Dust entrainment in photoevaporative winds: Densities and imaging

X-ray- and EUV- (XEUV-) driven photoevaporative winds acting on protoplanetary disks around young T-Tauri stars may crucially impact disk evolution, affecting both gas and dust distributions. We constrain the dust densities in a typical XEUV-driven outflow, and determine whether these winds can be observed at $\mu\mathrm{m}$-wavelengths in scattered and polarised light. For an XEUV-driven outflow around a $M_* = 0.7\,\mathrm{M}_\odot$ T-Tauri star with $L_X = 2 \cdot 10^{30}\,\mathrm{erg/s}$, we find a dust mass-loss rate $\dot{M}_\mathrm{dust} \lesssim 4.1 \cdot 10^{-11}\,\mathrm{M_\odot / yr}$ for an optimistic estimate of dust densities in the wind (compared to $\dot{M}_\mathrm{gas} \approx 3.7 \cdot 10^{-8}\,\mathrm{M_\odot / yr}$). The synthesised scattered-light images suggest a distinct chimney structure emerging at intensities $I/I_{\max} < 10^{-4.5}$ ($10^{-3.5}$) at $\lambda_\mathrm{obs} = 1.6$ ($0.4$) $\mu\mathrm{m}$, while the features in the polarised-light images are even fainter. Observations synthesised from our model do not exhibit clear features for SPHERE IRDIS, but show a faint wind signature for JWST NIRCam under optimal conditions. In conclusion, unambiguous detections of photoevaporative XEUV winds launched from primordial disks are at least challenging with current instrumentation; this provides a possible explanation as to why disk winds are not routinely detected in scattered or polarised light.