# ALMA and IRIS Observations of the Solar Chromosphere II: Structure and
Dynamics of Chromospheric Plage

Georgios Chintzoglou11affiliation: Lockheed Martin Solar & Astrophysics
Laboratory, Palo Alto, CA 94304, USA 22affiliation: University Corporation for
Atmospheric Research, Boulder, CO 80307-3000, USA , Bart De
Pontieu11affiliation: Lockheed Martin Solar & Astrophysics Laboratory, Palo
Alto, CA 94304, USA 44affiliation: Rosseland Center for Solar Physics,
University of Oslo, P.O. Box 1029 Blindern, NO0315, Oslo, Norway
55affiliation: Institute of Theoretical Astrophysics, University of Oslo, P.O.
Box 1029 Blindern, NO0315, Oslo, Norway , Juan Martínez-Sykora11affiliation:
Lockheed Martin Solar & Astrophysics Laboratory, Palo Alto, CA 94304, USA
33affiliation: Bay Area Environmental Research Institute, NASA Research Park,
Moffett Field, CA 94035, USA 44affiliation: Rosseland Center for Solar
Physics, University of Oslo, P.O. Box 1029 Blindern, NO0315, Oslo, Norway ,
Viggo Hansteen11affiliation: Lockheed Martin Solar & Astrophysics Laboratory,
Palo Alto, CA 94304, USA 33affiliation: Bay Area Environmental Research
Institute, NASA Research Park, Moffett Field, CA 94035, USA 44affiliation:
Rosseland Center for Solar Physics, University of Oslo, P.O. Box 1029
Blindern, NO0315, Oslo, Norway 55affiliation: Institute of Theoretical
Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO0315, Oslo, Norway
, Jaime de la Cruz Rodríguez66affiliation: Institute for Solar Physics,
Department of Astronomy, Stockholm University, AlbaNova University Centre,
SE-106 91, Stockholm, Sweden , Mikolaj Szydlarski44affiliation: Rosseland
Center for Solar Physics, University of Oslo, P.O. Box 1029 Blindern, NO0315,
Oslo, Norway 55affiliation: Institute of Theoretical Astrophysics, University
of Oslo, P.O. Box 1029 Blindern, NO0315, Oslo, Norway , Shahin
Jafarzadeh44affiliation: Rosseland Center for Solar Physics, University of
Oslo, P.O. Box 1029 Blindern, NO0315, Oslo, Norway 55affiliation: Institute of
Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO0315,
Oslo, Norway , Sven Wedemeyer44affiliation: Rosseland Center for Solar
Physics, University of Oslo, P.O. Box 1029 Blindern, NO0315, Oslo, Norway
55affiliation: Institute of Theoretical Astrophysics, University of Oslo, P.O.
Box 1029 Blindern, NO0315, Oslo, Norway , Timothy S. Bastian77affiliation:
National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA
22903, USA and Alberto Sainz Dalda11affiliation: Lockheed Martin Solar &
Astrophysics Laboratory, Palo Alto, CA 94304, USA 33affiliation: Bay Area
Environmental Research Institute, NASA Research Park, Moffett Field, CA 94035,
USA 88affiliation: Stanford University, HEPL, 466 Via Ortega, Stanford, CA
94305-4085<EMAIL_ADDRESS>
###### Abstract

We propose and employ a novel empirical method for determining chromospheric
plage regions, which seems to better isolate plage from its surrounding
regions compared to other methods commonly used. We caution that isolating
plage from its immediate surroundings must be done with care in order to
successfully mitigate statistical biases that, for instance, can impact
quantitative comparisons between different chromospheric observables. Using
this methodology, our analysis suggests that $\lambda$=1.25 mm free-free
emission in plage regions observed with _ALMA_ /Band6 may not form in the low
chromosphere as previously thought, but rather in the upper chromospheric
parts of dynamic plage features (such as spicules and other bright
structures), i.e., near geometric heights of transition region temperatures.
We investigate the high degree of similarity between chromospheric plage
features observed in _ALMA_ /Band6 (at 1.25 mm wavelength) and _IRIS_ /Si IV
at 1393 Å. We also show that _IRIS_ /Mg II h and k is not as well correlated
with _ALMA_ /Band6 as was previously thought, and we discuss the discrepancies
with previous works. Lastly, we report indications for chromospheric heating
due to propagating shocks supported by the _ALMA_ /Band6 observations.

##  1 Introduction

The chromosphere is the most complex and remains one of the least understood
layers of the solar atmosphere. It is the layer where the atmosphere
transitions from a plasma-dominated to a magnetic-field-dominated regime. It
is a medium where ion-neutral interactions matter (such as ambipolar
diffusion), and a place in the atmosphere where radiative transfer effects
from departures from local thermodynamic equilibrium (non-LTE) are important.
In addition, the chromosphere is the atmospheric shell through which energy
and mass from the photosphere must pass in order to heat the overlying corona
and power the solar wind.

From a modern (yet historical) observational standpoint, the chromosphere can
be split into three general regions: i.e., (a) active region (AR), sunspots
and surroundings, (b) quiet regions, and (c) regions of “ _plage_ ”. The AR
chromosphere plays a dominant role in the energy release during intense solar
flares. Often, filaments are seen to form and to erupt from neutral lines
produced by flux emergence or decay (e.g., Chintzoglou et al., 2017, 2019).
Sunspots seen in chromospheric wavelengths (e.g., in H$\alpha$) exhibit
“superpenumbras”, i.e., a system of chromospheric fibril-like structures lying
above the penumbra and which are oriented radially outwards, typically
extending beyond the end of the penumbra. Superpenumbras comprise a distinct
region near sunspots, commonly observed in the chromosphere of well-developed
sunspots. The superpenumbral fibrils suggest, in general, a more horizontal
magnetic orientation in the chromosphere, i.e., a canopy-like topology.
Several studies (e.g., Yurchyshyn et al. 2001; Zhang et al. 2003) have
explored the association of superpenumbras with moving magnetic features
(MMFs; Harvey & Harvey 1973) rushing radially outwards from sunspots in the
photosphere.

A major aspect of the physics of the quiet chromosphere is the ubiquitous
presence of shocks, propagating from the photosphere upwards (Carlsson &
Stein, 1997). Such shocks may play an important role in energizing the quiet
chromosphere. However, the most conspiquous features of the quiet chromosphere
are the so-called spicules (Secchi, 1877). Spicules are jets of chromospheric
material seen as rooted at the chromospheric network. About a decade ago, a
new class of spicules, known as “Type-II spicules”, was found in high-
resolution imaging observations taken at the Ca II H line (De Pontieu et al.,
2007b). These structures are more slender (apparent widths $\approx 1\arcsec$)
and exhibit higher plane-of-the-sky speeds ($\approx 50-100$ km s-1) than
their “traditional” counterparts.

Chromospheric _plages_ are regions of higher intensity in chromospheric lines
(e.g., traditionally in Ca II H&K, or H$\alpha$) with stronger magnetic fields
as compared to the typical quiet Sun, but weaker if compared to those in a
sunspot chromosphere. Therefore, plages can be viewed as areas in the solar
chromosphere that are intermediate between sunspots and the quiet Sun
conditions. In such plage regions we find short and dynamic structures called
“dynamic fibrils”, which are driven by slow-mode magnetoacoustic shocks that
propagate from the photosphere to the chromosphere and beyond (Hansteen et
al., 2006; De Pontieu et al., 2007a; Skogsrud et al., 2016; Carlsson et al.,
2019).

The definition of plage has never been done strictly; it was – and remains – a
loose observational term. Deslandres (1893) first used the term “plage”
metaphorically (which in French means “the beach” or “seashore”), to help
explain his interpretation that such bright regions seen in his early Ca II H
and K full-disk spectroheliograms correspond to elevated structures sticking
out of the photosphere, in an analogy to sandy beaches emerging from (and
appearing brighter than) the ocean111As it appears, Deslandres introduced the
term _plage_ to Solar Physics rather unintentionally, because after a full
paragraph of using that term (as a metaphor) he concluded that these bright
chromospheric regions shall be named “ _flammes faculaires_ ” (i.e., “facular
flames”, due to the association with faculae in the photosphere; Deslandres
1893).. As a result of this loosely-defined term that so poetically describes
regions with higher intensity of chromospheric lines as compared to those in
the typical quiet Sun, early and modern observers have been determining such
areas on the Sun with a relative freedom; either (a) “by eye”, i.e., manual
definition of the boundaries of a plage region (for a recent example see,
e.g., Carlsson et al. 2015); or, (b) in a quantitative manner, i.e., by
selecting a certain intensity threshold for a chromospheric image, or even an
area of moderately intense magnetic fields (e.g., Jafarzadeh et al. 2019 and
references therein). With the present paper we raise caution in that the exact
method of identifying and isolating plage from its immediate surroundings
(e.g., sunspots, pores, quiet Sun) can introduce statistical biases which can
have a significant impact on quantitative comparisons between chromospheric
observables (see § 3, § 4.1.1.1, § 5, and APPENDIX).

Quantitative comparisons between different observed diagnostics are a key way
to study the physics of the chromospheric plasmas and to understand the
diagnostic power of various chromospheric observables. Recently, the _Atacama
Large Millimeter/submillimeter Array_ (_ALMA_ ; Wootten & Thompson 2009) has
offered its unique capability in producing high-resolution ($<1\arcsec$) and
fast time-cadence (2 sec) imaging of free-free emission (from chromospheric
electrons) in the millimetric (mm) part of the spectrum.

Under chromospheric conditions the source function, $S_{\lambda}$, of the
free-free emission at mm-wavelengths is in LTE and so the source function is
the Planckian, $S_{\lambda}=B_{\lambda}(T)$. In addition, since the radiation
is in mm-wavelengths (i.e., low frequencies) the Rayleigh-Jeans approximation
holds true, which dictates that the source function is linearly proportional
to the blackbody temperature. This mm-emission becomes optically thick over a
rather narrow width of heights. Given that, we can measure the “brightness
temperature”, $T_{b}$, i.e., a temperature a blackbody would have to match the
brightness of the observed emission. $T_{b}$ can thus be used to infer the
local plasma temperature. The local conditions producing the optically-thick
free-free emission can originate from quite a wide range of geometric heights.
Additionally, the formation height depends on the electron density, which is
also expected to vary wildly in the chromosphere. Conversely, we do not know
the exact height where the free-free emission becomes optically thick and
therefore, we do not know where exactly $T_{b}$ is measured (Carlsson & Stein,
2002; Wedemeyer-Böhm et al., 2007; Loukitcheva et al., 2015; Rutten, 2017;
Martínez-Sykora et al., 2020). Rutten (2017) argued that _ALMA_ mm-emission
should be dominated by fibrils and spicules along the canopy as typically seen
in H$\alpha$ or with even higher opacities. In the present paper we are taking
advantage of the high spatial resolution _ALMA_ observations at $\lambda$=1.25
mm and address the formation height problem for this free-free mm-emission.

Bastian et al. (2017) presented the first quantitative comparison between UV
chromospheric emission and _ALMA_ free-free emission. These authors explored
how well the $T_{b}$ measured with _ALMA_ at 1.25 mm correlate with the
average chromospheric radiative temperatures, $T_{\rm rad}$, inferred by
converting the average _IRIS_ /Mg II h2v and h2r peak intensities,
$I_{\lambda}$, into $T_{\rm rad}$ via the Planck function:

$T_{\rm
rad}=\frac{hc}{k_{B}\lambda}\frac{1}{ln(\frac{2hc^{2}}{\lambda^{5}I_{\lambda}}+1)}$
(1)

where, $c$, the speed of light, $h$, the Planck’s constant, and, $\lambda$,
the average wavelength position of Mg II h2v and h2r peaks. This study
reported a positive correlation with some scatter mainly attributed to the
expectation that $T_{\rm rad}$ might not be perfectly correlated with $T_{b}$,
since the source function for Mg II h2v/h2r decouples from the local
temperature with increasing height in the atmosphere (because Mg II k&h are
scattering lines). Similar results were found by Jafarzadeh et al. (2019)
using the same _ALMA_ /_IRIS_ observations as in Bastian et al. (2018)
although they studied correlations between _ALMA_ /Band6 $T_{b}$ with $T_{\rm
rad}$ from Mg II but for each of its h and k line features individually. da
Silva Santos et al. (2020) performed inversions of _IRIS_ observations and
used _ALMA_ data as an additional constraint. Apart from several low
temperature regions they also found high temperature regions which seem to be
associated with shocks pervading the chromosphere. Wedemeyer et al. (2020)
presented _ALMA_ /Band3 interferometric maps and discussed the potential of
such observations for the study of the dynamic chromosphere on small scales
(such as small loops).

In this paper, we composed and analyzed a unique and comprehensive dataset
from joint observations with _ALMA_ , the _Interface Region Imaging
Spectrograph_ (_IRIS_ ; De Pontieu et al. 2014), and the _Solar Dynamics
Observatory_ (_SDO_ ; Pesnell et al. 2012). Our dataset is most appropriate
for investigating the rich dynamics of the solar chromosphere and transition
region in plage and its peripheral areas – including spicules and
chromospheric shocks – thanks to the synergy of high spatial and temporal
resolution of spectral and imaging observations by _IRIS_ with fast time-
cadence and unique temperature diagnostic capabilities from _ALMA_
interferometric observations. A companion publication (Paper I; Chintzoglou et
al 2020a) focuses on the evolution of a spicule in the western part of the
_IRIS_ raster. Here, using the same dataset, we focus on the general structure
and the dynamics of chromospheric plage. Since some of our results show
discrepancies with those reported by several previous studies, we perform and
present a thorough comparison to elucidate the reasons behind the
discrepancies. For carrying this investigation, we introduced a novel
empirical methodology to better determine the boundaries of regions of plage
in the observations and we also employed a state-of-the-art numerical model to
synthesize observables for comparison with the observations.

This paper is structured as follows: in § 2 we provide a description of the
observations and the model used in this work. In § 3 we describe our proposed
methodology for the determination of pure regions of plage, and in § 4 we
continue with our analysis and presentation of our results, followed by a
discussion of the discrepancies in § 5. We close with our summary and
conclusions in § 6.

##  2 Observations and Modeling

We observed a plage region in the leading part of NOAA AR12651 on 22-Apr-2017,
at heliographic coordinates N11$\arcdeg$E17$\arcdeg$, or at
($x$,$y$)=(-260$\arcsec$, 265$\arcsec$) in helioprojective coordinates (Figure
1a Paper I). The overall spatial distribution of the plage fields in the
target appeared semicircular in shape, as organized around the outer boundary
of a supergranule (Figure 1b Paper I). The common _IRIS_ -_ALMA_ field of view
(FOV) contained part of that plage, including a photospheric pore (e.g.,
Figure 1c Paper I). A very high degree of similarity between morphological
structures seen in _ALMA_ /Band6 maps and _IRIS_ /SJI 1400 Å images was
evident in our observations (Figure 1 of Paper I). We address the origin of
this outstanding similarity in § 4.1. For additional details regarding the
reduction of the _IRIS_ and _ALMA_ observations used here refer to § 2 of
Paper I. _ALMA_ captures in ultra-high cadence (2 s) dynamics in plage and
interesting evolution of linear-like structures, including indications for
shocks in the region of plage. In this work, we address the nature of the high
correlation we found between spatially-resolved features seen in _IRIS_ /Si IV
and _ALMA_ /Band6 and in other observables both in the observations and in the
model (§ 4.1).

###  2.1 General Morphology of the Dynamic Plage in _IRIS_ and _ALMA_ /Band6
Observations

To a top-level view, the chromospheric intensities in the observables (Figure
1) are brightest in the strongly magnetized regions and dimmer in the
interloping weakly magnetized area. Our _ALMA_ /_IRIS_ raster FOV contains
plage in the north and south parts but also contains the outskirts of plage,
i.e., plage “periphery”. For context imaging and for an image of the overal
magnetic distrinution in our target region see Figure 1b of Paper I. Here, we
address the physics of plage and the problem of defining regions of plage.
Therefore, we study the full FOV as well as the individual parts in the FOV
that are designated as (a) plage and (b) plage periphery (see following
sections). Last, in the same Figure 1 we indicate locations of intensity
features in SI IV 1392 Å rasters that show outstanding similarities (intensity
correlations) with _ALMA_ /Band6 (boxed regions). Remarkably, these regions
appear to be weakly correlated, or even found in anti-correlation between Mg
II 2796 Å rasters and _ALMA_ /Band6. We address the origin of this finding
with a rigorous analysis of the observations and we discuss the physical
implications using an advanced MHD model in § 4.

###  2.2 Bifrost Simulation of Dynamic Plage and Synthesis of _ALMA_ and
_IRIS_ Observables

The simulation analyzed in this paper produces Type-II spicules in several
locations in the computational domain, in-between regions of emerging flux and
plage (the latter containing dynamic fibrils). Additional details regarding
the simulation and the synthesis of observables can be found in Paper I and in
Martínez-Sykora et al. (2020a).

In order to perform a comparison of the physics and the evolution of the
observed plage and its periphery with those in the simulation, we focus on two
particular regions, (1) a low magnetic flux “spicule region” at $x=[40,45]$ Mm
(seen to develop at a favorable angle with the line of sight (LOS), Figure
2ab, annotated and pointed with arrows); and (2) a “fibril region” at
$x=[25,35]$ Mm above a stronger flux concentration (containing a dynamic
fibril). Thus, region (1) and (2) represent a plage periphery and a plage
region respectively, as appropriate to compare with our _IRIS-ALMA_
observations of plage and its periphery near disk center. The viewing geometry
chosen was for an “observer” looking from above down on the domain (i.e.,
assuming a LOS along the vertical direction in the simulation). In Figure 2 we
show space-time plots (hereafter, $x-t$) for _ALMA_ /Band6 (panel c), Mg II in
a wavelength range of 0.7 Å centered at the k3 rest wavelength (2796.35 Å;
panel e), and Si IV 1393 Å (panel g). We assume that the observed spicule’s
orientation is not such that our LOS intersects it perpendicularly over its
length, as the latter seems an extreme case for its orientation (likewise for
the case where the spicule is viewed along its axis). Thus, our geometry in
the model seems reasonable for the interpretation of the observations.”

##  3 An Empirical Method for Determining and Characterizing Areas of Plage

Chromospheric plage could be defined as the region of high chromospheric
intensities above magnetic spatial distributions, with stronger magnetic flux
than in the quiet Sun but weaker than that of sunspots and photospheric pores.
An observer can determine such areas either (a) “by eye” and cutting out a
region manually (e.g., as in Carlsson et al. 2015), or (b) in a quantitative
manner, i.e., by selecting a certain intensity threshold for a chromospheric
image, or even an area of moderately intense magnetic fields. However, since
we are interested in quantitative comparisons between different observables in
plage regions, care must be taken to exclude features that are not classified
as plage. Thus we should exclude: (i) photospheric pores, which may often form
sporadically in plage by random convergence of unipolar magnetic fields; and
(ii) dark fibrils or other small and cool filamentary structures often seen in
the vicinity of sunspot penumbras/superpenumbras. Therefore, in the present
study we consider plage to be the hot magnetic canopy above photospheric
magnetic concentrations typical for plage. We have been cautious to not
include other elements such as pores or the superpenumbra from nearby spots.

The flux-segmented (or thresholded) magnetograms were produced by clipping
values at $\pm$0.1 kG to distinguish between strongly and weakly magnetized
areas. We use the segmented magnetograms as a visual guide to aid the
determination of plage in our chromospheric observables. This confirms that
the FOV is naturally split into two distinct plage regions (one north and one
south in the FOV) separated by a weakly magnetized region in the middle. With
this in mind and given (i) the several linear-like structures (and spicule;
see Paper I) present in that quieter area, and, (ii) due to the small size of
the raster along the $x$-direction (5$\arcsec$), combined with (iii) the
knowledge that plage and magnetic fields reside at the west just outside the
raster FOV (Figure 1b of Paper I), we conclude that this middle region is part
of the _periphery_ of that same plage. We also note that the entire plage is
at sun-center angle of $\approx 20\arcdeg$. Here, our common _ALMA_ /_IRIS_
FOV contains just the east boundaries of this plage region. This simplifies
our task in determining the true chromospheric boundary of our plage on only
one side. However, we caution of possible systematic geometric offsets between
the boundaries of extended plage regions, e.g., if they were defined in the
photosphere (via a thresholded magnetogram maps), and used to describe the
boundaries of the higher-lying chromospheric plage area.

We inspected imaging in the continuum from _IRIS_ /SJI Mg II 2832 Å which
clearly shows the existence of a photospheric pore within the north part of
plage in the common _IRIS_ -_ALMA_ FOV. The pore is persistent for the most
part of the _IRIS_ -_ALMA_ /Band6 co-observations. Here we caution that
excluding the pore from the chromospheric plage pixels with the use of a
threshold on magnetogram maps is not a straightforward task. A pore’s area
determined at the photosphere is likely a smaller area than the pore’s
associated area at chromospheric heights due to lateral expansion/“fanning” of
the pore’s magnetic field with height. To properly remedy this issue, we
employ the _ALMA_ /Band6 maps222We note that any of the Mg II, Si IV, or C II
raster maps from _IRIS_ could be used equally well to remove the chromospheric
counterpart of the photospheric pore for a choice of threshold. However, since
_ALMA_ /Band6 maps are produced with an irregular resolution element, i.e.,
the so-called “beam”, here we make a mask from Band6 to further restrict the
accidental inclusion of lower $T_{b}$ values in our comparisons due to spatial
smearing from the beam. segmented at a low threshold $T_{b}\geq 6,500$ K. This
approach effectively removes the chromospheric counterpart of the pore in
plage. The final result from the application of our method can be seen in the
top panel of Figure 3, where we overplot on the _SDO_ /HMI map the regions of
plage within red contour and with orange contours showing the excluded area
above the pore region. The plage periphery is the area within the blue colored
contour where linear-like structures and spicules are seen to develop against
a significantly darker (and quiet-sun-like) background (see Paper I).

We summarize the observational quantities and requirements to define plage:

  * •

photospheric magnetogram to be used as a guide (threshold choice at $\pm$0.1
kG, although similar results can be found for even lower thresholds),

  * •

continuum maps to properly identify areas of pores within plage or sunspot
penumbras,

  * •

chromospheric intensity maps (e.g., Mg II or any other chromospheric
observable) to remove pores with proper intensity thresholds above the
identified regions of pores,

  * •

avoid the vicinity of well-developed sunspots, i.e., regions of sunspot
superpenumbra which typically extend further out than the sunspot penumbra.

By carefully considering these criteria we can determine “clean” regions of
chromospheric plage. As we show in the following paragraphs, when these are
not taken into consideration simultaneously, sources of bias appear which lead
to discrepancies between our results and previous studies.

##  4 Analysis and Results

###  4.1 Understanding the Origin of the Similarities Between _ALMA_ /Band6
and _IRIS_ Observables

The high degree of similarity between _ALMA_ /Band6 and Si IV observables is
illustrated in Figure 1. In that figure we point to locations in the FOV where
_ALMA_ /Band6 emission appears in anti-correlation with Mg II k intensity
patterns (boxed areas in rasters of Figure 1). Here we perform a quantitative
analysis on the degree of similarity between _ALMA_ /Band6 and other
chromospheric and transition region observables from _IRIS_ , to better
understand and constrain the diagnostic potential of _ALMA_ /Band6 as a tool
to measure the temperature of chromospheric plasmas. As we mentioned in § 1,
the actual formation height of _ALMA_ emission is not well known. In
particular, to link this work with previous studies, we first carry the
analysis using (a) observables time-averaged over the entire time-series
(§4.1.1) and we discuss the discrepancies with previous studies. Then we use
(b) observables without averaging in time to also consider the time-evolution
(§4.1.2). We then follow with results of our analysis from the model by
considering both the time-evolution and the height-wavelength dependence of
the _IRIS_ observables (§4.1.3).

####  4.1.1 Quantification of Morphological Similarities Between Observables
Time-Averaged Over the Entire Image Series

Here, we perform an intercomparison between wavelength-integrated rasters in
Si IV 1393 Å, and C II 1335 Å, Mg II k 2796 Å and also with _ALMA_ /Band6.

Comparison between the optically-thick observables _ALMA_ /Band6 $T_{b}$ and
Mg II is typically done with Mg II expressed as radiative temperature, $T_{\rm
rad}$, in units of temperature [K]. Previous studies (e.g., Bastian et al.
2017, 2018; Jafarzadeh et al. 2019) found that the intensity of Mg II k2 or h2
peaks correlates with mm-emission from _ALMA_ /Band6 observations, supporting
the expectation that _ALMA_ /Band6 emission forms at mid-to-low chromospheric
heights. To compare our study with previous works we perform double gaussian
fitting (Schmit et al., 2015) for the Mg II raster data and produce maps
representing each feature of the k and h lines, i.e., k2v, k2r, h2v, h2r, k3,
h3. We compute $T_{\rm rad}$ with eq. (1) for each of these maps. We also
consider the wavelength-integrated Mg II k quantity we produced and used in
the previous sections via eq. (1) and get $T_{\rm rad}$ at each wavelength
position of the rasters separately (between $\Delta\lambda$=0.7 Å from line
center). We then produce the average quantity of $T_{\rm rad}$ representing
the wavelength-integrated Mg II k data, by taking the average of $T_{\rm rad}$
produced in that range. The choice of this $\Delta\lambda$ offers the benefit
of including all line features of Mg II k (i.e., k2v, k2r, and k3) without
extending too much into the line continuum.

For the wavelength-averaged optically-thin observables, computing $T_{\rm
rad}$ is physically meaningless. We keep the observed values expressed in
arbitrary intensity units [DN s-1]. For Si IV, the integration was performed
for each frame in these rasters in a wavelength range of 0.2 Å. In order to
increase the S/N in the C II raster we sum both lines (each centered at 1334.5
Å and 1335.7 Å), and then integrate the sum in wavelength over 0.2 Å. The C II
(not always optically-thick so we keep it in [DN s-1]) rasters suffer from low
counts making the presence of hot pixels more impactful in the statistics,
with plenty of hot pixels being visible in the map from the average C II image
series. We determined that the hot pixels can be extracted easily, since their
values exceeded the values from persistent structures owing to real C II
signal. Thus, at each frame, we remove any hot pixels exceeding 10 DN s-1 and
substitute the resulting missing pixel values via linear interpolation from
values of the immediate neighboring pixels. While significant noise was still
present in each frame due to low photon counts, the inspection of the time-
averaged map before and after the removal of hot pixels showed that the S/N
was improved satisfactorily.

A common approach in multi-wavelength studies utilizing data from different
observatories/instruments is to ensure that any time-differences in the image
series between different observables are: (1) properly matched/synchronized;
and (2) small enough and appropriate for addressing particular science
questions. Both are required to effectively “freeze-in-time” the plasma
evolution between all the different wavelengths. This becomes a serious
concern in studies of the highly dynamic chromosphere, such as the one we
report in the present work. Here, we match our _ALMA_ /Band6 2 s-cadence
series by composing “rasters” that match the time of each slit sampling
position to within $\pm$1 s. We have also performed the analysis presented
here by selecting the frame at the time corresponding to the middle of each
raster scan (raster cadence 26 s, resulting to $\pm$13 s time-difference) but
found no significant change in our results (i.e., of order $\sim$ 1%). This
presents an improvement as compared to previous studies (e.g., Bastian et al.
2018; Jafarzadeh et al. 2019), where the minimization of time-differences was
limited due to the data series used, resulting in a highly variable time-
matching between _ALMA-IRIS_ observables (i.e., 0.5-2 min). In particular,
Jafarzadeh et al. (2019) acknowledge that significant evolution may be ongoing
during this period of time between the sampling of the _ALMA-IRIS_
observables, and also reported findings by a separate analysis where the time
difference was strictly chosen to be 0.5 min (marginally improving the
agreement between _ALMA-IRIS_ observables). Here, with a maximal difference of
$\pm$1 s we “freeze” the plasma evolution consistently and successfully
between each observable over our entire _ALMA-IRIS_ image series. However,
since the C II rasters have low photon counts, in this subsection we restrict
the comparison between time-averaged rasters over the entire _IRIS_ -_ALMA_
/Band6 common time series (for a time-dependent study _ALMA_ /Band6 and _IRIS_
Mg II k and Si IV see next subsection § 4.1.2).

To perform a fair comparison with _ALMA_ /Band6, we degrade the wavelength-
integrated _IRIS_ raster maps by convolving them with the Band6 beam size and
respective position angle at each time frame of our series. Finally, we apply
4-pixel binning along the slit direction for each observable to additionally
increase the S/N. The resulting Band6-beam-degraded and time-averaged _IRIS_
maps (before and after 4-pixel binning) are shown in the top panels of Figure
3. In the panels before binning (top left) we can see some cosmetic artifacts,
namely a dark line due to the fiducial point which blocks the light in the
slit, in addition to a linear-shaped intensity depression (mostly seen in the
FUV observables), which appears similar to the shadow produced by the fiducial
point. In our analysis, we mask out and exclude these two rectangular areas
(see dark bands along the $x$-direction in the 4-pixel binned maps).

#####  4.1.1.1 Quantitative Comparison Between Time-Averaged Observables in
Plage and its Periphery

At first sight, the similarity between C II and _ALMA_ /Band6 is striking. We
proceed by calculating the linear correlation coefficent (Pearson r, hereafter
“C.C.”) between each of the four observables (i) inside the plage region, (ii)
inside the region containing the periphery of plage, and (iii) for the full
FOV in the rasters mixing together plage with its periphery, first with the
presence of the pore (the respective C.C. values for each region are shown
within black boxes at the top of each scatter plot). Then we also calculate
the C.C. for regions (i) and (iii), after the pore area is excluded in each of
the observables (values shown within the dashed orange boxes in each scatter
plot; region (ii) is obviously unaffected from the removal of the pore
pixels). The inclusion of this low temperature _ALMA_ /Band6 region in the
calculation of the C.C. for plage and for the full FOV can be readily seen to
influence the values presented in the scatter plots in Figure 3abc. The pixels
in the region above the pore produce a clear “spire”-like feature or a “tail
of points” towards low _ALMA_ /Band6 $T_{b}$ values (i.e., $4,000\leq
T_{b}\leq 6,500$ K, i.e., our $T_{b}$ threshold choice for producing the pore
mask is fully consistent with representing this feauture). Removing those
pixels with the application of the pore mask improves the C.C. for the full
FOV and plage significantly (red points marked with an orange “$\times$”
symbol). However, we caution that the C.C. obtained over the full FOV leads to
different results since it mixes plage regions with much quieter regions in
the plage periphery, i.e., regions with very different physical conditions.

We first focus our analysis and discussion for the plage (excluding the pixels
above the photospheric pore) and periphery regions separately and keep the
analysis for the full FOV to link our work to previous studies. To facilitate
the presentation of the results, in the bottom panels of Figure 3 we organize
the various C.C. values obtained from each combination of the observables with
the aid of correlation matrices. The correlation matrix for plage shows that C
II is highly correlated with all other observables (C.C. ranging 0.73 to
0.79). In contrast to that, the observable with the lowest correlation between
observables in plage is Mg II k $T_{\rm rad}$. _ALMA_ /Band6 and Si IV and C
II form a triad with the highest C.C.. Perhaps this should not be a surprise,
since these high values are fully consistent with Si IV and _ALMA_ /Band6
forming close to each other, thus probing similar structures. In addition, we
emphasize that the Mg II $T_{\rm rad}$ is averaged over 0.7 Å so that it mixes
information from a wide range of heights. We note that if we use the
wavelength-averaged Mg II k time-averaged map expressed in intensity [DN
sec-1] instead of $T_{\rm rad}$ in [K] our results in the correlation study we
present here do not change beyond a few percent. In addition we emphasize that
if we impose thresholded magnetogram masks for the plage areas the results do
not change beyond 3-5% which further confirms the rubustness of our
methodology described in § 3.

The similarity between C II with Si IV has been mentioned previously in visual
comparisons between _IRIS_ C II, Si IV and Mg II rasters (e.g., Rathore et al.
2015a). In a study by Rathore et al. (2015b) (e.g., Figure 17 therein), Si IV
was found to form consistently higher (having normally a formation height in
the transition region, around $T\approx$80,000 K) than Mg II and C II,
although C II was found to form at heights either above or below Mg II k3.
However, it was also noted that C II primarily formed above the formation
height of Mg II.

Our results in the correlation matrix for plage (Figure 3) support this
finding, given that C II shows very high correlation with _ALMA_ /Band6 and Si
IV, the later being understood as all these observables have formation heights
relatively close to each other, effectively sampling the conditions along
similar parts of structures above plage. Mg II k $T_{\rm rad}$ seems poorly
correlated with all other observables but C II, suggesting that C II forms
above Mg II k but between Mg II k and _ALMA_ /Band6 and Si IV. To this we
should add that the interesting anti-correlation seen between maps of Mg II k
and _ALMA_ /Band6 and Si IV in certain locations of the FOV (Figure 1; boxed
regions in plage), presumably due to enhanced absorption, may have the effect
of weakening the correlation of Mg II k with the other observables.

The correlation matrix for the periphery of plage shows a similar picture. The
C.C. between C II and the other three observables remains the highest as
compared to any other combination of three (out of four) observables. The
significant strength of the correlations with C II for the periphery appears
consistent with the results of Rathore et al. (2015b), which place the
formation height of C II higher than Mg II and thus closer to Si IV in the
fibril regions (Figure 18 therein). Note, however, that Rathore et al. (2015b)
did not average Mg II k over 0.7 Å. The periphery of plage here contains
several linear-like structures, which suggest similar geometry as in the
simulations shown in Rathore et al. (2015b) (e.g., see in our Figure 3 the
persistent thread-like structures in the time-averaged maps). On the other
hand, this region also exhibits low signal in Si IV and _ALMA_ /Band6. This
may explain the significantly lower correlation between Mg II, Si IV, and
_ALMA_ /Band6 as compared to that in plage, since Mg II intensity seems more
diffuse in that region. For completeness, we also note here that a study of
correlations between C II $T_{\rm rad}$ and _ALMA_ /Band6 $T_{b}$ was
performed by Jafarzadeh et al. (2019) and also found a high Pearson C.C. of
0.83, although it was mentioned there that the origin of this high correlation
with _ALMA_ /Band6 was not understood.

Since our results are in contrast with previous studies we further discuss the
reasons behind the discrepancies in a separate paragraph § 5.

####  4.1.2 Time-Dependent Quantitative Study of Morphological Similarities
Between Observables

We note that during the time range of co-observations with _ALMA_ /Band6,
significant evolution was ongoing over the entire FOV. To get a clearer
picture and to assess the similarities by considering the dynamic evolution in
the common FOV, we further focus this analysis on Si IV and Mg II, which,
thanks to the higher photon counts, can be used to explore correlations with
_ALMA_ /Band6 at each time-step of our comprehensive dataset.

In order to determine which regions in the common _IRIS_ -_ALMA_ FOV exhibit
high morphological similarities between our set of observables, we split the
FOV in sub-regions, or “correlation bins”, and we measure the C.C. between the
different observables at each time step of our series. In the top panels of
Figure 4 we show the size of the correlation bins on time-averaged,
wavelength-integrated maps degraded with the _ALMA_ /Band6 beam and position
angle. Furthermore, we distinguish the sign of the C.C. – positive C.C.,
denoting positive correlation of the intensities, and negative C.C.,
representing anti-correlation. The latter will allow us to locate when and
where such anti-correlation between (1) Mg II k, and (2) either Si IV or
_ALMA_ /Band6 occurs. The time-evolution of the C.C. per bin is presented in
the form of time-plots in the bottom panels in Figure 4. For reference, we
also show time-plots of the average time-evolution within the correlation bins
for each of the observables as average intensity per bin. Note that for the
calculation of the C.C. per bin per time-step we did not perform spatial
averaging and we used all the individual pixels within each correlation bin at
each time step. Also note that we have degraded the _IRIS_ observables with
the _ALMA_ /Band6 beam size and position angle.

The resulting time-plots in Figure 4 vividly highlight the similarities and
the differences between the observables. Again, as before, the raster series
is integrated along wavelength centered on each line’s rest wavelength.
Remarkably, the FOV of Mg II k and Si IV is split in locations of positive
correlation and anti-correlation, confirming our initial visual determination
of some locations of anti-correlation between these two observables (e.g.,
Figure 1; boxed regions in rasters). In addition, at times, there are certain
locations where there is strong correlation between the intensities of Mg II k
and Si IV, particularly in the region containing the periphery of plage with
the linear-like structures and the Type-II spicule. However, the most
remarkable finding is the sporadic correlation (both in terms of intensity and
time persistence) of _ALMA_ /Band6 with Mg II k and the very high and more
persistent correlation between _ALMA_ /Band6 with Si IV across the entire FOV,
with only a few instances of anti-correlation. Mg II k is found in anti-
correlation with _ALMA_ /Band6 in several locations in the FOV. The strong
correlation between _ALMA_ /Band6 and Si IV suggests that the spatial extent
of bright features – as projected on the plane of the sky – is similar between
these two observables, supporting that the geometric height of line formation
of _ALMA_ /Band6 and Si IV is similar.

Conversely, Mg II k and _ALMA_ /Band6, even though they are nominally expected
to have similar plasma temperature sensitivity, appear to sample different
geometric heights in the solar chromosphere. This finding is consistent with
the synthetic data from the model (Figure 2). Previous works (e.g., Bastian et
al. 2017) considered that _ALMA_ /Band6 forms at the mid-range of Mg II
formation heights, but as we show later (§ 4.1.3) this does not appear to be
the case for our dataset. This is also supported by our study on time-averaged
observables in the previous subsection § 4.1.1.1. Note, however, that we use
wavelength-averaged rasters, and by averaging in wavelength the diagnostic
information regarding the formation height of the Mg II k line is biased to
lower heights as only Mg II k3 forms at the top of the chromosphere. In fact,
in the Mg II k $x-t$ plot for $\tau=1$ of Figure 2f for the maximum geometric
height, we find a good match with geometric heights for _ALMA_ /Band6
$\tau=1$. However, Mg II k3 forms due to absorption – and thus, rasters in k3
are capturing the maximum absorption in that line. It is therefore our
expectation that when Si IV and _ALMA_ /Band6 show emission in dynamic plage
structures (or spicules), Mg II k3 (which would be closer to _ALMA_ /Band6
heights) has low intensity due to enhanced absorption. This can lead to anti-
correlation with the other observables. We address this in the next section §
4.1.3.

For reasons of completeness, we perform this analysis on the synthetic
observables produced from our model. In this case, since the simulation is
2.5D, the synthetic observables can be likened to a “sit-and-stare” _IRIS_
observation, capturing the evolution across a “static 1D slit”. In Figure 5 we
show the results. In the top panels we show how we split the domain in
correlation bins (here, the bins are essentially 1D, arranged along the
simulation domain’s $x$-direction at each time-step). As in the previous
sections, the data have been degraded from the simulation’s scale size, 14 km
(grid point)-1, via gaussian convolution to adopt the nominal spatial
resolution of _IRIS_ rasters (0$\farcs$16 pix-1 along y-direction) and _ALMA_
(degraded with the Band6 maximum beam size of $0\farcs 8$). Then we further
degrade the synthetic _IRIS_ data by convolving the _ALMA_ /Band6 beam size.
In addition, we have masked out the location of emerging flux, which
effectively separates the “spicules region” at the top of the FOV from the
“plage region” at the bottom. The photospheric $B_{z}$ shows significantly
higher magnetic field strength for the plage region as compared to that in
other locations of the domain (i.e., of order $\approx$100 G). Since we used
the same “correlation bin” width with the observations in Figure 4, only a few
bins cover the domain in these time-plots. However, qualitatively, we get the
same picture as before.

In Figure 5 we highlight the region of spicules with a solid ellipse and we
use a dotted ellipse for the plage. For Mg II k and Si IV we see primarily
anti-correlation for the plage region (compare PC1 dashed ellipse with solid
PA1) and an alternation of correlation and anti-correlation for the spicule
region (compare solid ellipses SC1 and SA1). The latter seems consistent with
Figure 4 where the plage region in Mg II k and Si IV was more anti-correlated
and showed a more intermixed correlation/anti-correlation for the plage
periphery/spicule region (i.e., the anti-correlation plot in the observations
shows less strong anti-correlation as compared to the plage regions north and
south of the raster’s FOV). For _ALMA_ /Band6 and Si IV we primarily see
strong correlation for the plage (Figure 5; compare dotted ellipse PC2 with
PA2), and some alternation between correlation and anti-correlation (with
clear correlation during the time of the network jet, after $t$=3,600 s) for
the spicule region (compare area of solid ellipses SC2 with SA2). Last, for Mg
II k and _ALMA_ /Band6, we see anti-correlation for the plage region (compare
PA3 with PC3), but a somewhat sporadic occurrence of correlation for the plage
periphery/spicule region (compare area in solid ellipses SC3 with SA3; also
positive correlation during the time of the network jet) intermixed in areas
of anti-correlation, again in general agreement with previous comparison
between _ALMA_ /Band6 and _IRIS_ obervations (Figure 4).

####  4.1.3 Explaining the Morphological Similarities in the Synthetic
Observables

In order to understand this interesting correlation in the observations we
explore the time evolution in the emission and formation height of the
synthetic observables for the region with spicules and plage (Figures 6 and 7,
respectively; also see Paper I for a detailed analysis on the Type-II
spicule). For our discussion here, we select three representative time-steps
along the evolution of a region with spicules and plage in the simulation. In
addition, we select three wavelength positions for Si IV and Mg II k (taken in
velocity space at -13, 0 and +13 km s-1 from the line cores). By doing so, we
capture the wavelength dependence of the formation height of Si IV and Mg II k
during the ascending and the descending phase of the spicule’s evolution (see
also Figure 8 in Paper I). At each time shown in Figures 6 and 7 we provide a
wavelength-space plot (hereafter, “$\lambda-x$”) for Mg II k (i.e., full
spectral profile along the different positions in the simulation domain),
which add relevant information in support of our interpretation presented in
this subsection.

At the ascending phase of spicule 1 ($t$=3,350 s in Figure 6, position
$x=[42,44]$ Mm; spicule 2 has not started forming yet) we get emissivity in Si
IV delineating the spicular column at the blue wing (-13 km s-1; panel a; dark
green-to-white color outlining spicule 1), which closely corresponds to the
height of _ALMA_ /Band6 emission (shown with dark-red-to-white color in all
panels). At the same time, in the area where spicule 2 would eventually
develop (position $x=[40,42]$ Mm) we can see significant Mg II k intensity in
the blue wing (plotted at $\tau=1$) (Figure 6a). In Figure 6d we show the
$\lambda-x$ plot for this time with the Mg II k spectrum at each $x$-position
of the domain, with clear RBE-signatures in the location of formation of
spicule 2. Also, in the blue wing of Si IV (Figure 6a) we see a front at the
tip of the structure delineated by Mg II k intensity (heights around z=2.7
Mm). This is consistent with the effects of a traveling shock waves in the
chromosphere before the full development of a spicule.

At the intermediate time-step shown in Figure 6 ($t$=3,580 s; middle column),
spicule 2 has been fully developed and has almost reached its maximum
elongation (z=5 Mm from the photosphere); most of Si IV emissivity now comes
at the rest wavelength of the line (panel f; dark green-to-white color
outlining spicule 2). Similarly, at the time of maximum elongation, _ALMA_
/Band6 emission delineates the body of spicule 2 (note the close matching of
geometric heights of line formation between _ALMA_ /Band6 and Si IV; dashed
ovals along spicule 2). The spectral profile of the optically thick Mg II
(Figure 6h) shows that the k3 (“dark lanes” in the $\lambda-x$ plot
highlighted with white dotted lines) has shifted at different wavelength
positions accross the spicule (e.g., panels f and g), and the respective
geometric height of $\tau=1$ at those different wavelength positions
delineates different parts of the spicule (see dashed ovals in panels f and
g). In fact, the spicule in Mg II appears as a dark feature (as compared to
other locations in the domain), since the line is in absorption. This is
either due to the increased opacity or due to the lower source function.

In the last time-step shown here ($t$=3,620 s), spicule 2 has already begun to
recede and the occurrence of the network jet brightening along the spicule
strongly enhances the emission in Si IV at the core and in the red wing
(panels j and k). The impulsive heating of the plasma in the spicule is so
intense that forces _ALMA_ /Band6 emission to come from lower heights where
the plasma is cool enough (the spicule’s height seen in _ALMA_ /Band6
effectively drops from z$\approx$5 Mm to z$\approx$3 Mm; shown with arrows in
panels j). At the same time, while significant intensity in Mg II k emanates
from low geometric heights (dashed ovals between z=1 - 1.5 Mm; panels i,j) at
the blue wing and at line core, the Mg II k $\tau=1$ height in the red wing
(panel k) is much greater. There, we can see that Mg II k $\tau=1$ roughly
traces the length of the spicule, albeit in low intensity as compared to other
locations with lower geometric heights (note that the same intensity range is
used for each of the panels). This, again, is a manifestation of increased
absorption. Here, Figure 6 (panel l) reproduces this behavior during the time
of the network jet (pointed by an arrow in that panel).

The simulation captures clearly that the high correlation between spatially-
resolved structures seen in _ALMA_ /Band6 and Si IV is primarily due to the
fact that the respective emissions emerge from similar parts of the same
structure, both largely delineating the spicular column. Therefore, when
observed at the plane of the sky (looking from the top of the simulation
domain in this case, or, in other similar LOS, e.g., off the vertical) the
spicule would manifest in both said observables and the high-intensity
features would show up largely as spatially correlated. We cannot say the
same, however, for Mg II k, as the $\tau=1$ geometric height varies at
different wavelength positions. However, we note a characteristic trend:
during the ascending (descending) phase of the spicule, the $\tau=1$ height at
the blue (red) wing roughly delineates the spicule, albeit as a dark
structure. There is also the following possibility: if the viewing angle (LOS)
was tilted, say by 30$\arcdeg$ off the vertical towards small $x$ (left side
of the domain shown in Figure 6j,k), we would be seeing this effect to develop
as: (i) bright Si IV; (ii) bright _ALMA_ /Band6; and (iii) dark Mg II k, since
the high intensity in Mg II k would be at the root of the spicule and the
emission of (i) and (ii) would be projected against an area of low Mg II k
background emission (e.g., for $x>$44 Mm). This example illustrates one of the
possible reasons that at certain locations in the observations Mg II intensity
is anti-correlated to both Si IV and _ALMA_ /Band6.

The relationship between the ascending/descending phase of mass motions with
Doppler shift and emissivity in Si IV is also seen in the plage region of the
simulation (Figure 7). At $t$=3,400 s a dynamic fibril shoots mass upwards
($x=[27,29]$ Mm), where in the blue wing a “front” of Si IV emissivity is
closely followed by emission in _ALMA_ /Band6 (panel a; dashed oval). Mg II k
intensity comes from greater geometric heights but in absorption, again, in
contrast to other locations in the domain, which are brighter but at much
lower geometric heights ($z\approx$0.5-1 Mm). Similarly, relatively low
intensity is seen at the nominal rest wavelength of Mg II k (panel b). This,
again, pinpoints the reasons behind the anti-correlation we noted between Mg
II k and the well-correlated pair of _ALMA_ /Band6 and Si IV, both in the
simulation and the observations of plage. Moving forward at the times of the
other two time-steps ($t$=3,510 s and 3,580 s), we see a consistent
evolutionary pattern between _ALMA_ /Band6 and Si IV. That is, when the bulk
of the mass in the dynamic fibril stalls, we get emission from Si IV line-core
(panel f) and when the mass is receding back to the surface, Si IV emits in
the red wing, again, closely followed by _ALMA_ /Band6 emission (panel k). We
also note that at those times high intensity in Mg II k comes primarily from
lower heights in the atmosphere (see panels i, j, and dashed oval in panel k).

Therefore, we conclude that _ALMA_ is sensitive to the cool-to-warm plasma
existing at the highest parts of either spicules and dynamic fibrils but just
below their tips. These locations are subject to shocks or other
cooling/heating mechanisms (such as ambipolar heating or cooling by adiabatic
expansion), which may raise the plasma to high temperatures, eventually
causing it to emit in Si IV ($T\approx$80,000 K) or even lower temperatures.
Subsequently, the temperature drops down to a level that _ALMA_ /Band6 is
sensitive to (8,000-10,000 K), in geometric heights not far from those of
transition region temperatures. This finding gives insights on the multi-
thermal nature of spicules (Chintzoglou et al., 2018). All the above result in
the high similarity between Si IV and _ALMA_ /Band6 seen in the observations.
With regards to Mg II k, depending on the viewing angle and on how clearly
such effects are seen against the background, comparisons with the other
observables may show a loss of correlation, or, if there is regularity in the
appearance and positioning of such structures within the FOV, anti-correlation
may also arise (i.e., bright features in one observable/pass band
“complementing” dark structures in another). This seems to be reasonable when
spicules or dynamic fibrils are bright in Si IV and _ALMA_ /Band6 but manifest
as low intensity features in Mg II (due to enhanced absorption and/or due to
low intensity in comparison to Mg II k intensities from other locations; for
the case of dynamic fibrils this may be related to similar effects that were
seen in space-time plots of bright grains in the work of Skogsrud et al.
2016).

###  4.2 Measuring the Temperature Increase in the Aftermath of Shocks Above
Plage

Apart from the weak magnetic flux plage periphery, the common _IRIS_ and
_ALMA_ /Band6 FOV contains parts of a strong magnetic flux plage region that
is very dynamic. In this subsection we focus on the dynamics seen in the plage
region and we explore the potential of _ALMA_ /Band6 observations in measuring
the plasma temperature and its time evolution in regions dominated by the
passage of chromospheric shocks.

Here, with _IRIS_ observing in Mg II k and Si IV we can see the chromospheric
shocks as they propagate higher in the chromosphere/transition region.
Focusing on the north part of the common _IRIS_ and _ALMA_ /Band6 FOV we see a
lot of recurrent activity as brightenings above the plage, and also some
plane-of-the-sky motions of bright dynamic fibrils. Chromospheric plage
exhibits features known as dynamic fibrils, driven by slow-mode
magnetoacoustic shocks which pervade the plage region (Hansteen et al., 2006;
De Pontieu et al., 2007a; Langangen et al., 2008). From our 34 min-long time
series we calculate the autocorrelation at each pixel in the Mg II FOV to
determine locations of activity segmented by the characteristic lifetimes of
the signal, such as intensity modulations caused by chromospheric shocks. da
Silva Santos et al. (2020) have reported a periodicity for shocks in Mg II k
of 3.5 to 4 min in plage. In the areas above plage at Mg II k2v we found
autocorrelation times of $\approx$150-200 s but also some even “slower”
locations of $\approx$300 s. Using this autocorrelation map as a guide we
select a $1\arcsec\times 1\arcsec$ sub-region (corresponding to a 3$\times$6
pixels for _IRIS_ rasters and 6$\times$6 pixels for _ALMA_ /Band6) that is
well within plage (position $(x,y)=(4,17)\arcsec$ in the raster FOV of Figure
1) in order to explore if _ALMA_ can be used to study chromospheric shocks.
Within the selected region, we produce $\lambda-t$ plots for Si II and Mg II k
_IRIS_ rasters and extract the $T_{b}$ from _ALMA_ /Band6. Furthermore, to
improve the contrast in the $\lambda-t$ plots we filter them with an unsharp-
mask image processing operation with a 5-pixel radius. Also, to enhance weak
features that were still not visible in the wings of the lines, we produced
the time-derivative of the direct $\lambda-t$ maps. We present the results in
Figure 8.

As a shock passes through the chromosphere above plage, a typical behavior is
seen in $\lambda-t$ plots of chromospheric lines: a blue-shifted excursion
slowly drifts toward the red wing of the line, until a new blue-shifted
excursion appears again, and so on, producing a “sawtooth” pattern in the
$\lambda-t$ plot. This “sawtooth” pattern is seen in Mg II k $\lambda-t$ with
sudden increases of the intensity in the far blue wing that sweep through the
dark k3 core and then reach the red wing typically with a new enhacement in
the blue wing (Figure 8b; see enhancements above yellow line in the blue
wing). Similarly, blue-shifted enhancements appear in Si IV (Skogsrud et al.,
2016) in tandem with the excursions in Mg II k (Figure 8bd). We overplot the
_ALMA_ /Band6 $T_{b}$ over the $\lambda-t$ plots for the same selected region
above plage. Despite the data gaps in _ALMA_ /Band6 observations, the behavior
of $T_{b}$ jumps is strikingly similar to the wavelength-drift trends due to
the passage of the shocks in the chromosphere. In Figure 8ac we enhance the
signatures of the onsets of shocks in the time-derivative plots and mark them
with arrows. In fact, when looking at the blue wing, the similarity of the
$\lambda-t$ time evolution with _ALMA_ /Band6 is more obvious for Si IV than
for Mg II k (see prominent blueshifts in Si IV $\lambda-t$ plot in areas
pointed by arrows 2,3,4,5 in panel d), which may have to do with the
similarity of _ALMA_ /Band6 mm-emission formation height with Si IV we
determined in the present paper. This result may also be consistent with da
Silva Santos et al. (2020) who through inversions determined that during the
passage of shocks the _ALMA_ /Band6 emission appears to emerge from lower
optical depths.

Our interpretation is that the _ALMA_ /Band6 observations in plage are
sensitive to the localized heating of the upper chromosphere/lower transition
region, produced by the passage of shocks. The jumps in Tb are of order
10%-20% increase from a baseline value of $\approx$ 7,500 K (maximum jump at
8,500 K). The observed decay time down to the baseline value is of order
$\approx$60-120 s. However, note that for Si IV $\lambda-t$ the signal in the
selected pixel position in the raster occasionally becomes poor due to low
photon counts in the FUV range of the _IRIS_ spectrograph. The 3$\times$6
pixels for _IRIS_ seems to improve the signal. We also note that the bright
signatures of shocks seen in the rasters are not confined to one pixel
location and appear to move in the plane of the sky until they fade. Again,
the 3$\times$6 pixel window compensates for the most part of the plane-of-the-
sky motions seen in the movie. There are times when the recurrence of
brightenings took place every $\approx$120 s (at least in the early phase of
the plots; see arrows 1, 2 and 3 in panel b). This may suggest that a given
location above plage may be pervaded by shocks coming from different
directions which arrive at comparable timings. Such occasions may cause the
periodicity patterns to modulate with shorter or even irregular periods. In
addition, note that the spatial resolution of _ALMA_ /Band6 maps is
significantly worse as compared to that of the _IRIS_ rasters (by
approximately one order of magnitude), thus the filling factor of the shock
(at the _ALMA_ /Band6 beam size) is less than 1 (as compared to the spatial
scales resolved with _IRIS_). Therefore, even though such 1000 K-jumps in mm-
emission appear consistent with heating due to shocks suggested by Wedemeyer-
Böhm et al. (2007), we conclude that the true temperature enhancements may be
even higher locally. Nevertheless, our work presents indications for the
localized heating of the chromospheric plasma in plage regions by shocks that
travel through the geometric height of formation of _ALMA_ /Band6 free-free
emission.

##  5 Discussion on the Discrepancies with Previous Studies

The detailed comparison between $T_{\rm rad}$ (EUV) and $T_{b}$ (mm-
wavelengths) in spatially-resolved morphological features has recently became
possible thanks to the high-resolution and high-cadence _ALMA_ observations.
High positive correlations for Mg II $T_{\rm rad}$ and _ALMA_ /Band6 $T_{b}$
have been reported in the literature for regions of plage (e.g., Bastian et
al. 2017, 2018; Jafarzadeh et al. 2019). However, the C.C. we found for Mg II
and _ALMA_ /Band6 (see § 4.1.1.1) lies in the low end of those reported in
previous studies. Below we explore the methodology used in previous studies in
an attempt to replicate the higher C.C. reported for Mg II $T_{\rm rad}$ and
_ALMA_ /Band6 $T_{b}$ and to pinpoint the cause of the discrepancies with our
results.

Bastian et al. (2018) compared $T_{\rm rad}$ of Mg II h to _ALMA_ /Band6
$T_{b}$ and reported a very high, C.C. = 0.80, for plage. To perform a
comparison we should first discuss the differences between our work and that
of Bastian et al. (2018). First, the $T_{\rm rad}$ in Bastian et al. (2018)
was produced from maps of the average $T_{\rm rad}$ of Mg II h2v and h2r by
also including single-peak Mg II h profiles in those maps. Here, we integrated
Mg II k over 0.7 Å. The observing program that obtained the observations in
Bastian et al. (2018) did not allow for a good synchronization between the
_IRIS_ and _ALMA_ observables. In the present study, we obtained _IRIS_
/_ALMA_ observations with a less restrictive observing program to achieve a
minimal time-difference among all observables. We also note that Bastian et
al. (2018) determined plage regions with different criteria than ours (§ 3):
it was based on the visual identification of prominent morphological features
in the FOV (i.e., contours roughly containing high Mg II h2v and h2r average
$T_{\rm rad}$ and $T_{b}$ for plage; Bastian et al. 2017; Figure 1f therein).
Here we employ strict criteria for the definition of plage and its periphery,
based on the methodology presented in § 3. However, given the large
discrepancy in the C.C. (i.e., the C.C. reported in Bastian et al. (2018) is
40% larger than our value), here we also calculate the $T_{\rm rad}$ in the
same way as in Bastian et al. (2017, 2018). That is, we calculated $T_{\rm
rad}$ for the average Mg II h2v and h2r line. After doing so, we found that
the C.C. in that case was even lower, i.e., C.C. = 0.52, yielding an even
larger discrepancy between our results and the results reported in Bastian et
al. (2018) (i.e., 54% larger than our value).

One possibility behind the discrepancy mentioned above is that the visual
criteria employed for the definition of plage in Bastian et al. (2018) allowed
the inclusion of low $T_{\rm rad}$ and $T_{b}$ areas in plage. For instance,
the lower plage mask in Figure 1f of Bastian et al. (2017) clearly shows lower
intensities for the majority of the pixels therein. Thus, such pixels should
not be classified as plage, given the consideration we make in this paper (see
§ 3). The high C.C. of 0.80 that this study reported between Mg II h to _ALMA_
/Band6 $T_{b}$ was obtained for the entire common FOV. We emphasize that such
high correlation is not surprising if we consider the overall similarity over
a diverse set of features present within that FOV, such as plage, sunspot
umbra, and penumbra/superpenumbra, which “as a whole” appear morphologically
similar between Mg II h $T_{\rm rad}$ and _ALMA_ /Band6 $T_{b}$. For example,
if we take the region with sunspot umbra, i.e., a morphological feature that
is darker than the average intensity in the entire FOV in Mg II h, it also
appears dark in _ALMA_ /Band6 (compare Figure 1a and 1c therein). This
equivalence also holds true for the plage regions, which stand out as regions
of higher intensity in either chromospheric observable. Thus, mixing regions
with low $T_{\rm rad}$ and $T_{b}$ (e.g., sunspot umbras, plage periphery,
pores) together with brighter regions and treating this mix as “plage” may
effectively increase the C.C.. A quick comparison between our correlation
matrix for the full FOV (mixed) with that for plage in Figure 3 supports our
view. The mixed correlation matrix treats all plage and plage periphery points
as one population (still excluding the pore). While the C.C. for _ALMA_ /Band6
$T_{b}$ with Mg II k $T_{\rm rad}$ is 0.56 for plage and 0.57 for the
periphery, the calculation for the full FOV increases the value dramatically,
to a C.C. of 0.74, which amounts to 90% of the value reported in Bastian et
al. (2018). The total number of pixels in the plage mask is 650 which finally
becomes 578 pixels after excluding the pore region (recall that we performed
binning of 4 pixels along the y-direction). The total number of points in the
periphery is 480. Thus, the inclusion of an additional 80% of plage periphery
pixels (with about 2/3 showing low intensities) in the designated plage area
made a clear difference in the C.C. between _ALMA_ /Band6 $T_{b}$ and Mg II k.
While we cannot exclude the possibility of additional factors behind this
discrepancy (e.g., variability between different solar regions, different
calibration methods employed in Bastian et al. (2018), and that the pixels in
IRIS and ALMA observations were not selected based on minimal time-difference
constraints), including quieter pixels within plage regions may play a
significant role in increasing the C.C. from a marginal value (0.56) to a
value suggesting high positive correlation (0.80).

The study by Jafarzadeh et al. (2019) focused on _ALMA_ /Band6 and _IRIS_
observations of the same region analyzed in Bastian et al. (2018). This work
also investigated relationships between $T_{b}$ from _ALMA_ /Band6 and $T_{\rm
rad}$ from _IRIS_ Mg II k and h (for each line components), C II, and
intensities of the optically thin Si IV and O I. Their region of plage was
defined with a quantitative method, i.e., as a chromospheric region above
photospheric magnetic fields $\geq\pm$0.2 kG, a threshold value not too
different from the one we use here. Indeed our magnetic map does not change if
we use either $\pm$0.1 kG or $\pm$0.2 kG for thresholds. However, we point out
that their methodology lead to the inclusion of areas in the sunspot
penumbra/superpenumbra that in Bastian et al. (2018) were excluded from their
plage areas. Nevertheless, the region designated as plage in Jafarzadeh et al.
(2019) above that superpenumbra/penumbra comprises the vast majority of the
plage pixels in that work. To this we add that the regions of plage used in
Bastian et al. (2018) are only partially included within the FOV in Jafarzadeh
et al. (2019) (i.e., further reducing the similarity of plage regions selected
for the statistical studies in these two works). All these factors render the
comparison with Bastian et al. (2018) a difficult task. To keep this
discussion focused we moved some details to the APPENDIX.

Contrary to Bastian et al. (2018) who calculated the C.C. between _ALMA_
/Band6 $T_{b}$ and the mean $T_{\rm rad}$ from Mg II h2v and h2r, the C.C.
values in Jafarzadeh et al. (2019) were calculated separately for each
individual line feature of Mg II $T_{\rm rad}$ with _ALMA_ /Band6 $T_{b}$;
namely: for _ALMA_ /Band6 $T_{b}$ vs. $T_{\rm rad}$ Mg II k2v (and k2r) the
C.C. was 0.73 (and 0.80), and 0.68 (0.78) for Mg II h2v (h2r). Comparatively,
the _ALMA_ /Band6 with Mg II k2v (and k2r) was 48% (and 49%) higher than those
calculated from our dataset of plage with line fittting; as for the Mg II h2v
(h2r), that was 39% (42%) higher than our values, respectively. Reconciling
all the differences we mentioned between the work of Jafarzadeh et al. (2019)
and our study and also considering the fact that both studies focused on
pixels with the least time-difference possible, the discrepancies between our
scatter plots and theirs can be understood due to their inclusion of pores or
superpenumbra pixels in their statistics. If we do the same experiment as we
did earlier in our comparison to Bastian et al. (2018) and we include the
periphery in our calculations, then the C.C. reported in Jafarzadeh et al.
(2019) for Mg II k2v (and k2r) is only 7% (and 14%) higher than those
calculated from our dataset; and for the Mg II h2v (and h2r), that is only 2%
(and 11%) higher than ours, respectively. In Figure 3 and Figure 5e of
Jafarzadeh et al. (2019) the _ALMA_ and _IRIS_ maps and the map showing the
mask used for plage is provided. By consulting the time-difference map between
the _ALMA_ and _IRIS_ pixels shown in Figure 4f therein, we can identify
exactly which parts of the plage were used in the scatter plots of Figure 13
therein. There appear to be several locations with radial dark “lanes” or
“streaks” of low $T_{\rm rad}$ and $T_{b}$ around the superpenumbra/penumbra,
and the majority of these pixels were used in the plage scatter plots of
Jafarzadeh et al. (2019). Therefore, it is possible that the similarity of the
results for plage reported by Jafarzadeh et al. (2019) and Bastian et al.
(2018) and their discrepancy with our results may have the same origin: the
difference in the criteria used in distinguishing regions of plage from other
neighboring regions on the Sun.

##  6 Summary & Conclusions

In this work we focused on addressing the nature and the dynamics of
chromospheric/transition region structures found in plage, namely, fibrils,
jet-like features (Type-II spicules are covered in a companion paper,
Chintzoglou et al 2020a) and traveling shocks using high time-cadence and high
spatial resolution data from the _ALMA_ and _IRIS_ observatories. We employed
a 2.5D numerical simulation (Bifrost model) of a plage region considering
ambipolar diffusion in non-equilibrium ionization conditions. We produced
synthetic observables to compare the model with our observations from _ALMA_
/Band6 and _IRIS_. Last, we performed a first-cut study on the heating of the
chromosphere above plage by measuring the brightness temperature modulation
due to passing shocks with _ALMA_ /Band6.

Below we summarize our findings:

  1. 1.

We report a very high degree of similarity for features seen in plage between
_ALMA_ /Band6 and _IRIS_ /SJI 1400 Å and Si IV 1393 Å rasters (Figure 1). We
conclude that _ALMA_ /Band6 is sensitive to the cool plasma at the highest
parts of the spicules and dynamic fibrils (i.e., in plage), which is next
(because of the locally large temperature gradients) to plasma that emits in
Si IV ($T\approx$80,000K, transition region temperatures; this result also
provides support to the work of Rutten 2017).

  2. 2.

We present observations showing anti-correlation between intensity features
seen in Si IV and Mg II _IRIS_ rasters (intensity depressions Mg II k
highlighted in Figure 1) We conclude that the apparent anti-correlation or
lack of correlation has its origin in Mg II opacity effects in plage
structures. Strong absorption is the reason behind the low Mg II intensities
emerging from greater geometric heights in the locations of spicules (Figure
6).

  3. 3.

For plage we report a low linear correlation coefficient
(0.49$\leq$C.C.$\leq$0.55) for _ALMA_ /Band6 $T_{b}$ with Mg II for any of the
k2v/k2r/h2v/h2r line features and a maximum of 0.56 for wavelength-integrated
Mg II k that contains the k2v, k3, k2r line features. Our results are
quantitatively in contrast with previous works (e.g., Bastian et al. 2018, and
Jafarzadeh et al. 2019).We also determined that by including quieter areas in
the plage sample, i.e., considering a mixed area of plage and periphery of
plage as “plage”, it greatly increased the C.C. between _ALMA_ /Band6 $T_{b}$
with $T_{\rm rad}$ from Mg II k and h, producing values as high as those in
Bastian et al. (2018) and Jafarzadeh et al. (2019). We thus caution on the
different criteria employed for defining plage regions, which may skew
quantitative studies of correlations between different observables.

  4. 4.

The definition of the spatial extent of plage is not formally well-defined in
the previous literature. Here, our empirical approach focuses on isolating
plage from its surroundings in a different manner from previous approaches (§
3). We also add that the C.C. is a very sensitive statistical measure. A small
amount of outliers in a scatter plot can greatly affect the C.C. value. Thus
given the high sensitivity of C.C. and its application in cases where plage
cannot be robustly classified with conventional techniques (e.g. due to the
presence of pores, or being too close to sunspot penumbras) we caution that
the C.C. values between $T_{\rm rad}$ and $T_{b}$ in plage can be actually
lower, i.e., as low as those we report in the present paper.

  5. 5.

It has been previously reported (Bastian et al., 2017; Jafarzadeh et al.,
2019) that there is scatter between radiative temperatures from Mg II and
brightness temperatures from _ALMA_ /Band6, with a suggested cause of the
scatter being the decoupling of the Mg II source function from the local
conditions. Our work demonstrates that the scatter is more significant than
previously thought and highlights another reason behind its nature: both the
observations and the simulation suggest that the formation height for _ALMA_
/Band6 emission is above that of Mg II for most wavelengths along the Mg II
line, even though both Mg II and _ALMA_ /Band6 are sensitive to a similar
range of temperatures. This formation height difference can contribute to the
large scatter. We caution that the model should not be taken as a perfect
representation of the plage atmosphere. For example, the distribution of
modeled brightness temperatures of _ALMA_ /Band6 is lower by 2,000 K as
compared to the observations.

  6. 6.

We performed a thorough quantitative study on the similarities between time-
averaged Si IV, C II (wavelength-integrated intensities), Mg II k (average
$T_{\rm rad}$), and _ALMA_ /Band6 ($T_{b}$) maps (Figure 3). We report that
the highest C.C. is obtained between any combination of the triad of Si IV, C
II and _ALMA_ /Band6, the lowest C.C. is obtained between Mg II k - Si IV and
Mg II k - _ALMA_ /Band6. Additionally, C II is found in moderate-to-high C.C.
with all other observables. We conclude that this study provides evidence on
the general tendency for the order of the formation heights of all these
different obsevables with geometric height. That is, Mg II k (wavelength-
integrated) intensity ($T_{\rm rad}$) emerges from lower geometric heights in
the plage atmosphere, with Si IV forming at the greatest heights (with a
formation temperature T$\approx$80,000 K, placing it in the transition
region). The good agreement of C II with all observables is due to having, on
average, a formation height between that of Mg II k and Si IV. This result
seems consistent with the work of Rathore et al. (2015b) based on the analysis
of a numerical simulation.

  7. 7.

We present indications of heating by shocks propagating in the chromosphere
with _ALMA_ /Band6 (beam size $\approx$0$\farcs$7$\times$0$\farcs$8). We found
a repetitive increase-and-decrease of the local chromospheric plasma
temperature above plage of order 10-20% from a basal value of 7,500 K (for
comparison, the temperature for a location in the periphery of plage was found
$\approx$ 5,500 K), with a decay time back to the baseline of about 60-120 s
(Figure 8). We find indications of a recurrence at around 120 s. This may
suggest that a specific location in plage may be pervaded by shocks coming
from different directions and at different timings, leading to intensity (and
$T_{b}$) modulations of shorter (or even irregular) periods. da Silva Santos
et al. (2020) performed inversions of _IRIS_ with _ALMA_ and reported that
emission from shocks in the _ALMA_ /Band6 plage may be coming from lower
optical depths (i.e., higher geometric heights) as compared to weakly
magnetized areas (e.g., plage periphery). This is consistent with our
determination of the formation height for _ALMA_ /Band6, which seems to be
just below that of Si IV.

This work demonstrates the benefits of the synergy between _ALMA_ and _IRIS_
observations, which effectively expanded the diagnostic capabilities of each
observatory, and also tested and provided constrains for advanced numerical
simulations.

This paper makes use of the following _ALMA_ data:
ADS/JAO.ALMA#2016.1.00050.S. _ALMA_ is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint _ALMA_ Observatory is operated by ESO, AUI/NRAO
and NAOJ. We gratefully acknowledge support by NASA contract NNG09FA40C
(IRIS). JMS is also supported by NASA grants NNX17AD33G, 80NSSC18K1285 and NSF
grant AST1714955. VH is supported by NASA grant 80NSSC20K1272. JdlCR is
supported by grants from the Swedish Research Council (2015-03994), the
Swedish National Space Board (128/15) and the Swedish Civil Contingencies
Agency (MSB). This project has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (SUNMAG, grant agreement 759548). MS, SJ and SW are supported by the
SolarALMA project, which has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No. 682462), and by the Research Council of Norway
through its Centres of Excellence scheme, project number 262622. The
simulations and Mg II synthesis were ran on clusters from the Notur project,
and the Pleiades cluster through the computing project s1061, s1630, and s2053
from the High End Computing (HEC) division of NASA. This research is also
supported by the Research Council of Norway through its Centres of Excellence
scheme, project number 262622, and through grants of computing time from the
Programme for Supercomputing. _IRIS_ is a NASA small explorer mission
developed and operated by LMSAL with mission operations executed at NASA Ames
Research center and major contributions to downlink communications funded by
ESA and the Norwegian Space Centre. HMI and AIA are instruments on board _SDO_
, a mission for NASA’s Living with a Star program.

## References

  * Bastian et al. (2017) Bastian, T. S., Chintzoglou, G., De Pontieu, B., et al. 2017, ApJ, 845, L19
  * Bastian et al. (2018) —. 2018, ApJ, 860, L16
  * Carlsson et al. (2019) Carlsson, M., De Pontieu, B., & Hansteen, V. H. 2019, ARA&A, 57, 189
  * Carlsson et al. (2015) Carlsson, M., Leenaarts, J., & De Pontieu, B. 2015, ApJ, 809, L30
  * Carlsson & Stein (1997) Carlsson, M., & Stein, R. F. 1997, ApJ, 481, 500
  * Carlsson & Stein (2002) —. 2002, ApJ, 572, 626
  * Chintzoglou et al. (2018) Chintzoglou, G., De Pontieu, B., Martínez-Sykora, J., et al. 2018, ApJ, 857, 73
  * Chintzoglou et al. (2017) Chintzoglou, G., Vourlidas, A., Savcheva, A., et al. 2017, ApJ, 843, 93
  * Chintzoglou et al. (2019) Chintzoglou, G., Zhang, J., Cheung, M. C. M., & Kazachenko, M. 2019, ApJ, 871, 67
  * da Silva Santos et al. (2020) da Silva Santos, J. M., de la Cruz Rodríguez, J., Leenaarts, J., et al. 2020, A&A, 634, A56
  * De Pontieu et al. (2007a) De Pontieu, B., Hansteen, V. H., Rouppe van der Voort, L., van Noort, M., & Carlsson, M. 2007a, ApJ, 655, 624
  * De Pontieu et al. (2007b) De Pontieu, B., McIntosh, S. W., Carlsson, M., et al. 2007b, Science, 318, 1574
  * De Pontieu et al. (2014) De Pontieu, B., Title, A. M., Lemen, J. R., et al. 2014, Sol. Phys., 289, 2733
  * Deslandres (1893) Deslandres, H. 1893, Knowledge: An Illustrated Magazine of Science, 16, 230
  * Hansteen et al. (2006) Hansteen, V. H., De Pontieu, B., Rouppe van der Voort, L., van Noort, M., & Carlsson, M. 2006, ApJ, 647, L73
  * Harvey & Harvey (1973) Harvey, K., & Harvey, J. 1973, Sol. Phys., 28, 61
  * Jafarzadeh et al. (2019) Jafarzadeh, S., Wedemeyer, S., Szydlarski, M., et al. 2019, A&A, 622, A150
  * Langangen et al. (2008) Langangen, Ø., De Pontieu, B., Carlsson, M., et al. 2008, ApJ, 679, L167
  * Loukitcheva et al. (2015) Loukitcheva, M., Solanki, S. K., Carlsson, M., & White, S. M. 2015, A&A, 575, A15
  * Martínez-Sykora et al. (2020a) Martínez-Sykora, J., De Pontieu, B., de la Cruz Rodriguez, J., & Chintzoglou, G. 2020a, ApJ, 891, L8
  * Martínez-Sykora et al. (2020) Martínez-Sykora, J., Leenaarts, J., De Pontieu, B., et al. 2020b, ApJ, 889, 95
  * Pesnell et al. (2012) Pesnell, W. D., Thompson, B. J., & Chamberlin, P. C. 2012, Sol. Phys., 275, 3
  * Rathore et al. (2015a) Rathore, B., Carlsson, M., Leenaarts, J., & De Pontieu, B. 2015a, ApJ, 811, 81
  * Rathore et al. (2015b) Rathore, B., Pereira, T. M. D., Carlsson, M., & De Pontieu, B. 2015b, ApJ, 814, 70
  * Rutten (2017) Rutten, R. J. 2017, A&A, 598, A89
  * Schmit et al. (2015) Schmit, D., Bryans, P., De Pontieu, B., et al. 2015, ApJ, 811, 127
  * Secchi (1877) Secchi, A. 1877, Le Soleil. Seconde partie. Structure du Soleil (suite) – Activite extérieure (Gauthier Villars, Paris)
  * Skogsrud et al. (2016) Skogsrud, H., Rouppe van der Voort, L., & De Pontieu, B. 2016, ApJ, 817, 124
  * Wedemeyer et al. (2020) Wedemeyer, S., Szydlarski, M., Jafarzadeh, S., et al. 2020, A&A, 635, A71
  * Wedemeyer-Böhm et al. (2007) Wedemeyer-Böhm, S., Ludwig, H. G., Steffen, M., Leenaarts, J., & Freytag, B. 2007, A&A, 471, 977
  * Wootten & Thompson (2009) Wootten, A., & Thompson, A. R. 2009, IEEE Proceedings, 97, 1463
  * Yurchyshyn et al. (2001) Yurchyshyn, V. B., Wang, H., & Goode, P. R. 2001, ApJ, 550, 470
  * Zhang et al. (2003) Zhang, J., Solanki, S. K., & Wang, J. 2003, A&A, 399, 755

Figure 1: Inter-comparison of _IRIS_ and _ALMA_ /Band6 observations at an
intermediate time in our observing window. Raster scans are shown at selected
wavelength positions in Mg II (left panels) and Si IV (right panels) showing
the clear appearance of the rapidly evolving structure in Mg II and Si IV
(dashed circles). Boxed areas denote locations where intensity features in the
Mg II maps appear anti-correlated to those in Si IV and _ALMA_ /Band6 maps. In
the panels with the _SDO_ /HMI magnetogram (scaling clipped at $\pm$250 G) we
overplot an isocontour of $\pm$100 G. The FOV is thus split into two strongly
magnetized areas (north and south of the FOV) separated by a weakly magnetized
area (in the middle). An animated version of this figure can be found in the
online version of the journal.

Figure 2: Synthetic $x-t$ plots from the Bifrost simulation. Left column
panels show a snapshot from the simulation at $t$=3,500 s for (a) $log_{10}T$,
and (b) $log_{10}N_{e}$. Upper panels (c,e,g) show $x-t$ in _ALMA_ /Band6 Tb
(in red), Mg II k (in blue), and Si IV (in green) synthesized intensities,
respectively. Bottom panels (d, f, h) present $x-t$ plots for the geometric
height where $\tau=1$ for _ALMA_ /Band6, maximum $\tau=1$ height for the
wavelength-integrated Mg II k, and the height of maximum emission for Si IV.
Boxed areas denote the regions of spicules (best seen in Si IV) and plage.
With a red line in the $x-t$ plots we mark the time shown in panels (a) and
(b). An animated version of this figure can be found in the online version of
the journal.

Figure 3: Top panels: time-averages of Mg II k ($T_{\rm rad}$), C II, and Si
IV from _IRIS_ , and _ALMA_ /Band6 ($T_{b}$) together with their 4-pixel
binned version along slit (y-axis). In the middle we show the time-averaged
LOS magnetogram (green contour at $\pm$100 G) with the subregions considered
in the correlation plots (red/plage, blue/periphery of plage) and a Mg II 2832
Å SJI map showing the presence of a photospheric pore in the plage region.
Orange contours show pixel area determined as related to the pore, which is
excluded in our analysis. Middle panels (a)-(f): Scatter plots for each
combination of the 4-pix binned average series. Correlation coefficients
(C.C.) are given for (i) points inside the plage area (shown in red), (ii)
points inside the area containing the periphery of plage (blue), and (iii) for
the entire FOV (black) with and without the pixels in the pore region (top and
bottom group of C.C. values, respectively). Note the significantly high
correlation between _ALMA_ /Band6 and C II and Si IV. Bottom panels: C.C.
values excluding the pore pixels organized in correlation matrices. See text
for detailed discussion.

Figure 4: Time evolution of correlation and anti-correlation between Mg II,
_ALMA_ /Band6 and Si IV. The common FOV (covering the center of _ALMA_ /Band6
FOV) is segmented into 18 sub regions (correlation bins) covering both
magnetic and non-magnetic regions (illustrated with time-averaged maps; top
panels). Note that the _IRIS_ image raster series has been degraded with the
_ALMA_ /Band6 beam size and position angle at each individual frame. Bottom
panels: For illustration purposes we show the bin-averaged $x-t$ plot for Mg
II k, _ALMA_ /Band6 and Si IV 1393 Å. Note the clear distinction between areas
of moderate-to-high correlation and anti-correlation between Mg II k, Si IV
1393 Å. Note the very high degree of correlation between Si IV 1393 Å and
_ALMA_ /Band6 across all correlation bins, and the more sporadic distribution
of correlation for Mg II k.

Figure 5: Similar as in Figure 4 with analysis method applied on the synthetic
observables from the simulation. The spatial resolution in the _IRIS_ -_ALMA_
synthetic observables has been degraded accordingly to match the resolution of
each observatory and then degraded _IRIS_ to match _ALMA_ (with an average
_ALMA_ /Band6 beam size of 0$\farcs$8 along the y-direction; x-direction is
the time). The correlation bins have similar physical width across the
y-direction as with previous Figure 4. The emerging flux region is masked out
(blank space) virtually isolating a region of spicules (top region) from a
plage region (bottom region). Note the significant spatial extent of
persistent anti-correlation between synthetic Mg II k and _ALMA_ /Band6
observables.

Figure 6: Maps from the simulation for the region with the spicules, showing
the spatial distribution of _ALMA_ /Band6 emission from the spicules (at the
height of $\tau=1$), along with Si IV emissivity and the Mg II k specific
intensity (at the height of $\tau=1$) at three different wavelength positions
(corresponding to -13, 0, and +13 km s-1) and at three different times (one
per column). Note that at all times (at least until the brightening of the
spicule at 3,620 s, yellow arrow) _ALMA_ /Band6 follows closely the parts of
the spicule emitting in Si IV. At 3,620 s, the brightening occurs when the
spicular mass is receding back to the surface, showing significant emission at
redshifts (+13 km s-1). Bottom row shows the Mg II $\lambda-x$ plot with
colored dotted lines denoting the wavelength positions shown above. The dark
band seen in the spectra is a well-developed k3 component in Mg II k (parts of
it traced by a white dotted line). See text for discussion. An animated
version of this figure can be found in the online version of the journal.

Figure 7: Maps from the simulation for the plage region, showing the spatial
distribution of _ALMA_ /Band6 emission and intensity/emissivity from _IRIS_
observables at three different wavelength positions (corresponding to -13, 0,
and +13 km s-1) and at three different times (one per column, as in previous
Figure 6). Note that the location of _ALMA_ /Band6 emission follows the
locations of emissivity in Si IV more closely than Mg II k intensity, which is
consistent with the high degree of correlation of _ALMA_ /Band6 with Si IV
seen in plage regions both in the simulation and in the observations. As in
the previous figure, the bottom plots show the Mg II $\lambda-x$ plot with
colored dotted lines denoting the wavelength positions shown above. The dark
band seen in the spectra is a well-developed k3 component in Mg II k (traced
in part by a white dotted line). See text for discussion.

Figure 8: Top panels: $\lambda$-t plots for Mg II k (b) and its time
derivative (a) for the selected 1$\arcsec\times$1$\arcsec$ area above a plage
region with recurrent shocks. Bottom panels: Si IV and (d) its corresponding
time derivative (c). The $\lambda$-t panels are unsharp-masked to improve
contrast in the presentation of the figure. In all panels we overplot the
_ALMA_ /Band6 Tb. The error bars correspond to 5% uncertainty in $T_{b}$
values. The rest wavelength position is plotted with a dotted line in all
panels. Note the correlation of increases in Tb and blue shifts suggesting
chromospheric heating due to the passing of shocks in Si IV and Mg II (pointed
by arrows).

##  7 APPENDIX

To improve the readability of the main text we host here part of the
discussion found in § 5 where we highlight the large discrepancies between our
results (and our methodology) with previous studies (e.g., those presented in
Bastian et al. 2018; Jafarzadeh et al. 2019). In particular, here we highlight
the effects due to the inclusion (or insufficient exclusion) of pores in plage
as a source of bias, and we also emphasize our unprecedented time-
synchronization between rapid EUV rasters and rapid mm-emission imaging
observations in comparison to that achieved by previous studies.

In contrast to Bastian et al. (2018), Jafarzadeh et al. (2019) attempt to
remove the pores within the plage by applying a mask derived from an HMI
photospheric magnetogram with magnetic field values $\geq\pm$0.8 kG. However,
we note here that the small size of the pores in that plage cannot be fully
accounted for by the simple application of a mask from a photospheric
magnetogram, due to the natural expansion of fields as they reach chromosperic
and transition region heights. Conversely, this makes any pore region mask
produced from observations at the photosphere to contain only a part of the
associated area higher up, making the safe extraction of pores from the
immediate plage a challenging task. This is due to superposition effects and
confusion along the line of sight of structures in the chromospheric data. The
definition of pore regions within plage in Jafarzadeh et al. (2019) appears to
include real plage signal. In Figures 6 and 7 of Jafarzadeh et al. (2019) we
can see that the pore signal is included in the histograms done for other
regions in the FOV, namely “Penumbra and Pores”, “Sunspot and Pores”, where
the Mg II k2v and k2r and h2v and h2r are clearly skewed to the higher $T_{\rm
rad}$ with a sharp drop at 6,000 K. However, the histograms for “Umbra” and
“Quiet Regions” are clearly skewed to the low end of $T_{\rm rad}$ with a very
gradual drop towards 6,000 K. Thus, they share similarities with the
histograms for “Plage”, justifying our concerns for proper characterization of
plage from non-plage regions. In our work here, while we are not studying the
region above the pore, we are safely excluding it by applying a threshold on
_ALMA_ /Band6 $T_{b}$; this allows to account for the more extended boundaries
of structures as they expand from the photosphere to the chromosphere, leaving
behind a clean map for plage (Figure 3).

Also, we note that Jafarzadeh et al. (2019) distinguished the _ALMA_ /Band6
data into the four sub-bands and only used the one at $\lambda$=1.3 mm,
instead of taking the average of all sub-bands as in Bastian et al. (2018) and
in our present work. Such averaging results to Band6 maps at $\lambda$=1.25
mm. Finally, Jafarzadeh et al. (2019) strived to take into account the time-
differences between the _ALMA_ /Band6 mosaic and the scanning time of the
large _IRIS_ raster. Unfortunately, due to the nature of the mosaicking
scanning process of these particular _ALMA_ /Band6 observations (complicated
since it does not follow the scanning direction of the _IRIS_ raster, which
takes non-trivial amount of time) the authors had only a limited amount of
pixels with a minimal time-difference in their dataset. Thus, despite the
attempts to match the time between pixels from _ALMA_ and _IRIS_ , an adequate
amount of pixels for their statistics was obtained only after allowing for a
variable matching of the sampling time, i.e., spanning 0.5-2 min (Figure 4f in
Jafarzadeh et al. 2019). In addition, the same work explores correlations
between observables by limiting the time-differences to 0.5 min at the expense
of sample number. In comparison, Bastian et al. (2018) did not select pixels
with such criteria, thus significant chromospheric evolution is not captured
in that analysis. As we mentioned in the beginning of § 5, our sampling time
synchronization between datasets is superb, i.e., $\pm$1 s at worst and is
consistent throughout the data series analyzed in our work. This is due to the
fast _IRIS_ raster scanning times (26 s) for this particular observation and
also thanks to the rapid cadence (2 s) of our _ALMA_ /Band6 observations.