Galactic Cirri at High Galactic Latitudes: I. Investigating Scatter in Slopes between Optical and far-Infrared Intensities

Based on the slopes between DESI $g,r$ and IRAS 100 $\mu m$ intensities, specifically $k_{g}$ and $k_{r}$, we have constructed a substantial sample of Galactic cirri. This sample covers 561.25 deg$^2$ at high Galactic latitudes (|b| $\geq$ 30$^{\circ}$), allowing for a systematic study of the physical parameters of the Galactic cirrus on a large scale, such as $g-r$ color, dust temperature, asymmetry factor and albedo. The ratio of $k_{g}$ and $k_{r}$ is consistent with the diffuse Galactic starlight model, suggesting that the diffuse starlight within our own Galaxy serves as the primary illumination source for the cirrus. Both $k_{g}$ and $k_{r}$ decrease slowly with increasing Galactic latitudes and IRAS 100 $\mu m$ intensities, while they do not have a correlation with Galactic longitudes. The distribution of $k_{g}$ and $k_{r}$ confirms a significant scatter in the slopes, reaching a factor of 4-5. Such large scatter cannot be explained by the weak correlation between the slopes and Galactic latitudes and IRAS 100 $\mu m$ intensities. Instead, it is attributed to substantial variations in the intrinsic properties of the dust, e.g., asymmetry factor and albedo. We propose that the properties of dust particles play a critical role in the observed scatter in slopes, making them the primary contributing factors. Moreover, the variations in dust properties within the cirrus are localized rather than exhibiting large-scale gradients.