20 th Microlensing Workshop. Paris, 13 January 2016

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1 MICROLENSING PLANET DETECTION VIA EARTH ORBIT SATELLITES FEDERICO MOGAVERO 20 th Microlensing Workshop Paris, 13 January 2016

2 Resolving the degeneracy in the Einstein timescale t E ( M t E 1 day M Jup ) 1/2 ( ) 1/2 ( 4DL (D S D L ) DS ) 1/2 ( ) 200 km s 1 8 kpc V D S 2 The lens mass M and distance D L are hidden in t E. F Mogavero - 20 th Microlensing Workshop, Paris, January

3 Resolving the degeneracy in the Einstein timescale t E ( M t E 1 day M Jup ) 1/2 ( ) 1/2 ( 4DL (D S D L ) DS ) 1/2 ( ) 200 km s 1 8 kpc V D S 2 The lens mass M and distance D L are hidden in t E. Two primary methods to determine the lens properties: Microlensing parallax Flux characterization The parallax method M θ E /κπ E π E 1AU (D 1 L D 1 S )/θ E F Mogavero - 20 th Microlensing Workshop, Paris, January

4 Microlensing parallax F Mogavero - 20 th Microlensing Workshop, Paris, January

5 Microlensing parallax Two strategies: Two or more inertial observatories. A single non-inertial observatory: HST (Honma 1999) WFIRST in GEO (Gould 2013) F Mogavero - 20 th Microlensing Workshop, Paris, January

6 Microlensing parallax Two strategies: Two or more inertial observatories. A single non-inertial observatory: HST (Honma 1999) WFIRST in GEO (Gould 2013) Single non-inertial observatory No 4-fold degeneracy (Gould 1994) No coordination between several observatories F Mogavero - 20 th Microlensing Workshop, Paris, January

7 WFIRST in geosynchronous orbit (Gould 2013) Gould (2013) performs an analytical Fisher Matrix analysis for a geosynchronous satellite with σ mag 0.01 and 3-min exposures. ( ) 1/2 ( ) σ πe t E β ( ) 6.6 R 10%, P βt E and β 1 π E 20 days 0.05 R A WFIRST-like GEO satellite could provide masses and distances for most standard planetary events (t E 20 days). F Mogavero - 20 th Microlensing Workshop, Paris, January

8 Geosynchronous orbit satellite (Mogavero, Beaulieu 2016) σπe /πe Geosynchronous orbit satellite [σπe, min, σπe, max], β = 0.1 Gould (2013), β = 0.1 σπe, min, β = 0.05 σπe, min, β = σπe, min, β = 0.01 σπe, min, β = t E (days) A GEO satellite is naturally optimized for t E of few days F Mogavero - 20 th Microlensing Workshop, Paris, January

9 Geosynchronous orbit satellite (Mogavero, Beaulieu 2016) σπe /πe Geosynchronous orbit satellite [σπe, min, σπe, max], β = 0.1 Gould (2013), β = 0.1 σπe, min, β = 0.05 σπe, min, β = σπe, min, β = 0.01 σπe, min, β = t E (days) A GEO satellite is naturally optimized for t E of few days Let t E be the timescale which minimizes σ π E /π E, then: t E P β 1, σ πe, min π E t E P 1/2 β 1/2 R 1 F Mogavero - 20 th Microlensing Workshop, Paris, January

10 Geosynchronous orbit satellite (Mogavero, Beaulieu 2016) ( M t E 1 day M Jup ) 1/2 ( ) 1/2 ( 4DL (D S D L ) DS ) 1/2 ( ) 200 km s 1 8 kpc V D S 2 A GEOSYNCHRONOUS ORBIT SATELLITE COULD: detect π E for free-floating lenses with masses M Jup discover planets in tight orbits around low-mass brown dwarfs F Mogavero - 20 th Microlensing Workshop, Paris, January

11 Low Earth orbit satellite (Mogavero, Beaulieu 2016) 10 1 Low Earth orbit satellite [σπe, min, σπe, max], β = 0.1 σπe, min, β = 0.05 σπe, min, β = σπe, min, β = 0.01 σπe, min, β = σπe /πe t E (days) A LEO satellite is naturally optimized for t E of few hours F Mogavero - 20 th Microlensing Workshop, Paris, January

12 Low Earth orbit satellite (Mogavero, Beaulieu 2016) 10 1 Low Earth orbit satellite [σπe, min, σπe, max], β = 0.1 σπe, min, β = 0.05 σπe, min, β = σπe, min, β = 0.01 σπe, min, β = σπe /πe t E (days) A LEO satellite is naturally optimized for t E of few hours From σ π E, min π E t E P 1/2 β 1/2 R 1 and Kepler s third law P 2 R 3 : σ πe, min t π E β 1/2 R 1/4 E Only a factor of (6.6) 1/4 1.6 between a GEO and a LEO! F Mogavero - 20 th Microlensing Workshop, Paris, January

13 Low Earth orbit satellite (Mogavero, Beaulieu 2016) ( ) 1/2 ( ) 1/2 ( ) 1/2 ( ) M 4DL (D S D L ) DS 200 km s 1 t E 1.3 hours 8 kpc V M D S 2 Finite source size effects easily detectable: ( ) ( ) β β ( ) ( ) ( ) t E R DL V 0.5 ρ days R S 2D S 200 km s 1 A LOW EARTH ORBIT SATELLITE COULD: discover free-floating planets of few Earth masses F Mogavero - 20 th Microlensing Workshop, Paris, January

14 Earth s umbra F Mogavero - 20 th Microlensing Workshop, Paris, January

15 Earth s umbra The fraction η of the orbital period available to observe the source star: η 1 1 π [ 1 ( ) arcsin R 2 / ] R sin 2 R λ R cos λ R R km F Mogavero - 20 th Microlensing Workshop, Paris, January

16 Conclusions A GEOSYNCHRONOUS ORBIT SATELLITE COULD: detect π E for free-floating objects with masses M Jup discover planets in tight orbits around low-mass brown dwarfs A LOW EARTH ORBIT SATELLITE COULD: discover free-floating planets of few Earth masses LIMITATIONS: strong requirements on photometry: σ mag 0.01, f (3 min) 1 Earth s umbra in case of LEO F Mogavero - 20 th Microlensing Workshop, Paris, January

17 F. Mogavero and J. P. Beaulieu, 2016, A&A, 585, A62 F Mogavero - 20 th Microlensing Workshop, Paris, January

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