Resolution and calibration effects in high contrast polarimetric imaging of circumstellar scattering regions

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Table A.1

Polarization parameters for convolved and intrinsic models.

param.	description
parameters for the convolved maps
I(x, y)	intensity
Q(x, y)	linear Stokes polarization Q = I₀ − I₉₀
U(x, y)	linear Stokes polarization U = I₄₅ − I₁₃₅
Q_ϕ(x, y)	azimuthal parameters for the linear polarization
U_ϕ(x, y)	with respect to x₀, y₀ (Eqs. 8,9).
P(x, y)	intensity of the polarized flux (Eq. 10)
X(x, y)	expression for different parameter maps, e.g., X = {I, Q, U, P, Q_ϕ, U_ϕ}
Σ_intX	summed parameter in intergration region Σ_int used centro-symmetric apertures Σ_int ^a
Σ	round aperture for whole system
Σ₁	small, round aperture centered on the star
Σ₂	annular aperture including the disk
Σ₃	annular aperture for the halo
Σ_i	expression for all apertures Σ_i = {Σ, Σ₁, Σ₂, Σ₃}^b quadrant polarization parameters^c
Σ_iQ_xxx	Stokes Q quadrants Σ_iQ₀₀₀, Σ_iQ₀₉₀, Σ_iQ₁₈₀, Σ_iQ₀₀₀ ^d
Σ_iU_xxx	Stokes U quadrants Σ_iU₀₄₅, Σ_iU₁₃₅, Σ_iU₂₂₅, Σ_iU₃₁₅
Σ_iX_xxx	expression for all quadrant parameters
Σ_iX_xxx\|_ϕ	azimuthal quadrant parameters considering sign for positive Q_ϕ contribution (Sect. 4.3.2)
∆Q_xxx	differential quadrant value for Stokes Q (Eq. 15)
∆U_±	differential quadrant values for Stokes U (Eq. 17) azimuthal polarization in radial and azimuthal coordinates
Q_ϕ(r, ϕ)	used in the discussion for the Q_ϕ distribution in radial apertures Σ_iQ_ϕ and the angular distribution in quadrants Σ_iX_xxx\|_ϕ components of intrinsic models
$I_{s}^{'}, I_{d}^{'}$ $I_s^\prime ,I_d^\prime$	stellar and circumstellar (dust or disk) intensity
I′	total intensity $I^{'} (x, y) = I_{d}^{'} (x, y) + I_{s}^{'} (x_{0}, y_{0})$ $I'(x,y) = I_d^\prime (x,y) + I_s^\prime \left( {{x_0},{y_0}} \right)$
$Q_{s}^{'}, Q_{d}^{'}$ $Q_s^\prime ,Q_d^\prime$	same for Stokes Q′ (Eq. 3)
$U_{s}^{'}, U_{d}^{'}$ $Q_s^\prime ,Q_d^\prime$	same for Stokes U′ (Eq. 4)
$Q_{ϕ}^{'}$ $Q_\phi ^\prime$	circumstellar azimuthal polarization $Q_{ϕ}^{'} = Q_{ϕ, d}^{'}$ $Q_\phi ^\prime = Q_{\phi ,d}^\prime$
$U_{ϕ}^{'}$ $U_\phi ^\prime$	$U_{ϕ}^{'} = 0$ $U_\phi ^\prime = 0$ in the adopted models
$d_{'} (Σ)$ ${\cal P}_d^\prime ({\rm{\Sigma }})$	aperture polarization and position angle for disk
$θ_{d}^{'} (Σ)$ $\theta _d^\prime ({\rm{\Sigma }})$	(Eqs. A.1 and A.2)
$s_{'}, θ_{s}^{'}$ ${\cal P}_s^\prime ,\theta _s^\prime$	same for point like star ( $s_{'} = P_{s}^{'} (x_{0}, y_{0})$ ${\cal P}_s^\prime = P_s^\prime \left( {{x_0},{y_0}} \right)$ )

Notes. The polarization parameters are aligned with the x, y coordinates of the scattering models. ^(a)see Fig. 21; ^(b)there is Σ = Σ₁ + Σ₂ + Σ₃; ^(c)see Figs. 9, 21; ^(d)there is Σ_iQ = Σ_iQ₀₀₀ + Σ_iQ₀₉₀ + Σ_iQ₁₈₀ + Σ_iQ₀₀₀.

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