Measurements of Non-Thermal Line Widths in Solar Active Regions
aa r X i v : . [ a s t r o - ph . S R ] F e b D RAFT VERSION S EPTEMBER
19, 2018
Preprint typeset using L A TEX style emulateapj v. 08/17/12
MEASUREMENTS OF NON-THERMAL LINE WIDTHS IN SOLAR ACTIVE REGIONS D AVID
H. B
ROOKS
AND H ARRY
P. W
ARREN College of Science, George Mason University, 4400 University Drive, Fairfax, VA 22030 USA and Space Science Division, Naval Research Laboratory, Washington, DC 20375 USA
Draft version September 19, 2018
ABSTRACTSpectral line widths are often observed to be larger than can be accounted for by thermal and instrumentalbroadening alone. This excess broadening is a key observational constraint for both nanoflare and wave dis-sipation models of coronal heating. Here we present a survey of non-thermal velocities measured in the hightemperature loops (1–4 MK) often found in the cores of solar active regions. This survey of
Hinode
Extreme Ul-traviolet Imaging Spectrometer (EIS) observations covers 15 non-flaring active regions that span a wide rangeof solar conditions. We find relatively small non-thermal velocities, with a mean value of 17 km s − , and nosignificant trend with temperature or active region magnetic flux. These measurements appear to be inconsis-tent with those expected from reconnection jets in the corona, chromospheric evaporation induced by coronalnanoflares, and Alfv´en wave turbulence models. Furthermore, because the observed non-thermal widths aregenerally small, such measurements are difficult and susceptible to systematic effects. Subject headings:
Sun: corona–Sun: UV radiation–methods: data analysis INTRODUCTIONThe solution to the problem of how the solar corona main-tains its high temperature relative to the cool solar photo-sphere is still unresolved. There have been many explana-tions put forward, and there are several reviews on the topicin the literature from varying perspectives (e.g. Mandrini et al.2000; Walsh & Ireland 2003; Klimchuk 2006; Reale 2010;Parnell & De Moortel 2012; Arregui 2015). Two of the moststudied ideas are based on magnetic reconnection and MHDwaves. In the reconnection scenario, the magnetic field inthe corona is braided by turbulent convection in the photo-sphere, and the energy is released through small-scale eventspopularly known as nanoflares (Parker 1983, 1988). In theMHD wave scenario, the interaction between photosphericconvection and the magnetic field can produce waves thatpropagate upward along the magnetic field and dissipateenergy through a variety of possible mechanisms such asphase mixing (Heyvaerts & Priest 1983), or resonant absorp-tion (Ionson 1978). More recently, chromospheric jets havebeen suggested as a mechanism for supplying mass and en-ergy to the corona directly from the lower atmospheric layers(De Pontieu et al. 2009, 2011).There has been tentative observational evidence for severalof the predicted details of these models. De Pontieu et al.(2011), for instance, show examples of chromosphericspicules producing an apparent response at transition regionand coronal temperatures. Cirtain et al. (2013), show casesof large scale wrapped and twisted coronal structures thatcould be evidence of magnetic braiding. Testa et al. (2013)find evidence of rapid variability at the footpoints of hot loopsthat they interpret as signatures of heating associated with re-connection events occuring in the overlying loops. Very re-cently, Okamoto et al. (2015) observed decreasing amplitudewave-like motions in chromospheric images that they suggestare evidence of resonant absorption. Future observations andcomparisons with numerical models will clarify if these inter-pretations are correct. Present address: Hinode Team, ISAS/JAXA, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan
Despite these recent advances, and we have highlightedonly a few examples, in general it has been difficult to dis-criminate between the theoretical models and reconcile themwith all aspects of the observations. One diagnostic that hasthe potential to be a good discriminator is the measurementof non-thermal broadening in excess of the thermal and in-strumental broadening of EUV spectral lines. As pointedout by Cargill (1996), the nanoflare-heated corona model pre-dicts the existence of many reconnection jets in multiple di-rections along an observed line-of-sight, and this should leadto significant non-thermal velocities on the order of 250 kms − or larger. In contrast, hydrodynamic models of chro-mospheric evaporation in response to coronal nanoflares sug-gest non-thermal velocities of 20–36 km s − , increasing withtemperature, at coronal loop tops in the 1.1–5.6 MK tempera-ture range (Patsourakos & Klimchuk 2006). Models of shockheating driven by Alfv´en waves also predict high velocities, >
100 km s − , see e.g. Antolin et al. (2008), while mod-els of Alfv´en wave turbulence (van Ballegooijen et al. 2011)show non-thermal velocities of 25–35 km s − at the tops ofloops formed near 1.6 MK (Asgari-Targhi et al. 2014). Fur-thermore, models that attempt to explain the first ionizationpotential (FIP) effect based on the forces acting on propagat-ing waves suggest velocities on the order of 50–80 km s − (Laming 2004, 2012).These are significant differences that are, in principal, ob-servationally detectable, so that at least some of the possibleexplanations for the observed non-thermal broadening couldbe ruled out, even if the heating mechanism itself cannot beverified. For example, measurements of non-thermal veloci-ties of 40 km s − or so would tend to support a chromosphericevaporation or Alfv´en wave turbulence explanation, thoughclearly they could not discriminate between them. Con-versely, the nanoflare model may predict high non-thermalvelocities, but these may only be apparent immediately af-ter the energy release, and could be difficult to detect dueto the low emission measure of any hot plasma, a problemthat may be further exacerbated by non-equilibrium condi-tions (Bradshaw & Cargill 2006).The presence of a hot active region (AR) plasma component Brooks & Warrenis in fact a central prediction of impulsive heating models,and significant effort has been expended assessing whethersuch plasma can be observed. See e.g. Reale et al. (2009),Reale et al. (2009), and Schmelz et al. (2009) for initial re-ports of detections, Reale (2014) for a review of subsequentefforts, and O’Dwyer et al. (2011) and Winebarger et al.(2012) for reports of negative results and the difficulties ofobserving the appropriate temperature range. Notwithstand-ing these problems, measurements of non-thermal veloci-ties at high temperatures (and any trend with temperature)are clearly significant for establishing whether the nanoflare-heated corona model is viable.Previous measurements, however, have indicated that theexcess width of EUV and soft X-ray lines is smaller thansuggested by Cargill (1996). Early observations from Sky-lab indicated values of 10–25 km s − for UV coronal linesformed near 1.7 MK such as Fe XI and Fe XII , for exam-ple, see e.g. Cheng et al. (1979). Later measurements of theMg XI resonance line formed around 2.8 MK from the So-lar Maximum Mission were found to be somewhat larger:40–60 km s − (Acton et al. 1981; Saba & Strong 1991), butthese are also significantly smaller than expected from thehigh temperature reconnection jets. Recent studies us-ing Hinode /EIS (EUV Imaging Spectrometer, Culhane et al.2007) and SOHO/SUMER (Solar Ultraviolet Measurementsof Emitted Radiation, Wilhelm et al. 1995) have succeeded inobserving hot plasma emission from the Ca
XVII
XVIII
XVIII
974 ˚A and Fe
XIX
XXI − usinglines formed at 1.6–2.2 MK (Del Zanna 2008; Doschek et al.2008; Brooks & Warren 2011), and these values are some-what larger than observed in the AR core. Warren et al.(2008a) and Brooks & Warren (2009), for example, obtainedvalues of 20–30 km s − in the moss at the footpoints of1.6 MK loops.Despite these studies, there are relatively few accurate mea- TABLE 1A
CTIVE R EGION O BSERVATIONS a FOV a Exp.Time b Study ID1 eis l1 20100619 014433 2 100x240 30 2412 eis l1 20100621 011541 1 120x512 60 4203 eis l1 20100723 143210 1 120x512 60 4204 eis l1 20100929 223226 1 300x400 30 3565 eis l1 20110121 133954 1 120x512 60 4206 eis l1 20110131 102326 1 240x512 60 4377 eis l1 20110212 143019 1 240x512 60 4378 eis l1 20110411 105848 1 240x512 60 4379 eis l1 20110415 001526 1 240x512 60 43710 eis l1 20110419 123027 1 240x512 60 43711 eis l1 20110702 030712 1 120x512 60 42012 eis l1 20110725 090513 1 120x512 60 42013 eis l1 20110821 105251 1 360x512 60 47114 eis l1 20111108 181234 1 240x512 60 43715 eis l1 20111110 100028 1 360x512 60 471 a Units of arcseconds. b Units are seconds. surements of non-thermal velocities in AR core loops. One ofthe few cases is that of Imada et al. (2009), who performeda very interesting study of an AR core at the limb, and re-ported an average value of 13 km s − at 2.8 MK. They stud-ied the AR core as a whole, however, and did not isolate theemission from the high temperature loops, or investigate anytrend with temperature in detail. Since the region was alsoobserved at the limb, the mass motions may be diminisheddue to the line-of-sight. This effect was noted by Hara et al.(2008a), who found a decrease in the non-thermal velocities atthe footpoints of ∼ OBSERVATIONSFor this study of spectral line widths, we use observationsfrom EIS on
Hinode (Kosugi et al. 2007). EIS is a normalincidence spectrograph with multi-layer coatings on the mir-ror and grating. It observes the solar EUV spectrum in twowavelength channels: a short-wavelength (SW) channel cov-ering 170–210 ˚A, and a long-wavelength (LW) channel cov-ering 250–290 ˚A. This part of the spectrum is dominated byemission lines from the Fe
VII –Fe
XVII ionization stages ofIron, with numerous other lines from other elements. Theselines permit a very broad temperature coverage of observedsolar features, and many of the lines are also clean and rela-tively unblended, making them ideal for our purpose. Listsof EIS spectral line identifications have been compiled byYoung et al. (2007) and Brown et al. (2008).EIS builds raster scan spectral images by stepping its slitacross an area of the Sun using a scan mirror. There are fourslits: 1 ′′ , 2 ′′ , 40 ′′ , and 266 ′′ , with the narrowest 1 ′′ slit pro-ine Widths in Solar Active Regions 3 Si VII 275.352Å
Fe XI 180.401Å
Si X 258.375Å
Fe XII 192.394Å
Fe XIII 202.044Å
Fe XIV 264.787Å
Fe XV 284.160Å
S XIII 256.686Å
Fe XVI 262.984Å
Ca XIV 193.874Å I n t en s i t y ( DN ) Fe XI 180.401 Å180.2 180.3 180.4 180.5Wavelength (Å)−4−2024 ∆ I I n t en s i t y ( DN ) Fe XII 192.394 Å192.25 192.30 192.35 192.40 192.45 192.50 192.55Wavelength (Å)−20−1001020 ∆ I I n t en s i t y ( DN ) Fe XIII 202.044 Å201.95 202.00 202.05 202.10 202.15Wavelength (Å)−10−50510 ∆ I I n t en s i t y ( DN ) Fe XIV 264.787 Å264.65 264.70 264.75 264.80 264.85 264.90Wavelength (Å)−15−10−5051015 ∆ I I n t en s i t y ( DN ) Fe XV 284.160 Å284.05 284.10 284.15 284.20 284.25 284.30Wavelength (Å)−30−20−100102030 ∆ I I n t en s i t y ( DN ) S XIII 256.686 Å256.55 256.60 256.65 256.70 256.75 256.80Wavelength (Å)−6−4−20246 ∆ I I n t en s i t y ( DN ) Fe XVI 262.984 Å262.90 262.95 263.00 263.05 263.10Wavelength (Å)−10−50510 ∆ I I n t en s i t y ( DN ) Ca XIV 193.874 Å193.7 193.8 193.9Wavelength (Å)−4−2024 ∆ I F IG . 1.— Example spectral images of AR 1193 observed on 2011, April 19. We measured the line widths in the high temperature core loops for the regionindicated by the blue box. Example fits for several of the spectral lines are shown in the lower panels. Brooks & Warrenviding the best spectral resolution, which is about 22 m ˚A for1 EIS pixel. To obtain the most accurate line width measure-ments, we mostly use the highest spectral resolution slit inthis study (14/15 datasets). The choice of slit, field-of-view(FOV) of the raster scan, spectral line list, exposure time etc.are fixed when the EIS observing study is defined. We usedata from five different EIS studies in this paper. For easeof reference, we list the EIS datasets together with some per-tinent information in Table 1. The datasets are the same asused by Warren et al. (2012) to study the emission measure(EM) distributions in the hot AR core loops, so many detailsof the observations are also available in that paper.EIS data are affected by a number of instrumental issuesthat need addressed prior to analysis. There is a dark cur-rent pedestal that should be removed, and there are warm, hot,and dusty pixels, and others that have been struck by cosmic-rays. We removed these effects using the eis prep routine inSolarSoftware (SSW, Freeland & Handy 1998). The centroidpositions of the spectral lines also show a periodic variationaround the satellite orbit as a result of thermal variations inthe instrument structure. We removed this effect using a neu-ral network model that relates velocity shifts to instrumenttemperatures (Kamio et al. 2010).We show example spectral images for two of the datasetswe analyzed in Figures 1 and 2. We prepared these imagesby fitting single Gaussians to the observed spectra, exceptfor Fe
XII ∼ XII − change in non-thermal velocity. Furthermore, cases where thethermal broadening is sufficient to explain the uncalibratedline width can produce erroneously large values. These find-ings imply that previous measurements of line widths andnon-thermal velocities using calibrated EIS spectra should betreated with caution. Avoiding these additional uncertainties,together with the fact that for our study of line widths no ab-solute calibration is necessary, is the reason we analyze theraw data prior to applying any absolute calibration.Note that the non-thermal velocities shown in Figure 3 arecalculated from δλ = λ c r k B T i m + ξ ) + σ I (1)where δλ is the observed line width, λ is the line centroid, k B is Boltzmann’s constant, T i is the ion temperature, m is themass, ξ is the non-thermal velocity, and σ I is the instrumentalwidth.The instrumental width is a key parameter in the anal-ysis. It was measured in the laboratory prior to launch(Korendyke et al. 2006) and the full width at half maximum(FWHM) was found to be 0.047 ˚A for the SW channel us-ing the Mg III
187 ˚A line and 0.055–0.057 ˚A for the LWchannel using He II
256 ˚A and Ne
III
267 ˚A. Brown et al.(2008) examined solar spectra acquired by
Hinode in orbitpost-launch and found evidence that the SW instrumentalwidth is broader (0.054 ˚A) than measured on the ground inthe Rutherford Appleton Laboratory. Hara et al. (2011) in-vestigated the EIS instrumental width in detail by compari-son of observed Fe
XIV lines with ground based observationsof the Fe
XIV ∼ ∼ ∼ XII eis_slit_width ) in SSW, and we use this programto correct for the Y-variation in this paper by constructing anarray of pixel values using the Y-start position of the observa-tions, which is available in the EIS fits file header. In caseswhere we average over a small area, we also average the Y-correction values.The instrumental profile itself was found to be wellrepresented by a Gaussian function in the laboratory(Korendyke et al. 2006) and we have independently veri-fied this by re-examining the data for Ne
III
267 ˚A. Devi-ations from a Gaussian profile may therefore be importantsignatures of the heating process. For example, numeri-cal simulations of nanoflare heating predict some combina-tion of Doppler shifted or highly distorted line profiles inthe early phase, and subtle asymmetries later in the evolu-tion (Patsourakos & Klimchuk 2006). Although EIS line pro-files have been found to often show important asymmetries(Hara et al. 2008a), that does not seem to be the case for thefits to the profiles for the hot core loops, as can be seen inine Widths in Solar Active Regions 5
Si VII 275.352Å
Fe XI 180.401Å
Si X 258.375Å
Fe XII 192.394Å
Fe XIII 202.044Å
Fe XIV 264.787Å
Fe XV 284.160Å
S XIII 256.686Å
Fe XVI 262.984Å
Ca XIV 193.874Å I n t en s i t y ( DN ) Fe XI 180.401 Å180.2 180.3 180.4 180.5Wavelength (Å)−4−2024 ∆ I I n t en s i t y ( DN ) Fe XII 192.394 Å192.25 192.30 192.35 192.40 192.45 192.50 192.55Wavelength (Å)−20−1001020 ∆ I I n t en s i t y ( DN ) Fe XIII 202.044 Å201.95 202.00 202.05 202.10 202.15Wavelength (Å)−8−6−4−202468 ∆ I I n t en s i t y ( DN ) Fe XIV 264.787 Å264.65 264.70 264.75 264.80 264.85 264.90Wavelength (Å)−15−10−5051015 ∆ I I n t en s i t y ( DN ) Fe XV 284.160 Å284.05 284.10 284.15 284.20 284.25 284.30Wavelength (Å)−10−50510 ∆ I I n t en s i t y ( DN ) S XIII 256.686 Å256.55 256.60 256.65 256.70 256.75 256.80Wavelength (Å)−2−1012 ∆ I I n t en s i t y ( DN ) Fe XVI 262.984 Å262.90 262.95 263.00 263.05 263.10Wavelength (Å)−10−50510 ∆ I I n t en s i t y ( DN ) Ca XIV 193.874 Å193.7 193.8 193.9Wavelength (Å)−1.5−1.0−0.50.00.51.01.5 ∆ I F IG . 2.— Example spectral images of AR 1190 observed on 2011, April 11. We measured the line widths in the high temperature core loops for the regionindicated by the blue box. Example fits for several of the spectral lines are shown in the lower panels. Brooks & Warren C a li b r a t ed G au ss i an W i d t h s ( Å ) r=0.95 C a li b r a t ed N on − T he r m a l V e l o c i t y ( k m / s ) r=0.91 F IG . 3.— A comparison of line widths derived from Gaussian fits to calibrated and uncalibrated line profiles. Gaussian widths are shown on the left and theresulting non-thermal velocities are shown on the right. These calculations are for Fe XII
AIA Fe XVIII [1.12e+04]
AIA Fe XVIII [2.62e+04]
AIA Fe XVIII [6.32e+03]
AIA Fe XVIII [4.23e+03]
AIA Fe XVIII [1.47e+05] AIA Fe XVIII [2.27e+05]
AIA Fe XVIII [6.21e+04]
AIA Fe XVIII [1.65e+05]
AIA Fe XVIII [1.49e+05]
AIA Fe XVIII [2.45e+05] AIA Fe XVIII [1.10e+05]
AIA Fe XVIII [1.25e+05]
AIA Fe XVIII [5.22e+05]
AIA Fe XVIII [5.70e+05]
AIA Fe XVIII [9.35e+05] F IG . 4.— Fe XVIII
Figures 1 and 2. Nevertheless, since we are attempting tomeasure the line widths as accurately as possible, we exper-imented with fits using a Voigt function with a fixed damp- ing factor based on a free-fit Gaussian function combinedwith a Lorentzian constructed from the measured instrumentalwidth. These fits were quite close to a Gaussian, but showedine Widths in Solar Active Regions 7 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20100619_014433m=−5.1 ξ=13.5 km s −1 σ=5.3 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20100621_011541m=−26.5 ξ=15.1 km s −1 σ=5.7 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20100723_143210m=−0.3 ξ=19.3 km s −1 σ=4.2 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20100929_223226m=30.5 ξ=14.7 km s −1 σ=6.0 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110121_133954m=−18.7 ξ=21.6 km s −1 σ=6.7 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110131_102326m=−13.1 ξ=17.8 km s −1 σ=6.4 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110212_143019m=1.8 ξ=19.0 km s −1 σ=4.8 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110411_105848m=4.7 ξ=20.3 km s −1 σ=6.9 km s −1 F IG . 5.— Plots of non-thermal velocity as a function of temperature for 8 of the active region cores. The datasets, gradient of the overlaid linear fit (m), meannon-thermal velocity ( ξ ), and standard deviation ( σ ) are indicated in the legend. The blue dots are the non-thermal velocities for each spectral line with an entryin Table 2 for the corresponding dataset (cross-referenced in the Table and plot legend). The red dot is the non-thermal velocity calculated using the method ofImada et al. (2009) (see text). Data from all lines are included here. greater dispersion, indicating that we would gain no advan-tage from moving to a more complex fitting model. Further-more, we closely examined the details of the Gaussian fits inFigures 1 and 2, and we found that the total residual intensitywithin ±
100 km s − of the line centroids was always less than5% of the total intensity within the same wavelength range,indicating that the deviation from a Gaussian is small. Thisdeviation also appears to decrease with temperature, making a Gaussian function even more appropriate for the highest tem-perature lines which are of the most interest for this study. Forall of these reasons, and also for ease of comparison with theliterature results, we use only a simple Gaussian function forthe fits in this paper. Note that we also use relatively narrowspectral windows for our fits. This is to avoid interferencefrom background in the wings of the profiles (see the discus-sion related to Ca XIV N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110415_001526m=7.4 ξ=16.6 km s −1 σ=4.8 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110415_001526m=1.3 ξ=19.8 km s −1 σ=5.6 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110419_123027m=−13.7 ξ=16.2 km s −1 σ=6.7 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110702_030712m=−9.3 ξ=16.9 km s −1 σ=6.1 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110725_090513m=−21.5 ξ=16.0 km s −1 σ=5.7 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20110821_105251m=−17.2 ξ=18.8 km s −1 σ=6.0 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20111108_181234m=−37.6 ξ=19.2 km s −1 σ=8.7 km s −1 N on − T he r m a l V e l o c i t y ( k m s − ) eis_l1_20111110_100028m=−6.8 ξ=17.6 km s −1 σ=5.1 km s −1 F IG . 6.— Plots of non-thermal velocity as a function of temperature for 8 of the active region cores. The datasets, gradient of the overlaid linear fit (m), meannon-thermal velocity ( ξ ), and standard deviation ( σ ) are indicated in the legend. The blue dots are the non-thermal velocities for each spectral line with an entryin Table 3 for the corresponding dataset (cross-referenced in the Table and plot legend). The red dot is the non-thermal velocity calculated using the method ofImada et al. (2009) (see text). Data from all lines are included here. Ideally we would use only clean, unblended lines to obtainthe best line width measurements, but since we are interestedin any trend as a function of temperature, we have to compro-mise in some cases. Furthermore, most EIS datasets contain alimited number of spectral lines in order to conserve teleme-try, so in some cases we have had to choose additional linesthat we otherwise would not use. The lines we selected aregiven in Tables 2 and 3, and some more detailed comments on the reasons for selection are appropriate here.First, Fe X XI XII
XIII
XIV
XVI
XIV X X andine Widths in Solar Active Regions 9 e /K)020406080 N on − T he r m a l V e l o c i t y ( k m s − ) m=−5.2 ξ=17.6 km s −1 σ=5.3 km s −1 F IG . 7.— Non-thermal velocities as a function of line formation temper-ature for all 16 of the active region cores. Only lines with emission that iscorrelated with the emission of Ca XIV i /K)020406080 N on − T he r m a l V e l o c i t y ( k m s − ) ξ=17.2 km s −1 σ=4.5 km s −1 F IG . 8.— Non-thermal velocities calculated using the method ofImada et al. (2009) for all 16 of the active region cores. They are plottedas a function of the calculated ion temperature. Unlike Figures 5, 6, and 7,the trend is not a function of temperature within an AR core. Rather it is atrend between different AR cores. To avoid confusion, we have not drawn alinear fit to these data. Fe XII widths. Second, since not all of our datasets includethe Fe
XIV
XIV XV XIV andFe
XVI , which is otherwise quite large. We also include S
XIII
XVI
XIV
VII XV IX XIII
XVI ξ = m W − m W m − m ) (2)and T ion = W − W k B log 2 m m m − m (3)where W = δλ − σ I , and and indicate the ion species.Imada et al. (2009) used S XIII
XVI
XVIII
XVIII
XII − with meanvalues in the range 13.5–21.6 km s − with a standard devia-tion of 4.2–8.7 km s − . Linear fits to the non-zero measure-ments are overlaid to draw the eye to any trend in the data,but taking into consideration the scatter in the measurements,there is no statistically significant trend.We present the complete results in the figures and tablesso that they are on record, but it is not necessarily the casethat the emission at all temperatures comes from the hot coreloops. If that were the case we would expect these loops tohave broad EMs whereas Warren et al. (2012) found stronglypeaked EM distributions with a sharp fall below and abovethe peak temperature in most cases. In some of the weakerARs a shallower temperature distribution was observed, andthis highlights the need to adopt some method of quantita-tively determining if the emission comes from the hot coreloops or not. In our previous EM studies of warm coronalloops (Warren et al. 2008b; Brooks et al. 2012, 2013) we haveadopted the criterion that the cross-field intensity profile must0 Brooks & Warren TABLE 2L
INE
FWHM
S AND N ON -T HERMAL V ELOCITIES
Active Region Observation DateLine ID 20100619 20100621 20100723 20100929 20110121 20110131 20110212 20110411Fe X 184.536 0.069 [0.00] 0.061 [0.00] 0.062 [0.00] 0.062 [0.00] 0.069 [30.7] 0.062 [0.00] 0.065 [20.7] 0.063 [11.7]Fe XI 180.401 – 0.068 [26.0] 0.067 [23.7] – 0.071 [33.4] 0.070 [31.5] 0.066 [21.7] 0.072 [35.5]Fe XII 192.394 0.073 [13.3] 0.066 [13.4] 0.067 [17.8] 0.066 [14.5] 0.067 [20.2] 0.065 [12.4] 0.066 [17.9] 0.066 [16.8]Fe XII 195.119 0.071 [0.00] 0.066 [15.3] 0.066 [14.9] 0.065 [7.51] 0.065 [14.6] 0.065 [12.3] 0.064 [9.13] 0.066 [14.8]Fe XIII 202.044 0.073 [8.10] 0.066 [11.3] 0.067 [13.5] 0.066 [9.03] 0.066 [13.8] 0.066 [10.9] 0.065 [11.4] 0.066 [12.9]Fe XIV 264.787 – 0.073 [15.0] 0.075 [18.3] – 0.075 [20.7] 0.074 [17.4] 0.077 [23.5] 0.075 [19.4]Fe XIV 274.203 0.081 [16.8] – – – – – – –Fe XV 284.160 0.087 [23.4] 0.081 [23.5] 0.084 [27.8] 0.083 [25.8] 0.081 [25.1] 0.081 [24.2] 0.080 [23.9] 0.084 [27.1]Fe XVI 262.984 0.081 [9.70] 0.074 [8.68] 0.077 [17.7] 0.076 [14.7] 0.077 [19.4] 0.077 [16.3] 0.077 [19.1] 0.078 [20.3]Si X 258.375 – 0.076 [15.7] 0.079 [21.6] – 0.067 [0.00] 0.077 [17.8] 0.077 [20.7] 0.078 [21.5]S XIII 256.686 0.087 [9.86] 0.081 [9.13] 0.084 [19.0] 0.083 [17.0] 0.086 [23.8] 0.082 [13.2] 0.083 [17.9] 0.083 [18.1]Ca XIV 193.874 – 0.066 [0.00] 0.072 [0.00] 0.069 [0.00] 0.069 [0.00] 0.072 [0.00] 0.065 [0.00] 0.070 [0.00] ξ * The FWHMs are in units of ˚A and the non-thermal velocities are in km s − . ξ is the non-thermal velocity calculated using the Imada et al. (2009) method. TABLE 3L
INE
FWHM
S AND N ON -T HERMAL V ELOCITIES
Active Region Observation DateLine ID 20110415 20110415 20110419 20110702 20110725 20110821 20111108 20111110Fe X 184.536 0.062 [0.00] 0.064 [15.3] 0.059 [0.00] 0.063 [11.9] 0.063 [0.00] 0.061 [0.00] 0.071 [26.9] 0.069 [23.8]Fe XI 180.401 0.067 [22.6] 0.069 [29.2] 0.069 [28.1] 0.069 [29.1] 0.068 [24.3] 0.069 [29.9] 0.075 [35.0] 0.068 [20.1]Fe XII 192.394 0.066 [15.0] 0.067 [19.2] 0.065 [12.0] 0.065 [15.1] 0.067 [15.4] 0.067 [20.5] 0.070 [19.7] 0.069 [17.4]Fe XII 195.119 0.066 [11.3] 0.066 [16.7] 0.065 [9.67] 0.065 [13.2] 0.066 [10.6] 0.065 [12.8] 0.066 [0.00] 0.067 [11.1]Fe XIII 202.044 0.067 [11.6] 0.066 [10.5] 0.066 [7.11] 0.065 [10.0] 0.067 [9.88] 0.066 [14.0] 0.069 [13.8] 0.070 [18.2]Fe XIV 264.787 0.074 [16.8] 0.073 [16.2] 0.074 [16.7] 0.074 [17.2] 0.075 [16.7] 0.074 [18.7] 0.073 [7.80] 0.075 [14.3]Fe XV 284.160 0.084 [26.9] 0.084 [27.7] 0.082 [24.2] 0.081 [24.7] 0.082 [24.3] 0.084 [27.5] 0.086 [26.8] 0.087 [28.7]Fe XVI 262.984 0.076 [15.1] 0.078 [19.8] 0.076 [14.1] 0.075 [12.8] 0.076 [11.5] 0.075 [13.9] 0.078 [13.4] 0.078 [14.0]Si X 258.375 0.076 [14.2] 0.078 [20.6] 0.077 [18.7] 0.079 [22.7] 0.079 [20.3] 0.078 [20.6] 0.070 [0.00] 0.078 [15.3]S XIII 256.686 0.084 [17.4] 0.083 [17.4] 0.081 [11.0] 0.081 [12.6] 0.081 [9.50] 0.083 [16.8] 0.085 [15.8] 0.085 [16.6]Ca XIV 193.874 0.070 [0.00] 0.070 [0.00] 0.069 [0.00] 0.067 [0.00] 0.064 [0.00] 0.069 [0.00] 0.071 [0.00] 0.072 [0.00] ξ * The FWHMs are in units of ˚A and the non-thermal velocities are in km s − . ξ is the non-thermal velocity calculated using the Imada et al. (2009) method. be highly correlated with that of the spectral line with whichthey were identified (usually Fe XII r > . )with that of the highest temperature line (Ca XIV − with a standard deviation of 5.3 kms − , and as with the individual plots (Figures 5–6) the twomethods of non-thermal velocity calculation appear to givefairly consistent results.Note that the highest temperature Ca XIV
XVI XV ∼ − for a limb AR, which would be fairlyconsistent with our other results. Something is therefore miss-ing in our understanding of the EIS Ca XIV
XIV
XII
XIV
XII ∼
40% within 1.5 ˚A, however, so we consider this expla-nation unlikely.Another possibility is that Ca
XIV
XIV
XIV − . We have also inde-pendently verified that we can measure non-zero non-thermalvelocities in the Ca XIV
XIII
XVI
XIV − with a standarddeviation of 4.5 km s − , which is consistent with the previousresults shown. The ion temperatures fall in the range 2–3 MK,which are slightly lower than the temperature of the peak ofthe EM calculated by Warren et al. (2012), but not low enoughto solve the Ca XIV
XVIII intensity, andthe gradient of the EM slope below and above the peak. Wehave verified that there is no correlation between any of theseparameters and our measured non-thermal velocities.Finally, we also investigated any relationship between thenon-thermal velocities measured in Fe
XVI
XVIII SUMMARY AND DISCUSSIONWe have carried out a survey of non-thermal line widthsin the high temperature (1.1–3.6 MK) loops in the cores of15 non-flaring ARs spanning a wide range of solar condi-tions. We compute the non-thermal velocities considering theinstrumental and thermal broadening of the spectral lines inthe usual way, and we also utilize the method outlined byImada et al. (2009). The results from the two methods arebroadly in agreement, and we find non-thermal velocities of ∼
17 km s − on average. We also find no significant trendwith temperature, or with any other property of the ARs suchas total magnetic flux, or the slope of the loop EM distribu-tions. We do, however, detect a tendency for AR loops withthe highest ion temperatures to have smaller non-thermal ve-locities.We note that stellar observers have concluded that non-thermal velocities below ∼
20 km s − indicate that the spec-tral lines are basically thermally broadened (Linsky et al. 1998). While that is not strictly the case here, the modestvalues we find, and the lack of a temperature trend, are a chal-lenge for current coronal heating models to explain. Theseare two of the key measurements that in combination canbe used not just for discriminating between different coro-nal heating models, but also for distinguishing between thephysical processes within the same model. For example, inthe nanoflare model, reconnection jets are expected to existwhile the plasma is still too hot to have cooled sufficientlyfor emission to appear at lower temperatures. So a compar-ison with the non-thermal velocity dependence on tempera-ture is not appropriate. Conversely, emission at lower tem-peratures is dominated by the later phase after the nanoflarehas ended and such a comparison becomes possible. We findthat our measured non-thermal velocities are much smallerthan predicted from either the high temperature reconnec-tion jets in the nanoflare-heated corona model, or shock heat-ing associated with Alfv´en waves, both of which suggest ve-locities on the order of hundreds of km s − (Cargill 1996;Antolin et al. 2008). Models of chromospheric evaporationin response to coronal nanoflares are closer to the observa-tions around 1 MK, but predict that non-thermal velocitiesshould increase with temperature. This is because the emis-sion at cooler temperatures is low while chromospheric evap-oration is occurring and is dominated by the later slow drain-ing phase, whereas the emission at higher temperatures oc-curs earlier in the plasma evolution and is produced not justby draining but also by evaporation. This trend, however,is not observed, and leads to a discrepancy of a factor of 2around 4 MK (Patsourakos & Klimchuk 2006). Some mod-els of Alfv´en wave turbulence also produce values that arecloser to the observations around 1.6 MK, and show only lim-ited variations with temperature at the loop apex, but theyshow a large spread of predictions, and require the impositionof a random flow component parallel to the magnetic field(Asgari-Targhi et al. 2014).Of course, further modeling with different physical condi-tions may alter the predicted characteristics of the spectra. Forexample, non-equilibrium ionization will alter the line inten-sities, and this effect was recently demonstrated to be signif-icant in the case of flare-like reconnection jets (Imada et al.2011). A change in the line intensity implies a potential alter-ation of the line width. It seems more intuitive to think that amore violent plasma will produce more dynamic spectral sig-natures, but it is possible that this is not the case, and it shouldbe checked with numerical simulations. Temperature trendscould also be affected.For the nanoflare model it is possible that high temperaturereconnection jets exist, but we are unable to observe them inAR core loops because the EM is too low (as discussed ear-lier). Non-equilibrium ionization could contribute to surpress-ing the emission too (Bradshaw & Cargill 2006). In this pic-ture, the non-thermal broadening of the spectral lines wouldappear as it does in real flares, with the hot AR core loopscorresponding to post-flare loops observed in their coolingphase. In fact, EIS observations of flares do sometimes showsubstantial line broadening at high temperatures. Hara et al.(2008b) observed a long-duration event on the limb, and mea-sured significant non-thermal velocities of 125 km s − at thetop of cusp-shaped flare loops in the Ca XVII − ), which is consistent with the velocities diminish-ing as flare loops cool. Hara et al. (2008b) actually made themeasurements in post-flare loops on the limb.These results would appear to fit the idea that the heat-ing of AR core loops is truly flare-like, but we only observethe non-thermal broadening that remains well after the en-ergy release process is complete. In this sense, measurementsof non-thermal broadening are not a good diagnostic of theheating phase. In fact there have also been studies showingtentative signals of cooling plasma in the hot cores of ARs(Viall & Klimchuk 2012).The picture for flares, however, is incomplete.Doschek et al. (2014), for example, only measured val-ues of 20–60 km s − in Fe XXIV in their sample of M- andX-class flares. Furthermore, there is a body of evidence that suggests that the hot loops in the cores of ARs are notcooling, but instead are maintained at high temperaturesby continual high frequency heating (Antiochos et al. 2003;Brooks & Warren 2009; Warren et al. 2010).This work cannot draw a firm conclusion on the heatingprocess, but we present a systematic observational study ofnon-thermal broadening in high temperature core loops thatprovides an important observational constraint for coronalheating models.The authors would like to thank Peter Cargill for suggestingthis project. This work was funded by the NASA
Hinode pro-gram.
Hinode is a Japanese mission developed and launchedby ISAS/JAXA, with NAOJ as domestic partner and NASAand STFC (UK) as international partners. It is operated bythese agencies in co-operation with ESA and NSC (Norway).APPENDIXBACKGROUND INFLUENCE ON THE CA
XIV
XIV X VIII
XVI XI XIV
XIV
XIV
XIV
XIV ∼ XIV ∼ XIV X VIII
XIV ∼
15, but we know from Figure 3 in the main paper that line width changes of that order can result in significantchanges in computed non-thermal velocities. So we have overlaid red dots on the figure at the locations of the actual measuredprofile peak intensity to average background ratio for the 16 AR core loops in our study, to determine how much each of ouractual measurements would be affected. From the Figure it appears that our line width measurements could change by 9-25%,which is significant.The lower right panel of Figure 10 shows arrows indicating the change in computed non-thermal velocity for the sample ofCa
XIV
XIV − with an average value of 25 km s − . This is broadly in agreement with the results forthe other lines within the uncertainties. As noted in the main text, we have also verified that we can measure non-zero values forCa XIV
Log ( I n t en s i t y / DN ) F IG . 9.— Sample spectrum close to Ca XIV
Sample Spectra and Fits from Simulations × × × I n t en s i t y ( DN )
300 250 200 150 100 50 0Peak Intensity/Average Background0.0200.0250.0300.0350.040 G au ss i an W i d t h ( Å )