Joint Modelling of Dust Scattering and Thermal Emission: The Spider Complex

Observations across the electromagnetic spectrum of radiative processes involving interstellar dust -- emission, extinction, and scattering -- are used to constrain the parameters of dust models and more directly to aid in foreground removal of dust for extragalactic and cosmology observations. The more complementary observations, the better. Here, we quantify the relationship between scattered light and thermal emission from dust in a diffuse (cirrus) intermediate latitude cloud, Spider, using data from the Dragonfly Telephoto Array and the Herschel Space Observatory. A challenge for optical observations of faint cirrus is accurate removal of a contaminating spatially varying sky background. We present a technique to analyse two images of the same cirrus field concurrently, correlating pixel values to capture the relationship and simultaneously fitting the sky background as a complex non-correlating additive component. For the Spider, we measure a $g-r$ color of 0.644$\pm 0.024$ and a visible wavelength to 250 $\mu$m intensity ratio of $10^{-3} \times (0.855 \pm0.025)$ and $10^{-3} \times (1.55\pm0.08)$ for $g$ and $r$-band respectively. We show how to use any dust model that matches the thermal dust emission to predict an upper limit to the amount of scattered light. The actual brightness of the cirrus will be fainter than this limit because of anisotropic scattering by the dust combined with anisotropy of the incident interstellar radiation field (ISRF). Using models of dust and the ISRF in the literature we illustrate that the predicted brightness is indeed lower, though not as faint as the observations indicate.