8 ±2.5 cgs Mstar = 0.91 ±0.03 Msun Rstar = 0.82 ±0.04 Rsun MPl = 7.29 ±1.35 MEarth RPl = 1.58 ±0.10 REarth rPl = 10.2 ±2.7 cgs

  19. Demory et al. 2011 Good news: Bad News: There may be large diversity of short period Superearths so we need to find more of these to understand their true nature and formation.

  20. Kepler-10b Are CoRoT-7b and Kepler-10b Super Mercurys? CoRoT-7b 10 Iron enriched Earth-like 7 Earth Mercury r (gm/cm3) No iron 5 Venus Mars 4 3 Moon 2 From Diana Valencia 1 2 1.8 0.4 0.2 1 0.6 0.8 1.2 1.4 1.6 Radius (REarth)

  21. PLATO: PLAnetary Transits and Oscillations of stars Goal: Discover and characterise a large number of close-by exoplanetary systems, with a precision in the mass and radius of 1% → The planetary mass and radius depnds on the stellar mass and radius

  22. Summary • By allowing the nightly means in the RV to float one can remove the activity RV jitter with very few and very simple assumption. This method should work in any case where the planet orbital is less than the time scales of the activity • There is little evidence for the activity contributing strongly to the CoRoT-7b RV signal. • Absolutely no evidence for nightly systematic errors in the HARPS data • The mass of CoRoT-7b is 7.29 ± 1.35 MEarth • CoRoT-7b and Kepler-10b have similar mean densities consistent with a Mercury-like planet, but large errors! • Better density for CoRoT-7b → better radius • Better density for Kepler-10b → better mass

  23. The best fit to the data is provided with a 0.85-d period Note: We can remove assumption 1), we have found an 0.85-d period in the RV, we do not have to assume it.

  24. CoRoT-7b Mass Determinations • Queloz et al. 2009: Harmonic filtering w/correction • Queloz et al. 2009: Adopted (average 2 methods) • Queloz et al. 2009: Pre-whitening w/ correction • Queloz et al. 2009: Harmonic filtering no correction • Pont et al. 2010: Activity modeling • Ferraz-Melo et al. 2011: High pass filtering • Model independent • Hatzes et al. 2010: Model independent • Queloz et al. 2009: Pre-whitening • Boisse et al. 2011: Harmonic filtering

  25. Spots, long period planets, systematic errors K = 5 m/s Radial Velocity (m/s) Orbital Phase

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