giant.photometry.magnitude.HGPhaseMagnitudeModel

class giant.photometry.magnitude.HGPhaseMagnitudeModel(abs_visual_mag, phase_slope)

Bases: PhaseMagnitudeModel

Phase-Slope Model Typically used for Asteroids. This model takes the absolute magnitude and phase-slope brightness of the target into consideration.

This takes the form of

\[\begin{split}m(\alpha) &= H-2.5\log\left[[1-G]\Phi_1(\alpha)+G\Phi_2(\alpha)\right] \\ W &= \exp(-90.56\tan^2(\alpha/2)) \\ \Phi_1 &=W\phi_{1S}+(1-@)\phi_{1L} \\ \phi_{1S} &= 1-\frac{C_1\sin\alpha}{0.119+1.341\sin\alha-0.754\sin^2\alpha} \\ \phi_{1L} &= \exp(-A_1\left(tan\frac{\alpha}{2}\right)^{B_1}) \\ \Phi_2 &= W\phi_{2S}+(1-W)\phi_{2L} \\ \phi_{2S} &=1-\frac{C_2\sin\alpha}{0.119+1.341\sin\alpha-0.754\sin^2\alpha} \phi_{2L} &= \exp(-A_2\left(tan\frac{\alpha}{2}\right)^{B_2}) \end{split}\]

where \(\alpha\) is the phase angle in radian, \(H\) and \(G\) are the absolute visual magnitude and phase-slope of brightness respectively, and the cooeficiens take the following values:

\(A_1\) = 3.332 \(A_2\) = 1.862 \(B_1\) = 0.631 \(B_2\) = 1.218 \(C_1\) = 0.986 \(C_2\) = 0.238

This model comes from https://adsabs.harvard.edu/full/2010SASS…29..101B

For most targets, H and G can be retrieved from JPL’s Horizons database.

Parameters:

• abs_visual_mag (float) – Object absolute visual magnitude (H)

• phase_slope (float) – Phase slope of brightness (G)

Summary of Methods

magnitude_function