The Solar X-ray Limb III

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== Introduction ==
== Introduction ==
How big is the Sun? This question has to be answered with "it depends", since the observed diameter is wavelength dependent, as is evident in Figure 1.
How big is the Sun? This question has to be answered with "it depends", since the observed diameter is wavelength dependent, as is evident in Figure 1.
-
[[File:Rozelot.jpg|400px|thumb|center| Compilation of solar radius measurements at different wavelengths from EUV to microwaves (after [http://adsabs.harvard.edu/abs/2015ApJ...812...91R Rozelot et al. 2015])]]
+
[[File:Rozelot.jpg|400px|thumb|center|Figure 1: Compilation of solar radius measurements at different wavelengths from EUV to microwaves (after [http://adsabs.harvard.edu/abs/2015ApJ...812...91R Rozelot et al. 2015])]]
The IAU nominal value for the solar radius is given as 695.7 km ([http://adsabs.harvard.edu/abs/2016AJ....152...41P Prsa et al. 2016]). This value is based on optical measurements and depends on details of the atmosphere and radiative transfer models. In two previous nuggets we described a new technique that uses RHESSI visibilities of occulted solar flare sources to measure the height of the X-ray limb ([[The X-ray Limb]]) and reported on preliminary analysis of a suitable solar flare ([[The Solar X-ray Limb II]]). As reported in the second nugget there were some problems with the chosen flare, but having found a better suited candidate we can finally claim success!
The IAU nominal value for the solar radius is given as 695.7 km ([http://adsabs.harvard.edu/abs/2016AJ....152...41P Prsa et al. 2016]). This value is based on optical measurements and depends on details of the atmosphere and radiative transfer models. In two previous nuggets we described a new technique that uses RHESSI visibilities of occulted solar flare sources to measure the height of the X-ray limb ([[The X-ray Limb]]) and reported on preliminary analysis of a suitable solar flare ([[The Solar X-ray Limb II]]). As reported in the second nugget there were some problems with the chosen flare, but having found a better suited candidate we can finally claim success!
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== The event ==
== The event ==
The event that lead to our success, SOL2011-10-20T03:25, is the perfect candidate for several reasons. AIA context images provide independent confirmation that the event was indeed occulted. In addition, RHESSI's detector 2 was working well enough to provide usable data for this kind of work. This allowed us to perform a set of rigorous tests to confirm that the observed peak in visibility amplitude is indeed the signature of a limb-occulted source.
The event that lead to our success, SOL2011-10-20T03:25, is the perfect candidate for several reasons. AIA context images provide independent confirmation that the event was indeed occulted. In addition, RHESSI's detector 2 was working well enough to provide usable data for this kind of work. This allowed us to perform a set of rigorous tests to confirm that the observed peak in visibility amplitude is indeed the signature of a limb-occulted source.
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[[File:Limb_f1.png|600px|thumb|center|Left: AIA 131 A image of the flare SOL2011-10-20T03:25 with contours from a visibility forward fit. Middle and right: visibility amplitude as a function of position angle in RHESSI's grids 1 and 2. The dashed line gives the angle of the limb. The widths of the peaks (as found by fitting the Gaussian given as blue dotted line), their maximum amplitudes and the ration between the maximum amplitude in G1 and G2 are consistent with the expectations for an occulted source.]]
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[[File:Limb_f1.png|600px|thumb|center|Figure 2: Left: AIA 131 A image of the flare SOL2011-10-20T03:25 with contours from a visibility forward fit. Middle and right: visibility amplitude as a function of position angle in RHESSI's grids 1 and 2. The dashed line gives the angle of the limb. The widths of the peaks (as found by fitting the Gaussian given as blue dotted line), their maximum amplitudes and the ratio between the maximum amplitude in G1 and G2 are consistent with the expectations for an occulted source.]]
== The height of the X-ray limb ==
== The height of the X-ray limb ==
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We find (averaged over the measurements from G1 and G2) the X-ray limb radius a R_{X−ray} = 964.05\pm 0.15\pm 0.29 arcsec. The error includes both a statistical error from the visibility fits and a systematic error that includes the phase scatter of the visiblities that are associated with the limb, the length of the metering tube that holds the grids, and the accuracy of the Sun-center determination from the solar aspect system. How does this height compare with the optical limb height and with predictions for the X-ray limb height from models? This is shown in Figure 2. For the comparison, the standard VAL-C model ([http://www.example.com Vernazza et al. 1981]) was used.
+
We find (averaged over the measurements from G1 and G2) the X-ray limb radius a R_{X−ray} = 964.05\pm 0.15\pm 0.29 arcsec. The error includes both a statistical error from the visibility fits and a systematic error that includes the phase scatter of the visiblities that are associated with the limb, the length of the metering tube that holds the grids, and the accuracy of the Sun-center determination from the solar aspect system. How does this height compare with the optical limb height and with predictions for the X-ray limb height from models? This is shown in Figure 3. For the comparison, the standard VAL-C model ([http://www.example.com Vernazza et al. 1981]) was used.
-
[[File:Limb_f2.png|600px|thumb|center| Comparison of observed X-ray limb height with the optical limb height and the VAL-C model for photospheric abundances (solid black line) and coronal abundances (dotted black line). The horizontal bar of the observed X-ray limb height indicates the FWHM of the count spectrum peak. ]]
+
[[File:Limb_f2.png|600px|thumb|center|Figure 3: Comparison of observed X-ray limb height with the optical limb height and the VAL-C model for photospheric abundances (solid black line) and coronal abundances (dotted black line). The horizontal bar of the observed X-ray limb height indicates the FWHM of the count spectrum peak. ]]
== Conclusions ==
== Conclusions ==

Revision as of 15:23, 8 June 2017

Contents

Introduction

How big is the Sun? This question has to be answered with "it depends", since the observed diameter is wavelength dependent, as is evident in Figure 1.

Figure 1: Compilation of solar radius measurements at different wavelengths from EUV to microwaves (after Rozelot et al. 2015)

The IAU nominal value for the solar radius is given as 695.7 km (Prsa et al. 2016). This value is based on optical measurements and depends on details of the atmosphere and radiative transfer models. In two previous nuggets we described a new technique that uses RHESSI visibilities of occulted solar flare sources to measure the height of the X-ray limb (The X-ray Limb) and reported on preliminary analysis of a suitable solar flare (The Solar X-ray Limb II). As reported in the second nugget there were some problems with the chosen flare, but having found a better suited candidate we can finally claim success!

The event

The event that lead to our success, SOL2011-10-20T03:25, is the perfect candidate for several reasons. AIA context images provide independent confirmation that the event was indeed occulted. In addition, RHESSI's detector 2 was working well enough to provide usable data for this kind of work. This allowed us to perform a set of rigorous tests to confirm that the observed peak in visibility amplitude is indeed the signature of a limb-occulted source.

Figure 2: Left: AIA 131 A image of the flare SOL2011-10-20T03:25 with contours from a visibility forward fit. Middle and right: visibility amplitude as a function of position angle in RHESSI's grids 1 and 2. The dashed line gives the angle of the limb. The widths of the peaks (as found by fitting the Gaussian given as blue dotted line), their maximum amplitudes and the ratio between the maximum amplitude in G1 and G2 are consistent with the expectations for an occulted source.

The height of the X-ray limb

We find (averaged over the measurements from G1 and G2) the X-ray limb radius a R_{X−ray} = 964.05\pm 0.15\pm 0.29 arcsec. The error includes both a statistical error from the visibility fits and a systematic error that includes the phase scatter of the visiblities that are associated with the limb, the length of the metering tube that holds the grids, and the accuracy of the Sun-center determination from the solar aspect system. How does this height compare with the optical limb height and with predictions for the X-ray limb height from models? This is shown in Figure 3. For the comparison, the standard VAL-C model (Vernazza et al. 1981) was used.

Figure 3: Comparison of observed X-ray limb height with the optical limb height and the VAL-C model for photospheric abundances (solid black line) and coronal abundances (dotted black line). The horizontal bar of the observed X-ray limb height indicates the FWHM of the count spectrum peak.

Conclusions

After much hardship we managed to show that the method works in principle and we can report the first measurement of the X-ray limb height. You can read all the details in the forthcoming ApJ publication (Battaglia et al. 2017). However, many questions remain and new ones have been raised:

The next steps thus have to be better modelling and a systematic search for a larger number of events over the whole duration of the RHESSI mission to confirm this first detection and answer the above questions.

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