How Solar X-ray Irradiance is Affected by the Size of Field of View

Aki Takeda(MSU) and Shannon Boland(UOW)

Link to the verion 1 and the verion 2
22-Jan-2023 : paper version copied from ver.2

0. Abstract

1. Introduction

2. Data preparation

[Table 1] XRT images used for the study of the active corona. 
----------- Al-mesh --------------
  date       time    exposure time
                        (sec)
----------------------------------
16-JUL-2022 03:48:29   0.0020
16-JUL-2022 03:48:41   0.1280
16-JUL-2022 03:48:47   0.7255
16-JUL-2022 03:48:53   0.7251
16-JUL-2022 03:48:59   0.7255
16-JUL-2022 03:49:11   0.7240
16-JUL-2022 03:52:22   0.0020
16-JUL-2022 03:52:28   0.1280
16-JUL-2022 03:52:33   0.7255
16-JUL-2022 03:52:39   0.7250
16-JUL-2022 03:52:52   0.7239
16-JUL-2022 03:52:58   0.7255

19-JUL-2022 19:09:02   (*)
----------------------------------
(*) stray light image

----------- Al-poly --------------
  date       time    exposure time
                        (sec)
----------------------------------
16-JUL-2022 03:49:19   0.0123
16-JUL-2022 03:49:25   0.1812
16-JUL-2022 03:49:31   1.4454
16-JUL-2022 03:49:39   1.4438
16-JUL-2022 03:49:46   1.4453
16-JUL-2022 03:49:52   1.4449
16-JUL-2022 03:53:06   0.0123
16-JUL-2022 03:53:12   0.1812
16-JUL-2022 03:53:20   1.4438
16-JUL-2022 03:53:27   1.4453
16-JUL-2022 03:53:33   1.4449
16-JUL-2022 03:53:40   1.4453

19-JUL-2022 19:09:11   (*)
----------------------------------
(*) stray light image

----------- thin-Be --------------
  date       time    exposure time
                        (sec)
----------------------------------
16-JUL-2022 03:50:01   0.0163
16-JUL-2022 03:50:06   0.5127
16-JUL-2022 03:50:18   2.8977
16-JUL-2022 03:50:26   2.8995
16-JUL-2022 03:50:34   2.8989
16-JUL-2022 03:50:48   2.8977
16-JUL-2022 03:50:56   2.8992
16-JUL-2022 03:51:04   2.8989
16-JUL-2022 03:53:48   0.0163
16-JUL-2022 03:54:00   0.5120
16-JUL-2022 03:54:06   2.8992
16-JUL-2022 03:54:14   2.8989
16-JUL-2022 03:54:22   2.8992
16-JUL-2022 03:54:36   2.8977
16-JUL-2022 03:54:47   2.8992
16-JUL-2022 03:55:07   2.8977
----------------------------------

[Figure 1] prepared by hicorona/hicorona_syn4paper.pro, hicorona_syn_eps.pro
XRT composite images of the active corona processed from the images listed in Table 1 (see text for detail). Left: image processed for the Al-mesh filter. Middle: for the Al-poly filter. Right: for the thin-Be filter. Two arrows in the Al-poly image indicate the location of ghost pattern of XRT. Two lines appeared in the Al-mesh image is the location of the intensity profile shown in Figure 12.

[Table 2] XRT images used for the study of the minimum corona. 
----------- Al-mesh --------------
  date       time    exposure time
                        (sec)
----------------------------------
12-AUG-2009 20:05:12   0.5121
12-AUG-2009 20:05:18   5.7971
12-AUG-2009 20:14:12   0.5121
12-AUG-2009 20:14:18   5.7971
----------------------------------

----------- Al-poly --------------
  date       time    exposure time
                        (sec)
----------------------------------
12-AUG-2009 20:06:13n   0.5128
12-AUG-2009 20:06:18n   5.7971
12-AUG-2009 20:15:13n   0.5128
12-AUG-2009 20:15:18n   5.7971
----------------------------------

----------- thin-Be --------------
  date       time    exposure time
                        (sec)
----------------------------------
12-AUG-2009 20:07:44   32.7680
12-AUG-2009 20:16:44   32.7680
----------------------------------

[Figure 2] prepared by hicorona/get_disksig_20090812_paper.pro


3. Data analysis Method

3.1 : Collection of coronal signals

We collect the total intensity of the corona included in the NE-quadrant of the Sun. The mask having the shape of quater-disk was applied to collect intensity included only in the NE-quadrant area.

[Figure 3] prepared by hicorona/maskimg_figs.pro

[Figure 4] prepared by hicorona/get_disksig_hic4paper.pro
Left: Total XRT signals from the NE-region of the 2022/07/16 corona included in the different sizes of open area of the masking image shown in the Figure 3. The plus/cross/diamond symbols indicates the observed signals with XRT's Al_mesh/Al_poly/thin_Be analysis filters, respectively. Right: Same as the left plot but signals are normalized with respect to the value at 1.7Rs for each filter. The vertical dotted lines indicate the positions where the DN and its normalized value are listed in Table 3.
[click image to enlarge]

[Figure 5] prepared by hicorona/get_disksig_20090812_epsplot.pro
Total XRT signals from the 2009/08/12 corona included in the different sizes of open area of the masking image shown in the Figure 3. The plus/cross/diamond/square symbols indicates the observed signals with XRT's Al_mesh/Al_poly/thin_Be analysis filters, respectively. Right: Same as the left plot but signals are normalized with respect to the value at 1.3Rs for each filter. The vertical dotted lines indicate the positions where the DN and its normalized value are listed in Table 4.
[click image to enlarge]

[Figure 6] prepared by hicorona/gen_hialtsig_20090812_eps.pro
[click image to enlarge]

[Table 3]
XRT signals of the active corona observed with 3 X-ray filters. Readings of the plot in Fig. 4 for selected heights of the FOV. Signals are in the unit of 108 DN. Normalization was made relative to the value at 1.7Rs for each filter. 

-------------------------------------------------------------
FOV height   Al_mesh        Al_poly         thin_Be
 [Rs]    [10^8 DN](rel.) [10^8 DN](rel.)  [10^8 DN](rel.) 
-------------------------------------------------------------
 0.9      1.06  0.685     0.896 0.717      0.145  0.785
 1.0      1.25  0.812     1.05  0.838      0.166  0.901
 1.1      1.46  0.945     1.19  0.954      0.180  0.977
 1.2      1.50  0.974     1.22  0.977      0.182  0.988
 1.3      1.52  0.985     1.23  0.987      0.183  0.993
 1.5      1.53  0.994     1.24  0.995      0.184  0.997
 1.7      1.54  1.00      1.25  1.00       0.185  1.00 
-------------------------------------------------------------

[Table 4]
Same as Table 3, but for the minimum corona. 

--------------------------------------------------------
FOV height  Al_mesh        Al_poly         thin_Be
 [Rs]  [10^6 DN](rel.) [10^6 DN](rel.) [10^6 DN](rel.) 
--------------------------------------------------------
 0.9     8.94  0.469     1.85  0.399     0.0234  0.303
 1.0    12.4   0.652     2.63  0.567     0.0330  0.427
 1.1    17.5   0.916     4.02  0.868     0.0553  0.715
 1.2    18.4   0.965     4.36  0.943     0.0655  0.847
 1.3    18.7   0.980     4.48  0.967     0.0698  0.903
 1.5    18.9   0.991     4.55  0.984     0.0735  0.951
 1.7    19.1   1.00      4.63  1.00      0.0773  1.00 
--------------------------------------------------------

3.2 : Calculate Te and EM

The coronal intensities collected in the varying size of FOV are used to calculate electron temperature and emission measure with the Fileter Ratio Method.

[Figure 7] prepared by xrt_resp/get_fratio_ch10_aptb_eps.pro and get_fratio_ch10_aptb_eps.pro
The ratios of the temperature response functions used for this analysis. The left plot is for the Al_poly/Al_mesh filter ratio. The blue(orange) line are used for the analysis of 12-Aug-2009(16-Jul-2022) data, respectively. The right plot is the corresponding ratio curves from the thin_Be/Al_poly filter ratio.
[click image to enlarge]

[Figure 8] prepared by hicorona/sig2teem7_hicorona_eps.pro
Filter ratio temperatures and emission measures calculated for the active corona for the FOVs of varying size. The symbols in black are derived from the Al_poly/Al_mesh filter ratio, while those in green are from thin_Be/Al_poly filter ratio.
[click image to enlarge]

[Figure 9] prepared by hicorona/sig2teem7_20090812_ext_eps.pro
Same as Fig.8, but for the minimum corona calculated from the extended Te and EM plotted in Fig.6.
[click image to enlarge]

3.3 : Calculate soft X-ray irradiance (5-60A)

Isothermal coronal spectrum is calculated from the derived Te and EM using Chianti atomic DB ver 10.0. The irradiance is obtained by integrating the spectral energy for the wavelength range of 5 to 60A, for which XRT filters used in this study have the best response.

4. Results

Soft X-ray irradiance calculatded for the varying size of FOV.

[Figure 10] prepared by hicorona/teem2irr7_hic4paper.pro & teem2irr_20090812_4paper.pro
XRT irradiance (5-60A) obtained as a function of the size of FOV. Left : plot for active corona observed on 2022/07/16. Black symbols are data obtained from the Al_pol/Al_mesh filter ratio, while green symbols are from thin_Be/Al_poly filter ratio. The vertical dotted lines indicate the positions where the irradiance and its normalized value are listed in Table 5. Right : corresponding plot for the minumum corona observed on 2009/08/12.
[click image to enlarge]

[Table 5]
XRT irradiance for the active corona calculated from Al_poly/Al_mesh and thin_Be/Al_poly filter ratios. Readings of Fig. 10 for selected heights of FOVs were converted to a linear scale and listed in the unit of 10-4 W/m2. The third and sixth columns are relative values to those at 1.7Rs. The forth and seventh columns are exclusion fraction expressed in percentage. Note that these irradiance values are for a quarter area of the Sun. The full-Sun irradiance is estimated as roughly 4 times larger than the values listed here. 

---------------------------------------------------------------------------------
FOV height          Apol/Alms irrad.                    tnBe/Apol irrad.
 [Rs]     [10^(-4) W/m^2] (rel.) excl.frac.[%] [10^(-4) W/m^2] (rel.) excl.frac. [%]
---------------------------------------------------------------------------------
 0.9            1.72      0.623     37.7         0.816       0.630     37.0 
 1.0            2.14      0.761     23.9         0.985       0.760     24.0
 1.1            2.56      0.936      6.4         1.20        0.929      7.1
 1.2            2.69      0.973      2.7         1.25        0.964      3.6
 1.3            2.72      0.983      1.7         1.27        0.981      1.9
 1.5            2.75      0.993      0.7         1.29        0.992      0.8
 1.7            2.77      1.00       0.0         1.30        1.00       0.0
---------------------------------------------------------------------------------

[Table 6]
Same as Table 5, but for the minimum corona. Irradiances are in the unit of 10-5 W/m2. 

---------------------------------------------------------------------------------
FOV height          Apol/Alms irrad.                    tnBe/Apol irrad.
 [Rs]     [10^(-5) W/m^2] (rel.) excl.frac.[%] [10^(-5) W/m^2] (rel.) excl.frac.[%]
---------------------------------------------------------------------------------
 0.9          0.851      0.409    59.1            0.803     0.400     60.0
 1.0          1.20       0.576    42.4            1.15      0.572     42.8
 1.1          1.81       0.867    13.3            1.76      0.880     12.0
 1.2          1.96       0.939     6.1            1.94      0.969      3.1
 1.3          2.01       0.967     3.3            1.98      0.990      1.0
 1.5          2.06       0.991     0.9            1.98      0.988      1.2
 1.7          2.08       1.00      0.0            2.00      1.00       0.0
---------------------------------------------------------------------------------

[Table 7] calculated by calc_phnoise_20220716.pro, calc_phnoise_20090812.pro, hicorona_syn4unc_alms.pro, hic20090812_syn4unc_apol.pro, etc.
Statistical and non-statistial uncertainties calculated for the total XRT signals within FOVs. 

---------------------------------------------------------------------------------
FOV height         Al_mesh               Al_poly               thin_Be
             stat[%]  non-stat[%]   stat[%]  non-stat[%]   stat[%]  non-stat[%]
---------------------------------------------------------------------------------
2022/07/16 active corona images
---------------------------------------------------------------------------------
1.1          0.014      0.0114      0.016      0.0039        0.051    0.0080  
1.3          0.013      0.0110      0.016      0.0038        0.050    0.0079
1.5          0.013      0.0109      0.015      0.0038        0.050    0.0079
1.7          0.013      0.0109      0.015      0.0038        0.050    0.0079
---------------------------------------------------------------------------------
2009/08/12 minimum corona images
---------------------------------------------------------------------------------
1.1          0.022     0.0078       0.070      0.0105        0.855    0.1674
1.3          0.021     0.0083       0.067      0.0110        0.766    0.1634
---------------------------------------------------------------------------------

5. Discussion

[Figure 11] prepared by y_legacy/irrad4/connect_dailyirrad_330_4paper.pro
[click image to enlarge]

[Table 8] 

------------------------------------------------------------------------
Period           SXT 1.1/1.2  (AlMg/Al.1)                 XRT 1.1/1.2
           a     sigma   10^(-a) 10^(-a-s) 10^(-a+s)  Apol/Alms thBe/Apol 
------------------------------------------------------------------------
  I      0.0320  0.0189   0.929    0.889    0.970         ---    ---    
  II     0.0460  0.0257   0.899    0.848    0.954        0.923  0.907     
 III     0.0335  0.0161   0.926    0.892    0.961        0.952  0.960
------------------------------------------------------------------------

[Figure 12] prepared by y_legacy/irrad4/connect_dailyirrad_330b_4paper.pro
[click image to enlarge]

[Table 9]
Same as Table 8, but for the comparison of 0.9Rs vs 1.2Rs. 

------------------------------------------------------------------------
Period           SXT 0.9/1.2  (AlMg/Al.1)                 XRT 0.9/1.2
           a     sigma   10^(-a) 10^(-a-s) 10^(-a+s)  Apol/Alms thBe/Apol 
------------------------------------------------------------------------
  I      0.300   0.167     0.501   0.342   0.735       ---      ---
  II     0.354   0.200     0.443   0.279   0.701      0.434     0.414   
 III     0.336   0.161     0.461   0.318   0.668      0.639     0.653
------------------------------------------------------------------------

6. Conclusion

Appendix: Deriving Radial Intensity Variations

A.1 : 2022/07/16 --- medium active corona

[Figure 13] prepared by hicorona/disksig2rad_20220716_4paper.pro and rad_prof_20220716_4paper.pro
[click image to enlarge]

A.2 : 2009/08/12 --- minimum corona

[Figure 14] hicorona/disksig2rad_20090812_4paper.pro and rad_prof_20220716_4paper.pro
[click image to enlarge]

[Figure 15] prepared by hicorona/rad_prof_20220716_4paper.pro
[click image to enlarge]