| Abstract
| - Context. A segment of the early-type galaxy population hosts a prominent dust lane, often decoupled from its stellar body. Methods of quantifying the dust content of these systems based on optical imaging data usually yield dust masses that are an order of magnitude lower than dust masses derived from the observed far-IR (FIR) emission. The discrepancy is often explained by invoking a diffuse dust component that is hard to trace in the UV or optical. Aims. High-quality optical data from the Next Generation Virgo cluster Survey (NGVS) and FIR/sub-mm observations from the Herschel Virgo Cluster Survey (HeViCS) allow us to revisit previous methods of determining the dust content in galaxies and explore new ones. NGC 4370 is an edge-on, early-type galaxy with a conspicuous dust lane and regular morphology, making it suitable for several (semi-)analytical modelling techniques. We aim to derive the dust mass from both optical and FIR data and to investigate the need to invoke a putative diffuse dust component. Methods. We used different methods to determine the total dust mass in the dust lane. We used our exquisite optical data to create colour and attenuation maps, which are converted to approximate dust mass maps based on simple dust geometries. Dust masses were also derived from SED fits to FIR to sub-mm observations. Finally, inverse radiative transfer fitting was performed to investigate more complex dust geometries, such as an exponential dust disc and a dust ring and to treat the dust-starlight interaction in a self-consistent way. Results. We find that the empirical methods applied to the optical data yield lower limits of 3.4 × 10 5 M⊙, an order of magnitude below the total dust masses derived from SED fitting. In contrast, radiative transfer models yield dust masses that are slightly lower, but fully consistent with the FIR-derived mass. We find that the effect of a nuclear stellar disc on the derivation of the total dust mass is minor. Conclusions. Dust is more likely to be distributed in a ring around the centre of NGC 4370 as opposed to an exponential disc or a simple foreground screen. Moreover, by using inverse radiative transfer fitting, we are able to constrain most of the parameters that describe these geometries. The resulting dust masses are high enough to account for the dust observed at FIR/sub-mm wavelengths, so that no diffuse dust component needs to be invoked. We furthermore caution against interpreting dust masses and optical depths based on optical data alone, when using overly simplistic star-dust geometries and the neglect of scattering effects.
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