Abstract In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, ΩL, is the local Keplerian frequency ΩK. In terms of the standard dimensionless Shakura–Sunyaevαparameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by and , in whichHandcare the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where ΩL≥ ΩKand show that, under these conditions, the characteristic length and velocity scales are respectively and , where is twice the Rossby number. It follows that , where is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For , the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation.
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Measuring the Temperature of Starspots from Multi-filter Photometry
Abstract Using simultaneous multi-filter observations during the transit of an exoplanet around a K dwarf star, we determine the temperature of a starspot through modeling the radius and position with wavelength-dependent spot contrasts. We model the spot using the starspot modeling program STarSPot (STSP), which uses the transiting companion as a knife-edge probe of the stellar surface. The contrast of the spot, i.e., the ratio of the integrated flux of a darker spot region to the star's photosphere, is calculated for a range of filters and spot temperatures. We demonstrate this technique using simulated data of HAT-P-11, a K dwarf (Teff= 4780 K) with well-modeled starspot properties for which we obtained simultaneous multi-filter transits using Las Cumbres Observatory's MuSCAT3 instrument on the 2m telescope at Haleakala Observatory, which allows for simultaneous, multi-filter, diffuser-assisted high-precision photometry. We determine the average (i.e., a combination of penumbra and umbra) spot temperature for HAT-P-11's spot complexes is 4500 K ± 100 K using this technique. We also find for our set of filters that comparing the SDSS and filters maximizes the signal difference caused by a large spot in the transit. Thus, this technique allows for the determination of the average spot temperature using only one spot occultation in transit and can provide simultaneous information on the spot temperature and spot properties.
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- PAR ID:
- 10484827
- Publisher / Repository:
- American Astronomical Society
- Date Published:
- Journal Name:
- The Astronomical Journal
- Volume:
- 166
- Issue:
- 3
- ISSN:
- 0004-6256
- Page Range / eLocation ID:
- 92
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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