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

Open Access

Table A.2

Polarization parameter for the zp-corrected models.

param.	description
Σ_zp	zp-correction region Σ_zp = Σ_i
fractional polarization correction factor
⟨q_i⟩	equal to Σ_iQ/Σ_iI
⟨u_i⟩	equal to Σ_iU/Σ_iI
fractional Stokes polarization offsets
q_is, u_is	for interstellar polarization (Eqs. 6 and 7)
q_inst, u_inst	for instrumental polarization
q_s, u_s	for intrinsic stellar polarization
q_d,c, u_d,c	for intrinsic, unresolved circumstellar polarization
zp-corrected maps
Q^zi(x, y)	zp-corrected Stokes Q map for Σ_zp = Σ_i)
U^zi(x, y)	same for zp-corrected Stokes U map
$Q_{ϕ}^{z i} (x, y)$ $Q_\phi ^{zi}(x,y)$	Σ_i zp-corrected azimuthal polarization maps
$U_{ϕ}^{z i} (x, y)$ $U_\phi ^{zi}(x,y)$	derived from Q^zi(x, y) and U^zi(x, y)^a
integrated zp-corrected parameters
$Σ_{i^{'}} X^{z i}$ ${{\rm{\Sigma }}_{i'}}{X^{zi}}$	Σ_zp = Σ_i corrected X-parameter integrated in $Σ_{i^{'}} X^{z i}$ ${{\rm{\Sigma }}_{i'}}$
$Σ_{i^{'}}$ ${{\rm{\Sigma }}_{i'}}X_{xxx}^{zi}$	same for quadrant parameters
special quantities for center zp-correction
Σ₀	aperture for central pixels of the stellar PSF peak
q₀, u₀	fractional polarization for central pixels
Q₀(x, y)	Stokes flux q₀ΣI(x, y) and
U₀(x, y)	Stokes flux u₀ΣI(x, y)
Q^ex(x, y)	Stokes Q and U maps for center corrected, spatially
U^ex(x, y)	resolved polarization^b
$Σ_{i^{'}} X_{x x x}^{z i}$ $Q_\phi ^{{\rm{ex}}}(x,y)$	azimuthal polarization maps for center corrected,
$Q_{ϕ}^{ex} (x, y)$ $U_\phi ^{{\rm{ex}}}(x,y)$	spatially resolved polarization
integrated zp-corrected parameters
ΣQ^ex	integrated Stokes polarization for center corrected,
ΣU^ex	resolved polarization signal
$Σ X_{x x x}^{ex}$ ${\rm{\Sigma }}X_{xxx}^{{\rm{ex}}}$	corresponding quadrant polarization values
$Σ Q_{ϕ}^{ex}$ ${\rm{\Sigma }}Q_\phi ^{{\rm{ex}}}$	integrated azimuthal polarization for center
$Σ U_{ϕ}^{ex}$ ${\rm{\Sigma }}U_\phi ^{{\rm{ex}}}$	corrected, resolved polarization signal
ΣQ, ΣU	total signal ΣQ = ΣQ₀ + ΣQ^ex and ΣU = ΣU₀ + ΣU^ex

Notes. The polarization parameters are aligned with the x, y coordinates of the scattering models. ^(a)see Table E.1 for all possible combinations; ^(b)Q^ex and U^ex are equal to Q⁰ and U⁰.

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