# Alfvénic Perturbations in a Sunspot Chromosphere Linked to Fractionated
Plasma in the Corona

Deborah Baker University College London, Mullard Space Science Laboratory,
Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK  Marco Stangalini ASI Italian
Space Agency, Via del Politecnico, s.n.c 00133 – Roma, Italia  Gherardo Valori
University College London, Mullard Space Science Laboratory, Holmbury St.
Mary, Dorking, Surrey, RH5 6NT, UK  David H. Brooks College of Science, George
Mason University, 4400 University Drive, Fairfax, VA 22030, USA  Andy S.H. To
University College London, Mullard Space Science Laboratory, Holmbury St.
Mary, Dorking, Surrey, RH5 6NT, UK  Lidia van Driel-Gesztelyi University
College London, Mullard Space Science Laboratory, Holmbury St. Mary, Dorking,
Surrey, RH5 6NT, UK  LESIA, Observatoire de Paris, Université PSL, CNRS,
Sorbonne Université, Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules
Janssen, 92195 Meudon, France  Konkoly Observatory, Research Centre for
Astronomy and Earth Sciences, Hungarian Academy of Sciences, Konkoly Thege út
15-17., H-1121, Budapest, Hungary  Pascal Démoulin LESIA, Observatoire de
Paris, Université PSL, CNRS, Sorbonne Université, Univ. Paris Diderot,
Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France  David
Stansby University College London, Mullard Space Science Laboratory, Holmbury
St. Mary, Dorking, Surrey, RH5 6NT, UK  David B. Jess Astrophysics Research
Centre, School of Mathematics and Physics, Queen’s University Belfast,
Belfast, BT7 1NN, UK  Department of Physics and Astronomy, California State
University Northridge, Northridge, CA 91330, U.S.A.  Shahin Jafarzadeh
Rosseland Centre for Solar Physics, University of Oslo, P.O. Box 1029
Blindern, NO-0315 Oslo, Norway  Institute of Theoretical Astrophysics,
University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway

(Received XXXX, 2020; Revised XXXX, 2020; Accepted November 15, 2020)

###### Abstract

In this study, we investigate the spatial distribution of highly varying
plasma composition around one of the largest sunspots of solar cycle 24.
Observations of the photosphere, chromosphere, and corona are brought together
with magnetic field modelling of the sunspot in order to probe the conditions
which regulate the degree of plasma fractionation within loop populations of
differing connectivities. We find that in the coronal magnetic field above the
sunspot umbra, the plasma has photospheric composition. Coronal loops rooted
in the penumbra contain fractionated plasma, with the highest levels observed
in the loops that connect within the active region. Tracing field lines from
regions of fractionated plasma in the corona to locations of Alfvénic
fluctuations detected in the chromosphere shows that they are magnetically
linked. These results indicate a connection between sunspot chromospheric
activity and observable changes in coronal plasma composition.

Sun: abundances - Sun: corona - Sun: magnetic fields

††journal: AJ

draft

##  1 Introduction

Early observations of elemental abundance variations on the Sun showed
systematic differences between the composition of the corona and that of the
photosphere (e.g. Widing & Feldman, 1989, 1995; Sheeley, 1995, 1996). In the
closed-loop solar corona, in the slow solar wind, and in solar energetic
particles (SEPs), elements with low first ionization potential (FIP $<$10 eV)
are more abundant by a factor of 2–4 compared to the photosphere (e.g. Meyer,
1985a, b; Gloeckler & Geiss, 1989; Feldman & Widing, 2003; Brooks et al.,
2015), whereas, high FIP elements (FIP $>$ 10 eV) retain their photospheric
elemental distribution. Plasma composition in the open magnetic field of
coronal holes remains relatively unfractionated when it is observed in the
corona (e.g. Feldman & Widing, 1993; Feldman et al., 1998; Doschek et al.,
1998; Brooks & Warren, 2011). Abundance variations are typically characterized
by FIP bias which is the ratio of an element’s abundance in the solar
atmosphere to its abundance in the photosphere. FIP bias of $\sim$1 indicates
unfractionated photospheric plasma composition and $>$1.5 is fractionated
plasma of coronal composition.

Feldman et al. (1990) provided one of the few early studies of plasma
composition around a sunspot based on spatially unresolved, slit observations
obtained from a rocket flight of the High Resolution Telescope and
Spectrograph (HRTS). The authors determined that in the atmosphere above a
sunspot, the elemental abundances had a photospheric distribution compared to
the plasma of the nearby plage region, which was highly enriched in low FIP
elements. Similarly, Sheeley (1995) noted in a _Skylab_ slitless spectrogram
that plasma above a sunspot umbra was enriched in high-FIP Ne VI whereas in
the adjacent penumbra, the plasma was enriched in low-FIP Mg VI. Ne VI rich
plasma occurred only in areas of flux emergence in two nearby active regions.

Subsequent studies of high FIP bias plasma in active regions refer to features
such as Mg IX sprays (Sheeley, 1996), spikes at the edges of active regions
(Young & Mason, 1997), fan loops (Warren et al., 2016), and upflow/outflow
regions (e.g. Brooks & Warren, 2011). Typically, the magnetic field associated
with these features is the decaying or dispersed unipolar areas of strong
magnetic field at the periphery of active regions. Strong plasma fractionation
is observed at the footpoints of loops rooted in the unipolar regions where
FIP bias levels are 3–4 (Brooks & Warren, 2011; Baker et al., 2013; Brooks et
al., 2015). High FIP bias of $\sim$3 is also observed in the cores of
quiescent active regions (Del Zanna & Mason, 2014).

According to the plasma fractionation model of Laming (2015), a compelling
explanation for the separation of ions from neutrals is the ponderomotive
force arising from the reflection or refraction of Alfvén waves in the
chromosphere. The Alfvén waves act only on the ions while leaving neutral
elements unaffected. Though the fractionation is influenced by the origin and
flux of the Alfvén waves as well as the wave-wave interactions in the
chromosphere, in general, the time averaged ponderomotive force is directed
upward, giving rise to the enrichment of easy-to-ionize low FIP elements in
the corona (Laming, 2015, 2017). The direction and ultimately the resonance of
the Alfvén waves are all-important to the degree of fractionation observed in
the corona (Laming et al., 2019). These features are set by where the Alfvén
waves are generated. In open field regions, typical waves with 3 and 5 min
periods (e.g. Khomenko & Collados, 2015, and references therein) generated
from below the photosphere propagate upward at the base of the field and
either continue along the open field or are reflected back down; there is
little resonance, therefore, little fractionation. Upward propagating waves
with such long periods do not resonate with the closed loop corona so like
with open field regions, the waves are reflected back down at the loop
footpoints resulting in little or no fractionation. Conversely, Alfvén waves
generated in the corona due to magnetic reconnection are directed downward to
loop footpoints at the top of the chromosphere and then are reflected back
upward at the steep density gradient located there. Laming (2017) proposed
that resonant waves are excited within the coronal loop itself as a result of
nanoflare reconnection in the corona thereby creating enhanced fractionation
at magnetically connected loop footpoints (Baker et al., 2013; Dahlburg et
al., 2016; Laming, 2017; Laming et al., 2019). It is not observationally clear
if these oscillations generated by reconnection in the corona are linked to
enhanced fractionation, however.

In this regard, the quest for magnetic fluctuations associated with magneto-
hydrodynamic waves (MHD) in solar magnetic structures assumes a particular
importance. Observationally, MHD waves in solar magnetic structures are
generally detected as intensity and velocity oscillations (Bogdan, 2000;
Centeno et al., 2006; Chorley et al., 2010; Morton et al., 2011; Stangalini et
al., 2012; Grant et al., 2015; Jafarzadeh et al., 2017; Jess et al., 2017),
although simultaneous magnetic fluctuations are also expected from theory for
different types of MHD modes (Edwin & Roberts, 1983; Roberts, 1983). The
required magnetic oscillations for ponderomotive fractionation to take place
can therefore be associated with a number of different wave modes (Roberts,
1983; Khomenko et al., 2003; Goossens et al., 2009; Morton et al., 2015) e.g.
locally excited waves (Alfvén, magneto-acoustic fast mode in high-$\beta$
regimes), or global eigenmodes of the magnetic structure (e.g. sausage mode,
torsional Alfvén mode,…). We will refer to magnetic fluctuations associated
with any wave mode as Alfvénic waves, to distinguish from a purely Alfvén
mode. The detection of magnetic oscillations associated with MHD modes is a
difficult task as opacity effects or instrumental crosstalk with other
physical quantities can easily mimic the effect of these oscillations (e.g.
Khomenko & Collados, 2015; Joshi & de la Cruz Rodríguez, 2018, and references
therein). One way to disentangle intrinsic magnetic oscillations in the solar
atmosphere is through the investigation of the phase lag between the
polarization signals associated with magnetic field disturbances and other
physical quantities such as intensity and Doppler velocity (Stangalini et al.,
2018, 2020). Oscillating physical quantities associated with MHD waves may
have different phase relations depending on the MHD mode and the propagation
state of the wave (Fujimura & Tsuneta, 2009; Moreels et al., 2013; Moreels &
Van Doorsselaere, 2013; Hinode Review Team et al., 2019), thus the analysis of
the phase relations between them can be exploited for their identification
(Stangalini et al., 2018), and the identification of the specific mode
producing them.

In this paper, we show a detailed, spatially resolved coronal composition map
of a strong and coherent leading sunspot in AR 12546. We find that the
elemental abundance variation in the corona above the sunspot is highly
structured with extremes in the level of fractionation among the distinct loop
populations. The distribution of the highly fractionated plasma appears
correlated with the spatial locations at which intrinsic magnetic oscillations
are identified in nearly simultaneous high spatial resolution
spectropolarimetric observations of the solar chromosphere (Stangalini et al.,
2020). Magnetic field modeling is used to investigate the connectivities of
the loop populations within the sunspot to seek an understanding of the
distribution of plasma composition observed there. We interpret our findings
in the wider context of coronal heating and the ponderomotive force model of
elemental fractionation (Laming, 2015).

Figure 1: _SDO_ /AIA 193 Å (a) and 171 Å (b) images at the time of the EIS
observation at 07:24 UT on 2016 May 20. _SDO_ /HMI magnetograms on May 18 at
12:00 UT (c), May 20 at 07:24 UT (d), and May 20 at 13:40 UT (e). All images
are overlaid with boxes showing the larger _Hinode_ /EIS (black) and smaller
IBIS (red) FOVs. At 07:24 UT, the _SDO_ /AIA and HMI FOV is X =
[-300$\arcsec$, 200$\arcsec$] and Y = [-280$\arcsec$, 140$\arcsec$]. Images of
the figure are from the included movie labeled as fig1anim.mp4. It covers the
time period from 12:00 UT on May 18 to 14:55 UT on May 20 and lasts 30 s.

##  2 Observations and Methods

###  2.1 Overview of AR 12546

The observations of AR 12546 were obtained on 2016 May 20 using the _Hinode_
EUV Imaging Spectrometer (EIS; Culhane et al., 2007), the Interferometric
BIdimensional Spectrometer at the National Solar Observatory Dunn Solar
Telescope (IBIS; Cavallini, 2006; Reardon & Cavallini, 2008), the Solar
Dynamics Observatory (_SDO_)/Atmospheric Imaging Assembly (AIA; Lemen et al.,
2012) and _SDO_ /Helioseismic and Magnetic Imager (HMI; Scherrer et al.,
2012). Figure 1 shows high resolution (Morgan & Druckmüller, 2014) _SDO_ /AIA
193 Å (a) and 171 Å (b) context images centered on the active region overlaid
with contours indicating the positions of the EIS and IBIS fields of view
(FOVs). At the time of the EIS raster, the sunspot is located at the solar
central meridian (CM) approximately 100$\arcsec$ south of the equator. The
bottom panel of the figure contains a series of _SDO_ /HMI magnetograms (c–e)
also with the EIS and IBIS FOVs. Figure 1 includes an animation of these
observations for 2016 May 18–20.

AR 12546, one of the largest ARs of the last 20 years, was a relatively
simple, bipolar region composed of a strong, coherent leading positive
polarity sunspot and a dispersed following field of negative polarity.
Asymmetric flux concentrations are typical of bipolar regions, however, both
the extent of the dispersion of the following polarity and the coherency of
the leading spot are extreme in this case. At the time of its CM crossing on
May 20, half of the total unsigned magnetic flux of the active region was
4.1$\times$1022 Mx and the magnetic field strength was exceptionally high,
exceeding 4,000 G in the center of the sunspot umbra in the photosphere
(Stangalini et al., 2018). There was no significant evolution of the large-
scale field during the two days prior to the EIS and IBIS observations; the
sunspot was globally stable. Small-scale evolution was limited to moving
magnetic features streaming radially from the positive-polarity sunspot and
ongoing fragmentation and dispersal of the negative field of the following
polarity in the decaying active region (see also Murabito et al., 2019).

During the period of May 18–20, there were no flares $>$ B-class or coronal
mass ejections (CMEs) attributable to AR 12546. The stability of the loops
rooted in the sunspot umbra and penumbra and the lack of activity reflect the
absence of consequential evolution in the magnetic field (see the included
animation of Figure 1).

Figure 2: Top: Photospheric IBIS Fe I 6173 Å (a) and chromospheric Ca II 8542
Å core intensity (b) images at 13:39 UT on 20 May. Bottom panel: Stokes _V
max_/_I cont_ $CP$ map without/with (c/d) blue dots overplotted. The blue dots
indicate the locations where the magnetic waves are detected (cf. Figures 5, 6
and see the discussion in Section 4). The $CP$ map is saturated at 0.3
(white).

###  2.2 IBIS Observations and Methods

IBIS full Stokes spectropolarimetric scans were used to identify possible
signatures of magnetic field oscillations in circular polarization ($CP$)
measurements in the umbra. A full account of the observations and data
reduction techniques is provided in Stangalini et al. (2018); Murabito et al.
(2019); Houston et al. (2020), and Stangalini et al. (2020). Here we precis
the aspects which are relevant to this analysis. The data set consists of a
time series of Ca II 8542 Å scans beginning at 13:39 UT on May 20 and
continuing for 184 minutes at a cadence of 48 sec. The Ca II is a
chromospheric magnetically sensitive line and therefore suitable for detecting
magnetic field oscillations at chromospheric heights. Figure 2 shows an IBIS
intensity image in the photospheric Fe I 6173 Å line for context (a) and an
intensity image in the Ca II 8542 Å line (b). The IBIS FOV of
28$\arcsec$$\times$70$\arcsec$ encompasses the umbra in the X-direction and a
significant portion of the penumbra in the Y-direction. The $CP$ measurements
were obtained from the amplitude of the Stokes-_V_ profile. $CP$ is defined as
follows:

$CP=\frac{\lvert V_{max}\rvert}{I_{cont}}\cdot sign{\left(V_{max}\right)},$
(1)

where _V max_ is the maximum amplitude of the Stokes _V_ spectral profile and
Icont is the local continuum intensity (Stangalini et al., 2018).

To identify possible intrinsic magnetic field oscillations in the same IBIS
data set, Stangalini et al. (2020) performed a specific phase lag analysis,
between the $CP$ and the core intensity of the Ca II. The Figure 2 (c) shows
the Stokes _V max_/_I cont_ $CP$ map saturated at 0.3. The authors selected
the $CP$ instead of Doppler velocity of the Ca II line for the phase lag
analysis due to the presence of shocks that can turn the Ca II line from
absorption to emission, rendering the line Doppler velocity undefined. The
$CP$ is directly related to line-of-sight magnetic field but its variation can
be caused by either intrinsic magnetic oscillations or opacity effects. In the
case of opacity effects, the intensity is expected to be in/out of phase due
to the fluctuation of the line formation height. This does not mean that real
magnetic waves with the same phase relations (i.e. $\pm$$\pi$) do not exist,
but the phase lag analysis provides a high level of confidence we are not
observing a mix of real and unreal oscillations. A strong coherence is needed
to ensure that unreliable phase measurements are excluded from the analysis.
In this work we make use of the results of Stangalini et al. (2020) and
investigate the spatial distribution of the $CP$ oscillations with the aim of
assessing their role in the distribution of the observed FIP bias in and
around the sunspot.

Figure 3: _Hinode_ /EIS Fe XII intensity, Doppler velocity, non-thermal
velocity maps, Fe XIII density and Si X/S X FIP bias (or composition) maps at
07:24 UT on 20 May 2016. _SDO_ /HMI continuum contours show the locations of
the umbra and penumbra boundary. Dashed lines enclose the fan loops rooted on
the western side of the sunspot. The EIS FOV is X = [$-$60$\arcsec$,
60$\arcsec$] and Y = [$-$170$\arcsec$, $-$30$\arcsec$] (coordinates from Sun
center). Regions in the density map sample loop populations with mean density
values provided for each white box. (The black stripes in the composition map
are artefacts of the CCD and should not be confused with the IBIS FOV
boundaries shown in the left panel of Figure 5).

###  2.3 _Hinode_ /EIS Observations and Methods

_Hinode_ EIS spectral data were used for the plasma composition analysis of
the sunspot within AR 12546. A FOV of 120$\arcsec$$\times$160$\arcsec$ was
created using the 2$\arcsec$ slit in 2$\arcsec$ steps, taking 60 sec exposures
at each slit position. The single scan began at 07:24 UT on May 20 and
finished two hours later. Study $\\#$404 (Atlas$\\_$60) is a full spectral
atlas of both CCDs therefore it contains the diagnostic spectral lines
required for constructing a spatially resolved composition map.

Data reduction was carried out using the eis$\\_$prep routine that is
available in Solar SoftWare (Freeland & Handy, 1998). The CCD signal in each
pixel was converted into calibrated intensity units of erg cm-2 s-1 sr-1 Å-1
and pixels affected by cosmic ray hits, dust, and electric charge were
removed/replaced. All data were corrected for instrumental effects of orbital
spectrum drift (Kamio et al., 2010), CCD spatial offsets, and the grating
tilt.

Diagnostics | Ion | Wavelength (Å)
---|---|---
Emission Measure | Fe VIII | 185.21, 186.60
| Fe IX | 188.50, 197.86
| Fe X | 184.54
| Fe XI | 188.21(b)
| Fe XII | 192.39, 195.12(b)
| Fe XIII | 202.04, 203.83(b)
| Fe XIV | 264.79, 270.52(b)
| Fe XV | 284.16
| Fe XVI | 262.98
| Fe XVII | 254.87
FIP Bias | Si X | 258.38
| S X | 264.23
Density | Fe XIII | 202.04, 203.83(b)
Table 1: _Hinode_ /EIS emission lines used for various plasma diagnostics in
this study. Blended lines (b) are fit with multiple Gaussian functions.

To construct the composition map, spectral lines from consecutive ionization
stages of Fe VIII–Fe XVII and the low FIP Si X (FIP = 8.15 eV) and high FIP S
X (FIP = 10.36 eV) were fit with single Gaussian functions except where the
lines are blended in which case the line was fit with multiple Guassian
functions. The Si X/S X line ratio was used to determine FIP bias and the
density was measured with the Fe XIII 202.04 Å/203.83 Å line ratio. The
specific emission lines are given in Table 1. The CHIANTI Atomic Database,
Version 8.0 (Dere et al., 1997; Del Zanna et al., 2015) was used to carry out
the contribution function calculations, applying the photospheric abundances
of Grevesse et al. (2007) for all of the spectral lines while assuming the
measured Fe XIII densities. The Markov-Chain Monte Carlo (MCMC) algorithm
contained within the PINTofALE software package (Kashyap & Drake, 2000) was
used to compute the emission measure (EM) distribution for the Fe lines. The
EM distribution was then convolved with the contribution functions and fit to
the observed intensities of the low-FIP Fe spectral lines. Si is also a low-
FIP element therefore the EM derived from the Fe lines was scaled to reproduce
the intensity of the Si X line. Finally, the FIP bias was determined to be the
ratio of the predicted to observed intensity for the high FIP S X line. The
estimated uncertainty of the FIP bias ratio is 0.30 assuming an intensity
error of 20$\%$. A full account of the method is available in Brooks et al.
(2015) and Baker et al. (2018).

Fe XII 195.12 Å relative Doppler velocities were measured versus a reference
wavelength defined by averaging the centroid wavelengths of all pixels within
the data array. This method was adopted as EIS does not have an absolute
wavelength calibration. Excess broadening in the deblended Fe XII 195.12 Å
emission line spectra was calculated from

$\delta\lambda=\frac{\lambda_{0}}{c}~{}\sqrt{4~{}ln~{}2\left(\frac{2~{}k_{B}T_{i}}{m}~{}+~{}\xi^{2}\right)~{}+~{}\sigma_{I}^{2}},$
(2)

where $\delta$$\lambda$ is the observed line width, $\lambda$0 is the line
centroid, kB is Boltzmann’s constant, Ti is the ion temperature, $m$ is the
mass, $\xi$ is the nonthermal velocity, and $\sigma$I is the instrumental
width (e.g. Brooks & Warren, 2016). Figure 3 shows the _Hinode_ /EIS Fe XII
intensity, Doppler and nonthermal velocity maps, Si X/S X composition map, and
Fe XIII density map at 07:24 UT on 2016 May 20. _SDO_ /HMI continuum contours
have been overplotted on the EIS maps to mark the umbral and penumbral
boundaries of the sunspot.

Above the umbra, the plasma is blue-shifted with upflow speeds of 10–20 km s-1
and nonthermal velocities range from $\sim$15 km s-1 above the center to
$\sim$30 km s-1 toward the umbra/penumbra boundary. Plasma density is
$\sim$5$\times$108 cm-3. Plasma composition above the umbra is photospheric
with a FIP bias of 1 above its core; toward the boundary, the composition
becomes more fractionated with FIP bias $\sim$1.5–2, especially on the eastern
edge.

Plasma parameters are more extreme above the penumbra where the loops
surrounding the sunspot are rooted. Upflows transition to downflows in the
loops at the outer boundary. Nonthermal velocities are 30–50 km s-1 in loops
located to the east and south of the penumbra; they are $\sim$30–40 km s-1 in
the west (in between the dashed lines in the EIS maps). Plasma density
increases by an order of magnitude above the penumbra compared with the umbra.
FIP bias exceeds 3+ above the eastern penumbra and reaches 4+ at the boundary
in the east and to the south. The strongest fractionation is located in the
southern region in the vicinity of the highest nonthermal velocities of 45–50
km s-1.

##  3 Coronal Loop Connectivities

Figure 4: Selected field lines of the PFSS extrapolation of AR 12546 based on
an _SDO_ /HMI synoptic radial field magnetogram at 13:00 UT on 2016 May 20.
Field lines are color-coded as closed within the same active region (red),
closed to a neighboring active region (orange), or open (yellow); the radial
magnetic field saturated at 100 G is represented in greyscale, and the green
contour on the sunspot represents its 500 G isocontour.

A Potential Field Source Surface (PFSS) extrapolation was computed to model
the coronal loop system surrounding the sunspot. The rationale behind the use
of the PFSS extrapolation is that this model captures the global field of the
sunspot for comparison with the _SDO_ /AIA coronal images of Figure 1. The
PFSSPY package (Yeates, 2018; Stansby, 2019) was employed to extrapolate the
coronal field from the HMI synoptic radial field map of CR2177. Figure 4 shows
the extrapolation with selected field lines. A green contour represents 500 G
in the positive polarity sunspot. In general, there is good qualitative
correspondence of the loops in the _SDO_ /AIA images at the times of the EIS
and IBIS observations with field lines in the extrapolation (Figure 4).

The coronal loop configuration of AR 12546 is characteristic of a bipolar
region with distinct loop populations. Yellow field lines on the western side
of the sunspot are long, extended loops that reach the source surface of the
PFSS model (=2.5 Rsun) therefore these field lines are considered to be open.
To the north, the orange, long loops are connected with the negative polarity
of the active region located to the north-east of AR 12546. The plasma density
in these regions is $\sim$5–6$\times$108 cm-3 (see the mean densities within
the boxes of the density map in Figure 3) and plasma composition is partially
fractionated with FIP bias of 1.5–2. In contrast, the red loops on the east
and south of the sunspot are compact loops that connect mainly with the
opposite polarity within the active region. The density of the short, closed
loops is an order of magnitude higher and the plasma is highly fractionated
with FIP bias of 3–4.

##  4 Alfvénic Perturbations in the Sunspot Chromosphere

Figure 5: (a) _Hinode_ /EIS Si X/S X FIP bias map at 07:24 UT on 2016 May 20.
Contours: (i) _SDO_ /HMI continuum umbra and penumbra boundaries (thin black
lines), (ii) _SDO_ /HMI LoS magnetogram $\pm$500 G (thick green/black lines =
positive/negative polarity), (iii) Location of Alfvénic waves from IBIS Ca II
observation (blue dots), (iv) IBIS FOV (white dashed box). (b) Selected high-
FIP bias field lines connecting high FIP bias in the corona to the umbra-
penumbra boundary (orange) started from values of FIP bias $>$ 2.7. The height
of the FIP bias map is $z=$3.6 CEA-deg and the value of the linear force-free
parameter $\alpha=-0.2$ CEA-deg-1 (The conversion factor is 1 CEA-deg $\simeq$
12.17 Mm). The green contour represents the 500 G isocontour of the vertical
magnetic field in the SHARP data.

Stangalini et al. (2020) found the presence of Alfvénic perturbations in the
sunspot chromosphere in the 3-minute band of the IBIS Ca II time series (see
Section 2.2). The frequency band corresponding to this period, which is also
the dominant period in the solar chromosphere (e.g. Khomenko & Collados, 2015,
and references therein), is smaller than the ion-cyclotron frequency, thus in
the regime appropriate for the model of Laming (2015). A phase lag analysis
between $CP$ and intensity ruled out the possibility of opacity and other
spurious effects by identifying a specific phase lag of the order of $-35$
degrees between the two quantities, which is not consistent with the phase
values expected from cross-talk or radiative opacity effects. Due to the
vertical gradient of the magnetic field, any plasma density perturbation can
induce a height variation of the response function of the spectral line, thus
resulting in an observed spurious magnetic oscillation which is merely a
consequence of an opacity change and has nothing to do with a real magnetic
wave. In this regard, the study of the phase relation between different
diagnostics is helpful in the identification of real magnetic oscillations.
Indeed, by collecting phase measurements corresponding to high coherence it
was possible to discriminate between different effects and identify real
magnetic oscillations in the sunspot chromosphere. Coherence is independent of
the wave amplitude, thus this technique is able to detect correlations between
two signals even if their amplitudes are small. It is worth noting that
Alfvénic shocks were independently detected by Houston et al. (2020) at the
same spatial locations, thereby confirming the interpretation of these
disturbances in terms of real magnetic fluctuations. The locations of the
Alfvénic perturbations are indicated by the blue dots overplotted on the
_Hinode_ /EIS FIP bias map of Figure 5(a) and on the $CP$ map in Figure 2(d).
The dots are aligned in a distinct C-shaped structure running from the north
to the south along the eastern edge of the sunspot umbra.

Within the same EIS FOV in Figure 5(a), coronal loops containing highly
fractionated plasma are present with particularly high values both to the east
and to the south-west of the sunspot. The projected spatial proximity of the
C-shaped structure and high FIP bias values poses the question whether the
loops of highly fractionated plasma observed in the corona are magnetically
connected to the specific locations of Alfvénic perturbations in the
chromosphere identified by Stangalini et al. (2020). The context to this
question is provided by theoretical models based on the hypothesis that the
fractionation process producing the FIP-effect is powered by the conversion of
magnetic waves at chromospheric heights (e.g. Schwadron et al., 1999; Laming,
2015).

In order to answer this question, a magnetic model of the sunspot area is
needed that is representative of the sunspot field so that we can determine if
the field lines threading regions of high FIP bias values are rooted in the
blue dots of Figure 5. The main difficulty is that the FIP bias map is the
result of a pixel-dependent, line-integrated emission of coronal lines to
which it is challenging to attribute a height, and even more so a single
height for the entire map. In addition, the paths followed by the modelled
field lines depend on the properties of the chosen magnetic field model.
Finally, there are more than eight hours between the beginning of the EIS
observation, which was used to compute the FIP bias map, and the end of the
IBIS observation, which was used to identify the Alfvénic perturbations. This
complicates the alignment of the different observations, especially
considering that both EIS and IBIS lack absolute pointing information.
Therefore, the choice of the time of the magnetic field observations that are
used to build the magnetic field model is also a factor of uncertainty. Given
these difficulties, we adopted a heuristic approach by testing whether a
combination of magnetic model and height of the FIP bias map exists where
field lines starting from areas of high FIP bias values are rooted in the
proximity of the blue dots.

A magnetic model for the sunspot can be obtained using a force-free
extrapolation of photospheric measurements (see, e.g. Wiegelmann & Sakurai,
2012). The photospheric magnetogram used as input for the extrapolation is the
_SDO_ /HMI SHARP magnetogram taken at 13:00 UT, in between the end of EIS
rastering and the start of the IBIS observation. SHARP data provide vector
magnetograms of regions of the Sun in a Cylindrical Equal Area (CEA)
projection, where the spatial dimensions are given in CEA degrees with 0.03
CEA-deg $\simeq$ 0.5$\arcsec\simeq 365$ km at the center of the disk. We use
this approximate conversion factor in the scale estimations given below. The
full SHARP field presents a significant flux imbalance (about 15%), therefore
we use the linear force-free extrapolation method of Seehafer (1978) which
does not require strict flux balance to be enforced. The entire FOV of the
SHARP magnetogram covering an area of 22.89$\times$12.99 CEA-deg was used to
compute the Fourier coefficient of Seehafer’s solution. However, in order to
reduce the computing time required by the parametric study described below,
the extrapolated magnetic field was computed in a smaller volume above the
sunspot of size [11.22, 11.22, 16] CEA-deg. The extrapolation volume was
discretized with a uniform resolution of 0.06 CEA-deg in the horizontal
directions and with an exponentially stretched axis in the vertical direction
such that the pixel size increases from 0.06 at the bottom to 0.96 at the top.

The ratio of the vertical current density to the vertical magnetic field,
$\alpha_{NL}=J_{z}/B_{z}$, represents the local torsion of field lines and is
constant along individual field lines in force-free extrapolations. Within the
linear approximation, this function is a free, constant parameter that is
limited in magnitude by the inverse of the linear dimension of the
extrapolated magnetogram. For Seehafer’s method applied to the entire FOV of
the SHARP magnetogram, $\alpha_{\rm max}=$ 0.27 CEA-deg-1 (corresponding to
0.022 Mm-1). Different magnetic field models are then obtained for different
values of the constant $\alpha$ ($|\alpha|<\alpha_{\rm max}$) and the same
magnetogram at the bottom boundary.

The alignment problem between the magnetic model based on the reprojected
SDO/SHARP magnetogram on the one hand, and the plane-of-the-sky SDO/AIA, IBIS,
and EIS observations on the other was treated as follows. First, the locations
of the Alfvénic perturbations were derotated from 13:39 UT (starting time of
the IBIS measurements) to the starting time of the EIS raster. Second, since
both EIS and IBIS lack absolute pointing information, the EIS raster and
derotated locations of Alfvénic perturbations were aligned to multiple images
of SDO at the time of the EIS raster. In particular, this operation produces a
co-alignment between the (derotated) location of the Alfvénic perturbations
and the HMI line of sight magnetogram at 07:24 UT. Finally, a 500 G
isocountour of the latter was used to match a similar contour in the SHARP
vertical magnetic field (at 13:00 UT) to co-align the location of the Alfvénic
perturbations and FIP bias map with the extrapolated field of the coronal
models.

Figure 6: (a) Distribution of $\alpha_{NL}$ on the sunspot, saturated between
$-$1 and 1, derived from the SHARP magnetogram. The blue contour identifies
the spatial distribution of the blue dots in panels (b-h). The remaining
panels (b-h) illustrate the match between the footpoints of high FIP bias
field lines (orange dots) and the location the Alfvénic perturbation (blue
dots), for positive values of $\alpha=$0.1, 0.2, 0.25 (panels b-d,
respectively), for $\alpha=0$ (panel e), and for negative values of
$\alpha=-0.1,-0.2,-0.25$ (panel f-h, respectively), in CEA-deg-1. The selected
heights of the FIP bias maps are 3.6, 4.2, 4.5, 3.3, 3.3, 3.6, 3.6 CEA-degrees
for cases (b-h), respectively. The conversion factor is 1 CEA-deg
$\simeq$12.17 Mm. On all panels, the green contour represents the 500 G
isocontour of the vertical magnetic field in the SHARP data. Annotations on
panels e) and g) highlight the matching criteria discussed in the text.

In summary, the heuristic method that we adopted consists of the following
steps:

  1. 1.

producing magnetic field models for different (constant) $\alpha$ values
between $-\alpha_{\rm max}$ and $+\alpha_{\rm max}$;

  2. 2.

for each field model, placing the co-aligned FIP bias map at different
heights;

  3. 3.

for each height of the FIP bias map, tracing the field lines in the given
model starting from FIP bias values above 2.7 in the entire EIS FOV. The value
2.7 is chosen as the lowest possible value consistent with capturing most of
the yellow area in the Figure 5(a), but reducing the number of pixels at the
edge of the FIP bias map. This is done to avoid that the rectangular shape of
the EIS FOV produces a misleading boundary of the field line distribution in
the following steps. The filtering of field line seeds results in selecting
relatively high-FIP bias field lines. As an example, Figure 5(b) shows the 3D
rendering of the spatial arrangement of Alfvénic oscillations (blue dots), a
few selected field lines (orange), and the EIS map for the parameters of
Figure 6(g);

  4. 4.

flagging the footpoints of the field lines with high FIP bias at chromospheric
heights (1$\arcsec$);

  5. 5.

comparing the location of the footpoints of field lines with high FIP bias
with the location of the co-aligned Alfvénic oscillations;

  6. 6.

finally, verifying if combinations of $\alpha$ and FIP bias map height exist
that produce a distribution of high FIP bias field line footpoints similar to
the distribution of blue dots in Figure 5(a).

The above procedure yielded the maps in Figure 6(b-h), where, in addition to
the blue dots representing the location of Alfvénic oscillations, the
footpoints of the high FIP bias field lines are shown as orange dots. These
maps answer our initial question: there are indeed combinations of model
parameters for which the orange and blue dots are closely located. In other
words, our parametric, heuristic study supports the existence of a magnetic
link between high FIP bias values and the locations of Alfvénic perturbations
in the chromosphere identified by Stangalini et al. (2020).

One can further try to deduce which is the value of $\alpha$ that results in
the best match between the orange and blue dots in Figure 6(b-h). This is
inevitably very subjective, as it strongly depends on which subset of dots is
given priority in the match. If, for instance, only the number of orange dots
overlapping the blue structure is considered, one would likely choose the
potential case ($\alpha=0$ in panel e) or even a slightly positive value of
$\alpha$ as the best matching case. This criterion discards the more isolated
dots in the center and upper parts of the sunspot as not significant. On the
other hand, if the shape of the distribution is chosen as the primary matching
criteria, then one may recognize how, similarly to the blue dots, the orange
dots in Figure 6(b-h) are arranged in a pattern roughly shaped as a C with
straight arms (except for few orange dots in the center of the sunspot). The
red arrows on panels (e) and (g) of Figure 6 indicate how the arms of the
C-shape of the orange dots in two cases are identified. For instance, as the
annotations in panel (e) indicate, in the potential case both the vertical and
upper orange arms are at an angle with the corresponding blue arms, whereas we
deem the overlap of the whole structures to be better in panel g. By matching
the blue and orange C-shapes as a whole, we would then identify the
$\alpha=-0.2$ CEA-deg-1 as best matching case.

Hence, adopting different matching criteria results in different values for
the best matching $\alpha$, pointing at the limitations that a
constant-$\alpha$ model of the magnetic field has in this particular
application. Also, we stress again that to treat the FIP bias map as a flat
horizontal plane at a given height is a very crude approximation. On the other
hand, the range of heights between 40 and 55 Mm of the FIP bias maps
identified in Figure 6(b-h) yields coronal electron temperatures in the range
of $\approx$ [0.9, 1.2] MK, assuming hydrostatic equilibrium (Aschwanden &
Schrijver, 2002). This is consistent with the temperature range for which the
Si X–S X FIP bias line-pair is an effective diagnostic of coronal plasma
composition (Feldman et al., 2009; Brooks & Warren, 2011)

The space-dependent distribution of $\alpha$ in the sunspot area can be
computed as $J_{\rm z}/B_{\rm z}$ using the photospheric observation of the
SHARP magnetogram. This is plotted in Figure 6a, with the blue contour
identifying the distribution of the blue dots, showing that, while still
predominantly positive, $\alpha$ values of both signs are present. It is
interesting to note that a C-shaped concentration of negative $\alpha$ values
is present right to the east of the C-shaped contour of the blue dots. The
blue contour and the negative $\alpha$ values are not exactly overlapping, but
their appearance is very similar in shape with just a slight shift (of about
0.3 CEA-deg) that is comparable to the alignment accuracy among the different
instruments/maps. The possible spatial correlation between Alfvénic
oscillations and negative values of $\alpha$ suggested by Figure 6(a) is
interesting because it may give some clues about the background field in which
the oscillations took place. However, given the limitations of alignment and
modeling discussed so far, we do not pursue this point any further, and leave
the investigation of this aspect to future studies on the nature of the
Alfvénic oscillations (e.g. Section 6).

In summary, the heuristic method defined two parameters (the magnetic twist
and the height of the FIP bias map) that resulted in a positive spatial
correlation between high values of FIP bias and the Alfvénic 3-minutes
magnetic oscillations detected in the IBIS Ca II time series by Stangalini et
al. (2020). This is indicative of a magnetic connection between chromospheric
magnetic oscillation regions and high values of FIP bias observed in the
corona above the sunspot. Given the intrinsic limitations of observations and
magnetic modeling discussed above, these findings are nevertheless consistent
with the theory of FIP fractionation outlined in Laming (2015).

##  5 Discussion

In this work, we have investigated the spatial distribution of coronal plasma
composition in the vicinity of the large sunspot of AR 12546. _Hinode_ /EIS
observations revealed that compositional variation ranged from little or no
fractionation in the corona above the core of the umbra to partially or highly
fractionated plasma in groups of coronal loops rooted in the surrounding
penumbra.

Using a PFSS extrapolation of the large scale magnetic field of the positive-
polarity sunspot, we identified distinct loop populations based on their
connectivities: open field or long loops connected externally to the negative
polarity of an active region $\sim$ 570 Mm to the northeast and short, dense
loops internally connected to the negative polarity of the active region.

Plasma composition is relatively uniform within each loop population but
varies across populations. FIP bias was 1.5–2 in the open field or long loops
connecting externally to a another active region whereas it was 3–4 in the
loops connecting to the opposite polarity within AR 12546 (Figure 3). Loops
within a particular group are likely to share similar global properties and
evolve together. In AR 12546, the very simple bipolar topology coupled with
little evolution of the large-scale magnetic field prior to the EIS and IBIS
observations, suggest that there was limited mixing of plasma compositions via
magnetic reconnection of different loop populations.

Among the global properties shared by coronal loops within the same
population, loop length and resonance frequencies are at least theoretically
related to the observed plasma fractionation distribution in and around the
sunspot. The Laming ponderomotive force fractionation model predicts that
resonant Alfvénic waves, generated by nanoflaring reconnection in the corona,
increase plasma fractionation in the vicinity of footpoints of resonant closed
loops whereas there is little resonance and fractionation along open field. In
support of the Laming model, numerical simulations of Dahlburg et al. (2016)
showed that ponderomotive acceleration occurs at loop footpoints as a
consequence of MHD waves generated by magnetic reconnection in the corona and
that the FIP effect is a natural outcome of coronal heating. Significantly,
the ponderomotive acceleration increases with increasing temperature and with
decreasing length in closed coronal loops in the simulations. In the corona
above the umbra of the large sunspot, the field had photospheric plasma
composition. At photospheric and chromospheric heights, sunspot umbrae are
regions of temperature minima so that elements are mainly neutral or singly
ionized (e.g. Loukitcheva et al., 2014; Lodders, 2019). As a consequence,
local temperatures are not high enough to create a sufficient reservoir of
ionized elements in the chromosphere, inhibiting plasma fractionation. Plasma
transported from the chromosphere to the coronal field above the umbra is
therefore likely to be unfractionated photospheric plasma.

On the western side of the sunspot, which is magnetically connected to another
active region or has open field lines, FIP bias values were somewhat higher,
between 1.5 and 2. The highest FIP bias of 3–4 was found on the
eastern/southern sides of the spot in high temperature active region core
loops. These loops are rooted in the penumbra and are subject to convection-
driven footpoint motions leading to higher frequency heating than in the loops
rooted in the umbra (see Del Zanna & Mason, 2018, and references therein).

Our results are consistent with the predictions of the Laming model and the
output from the simulations of Dahlburg et al. (2016) in that high FIP bias
plasma occurs in high temperature, short loops where nanoflaring in the model
generates high Alfvénic wave flux which is amplified by resonance. In the
other sets of loops with different connectivities e.g., open field lines,
lower wave flux is expected as there is no repeated reflection of any
potential Alfvénic waves created there, and consequently, these loops are
likely to contain plasma with lower FIP bias. In fact, these findings do not
exclude other theoretical models based on either wave interactions with
chromospheric ions e.g. the ion cyclotron wave heating model of Schwadron et
al. (1999) or on processes linked to coronal heating e.g. heat conduction of
the thermoelectric driving model of Antiochos (1994).

In the wider context, we still fundamentally lack an understanding of what is
happening in the chromosphere when we see activity in the corona, and a key
goal generally is to elucidate the connection between activity in the low
atmosphere and observable changes higher up. We have found that the internally
connecting core loops with the highest FIP bias are rooted in areas where the
Alfvénic perturbations were found in the chromosphere. This is the first
observational evidence of detectable Alfvénic perturbations in the
chromosphere being linked to coronal loops containing highly fractionated
plasma. Whether this is the result of a response to coronal heating, as in the
ponderomotive force model, or further evidence of heating at coronal heights
being driven from below, remains an open question.

##  6 Concluding Remarks

This work represents a first attempt to investigate the role of magnetic
fluctuations in plasma fractionation, made possible thanks to nearly
simultaneous observations at chromospheric and coronal heights by IBIS and
EIS, respectively. Our results demonstrate a possible link between magnetic
perturbations observed at chromospheric heights as small fluctuations of the
spectropolarimetric quantities, and the locations of high FIP bias observed in
the corona. They therefore observationally support a role for MHD waves in the
generation of the FIP effect and wave-based theoretical models.

Some questions still remain open and identify possible future research
directions. As already mentioned, magnetic fluctuations are expected for a
number of different MHD wave modes. These can be magneto-acoustic modes which
are locally excited within the umbra by residual convection and/or p-mode
absorption, or globally excited eigenmodes of the sunspot. In this study, the
exact identification of the wave mode responsible for the observed magnetic
fluctuations was not possible with the available data. Indeed, different modes
can co-exist in the same structure hampering the identification process.
However, as noted in Stangalini et al. (2020), the locations where the
Alfvénic waves are observed correspond to a narrow range of magnetic field
inclinations, suggesting a possible role of the magnetic field geometry. In
this regard, it is worth recalling that MHD waves in magnetic structure can
undergo a mode conversion at the Alfvén-acoustic equipartition layer, with
part of the energy contained in the acoustic-like components (fast MHD mode in
the plasma-$\beta>1$ regime) being converted to a combination of fast magneto-
acoustic (in the plasma-$\beta<1$ regime) and magnetic-like waves. This
physical mechanism is dependent on the attack angle between the wavevector and
the field lines (see for instance Gary, 2001; Newington & Cally, 2010; Cally,
2011; Hansen et al., 2016; Cally, 2011), thus Stangalini et al. (2020)
speculated on the possible role of the mode conversion and magnetic field
geometry in the appearance of magnetic waves at chromospheric heights. In
support of this scenario, Grant et al. (2018) uncovered evidence for Alfvénic
waves, with the observed signatures being consistent with induced
ponderomotive forces at the umbra/penumbra boundary of a sunspot chromosphere,
suggesting that such wave-coupling effects may be linked to the increasing
attack angles found in these locations.

Nevertheless, the Alfvénic waves identified by Stangalini et al. (2020) might
be associated with different wave modes not all necessarily producing the
fractionation, however, they could be considered a proxy to identify the
spatial locations where, given a magnetic field geometry, the conversion of
acoustic-like to magnetic-like waves is particularly efficient.

In addition to the unambiguous identification of the wave process responsible
for the magnetic waves, another important aspect is the propagation direction
of the MHD waves, which plays a significant role in the FIP and I-FIP model of
Laming (2015). Both the equipartition layer and the transition region can
represent a reflective mirror for different types of waves (e.g. Hansen et
al., 2016). For this reason, MHD waves can undergo several
reflections/conversions, thus leaving open both the possibilities of waves
coming from below or above (i.e. due to nanoflares).

In our view, these remain important aspects to be further addressed in the
future, and they may provide useful information to constrain and validate
existing theoretical models. The heuristic method employed in this study
combines the linear extrapolation of photospheric magnetic field and the FIP
bias map to investigate the possible connectivity of the Alfvénic
chromospheric perturbations identified by Stangalini et al. (2020). However,
further studies that involve the full inversion of the chromospheric
spectropolarimetric signals at the location of the perturbations are required
to properly identify the properties of the background and transient magnetic
field.

Hinode is a Japanese mission developed and launched by ISAS/JAXA,
collaborating with NAOJ as a domestic partner, and NASA and STFC (UK) as
international partners. Scientific operation of Hinode is performed by the
Hinode science team organized at ISAS/JAXA. This team mainly consists of
scientists from institutes in the partner countries. Support for the post-
launch operation is provided by JAXA and NAOJ (Japan), STFC (UK), NASA, ESA,
and NSC (Norway). _SDO_ data were obtained courtesy of NASA/_SDO_ and the AIA
and HMI science teams. D.B. and D.S. are funded under STFC consolidated grant
number ST/S000240/1 and L.v.D.G. is partially funded under the same grant.
G.V. acknowledges the support from the European Union’s Horizon 2020 research
and innovation programme under grant agreement No 824135 and of the STFC grant
number ST/T000317/1. The work of D.H.B. was performed under contract to the
Naval Research Laboratory and was funded by the NASA Hinode program. D.B.J.
wishes to thank Invest NI and Randox Laboratories Ltd for the award of a
Research $\&$ Development Grant (059RDEN-1). S.J. acknowledges support from
the European Research Council under the European Unions Horizon 2020 research
and innovation program (grant agreement No. 682462) and from the Research
Council of Norway through its Centres of Excellence scheme (project No.
262622). The authors wish to acknowledge scientific discussions with the Waves
in the Lower Solar Atmosphere (WaLSA; www.WaLSA.team) team, which is supported
by the Research Council of Norway (project number 262622), and The Royal
Society through the award of funding to host the Theo Murphy Discussion
Meeting “High resolution wave dynamics in the lower solar atmosphere” (grant
Hooke18b/SCTM). This research has received funding from the European Union’s
Horizon 2020 Research and Innovation program under grant agreement No 82135
(SOLARNET) and No 739500 (PRE-EST). This research has made use of the IBIS-A
archive. We recognise the collaborative and open nature of knowledge creation
and dissemination, under the control of the academic community as expressed by
Camille Noûs at http://www.cogitamus.fr/indexen.html.

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