1810.05118 journalname

t1Published in Journal of Community Safety and Well-Being, 3(3):105–109. DOI:
10.35502/jcswb.82. Pre-print was previously mentioned on the _Improbable
Research Blog_.

# Canadian Crime Rates in the Penalty Box

Simon<EMAIL_ADDRESS>[

###### Abstract

Over the 1962 to 2016 period, the Canadian violent crime rate has remained
strongly correlated with National Hockey League (NHL) penalties. The Canadian
property crime rate was similarly correlated with stolen base attempts in the
Major League Baseball (MLB). Of course, correlation does not imply causation
or prove association. It is simply presented here as an observation. Curious
readers might be tempted to conduct additional research and ask questions in
order to enhance the conversation, transition away from a state of confusion,
clarify the situation, prevent false attribution, and possibly solve a problem
that economists call identification.

crime,

penalties,

stolen bases,

correlation,

hockey,

baseball,

NHL,

MLB,

###### keywords:

.

##  1 Introduction

This short research note highlights surprisingly strong correlations between
Canadian aggregate crime trends and certain professional sport trends that
were observed throughout the 1962-2016 period.

Beyond any entertainment value, these empirical relationships provide new
opportunities to test, validate or refute criminological theories. In the
United States, for example, there appears to be a strong negative correlation
between measures of consumer sentiment and rates of not only robbery and
property crime (Rosenfeld and Fornango, 2007) but also homicide (Blumstein and
Rosenfeld, 2008) and felony homicide in particular (Rosenfeld, 2009). This
suggests that changing economic conditions can have an impact on crime.
Similarly, divorce rates and crime rates also seem to move together over time
(Greenberg, 2001), supporting the idea that major social changes and family
strains can engender crime.

##  2 Data

The analysis relies on police-reported data compiled by Statistics Canada as
part of its Uniform Crime Reporting (UCR) Survey. The aggregate UCR Survey
data permits historical comparisons back to 1962 (Allen, 2018). Following
convention, crime numbers are converted into rates per 100,000 resident
population to facilitate year-over-year comparisons that take into account
population growth. The focus of the analysis is on violent crime, property
crime, and homicide rates.

Penalty data for the National Hockey League (NHL) was extracted directly from
its official website (NHL.com, 2018). This NHL data includes the total number
of penalties (Pen) and the associated number of penalty infraction minutes
(PIM) for each season.

Batting data for the Major League Baseball (MLB) was downloaded from the
website Baseball-Reference.com (2018). This MLB data includes various
statistics intending to reflect offensive productivity. The analysis focuses
on stolen base attempts or stolen base opportunities, which is the combination
of stolen bases (SB) and caught stealing events (CS).

##  3 Results

###  3.1 Violent crime in the NHL penalty box

First, it turns out that the Canadian violent crime rate is positively
correlated with the number of NHL penalties and penalty minutes in a
surprisingly strong manner, as measured by Pearson’s correlation coefficients
($r=0.951$ and $0.925$, respectively). Fig. 1 illustrates the quality of the
linear fit. The ordinal association is also quite strong, as measured by
Kendall’s rank correlation coefficients ($\tau=0.775$ and $0.750$,
respectively).

Figure 1:  Canadian violent crime rate and NHL penalties, 1962-2016. Two NHL
lockouts shortened the 1994-95 and 2012-13 regular seasons to 48 games instead
of 82 games per team. The totals for those seasons are manually adjusted
(normalized) to account for lost games and to make year-over-year comparisons
possible. For its part, the 2004 NHL lockout led to a completely cancelled
season. In that case, fictitious 2004 data are imputed by simply interpolating
between 2003 and 2005 data points.

This statistical relationship is notable because NHL penalties are typically
assessed by referees for excessive toughness and physical violence and are
therefore the closest thing to a violent crime in the context of professional
ice hockey (Heckelman and Yates, 2003), besides actual on-ice criminal
assaults (CityNews Staff, 2016).

Possible underlying factors that could drive such a strong correlation between
violent crime and NHL penalties include all factors that professional hockey
players would have been exposed to with essentially the same timing and same
intensity as the rest of the general population. This could plausibly
encompass, for example, early childhood lead exposure (Nevin, 2000, 2007;
Wolf, 2014) and a social civilizing or pacifying process (Spierenburg, 2001;
Stille, 2003; Restrepo, 2015).

The latter argument is a sociological one. It is based on the idea that
society in general may have become more enlightened over the last few decades.
Better self-control and social pressures would therefore explain parallel
reductions in both crime and on-ice penalties. The former argument is built on
the idea that hockey players who played in the NHL throughout the late 1980s
and early 1990s may have been exposed to harmful amounts of lead when they
were growing up in the 1960s and 1970s, _before_ leaded gasoline and lead-
based paint became regulated (Wolf, 2014). In contrast, hockey players born
after the mid-1970s were more likely to grow up with healthier brains and a
lower propensity for violence. Canadians and Canadian youths in particular
would have been similarly affected.

It is not possible at this stage to completely eliminate the possibility that
NHL penalties might actually stimulate violent crime at the national level,
through some kind of copycat or emulation effect for instance (Moser, 2004;
Adubato, 2011; Card and Dahl, 2011; Kirby, Francis and O’Flaherty, 2014).
Although this may sound far-fetched at first glance, earlier studies did
reveal some correlation between the success of sports teams and reductions in
suicide (Joiner Jr., Hollar and Van Orden, 2006) and even homicide rates
(Fernquist, 2000). In fact, some studies examined the relationship between
homicide rates and the introduction of television in certain countries and
found a consistently positive correlation between the two (Centerwall, 1989),
revealing that not only televised sport – but television more generally – has
the potential to engender violence in society (Centerwall, 1992).

We note in passing that the correlation between violent crime and NHL
penalties is unlikely to be explained away by annual weather or temperature
variations (Burke, Hsiang and Miguel, 2015) because NHL games are generally
played in a climate-controlled environment, unlike baseball (Reifman, Larrick
and Fein, 1991; Larrick et al., 2011) or American football games (Craig et
al., 2016) for instance.

###  3.2 Property crime around the baseball diamond

Second, it turns out that the Canadian property crime rate is positively
correlated with the rate of stolen base attempts in the MLB ($r=0.894$ and
$\tau=0.696$). Fig. 2 illustrates the quality of the linear fit.

Figure 2:  Canadian property crime rate and stolen base attempts in the MLB,
1962-2016. Three significant MLB strikes resulted in lost games during the
1972, 1981, 1994, and 1995 seasons. However, the MLB data are averaged on a
per-game basis, which removes the need to normalize the data or simulate full
seasons in order to account for lost games.

Stolen base attempts reflect the propensity of baseball players to
opportunistically try to move forward around the bases at the expense of the
defensive team, in order to possibly score more runs as a result. Stolen base
opportunities can therefore properly be seen as the professional baseball
equivalent of a _lawful_ property crime.

Plenty of explanations have been professed to explain the relative rise of
base stealing in the mid-1970s (McMurray, 2015), its peak throughout the 1980s
(James, 1982), and its decline in the mid-1990s (Kurkjian, 1994). However,
identifying the underlying factors that could explain why stolen bases in the
MLB may be related to property crime in Canada remains an open problem.

As a side note, Farrell, Hodgkinson and Andresen (2018) already highlighted
that there was a remarkable similarity between historical property crime and
homicide rates in Canada, once attempted murders and actual homicides are
aggregated into a single measure of total homicides ($r=0.91$). In that
context and in light of the previously discussed results, it should not come
as a surprise that Canadian homicides and attempted murders, like property
crimes, are also correlated with stolen base attempts ($r=0.894$ and
$\tau=0.695$). This is shown by Fig. 3.

Figure 3:  Canadian homicide rate and stolen base attempts in the MLB,
1962-2016. The Canadian homicide rate is actually correlated most strongly
with _failed_ stolen base attempts where the runner was caught stealing
($r=0.822$), while the rate of attempted murders is actually correlated most
strongly with _successful_ stolen bases ($r=0.906$). This may look incongruent
at first glance, but this is only because stolen bases are defined from the
point of view of the runner. From the point of view of the defensive team, a
runner who is caught stealing represents a _successful_ out.

Farrell, Hodgkinson and Andresen (2018) speculated that similarities between
historical homicide and property crime rates may have been driven by the
progressive implementation of security improvements, especially in the second
half of the 1990s. While it is not immediately obvious whether (or how) this
security hypothesis may also apply to stolen base opportunities in the MLB,
more research into this area could be enlightening (and probably
entertaining).

##  4 Conclusion

Correlation does not imply causation and it is entirely possible that the
statistical relationships presented in this short research note may be
coincidental or spurious, in the vein of Andersen (2012) and Vigen (2015) for
example. However, they also very well could be examples of life imitating
sports (Steen, 2014) or vice versa (Goldstein, 1989).

More research would obviously be required to assess whether these statistical
relationships are purely coincidental, to determine to what extent both trends
might be influenced by common underlying factors, and to investigate the
possibility that they might be fueled endogenously through a copycat effect,
among many other possible pathways.

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11institutetext: SUPA School of Physics and Astronomy, The University of
Glasgow, Glasgow, G12 8QQ, UK
11email<EMAIL_ADDRESS>22institutetext: LESIA, Observatoire de
Paris, Université PSL , CNRS, Sorbonne Université, Université Paris-Diderot, 5
place Jules Janssen, 92190 Meudon, France 33institutetext: KU Leuven, Belgium
44institutetext: PMOD/WRC, Dorfstrasse 33, CH-7260 Davos Dorf, Switzerland
55institutetext: ETH-Zurich, Hönggerberg campus, HIT building, Zürich,
Switzerland

# Solar prominence diagnostics from non-LTE modelling of Mg ii h&k line
profiles

A. W. Peat 11 N. Labrosse 11 B. Schmieder 112233 K. Barczynski 224455

###### Abstract

Aims. We investigate a new method to for obtaining the plasma parameters of
solar prominences observed in the Mg ii h&k spectral lines by comparing line
profiles from the IRIS satellite to a bank of profiles computed with a one-
dimensional non-local thermodynamic equilibrium (non-LTE) radiative transfer
code.

Methods. Using a grid of 1007 one-dimensional non-LTE radiative transfer
models, some including a prominence-corona transition region (PCTR), we carry
out this new method to match computed spectra to observed line profiles while
accounting for line core shifts not present in the models. The prominence
observations were carried out by the IRIS satellite on 19 April 2018.

Results. The prominence is very dynamic with many flows, including a large arm
extending from the main body seen near the end of the observation. This flow
is found to be redshifted, as is the prominence overall. The models are able
to recover satisfactory matches in areas of the prominence where single line
profiles are observed. We recover: mean temperatures of 6000 to 50 000K; mean
pressures of 0.01 to 0.5 dyne cm-2; column masses of 3.7$\times 10^{-8}$ to
5$\times 10^{-4}$ g cm-2; a mean electron density of 7.3$\times 10^{8}$ to
1.8$\times 10^{11}$ cm-3; and an ionisation degree
${n_{\text{HII}}}/{n_{\text{HI}}}=0.03-4500$. The highest values for the
ionisation degree are found in areas where the line of sight crosses mostly
plasma from the PCTR, correlating with high mean temperatures and
correspondingly no H$\alpha$ emission.

Conclusions. This new method naturally returns information on how closely the
observed and computed profiles match, allowing the user to identify areas
where no satisfactory match between models and observations can be obtained.
The inclusion of the PCTR was found to be important when fitting models to
data as regions where satisfactory fits were found were more likely to contain
a model encompassing a PCTR. The line core shift can also be recovered from
this new method, and it shows a good qualitative match with that of the line
core shift found by the quantile method. This demonstrates the effectiveness
of the approach to line core shifts in the new method.

###### Key Words.:

Sun: filaments, prominences – Sun: chromosphere – Sun: UV radiation

##  1 Introduction

Solar prominences, filaments when viewed on disc, are structures in the solar
corona comprising of relatively cool and dense plasma. They form in filament
channels, which manifest above polarity inversion lines seen in photospheric
magnetograms, suspended in dips in the magnetic field (Labrosse et al., 2010;
Mackay et al., 2010; Vial & Engvold, 2015). The high spatial and temporal
resolution of space-based observations opens a new era of study into the
dynamics, evolution, and structure of solar prominences. These properties are
key to our understanding of prominence physics.

Since the launch of the Solar Dynamics Observatory (SDO; Pesnell et al.,
2012), studies of extreme ultraviolet (EUV) prominence observations with the
Atmospheric Imaging Assembly (AIA; Lemen et al., 2012) have revealed new
information about prominence barbs and the prominence-corona transition region
(PCTR; Parenti et al., 2012; Ruan et al., 2018). The Interface Region Imaging
Spectrograph (IRIS; De Pontieu et al., 2014) allows for the acquisition of
spectroscopic observations of prominences in the near ultraviolet (NUV) and
far ultraviolet (FUV). Many past studies have focused on the information one
is able to ascertain from statistics of the line profiles (Heinzel et al.,
2014; Ruan et al., 2018; Kucera et al., 2018; Levens et al., 2016; Liu et al.,
2015).

Recent studies have focused on attempts to invert solar prominence atmospheres
to obtain diagnostic information pertaining to that of the atmospheric
conditions from IRIS observations of Mg ii (Jejčič et al., 2018; Zhang et al.,
2019; Levens & Labrosse, 2019). Such inversions have been done by generating
grids of models and matching them with observational data through different
statistical methods. These comparisons between observed and computed spectra
are based on integrated line intensities and line widths. However, these
studies did not provide detailed information on how closely the models match
the observations: a ‘best match’ model is always returned, even if the
observed and computed line shapes are very different. Heinzel et al. (2015)
fitted a computed line profile to the mean of six line profiles with a focus
on the shape of the line profiles rather than the integrated line intensities
and line widths. In this paper, a similar type of inversion is done, but here
we look at each line profile separately, point-for-point, using a statistical
test to assess where the models yield good comparisons with the observations.

The paper is organised as follows. In Section 2 we present observations of a
solar prominence obtained on 19 April 2018. In Section 3, we perform a
detailed analysis of the characteristics of the Mg ii h&k line profiles
observed with IRIS. In Section 4, we present the models used in this work and
the method developed to compare models and observations, as well as the
results that we obtain. In Section 5 we offer our conclusions.

##  2 Observations

A filament appeared on the south-western solar disc on 17 April 2018 in
H$\alpha$ observations from the Meudon
Spectroheliograph111http://bass2000.obspm.fr (see Figure 1).

Figure 1: H$\alpha$ observations from the Meudon Spectroheliograph of the
solar limb on the days leading up to the coordinated observation. The filament
is highlighted with a red circle.

This then later manifested as a prominence off the south-western solar limb on
19 April 2018. The prominence was observed with IRIS, and Hinode (Kosugi et
al., 2007) as part of a coordinated observation with the Multichannel
Subtractive Double Pass (MSDP) spectrograph (Mein, 1991) in the Meudon Solar
Tower and other ground-based observatories. The IRIS and Hinode observations
start from 14:14 and end at 19:15 UTC. The IRIS observations are comprised of
a set of 18 very large coarse 32-step rasters of the C ii (1331.7 Å to 1358.3
Å), Si iv (1388.0 Å to 1406.7 Å), and Mg ii (2783.2 Å to 2835 Å) filters,
along with their complimentary slit-jaw imager (SJI) observations centred at
1330 Å, 1400 Å, and 2796 Å, respectively. The rasters had a field of view
(FOV) of 63.9″$\times$182.3″ centred on helioprojective coordinates 632.5″,
-753.2″, with a clockwise satellite rotation angle of 51°, such that the solar
limb was parallel to the y axis of the instruments. The Hinode observations
consisted of X-Ray Telescope (XRT; Golub et al., 2007) observations with three
filter combinations, Al poly/Open, Open/Gband, and Open/Ti with an FOV of
263.3″$\times$263.3″, centred on helioprojective coordinates 607.2″, -749.7″.
The MSDP observations start at 12:05 UTC and end at 16:35 UTC with a
reconstructed FOV of 270″$\times$370″(see Barczynski et al., 2021). AIA whole-
disc observations were also available. Figure 2 shows a depiction of the
configuration of the AIA, IRIS, and Hinode observations.

Figure 2: IRIS and XRT (FOV) overlaid on AIA 171 Å

###  2.1 Hinode/XRT

The images from the Al poly/Open filter of XRT on board Hinode clearly show
the coronal cavity in which the prominence sits. However, over the course of
the observation, these images do not show any appreciable change or
brightenings (see Figure 3).

Figure 3: Hinode/XRT Al poly/Open observation of the prominence at 15:22UTC.
The coronal cavity in which the prominence sits is clearly seen near (650″,
-750″).

###  2.2 IRIS

The IRIS FITS files were retrieved from the Lockheed Martin Solar and
Astrophysics Laboratory (LMSAL) website as level 2 FITS. Radiometric
calibration was performed in Python through the method described in Pereira et
al. (2018), with the response function retrieved through iris_get_response.pro
from SolarSoft (SSW). The data were also deconvolved through Python using a
procedure following similar operations to iris_sg_deconvolve.pro from SSW.
Coronal and noisy pixels were removed from the Mg ii rasters. This was done by
calculating a histogram of the full width at half maximum (FWHM) of both Mg ii
h and Mg ii k in every pixel of every raster. The FWHM was calculated via the
quantile method (see section 3). These FWHM histograms exhibit a local minimum
near the centre of the distributions. Any pixel that exhibits a spectrum with
a FWHM above this local minimum is assumed to be a noisy and/or coronal pixel.
This can be assumed as random noise will appear to yield a large FWHM via the
quantile method. However, some pixels contain spectra with more than one peak,
leading to an erroneous measurement of a large FWHM, and some pixels contain
spectra that truly have a large FWHM. To combat this, all pixels that fail the
FWHM test were then subject to a second test, a simple intensity filter. The
limit for this intensity filter was twice the mean of the values of every
pixel in every raster in the wavelength range where one would expect Mg ii h
or Mg ii k emission. Anything above the FWHM limit and below the intensity
limit was assumed to be noisy or coronal, and was filtered out. The result of
this filtering is presented in Figure 4.

Figure 4: Example of filter. Mg ii h emission with (right) and without (left)
the filter applied to remove noisy and coronal pixel emission.

In this paper, we focus on the Mg ii (NUV) filter. The prominence only appears
very faintly in the Si iv and C ii rasters, making analysis of the FUV bands
difficult. We note that reducing the colour-bar limit of the FUV SJI images
enough to see the prominence at this low intensity leads to the manifestation
of a ghost image of the aperture of the telescope. This is due to parasitic
infrared and visible light and only affects off limb observations in the FUV
channels; the NUV channel is unaffected (Wülser et al., 2018).

In the 2796 Å SJI images, the prominence shows very dynamic behaviour with
many flows towards the south-western limb. This culminates in a large flow
extending down from a rise of material seen to branch out from the main
section of the prominence that persists through the observation. These three
stages are shown Figure 5.

Figure 5: Three main stages of the evolution of the prominence. The top,
middle, and bottom rows show, Mg ii k IRIS/SJI, 304 Å SDO/AIA, and 171 Å
SDO/AIA, respectively. The left, centre, and right columns show small flows
from main body, the end of the rise of material, and the large flow of this
risen material, respectively.

###  2.3 AIA

The AIA files were retrieved from the Virtual Solar Observatory (VSO) as level
1 FITS. These were then prepared to level 1.5 through the use of aia_prep.pro
from SSW in IDL. The 304 Å filter shows a similar evolution to that seen in
the Mg ii k SJI from IRIS. This is expected as the emission in both channels
have some chromospheric origins (De Pontieu et al., 2014; Lemen et al., 2012).
The limb, however, appears higher in 304 Å than in Mg ii k; this is likely due
to the transition region contribution to the 304 Å filter.

The 171 Å filter clearly shows a small pillar-like barb extending into the
region where the prominence is clearly seen in chromospheric filters. This
corresponds to the central and densest part of the prominence. One would
expect to see strong central reversals in the Mg ii h&k spectra (see Section
3) in this area owing to the high density of material. This is where the
prominence appears to be anchored to the surface. In 171 Å, we also observe a
fainter structure enveloping the barb. This can be interpreted as the PCTR
since the region of the solar atmosphere imaged by 171 Å includes the upper
transition region (TR).

After the end of the IRIS and Hinode observations, the prominence is still
seen in the 171 Å and 304 Å filters of AIA. In 304 Å the prominence remains
fairly dynamic and appears to fall away towards the limb over the next 24
hours. This can be attributed to the projection effect and the prominence is
simply rotating out of view. A similar conclusion is drawn from the 171 Å
filter. However, the PCTR and barb of the prominence appear to fade over the
next 24 hours as emission from brighter coronal material begins to occult
these structures. No filament eruption is observed. On 22 April, the structure
reappears in the 171 Å and 304 Å EUVI filters of the Sun Earth Connection
Coronal and Heliospheric Investigation (SECCHI; Howard et al., 2008) on board
the Solar Terrestrial Relations Observatory (Ahead) (STEREO-A; Driesman et
al., 2008) and continues to transit across the disc. At this time, the angular
separation of STEREO-A from the Earth was approximately 117°.

##  3 IRIS spectra

Some of the Mg ii h&k spectra obtained by IRIS show complex structure. This
implies that some regions of the prominence have more than one structure along
the line of sight. A notable example is seen in the top of Figure 6 near 120″
in slit position 7. Here we see what appears to be a single peaked profile in
Mg ii h&k with a secondary redshifted peak. This is not unique to this slit
position, though this is the most extreme case. There are many areas where
line profiles are composed of many intensity peaks. These lead to the
appearance of more than one, or complex, looking line profiles. Figure 7 shows
the distribution of the spectral line shapes observed by IRIS. While the
distribution of line profile types is dominated by single peaked profiles, the
number of double peaked and complex profiles are not negligible – with
approximately 20% of line profiles appearing complex.

Here we use the quantile method (Kerr et al., 2015; Ruan et al., 2018) to
determine the FWHM, line core shift, and asymmetry of the line profiles to
investigate the internal structure and dynamics of the prominence. The
quantile method involves calculating the cumulative distribution function
(CDF) of the intensity of the individual line profiles over some wavelength
range. Here, we employ a 3Å window centred on the rest vacuum wavelengths of
Mg ii h&k. The wavelength at which the 50% level of the CDF is found
($\lambda_{50}$) is defined as the line core. The FWHM can be calculated by
taking the difference between the wavelength at which the 88% ($\lambda_{88}$)
and the 12% ($\lambda_{12}$) level of the CDF is found. Additionally, the
asymmetry of the line profiles is calculated by,

$\text{Asymmetry}=\frac{(\lambda_{88}-\lambda_{50})-(\lambda_{50}-\lambda_{12})}{\lambda_{88}-\lambda_{12}}.$
(1)

The rest wavelengths of the Mg ii h&k line cores were calculated by performing
quantile analysis on every pixel of the first slit position of every raster,
taking $\lambda_{50}$ as the line core. This was done as the first slit
position of each raster is on the solar disc, which gives us a rotation
independent measure of the line cores. We use the nominal wavelength
calibration provided in the data header. From this, 9360 measurements of the
line core were obtained for h&k, of which the mean was taken. The rest
wavelengths for the Mg ii h&k line cores were found to be 2803.494 Å and
2796.348 Å respectively, whereas the rest vacuum wavelengths are 2803.53 Å and
2796.35 Å respectively (Levens & Labrosse, 2019). The spectral resolution of
the Mg ii observations were 0.051 Å, giving these measured values an error of
$\pm 0.0255$Å. The calculated wavelengths of the line cores are used here as
reference wavelengths in order to effectively transform into the inertial
frame of the solar limb such that its rotation is not included in the line
core shift calculations.

Figure 6: Mg ii h&k spectra at select slit locations. See Figure 10 for
context.

###  3.1 Line profile distribution

Figure 7: Mg ii h line profile types seen in raster 15.

The prominence presents a variety of line profile types. These were found by
using a finite difference approximation of the derivative of values above the
standard deviation of the intensity of the currently considered pixel. From
this, stationary points could be counted. If two, or more than three
stationary points were found, the line profile was classified as complex. Such
a complex line profile is discussed in Section 3.3. Figure 7 shows an example
of the distribution of line profile types in raster 15. Parts of the
prominence nearest the edges of the structure are more likely to exhibit
single peaked behaviour relative to those in nearer the centre. Those under
motion also favour single peaked behaviour.

We observe a large arm extending from the main body of the prominence near the
end of the observation that displays mainly single peaked line profiles. This
arm also contains a few classic double peaked line profiles. In addition, it
exhibits complex profiles that appear to be double peaks suffering from the
effect further discussed in Section 3.2 where the emission of h2v and k2v is
greatly reduced, resulting in only h2r and k2r peaks. This is due to the
intensity of h2v and k2v peaking lower than h3 and k3, which causes no defined
peaks at these locations. Double peaks in the arm can be interpreted in one of
two ways – there is a large volume of material in the arm along the line of
sight or there exists more than one strand in the composition of this arm with
different line-of-sight velocity shifts. In the former case, the optical
thickness of the plasma would result in a double peaked profile. However,
judging by the extent of the arm in the plane-of-sky, this interpretation is
unlikely. For it to be extended enough along the line of sight to cause this
effect, would mean it would take the form of a sheet-like structure and we see
no evidence of this morphology. A more plausible interpretation is the latter.
This would lead to a measured line core shift, as if it were the former case,
resulting in a lower measured velocity. This may also be another reason for
the broadened wings of the line core shift distribution discussed in Section
3.2. Admittedly, this would be a rather small effect on the distribution, and
the more likely cause is the effect that asymmetry has on measured Doppler
velocity when using the quantile method. Highly asymmetric profiles have bias
in the measure of their Doppler velocity due to the increased emission of the
red or blue sides of these line profiles. This effect is discussed in detail
in Section 3.2.

The double peaked line profiles of the main body of the prominence are most
likely due to a large amount of material along the line of sight. The optical
thickness would assist in producing the classic double peaked look of Mg ii
h&k emission. The pixels classified as complex in figure 7 are likely due to
many different structures or threads in that pixel. These areas of complexity
appear to correlate with areas of large FWHM and asymmetry, giving more
evidence towards this interpretation. The south-eastern edge of the prominence
displays mainly single peaked profiles, which can be attributed to a few
causes. This area of the prominence is seen to contribute to many small flows,
causing a loss of plasma to this area, which could lead to a lower density, or
there could be less plasma along the line of sight here, or perhaps both of
these factors contribute towards the observed emission.

###  3.2 Line core shift

Figure 8: Line core shift histograms of both Mg ii h&k across all 18 rasters
with Gaussian fits.

We calculate line core shifts by computing the Doppler velocity of each pixel
using the 50% quantile ($\lambda_{50}$) of each pixel as the line core. From
this, we find a range of line core shifts in the prominence, with the extrema
ranging from -74 to 78 km s-1 in Mg ii h and -72 to 85 km s-1 in Mg ii k. The
total distribution is a Gaussian-like centred on a redshifted line core of
around 8.20 km s-1 and 5.20 km s-1 with standard deviations of 5.98 km s-1 and
6.61 km s-1 in Mg ii h&k, respectively. These distributions can be seen in
Figure 8.

Mg ii h&k line shifts are an excellent diagnostic tool for the Doppler
velocities seen in the structure (Leenaarts et al., 2013). These recovered
velocities are quite typical of past prominence observations. Liggett & Zirin
(1984) observed velocities ranging from 12 to 75 km s-1, and Schmieder et al.
(2017) found maximum velocities of around 60 km s-1 . Table 6 in the review by
Labrosse et al. (2010) shows a range of velocities exhibited by prominences in
the EUV, with an extremum of 70 km s-1, centred around 20 km s-1.

The wings of the Gaussian fits used in Figure 8 do not seem to model the
velocity distributions well. The cause of this shape is suggested by Figure 9.
Asymmetry and measured Doppler velocity appear to be anti-correlated,
plateauing at high measured velocities. The root of this trend lies in the
optical thickness of the lines. At rest, the line cores of Mg ii h&k are
optically thick, but the wings are optically thin. Therefore, line profiles of
high redshift will display a negative (red) asymmetry due to h2v and k2v being
shifted into the more optically thick area of the line. This leads to the
quantile method measuring a larger-than-true velocity due to the absorbed h2v
and k2v giving more credence to the intensity of h2r and k2r. This effect is
amplified by h2r and k2r moving more into the optically thin regime of the
wings. The opposite is also true for the blueshifted profiles that see
absorption and enhancement of h2r and k2r and h2v and k2v, respectively. The
extensions of the wings of the Doppler velocities are likely due to this
effect. It is therefore sensible to assume these high velocities are measured
to be larger than in reality, and the true distribution may still be of a
Gaussian shape. The velocities of areas where the asymmetry is much greater
than zero are likely unreliable, and only those where the asymmetry is
approximately 0, can be considered reliable.

Figure 9: Scatter plot of relationship between asymmetry and measured line
core shift of all post-filter Mg ii h pixels.

###  3.3 Line widths

Here, we use the difference between the 88% and 12% quantiles
($\lambda_{88}-\lambda_{12}$) to measure the FWHM, as in Ruan et al. (2018).
If you assume that the line profiles are of a Gaussian shape, the difference
between the 88% and 12% quantiles is the FWHM. FWHM maps clearly separate the
prominence (and spicules) from the solar disc. They also separate the
prominence and solar disc from the background corona as discussed in Section
2.2. These FWHM maps allow for the location of flows and structures not easily
seen in intensity maps. The FWHM of the lines profiles within the prominence
are relatively small, ranging from around 0.1 Å to 0.6 Å, whereas the FWHM
within the solar disc have values of around 0.8 Å to 1 Å. In the first raster
(14:13UTC; see Figure 10), we see a structure of large FWHM, in comparison to
the same location in later rasters, around (10″, 110″). This structure is seen
in both Mg ii h&k , suggesting that this is a physical phenomena. On further
inspection, the spectra in both Mg ii h&k, in this area, show two distinct
line profiles, one of which is highly redshifted. The shape and location of
this structure seems very similar to that of the pillar-like barb easily seen
in 171 Å. One of the drawbacks of the quantile method here is that it cannot
distinguish between line profiles. If a pixel displays more than one line
profile, or one of a more complex nature, the algorithm is still able to
produce a number for this, albeit a large one. This can then be used as a
proxy for whether a spatial pixel contains more than one line profile.

Figure 10: Mg ii h statistics maps of the three main stages of the prominence
observation calculated via the quantile method. In the first raster we see a
rather static structure. In raster 12, the rise that eventually leads into a
flow begins to form. In raster 15, the flow seen in raster 12 is beginning.
The times associated with these plots are the time at the beginning of the
associated raster. The dashed lines represent the slit positions in Figure 6.
Mg ii k produces similar plots and these can be seen in Figure 21. An animated
version of this figure is available online.

###  3.4 Asymmetry

Asymmetry is most apparent in the extended arm protruding from the main
prominence body as seen in raster 15 (see Figure 10). Most emission in this
area is seen to have asymmetry in the range [0,-1). However, these line
profiles may just have too low of an intensity, which gives too much credence
to the noise in the quantile analysis. Many of these profiles do not appear
asymmetric, just highly Doppler shifted. This can be seen in Figure 10 as the
areas of high redshift appear to correlate to those of non-negligible
asymmetry and low integrated intensity. However, there does appear to be an
anticorrelation between the line core shift and the asymmetry as can be seen
in Figure 9 The only structure that appears to break this trend, is the
structure of large FWHM discussed in Section 3.3. Its large asymmetry is
likely due to the two line profiles seen in this area, leading to a erroneous
measurement of asymmetry. This shows that asymmetry calculated via the
quantile method, when combined with its complimentary FWHM, is a better proxy
for whether a pixel contains more than one line profile than either diagnostic
on its own.

Parameter | Unit | Value
---|---|---
$T_{\text{cen}}$ | K |  | 6000, 8000, 10000, 15000,
---
20000, 25000, 30000,
35000, 40000
$T_{\text{tr}}$ | K | 100000
$p_{\text{cen}}$ | dyne cm-2 | 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1
$p_{\text{tr}}$ | dyne cm-2 | 0.01
Slab Width | km | 200 – 124100
M | g cm-2 |  $3.7\times 10^{-8}$–$5.1\times 10^{-4}$
$v_{T}$ | km s-1 | 5
$H$ | km | 1000
$\gamma$ |  | 0, 2, 5, 10
Table 1: Parameters of the models.

##  4 Model comparisons

Levens & Labrosse (2019) discussed an extension to the one-dimensional
radiative transfer code developed by Gouttebroze et al. (1993), PROM, such
that it was able to produce Mg ii line profiles with both isobaric and
isothermal atmospheres, and atmospheres containing a PCTR. The latter
atmosphere was itself added as an extension by Labrosse & Gouttebroze (2004).
This Mg ii extension is similar to that discussed by Zhang et al. (2019), but
independently developed. In this model, prominences are represented by a one-
dimensional semi-infinite plane-parallel slab perpendicular to the solar
surface. This block is illuminated on both sides by isotropic radiation from
the solar disc. Using this extension developed by Levens & Labrosse (2019), we
produced a total of 1007 Mg ii model profiles, 252 of which are isothermal and
isobaric, where the remaining 755 include a PCTR (one of the original set of
756 did not converge). The parameters of these atmospheres can be seen in
Table 1. $T_{\text{cen}}$ and $p_{\text{cen}}$ are the central temperature and
pressure, respectively. $T_{\text{tr}}$ and $p_{\text{tr}}$ are the
temperature and pressure at the edge of the slab, respectively. Slab width is
the width of the slab. $M$ is the column mass. $v_{T}$ is the microturbulent
velocity inside the prominence. $H$ is the height above the solar surface.
$\gamma$ is a dimensionless number that dictates the extent of the PCTR. A
$\gamma$ value of 0 indicates the model is isothermal and isobaric – without a
PCTR. For isothermal and isobaric models, $T_{\text{tr}}=T_{\text{cen}}$, and
$p_{\text{tr}}=p_{\text{cen}}$. For non-zero values of $\gamma$, the lower the
value of $\gamma$ the more extended the PCTR is. All of the above combinations
amount to 1008 models; however, one model did not converge, so we only
consider the 1007 that did. The PCTR models used here adopt the same
parametric description of the PCTR as in Anzer & Heinzel (1999). The pressure
profile derives from magnetohydrostatic equilibrium and is given as a function
of the column mass $m$ by

$p(m)=4p_{c}\frac{m}{M}\left(1-\frac{m}{M}\right)+p_{\text{tr}}\ ,$

where $p_{c}$ is the difference in pressure between slab centre and slab edge
($p_{\text{cen}}=p_{c}+p_{\text{tr}}$), and $M$ is the total column mass. The
temperature profile is taken to be

$T(m)=T_{\text{cen}}+(T_{\text{tr}}-T_{\text{cen}})\left(1-4\frac{m}{M}\left(1-\frac{m}{M}\right)\right)^{\gamma}\
,$ (2)

Using these models we are able to estimate the internal plasma properties of
the prominence. The models contain the five main Mg ii lines, here, we focus
on the h&k lines in particular. The computed line profiles are symmetrical
around their respective rest wavelengths due to the omission of radial
velocities, which would introduce the effects of Doppler dimming and/or
Doppler brightening (Hyder & Lites, 1970; Labrosse et al., 2007).

In order to compare these model line profiles with the observations, we
developed a ‘rolling root mean squared (RMS)’ procedure in Python. This works
by first downgrading, through linear interpolation, the resolution of the
model line profiles to that of our IRIS observations. The models and
observations have a resolution of 3$\times 10^{-3}$Å and 51$\times 10^{-3}$Å,
respectively. Once downgraded, a spectral window of 3Å centred first on the
rest wavelength of Mg ii h, then Mg ii k, is considered. This spectral window
is considerably larger than the model range, and so, the models are padded
with zeroes to match the size of the spectral window.

$\text{RMS}=\sqrt{\frac{1}{n}\sum_{n}\left(\text{data}-\text{model}\right)^{2}}.$
(3)

We define RMS as seen in equation 3, where $n$ is the number of wavelength
points. The RMS is first measured between the downgraded model at beginning of
this spectral window and the observations. The model is then shifted one pixel
to the right, and the RMS is measured again. This process repeats until the
model reaches the end of the spectral window. The lowest measured RMS from
this ‘roll’ is recorded, along with the pixel shift required to achieve this.
The next model in the set is then tested. This process is repeated until all
of the models have been tested. This is run for both h&k. The RMS values for
h&k are then summed, and the model that produces the lowest overall RMS sum is
then selected as the model indicative of the plasma parameters if the RMS is
lower than a certain threshold. RMS values that are larger than that threshold
indicate that the computed and observed line profiles are too different, and
that no model could be found to satisfactorily reproduce the observed line
profiles.

By ‘rolling’ our models through the spectral window, this gives us a measure
of the wavelength of the line core (from the recorded pixel shift required to
minimise the RMS) and allows us to calculate a Doppler velocity. The rolling
RMS (rRMS) procedure is also able to measure pixel shift with sub-pixel
precision. However, the run time of the procedure scales linearly with the
number of sub-pixels requested. This works identically to without sub-pixel
precision, but before the rolling begins, the models and data are interpolated
up to match the sub-pixel precision requested.

###  4.1 Results

After the procedure was run, twelve line profiles were selected at random to
illustrate where the procedure found good matches and where it did not (see
Figure 11).

Figure 11: Four of the twelve random line profiles where a good fit is found
for six and an unsatisfactory fit is found for the other six. The top two
panels are the unsatisfactory fits, and the bottom two panels are the
satisfactory fits.

The goodness of these fits were judged by eye. The measured RMS of these
twelve line profiles were used to arrive at a cut off value above which
matches would be considered unsatisfactory. This value was determined to be
15000, concluding that 49%, 35617/72536, of the matches were satisfactory.
Figure 12 shows that areas of higher k/h ratio weakly correlate with areas
that give a satisfactory fit. High values of the k/h ratio are related to
areas of lower optical thickness. Therefore, this demonstrates that areas of
lower optical thickness lead to better matches with the models. This could
also be due to the one-dimensional nature of the code as the satisfactory fits
seem to also correlate with areas of single peaked line profiles, as seen in
Figure 7. These values for the k/h ratio appear to be consistent with
Alissandrakis et al. (2018) where they found a k/h ratio of 1.22 on approach
to the limb and values up to 1.96 in the spicules.

Figure 12: Comparison of k/h ratio and satisfactory fits. This demonstrates
the weak correlation between high k/h ratio and satisfactory fits. (left) k/h
ratio of raster 15. (right) Satisfactory fits of raster 15. Raster 15 was
taken between 18:08 and 18:25 UTC.

Figure 13: MSDP H$\alpha$ integrated intensity with corresponding satisfactory
matches. Top Left: Raster 9 satisfactory matches. Top Right: MSDP H$\alpha$
integrated intensity. Bottom: H$\alpha$ integrated intensity map from MSDP
with the satisfactory matches of raster 9 overlaid in white.

Figure 13 shows that in the most part, areas in which we see H$\alpha$
emission in the prominence correspond to where computed Mg ii line profiles do
not satisfactorily match the observed ones. The observed H$\alpha$ line
profiles are generally complex in shape and much wider than the models
produce. This issue is seen when attempting direct one-dimensional forward
modelling of H$\alpha$ prominences. For example, Ruan et al. (2019)
demonstrated that areas with wide H$\alpha$ line profiles can be better fit by
models with high microturbulent velocities. Whether this is also true for Mg
ii line profiles is currently unclear. Figure 14 presents the temporal
evolution of the mean pressure and mean temperature as derived from the
comparison between computed and observed Mg ii h&k line profiles, while Fig.
15 shows these parameters for the pixels in rasters 1, 12, and 15 recovered by
the procedure. Figure 16 presents diagnostic maps for electron density,
ionisation degree, $\gamma$ (i.e. temperature gradient), and column mass for
raster 15. We stress that the plasma parameters obtained with this method are
only reliable where our RMS values are low enough, as indicated with the
satisfactory matches in the right panel of Figure 12.

####  4.1.1 Pressure

Figure 14: Temporal evolution of (top) mean pressure and (bottom) mean
temperature. These plots only include the satisfactory matches. The large
spike near the end is due to interference seen in half of the slit positions
of that raster. This caused a lot of the previously lower temperature regions
to be filtered out, and therefore only the higher temperature areas are
included in the calculation of the mean. A similar (but less extreme)
situation occurred where the second highest peak is seen in the plot of
pressure; however, the mean temperature plot seems unaffected by this.

The mean pressure appears to remain stable during the IRIS observation, with
the mean pressure fluctuating on average between 0.18 and 0.26 dyne cm-2 (Fig.
14). The pressures of 1 dyn cm-2 found towards the core of the structure
correlate closely with the unsatisfactory fits (Fig. 15). This high pressure
is at the upper limit of that outlined in Table 1 of Labrosse et al. (2010).
These selected models could be explained by the procedure finding that
broadened profiles produce a smaller RMS for line profiles that exhibit a
complicated structure due to the large volume of the prominence to travel
through (a larger optical depth) coupled with many different threads along the
line of sight as seen in this area of the prominence. Pressure near the outer
edges of the prominence is, in general, lower as we move through the PCTR
towards the corona where the gas pressure is lower (Aschwanden, 2004).

####  4.1.2 Temperature

Figure 15: Evolution of mean temperature and pressure in the prominence from
the model comparisons with rasters 1, 12, and 15.

The mean temperature, like pressure, also appears stable during the
observation, with the mean temperature staying on average between
$7\leavevmode\nobreak\ 800$K and $11\leavevmode\nobreak\ 500$K (see Figure
14). This is consistent with expected results. The formation height of Mg ii
h&k ranges from the upper photosphere to the upper chromosphere (De Pontieu et
al., 2014). However, in a prominence, we expect a range of chromospheric to
PCTR temperatures. The temperature of the prominence increases towards the
outer edges where one would expect to see the PCTR in the plane of sky (Fig.
15). Figure 16 further reveals higher values nearer to the edges of the
prominence. The arm seen near the end of the observation appears to be a
tenuous and hot structure reaching upper chromospheric temperatures of a few
$10^{4}$ K.

Figure 16: Output diagnostics for raster 15: (top left) mean electron density;
(top right) ionisation degree; (bottom left) column mass; (bottom right)
$\gamma$ values. Raster 15 was taken between 18:08 and 18:25 UTC.

Equation 2 describes the relationship between $\gamma$ and the temperature
profile $T(m)$ (a function of column mass). In Table 1, models where
$\gamma=0$ in fact correspond to isothermal and isobaric models without a
PCTR. Many of the satisfactory fits having $\gamma\neq 0$ shows that the PCTR
extension to PROM by Labrosse & Gouttebroze (2004) implemented into the Mg ii
extension by Levens & Labrosse (2019) is important to obtain a better
agreement to the data than isothermal and isobaric models. Our mean
temperatures are greater than temperatures obtained by Zhang et al. (2019).
However, the authors of that study employed isobaric and isothermal models
whereas our models include a PCTR, as mentioned before. This allows our
inferred mean temperatures to be much greater. Areas where $\gamma=0$,
indicating isothermal models, correlate with areas of lower temperature, which
agrees with their study. In future, a finer grid of $\gamma$ values could help
with a better resolution of the temperature gradient of the PCTR.

####  4.1.3 Column mass

The mass along the line of sight conveys that the extensions of the prominence
have comparatively low mass (Fig. 16). The region where unsatisfactory fits
are found is much higher density than the surrounding material. While these
fits may be unsatisfactory, we can infer from the line profiles of that area
that there are several threads along the line of sight that contribute to the
line profiles. This includes profiles such as those shown in Figure 17. The
unsatisfactory fits here are due to the single slab nature of the models,
which does not account for several threads along the line of sight. A single
slab model can only apply, when there are several threads, if the threads are
comoving, which would result in a single line profile. The arm seen near the
end of the IRIS observations appears to be comparatively low mass. This
explains the single peaked line profiles observed in the arm. The intensity of
the central reversal is anticorrelated with formation height due to optical
depth (Leenaarts et al., 2013). This reinforces the finding of low column mass
not just in the arm, but where single peaked line profiles are observed.

Figure 17: Line profiles of Mg ii h&k in the region where unsatisfactory fits
are found. These line profiles can be explained by many threads being seen
along the line of sight moving at different velocities. The large spike around
2801.3Å is noise.

####  4.1.4 Electron density

The majority of the prominence appears to have an electron density of less
than 0.6$\times 10^{11}$cm-3, with the exception of a few places where it is
greater than 1$\times 10^{11}$cm-3 (Fig. 16). The arm appears to be of
generally comparatively low electron density. Even though it is of a
comparatively high temperature compared to the rest of the prominence, its low
pressure can explain the low electron density found.

####  4.1.5 Ionisation degree

Figure 18: Exponential increase of ionisation degree above 30 000K and
breakdown of the assumption that $n_{\text{HII}}\approx n_{e}$ at high
temperatures. Top: Ionisation degree defined by
$n_{\text{HII}}/n_{\text{HI}}$. Bottom: Excess electrons. Number of free
electrons per H II. This illustrates that the commonly used approximation for
ionisation degree will overestimate the value of $n_{\text{HII}}$ at high
temperatures.

Ionisation degree is defined by the mean number density of H II
($n_{\text{HII}}$) to H I ($n_{\text{HI}}$) (Tandberg-Hanssen, 1995). Past
works (such as Zhang et al., 2019) assume that the mean number of electrons
($n_{\text{e}}$) is equal to the mean number of protons ($n_{\text{p}}$), and
further that the mean number of protons is equal to the mean number density of
H II and that the mean number density of H I is dominated by the mean number
density of ground state Hydrogen ($n_{\text{H0}}$) then,

$\frac{n_{\text{HII}}}{n_{\text{HI}}}\approx\frac{n_{\text{e}}}{n_{\text{H0}}}.$
(4)

However, the assumption that $n_{\text{e}}\approx n_{\text{p}}\approx
n_{\text{HII}}$ does not hold with PROM because not all of the electrons are
liberated from H I. There is a fixed contribution of electrons from other
species, such as helium, that contribute to the total number of electrons
(named excess electrons from here on). This increase is most apparent at high
temperatures when the number density of H II and excess electrons increase
dramatically. Figure 18 shows the behaviour of ionisation degree and excess
electrons with increasing temperature. At temperatures above 30 000K, these
species are responsible for a 20% increase in the total number of electrons
(see Figure 18 bottom). So here we focus on the definition from Tandberg-
Hanssen (1995). Some sections of the prominence are found to have a very large
ionisation degree when compared to past studies. Vial (1998) summarised that
the ionisation degree in a prominence does not change much with temperature,
given that the density is low. This was based on studies by Gouttebroze et al.
(1993) and Heinzel et al. (1994). However, the highest temperature considered
in these studies is 15 000K. Figure 18 shows that the ionisation degree is
fairly constant up until 15 000K, consistent with these studies, but then
rises sharply at higher temperatures. Additionally, at 15 000K, the excess
electrons are responsible for only a roughly 7% increase in the number of free
electrons (as in Figure 18 bottom).

The areas where a high ionisation degree is found (see top right panel of Fig.
16) correlate strongly with areas of high mean temperature and non-zero values
of gamma. The model that yields the highest ionisation degree has a central
temperature of 40 000 K and a surface temperature of $10^{5}$ K.

###  4.2 Recovered line core shift

Figure 19: Comparison of line core shift recovered by quantile method and
rolling RMS procedure. Left: Line core shift recovered by quantile method.
Right: Line core shift recovered by rolling RMS procedure.

Due to the rolling aspect of the procedure, we recover a measure of the line
core shift. The resolution of the line core shifts from the rolling RMS
procedure is 2.7 km s-1. This comes from the minimum measurable line core
shift that is equal to the wavelength resolution of the instrument, divided by
the number of sub-pixels plus 1. Figure 19 shows the line core shift measured
by the quantile method and measured by the rolling RMS procedure. These plots
qualitatively agree. With the other diagnostics, there is a degree of
scepticism surrounding regions where unsatisfactory fits were found. However,
while those models do not represent the underlying conditions of the
prominence in those regions, the fit found by the procedure will still give a
good measure of line core shift. The lowest RMS will be found where the model
profile is centred on the data profile, regardless of how good the fit is.
Therefore, we can reasonably trust the line core shifts found by the rolling
RMS procedure, even in regions where unsatisfactory fits are found.

Figure 20: Histograms of line core shift recovered by the rolling RMS
procedure of both Mg ii h&k across all 18 rasters with Gaussian fits. These
include the unsatisfactory matches and have the filters discussed in Section
2.2 applied.

Figure 20 shows a similar plot to that of Figure 8, but for the line core
shift recovered by the rolling RMS procedure. Fewer bins are used in the
histogram of Figure 20 than in Figure 8 as the velocity resolution of Figure 8
is much greater than that of Figure 20. The distributions in Figure 20 display
a Gaussian-like distribution, similar to what is found in Figure 8, centred on
a redshifted line core of around 5.3 km s-1 and 5.6 km s-1 with standard
deviations of 9.8 km s-1 and 10.2 km s-1 in Mg ii h&k respectively. Due to the
limited resolution of the line core shifts recovered by the rolling RMS
procedure, an estimate of the uncertainty on these values is given as $\pm$
1.35 km s-1, half of the velocity resolution of the recovered line core shift.
The central line core shift of Mg ii k found by the quantile method, is within
the uncertainty of the central line core of Mg ii k recovered by the rolling
RMS procedure. However, the central line core shift of Mg ii h does not give
the same result. This could be due to the introduced asymmetry bias discussed
in Section 3.2.

##  5 Conclusions

The prominence observed on the south-western solar disc on 19 April 2018
exhibited many dynamic flows seen both in AIA and IRIS. These flows were best
seen in chromospheric filters. Coronal filters showed the barb of the
prominence, and when it was sufficiently raised in altitude, an outline of the
PCTR was also seen.

From the line core shift measurements via the quantile method, we find that
the prominence is dominated by redshifted flows relative to the solar disc.
Large values of asymmetry can be attributed to the plasma moving fast enough
such that part of the line is emitted in the optically thin regime, closer to
the wings of Mg ii h&k emission from plasma at rest. This resulting large
asymmetry biases the line core shift calculations to be redder or bluer
depending on the direction that the plasma is moving and as such measures
higher magnitudes for line core shift than would be expected if it were
emitted closer to the rest line core. Therefore, using this method, the
distribution of line core shifts may deviate from the expected Gaussian shape
in the wings of the line core shift distribution. The prominence exhibited a
wide range of line profile shapes, a majority of which were single peaked, due
to the low column mass exhibited by the majority of the prominence.

Through comparisons with one-dimensional radiative transfer models, we
retrieve internal plasma diagnostics of the prominence. The prominence was
found to display a wide range of pressures, ranging from 0.01–0.5 dyne cm-2.
Mean temperatures ranged from 6 000–50 000K. These results included models
with a PCTR, so while these temperatures may seem higher than classically
thought of in a prominence, these suggest the line of sight intercepts the
prominence material and much of the PCTR. We also note that the high mean
temperature values returned by the models fitting the Mg ii lines are found in
areas where there is no detectable H$\alpha$ emission. This demonstrates the
importance of the inclusion of the PCTR in prominence modelling. The column
mass ranges from 3.7$\times 10^{-8}$–5$\times 10^{-4}$ g cm-2.

The line core shifts recovered from our Mg ii line profile comparison
procedure agree well with the measured line core shifts for Mg ii k. For Mg ii
h, they are of the same order of magnitude. This demonstrates that the
unsatisfactory fits are not a result of the rolling RMS procedure but are a
consequence of the limitations of the one-dimensional radiative transfer
models. Models with multiple threads (Labrosse & Rodger, 2016; Gunár et al.,
2007, 2008) are likely to produce line profiles in better agreement with the
observations.

###### Acknowledgements.

AWP acknowledges financial support from STFC via grant ST/S505390/1. NL
acknowledges support from STFC grants ST/P000533/1 and ST/T000422/1. The
authors would like to thank Dr G. S. Kerr for their assistance in the
deconvolution of the IRIS spectral data, and Dr P. Mein for supplying the
H$\alpha$ data from MSDP. 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. AIA data courtesy of NASA/SDO and the AIA, EVE,
and HMI science teams. STEREO Full-disk EUVI images are supplied courtesy of
the STEREO Sun Earth Connection Coronal and Heliospheric Investigation
(SECCHI) team. Hinode is a Japanese mission developed and launched by
ISAS/JAXA, collaborating with NAOJ as a domestic partner, NASA and UKSA as
international partners. Scientific operation of the Hinode mission is
conducted by the Hinode science team organized at ISAS/JAXA. This team mainly
consists of scientists from institutes in the partner countries. Support for
the post-launch operation is provided by JAXA and NAOJ (Japan), UKSA (U.K.),
NASA, ESA, and NSC (Norway). This research used version 2.0.3 of the SunPy
open source software package (The SunPy Community et al., 2020), version 3.3.2
of Matplotlib (Hunter, 2007), version 1.20.2 of NumPy (Harris et al., 2020),
version 1.5.3 of SciPy (Virtanen et al., 2020), and version 4.0.1 of Astropy,
(http://www.astropy.org) a community-developed core Python package for
Astronomy (Astropy Collaboration et al., 2013, 2018)

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##  Appendix A Mg ii k diagnostic maps

Figure 21: Mg ii k statistics maps of the three main stages of the prominence
observation calculated via the quantile method. The times associated with
these plots are the time at the beginning of the associated raster. The dashed
lines represent the slit positions in Figure 6. An animated version of this
figure is available online.