Modeling the Optical Colors of Galactic Cirrus Clouds in the Stripe 82 Region

TL;DR

Radiative-transfer modeling through fractal, lognormal ISM density fields shows how optical colors of Galactic cirrus arise from scattered ISRF light and depend on cloud depth $\tau_g^{\rm h}$ and turbulence $M_{ m s}$. Using MoCafe, the study reproduces Stripe 82 colors best for $M_{ m s}\sim3$–6 and $\tau_g^{\rm h}\sim0.8$–1.4 when the ISRF in the $i$ and $z$ bands is slightly reduced (or equivalently the $g$ and $r$ bands are enhanced), with similar results achievable via albedo adjustments. The color-color diagrams, especially $(r-i)$ versus $(g-r)$, provide a robust means to distinguish cirrus from extragalactic LSB features and to constrain the ISRF and dust scattering properties. Overall, optical colors offer a practical probe of Galactic dust and ISRF, informing foreground models for deep optical surveys and enabling joint constraints on ISRF SEDs and grain properties.

Abstract

Observations have shown that the optical colors of Galactic cirrus clouds differ significantly from those of extragalactic sources; thus, they can be used to distinguish Galactic cirrus from extragalactic low surface brightness (LSB) features. To understand these properties, we calculate radiative transfer models in dust clouds, where photons are incident from the ambient interstellar medium (ISM). Dust clouds are modeled to mimic a turbulent medium using a fractional Brownian motion algorithm, resulting in a lognormal density distribution and a power-law power spectral density that are appropriate for the ISM. The results are compared with optical observations of cirrus clouds in the Stripe 82 region. The observed color--color ($g-r$, $r-i$, and $i-z$) diagrams of the cirrus clouds can be reproduced by scattered light if the interstellar radiation field (ISRF) of Mathis et al. (as updated by Draine) is modified, either by reducing the intensities in the $i$ and $z$ bands or by enhancing those in the $g$ and $r$ bands. Similar results can also be obtained by adjusting the scattering albedos at the corresponding wavelengths. This demonstrates that the color--color diagrams are effective not only for identifying extragalactic LSB features but also for studying the ISRF and the properties of interstellar dust.

Figures (10)

• Figure 1: SEDs of the two ISRF models. The left and right panels show the SEDs in surface brightness units of erg cm$^{-2}$ s$^{-1}$ sr$^{-1}$ Å$^{-1}$ and mag arcsec$^{-2}$, respectively. The models of Mathis1983 (as updated by Draine2011book) and Bianchi2024 are plotted as blue and red curves, respectively. The blue and red filled circles indicate the intensities at the central wavelengths of the SDSS bands, calculated by weighting with the SDSS filter functions.
• Figure 2: Maps of scattered light in the SDSS wavelength bands ($u$, $g$, $r$, $i$, and $z$) for two realizations with different Mach numbers: $M_{\rm s}=1$ (top panels) and $M_{\rm s}=6$ (bottom panels). The homogeneous optical depth in the $g$ band is assumed to be $\tau_g^{\rm h}=1.0$ in both cases. The maps are based on two typical random realizations of a lognormal density structure. The numbers (#3 and #7) in parentheses indicate the sample indices among the 10 random realizations of the density distribution. Scattered light intensities are normalized by the incident ISRF intensity, i.e., $I_{\rm scatt}/I_{\rm ISRF}$. The effective optical depth $\tau^{\rm eff}_\lambda$, defined in Equation (\ref{['eq04']}), and the standard deviation $\sigma_\lambda$ of scattered light (for $\lambda = u$, $g$, $r$, $i$, and $z$) are indicated in each map.
• Figure 3: Mean scattered-light intensities as functions of $\tau_g^{\rm h}$ for various $M_{\rm s}$. The intensities are averaged over 10 random realizations of the density structure in the RT simulations. Standard deviations across the 10 samples are shown as error bars.
• Figure 4: Mean colors ($u-g$, $g-r$, $r-i$, and $i-z$) as functions of $\tau_g^{\rm h}$ for various $M_{\rm s}$. The values are averaged over 10 random realizations of the density structure in the RT simulations. Standard deviations are also shown as error bars. The ISRF SED of MMP83D was used.
• Figure 5: Mean color--color diagrams constructed for $\tau_g^{\rm h}=0.2$--4.0 and $M_{\rm s} = 0.5$--20. Rainbow-colored dots show the simulation results with the unmodified MMP83D ISRF, while light-blue dots represent cases where the incident ISRF in the $i$ and $z$ bands is scaled down by a factor of 0.9 to reproduce the observed data. Each dot represents the average across 10 realizations for a given combination of $\tau_g^{\rm h}$ and $M_{\rm s}$, as in Figures \ref{['fig03']} and \ref{['fig04']}. In the rainbow-colored series, each color corresponds to a fixed $M_{\rm s}$ as $\tau_g^{\rm h}$ varies. The red arrow indicates the color trend with increasing $\tau_g^{\rm h}$, while the blue arrow show the trend with increasing $M_{\rm s}$. The black crosses mark the observational results of Roman2020. In the left panel ($r-i$ vs. $g-r$), the red dashed line denotes the empirical relation used by Roman2020 to separate cirrus clouds from extragalactic LSB features. The reddening with increasing $\tau_g^{\rm h}$ is due to stronger extinction at shorter wavelengths, whereas the blueing with increasing $M_{\rm s}$ results from the larger volume fraction of low-density regions.