Christoph Keller, Michiel Min, Rik van Lieshout, Ignas Snellen
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Christoph Keller, Michiel Min, Rik van Lieshout, Ignas Snellen
• Irregular light curve
• Uncorrelated deep and shallow transits
Rappaport et al. 2012
Normalized flux of KIC 12557548b
Rappaport et al. 2012
KIC 12557548b
Rappaport et al. 2012
KIC 12557548b
KIC12557548b(Rappaport et al. 2012)
KOI-2700b(Rappaport et al. 2014)
K2-22b(Sanchis-Ojeda et al. 2015)
15.7 hours 21.8 hours 9.1 hours
Credit: NASA/JPL-Caltech
Particle size of ~0.1𝜇𝜇m (Brogi +12)
Particle size of ~0.1𝜇𝜇m (Brogi +12)
Mass loss rate:1 Earth mass/Gyr(Rappaport+12)
van Lieshout et al. 2016
tail length depends on the sublimation properties of the dust grains
• No wavelength dependence • Croll el al. 2014• Schlawin et al. 2016• Felipe, PhD thesis, 2013
• Hint of wavelength dependence
• Bochinski+ 2015
Schematic diagram (not to scale)
star dust in tail
star
planet
Not to scale
dust
star
planet
Not to scale
dust
𝑭𝑭𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈, 𝒔𝒔𝒔𝒔𝒈𝒈𝒈𝒈
star
planet
Not to scale
dust
𝑭𝑭𝒈𝒈𝒈𝒈𝒓𝒓
star
planet
Not to scale
dust𝑭𝑭𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈, 𝒑𝒑𝒑𝒑𝒈𝒈𝒑𝒑𝒑𝒑𝒔𝒔
star
planet
Not to scale
dust
flux reduced flux, 𝑭𝑭𝑭𝒈𝒈𝒈𝒈𝒓𝒓
Where• 𝛽𝛽 = 𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟
𝐹𝐹𝑔𝑔𝑟𝑟𝑟𝑟𝑔𝑔(Independent of distance from star)
• 𝑇𝑇 = the fraction of flux not absorbed by closer particles (from 0 to 1) • 𝜔𝜔 = the planet’s orbital angular velocity • 𝒈𝒈 = vector from dust particle to star • 𝒓𝒓 = vector from dust particle to planet • 𝑀𝑀∗ = mass of star • 𝑚𝑚𝑝𝑝 = mass of planet
𝑑𝑑2𝒈𝒈𝑑𝑑𝑡𝑡2
= −𝐺𝐺𝑀𝑀∗ 1−𝑇𝑇𝑇𝑇𝒈𝒈 3 𝒈𝒈 − 2𝝎𝝎 × 𝑑𝑑𝒈𝒈
𝑑𝑑𝑡𝑡− 𝝎𝝎 × 𝝎𝝎 × 𝒈𝒈 − 𝐺𝐺𝑚𝑚𝑝𝑝
𝒓𝒓 3 𝒓𝒓
Stellar gravity and radiation
pressure
Coriolis acceleration
Centrifugal acceleration Planet gravity
To observer
To observer
Launching particles vertically (cone with 20° angle)
Optically thick dynamics
Initial particle size 1𝜇𝜇m
To observer
Launching particles vertically (cone with 20° angle)
Optically thick dynamics
Initial particle size 1𝜇𝜇m
To observer
• Tail propagates away in the launch direction To observer
• Reduced radiation pressure from optical depth allows Coriolis force to dominate
• Clockwise dust motion• Coriolis force
• Clockwise motion also from other launch directions in the plane
• Would give early ingress• Can rule out
To observer
• MCMC ray-tracing • Scattering • Absorption
• Generates images• Multiple wavelengths • Polarized light
• Can generate transit light curves by rotating around the fixed dust distribution
1 2
3 4
Optically thin:wavelength dependence
Optically thick:no wavelength dependence
Time (arbitrary units) Time (arbitrary units)
Sanchis-Ojeda et al. 2015
Perez-Becker & Chiang 2013
Croll+ 2014
No wavelength dependence of KIC1255b (0.5𝜇𝜇m particles)
Bochinski+ 2015
Wavelength dependence of KIC1255b (0.25 – 1 𝜇𝜇m particles)
Schlawin+ 2016
No wavelength dependence of KIC1255b (0.5 – 1 𝜇𝜇m particles)
D. Felipe, PhD thesis, 2013, Alonso et al. in prep.
No wavelength dependence of KIC1255b (slightly higher red likely instrumental)
Sanchis-Odjeda et al. 2016
Constraints on composition
van Lieshout et al. 2016
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