https://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&feed=atom&action=historyModelling spatially resolved X-ray polarization - Revision history2024-03-28T20:47:10ZRevision history for this page on the wikiMediaWiki 1.16.0https://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4833&oldid=prevHhudson at 16:56, 19 December 20112011-12-19T16:56:54Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|second_author = Eduard Kontar</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|second_author = Eduard Kontar</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|publish_date = 12 December 2011</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|publish_date = 12 December 2011</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>|next_nugget = [[]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>|next_nugget = [[<ins class="diffchange diffchange-inline">No Hard X-rays from Comet Lovejoy</ins>]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|previous_nugget = [[Slowly but surely towards the huge amount of energy II]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|previous_nugget = [[Slowly but surely towards the huge amount of energy II]]</div></td></tr>
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</table>Hhudsonhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4823&oldid=prevHhudson: light editing and some further links2011-12-12T16:43:27Z<p>light editing and some further links</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Polarization of hard X-ray sources ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Polarization of hard X-ray sources ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar <del class="diffchange diffchange-inline">flare accelerated electrons </del>are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#c2 bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of the radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by <ins class="diffchange diffchange-inline">electrons accelerated during </ins>solar <ins class="diffchange diffchange-inline">flares </ins>are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#c2 bremsstrahlung] and their <ins class="diffchange diffchange-inline">linear </ins>polarization <ins class="diffchange diffchange-inline">(a natural consequence of [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton scattering] </ins>should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of the radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire HXR source, but what <del class="diffchange diffchange-inline">about many </del>spatially resolved polarization measurements across a single HXR source? If we had <del class="diffchange diffchange-inline">the instrumentation to measure this</del>, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer <del class="diffchange diffchange-inline">is </del>no<del class="diffchange diffchange-inline">, but </del>all sources sitting at height h above the photosphere, up to ~100 keV, <del class="diffchange diffchange-inline">should </del>consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire HXR source, but what <ins class="diffchange diffchange-inline">would </ins>spatially resolved polarization measurements across a single HXR source <ins class="diffchange diffchange-inline">add to this</ins>? </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>If we had <ins class="diffchange diffchange-inline">imaging polarimetric data</ins>, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung <ins class="diffchange diffchange-inline">from an isotropic electron distribution function</ins>, then the answer <ins class="diffchange diffchange-inline">would be "</ins>no<ins class="diffchange diffchange-inline">."</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">But </ins>all sources sitting at height <ins class="diffchange diffchange-inline">''</ins>h<ins class="diffchange diffchange-inline">'' </ins>above the photosphere, up to ~100 keV, <ins class="diffchange diffchange-inline">must </ins>consist of two components; the directly emitted bremsstrahlung component and a backscattered <ins class="diffchange diffchange-inline">[http://en.wikipedia.org/wiki/Albedo </ins>albedo<ins class="diffchange diffchange-inline">] </ins>component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Albedo polarization patterns ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Albedo polarization patterns ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In Figure 4 we take a chosen mid-point location at cos(heliocentric angle) of μ~0.80 (or <del class="diffchange diffchange-inline">the </del>source <del class="diffchange diffchange-inline">corresponding to </del>~542 ' ' <del class="diffchange diffchange-inline">disk location</del>), and view the changes across DOP and direction of polarization Ψ in the radial direction of the source through Y=0 ' ', for three different photon distributions. Firstly with spatially resolved polarization, we have two quantities to work with. This has the advantage over a single entire source polarization measurement already; where we only ever get directivity information from the DOP. Secondly, we see distinctive changes in both of these quantities across the source with increasing photon directivity. At the side of the source closest to the disk centre, we see that the DOP falls with increased photon beaming while the direction of polarization Ψ roughly remains at 90 degrees. On the limb-side of the source, we see that the DOP increases with photon beaming and Ψ decreases with photon beaming. Not only are these results useful, they also require no manipulation, i.e. there is no need to worry about separating the primary and albedo components - these are now used together as one measurement to determine the photon anisotropy. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In Figure 4 we take a chosen mid-point location at cos(heliocentric angle) of μ~0.80 (or <ins class="diffchange diffchange-inline">a </ins>source <ins class="diffchange diffchange-inline">at </ins>~542 ' ' <ins class="diffchange diffchange-inline">central distance</ins>), and view the changes across DOP and direction of polarization Ψ in the radial direction of the source through Y=0 ' ', for three different photon distributions. Firstly with spatially resolved polarization, we have two quantities to work with. This has the advantage over a single entire source polarization measurement already; where we only ever get directivity information from the DOP. Secondly, we see distinctive changes in both of these quantities across the source with increasing photon directivity. At the side of the source closest to the disk centre, we see that the DOP falls with increased photon beaming while the direction of polarization Ψ roughly remains at 90 degrees. On the limb-side of the source, we see that the DOP increases with photon beaming and Ψ decreases with photon beaming. Not only are these results useful, they also require no manipulation, i.e. there is no need to worry about separating the primary and albedo components - these are now used together as one measurement to determine the photon anisotropy. </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conclusions ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conclusions ==</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In conclusion, spatially resolved polarization could provide us with an effective method of determining the directivity of the radiating electron distribution, if and when in the future we have the instrumentation available to <del class="diffchange diffchange-inline">measure </del>reliable and <del class="diffchange diffchange-inline">trustworthy </del>polarization measurements. Our full results are shown in Jeffrey & Kontar (2011) [http://adsabs.harvard.edu/abs/2011arXiv1110.4993J [1]].</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In conclusion, spatially resolved polarization could provide us with an effective method of determining the directivity of the radiating electron distribution, if and when in the future we have the instrumentation available to <ins class="diffchange diffchange-inline">make </ins>reliable and <ins class="diffchange diffchange-inline">sensitive </ins>polarization measurements. Our full results are shown in Jeffrey & Kontar (2011) [http://adsabs.harvard.edu/abs/2011arXiv1110.4993J [1]].</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>This work was financially supported by STFC and SUPA. [[File:stfc_logo.jpg|200 px]] [[File:SUPA_Logo.jpg|100 px]] </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>This work was financially supported by STFC and SUPA. [[File:stfc_logo.jpg|200 px]] [[File:SUPA_Logo.jpg|100 px]] </div></td></tr>
</table>Hhudsonhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4822&oldid=prevNjeffrey at 21:21, 9 December 20112011-12-09T21:21:14Z<p></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[File:spatpol2.png|frame|center|Figure 2: Albedo polarization maps from <del class="diffchange diffchange-inline">a </del>isotropic, unpolarised source sitting at four different heliocentric angles. Blue ellipse=albedo source and green ellipse=total source while the red arrows indicate the direction of polarization Ψ and the length of the arrows indicate the DOP, with 2 ' ' equaling 100 % polarization.]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[File:spatpol2.png|frame|center|Figure 2: Albedo polarization maps from <ins class="diffchange diffchange-inline">an </ins>isotropic, unpolarised source sitting at four different heliocentric angles. Blue ellipse=albedo source and green ellipse=total source while the red arrows indicate the direction of polarization Ψ and the length of the arrows indicate the DOP, with 2 ' ' equaling 100 % polarization.]]</div></td></tr>
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</table>Njeffreyhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4821&oldid=prevNjeffrey at 21:13, 9 December 20112011-12-09T21:13:30Z<p></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[File:spatpol3.png|frame|center|Figure 3: The resulting total polarization maps for a nearly isotropic, unpolarised source sitting at a chromospheric height of 1.4 ' ' and with a source <del class="diffchange diffchange-inline">FWHM </del>of 5 ' ' at four different heliocentric angles. Orange ellipse/dot = primary size/centroid position, blue ellipse/dot = albedo size/centroid position and green ellipse/dot = total size/centroid position while the red arrows indicate the polarization <del class="diffchange diffchange-inline">angle </del>and the length of the arrows indicate the DOP, with 2 ' ' equaling 100 % polarization.]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[File:spatpol3.png|frame|center|Figure 3: The resulting total polarization maps for a nearly isotropic, unpolarised source sitting at a chromospheric height of 1.4 ' ' and with a source <ins class="diffchange diffchange-inline">size </ins>of 5 ' ' at four different heliocentric angles. Orange ellipse/dot = primary size/centroid position, blue ellipse/dot = albedo size/centroid position and green ellipse/dot = total size/centroid position while the red arrows indicate the <ins class="diffchange diffchange-inline">direction of </ins>polarization <ins class="diffchange diffchange-inline">Ψ </ins>and the length of the arrows indicate the DOP, with 2 ' ' equaling 100 % polarization.]]</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:anim_spatpol_frame1.png|frame|center|300 px|center|Figure 4: Click [http://www.astro.gla.ac.uk/users/eduard/rhessi/natasha_spatpol_nugget/ here] to view the animation. Animation showing how the spatially resolved DOP and polarization <del class="diffchange diffchange-inline">angle </del>Ψ change with increasing photon (electron) anisotropy for a source sitting at one disk location of μ ∼ 0.80. Labels 1-3 indicate increasing photon anisotropy from near isotropic to a highly beamed distribution towards the photosphere. Orange=primary source, Blue=albedo source and Green=total source.]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:anim_spatpol_frame1.png|frame|center|300 px|center|Figure 4: Click [http://www.astro.gla.ac.uk/users/eduard/rhessi/natasha_spatpol_nugget/ here] to view the animation. Animation showing how the spatially resolved DOP and <ins class="diffchange diffchange-inline">direction of </ins>polarization Ψ change with increasing photon (electron) anisotropy for a source sitting at one disk location of μ ∼ 0.80. Labels 1-3 indicate increasing photon anisotropy from near isotropic to a highly beamed distribution towards the photosphere. Orange=primary source, Blue=albedo source and Green=total source.]]</div></td></tr>
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</table>Njeffreyhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4820&oldid=prevNjeffrey at 20:47, 9 December 20112011-12-09T20:47:08Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Polarization of hard X-ray sources ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Polarization of hard X-ray sources ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar flare accelerated electrons are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#<del class="diffchange diffchange-inline">c2l </del>bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of the radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar flare accelerated electrons are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#<ins class="diffchange diffchange-inline">c2 </ins>bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of the radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire HXR source, but what about many spatially resolved polarization measurements across a single HXR source? If we had the instrumentation to measure this, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer is no, but all sources sitting at height h above the photosphere, up to ~100 keV, should consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire HXR source, but what about many spatially resolved polarization measurements across a single HXR source? If we had the instrumentation to measure this, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer is no, but all sources sitting at height h above the photosphere, up to ~100 keV, should consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td></tr>
</table>Njeffreyhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4819&oldid=prevNjeffrey at 20:39, 9 December 20112011-12-09T20:39:11Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Polarization of hard X-ray sources ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Polarization of hard X-ray sources ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar flare accelerated electrons<del class="diffchange diffchange-inline">, </del>are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#c2l bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of the radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar flare accelerated electrons are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#c2l bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of the radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire HXR source, but what about many spatially resolved polarization measurements across a single HXR source? If we had the instrumentation to measure this, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer is no, but all sources sitting at height h above the photosphere, up to ~100 keV, should consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire HXR source, but what about many spatially resolved polarization measurements across a single HXR source? If we had the instrumentation to measure this, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer is no, but all sources sitting at height h above the photosphere, up to ~100 keV, should consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td></tr>
</table>Njeffreyhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4818&oldid=prevNjeffrey at 16:32, 9 December 20112011-12-09T16:32:44Z<p></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[Image:anim_spatpol_frame1.png|frame|center|300 px|center|Figure 4: Click [http://www.astro.gla.ac.uk/users/eduard/rhessi/natasha_spatpol_nugget/ here] to view the animation. Animation showing how the spatially resolved DOP and polarization angle Ψ change with increasing photon (electron) anisotropy for a source sitting at one disk location of μ ∼ 0.80. Labels 1-3 indicate increasing photon anisotropy from near isotropic to a highly beamed distribution towards the photosphere.]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:anim_spatpol_frame1.png|frame|center|300 px|center|Figure 4: Click [http://www.astro.gla.ac.uk/users/eduard/rhessi/natasha_spatpol_nugget/ here] to view the animation. Animation showing how the spatially resolved DOP and polarization angle Ψ change with increasing photon (electron) anisotropy for a source sitting at one disk location of μ ∼ 0.80. Labels 1-3 indicate increasing photon anisotropy from near isotropic to a highly beamed distribution towards the photosphere<ins class="diffchange diffchange-inline">. Orange=primary source, Blue=albedo source and Green=total source</ins>.]]</div></td></tr>
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</table>Njeffreyhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4817&oldid=prevNjeffrey at 16:18, 9 December 20112011-12-09T16:18:00Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar flare accelerated electrons, are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#c2l bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of the radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar flare accelerated electrons, are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#c2l bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of the radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire source, but what about many spatially resolved polarization measurements across a single HXR source? If we had the instrumentation to measure this, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer is no, but all sources sitting at height h above the photosphere, up to ~100 keV, should consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire <ins class="diffchange diffchange-inline">HXR </ins>source, but what about many spatially resolved polarization measurements across a single HXR source? If we had the instrumentation to measure this, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer is no, but all sources sitting at height h above the photosphere, up to ~100 keV, should consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Albedo polarization patterns ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Albedo polarization patterns ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Albedo produces a distinctive polarization pattern across an HXR source, changing both the [http://demonstrations.wolfram.com/LightPolarizationAndStokesParameters/ degree of linear polarization (DOP) and the direction of polarization Ψ]. Figure 1 shows a simple cartoon of three sources at different positions above the solar disk. To understand the pattern, take the easiest example of an initially isotropic and unpolarised HXR source sitting exactly above the solar centre and examine the DOP pattern produced across the albedo patch in the photosphere due to Compton scattering. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Albedo produces a distinctive polarization pattern across an HXR source, changing both the [http://demonstrations.wolfram.com/LightPolarizationAndStokesParameters/ degree of linear polarization (DOP) and the direction of polarization Ψ]. Figure 1 shows a simple cartoon of three <ins class="diffchange diffchange-inline">HXR </ins>sources at different positions above the solar disk. To understand the pattern, take the easiest example of an initially isotropic and unpolarised HXR source sitting exactly above the solar centre and examine the DOP pattern produced across the albedo patch in the photosphere due to Compton scattering. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The largest changes in DOP occur when the scattering angle is equal to 90 degrees and no changes occur for scattering angles of 0 degrees and 180 degrees. Photons scattered from the edges of the albedo patch towards the observer have scattered at angles closer to 90 degrees, producing the largest change in DOP and in this case the DOP of the outgoing photon beam heads towards 100 %. Photons directly below the source have had to scatter at angles close to 180 degrees to reach the observer, which causes no change in DOP (i.e. 0 % in this case). Hence, we get this increase in DOP from 0 % and tending towards 100 % as we head out to the edges of the source. This pattern emerges at other source locations but is altered slightly due to projection effects (Figure 2). In Figure 2, we can also see that albedo produces a distinctive pattern in the direction of polarization Ψ, which sits at an angle tangential to the line connecting the observed point on the source and the source centre. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The largest changes in DOP occur when the scattering angle is equal to 90 degrees and no changes occur for scattering angles of 0 degrees and 180 degrees. Photons scattered from the edges of the albedo patch towards the observer have scattered at angles closer to 90 degrees, producing the largest change in DOP and in this case the DOP of the outgoing photon beam heads towards 100 %. Photons directly below the source have had to scatter at angles close to 180 degrees to reach the observer, which causes no change in DOP (i.e. 0 % in this case). Hence, we get this increase in DOP from 0 % and tending towards 100 % as we head out to the edges of the source. This pattern emerges at other source locations but is altered slightly due to projection effects (Figure 2). In Figure 2, we can also see that albedo produces a distinctive pattern in the direction of polarization Ψ, which sits at an angle tangential to the line connecting the observed point on the source and the source centre. </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Spatially resolved polarization - simulation results ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Spatially resolved polarization - simulation results ==</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We used [http://mathworld.wolfram.com/MonteCarloMethod.html Monte Carlo simulations] to study spatially resolved polarization due to albedo and input photon distributions into our simulations created from three different electron directivities; from the near isotropic to a highly beamed distribution, labelled 1-3 respectively in the animation shown in Figure 4 . [http://adsabs.harvard.edu/abs/2011arXiv1110.4993J For each of these distributions we used a source height of 1.4 ' ' above the photosphere and a source size of 5 ' ']. The resulting polarization maps for the near isotropic distribution over the energy range of 20-50 keV are shown in Figure 3. Although the DOP and Ψ patterns <del class="diffchange diffchange-inline">across the sources </del>at different points on the solar disk for a single distribution are very interesting, the observationally useful information comes from the changes at a single location due to varying photon (and electron) directivity. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We used [http://mathworld.wolfram.com/MonteCarloMethod.html Monte Carlo simulations] to study spatially resolved polarization due to albedo and input photon distributions into our simulations created from three different electron directivities; from the near isotropic to a highly beamed distribution, labelled 1-3 respectively in the animation shown in Figure 4 . [http://adsabs.harvard.edu/abs/2011arXiv1110.4993J For each of these distributions we used a source height of 1.4 ' ' above the photosphere and a source size of 5 ' ']. The resulting polarization maps for the near isotropic distribution over the energy range of 20-50 keV are shown in Figure 3. Although the DOP and Ψ patterns <ins class="diffchange diffchange-inline">for each source </ins>at different points on the solar disk for a single distribution are very interesting, the observationally useful information comes from the changes at a single location due to varying photon (and electron) directivity. </div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In Figure 4 we take a chosen mid-point location at cos(heliocentric angle) of μ~0.80 (or the source corresponding to ~542 ' ' disk location), and view the changes across DOP and direction of polarization Ψ in the radial direction of the source through Y=0 ' ' . Firstly with spatially resolved polarization, we have two quantities to work with. This has the advantage over a single entire source polarization measurement already; where we only ever get directivity information from the DOP. Secondly, we see distinctive changes in both of these quantities across the source with increasing photon directivity. At the side of the source closest to the disk centre, we see that the DOP falls with increased photon beaming while the direction of polarization Ψ roughly remains at 90 degrees. On the limb-side of the source, we see that the DOP increases with photon beaming and Ψ decreases with photon beaming. Not only are these results useful, they also require no manipulation, i.e. there is no need to worry about separating the primary and albedo components - these are now used together as one measurement to determine the photon anisotropy. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In Figure 4 we take a chosen mid-point location at cos(heliocentric angle) of μ~0.80 (or the source corresponding to ~542 ' ' disk location), and view the changes across DOP and direction of polarization Ψ in the radial direction of the source through Y=0 ' '<ins class="diffchange diffchange-inline">, for three different photon distributions</ins>. Firstly with spatially resolved polarization, we have two quantities to work with. This has the advantage over a single entire source polarization measurement already; where we only ever get directivity information from the DOP. Secondly, we see distinctive changes in both of these quantities across the source with increasing photon directivity. At the side of the source closest to the disk centre, we see that the DOP falls with increased photon beaming while the direction of polarization Ψ roughly remains at 90 degrees. On the limb-side of the source, we see that the DOP increases with photon beaming and Ψ decreases with photon beaming. Not only are these results useful, they also require no manipulation, i.e. there is no need to worry about separating the primary and albedo components - these are now used together as one measurement to determine the photon anisotropy. </div></td></tr>
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</table>Njeffreyhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4816&oldid=prevNjeffrey at 16:06, 9 December 20112011-12-09T16:06:23Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Polarization of hard X-ray sources ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Polarization of hard X-ray sources ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar flare accelerated electrons, are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#c2l bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of <del class="diffchange diffchange-inline">a </del>radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Hard X-ray (HXR) sources produced by solar flare accelerated electrons, are our best investigative tool for probing the properties of the radiating electron distribution. These HXRs are emitted via [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html#c2l bremsstrahlung] and their polarization should directly tell us about the anisotropy of the radiating electron distribution, hence helping to constrain models of electron transport and acceleration. Linear polarization measurements from a dedicated X-ray polarimeter may allow us to determine the anisotropy of <ins class="diffchange diffchange-inline">the </ins>radiating electron distribution from a single flare, without the need for two spacecraft or assumptions made by statistical surveys etc. While in theory this is a great method, measuring HXR polarization successfully through the years has proved to be a difficult task. </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire source, but what about many spatially resolved polarization measurements across a single HXR source? If we had the instrumentation to measure this, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer is no, but all sources sitting at height h above the photosphere, up to ~100 keV, should consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>All linear polarization measurements to date have been single measurements across the entire source, but what about many spatially resolved polarization measurements across a single HXR source? If we had the instrumentation to measure this, would it prove useful? If all HXRs from the source were directly observed after bremsstrahlung, then the answer is no, but all sources sitting at height h above the photosphere, up to ~100 keV, should consist of two components; the directly emitted bremsstrahlung component and a backscattered albedo component created by [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html Compton backscattering] in the photosphere (see nuggets [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Albedo_and_the_modification_of_RHESSI_results Nugget #130], [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Solar_Hard_X-ray_Albedo Nugget #119] and [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 Nugget #42]). It is the existence of this albedo component, particularly present over peak energies of 20-50 keV, that motivates the need for and the usefulness of spatially resolved polarization measurements. Without the albedo component, this would prove to be a rather pointless task since only albedo provides a variation in polarization across the source. This is a useful property, not just for albedo detection but for determining photon directivity.</div></td></tr>
</table>Njeffreyhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Modelling_spatially_resolved_X-ray_polarization&diff=4815&oldid=prevNjeffrey at 15:54, 9 December 20112011-12-09T15:54:36Z<p></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">From </del>Figure 4<del class="diffchange diffchange-inline">, </del>we take a chosen mid-point location at cos(heliocentric angle) of μ~0.80 (or the source corresponding to ~542 ' ' disk location), and view the changes across DOP and Ψ in the radial direction of the source through Y=0 ' ' . Firstly with spatially resolved polarization, we have two quantities to work with. This has the advantage over a single entire source polarization measurement already; where we only ever get directivity information from the DOP. Secondly, we see distinctive changes in both of these quantities across the source with increasing photon directivity. At the side of the source closest to the disk centre, we see that the DOP falls with increased photon beaming while Ψ roughly remains at 90 degrees. On the limb-side of the source, we see that the DOP increases with photon beaming and Ψ decreases with photon beaming. Not only are these results useful, they also require no manipulation, i.e. there is no need to worry about separating the primary and albedo components - these are now used together as one measurement to determine the photon anisotropy. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">In </ins>Figure 4 we take a chosen mid-point location at cos(heliocentric angle) of μ~0.80 (or the source corresponding to ~542 ' ' disk location), and view the changes across DOP and <ins class="diffchange diffchange-inline">direction of polarization </ins>Ψ in the radial direction of the source through Y=0 ' ' . Firstly with spatially resolved polarization, we have two quantities to work with. This has the advantage over a single entire source polarization measurement already; where we only ever get directivity information from the DOP. Secondly, we see distinctive changes in both of these quantities across the source with increasing photon directivity. At the side of the source closest to the disk centre, we see that the DOP falls with increased photon beaming while <ins class="diffchange diffchange-inline">the direction of polarization </ins>Ψ roughly remains at 90 degrees. On the limb-side of the source, we see that the DOP increases with photon beaming and Ψ decreases with photon beaming. Not only are these results useful, they also require no manipulation, i.e. there is no need to worry about separating the primary and albedo components - these are now used together as one measurement to determine the photon anisotropy. </div></td></tr>
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