Brightness variability in polar circumbinary disks

TL;DR

The paper addresses illumination variability in polar-aligned circumbinary disks caused by the binary’s vertical motion. It combines analytic light-curve modeling and radmc3d radiative transfer to predict phase-locked brightness variations across near-infrared and millimeter wavelengths, focusing on the HD 98800B system. A key finding is that the light curve exhibits two maxima per binary orbit, with amplitude and timing strongly dependent on disk geometry, including razor-thin, flared, and inner-rim puffed configurations, and the disk thermal response relative to the orbital period. These results imply multiple observable signatures that can constrain disk vertical structure, geometry, and cooling timescales, making long-term, multi-wavelength monitoring of HD 98800B particularly valuable for understanding misaligned disk dynamics and planet formation in such environments.

Abstract

In binary systems with a strongly misaligned disk, the central binary stars can travel a significant vertical distance above and below the disk's orbital plane. This can cause large changes in illumination of the disk over the course of the binary orbital period. We use both analytic and radiative transfer models to examine the effect of changes in stellar illumination on the appearance of the disk, particularly in the case of the polar disk HD 98800B. We find that the observed flux from the disk can vary significantly over the binary orbital period, producing a periodically varying lightcurve which peaks twice each binary orbit. The amount of flux variation is strongly influenced by the disk geometry. We suggest that these flux variations produce several observable signatures, and that these observables may provide constraints on different properties of the disk such as its vertical structure, geometry, and cooling rate.

Figures (9)

• Figure 1: Illumination of the disk at different points of the binary orbit, for an equal mass central binary of $e=0.5$. Each column shows the position of the binary stars (top), along with the illuminated flux received by a razor-thin disk (middle) and a flared disk (bottom). For the flared disk model, dashed lines along the disk face indicate the regions where the incoming starglight would be shadowed due to the presence of a puffed inner rim; gray and white dashed lines show shadowed regions for puff heights of $1.5h_{\rm in}$ and $2.0h_{\rm in}$, respectively. Note that, for the second column, the stars are shown with a small vertical displacement to show asymmetric lighting effects close to plane crossing.
• Figure 2: Synthetic light curves showing incoming flux to a polar-aligned disk as a function of binary orbital phase, plotted for various binary eccentricities. All curves are normalized to their peak brightness value, which occurs at binary apocenter.
• Figure 3: The effect of different disk models on the phase light curve for a disk around an $e=0.5$ central binary. Unlike Figure \ref{['fig:analytic_lightcurve']}, values are not normalized in order to highlight the differences in brightness between the models. Flared disks appear slightly brighter than the razor-thin disk, while puffed disks show a longer minimum during binary pericenter.
• Figure 4: Synthetic radiative transfer images created from radmc-3d. Each column shows the disk at a particular observing wavelength, while each row shows the disk at a particular point in the binary orbit. From top to bottom, the images are shown at: binary pericenter, during disk plane crossing, mid-orbit, the point of greatest horizontal displacement of the binary, and binary apocenter. From left to right: observing wavelengths of $1.65\mu$m (H-band), $800\mu$m, and 1.3mm (ALMA Band 7).
• Figure 5: Comparison of 1.3mm and H-band lightcurves created from the radmc-3d radiative transfer models, with a disk scale height of $h/r=0.01$. In the top panel, curves normalized to their peak brightness at apocenter to emphasize the amount of variability. For the top panel we also show the numerical flux calculated from the razor-thin disk model (Fig. \ref{['fig:analytic_lightcurve']}), with an exponent of 1/4 to represent disk temperature and thermal emission at millimeter wavelengths. In the bottom panel, we plot the absolute flux density assuming the disk is viewed face-on at a distance of $d=45$ pc, the distance of HD 98800B. Solid and dashed curves indicate observations at $\lambda=1.3$mm and $1.65\mu \rm{m}$ (H-band), respectively.