Evidence of Significant Energy Input in the Late Phase of a Solar Flare from NuSTAR X-Ray Observations

0.67 MB·

by  Matej Kuhar

Draftversion January27,2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
EVIDENCE OF SIGNIFICANT ENERGY INPUT IN THE LATE PHASE OF A SOLAR FLARE FROM NUSTAR
X-RAY OBSERVATIONS
Matej Kuhar1,2, Sa¨m Krucker1,3, Iain G. Hannah4, Lindsay Glesener5, Pascal Saint-Hilaire3, Brian W.
Grefenstette6, Hugh S. Hudson3,7, Stephen M. White8, David M. Smith9, Andrew J. Marsh9, Paul J. Wright4,
Steven E. Boggs3, Finn E. Christensen10,William W. Craig3,11, Charles J. Hailey12, Fiona A. Harrison6, Daniel
Stern13, William W. Zhang14
Draft version January 27, 2017
7
1 ABSTRACT
0
WepresentobservationsoftheoccultedactiveregionAR12222duringthethirdNuSTARsolarcam-
2
paign on 2014 December 11, with concurrent SDO/AIA and FOXSI-2 sounding rocket observations.

n The active region produced a medium size solar flare one day before the observations, at 18UT on
a 2014 December 10, with the post-flare loops still visible at the time of NuSTAR observa∼tions. The
J time evolution of the source emission in the SDO/AIA 335˚A channel reveals the characteristics of

6 an extreme-ultraviolet late phase event, caused by the continuous formation of new post-flare loops
2 that arch higher and higher in the solar corona. The spectral fitting of NuSTAR observations yields
an isothermal source, with temperature 3.8 4.6 MK, emission measure 0.3 1.8 1046 cm−3, and
R] density estimated at 2.5 6.0 108 cm−3. T−he observed AIA fluxes are cons−istent×with the derived
− ×
NuSTAR temperature range, favoring temperature values in the range 4.0 4.3 MK. By examining
S −
the post-flare loops’ cooling times and energy content, we estimate that at least 12 sets of post-flare
.
h loops were formedand subsequently cooledbetween the onset of the flare andNuSTAR observations,
p with their total thermal energy contentan order of magnitude largerthan the energy content at flare
- peak time. This indicates that the standard approach of using only the flare peak time to derive the
o
total thermal energy content of a flare can lead to a large underestimation of its value.
r
t Subject headings: Sun: flares — Sun: particle emission — Sun: X-rays
s
a
[
1. INTRODUCTION sources on the Sun due to its ten-times higher effective

1 area and orders of magnitude reduced backgroundwhen
The Nuclear Spectroscopic Telescope ARray (NuS-
v comparedtostate-of-theartsolarHXRinstrumentssuch
TAR) is a focusing hard-X ray (HXR) telescope operat-
9 as Reuven Ramaty High Energy Solar Spectroscopic Im-
ingintheenergyrangefrom3to79keV(Harrison et al.
5 ager (RHESSI, Lin et al. 2002). However, because it is
2013). While primarily designed to observe far, faint as-
7 optimizedforobservationsofastrophyscialobjects,NuS-
trophysicalsourcessuchasactivegalacticnuclei(AGN),
7 TARexperiencessometechnicalchallengeswhenobserv-
blackholesandsupernovaremnants,itis alsocapableof
0
ing the Sun; these include ghost-rays and low through-
. observing the Sun. With its focusing optics system, it
1 can directly observe HXRs from previously undetected put. Ghost-rays are unfocused, single-bounced photons
0 (in contrast to properly focused photons which reflect
7 twice off the Wolter-I mirrors)coming from sources out-
1University of Applied Sciences and Arts Northwestern
1 sidethefield-of-view(Madsen et al.2015). Thethrough-
Switzerland,Bahnhofstrasse6,5210Windisch,Switzerland
v: 2Institute for Particle Physics, ETH Zu¨rich, 8093 Zu¨rich, putofNuSTAR’sfocalplane detectorelectronics,witha
Switzerland maximum of 400 counts per second per telescope, can
Xi 3Space Sciences Laboratory, University of California, Berke- effectively diminish the hard X-ray sensitivity in the
ley,CA94720-7450, USA
r 4SUPA School of Physics & Astronomy, University of Glas- presence of extremely bright sources (Grefenstette et al.
a gow,GlasgowG128QQ,UK 2016), making detections of fainter spectral components
5SchoolofPhysicsandAstronomy,UniversityofMinnesota- (such as a non-thermal component) difficult.
TwinCities,Minneapolis,MN55455, USA
Despite these challenges, NuSTAR has begun to pro-
6CahillCenterforAstrophysics,1216E.CaliforniaBlvd,Cal-
vide critical new observations of faint X-ray sources on
iforniaInstituteofTechnology, Pasadena, CA91125, USA
7School of Physics and Astronomy, University of Glasgow, the Sun (Hannah et al. 2016) andgiving us new insights
Glasgow G128QQ,UK into the coronal heating problem and particle energiza-
8AirForceResearchLaboratory,Albuquerque,NM,USA
9Physics Department and Santa Cruz Institute for Particle tion in solar flares. In that respect, occulted active re-
Physics,UniversityofCalifornia,SantaCruz,1156HighStreet, gions are priority targets in the planning of NuSTAR
SantaCruz,CA95064,USA observations. Withthe brightestemissionfromthe foot-
10DTUSpace,NationalSpaceInstitute,TechnicalUniversity points and low corona hidden, NuSTAR can search for
ofDenmark,Elektrovej327,DK-2800Lyngby, Denmark
11Lawrence Livermore National Laboratory, Livermore, CA faint coronal signature of heated material and particle
94550, USA acceleration. In order to maximize NuSTAR livetime
12Columbia Astrophysics Laboratory, Columbia University, andminimize ghost-raysduring these observations,they
NewYork,NY10027, USA shouldbecarriedoutduringlow-activityperiods(prefer-
13JetPropulsionLaboratory, CaliforniaInstitute ofTechnol-
ably with no other active sources on disk).
ogy,4800OakGroveDrive,Pasadena, CA91109, USA
14NASAGoddardSpaceFlightCenter,Greenbelt,MD20771, In this paper, we analyze the occulted active region
USA AR12222 which produced a C5.9 GOES (Geostation-
2
x 10−5 M
u
fl

S
E
O 10−6 C
G
193Å
211Å
171Å
107
106
]
−1 335Å 131Å
s 304Å

N
94Å
D
[ 105 FeXVI
x
u 1.1
fl
ux 1.0 FeXVIII
104 m. fl
or 0.9
N Fe XVIII
0.8 NuSTAR 2.5−6 keV
103
18:4018:4418:4818:5218:5619:0019:04
17:00 22:00 03:00 08:00 13:00 18:00
Start Time (10−Dec−14 13:06:40)
Fig.1.—TimeprofilesofGOES,7EUVchannelsofSDO/AIA,Fexvi,FexviiiandNuSTARFPMBfluxesfromtheflaringareaabove
the west limb as marked by the black box in the Fe xviii map in the inset. Vertical dashed lines represent the time range of NuSTAR
observations of the occulted active region AR12222. The inner plot shows the normalized Fe xviii (olive line) and NuSTAR fluxes (blue
dots)duringtheobservations.
Thegreyshadedarearepresentsanassumeduncertaintyof10%intheFexviiiflux.
ary Operational EnvironmentalSatellite)classflare 24 West & Seaton (2015), among others; a theoretical
∼
hours before NuSTAR observations. AR12222 was ob- model of the subsequent magnetic reconnections (and
servedinthe thirdNuSTARsolarcampaignon2014De- itssuccessfuldescriptionoftheflareSOL1973-07-29T13)
cember 11. The active region was also observed by So- is given in Kopp & Poletto (1984). More recently,
lar TErrestrial RElations Observatory (STEREO), At- Liu et al. (2013) proposed that the subsequent loop sys-
mospheric Imaging Assembly on Solar Dynamics Obser- tem(s)isproducedbymagneticreconnectionoftheover-
vatory (SDO/AIA) and the second launch of Focusing lying active region magnetic field lines and the loop ar-
Optics X-ray Solar Imager (FOXSI-2) sounding rocket. cade produced by the flare, adding more complexity to
The goal of this paper is to analyze the time evolution the theoretical description of these events.
of the X-ray and extreme-ultraviolet (EUV) emission of This paper is structured as follows. In Section 2 we
the observed source above the solar limb in the context give an overview of NuSTAR, SDO/AIA, STEREO and
of the flare evolution scenario proposed by Woods et al. FOXSI-2 observations of AR12222. We present the re-
(2011) and Woods (2014). In these papers, the au- sults of NuSTAR spectroscopy in Section 3, along with
thors argue that flares may have four distinct phases the comparisonofNuSTARderivedparameterswith ob-
in their evolution: (1) impulsive phase (best seen in servations in other wavelengths. The discussion of the
HXRs), (2) gradual phase seen in SXR/EUV from the results, as well as possible future studies, is presented in
post-flare loops, (3) coronal dimming, best seen in the Section 4.
171˚A line and (4) an EUV-late phase, best seen as a
second peak in the 335˚A line few (up to 6) hours af- 2. OBSERVATIONS
ter the flare onset. The explanation of the EUV late- The data presented in this paper come from the third
phase emission lies in the formation of subsequent flare set of solar observations with NuSTAR, which were car-
loops, overlying the original flare loops, which result ried out on 2014 December 11. The observations con-
from the reconnection of magnetic fields higher than sisted of observations of the north pole region (quiet
thosethatreconnectedduringtheflare’simpulsivephase. Sun observations) and the solar limb (from 18:39:00 to
Similar observations of “giant post-flare loops” and “gi- 19:04:00UT) that is discussed in this paper.
ant arches” can be found in MacCombie & Rust (1979), The target for the limb pointing and of this study is
Sˇvestka et al. (1982), Sˇvestka (1984), Sˇvestka et al. the active region AR12222,located 35 degrees behind
∼
(1995), F´arn´ık et al. (1996), Parenti et al. (2010) and the south-west solar limb at the time of the NuSTAR
observations. AR12222producedaGOESC5.9flareone
3
FeXVIII: 10-Dec-2014 18UT FeXVIII: 11-Dec-2014 00UT FeXVIII: 11-Dec-2014 14UT
-100 -100 -100
-200 -200 -200
s) -300 s) -300 s) -300
c c c
e e e
s s s
c c c
ar -400 ar -400 ar -400
Y ( Y ( Y (
-500 -500 -500
-600 -600 -600
700 800 900 1000 1100 1200 700 800 900 1000 1100 1200 700 800 900 1000 1100 1200
X (arcsecs) X (arcsecs) X (arcsecs)
NuSTAR A > 2 keV: 18:39-19:04UT NuSTAR B > 2 keV: 18:39-19:04UT FeXVIII: 18:39-19:04 UT
-100 -100 -100
-200 -200 -200
s) -300 s) -300 s) -300
c c c
e e e
s s s
c c c
ar -400 ar -400 ar -400
Y ( Y ( Y (
-500 -500 -500
-600 -600 -600
700 800 900 1000 1100 1200 700 800 900 1000 1100 1200 700 800 900 1000 1100 1200
X (arcsecs) X (arcsecs) X (arcsecs)
Fig. 2.—Upperrow: Fexviiimapsoftheflareonset(left panel),post-flareloops6hoursaftertheflare(central panel),andtheremaining
loops 20 hours after the flare (right panel). Bottom row: 25-minute integrated NuSTAR FPMA (left panel) and FPMB (central panel)
andAIAFexviii(right panel)maps;thelatterincludesthe30%,50%,70%and90%NuSTARcontoursinblue. Dashedlinesdenotearea
affected bytheNuSTARchipgapduringthisobservation. Thewhiteboxistheregionchosenforthespectralanalysis.
day before the NuSTAR observations, at 18UT on 2014 the flare. As previouslynoted(e.g., Stewart et al.1974;
December10. Figure1presentsthetimeevolutionofthe Rust & Hildner 1976; Hudson et al. 1998; Zarro et al.
GOESflux,the7SDO/AIAEUVchannelsandtheAIA- 1999; Howard & Harrison 2004; McIntosh et al. 2007),
derived Fe xvi and Fe xviii fluxes from flare onset until there is a strong correlation between coronal dimming
more than a day later. The NuSTAR observing period andcoronalmassejection(CME)events;indeed,astrong
is indicated with vertical dashed lines. Smaller spikes CME with the velocity of 1000 km s−1 was associated
in the GOES curve between the flare and NuSTAR ob- with this nominally C-clas∼s flare15.
servations represent various fainter flares coming from The olive curve in Figure 1 presents the time evo-
other active regions (AR12233, AR12230, AR12235) on lution of the Fe xviii line flux. An estimate of the
the solardisk. Due to the high occultation,the estimate emission in the Fe xviii line can be constructed from
of the GOES class as given above of the flare SOL2014- the 94˚A line, by subtracting the lower temperature re-
12-10T18 is a severe lower limit of the actual GOES sponsesfromthe 171˚A, 193˚Aand/or211˚Achannels(see
class. The STEREO satellites can generally be used to Del Zanna 2013; Reale et al. 2011; Testa & Reale 2012;
give a prediction of the actual GOES class as they view Warren et al. 2012). In obtaining the Fe xviii flux, we
the Sun from a different angle (Nitta et al. 2013). Even followedtheapproachofDel Zanna(2013),usingthefor-
thoughSTEREO Awasatthe rightlocationatanangle mula
of 175◦ withrespecttotheEarth,itwasnotobserving
du∼ring the main and gradual phases of the flare; there- F(Fe xviii) F(94˚A) F(211˚A)/120 F(171˚A)/450,
≈ − −
fore,wecannotgiveanaccurateGOESclassestimatefor (1)
this flare. whereF(Fe xviii) is the Fe xviiiflux, F(94˚A),F(211˚A)
The time evolution of fluxes in different AIA channels and F(171˚A) are the fluxes in the 94˚A,211˚A and 171˚A
reveals two main characteristics of an EUV late-phase channels,respectively. The Fe xviiiline has a strong re-
event, as described in Woods et al. (2011) and Woods sponse in the temperature range from 3 to 10 MK,
(2014): a second (in this case weaker) peak in the 335˚A with the peak around 6.5 MK. The Fe∼xviii ∼time evo-
line a few hours after the flare, and coronal dimming in
the 171˚A line with the local minimum 5 hours after 15 Data taken from the LASCO CME Catalog:
∼ http://cdaw.gsfc.nasa.gov/CME_list/.
4
lution shows a strong peak due to the flare, with a long andFexviiimapsshowthesamesources,suchasthetop
decay phase lasting past the NuSTAR observations. parts of the coronal loops, and the high emission source
Similar to the Fe xviii line, a lower-temperature Fe above them (MacCombie & Rust 1979).
xvi line can be constructed from the 335˚A and 171˚A
lines (Del Zanna 2013):
F(Fe xvi) F(335˚A) F(171˚A)/70. (2)
≈ −
Similar to Fe xviii, the above formula is just anapprox-
imation of the Fe xvi flux. The Fe xvi line has a tem-
perature response of similar shape to the Fe xviii line,
with its peak at a lower temperature of 2.5 MK. The
time evolutionof the Fe xvi flux is also s∼hownin Figure
1. It is characterized by a strong dip followed by the
initial rise, soon after which a decrease is observed, due
to the fact that the flare becomes weaker. After 8UT
on 2014 December 11, the time evolution of Fe x∼vi flux
is determined by fore- and background emission along
the line-of-sight, making the post-flare loops no longer
observable in this line.
The evolution of 5-minute integrated NuSTAR fluxes
(blue dots) and Fe xviii fluxes (olive line) is given in
the inset of Figure 1. The NuSTAR and Fe xviii time
evolutionsshowsimilarbehaviour,withthe (slow)decay
rate of the two agreeing within the error bars and the
only difference being the steeper decay of NuSTAR flux
towards the end of the observation, which is likely an
instrumentaleffect. TheNuSTARfocalplaneconsistsof
a2 2arrayofCdZnTedetectors,whicharedividedinto
×
quadrants by a chip gap (Harrison et al. 2013). As the
telescopepointingdriftedslowlyduringtheobservations,
the gapcoveredpart of the area used for calculating the Fig.3.— STEREO A 195˚A imageof active regionAR12222 an
flux. Therefore, it is probable that the steeper decay of hour before the NuSTAR observations. The orange line presents
the solar limbas viewed from the Earth, whilethe red lineis the
theNuSTARemissiontowardstheendoftheobservation
line-of-sightfromtheEarththroughtheNuSTARsource.
is not due to solar variability, but rather a consequence
of the telescope drift. This might also have some effect
In Figure 3 we present the STEREO A image of
on the determination of the temperature and emission
active region AR12222 an hour before the NuSTAR
measure of the source, which will be discussed in the
observation. The orange line shows the solar limb
following sections.
as viewed from the Earth, while the red line is a
Due to the slow decay of Fe xviii emission, we were
projection of the line-of-sight from the Earth to the
abletomakeFexviiiimagesevenatthetimeofNuSTAR
NuSTAR source, passing right above AR12222 located
observationsone day after the flare onset (see Figure 2). at [ 730′′, 330′′]intheSTEREO A195˚Aimage. The
TheupperrowpresentstheFexviiimapsoftheflareon- ∼− −
NuSTARsourceis notevidentinthis imageas the 195˚A
set,thepost-flareloops6hoursaftertheflare,andthere-
channel is sensitive only to lower temperatures. From
mainingfeatures20hoursaftertheflare. Leftandcentral
STEREO images, it is possible to calculate the height
panels in the bottom row present 25-minute integrated
of the post-flare loops, defined as the distance between
NuSTAR images above 2 keV from focal plane modules
AR12222 and the mid-point of the line that minimizes
A(FPMA)andB(FPMB).Dashedlinesdenotethearea
thedistancebetweentheEarth-Sunline-of-sightandthe
covered by the gap during the observations that is fur-
radial extension above the active region. We estimate
ther enlarged due to the drift of the telescope. As the
this height to be 300′′. If we assume the height
driftwasdominantly alongthe x-direction(45 arcsecsin of the original loop∼s at the flare onset to be 50′′ (as
total) and negligible in the y-direction, the area affected
there are no STEREO observations of this active region
by the gap is much larger in the x-direction. The region
immediately after the flare, we assume this height as a
of interest for the analysis that will be presented in the
nextsection,withanareaof50′′ 50′′ =2500 arcsec2,is common value for ordinary flares), this yields a radial
markedby the white box. The la×st image in the bottom velocity of 2 km s−1 when averaged over the whole
∼
rightcorneristhe25-minuteintegrated(sametimerange day. This is similar to typical speeds of rising post-flare
as NuSTAR) Fe xviii map of the source together with loops very late in an event (e.g., MacCombie & Rust
the 30, 50, 70 and 90% contours of NuSTAR emission 1979; Gallagher et al. 2002), giving further evidence
in blue. As the uncertainty in NuSTAR absolute point- that the NuSTAR source is indeed associated with the
ing accuracy is relatively large (see Hannah et al. 2016, flare that occurred a day earlier.
Grefenstette et al.2016),theNuSTARimagewasshifted
by 100′′ and25′′ inthexandydirections,respectively,
ino−rdertomatchthe Fe xviiisourcelocation. NuSTAR 3. ANALYSIS OF THE HIGH CORONAL SOURCE
5
1100000000
A: T= 3.8 MK, EM= 1.6×1046 cm-3 A: T= 3.9 MK, EM= 1.3×1046 cm-3
B: T= 3.8 MK, EM= 1.8×1046 cm-3 B: T= 4.1 MK, EM= 0.8×1046 cm-3
11000000
1
-V
e
1 k 110000
-s
s
nt
u 1100
o
C
11
10000
A: T= 4.1 MK, EM= 0.8×1046 cm-3 A: T= 3.9 MK, EM= 1.1×1046 cm-3
B: T= 4.1 MK, EM= 1.0×1046 cm-3 B: T= 4.6 MK, EM= 0.3×1046 cm-3
1000
1
-V
e
1 k 100
-s
s
nt
u 10
o
C
1
2 3 4 5 6 7 2 3 4 5 6 7
Energy [keV] Energy [keV]
Fig.4.—NuSTARcountspectraforFPMA(red)andFPMB(blue)integratedoverthewholeobservationtimerange(18:39−19:04),
together withisothermalfitsfordifferentenergyranges: 2.5−5.2keV(upper left ),3.0−5.2keV(upper right),3.5−5.2keV(lower left)
and 4.0−5.2 keV (lower right). Energy ranges for spectral fitting areshown with grey shaded areas. The best-fit values of temperature
andemissionmeasureforindividualfocalplanemodulescanbefoundonthetopofeachgraph.
3.1. Spectral fitting The temperature gets higher and the emission measure
gets lower as we go to higher energies. The 67% confi-
We fitted the NuSTAR count spectrum inside the re-
dence ranges of temperature and emission measure were
gion of interest from Figure 2 separately for FPMA and
calculated using the standard Monte Carlo procedure in
FPMB, following the approach of Hannah et al. 2016,
usingSolarSoft/OSPEX16.The countswerebinned with OSPEXandaregivenin Table1 togetherwiththe best-
fit values. A point to note is that our region of interest
0.2keVenergyresolution,whiletheintegrationtimewas
is located very close to the gap between the detectors,
25minutes(fullNuSTARobservingtimeoftheactivere-
which leads to fewer counts, especially in later phases of
gion). As the livetime was around 1% during the whole
the integration interval. The reason for this is the slow
observation period, this is roughly equal to 15 seconds
drift of the spacecraft pointing with time, resulting in
of exposure at full livetime. In order to investigate the
coveringa part of the regionof interest by the gap. The
influence of the adopted energy range on the fitted tem-
missing counts could lead to an underestimation of the
perature and emission measure, we fitted CHIANTI 7.1
emissionmeasure,butdonotchangethevalueofthede-
isothermal models (Dere et al. 1997; Landi et al. 2013)
terminedtemperature(asitisdeterminedbytheslopein
to our data for different energy ranges: 2.5–5.2, 3.0–5.2,
the counts spectrum). A single temperature component
3.5–5.2, 4.0–5.2 keV. These fits are presented in Figure
isenoughto fitthe observations,similarto the resultsof
4. The lower limit of 2.5 keV was chosen as the low-
Hannah et al. (2016). We determine the density of the
est energy for which the calibration is still completely
understood and reliable (Grefenstette et al. 2016), while sourceto be (assumingavolume of50 50 50arcsec3)
the upper limit of 5.2 keV was chosen as the highest inthe range2.5 6.0 108cm−3 (rough×ly10× 100times
− × −
energy with a significant number of counts (> 3 counts the density of the quiet Sun corona at this height; see
per bin). Both focal plane modules give consistent re- e.g.,Withbroe1988),suggestingthedensityoflate-phase
sults, withtemperature 3.8 4.6 MK andemissionmea- loopstobesignificantlyhigherthanthatofthequietSun
sure 0.3 1046 cm−3 1.8− 1046 cm−3, depending on corona.
× − ×
the lower limit of the energy range used in the fitting.
16 http://hesperia.gsfc.nasa.gov/ssw/packages/spex/doc/.
6
10.00
Fit 2.5-5.2 keV
Fit 3.0-5.2 keV
Fit 3.5-5.2 keV
Fit 4.0-5.2 keV
Loci curves:
AIA FeXVIII
1.00 NuSTAR 2.4-3.0 keV
]
3 NuSTAR 3.0-3.6 keV
-m
NuSTAR 3.4-4.0 keV
c
NuSTAR 4.0-4.6 keV
46 2.0
0
1 FPMA
M [ 1.5 FPMB
E 0.10
1.0
0.5
0.0
3 4 5 6
0.01
2 4 6 8 10 12 14
Temperature [MK]
Fig.5.—ComparisonofFexviiiandNuSTARlocicurves. Temperaturesandemissionmeasuresfromthefitsindifferentenergyranges
aremarkedbysymbolswithcorrespondingconfidence rangesinblack(FPMA)andgrey(FPMB).Theinsetrepresents themagnification
ofthegivenplotinthetemperaturerange3−6MK,onalinearscale.
FPMA
the following formula
Energyrange[keV] 2.5−5.2 3.0−5.2 3.5−5.2 4.0−5.2
F S
T[MK] 3.77−+00..0044 3.86−+00..0099 4.05−+00..1186 3.94−+00..4434 EM = R(·T), (3)
EM[1046cm−3] 1.60−+00..1142 1.30−+00..2283 0.82−+00..3265 1.11−+30..1782 where EM is the emission measure[cm−3], F is the flux
[DN s−1pix−1], S is the area of the region [cm2] and
FPMB R(T)isthetemperatureresponsefunctionoftheFexviii
Energyrange[keV] 2.5−5.2 3.0−5.2 3.5−5.2 4.0−5.2 line [DNcm5s−1pix−1]. The NuSTAR loci curves are ex-
T[MK] 3.79−+00..0045 4.12−+00..1100 4.06−+00..1166 4.57−+00..6425 rtreaspctoendseinfuanscitmioinla,rdwetaeyrmfrionmedthbeyNfoulSdTinAgRthteemgepneeraratuterde
EM[1046cm−3] 1.75−+00..1152 0.84−+00..1175 0.99−+00..4248 0.30−+00..7270 pNhuoStToAnRspreecstproanfsoermdaifftreirxe.ntTtheemgpoeordatuargerseetmheronutgohf othuer
results is best seen in the inset of Figure 5, where we
TABLE 1 plot the loci curves and the determined EM T pairs
Best-fit valuesoftemperature andemission measureand onlinearscale. TheintersectionoftheFexviii−locicurve
their 67% confidence ranges. with the NuSTAR loci curves in the temperature range
4.0 4.3MKis consistentwiththe EM T pairsshown
− −
in Figure 4, except for the fit including the lowest ener-
3.2. Comparison of NuSTAR to SDO/AIA
gies. A part of these low energy counts might originate
3.2.1. Comparison to Fe xviii fromcoolerpost-flare loops,which will alsobe discussed
Inorderto investigatethe extentof the agreementbe- in more detail in the next sections.
tweenNuSTARandFexviiisources,wecomparethe Fe
3.2.2. Comparison to other AIA channels
xviiilocicurvewiththeNuSTARlocicurvesindifferent
energy channels. For reference, the results of NuSTAR It is also possible to investigate the results of NuS-
spectral fitting from the previous section for both focal TAR fitting to other AIA channels by calculating the
plane modules are presented in Figure 5 with different expected count rates in different AIA channels from the
symbols for different energy ranges, together with the source with the emission measure and temperature as
Fe xviii and NuSTAR loci curves. The Fe xviii loci given by NuSTAR, and compare them to the observed
curve is extracted from the temperature response func- fluxes in AIA maps. The difficulty of this comparison is
tions(Boerner et al.2014)andtheobservedfluxes using thatthefractionofthecoldbackgroundemission(inthe
7
can observe.
10.00
-1pix] 211 193 3.3. Comparison of NuSTAR to FOXSI
-1N s 335 171 TheFOXSI(Krucker et al.2014)sounding rocketalso
D uses direct focusing HXR optics, but is optimized espe-
R [ 1.00 FeXVI
A FeXVIII 94 131 cially for solar purposes. FOXSI has about one fifth of
ST 304 NuSTAR’seffective area with a higher spatialresolution
u
N % (FWHM of 9 arcsec). The main difference for solar
x from 0.10 10500% olobwseervnaetrigoynsthbreetswheoeldn.thWehtiwleoNteuleSsTcAopResdiestetchtesdpihffoetroennst
u 2.5-5.2 keV: T=3.8 MK,
xpected fl 10% 5% 1% 4 . 0 - 5 . 2EE kMMe==V10: ..T83 =⋅⋅ 411.00644 66M ccKmm,--33 dainlolgwyanblttoyocpk∼isc2atlhkpeeVelaa,krtghienenFtuhOmeXbcSeorIuneontftlsropawenccetenruewrmignydaorpowhuonitndotne5sn,tkigeoiVnv--.
E 0.01 The entrance window largely reduces the number of in-
0.1 1.0 10.0 100.0 1000.0 coming photons, keeping the livetime high for the faint,
Observed AIA flux [DN s-1 pix-1]
higher-energy components. For example, a 25 minute
Fig.6.—Comparisonofexpectedandobservedfluxesfor7AIA observation by NuSTAR at 1% livetime and five times
channelsandthederivedFexviandFexviiichannels,forthetwo the effective area is equal to a FOXSI observation of 75
extremepairsoftemperatureandemissionmeasure(valuesgivenin s at full livetime. However, this also means that FOXSI
thelegend)fromfitsinFigure4. Thediagonallinesdenote1,5,10,
isnotsensitivetolowtemperatureplasmasthatarebest
50and100% ratiosoftheexpected AIAfluxesfromtheNuSTAR
source and the observed AIA fluxes. The red lines denote the seen below 4 keV.
(forbidden) areawhere the predicted AIA flux fromthe NuSTAR The FOXSI-2 rocket flew for a 6.5-minute observa-
sourceislargerthanthetotal observedAIAflux. tion interval during the NuSTAR solar pointing dis-
cussed here. FOXSI-2 targeted AR12222 for 35.2 sec-
temperature range below 3 MK) in these channels is onds, though 12 minutes after the NuSTAR observation
unknownandnon-removab∼le. Thisisnotanissueforthe finished. As the NuSTAR/AIA source has a slow time
derived Fe xviii channel, which is not sensitive to this variation,thetimedifferencebetweentheobservationsis
cooler plasma. The expected AIA fluxes are calculated ofminorimportance,atleastfor the order-of-magnitude
by inverting Equation 3. This is a NuSTAR-predicted estimate discussed here. Using the temperature and
AIAfluxcomingfromtheNuSTARsourcealone,without emission measure derived from NuSTAR (T = 3.8 MK
anyadditionalcontributionfromthecoolerplasma. The andEM =1.7 1046 cm−3), theexpectedFOXSIcount
×
comparison between NuSTAR-predicted and observed rate is 1.6 counts for the FOXSI-2’s most sensitive op-
∼
fluxes is presented in Figure 6. The circles are the pre- tics/detector pair D6. This value is computed above 5
dicted fluxes for NuSTAR spectral fitting in the range keV and with the integration time of 35.2 seconds (inte-
2.5 5.2 keV, and the stars for 4.0 5.2 keV. We use gratingduringthe wholeobservationperiod). Intotal,4
the−fitted values of FPMB in both ran−ges,as they repre- counts were observed by D6. This is a reasonable value
sent the two extreme T EM fits. The full and dashed giventhattheestimatednon-solarbackgroundfluxis1.8
lines represent 1, 5, 10, 5−0 and 100%ratios of NuSTAR- counts, while the expected count rate due to ghost-rays
predicted and observed fluxes in different AIA channels. from sources outside of the FOV is unknown. Given the
TheareawherethepredictedAIAfluxfromtheNuSTAR small-numberstatisticsandtheuncertaintyoftheghost-
sourceislargerthanthetotalobservedfluxisshownwith ray background, the observed FOXSI-2 measurement is
the red lines. If the NuSTAR -predicted flux for a given consistent with the values expected for the plasma ob-
AIAchannelisclosetotheobservedflux(e.g.,regionbe- served with NuSTAR, but does not provide any further
tween 50% and 100% lines in the plot), the emission in diagnostics for this event.
thatAIA channelis dominatedbythe same plasmathat
NuSTAR observes. Unsurprisingly, this is best achieved 4. DICUSSION AND CONCLUSIONS
forthe94˚Achanneland,consequently,theFexviiichan- In this paper, we have presented the first observations
nel. ForthefirstT EM fit,theNuSTAR-predictedflux oftheEUVlate-phaseofasolarflareinX-rayswithNuS-
fortheFexviiicha−nnelisgreaterthantheobservedflux. TAR. NuSTARhas providedunique opportunity to per-
This result indicates that a single temperature fit is not formspectroscopyonX-raysfroma coronalsourceafull
enough to fit the observations at the lowest energies, as dayaftertheflareonset. Withknowledgeofthelocation
some of the low-energy counts are produced by a lower of this faint source from NuSTAR, we were also able to
temperature plasma. The ratio for the Fe xviii chan- find it in Fe xviii by eliminating the lower temperature
nel for the fit at higher energies (second T EM fit) response of the AIA 94˚A channel and integrating for 25
−
lies inthe rangebetween50%and100%,while the 335˚A minutes (adding together 125 maps to obtain a higher
channelanditsderivedFexvichannelhaveratiosinthe signal-to-noise ratio). Here, NuSTAR played a crucial
range 5 10 %. These results are in agreementwith the role in providing the information needed for extracting
fact tha−t the Fe xviii source showed the same spatial the very faint signal which was far from evident in the
features as the NuSTAR source, while we were not able 94˚A maps.
to detect the Fe xvi source. Cooler lines at 171˚A,211˚A The fact that the post-flare loops have been observed
and193˚AhaveratiosofNuSTAR-predictedfluxestothe so late in the flare evolution points to continuing energy
observed fluxes at a percent level, which is expected as input in the later phases of the solar flare evolution. To
these lines are sensitive to plasma cooler than NuSTAR quantify this statement, we estimate the cooling times
8
of subsequent post-flare loops and compare them to the tion we use is that new loop systems are only produced
flare duration. We follow the approach of Cargill et al. when the old ones vanish. This assumption is in prin-
(1995), with the following formula for the cooling time ciple not valid as new systems are produced while the
of post-flare loops: old ones persist, but it gives us an approximate lower
limitonthe totalthermalenergycontentinallthe loops
τcool =2.35·10−2·L5/6·ne−1/6·Te−1/6, (4) systems. The sequence is as follows: original post flare
loops vanish after 1 hour, and during this time den-
where τcool [s] is the cooling time (the time needed for sity, temperature a∼nd volume change as well, and a new
post-flareloopstocooldownto 105 K)andL[cm], n
[cm−3] and T [K] areloop lengt∼h, density and temperae- loop system with a different cooling time is produced.
e We calculate that this sequence repeats about 12 times
ture at the start time. The temperature estimate of the
duringthe24hoursbetweentheflareonsetandNuSTAR
original post-flare loops from the GOES observations is
observations, with the total energy content in those 12
10.5 MK, while the emission measure is 5 1048cm−3.
cycles of reconnection and cooling estimated at a factor
×
Even though the above estimates might only be a rough
of 13largerthantheonereleasedduringtheimpulsive
approximation because of the high occultation of the ∼
phase of the flare only.
flare, we are anyway making only an approximate cal-
Previousestimates ofthe additionalenergy input dur-
culation of the cooling time. By assuming the length of
ing the decay phase of solarflareswere derivedusing ra-
theoriginalpost-flareloopstobe 50′′,weestimatethe
diativelossesatspecificwavelengthranges. Woods et al.
densitytobe9 109cm−3. Thisgi∼vesusacoolingtimeof
(2011) calculate the total radiated energy in the EUV
×
1hour,indicating thatthe originalpost-flare loopsare
band during the late phase to be between 0.4 and 3.7
∼
long-goneat the time of NuSTAR observations and that
times the flare energy in the X-rays during the peak.
the additional heating took place during the evolution
Emslie et al.(2012) conclude in their statisticalstudy of
ofthe post-flaresystem. The mostprobableexplanation
38solarflaresthat,onaverage,thetotalenergyradiated
is the previouslymentioned scenarioof subsequent mag-
fromhotSXR-emittingplasmaexceedsthepeakthermal
netic reconnections,resulting inreconnectedloops being
energycontentbyafactorof 3. Itisimportanttonote
produced higher and higher in the corona. ∼
that the above studies used non-overlapping wavelength
The above results are in agreement with original Sky-
ranges,thusmissingthecontributiontototalenergycon-
lab and SMM results, and the recent observations of a
tent from the wavelength range of the other study (and
largepost-flareloopsystembetween2014October14 16
the rest of the wavelength spectrum). Our results for
−
by West & Seaton (2015). They conclude that the giant
a single event are consistent with these statistical stud-
late-phasearchesaresimilarinstructure tothe ordinary
ies, especially as we compare our value with statistical
post-flare loops, and formed by magnetic reconnection.
averagesthat miss significant energy contributions.
TheirreasoningfollowstheworkofForbes & Lin(2000),
Insummary,allresults indicate thatthe impulsive en-
inwhichitispointedoutthatthereconnectionratemay
ergy release is only a fraction of the energy release in
not depend only on the magnetic field (in which case,
the late phase of the flare evolution, at least for events
it would decreasewith height), but possibly on the local
with clearly observable late phase emission. This state-
Alfvenspeed,whichisproportionaltoB/√ρ,whereB is mentcallsforre-examiningtheapproachofusingjustthe
the magnetic field strength and ρ the density. So, if the
peak energy content or the non-thermalemission during
density decreases sufficiently fast, the reconnection rate
theimpulsivephaseoftheflareastheestimateoftheto-
couldremainconstantout to 0.5R⊙ despite the decreas- tal energy content of the flare. In order to assess this in
ing magnetic field strength, and thus produce the giant
moredetail,astatisticalstudyofsimilareventsshouldbe
post-flare loops analyzed by West & Seaton (2015) or in
carried out. However, NuSTAR is not a solar-dedicated
this study.
observatory, and therefore the observations are few and
From NuSTAR and GOES data, it is possible to es-
sporadic, making statistical studies difficult. Addition-
timate the additional energy input needed to form the
ally, it is most likely that faint signals such as presented
subsequent, rising post-flare loops. The total thermal
inthisstudycanonlybeobservedwhentheflare(andthe
energy of the loop system is proportionalto the density,
activeregion)isoccultedoratleastoverthelimb,asthe
temperature and volume (e.g., Hannah et al. 2008):
emission from these kinds of coronalsources on the disk
would likely be masked by the much stronger emission
E =3NkT =3k nVT, (5)
th
· of the active region beneath. Nevertheless, a statistical
while k is the Boltzmann constant. We have obtained search for SDO/AIA Fe xviii sources in above-the-limb
allthe aboveparametersforthe originalflareloops from flares could give us new insights about the influence of
GOESandforthepost-flareloopsadayafterfromNuS- the long-lasting decay phase on flare energetics.
TAR. We estimate that the thermal energy content in
NuSTAR-loops is 5% of the thermal energy content of
the original flare loops, indicating there is still signifi- ThisworkmadeuseofdatafromtheNuSTARmission,
cant energy release even a full day after the flare onset. a project led by the California Institute of Technology,
Next,byassuminglinearityinthechangeofdensity,loop managed by the Jet Propulsion Laboratory, and funded
length and temperature over time (for simplicity), it is by NASA. We thank the NuSTAR Operations,Software
possible to calculate the change in cooling times of all and Calibration teams for support with the execution
the post-flare loops formed in between. Although the and analysis of these observations. This research made
above assumption might not be accurate for all (or any) use of the NuSTAR Data Analysis Software (NuSTAR-
of the parameters, we are only interested in calculating DAS),jointlydevelopedbythe ASI ScienceDataCenter
anorderofmagnitudeestimatehere. Theotherassump- (ASDC, Italy) and the California Institute of Technol-
9
ogy (USA). M.K. and S.K. acknowledge funding from ence Fellowship award NNX13AM41H. I.G.H. is sup-
the Swiss NationalScience Foundation(200021-140308). ported by a Royal Society University Research Fellow-
Funding for this work was also provided under NASA ship. P. J. W. is supported by an EPSRC-Royal Soci-
grants NNX12AJ36G and NNX14AG07G. A.J.M.’s par- ety fellowship engagement grant. FOXSI was funded by
ticipationwassupportedbyNASAEarthandSpaceSci- NASA LCAS grant NNX11AB75G.
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