AIA Response Function Tests



In [3]:

    
import os
import sys
import pickle

import numpy as np
import scipy
import matplotlib.pyplot as plt

import ChiantiPy.core as ch
import sunpy.instr.aia as aia

%matplotlib inline

The goal of this notebook is to test the wavelength and temperature response function calculations that are currently being developed in SunPy.

Wavelength Response Functions

First, we'll calculate the wavelength response functions for 6 of the 7 AIA EUV channels: 171, 193, 131, 335, 211, and 94 $\mathrm{\mathring{A}}$.



In [4]:

    
response = aia.Response(path_to_genx_dir='../ssw_aia_response_data/')



In [5]:

    
response.calculate_wavelength_response()
response.peek_wavelength_response()

Contribution Functions, $G(n,T)$

Next, we'll calculate the contribution functions for a couple of ions, hopefully ones that are relatively important to each channel. According to the AIA LMSAL webpage,

Channel ($\mathrm{\mathring{A}}$)	Primary Ions	Characteristic Temperature, $\log{T}$ (K)
94	Fe XVII	6.8
131	Fe VIII, XX, XXIII	5.6, 7.0, 7.2
171	Fe IX	5.8
193	Fe XII, XXIV	6.1, 7.3
211	Fe XIV	6.3
335	Fe XVI	6.4

First, choose a temperature range and constant density.



In [7]:

    
temperature = np.logspace(5.,8.,50)
density = 1.e+9

Now, make a list of all the ions that we care about so that we can easily iterate through them.



In [8]:

    
ions = ['fe_8','fe_9','fe_12','fe_14','fe_16','fe_17','fe_20','fe_23','fe_24']
search_interval = np.array([-2.5,2.5])
ion_wvl_ranges = [c+search_interval for c in [131.,171.,193.,211.,335.,94.,131.,131.,193.]]

Finally, iterate through all of the ions and store the contribution function and associated information.



In [10]:

    
#warning! This takes a long time!
contribution_fns = {}
for i,iwr in zip(ions,ion_wvl_ranges):
    tmp_ion = ch.ion(i,temperature=temperature,eDensity=density,em=1.e+27)
    tmp_ion.gofnt(wvlRange=[iwr[0],iwr[1]],top=3,plot=False)
    plt.show()
    contribution_fns[i] = tmp_ion.Gofnt

Calculating Temperature Response Functions

From Boerner et al. (2012), the temperature response function $K_i(T)$ is given by $$ K_i(T)=\int_0^{\infty}\mathrm{d}\lambda\,G(\lambda,T)R_i(\lambda) $$ First, we need to reshape the contribution functions for our discrete number of ions into $G(\lambda,T)$ such that each column of $G$ is $G_{\lambda}(T)$. Then we can interpolate each $R_i$ over that discrete number of wavelengths.



In [11]:

    
sorted_g = sorted([g[1] for g in contribution_fns.items()],key=lambda x: x['wvl'])
g_matrix = np.vstack((g['gofnt'] for g in sorted_g)).T
discrete_wavelengths = np.array([g['wvl'] for g in sorted_g])



In [123]:

    
for key in wavelength_response_fns:
    wavelength_response_fns[key]['wavelength_interpolated'] = discrete_wavelengths[:,0]
    wavelength_response_fns[key]['response_interpolated'] = np.interp(discrete_wavelengths,
                                                                      wavelength_response_fns[key]['wavelength'],
                                                                      wavelength_response_fns[key]['response'])[:,0]



In [124]:

    
temperature_response = {}
for key in wavelength_response_fns:
    g_times_r = g_matrix*wavelength_response_fns[key]['response_interpolated']
    temperature_response[key] = np.trapz(g_times_r,
                                         wavelength_response_fns[key]['wavelength_interpolated'])

Finally, try to plot all of the temperature response functions.



In [125]:

    
fig = plt.figure(figsize=(10,10))
ax = fig.gca()
for tresp in temperature_response.items():
    ax.plot(temperature,tresp[1],label=str(tresp[0]),color=sns.xkcd_rgb[channel_colors[tresp[0]]])
ax.set_ylim([1e-28,1e-22])
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel(r'$T$ (K)')
ax.set_ylabel(r'$K_i(T)$')
ax.legend(loc='best',title=r'Channel ($\mathrm{\mathring{A}}$)')









    Out[125]:





<matplotlib.legend.Legend at 0x1194fcf28>

Compare this to the top panel of Fig. 11 in Boerner et al. (2012)



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