GPU-accelerated X-ray pulse profile modeling | Astronomy & Astrophysics (A&A)

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Table 2

Angles in the geometric setup.

Symbol	Description
i	Inclination: angle between $\hat{z}$ $Mathematical equation: ${\hat z}$$ and $\hat{k}$ $Mathematical equation: ${\hat k}$$ .
θ	Colatitude: angle between $\hat{z}$ $Mathematical equation: ${\hat z}$$ and ȓ.
ϕ	Azimuth of ȓ in the star frame.
ψ	Angle between ȓ and $\hat{k}$ $Mathematical equation: ${\hat k}$$ , with cos $ψ = \hat{r} \cdot \hat{k} = \sin i \sin θ \cos ϕ + \cos i \cos θ$ $Mathematical equation: $\psi = \hat r \cdot \hat k = \sin i\sin \theta \cos \phi + \cos i\cos \theta$$ .
η	Angle between ȓ and $\hat{n}$ $Mathematical equation: $\hat n$$ (zero for spherical stars; nonzero for oblate stars).
α	Angle between ȓ and ${\hat{k}}_{0}$ $Mathematical equation: ${\hat k_0}$$ (emission angle relative to the radial direction).
σ	Angle between $\hat{n}$ $Mathematical equation: $\hat n$$ and ${\hat{k}}_{0}$ $Mathematical equation: ${\hat k_0}$$ (emission angle relative to the local normal).
ξ	Angle between $\hat{β}$ $Mathematical equation: $\hat \beta$$ and ${\hat{k}}_{0}$ $Mathematical equation: ${\hat k_0}$$ ; $\cos ξ \equiv \hat{β} \cdot {\hat{k}}_{0} = - \sin α \sin i \sin φ / \sin ψ$ $Mathematical equation: $\cos \xi \equiv \hat \beta \cdot {\hat k_0} = - \sin \alpha \sin i\sin \varphi /\sin \psi$$ .

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