A first spectroscopic measurement of the magnetic field strength for an active region of the solar corona
Ran Si, Tomas Brage, Wenxian Li, Jon Grumer, Meichun Li, Roger Hutton
DDraft version August 18, 2020
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A FIRST SPECTROSCOPIC MEASUREMENT OF THE MAGNETIC FIELD STRENGTH FORAN ACTIVE REGION OF THE SOLAR CORONA
Ran Si,
1, 2
Tomas Brage, Wenxian Li,
1, 3
Jon Grumer, Meichun Li,
5, 6 and Roger Hutton Division of Mathematical Physics, Department of Physics, Lund University, 221 00 Lund, Sweden Spectroscopy, Quantum Chemistry and Atmospheric Remote Sensing (SQUARES), CP160/09, Universit´e libre de Bruxelles, Av. F.D.Roosevelt 50, 1050 Brussels, Belgium Department of Materials Science and Applied Mathematics, Malm¨o University, SE-20506 Malm¨o, Sweden Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden Shanghai EBIT Laboratory, Key Laboratory of Nuclear Physics and Ion-beam Application, Institute of Modern Physics, Department ofNuclear Science and Technology, Fudan University, 200433 Shanghai, China School of Electronic Information and Electrical Engineering, Huizhou University, 516007 Huizhou, China
ABSTRACTFor all involved in astronomy, the importance of monitoring and determining astrophysical magneticfield strengths is clear. It is also a well-known fact that the corona magnetic fields play an importantpart in the origin of solar flares and the variations of space weather. However, after many years of solarcorona studies, there is still no direct and continuous way to measure and monitor the solar magneticfield strength. We will here present a scheme which allows such a measurement, based on a carefulstudy of an exotic class of atomic transitions known as magnetic induced transitions in Fe . In thiscontribution we present a first application of this methodology and determine a value of the coronalfield strength using the spectroscopic data from HINODE. INTRODUCTIONMagnetic field holds a central position within solar research, continuous or on-demand measurements of the mag-netic fields in the solar corona remain one of the major challenges in solar physics (Casini et al. 2017). It is ofimportance to the prediction of solar events such as flares or coronal mass ejections, and ultimately for space-weatherforecasting to avert damage to navigation and communication satellites, interference with airplane navigation systemsand disruptions in power grids which could cause large-scale black-outs (Schrijver et al. 2015). Due to the potentialthreat to society and human well-being from variations in the space weather, it is important to develop methods tocontinuously monitor the magnetic fields of the corona and measure their strengths. The very recent inaugurationof NSFs DKIST (Tritschler et al. 2016) and the launchings of the NASA mission Parker Solar Probe (PSP, launchedin August 2018) and the ESA/NASA mission Solar Orbiter (launch in February 2020) observatories are forming anunprecedented solar corona and inner heliospheric campaign targeted at understanding how stars create and controltheir magnetic environments (Martinez Pillet et al. 2020). Unfortunately, a candidate for such a measurement haseluded the solar physics community. This may be the largest single factor blocking progress in coronal physics andis hindering the attempts to answer questions related to coronal heating, the triggering of flares and coronal massejections, as well as the acceleration of the fast and slow solar wind (Solanki et al. 2006).To address this, we have over the past few years been investigating a spectroscopic method based on quantum-interference effects in the Fe ion (Li et al. 2015, 2016; Judge et al. 2016; Si et al. 2020). This particular interferenceis caused by magnetic fields external to the ion, and hence this idea has the potential to act as a probe of the coronalfield strengths. In this contribution we present a first application of this methodology and determine the values of thecoronal field strengths using pre-existing spectroscopic data from Extreme-Ultraviolet Imaging Spectrometer (EIS) onthe Hinode satellite (Culhane et al. 2007; Brown et al. 2008). The measurement is even fast enough, relative to thelifetime of solar flares, that we could track the development of the field as the flare develops. Corresponding author: Tomas [email protected] author: Roger [email protected] a r X i v : . [ phy s i c s . a t o m - ph ] A ug Observing a single spectral line from an element in a certain charge state provides little information about theenvironment in which it was emitted, while a group of lines can give us a much more detailed picture. Just to givean example on how two lines can be used, their intensity ratio - especially if close-by in wavelength and from a singleatomic charge state - often acts as a probe of the local electron density and temperature in the plasma (Feldman et al.1978). To determine local plasma properties, the strategy is therefore reduced to finding a pair of lines of similarwavelength, where one originates from an upper level with a radiative decay rate of the same order of magnitude asthe electron collisional de-excitation rate. The other line, which we will refer to as the normalization line, should havea radiative decay rate that is signifcantly faster and therefore its decay rate is insensitive to the collisional rates.The same principle, where the intensity of one spectral line is sensitive and one insensitive to a certain environmentalvariable, can be used to measure other plasma properties. In this letter we will discuss the strength of the magneticfield local to the observed ions and how it can induce new lines, so called magnetic-field induced transitions (MIT’s).It has been illustrated that the intensity of these lines can show a strong, to first order quadratic dependence on theexternal field strength (Grumer et al. 2014). Since the magnetic fields inside the ions are enormous (in the ions ofinterest here on the order of hundreds or even thousands of Tesla), it requires, in the general case, strong externalfields to induce these lines from perturbations of the atomic structure. As an example, in Ne-like ions and for fieldstrengths of a few Tesla, MIT’s have been observed using an Electron Beam Ion Trap (Beiersdorfer et al. 2003, 2016).Such cases are not of particular interest in solar physics, since the strongest fields we can observe are in sunspot, andthey are always weaker than 1 T.The rate, and therefore the intensity, of an MIT of electric dipole (E1) type is to first order given by A MIT ∝ A E1 B (∆ E ) (1)where B is the strength of the external magnetic field, ∆ E is the energy separation between a metastable level and aclose-by upper level of a fast E1 transition, in the following referred to as the feeding level, while A E1 is the decay rateof the feeding level. The metastable and feeding levels are mixed in the presence of an external magnetic field, whichcauses them to share their properties. This leads to the emergence of a new radiative transition from the metastablelevel, the MIT. Therefore, if one can find a metastable level which is close to a short-lived one in an abundant atomiccharge state, one can expect that MIT’s could be observed in the presence of a magnetic field. Of particular interestare those cases where this energy separation is small enough to cause a pseudo-degeneracy, which leads to a dramaticincrease in the MIT rate of Eq. 1 and thus also in the sensitivity of the rate to the magnetic field. Such degeneraciesare however not necessarily predicted by the symmetries and the gross structure model of the ion, but could insteadoccur by chance as a result of a rather complex atomic structure.A search for an atomic system involving a suitable pseduo-degeneracy was initiated a few years ago (Li et al. 2015,2016; Judge et al. 2016; Si et al. 2020), motivated by its potential as a magnetic-field probe. This led to the discoveryof Fe where the excited levels 3 p d D / and D / fulfill the requirements of being very close in energy and havingsignificantly different lifetimes. Fortunately, for astrophysical applications, this pseudo-degeneracy exists in an iron-ionwith a large abundance in many celestial objects, amongst them the Sun. It was found that this system could giverise to a considerable MIT even for field strengths of the same order of magnitude as one might expect in the solarcorona, which presently are inaccessible from direct measurements. This motivated further studies of the Fe systemand investigations of its potential as a probe of coronal magnetic fields. However, the pseudo-degeneracy of D / , / makes the two lines to the ground state a challenge to resolve since the transitions are in the VUV-region whereas theenergy difference is only around 3.6 cm − , to move to an actual determination of the coronal field this method had tobe refined and supported by complex atomic and solar models. In this report we can finally, for the first time, presenta direct determination of these field strengths. MODELLING AND ANALYSISFor the spectral modelling we use the
ChiantiPy spectral synthesis code, which is tailored for interpretation ofspectra from high-temperature, optically-thin astrophysical sources, together with electron collision data from theChianti database (Dere, K. P. et al. 1997; Landi et al. 2013) and radiative transition data from Wang et al. (2020).A partial energy level diagram of Fe is shown in Fig. 1, illustrating the levels and transitions of interest in thiswork. The synthetic Gaussian fitted spectra recorded by EIS on Hinode satellite (Culhane et al. 2007; Brown et al.2008) nearby the present interested lines is shown in Fig. 2, demonstrates the lines in Fig. 1 are well resolved by EIS. M2 MIT E1 E1 E1257.262 Å 175.266 Å 174.534 Å
5 2 P o D e2 D e Figure 1.
Schematic energy level diagram and decay channels for the levels in Fe that are relevant to the method discussedin this work (see text). Wavelengths are given in ˚A. The main feature for this project is a blended group of three lines marked as having the wavelength of 257.262 ˚A(denoted by E1, M2 and MIT in Fig. 1). These are from two different upper levels, one being the 3 s p d D / decaying to the ground level 3 s p P o3 / through a so-called E1 spin-induced transition. This level represents thefeeding level in our model. The other upper level is the 3 s p d D / level, with a decay dominated by a forbiddenM2 decay, in the absence of external magnetic fields, with a low transition rate. Finally, due to the very near energydegeneracy (∆ E ≈
0) of this level with the D / level, an external magnetic field induces a mixing of these two levelscausing a magnetic-field induced E1 transition to the P o3 / ground level. For the important ∆ E parameter introducedin Eq. 1 we use value of 3 . − from the most accurate determination to date (Judge et al. 2016). The two transitionrates required to model the MIT spectral line are (Wang et al. 2020), A E1 ( D / → P o3 / ) = 6 . × s − , (2) A M2 ( D / → P o3 / ) = 5 . × s − . (3)As pointed out above, in the presence of a magnetic field, the metastable and feeding levels will interact, which isrepresented by the mixed state | “7 / (cid:105) = c | / (cid:105) + c | / (cid:105) (4)where J = 7 / / c and c are obtained by determining and diagonalizing the interaction matrix fordifferent magnetic fields, using the Grasp atomic structure suite of programs (Fischer et al. 2019, 2016; J¨onsson et al.2013) together with the
Hfszeeman add-on module (Andersson & J¨onsson 2008; Li et al. 2020). The ( B/ ∆ E ) pro-portionality of Eq. 1 is due to the c mixing coefficient, since an estimated value for the rate in first-order representationcan be written as, A MIT ( D / → P o / ) = | c | A E1 ( D / → P o / ) . (5)By adding this rate for a number of magnetic field strengths to the M2 rate, we can predict the intensity ratio for thecombined transition from the D / , / levels, to the normalization lines and compare it to the observed ratio fromthe HINODE data (Brown et al. 2008).The decay of the metastable D / level is dominated by slow M2 and MIT radiative channels resulting in a lifetimeof the order of 10 − s, implying that the blended spectral feature could be sensitive to the electron densities found in thecorona. In order to evaluate these collisional effects, the proposed method thus also requires simultaneous determinationof the local electron density. From the ChiantiPy line intensity modelling at the wavelength range 165 ˚A −
290 ˚A andelectron density range 10 − cm − , we found that the 174.534 ˚A line (3 s p d D / − s p P o3 / as shown inFig. 1) is the strongest at all densities, while the relative intensity of the 175.266 ˚A line (3 s p d D / − s p P o1 / ) Gaussion Area (DN)
F e V I I1 7 6 . 9 7 7 (cid:1)
F e X1 7 5 . 2 6 6 (cid:1)
F e X1 7 4 . 5 3 4 (cid:1) w a v e l e n g t h ( (cid:1) ) ( a ) H e I I2 5 6 . 3 3 2 (cid:1) w a v e l e n g t h ( (cid:1) ) Gaussion Area (DN)
F e X2 5 7 . 2 6 2 (cid:1)
S i X2 5 8 . 3 7 5 (cid:1)
F e X I I2 5 9 . 4 9 1 (cid:1) ( b )
Figure 2.
Synthetic Gaussian fitted spectra from the EIS short wave band (a) and long wave band (b) nearby the 257 MIT line(bottom panel) and reference lines (top panel) shown in Fig. 1 for AR2. FWHM= 0 .
06 ˚A for short wave band, FWHM= 0 .
07 ˚Afor long wave band, as recommended in Brown et al. (2008). to the 174.534 ˚A line increases with the electron density. By adjusting the spectral model to simulate the measuredintensity ratio, electron densities of 1 . × cm − were established for one active region (AR2 in Brown et al. (2008)).With these electron densities and the selected normalization lines 174.534 ˚A and 175.266 ˚A, magnetic field strengthscan finally be determined through comparisons of the spectral model with observed line ratios.By combining theoretical modelling with the observation from HINODE, we estimate solar magnetic fields forAR2. Fig. 3 present modelled line ratios as functions of magnetic field strengths. Comparing with the observed lineintensities from the active region, the best-fit magnetic fields only differ by about four percent, giving an estimatedaverage field of B e = 270 G from 265 G and 275 G obtained from the line ratios with lines at 174.534 ˚A (Fig. 3 (a))and 175.266 ˚A (Fig. 3 (b)) respectively. This accords with previous estimations of 100 −
300 G based on extrapolationfrom magnetograms at the lower boundary, using a potential or force-free field model (Aschwanden 2014), however isnot a direct measurement of the coronal magnetic fields.There are a number of uncertainties to be considered, the dominating one coming from the determination of the finestructure energy (3 . ± . − (Judge et al. 2016)). The shaded areas of Fig. 3 show limits for the estimated magneticfields due to the uncertainty in ∆ E , with upper and lower boundaries at roughly B e /
16 and 3 ∗ B e , respectively. Thereare also possible uncertainties in the atomic data, especially in the M2 and the MIT rates. The MIT rate depends onthe transition rate of the D / which is in itself a spin-forbidden transition to the P o3 / ground state level. Theoreticaldetermination of transition rates for spin-forbidden transitions have been improved considerably over the years, butit is hard to give an exact value of the uncertainty of this rate as no measurement of the D / rate for any ion inthe Cl-like sequence is available (and this situation is not likely to change with the demise of beam-foil spectroscopy B ( G ) ( a ) ( b ) B ( G ) Figure 3.
Simulated intensity ratio (black line) of (a) 174.534/257.262 and (b) 175.266/257.262 as a function of the magneticfield in the AR area. The grey shaded area shows the uncertainty caused by the uncertainty in the ∆ E -parameter (see text).The horizontal dashed line is the line ratio measured from HINODE. The vertical dotted line shows our estimated magneticstrength. some years back (Tr¨abert 2008)). The estimated uncertainty of the present cited transition rate is ≤
25% (Wang et al.2020), which will cause a maximum uncertainty of 12.5% in the estimated magnetic field strengths. This is considerablysmaller than the uncertainty introduced from the estimates of the ∆ E and can at the present stage of analyses beignored. The M2 rate is easier to compute, but an added complication is that this decay component of the D / hasa different angular dependence of its polarisation pattern than the MIT (which is an electric dipole transition). Oneof the authors has investigated the magnetic-field-dependent angular distributions and linear polarization of E1, M2and MIT transitions for the Ne-like ions (Li et al. 2014). When other error sources are reduced, it should be furtherinvestigated for Fe X, but we estimate it to be negligible compared to other sources of uncertainties in the presentsituation.It is clear that the proposed method is a viable candidate for direct and continuous measurements of coronal fields.To outline a future space-based instrument designed from the proposed scheme, it would need a simple spectrometerisolating two narrow spectral regions, the short wavelength region covering the 174.543 ˚A and 175.266 ˚A lines anda higher wavelength region for the 257.262 ˚A line. The spectrometer should be intensity calibrated, similarly to thepresent spectrometer aboard HINODE. The other requirement that is of vital importance is the optimization of thesignal to noise ratios. As can be seen that the AR area line ratio in Fig. 3 (b) changes from 0.72 to 0.69 over a rangeof magnetic field from 200 to 400 G, i.e. a factor of two change in the field strength only results in a bit over 4%change in the line ratio. Therefore the EIS LW-SW calibration and optimization of the signal-to-noise ratio are alsocritical factors for the success of this technique, although at the present stage the ∆ E uncertainty is clearly the mostimportant source of error. CONCLUSIONWe present for the first time direct, space-based measurements of the solar corona magnetic field strength. Themeasurements are based on a magnetic-field induced transition, MIT, in the spectrum of Fe . So far, the MIT usedhere is the only one known to be sensitive to the relatively weak magnetic fields found in astrophysical plasmas suchas the solar corona. The field strength we determine is around 270 G. The most severe uncertainties come from thedetermination of the D fine structure and measured the line intensities. Both of these are possible to improve infuture work, by more accurate laboratory measurement (for the former one) and an optimised design of a space-basedobservation (for the latter). ACKNOWLEDGMENTSThis work was supported by the Swedish Research Council (VR) under Contract No. 2015-04842 and the NationalNatural Science Foundation of China under Contract No. 11474069. JG would like to acknowledge financial supportfrom the the project grants “The New Milky Way” (2013.0052) and “Probing charge- and mass- transfer reactions onthe atomic level” (2018.0028) from the Knut and Alice Wallenberg Foundation. We also thank J. Leenaarts for helpfuldiscussions. REFERENCES