Returning to the case of HL Tau, where the possible contribution of an infalling envelope is not an issue, how can one reconcile the strong indication of a dominant radial field component in the polarization map with the expectation that the bulk of the mm-wavelength emission originates near the disc mid-plane, where the azimuthal field component dominates? One possibility is that the non-negligible optical depth inferred in the bright emission rings of HL Tau at mm-wavelengths (Jin et al. 2016; Pinte et al. 2016) shifts the emission centroid to finite disc elevations where the magnetic field already has a measurable radial component. However, in view of the very small scale height inferred for the mm-emitting dust in this source, this is unlikely to be the main explanation. Perhaps a more likely possibility is that, even in this comparatively young source, the grains near the mid-plane, which dominate the total intensity, have already grown to sizes that exceed the maximum size $a_\mathrm{max} = \lambda /2\pi$ for producing polarized emission at wavelength λ (e.g. Cho & Lazarian 2007; for λ = 1.25 mm, amax = 0.2 mm), while the smaller grains (with sizes a amax), which contribute efficiently to the polarized flux, remain suspended at high elevations (where the field is predominantly radial). Another effect that could lower the polarized emission from grains that have settled to the mid-pane is the likelihood that grains become less elongated as they grow (e.g. Hughes et al. 2009), which would tend to reduce the value of the coefficient C in equation (2) (C → 0 as the grain axis ratio → 1).7 This interpretation is supported by the finding in the high-resolution observations of IRAS 4A (Cox et al. 2015) of an average polarization of 15 per cent at 8 mm and 10 per cent at 10 mm, with a peak fractional polarization of ∼20 per cent. If the intrinsic degree of mm-wavelength polarization in HL Tau is also of the order of 20 per cent, then it may be possible to explain the factor of ∼10 lower value of P measured in this source at 1.25 mm8 in terms of a dilution of the polarized emission from a ≲ 0.1 mm grains at high disc elevations by weakly polarized emission of larger grains residing near the mid-plane. In this scenario, most of the grains that are responsible for the mm-wavelength flux have settled to the mid-plane and grown to sizes a ≳ 1 mm.9 Although a fraction of these grains may have sizes in excess of 1 mm and would therefore emit less efficiently at that wavelength than a ≲ 1 mm grains (e.g. Miyake & Nakagawa 1993), the mid-plane region should still dominate the total mm-wavelength flux if most of the a ≳ 1 mm grains are concentrated there. Grains of size a ≲ 0.1 mm may be kept at high elevations by turbulent motions that can persist below the wind-driving surface layers (e.g. Simon et al. 2013, 2015; Bai 2015) as well as by the emerging outflows within these layers (see Safier 1993), with porosity effects (e.g. Ormel, Spaans & Tielens 2007) possibly also helping to mitigate gravity's pull towards the mid-plane. This scenario of course needs to be backed by detailed calculations and observational tests. One such test would be to obtain a polarization map of HL Tau at longer ( ≳ 1 cm) wavelengths: if the above picture is correct and the grains in the mid-plane region are aligned, such a map could reveal a stronger (or even dominant) contribution from the azimuthal and (especially if Λ0 ≪ 1) vertical field components.10 It is, however, conceivable that the large grains in this source are not well aligned because the radiative torque mechanism does not operate efficiently on them: this could happen if the characteristic wavelength of the anisotropic component of the local radiation field were much smaller than the mid-plane grain sizes (e.g. Cho & Lazarian 2007) or if the anisotropic radiation component inside the dust disc were weak due to finite optical depth effects. Note that the possibility of the mid-plane grains not being well aligned provides another reason for why the polarized mm-wavelength emission from this region could be weak.
Citation: Cho & Lazarian 2007
Citation function: Future Work
Citation: Cho & Lazarian 2007
Citation function: Uses; Uses