The Kepler Spacecraft has discovered that most stars harbor Earth to Neptune-sized planets at orbital periods less than a year, challenging current theories of planet formation. In this paper, we have explored how the properties of these planets vary with the mass of their host star, and how these properties may inform planet formation theories by linking them to the scaling laws observed in protoplanetary disks.

Kepler has observed stars from spectral type M to F, covering about a factor of three in stellar mass. I have written a code to calculate the true occurrence of planets taking into account various observational biases, in particular the stellar properties.

We find that lower mass stars harbor planets more frequently: low-mass M stars have double the amount of Earth to Neptune-sized planets as G stars, a feature currently not predicted by planet formation models. We also find that the population of planets around low-mass stars extends closer in to their host stars. This trend matches the inner boundary of the gas in protoplanetary disks, suggesting planets migrate to their current locations and get trapped, rather than form in-situ.

link: Mulders et al. 2015 (arXiv)
press release

One of the ways of suppressing starlight to detect exo-planets and circumstellar material is Angular Differential Imaging or ADI. ADI makes use of the field rotation on a ground-based telescope to subtract out the central star, revealing fainter sources close to the star, such as planets. In the case of extended emission from a disk, some of the disk flux is also distracted, and the resulting observed image becomes distorted.

To derive the true underlying geometry of the transitional disk LkCa 15 from ADI observations, we have performed a full forward modeling approach using the 2D radiative transfer code MCMax. Based on constraints from the spectral energy distribution, we explore a 9-dimensional parameter space for the disk geometry, and simulate what the observed ADI image would look like for each set of parameters to identify the best-fit solution.

We find evidence for an eccentric gap, with a rounded-off outer edge, both being consistent with hydrodnamical simulations of a giant planet shaping the disk and explaining the transitional disk morphology. 

link: Thalmann, Mulders et al. 2014 (arXiv)

Transitional disks are protoplanetary disks that contain annular gaps or inner holes, which may indicate they are being dynamically sculpted by forming protoplanets. But exactly how planets shape protoplanetary disks into transitional disks remains unclear.

In this work, we explore using hydrodynamical models what type of planet is necessary to open the observed gap (~13 AU) in the disk of HD 100546. We use radiative transfer models to constrain the shape of the outer edge of the gap from mid-infrared interferometric observations and the SED. The gap edge is seen to be rounded off, which is naturally explained by a gradual increase in surface density at the gap edge. 

The extreme roundness of the gap edge in HD 100546, combined with it's depth, indicates both that the disk is very viscous, and that the planet needs to be very heavy. Instead, the observations are best explained by hydrodynamical simulations with a 60 Jupiter mass brown dwarf, though a super-Jupiter remains within the range of possibilities.

This article was also featured on astrobites!

link: Mulders et al. 2013b (arXiv)
related: Panic et al. 2014 

Why are protoplanetary disks so faint in scattered light?

(sub)micron-sized dust grains are thought to populate the upper layers of protoplanetary disks. Such small grains should be efficient scatterers in the optical and near-infrared, yet these disks are observed to be very faint at those wavelengths.

In this paper, we propose this observed faintness of disks can be explained by the presence of larger, but fluffy dust aggregates rather than small compact particles. The large size causes extreme forward scattering, resulting in a relatively faint disk with a grey to red color, while the phase function appears relatively isotropic at intermediate angles, mimicking the appearance of smaller grains. 

We demonstrate that extreme forward scattering can explain the brightness and color of HD 100546, by comparing detailed radiative transfer models with anisotropic scattering to new and archival scattered light images from the Hubble space telescope.

link: Mulders et al. 2013 (arXiv)

Does the structure of a protoplanetary disk depend on the mass of its host star?

The final outcome of the planet formation process depends on the properties of the protoplanetary disks planets form in.  Some of these properties vary with stellar spectral type due to different stellar masses and luminosity, while others don't. Previous work had found indications that these disks become flatter towards lower stellar masses.

In this work, we investigate whether the disk structure varies with stellar mass from low-mass brown dwarfs to intermediate-mass Herbig Ae stars. Using radiative transfer models including vertical structure calculations with self-consistent dust settling, we constrain the strength of turbulent mixing from fitting a sample of SEDs for each stellar mass group. We find no significant variations in turbulent mixing strength, and develop a set of scaling relations that show the disk structure is independent of stellar mass when considering regions of similar temperature.

link: Mulders & Dominik 2012 (arXiv)