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Table A.1
IDL procedure for the calculation of disk-averaged scattering functions and normalized quadrant polarization parameters.
| pro quadrants,ideg,g,fiavg,fphiavg,qpp | |
|---|---|
| incl = ideg*!pi/180. | ; inclination i in radians |
| ; array of disk azimuth angles φd for disk ring: 3600 point with [0, 0.1, .., 359.9] degrees in radians | |
| phi_d = findgen(3600)*!pi/1800. | |
| x = -sin(phi_d) | ; x-sky for inclined disk ring |
| y = cos(incl)*cos(phi_d) | ; y-sky |
| z = -sin(incl)*cos(phi_d) | ; z along line of sight |
| phi = atan(-x,y) | ; sky azimuth angle ϕxy(φd, i) (Eq. 34) |
| theta = acos(z) | ; scattering angle θ(φd, i) (Eq.30) |
| ; scattering intensity using HG-phase function 4π fI(θ, g) (Eq. 19) | |
| fi = (1.-g∧2)/(1.+g∧2-2.*g*cos(theta))∧1.5 | ; 4π fI (φd, i) (Fig. 6) |
| ; polarized intensity using Rayleigh scattering splitting with pmax = 1 (Eqs. 21,22) | |
| fper = fi/(1.+(cos(theta))∧2) | ; f⊥ or azimuthal intensity |
| fpar = fi*(cos(theta))∧2 / (1.+(cos(theta))∧2) | ; f∥ or radial intensity |
| fphi = fper-fpar | ; 4π fϕ (φd, i): azimuthal polarization (Fig. 6) |
| fq = fphi*(-cos(2.*phi)) | ; 4π fQ (φd, i) for Stokes Qd (Fig. 7) |
| fu = fphi*(-sin(2.*phi)) | ; 4π fU (φd, i) for Stokes Ud (Fig. 7) |
| ; disk averaged scattering functions ⟨f(i, g)⟩ | |
| fiavg = mean(fi) | ; intensity ⟨fI(i, g)⟩ (Eq. 37) |
| fphiavg = mean(fphi) | ; azimuthal polarization ⟨fϕ(i, g)⟩ (Eq. 38) |
| ; normalized quadrant polarization parameters | |
| qpp = fltarr(5) | ; initialize quadrant values |
| ; sum-up of relevant ϕxy(φd, i)-points for each quadrant (according to Tab. 2) | |
| for j=0,3599 do begin | |
| if (phi[j] gt -0.25*!pi and phi[j] lt 0.25*!pi)then qpp[0]=qpp[0]+fq[j]/3600. | ; quadrant Q000 |
| if (phi[j] gt 0. and phi[j] lt 0.50*!pi) then qpp[1]=qpp[1]+fu[j]/3600. | ; quadrant U045 |
| if (phi[j] gt 0.25*!pi and phi[j] lt 0.75*!pi) then qpp[2]=qpp[2]+fq[j]/3600. | ; quadrant Q090 |
| if (phi[j] gt 0.50*!pi and phi[j] lt 1.00*!pi) then qpp[3]=qpp[3]+fu[j]/3600. | ; quadrant U135 |
| if (phi[j] gt 0.75*!pi or phi[j] lt -0.75*!pi) then qpp[4]=qpp[4]+fq[j]/3600. | ; quadrant Q180 |
| endfor | |
| return | |
| end | |
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