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Previous (sub)millimeter observations have found that the spectral indices ofdust emission from some young stellar objects are lower than that of the blackbody emission in the Rayleigh-Jeans limit (i.e., 2.0). In particular, therecent Atacama Large Millimeter Array observations have spatially resolved thatthe innermost regions of the protoplanetary disks TW\,Hya and HD\,163296present anomalously low (i.e., $<$2.0) millimeter spectral indices. In someprevious works, such anomalously low millimeter spectral indices wereconsidered unphysical and were attributed to measurement errors. The presentwork clarifies that if the albedo is high and is increasing with frequency, itis possible to reproduce such anomalously low spectral indices when theemission source is optically thick. In addition, to yield lower than 2.0spectral index at (sub)millimeter bands, the required dust maximum grain size\amax is on the order of 10-100 \micron, which is very well consistent with thepreviously derived \amax values based on multi-wavelength dust polarimetricobservations. In light of this, measuring Stokes I spectral index may alsoserve as an auxiliary approach for assessing whether the observed dustpolarization is mainly due to dust scattering or is due to the aligned dustgrains.

The anomalously low (sub)millimeter spectral indices of some protoplanetary disks may be explained by dust self-scattering