A Flare in 3D

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|second_author = Juan Carlos Martinez Oliveros  
|second_author = Juan Carlos Martinez Oliveros  
|publish_date = 10 October 2011
|publish_date = 10 October 2011
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"ribbons" or "footpoints".
"ribbons" or "footpoints".
Many RHESSI Science Nuggets (e.g.,  
Many RHESSI Science Nuggets (e.g.,  
-
<http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Kernels_and_Ribbons [1]>)  
+
[http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Kernels_and_Ribbons [1]])  
have dealt with various aspects of these fascinating places.
have dealt with various aspects of these fascinating places.
From the RHESSI perspective of high-energy astrophyics, the deepest
From the RHESSI perspective of high-energy astrophyics, the deepest
parts of the solar atmosphere are necessarily dominant: a fast ion or
parts of the solar atmosphere are necessarily dominant: a fast ion or
electron propagates to the end of its  
electron propagates to the end of its  
-
<http://en.wikipedia.org/wiki/Stopping_power_(particle_radiation) range>,
+
[http://en.wikipedia.org/wiki/Stopping_power_(particle_radiation) range],
which can be measured in a <i>column density</i> of order  
which can be measured in a <i>column density</i> of order  
1 gram/cm<sup>2</sup>.
1 gram/cm<sup>2</sup>.
-
For example, <http://www.nobelprize.org/nobel_prizes/physics/laureates/1906/thomson-bio.html Thomson>
+
For example, [http://www.nobelprize.org/nobel_prizes/physics/laureates/1906/thomson-bio.html Thomson]
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<http://en.wikipedia.org/wiki/Thomson_scattering scattering>,
+
[http://en.wikipedia.org/wiki/Thomson_scattering scattering],
the basic process of hard X-ray interaction with matter,  
the basic process of hard X-ray interaction with matter,  
has about this range.
has about this range.
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The remarkable coincidence here is that the solar atmosphere, from the
The remarkable coincidence here is that the solar atmosphere, from the
photosphere out to infinity, has a  
photosphere out to infinity, has a  
-
<http://sprg.ssl.berkeley.edu/~stephchow/plasma/webpage/columndensity.html  
+
[http://sprg.ssl.berkeley.edu/~stephchow/plasma/webpage/columndensity.html column thickness]
-
column thickness> of only a few gram/cm<sup>2</sup>.  
+
of only a few gram/cm<sup>2</sup>.  
By contrast our protective  
By contrast our protective  
-
<http://en.wikipedia.org/wiki/Atmosphere_of_Earth Earth's atmosphere>
+
[http://en.wikipedia.org/wiki/Atmosphere_of_Earth Earth's atmosphere]
approaches a thousand times that thickness.
approaches a thousand times that thickness.
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precisely in terms of an actual physical height (e.g., measured in cm from
precisely in terms of an actual physical height (e.g., measured in cm from
Sun center), but instead in terms of  
Sun center), but instead in terms of  
-
<http://scienceworld.wolfram.com/physics/OpticalDepth.html optical depth>
+
[http://scienceworld.wolfram.com/physics/OpticalDepth.html optical depth]
in visible radiation.
in visible radiation.
This is convenient observationally, but leaves the relationship between
This is convenient observationally, but leaves the relationship between
-
optical depth and physical height uncalibrated observationally.
+
optical depth and physical height essentially uncalibrated.
Images at disk center only show their two dimensions and provide no
Images at disk center only show their two dimensions and provide no
-
clues, in an <http://en.wikipedia.org/wiki/Optical_depth optically thin>
+
clues, in an [http://en.wikipedia.org/wiki/Optical_depth optically thin]
medium.
medium.
In principle any telescope has the power to tell you where something is,
In principle any telescope has the power to tell you where something is,
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For an optically thick radiation, this expresses itself in terms of
For an optically thick radiation, this expresses itself in terms of
the  
the  
-
<http://spiff.rit.edu/classes/phys440/lectures/limb/limb.html limb darkening function>,
+
[http://spiff.rit.edu/classes/phys440/lectures/limb/limb.html limb darkening function],
but for an optically thin object in principle one could just look at see  
but for an optically thin object in principle one could just look at see  
-
where it is on the sky, and for source known to be at the limb, that would
+
where it is on the sky, and for a source ''known'' to be at the limb, that would
be the height.
be the height.
The problem is that the chromosphere is quite thin, at least based on 2D
The problem is that the chromosphere is quite thin, at least based on 2D
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perspective views by just putting our telescopes sufficiently far
perspective views by just putting our telescopes sufficiently far
out into space.
out into space.
-
The two <http://stereo.gsfc.nasa.gov/ STEREO>
+
The two [http://stereo.gsfc.nasa.gov/ STEREO]
spacecraft do this, approximately in Earth's orbit, and have been
spacecraft do this, approximately in Earth's orbit, and have been
giving us 3D perspective views of solar objects such as  
giving us 3D perspective views of solar objects such as  
-
<CMEs> since launch in 2006.
+
[http://solarscience.msfc.nasa.gov/CMEs.shtml CMEs] since launch in 2006.
This Nugget shows how these data can also be used to locate flare effects
This Nugget shows how these data can also be used to locate flare effects
in the lower solar atmosphere, in the third dimension.
in the lower solar atmosphere, in the third dimension.
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for a white-light flare at the limb, SOL2010-02-24T07:35 (M3.5).
for a white-light flare at the limb, SOL2010-02-24T07:35 (M3.5).
The white-light data come from the  
The white-light data come from the  
-
<http://hmi.stanford.edu/ HMI>
+
[http://hmi.stanford.edu/ HMI]
instrument on
instrument on
-
<http://sdo.gsfc.nasa.gov/ SDO>.
+
[http://sdo.gsfc.nasa.gov/ SDO].
Because of projection, the EW coordinate basicaly measures source height,
Because of projection, the EW coordinate basicaly measures source height,
so this comparison shows that these two radiations come from the same
so this comparison shows that these two radiations come from the same
Line 113: Line 113:
We can learn exactly where the flare was, in this case, because it was  
We can learn exactly where the flare was, in this case, because it was  
near disk center as viewed from STEREO-Behind (which trails  
near disk center as viewed from STEREO-Behind (which trails  
-
<http://stereo-ssc.nascom.nasa.gov/where.shtml behind> the
+
[http://stereo-ssc.nascom.nasa.gov/where.shtml behind] the
Earth, and thus sees above the E limb right now.
Earth, and thus sees above the E limb right now.
Figure 3 illustrates the mapping of the flare position, as seen by STEREO,
Figure 3 illustrates the mapping of the flare position, as seen by STEREO,
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[[File:160f3.png|thumb|center|700px|'''Figure 3''':
[[File:160f3.png|thumb|center|700px|'''Figure 3''':
-
Welcome to 3D <http://en.wikipedia.org/wiki/Astrometry astrometry>!
+
Welcome to 3D [http://en.wikipedia.org/wiki/Astrometry astrometry]!
The image at the left shows the flare observed by STEREO-B, unfortunately
The image at the left shows the flare observed by STEREO-B, unfortunately
with detail lost because of saturation.
with detail lost because of saturation.
-
On the right, the projection of saturated positions (+-10 pixels)
+
Here the solid line is the location of the HMI/RHESSI limb.
 +
On the right, the projection of saturated positions  
on the HMI image.
on the HMI image.
 +
The solid line is the projected location of the actual photosphere, at the line of positions
 +
determined by the centroids of the saturation streaks, whereas the dashed lines are +-10 EUVI
 +
pixels as a rough guide to uncertainty.
Because of the extreme projection, the STEREO location does not need to
Because of the extreme projection, the STEREO location does not need to
be determined very precisely.
be determined very precisely.
]]
]]
-
== Conclusions
+
In the right-hand panel of Figure 3, the true height of the WL/HXR sources is the very small difference between
 +
the solid line and the centroids of the sources - in this case, 0.7+-1.2 Mm, where the error is dominated by
 +
the EUVI image saturation.
 +
 
 +
== Conclusions ==
The RHESSI centroid determination has a precision well below one arc sec,
The RHESSI centroid determination has a precision well below one arc sec,
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== References ==
== References ==
-
[1] <http://adsabs.harvard.edu/abs/1998ApJ...500L.195B "Accurate Determination of the Solar Photospheric Radius">
+
[1] [http://adsabs.harvard.edu/abs/1998ApJ...500L.195B "Accurate Determination of the Solar Photospheric Radius"]

Latest revision as of 17:08, 22 August 2018


Nugget
Number: 160
1st Author: Hugh Hudson
2nd Author: Juan Carlos Martinez Oliveros
Published: 10 October 2011
Next Nugget: Quasi-Periodic Pulsations: Fermi/GBM Results
Previous Nugget: Solar Max Arrives
List all



Contents

Introduction

A solar flare is most spectacularly visible in the faintest part of the solar atmosphere, the corona, but we have long known that the most energetic parts of a flare are its lowest layers - we call these regions "ribbons" or "footpoints". Many RHESSI Science Nuggets (e.g., [1]) have dealt with various aspects of these fascinating places. From the RHESSI perspective of high-energy astrophyics, the deepest parts of the solar atmosphere are necessarily dominant: a fast ion or electron propagates to the end of its range, which can be measured in a column density of order 1 gram/cm2. For example, Thomson scattering, the basic process of hard X-ray interaction with matter, has about this range.

Figure 1: Illustration of the "thick target model", as drawn by Lyndsay Fletcher. This schematically shows the relationship between a coronal particle source and its radiation sinks in the lower solar atmosphere (ribbons and footpoints).

The remarkable coincidence here is that the solar atmosphere, from the photosphere out to infinity, has a column thickness of only a few gram/cm2. By contrast our protective Earth's atmosphere approaches a thousand times that thickness.

What is the actual height of a flare?

The discussion above clearly places the important part of a flare - at least, its energetically significant radiation - in the thin layer at the bottom of the solar atmosphere. But how high above the photosphere is this layer? For the most part, stellar astronomers do not try to answer this question precisely in terms of an actual physical height (e.g., measured in cm from Sun center), but instead in terms of optical depth in visible radiation. This is convenient observationally, but leaves the relationship between optical depth and physical height essentially uncalibrated. Images at disk center only show their two dimensions and provide no clues, in an optically thin medium. In principle any telescope has the power to tell you where something is, and so the third dimension might come from a limb view. For an optically thick radiation, this expresses itself in terms of the limb darkening function, but for an optically thin object in principle one could just look at see where it is on the sky, and for a source known to be at the limb, that would be the height. The problem is that the chromosphere is quite thin, at least based on 2D radiative-transfer models, and so very high angular resolution is necessary. Also, how do you really know what object is just at the limb?

Enter STEREO: the flare of 24 February 2011

The Sun is close enough, as an astronomical object, for us to get perspective views by just putting our telescopes sufficiently far out into space. The two STEREO spacecraft do this, approximately in Earth's orbit, and have been giving us 3D perspective views of solar objects such as CMEs since launch in 2006. This Nugget shows how these data can also be used to locate flare effects in the lower solar atmosphere, in the third dimension.

Figure 2: White light (HMI) and hard X-ray (RHESSI) views of SOL2010-02-24. The background shows a difference with a reversed color table, so the white-light flare shows up as dark. The image on the right shows soft X-ray loops connecting the footpoints.

Figure 2 shows a comparison between white light and hard X-ray sources for a white-light flare at the limb, SOL2010-02-24T07:35 (M3.5). The white-light data come from the HMI instrument on SDO. Because of projection, the EW coordinate basicaly measures source height, so this comparison shows that these two radiations come from the same height, within errors. But how high is that really? To answer this question we must know the image scale very precisely; that information comes from a comparison with the adjacent limb. The problem is that the limb is not at a height corresponding to the radius of the Sun directly (see Reference [1] for a discussion of this point). Instead it lies some 500 km above the true photosphere, ie that viewed at disk center. Thus the flare sources appear artificially near to the limb in Figure 2.

A final problem in learning about the third dimension (the flare height) can be solved directly by STEREO. We can learn exactly where the flare was, in this case, because it was near disk center as viewed from STEREO-Behind (which trails behind the Earth, and thus sees above the E limb right now. Figure 3 illustrates the mapping of the flare position, as seen by STEREO, on to the view from HMI.

Figure 3: Welcome to 3D astrometry! The image at the left shows the flare observed by STEREO-B, unfortunately with detail lost because of saturation. Here the solid line is the location of the HMI/RHESSI limb. On the right, the projection of saturated positions on the HMI image. The solid line is the projected location of the actual photosphere, at the line of positions determined by the centroids of the saturation streaks, whereas the dashed lines are +-10 EUVI pixels as a rough guide to uncertainty. Because of the extreme projection, the STEREO location does not need to be determined very precisely.

In the right-hand panel of Figure 3, the true height of the WL/HXR sources is the very small difference between the solid line and the centroids of the sources - in this case, 0.7+-1.2 Mm, where the error is dominated by the EUVI image saturation.

Conclusions

The RHESSI centroid determination has a precision well below one arc sec, in good conditions, and this makes it interesting as a way of measuring source height for a projected event as described here. Uniquely in this case, thus far, we have used the STEREO data to get a confirmation of the flare location (front side, near the RHESSI/HMI limb). We expect that STEREO location determination, for otherwise invisible flares, will be helpful for other kinds of 3D astrometry in the future.

References

[1] "Accurate Determination of the Solar Photospheric Radius"

Facts about A Flare in 3DRDF feed
RHESSI Nugget Date10 October 2011  +
RHESSI Nugget First AuthorHugh Hudson  +
RHESSI Nugget Index160  +
RHESSI Nugget Second AuthorJuan Carlos Martinez Oliveros  +
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