Supported light profiles

Supported light profiles#

The equations for elliptical profiles provided in the following are valid for coordinates \((x,y)\) centered on the origin and with the major axis of the ellipsoid along the \(x\) axis which corresponds to a position angle \(\phi=-90^\circ\) following COOLEST conventions.

Analytical light profiles#

Sérsic profile#

Availability

Implemented in both coolest.template and coolest.api.

The brightness profile of the elliptical Sérsic profile is given by: $$ I(x,y) \equiv I_{\rm eff} \exp \left( -b_n \left( \left(\frac{\sqrt{qx^2 + y^2/q}}{\theta_{\rm eff}}\right)^{1/n} - 1\right) \right), $$ where \(b_n\) is calculated by :cite:t:Capaccioli1989: as: $$ b_n = 1.9992n - 0.3271. $$ The halt-light radius, \(\theta_{\rm eff}\), is where the brightness of a circular profile is equal to \(I_{\rm eff}\). Similarly for the elliptical case, where the brightness is equal to \(I_{\rm eff}\) on the ellipse whose major axis (located on the x-axis) is equal to \(\theta_{\rm eff}\).

If the total magnitude, \(M_{\rm tot}\), of such a source is given for an instrument with known zero-point, \(ZP\), then: $$ I_{\rm eff} = \frac{b_{\rm n}^{2n},10^{-0.4(M_{\rm tot} - ZP)}}{2\pi, \theta_{\rm eff}^2 , n , e^{b_{\rm n}} , \Gamma(2 n ), q}, $$ where \(\Gamma\) is the gamma function.

Pixelated profiles#

Regular grid of pixels#

Availability

Implemented in both coolest.template and coolest.api.

The surface brightness of components modeled on a regular grid of square pixels is stored in the template following the PixelatedRegularGrid class. The JSON keys reflect the class attributes.

The actual pixel values are stored as an ImageHDU in FITS format. The FITS file should be placed within the same directory as the template, linked via the FitsFile attribute.

Irregular grid of pixels#

Availability

Implemented in both coolest.template and coolest.api.

The surface brightness of components modeled on an irregular grid of pixels (e.g., following a Delaunay tesselation) is stored in the template following the IregularGrid class. The JSON keys reflect the class attributes.

The actual pixel values are stored as an BinTableHDU in FITS format. The columns of the BinTableHDU should be named 'x', 'y' and 'z' (in that order) and contains coordinates (\(x\), \(y\)) and intensity values (\(z\)), respectively. The FITS file should be placed within the same directory as the template, linked via the FitsFile attribute.

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