The Chocolate Chip Cookie Model: Dust Geometry of Milky-Way like Disk Galaxies

We present a new two-component dust geometry model, the \textit{Chocolate Chip Cookie} model, where the clumpy nebular regions are embedded in a diffuse stellar/ISM disk, like chocolate chips in a cookie. By approximating the binomial distribution of the clumpy nebular regions with a continuous Gaussian distribution and omitting the dust scattering effect, our model solves the dust attenuation process for both the emission lines and stellar continua via analytical approaches. Our Chocolate Chip Cookie model successfully fits the inclination dependence of both the effective dust reddening of the stellar components derived from stellar population synthesis and that of the emission lines characterized by the Balmer decrement for a large sample of Milky-Way like disk galaxies selected from the main galaxy sample of the Sloan Digital Sky Survey (SDSS). Our model shows that the clumpy nebular disk is about 0.55 times thinner and 1.6 times larger than the stellar disk for MW-like galaxies, whereas each clumpy region has a typical optical depth $\tau_{\rm{cl,V}} \sim 0.5$ in $V$ band. After considering the aperture effect, our model prediction on the inclination dependence of dust attenuation is also consistent with observations. Not only that, in our model, the dust attenuation curve of the stellar population naturally depends on inclination and its median case is consistent with the classical Calzetti law. Since the modelling constraints are from the optical wavelengths, our model is unaffected by the optically thick dust component, which however could bias the model's prediction of the infrared emissions.