Calculating the temperature and emission measure

In this example, we will showcase how to use the filter method to calculate the temperature and emission measure of the X-ray Telescope (XRT) on Hinode.

import matplotlib.pyplot as plt
import sunpy.map
from astropy.visualization import ImageNormalize, LogStretch
from sunpy.net import Fido
from sunpy.net import attrs as a

from xrtpy.response import temperature_from_filter_ratio

To start, we will get XRT data via sunpy.

It is important to use images that same size and with the smallest time separation. Note that not all filter ratios produce good results.

query = Fido.search(
    a.Time("2011-01-28 01:31:55", "2011-01-28 01:32:05"), a.Instrument("xrt")
)
data_files = Fido.fetch(query)
xrt_map_1 = sunpy.map.Map(data_files[0])
xrt_map_2 = sunpy.map.Map(data_files[1])

The xrtpy.response.temperature_from_filter_ratio function has several options, mirroring the IDL routine xrt_teem.pro in SolarSoft in most respects.A simple call with no extra parameters calculates the temperature and (volume) emission measure for the two images without any binning or masking of the data.

T_EM = temperature_from_filter_ratio(xrt_map_1, xrt_map_2)

The output is a namedtuple with attributes Tmap, EMmap, Terrmap, and EMerrmap. As with the SolarSoft IDL routine xrt_teem.pro, the output images are logs of the quantities.

Tmap is the electron temperature, EMmap is the volume emission measure, Terrmap is a measure of the uncertainties in the temperature determined for each pixel and EMerrmap is the same for the emission measure.

T_e = T_EM.Tmap

fig = plt.figure()

ax = plt.subplot(projection=T_e)
T_e.plot(
    title="Derived Temperature",
    cmap="inferno",
    norm=ImageNormalize(vmin=6, vmax=7, stretch=LogStretch(10)),
)
T_e.draw_limb()
T_e.draw_grid()
plt.colorbar(label="T (K)")
plt.tight_layout()

plt.show()

If you want to do the same for Level 2 synoptic composite images, you have to use make_exposure_map to generate the exposure maps for the composite images. This is then passed to xrtpy.response.temperature_from_filter_ratio as the expmap1 and expmap2 arguments. Otherwise without accounting for the different exposure time per pixel, the temperature and emission measure will be incorrect.