HG Model Plotting

I generated two plots by writing scripts in both Python and IDL respectively. Da function I intended to plot is Marcus’ compound HG model, namely,

 \phi(\theta)=\frac{\delta_{90}}{1+\delta_{90}}[k(\frac{1+g_f^2}{1+g_f^2-2g_f\cos(180-\theta)})^{\frac{3}{2}}+(1-k)(\frac{1+g_b^2}{1+g_b^2-2g_b\cos(180-\theta)})^{\frac{3}{2}}+\frac{1}{\delta_{90}}]

where \theta is the phase angle, \phi(\theta) is the scattering function, which can be easily converted into the form in terms of magnitudes by the relationship \Phi(\theta)=-2.5\log{[\phi(\theta)]}, \delta_{90} is the dust-to-gas light ratio of the coma at phase angle \theta=90°, g_f and g_b are respectively the asymmetry factors for forward scattering and the backscattering with confinements 0\leqslant g_f\leqslant1 and -1\leqslant g_f\leqslant0, and k is called the partitioning coefficient between foward scattering and backscattering with the property 0\leqslant k\leqslant1.

N now da plot generated by Python:

Da phase function by Python

N da plot by IDL:

Da phase function by IDL

Careful enough, u might hav noticed that ther’s a difference between da y-axes of da plot by Python n da plot by IDL. Right, but da y-axis in da plot by Python isn’t inverse to achieve our common sense that da brighter a body is, da smaller its magnitude is. When writing da script in Python, I was permanently notified by an error that d inversion format had been incorrect. So lazy I was, that I directly deleted the scripts n juz added another negative to da phase function \Phi(\theta).

D above’s not somthing serious whatsoever. In fact da two plots r totally da same. Weird results with a great difference at y-axes was obtained that d original one by Python plotted a dusty comet’s curve finally came merely to mag. 20, which is absolutely implausible otherwise great comets visible in broad daylight would hav occurred on a frequent basis. I din’t realize where da mistake was until juz now I suddenly understood that da function “log” in Python actually means \ln other than \log after reviewing da tutorials! Evrything turned normal juz with da correction of d error.

Frankly speaking I’m not content with da legend. A special routine called TEXTOIDL has been applied, however, it din’t correctly exhibit Greek letters to me. d_{90} within da plot by IDL should actually hav been \delta_{90}. Yet once exploiting da window graph, da Greek letters stood normally. I havn’t yet found out ways to solve da bug, roping still.

Lately I’v been preoccupied with learning IDL myself. Seems that professional astronomers won’t implement da softwares that are widely used amongst amateur astronomers. Da more I learn about IDL, da more important IDL’s to me. Once getting hang of it, I’l b capable of processing images in a scientific means n conduct analysis relatively with ease.

I’v adopted M. Knight’s procedures to analyze LASCO/STEREO images, however, simultaneously none of da softwares I possess has da capability to do photometric work — da dynamic range becomes too short for, for instance, Astrometrica to simply illustrate these images, so that makes measurements impossible.

It’s of great necessity for me to calibrate da LASCO/STEREO images and proceed to analysis; I has some ideas with bodies within these images to write a paper. Before this I must master IDL as soon as possible. In addition, da coach of my uni’s soccer team called me to join da team himself, and if it doesn’t rain, I need to go to da training evry two days. Definitely I become even busier!

I must make good use of time n hurry up. Gambate n Cố lên!

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HG Model Plotting

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