Thick Disks around White Dwarfs viewed 'Edge-off': Effects on Transit Properties and Infrared Excess

TL;DR

This paper demonstrates that geometrically thick, Gaussian-vertical white-dwarf debris disks can simultaneously account for photometric transits and infrared excess, addressing a long-standing tension in flat-disk models. By introducing a thick-disk framework with inner-rim irradiation, optically thin outer layers, and efficient backwarming, it reproduces observed transit reddening (as in WD J1013$-$0427) and infrared flux in systems like WD 1145$+$017, WD 1232$+$563, and G29-38. The work highlights the importance of disk height, inclination, and grain-size distributions (Angstrom exponent) in shaping both transit colors and IR SEDs, and it argues for more detailed radiative-transfer studies and targeted infrared observations (e.g., JWST, SPHEREx). Overall, thick-disk effects emerge as significant and testable components of WD debris-disk phenomenology, with implications for disk mass budgets and accretion histories.

Abstract

A significant fraction of white dwarfs (WDs) host dust/debris disks formed from the tidal disruption of asteroids and planetesimals. Several studies indicate that the disks can attain significant vertical heights through collisional cascade. In this work I model the effects of geometrically thick disks on two primary observables: photometric transits by the disk when viewed at high inclinations and infrared dust emission. Specifically, I consider disks with a Gaussian vertical profile with scale heights comparable to or larger than the WD radius. I primarily focus on inclinations $\gtrsim$$87$ degrees (`edge-off'), which can produce significant transits with moderate disk thickness. Both the transit depth and color become strong functions of inclination, and I explore their dependence on the disk parameters. I show that such a setup can produce the recently discovered reddening in the transit of WD J1013$-$0427. Moving to infrared emission, I show that the contribution from the heated inner rim can be substantial even at high inclinations. It can potentially explain the infrared excess observed in two transiting debris systems, WD 1145$+$017 and WD 1232$+$563, consistently with the transits. The other two important radiation components are the optically thin dust emission from the disk's outer layers and the optically thick emission from the backwarmed disk interior. Extending my analysis to G29-38 shows that the former can adequately produce the silicate emission feature with optically thin dust mass of $>$$10^{17}$ grams. The inner dense layers, on the other hand, allow the disk to contain orders of magnitude larger net dust mass. Overall, I show that thick disk effects can be significant and should be taken into account. I motivate detailed studies to quantify the effects accurately.

Figures (14)

• Figure 1: Cartoon (not to scale) showing the thick disk configuration and the observer line of sight responsible for the transits. All the disk parameters are marked. For the edge-on case, $z\equiv h$ which is discussed in Section \ref{['subsec:edgeon']}. In the edge-off case, $f_1\equiv f_1(a,\,\Delta a,\,i,\,z)$ and is discussed in Section \ref{['sec:edgeoff']}.
• Figure 2: The color, $D_g-D_r$, as a function of the $r$-band depth, $D_r$ for a broad range of parameters for edge-on view. From left to right, the three values of $\alpha$ considered are mentioned in the figures. For each panel, I have considered four cases of $\tau_{0,~\rm ref}$, as mentioned in the second panel. For each optical depth, I consider a range of heights as indicated by the color-bar. The two primary takeaways are: 1) increasing $\alpha$ leads to increase in the color for a given depth, and 2) For a given optical depth and $\alpha$, there is a limit to the maximum color attainable. The depth and color of WD 1013$-$0423 Bhattacharjee25 is marked in all the panels for comparison.
• Figure 3: The color as a function of depth for fixed $\tau_{0,~\rm ref}$ (top panel) and $h_z$ (bottom panel) when $a=100~R_{\rm WD}$ and $\Delta a=10~R_{\rm WD}$ are assumed. The parameters being varied are specified as in-figure texts and the colorbar. In all the cases, $\alpha$ is fixed at $3$ to achieve the maximum color-dependence. It is evident that edge-off viewing can achieve significant color, given the scale height is sufficiently large. The position of WD J1013$-$0427 is marked in both panels for comparison. The transit properties of this object can indeed be explained with edge-off view of a geometrically thick disk with a high mid-plane optical depth. The results remain qualitatively the same for larger $a$, but the allowed inclination angles become limited (see Appendix \ref{['app:transit_a_dep']}).
• Figure 4: The effect of $\Delta a$ in the transit depth and color. In this figure, we fix the other parameters at $a=100~R_{\rm WD}$, $h_z/R_{\rm WD}=1.75$, and $\tau_{0,~\rm ref}=10^3$. $\Delta a$ is varied from $1~R_{\rm WD}$ to $50~R_{\rm WD}$. WD J1013$-$0427 is marked for comparison. Lower inclination requires a smaller $\Delta a$ to satisfy the object's transit properties.
• Figure 5: The depth as a function of inclination for $\alpha=0.5$, $\tau_{0,~\rm ref}=10^3$, and $\Delta a=10~R_{\rm WD}$ with the stellar parameters of WD 1145$+$017. The four disk heights considered are labeled in the figure and the corresponding curves are colored according to the transit color. The shaded region marks the range of transit depths observed. The transit colors are all within the upper limit derived in Izuierdo18, still maintaining the observed depths. Lowering $\alpha$ (or increasing $\tau_{0,~\rm ref}$, though this effect is marginal) enables broader range of edge-off inclination. Increasing $\Delta a$ effectively shifts the curves rightward while slightly increasing the maximum color.