# Evolution of the Thermodynamic Properties of a Coronal Mass Ejection in the
Inner Corona

Jyoti Sheoran 1, Vaibhav Pant 1, Ritesh Patel 1,2, and Dipankar Banerjee 1,3,4

###### Abstract

## 1

The thermodynamic evolution of Coronal Mass Ejections (CMEs) in the inner
corona ($\leq$ 1.5 Rsun) is not yet completely understood. In this work, we
study the evolution of thermodynamic properties of a CME core observed in the
inner corona on July 20, 2017, by combining the MLSO/K-Cor white-light and the
MLSO/CoMP Fe XIII 10747 Å line spectroscopic data. We also estimate the
emission measure weighted temperature (TEM) of the CME core by applying the
Differential Emission Measure (DEM) inversion technique on the SDO/AIA six EUV
channels data and compare it with the effective temperature (Teff) obtained
using Fe XIII line width measurements. We find that the Teff and TEM of the
CME core show similar variation and remain almost constant as the CME
propagates from $\sim$1.05 to 1.35 Rsun. The temperature of the CME core is of
the order of million-degree kelvin, indicating that it is not associated with
a prominence. Further, we estimate the electron density of this CME core using
K-Cor polarized brightness (pB) data and found it decreasing by a factor of
$\sim$3.6 as the core evolves. An interesting finding is that the temperature
of the CME core remains almost constant despite expected adiabatic cooling due
to the expansion of the CME core, which suggests that the CME core plasma must
be heated as it propagates. We conclude that the expansion of this CME core
behaves more like an isothermal than an adiabatic process.

##  2 Keywords:

Solar Atmosphere, Corona, Coronal Mass Ejections (CMEs), Spectroscopy,
Thermodynamics

##  3 Introduction

Coronal mass ejections (CMEs) are large structures of plasma and magnetic
fields ejected from the solar atmosphere into the heliosphere (Hundhausen et
al. 1984; Webb and Howard 2012). CMEs are the major drivers of space weather
because they can cause interplanetary disturbances and shock waves that can
lead to the disruption of a range of technologies on Earth (Gosling 1993;
Schwenn 2006; Pulkkinen 2007). Thus, it is important to understand their
evolution in the solar atmosphere. CMEs have been studied for several decades
using remote sensing and in-situ instruments. To study the evolution of CMEs,
one uses data from space and ground-based instruments such as the Sun Earth
Connection Coronal and Heliospheric Investigation (SECCHI; Howard et al.
2008), COR-1, COR-2 and Extreme ultraviolet imager (EUVI; Wuelser et al. 2004)
instruments on board Solar Terrestrial Relations Observatory (STEREO; Kaiser
2005; Vourlidas et al. 2012), the Large Angle Spectrscopic COronagraph (LASCO;
Brueckner et al. 1992) coronagraphs and Extreme-Ultraviolet Imaging Telescope
(EIT; Delaboudinière et al. 1995) on board the Solar and Heliospheric
Observatory (SOHO; Domingo et al. 1995), the Mark IV, K-Coronagraph (K-Cor),
Coronal Multi-channel Polarimeter (CoMP; Tomczyk et al. 2008) instruments at
the Mauna Loa Solar Observatory (MLSO; Elmore et al. 2003), Atmospheric
Imaging Assembly (AIA; Lemen et al. 2012) telescopes onboard the Solar Dynamic
Observatory (SDO) and the EUV Imaging Spectrometer (EIS; Culhane et al. 2007)
onboard Hinode. Most of earlier studies focused on the signature of origins of
CMEs, determination of their mass/density, dynamic evolution, and the
connection between magnetic flux ropes measured in-situ and CME’s morphology
observed by the white-light coronagraphs and heliospheric imagers.
Nevertheless, from white-light data, one cannot estimate the plasma properties
of CMEs, such as plasma temperature and elemental composition. CMEs may
contain a cool ($\sim 10^{4}$ K) chromospheric material (prominence/filament),
a hot coronal material ($\sim 10^{6}$ K), and flare plasma ($\sim 10^{7}$ K),
thus, giving rise to the emission in the broad wavelength range. Many
processes occurring during CME propagation can interchange different forms of
energies (electromagnetic, kinetic, potential, thermal, etc.), causing plasma
heating or cooling (Bemporad et al. 2007). Thus, to understand these
processes, it is crucial to study the evolution of thermodynamic properties
(such as density, temperature, thermal pressure, etc.) of CMEs, as it
propagates.

However, the evolution of CMEs in the inner corona ($\leq$ 1.5 Rsun) is not
yet completely understood, primarily due to the lack of continuous
observations of the inner corona. The dynamics of CMEs in the inner corona are
important because this region exhibits kinematics of CME, such as rapid
expansion, impulsive acceleration, etc. (Zhang et al. 2001, 2004; Gallagher et
al. 2003; Temmer et al. 2010; Bein et al. 2011; Joshi and Srivastava 2011;
Sarkar et al. 2019; Cremades et al. 2020; Majumdar et al. 2020, 2021, 2022).
However, simultaneous spectroscopy and white-light imaging in the inner corona
are needed to improve our understanding of the temperature and kinematics
evolution of the CMEs during their initial phase of propagation. There are few
studies using ultraviolet (UV) and extreme UV (EUV) imaging and spectral
observations, X-ray, and in situ observations where the thermodynamic
properties of the CMEs have been studied.

The spectroscopic UV observations of CMEs acquired by the Ultraviolet
Coronagraph Spectrometer (UVCS; Kohl et al. 1995) on board the SOHO has helped
us to understand the evolution of CME plasma physical parameters such as
densities, temperatures, abundances in the CME core and leading front, and
their 3-D velocity structures in the corona from 1.5 to 10 Rsun. In this
heliocentric distance range, the density of the CME leading front (LF) is
found to be in the range 104 \- 106 cm-3 (Ciaravella et al. 2003, 2005), and
the temperature has been inferred ranging from 6.0 $\times$ 103 to 2.0
$\times$ 106 K at 1.5 Rsun (Ciaravella et al. 1997; Bemporad et al. 2007). The
study by Bemporad (2022) found CME LF density of order 1 $\times$ 107 cm-3 and
peak temperature $\simeq$ 1.9 $\times$ 106 K at 1.6 Rsun, and density $\simeq$
7 $\times$ 106 cm-3 and peak temperature $\simeq$ 2.1 $\times$ 106 K at 1.9
Rsun. The bright cores of CMEs are usually believed to contain the
filament/prominence material. The densities of the CME core have been found to
range from 1.4 $\times$ 106 to 7.0 $\times$ 108 cm-3 at 1.3 Rsun, and density
decreases from 1.3 $\times$ 106 to 4.0 $\times$ 107 cm-3 at 3.0 Rsun (Akmal et
al. 2001; Raymond and Ciaravella 2004). However, Bemporad (2022) found CME
core density of order 1.1 $\times$ 107 cm-3 at 1.6 Rsun and 9 $\times$ 106
cm-3 at 1.9 Rsun, and core peak temperature $\simeq$ 2.4 $\times$ 106 K at 1.6
Rsun and $\simeq$ 3.2 $\times$ 106 K at 1.9 Rsun. Furthermore, these studies
were limited to a certain heliocentric distance and/or a particular time.

Furthermore, the differential emission measure (DEM) analysis has also been
applied to diagnose the physical properties of CMEs. Many CME eruptions have
been studied using UV-EUV imagers such as the EIT on board SOHO, the
STEREO/EUVI instruments, the AIA telescopes on board SDO, and Hinode/EIS
spectroscopic observations. Long et al. 2018 studied the evolution of a
coronal cavity using spectroscopic Hinode/EIS and broadband SDO/AIA
observations. The DEM inversion techniques on EUV images have enabled us to
infer the 2-D distribution of plasma temperatures and densities inside CMEs.
The main results emerge from these studies are that the CME core temperature
ranges from 0.8 - 2.0 MK for CMEs associated with prominence eruption, and the
core temperature was found to be $\geq$8.0 MK for CMEs associated with a flux
rope (Chmielewska et al. 2016). It was found that the CME core regions were
heated during the CME eruption (Cheng et al. 2012; Landi et al. 2010; Hannah
and Kontar 2013), presumably through magnetic reconnection.

In most CME thermodynamic models, the evolution of thermal energy is derived
under the assumption of adiabatic expansion of plasma material (Durand-
Manterola et al. 2017). However, many studies addressing the energy budget of
CME plasma demonstrate the presence of an additional energy source responsible
for the heating of the CME plasma. The additional heating source provides
thermal energy that was found to be comparable to the total kinetic and
potential energies gained by the eruptions (Akmal et al. 2001; Ciaravella et
al. 2003; Murphy et al. 2011). While in some cases, it was found to be much
larger than the total kinetic and potential energies gained by the eruptions
(Lee et al. 2009; Landi et al. 2010). Also, based on in-situ observations of
ICMEs, the polytropic index ($\gamma$) of ICME plasma was suggested to be of
the order of 1.1 to 1.3 from 0.3 and 20 AU (Liu et al. 2005, 2006), implying
the local heating of ICMEs plasma. Mishra and Wang 2018 found that the
polytropic index of a CME plasma decreased from 1.8 to 1.35 as the CME moved
from 5.9 to 13.9 Rsun, implying that CME first released heat to reach an
adiabatic state and then absorbed heat. However, our understanding of the
evolution of thermodynamic properties of CME during its propagation is still
limited.

Despite this, we still lack an understanding of how the thermodynamic
properties of CMEs change during their propagation in the inner corona (up to
$\sim$ 1.5 Rsun). Using UVCS spectroscopic data, the physical parameters of
CME plasma have been obtained at fixed heliocentric distances starting from
1.5 to 10 Rsun. However, the DEM analysis using SOHO/EIT, STEREO/EUVI, $\&$
SDO/AIA, has enabled us to estimate the physical parameters of CME in the
inner corona (up to $\sim$ 1.5 Rsun). Nevertheless, in none of these studies,
the continuous evolution of the thermodynamic parameters of CME structures in
the inner corona has been studied. Hence, the motivation behind the work
presented here. In this paper, by combining the K-Cor white-light data and the
CoMP Fe XIII 10747 Å line spectroscopic data, we present the spectroscopic
diagnostics of the temperature and density of a CME core observed in the inner
corona on July 20, 2017. We studied the continuous evolution of the
thermodynamic properties, such as the temperature and density of the CME core
from $\sim$ 1.05 to 1.35 Rsun. In Section 4, we provide the details of the
observations. In Section 5, we describe the methods used to derive the
temperature and density of this CME core and present the main results,
followed by a summary & discussion in Section 6.

##  4 Observations

Figure 1: (a) July 20, 2017, CME as observed by the K-Cor. All three parts of
the CME are clearly visible. The yellow rectangular box shows the ROI chosen
for the analysis. (b) The CoMP 10747 Å channel enhanced intensity image. When
CoMP observation started, only the core of the CME was visible in the CoMP
FOV. The yellow box is the CoMP ROI aligned with the K-Cor ROI shown in Figure
(a). (c) The AIA 193 Å channel image processed using MGN to enhance the CME
core structures. The yellow box is the AIA ROI aligned with the CoMP ROI shown
in Figure (b). (An animation of the evolution of the CME core in the K-Cor,
CoMP 10747 Å, and AIA 193 Å channel is available in the Electronic
Supplementary Material. The yellow circle in the animation represents the CoMP
FOV.)

On July 20, 2017, the MLSO/K-Cor observed a CME propagating outward from the
west limb starting at around 17:00 UT. The event is observed with multiple
instruments, including the K-Cor and CoMP, the AIA onboard SDO, and the white-
light coronagraph (COR-1A) of SECCHI onboard STEREO. The K-Cor records
polarized brightness (pB) images of the inner corona from 1.05 - 3 Rsun in 720
- 750 nm passband with a cadence of 15 seconds. The K-Cor images have a pixel
scale of $\approx 5.6$ arcsecs pixel-1. We used white-light level-2 pB data to
estimate the electron density. Figure 1(a) shows the three-part CME in the
K-Cor FOV.

The eruption was also seen in the CoMP Fe XIII 10747 Å channel. The CoMP takes
observation of the polarization state at a few spectral locations across the
profiles of three infrared lines (Fe XIII 10747 Å, 10798 Å & He I 10830 Å)
using a narrow-band tunable filter. It has a field of view (FOV) of 1.05 - 1.4
Rsun, a pixel-scale of 4.46 arcsecs pixel-1, and a typical cadence of 30
seconds. The details of the acquisition and reduction of CoMP data are
described in Tomczyk et al. 2008, and the calculation process is given by Tian
et al. 2013. We used Fe XIII 10747 Å level 2 dynamic data, which contains line
peak intensity, edge enhanced line peak intensity, line-of-sight (LOS) Doppler
velocity, and line width images. On this day, the CoMP observation started at
around 16:57 UT, and only the core of this CME was visible in the CoMP FOV, as
shown in Figure 1(b). This eruption was seen as a braided structure moving out
in CoMP Fe XIII 10747 Å channel and caused a significant enhancement in Fe
XIII line width.

This eruption was also recorded in all SDO/AIA EUV channels from around 15:00
to 18:00 UT. The AIA takes full-disk images of the corona and transition
region up to 1.3 Rsun simultaneously in seven extreme-ultraviolet (EUV)
narrow-band filters. AIA has a pixel-scale of 0.6 arcsecs pixel-1 and a
cadence of 12 seconds. Using aia_prep.pro AIA images were normalized by their
exposure times, rotated, and re-scaled to ensure that each pixel is examining
the same spatial location across the different wavelengths. We also checked
AIA 304 Å data-set to determine if this CME has an associated filament. No
filament could be seen in AIA 304 Å channel prior to the period of study. We
used 94, 131, 171, 193, 211, and 335 Å pass bands images, sensitive over a
temperature range from 105 K to 107 K for the DEM analysis. Since AIA 193 Å
and CoMP 10747 Å images have similar temperature responses, the core of this
CME as seen in AIA 193 Å channel, is shown in Figure 1(c). The AIA 193 Å
channel image has been processed using Multiscale Gaussian Normalization (MGN:
Morgan and Druckmüller, 2014) to enhance the CME core structures.

The yellow rectangular box in all panels of Figure 1 corresponds to the region
of interest (ROI) chosen for the analysis. We have aligned CoMP 10747 Å ROI
with respect to AIA 193 Å ROI. The yellow dashed lines in Figure 2 (a)
indicate the position of four artificial slits at the same location in both
AIA and CoMP ROIs. Each slit is approximately ten arcsec wide and the location
of these slits is such that they cover almost the entire CME core. Since K-Cor
images capture white-light and CoMP images capture narrow-band emission, we
could not use intensity/brightness to align their FOVs as the features look
different in white-light and narrow-band emission images. The CoMP and the
K-Cor both have 1.05 Rsun occulter. We use it as a reference to align the CoMP
& the K-Cor ROIs.

This CME is also observed by the STEREO/COR-1A coronagraph. The COR-1A
coronagraph offers high-cadence (5 minutes) data with FOV from 1.4-4 Rsun, and
a pixel scale of 7.5 arcsecs pixel-1. There is a filament behind the limb,
which could be seen in STEREO EUVI 304 Å channel around 11:46 UT on July 20,
2017 which erupts around 12:46 UT, seen in COR-1A FOV $\sim$13:00 UT. Around
15:00 UT, a braided structure is seen to rise in EUVI 304 Å and 195 Å FOV,
which propagates out and a CME appears (case event for this study) in COR-1
FOV at around 16:40 UT. Therefore, our case event does not have a filament
associated with it. To determine the parameters like LOS depth and volume of
this CME, we used the graduated cylindrical shell (GCS) model (Thernisien et
al. 2009) to fit this CME using the K-Cor & COR-1A vantage point observations.
For GCS fitting, we have used K-Cor white light level 2 Normalizing Radially
Graded Filter (NGRF; Morgan et al. 2006) data and COR-1 level 1 data filtered
using Simple Radial Gradient Filter (SiRGraF; Patel et al. 2022).

##  5 Analysis and Results

###  5.1 Determination of the Electron Temperature

In this work, we determined the two-dimensional plasma temperature
distribution across the CME core using two methods. First, using DEM analysis
on AIA six EUV channels data, and second, using the line broadening of Fe XIII
emission line centered at 10747 Å.

####  5.1.1 Temperature using the Differential Emission Measure Analysis

To infer the DEM from AIA six EUV channels data, we applied the inversion
technique developed by Cheung et al. 2015. For the inversion, we used a
temperature grid spanning log T/K $\in[5.7,7.7]$ with a grid spacing of log T
= 0.1. The emission measure in each temperature grid was obtained using
aia_sparse_em_init.pro in the SolarSoftware (SSWIDL) package. The total
emission measure (EM) was then obtained by summing the EM in all temperature
bins:

$EM=\sum_{j}^{n}EM_{j},$ (1)

where EMj is the EM contained in the jth temperature bin, and n is the total
number of bins (in our case n = 21). The mean temperature can be estimated by
the emission-weighted temperature,

$log\>T_{EM}=EM^{-1}\left[\sum_{j}^{n}EM_{j}\>log\>T_{j}\right],$ (2)

$W_{EM}^{2}=EM^{-1}\left[\sum_{j}^{n}EM_{j}\bigl{(}log\>T_{j}\>-\>log\>T_{EM}\bigr{)}^{2}\right],$
(3)

here log TEM is the EM-weighted log temperature and WEM is the effective width
of the distribution in log T space.

We created DEM maps at each pixel for the logarithmic temperature spanning
from 5.7 to 7.7. The colored boxes in the left panel of Figure 2 (b) show the
selected sub-regions of AIA ROI used to reconstruct the DEM curves. Note that
we have processed AIA 193 Å channel images using the MGN technique to enhance
the CME core structures, the MGN technique has not been used for DEM analysis.
The DEM curves for these box regions are shown in the right panel. The DEM in
all regions peaked at around log T/K $\sim$6.3. Figure 2 (c) show the EM maps
of the AIA ROI at 2017-07-20 T 17:16:11 UT. We can see that the EM of the core
of the CME is mostly confined in log T/K $\in$ [6.05, 6.65]. Then using
Equation (2) we created EM-weighted log temperature (log TEM) maps of the AIA
ROI. We obtained the intensity and log TEM values along the AIA slits (shown
in the right panel of Figure 2 (a)) and took their averaged over the width of
each slit to ensure a good signal-to-noise ratio. To illustrate the full
evolution of the core of the CME, we constructed space-time maps for all four
slits. The left panel of Figure 3 shows the AIA 193 Å intensity space-time
maps, and the right panel shows the log TEM space-time maps for slit 2 and 3.
We visually inspected the AIA 193 Å intensity space-time map of slit 2 and
tracked the eruption along this slit as shown by the blue dashed curve in the
top left panel of Figure 3, which we fitted using the cubic spline
interpolation method. Using these height-time values, we fitted the spline
curve on log TEM space-time map of slit 2 as shown in the top right panel of
Figure 3 by blue dashed curve and obtained the values of log TEM and WEM (WEM
is calculated using Equation (3)) along this curve. The same procedure is
repeated for the remaining slits. Note that the spline fitted curve has approx
24 arcsec spatial extent at a particular time.

Figure 2: (a) The left panel shows the AIA ROI (shown by yellow box in Figure
1 (c)), and right panel shows the CoMP ROI (shown by yellow box in Figure 1
(b)). The yellow dashed lines in both panels show the locations of four co-
spatial slits chosen in the two ROIs. (b) The left panel shows AIA 193 Å ROI
image at 2017-07-20 T 17:16:17 UT. The colored boxes show the selected sub-
regions used to reconstruct the DEM curves. The DEM curves for these box
regions are shown in the right panel. The DEM in all regions peaked at around
log T/K $\sim$ 6.3. (c) EM maps of the AIA ROI at 2017-07-20 T 17:16:11 UT.
The color coding indicates the total EM contained within a log temperature
range indicated in the bottom left corner of each panel. (An animation is
available in the Electronic Supplementary Material.)

Figure 3: The left panel shows AIA 193 Å intensity space-time maps, and the
right panel shows the EM-weighted log temperature space-time maps for all
slits. We visually traced the eruption along each slit intensity space-time
map shown by the blue dashed curve in the left panel, which is fitted using
the cubic spline interpolation method. The same curve is overplotted over log
TEM space-time map of the respective slit.

The calculation of EM-weighted temperature is based on the assumption that the
plasma is isothermal along the LOS. However, the left panel of Figure 2 (b)
demonstrates that the emission measure has a spread over a range of
temperatures. To investigate the temporal evolution of the CME core emission
in different temperature bins, we produce space-time maps of log EM for slit
3. Figure 4 shows temporal variation in log EM along slit 3 for different
temperature bins. The space-time maps show that the CME core rises gradually,
and at $\sim$17:30 UT, the CME core moves out of the AIA FOV. The CME core
appears in most of the temperature bins indicating that the CME core is multi-
thermal. However, the EM of the CME core is mainly confined in log T/K $\in$
[6.05, 6.65]. The blue dashed curve in all panels of Figure 4 is the same
spline curve as in the bottom panel of Figure 3.

Figure 4:  The temporal variation in log EM along slit 3 for different
temperature bins. The blue dashed curve in all panels of is the same spline
curve as in the bottom panel of Figure 3.

####  5.1.2 Effective temperature from Fe XIII Line Width

Using the Fe XIII line width and considering that the broadening of the line
may occur due to the thermal motions of ions, the non-thermal motions in the
corona, the instrumental broadening, the expansion of CME as it moves outward,
and the additional turbulence created by the CME propagation in the corona,
the CME plasma temperature can be obtained. In order to calculate the non-
thermal line width (NTLW) in the corona, we used the previous day, i.e., July
19, 2017, CoMP Fe XIII 10747 Å line width data when CME is not present. We
subtract the thermal width (21 km s-1, corresponding to the peak formation
temperature of Fe XIII of $\sim$1.6 MK) and instrumental width (21 km s-1)
calculated by Morton et al. 2015 from the line width obtained for each pixel
(McIntosh and De Pontieu 2012). To obtain the radial profile of NTLW, we took
a median value of NTLW of pixels lying along 40 degrees (to ensure a good
signal-to-noise ratio) about the equator at each radius. Figure 5 shows the
variation of the NTLW with height above the solar surface. We found that the
NTLW did not vary significantly with height. Therefore, for our calculations,
we used the mean value of NTLW, 19.32 km s-1.

Figure 5: The variation of NTLW with height above the solar surface.

We subtract non-thermal width (NTLW) and instrument width in quadrature from
the total line width; the residual width is Doppler/thermal width (i.e., width
due to thermal motions of ions). Furthermore, the plasma temperature can be
estimated using the following Equation:

$T=\frac{1}{2}\frac{m}{k_{B}}v_{1/e}^{2},$ (4)

where m is the mass of the Fe XIII ion, kB is the Boltzmann constant, and v1/e
is the velocity derived from the Doppler half-width, $\Delta\lambda_{1/e}$.
Note that we did not take into account the broadening of the line due to the
expansion of the CME core and the additional turbulence created by the
propagation of the CME. Hence Equation 4 provides the upper limit to the
plasma temperature. We refer to it as effective temperature, Teff.

We selected an ROI from the CoMP (Figure 1 (b)) image same as AIA 193 ROI and
placed four artificial slits co-spatial with AIA slits (Figure 2 (a)). We
averaged the Fe XIII line enhanced intensity and line width over the width of
the slits and created the space-time maps of line enhanced intensity and total
width as shown in the left and right panels of Figure 6, respectively. Then,
using the height-time values along the spline fitted curve on AIA 193 slit 2
intensity space-time map, we fitted the Fe XIII enhanced intensity and line
width space-time maps of slit 2, which is shown by the blue dashed curve in
the top panel of Figure 6. Since the CoMP has a larger FOV than AIA, we
visually tracked the eruption in CoMP FOV outside the AIA FOV shown by the
cyan curve in Figure 6. The line width values were obtained along the blue and
the cyan curves. Moreover, to calculate the Doppler/thermal width values, the
NTLW (19 km s-1) and instrumental width (21 km s-1) were subtracted from the
total line width values. The effective temperature was calculated using
Equation (4). This procedure is repeated for the remaining slits also.

Figure 6: The left panel shows the CoMP Fe XIII 10747 Å enhanced-intensity
space-time maps, and the right panel shows the Fe XIII line width space-time
maps. The blue dashed curve in each slit space-time map is fitted using the
height-time values obtained from spline fitting AIA 193 Å intensity space-time
map of the respective slit. The eruption is further tracked in the CoMP FOV
outside the AIA FOV and is shown by the cyan curve. Black stripes represent
gaps in data.

In addition to this, expansion of the CME core and additional turbulence
created by the CME propagation will also contribute to the non-thermal
broadening. To model the expansion of the CME core, we used the graduated
cylindrical shell (GCS) model developed by Thernisien et al. 2009; Thernisien
2011 and followed the fitting procedure described in Majumdar et al. 2022. We
used the GCS ice-cream cone model to fit the core of the CME. Figure 7 shows
the variation of the LOS nominal depth of the CME core plasma (LCME) with time
and heliocentric distance of the CME core front. We found that the LCME of the
CME core increases almost two times as the core evolves during this period.
The expansion velocity of the CME core is found to be approx. 50.76 km/s,
which is larger than the total line width. Since the features look different
in the white-light $\&$ IR emission band ( Fe XIII 10747 Å), we conclude that
we may not be modelling the same feature using the GCS model fit, which we are
tracking in IR emission. Therefore, the expansion factor for these two
wavelength regimes would be different, which makes it difficult to apply the
expansion factor obtained from the GCS model to account for the broadening of
the Fe XIII 10747 Å line due to the expansion of the CME core.

Figure 8 shows the evolution of log temperature of the CME core with height
and time. The green diamond symbols show the variation of the EM-weighted log
temperature (log TEM) averaged over the spatial direction along the blue curve
shown in Figure 3. The shaded grey region shows the effective width of the
distribution in log T space, which is obtained by adding WEM and the standard
deviation for this spline-fitted curve. We found that within this region of
uncertainty, the EM-weighted temperature of the core of the CME remains almost
constant as CME evolves, and the mean value of log TEM/K of the core of the
CME is found to be in the range of 6.28 - 6.36. The blue cross symbols in the
Figure 8 show the variation of log effective temperature averaged over the
spatial direction along the blue and the cyan curves shown in Figure 6, and
the red bars are one sigma deviation in log Teff values. The log effective
temperature of the core of the CME has a similar variation to the EM-weighted
log temperature and has mean values in the range of 5.97 - 6.57.

Figure 7:  The variation of LOS width (LCME) of the CME core with time or
heliocentric height.

Figure 8: The evolution of log temperature of the CME core with height and
time. The green diamond symbols show the variation of the EM-weighted log
temperature (log TEM) averaged over the spatial direction along the blue curve
shown in Figure 3. The grey shaded region is the effective width of the
distribution in log T space. The blue cross symbols show the variation of log
effective temperature averaged over the spatial direction along the blue and
the cyan curves shown in Figure 6, and the red bars are one sigma deviation in
log Teff values.

###  5.2 Estimation of the Electron Density

The electron density can be derived using the CoMP Fe XIII 10747 $\&$ 10798 Å
density-sensitive line pair. Since there were no good signal-to-noise ratio
data frames available during the period of CME under consideration, we could
not use this line pair for density calculation. Therefore, we use K-Cor
polarized brightness data to derive the electron density.

The polarized brightness observed by the white-light coronagraphs primarily
depends on the column electron density (LOS integration of the electron
density). Transient phenomena, such as CMEs, cause the intensity (hence,
density) enhancements in a sequence of coronagraph images. A suitable pre-
event image is subtracted from the frames containing the CME to calculate the
CME density. Since no pre-event frame was available for the CME event on July
20, 2017, we chose a frame on July 21, 2017, at around 02:21:59 UT, much later
after the CME had passed the K-Cor FOV, and subtracted this image from the CME
frames. As a result, the background F-corona and static K-corona are removed,
leaving us with the brightness changes caused by the CME.

The excess column electron density Ne (due to the CME) can be estimated by
taking the ratio of the excess observed pB (pBobs) to the polarized brightness
of a single electron (pBe) assumed to lie on the plane of sky (POS) (Colaninno
and Vourlidas 2009). The POS assumption is valid for July 20, 2017, CME as
indicated by very small LOS Doppler velocities values in CoMP Fe XIII 10747 Å
data. The pBe is computed analytically from the scattering geometry using the
equations given in Billings 1966. We used eltheory.pro in the SolarSoftware
(SSWIDL) package to calculate the pBe, and the limb darkening coefficient used
in this routine was calculated using the Equation (5) of Hestroffer and Magnan
1998 for wavelength = 735 nm (for the K-Cor). The CME electron density ne, can
be obtained by dividing the derived column density Ne to the LOS nominal depth
of the CME plasma LCME, ne = Ne/LCME (Bemporad 2022).

We determined the column electron density for the entire K-Cor ROI (the yellow
box in Figure 1(a)) and chose four slits co-spatial with AIA and CoMP slits.
The resulting 2-D maps of the column density (Ne) for slit 2 $\&$ 3 are shown
in Figure 9. The green region in all panels shows the evolution of the core of
the CME with time along the respective slit. The blue and cyan curves are the
same as described in section 5.1.2. We obtained the values of Ne along the
spline fitted curves and divided it by LCME to obtain the CME core electron
density values (ne). The variation of the CME core electron density (ne) along
the spline fitted curves for slit 2 $\&$ 3 is shown in Figure 10 by blue cross
symbols. The dark grey bars show one sigma uncertainty in the electron
density. We found that the CME core’s density falls by a factor of $\sim$3.6
as the core evolves. The density values of the CME core are in the range
(5.85- 20.85)$\times$ 107 cm-3. We also derived the volume of the CME core
using the GCS model fitted parameters. The volume of the CME core increases
approx. six times while the core evolves in the K-Cor FOV. Hence, the decrease
in CME core density is consistent with the volume increase of the CME core.
Similar results were also obtained for slits 1 $\&$ 4.

Figure 9: The column electron density space-time maps. The blue and the cyan
curves are the same as in Figure 6.

Figure 10: The evolution of electron density (ne) of the CME core with height
and time. The blue cross symbols show the variation of ne averaged over the
spatial direction along the blue and the cyan curves shown in Figure 9, and
the dark grey bars are one sigma deviation in ne values.

##  6 Summary and Discussions

In this work, we carried out the spectroscopic diagnostics in the inner corona
(1.05 - 1.35 Rsun) to derive the thermodynamic property of a CME by combining
the CoMP Fe XIII 10747 Å line width data and the K-Cor polarized brightness
(pB) data. We studied the evolution of a CME core’s thermodynamic properties
that occurred on July 20, 2017. We obtained the effective temperature of the
CME core using the line broadening of the Fe XIII emission line centered at
10747 Å. We have also applied the DEM inversion technique on AIA six EUV
channels data to determine the EM - weighted temperature of the CME core and
compare it with the effective temperature obtained using Fe XIII line width.
The column density of the CME core is derived using the K-Cor pB intensity. To
obtain the LOS depth (LCME) and volume of the CME core, we used the graduated
cylindrical shell (GCS) model to fit this CME core using the two (K-Cor &
COR-1A) vantage point observations. We obtained the electron density of the
CME core by dividing the CME core column density by LCME of the CME core
plasma.

We find that within one sigma error, the EM-weighted temperature of the CME
core remains almost constant as CME evolves, and the mean log TEM/K of the CME
core is found to be in the range 6.28 - 6.36. The effective temperature of the
CME core also has a similar variation to the EM- weighted temperature, and
mean log Teff/K has values in the range of 5.97 - 6.57. The non-thermal
motions in the corona contribute significantly to the broadening of a spectral
line (McIntosh and De Pontieu 2012; Brooks and Warren 2016; Pant et al. 2019).
In earlier studies, the plasma temperatures have also been obtained using the
width of spectral lines (e.g., H I Ly-$\alpha$ and Ly-$\beta$, C III, etc.)
observed in the CMEs (Ciaravella et al. 2000; Heinzel et al. 2016).
Nevertheless, these studies did not take into account the contribution of non-
thermal motions in the width of the spectral line. Hence, the plasma
temperature limit provided by these studies is not quite accurate. Therefore,
it is required to subtract NTLW from the total width of a spectral line
(Heinzel et al. 2016). In our analysis, we have calculated NTLW and subtracted
this from the total width of the Fe XIII 10747 Å line. The consequence is that
the CME core’s effective and EM-weighted temperatures have similar values
within the error bars. Thus, we can conclude that the effective temperature
derived from line width by taking into account the non-thermal in the corona
and instrumental broadenings is a good measure of CME plasma temperature. The
million-degree kelvin temperature of the CME core indicates that the core of
this CME is not associated with a prominence material.

We find that the CME core’s electron density falls by a factor of $\sim$3.6 as
the core evolves and has values in the range (5.85- 20.85)$\times$ 107 cm-3.
As pointed out by Bemporad et al. 2018, the uncertainty in the density
determination using pB is mainly due to the POS assumption (the assumption
that all the plasma is located on the POS) and due to the uncertainty in the
depth of a CME structure along the LOS (LCME). However, the POS assumption is
valid for July 20, 2017, CME as indicated by very small LOS Doppler velocities
values in CoMP Fe XIII 10747 Å data, and we get a better estimate of LCME by
performing GCS model fit to the CME core.

We find that the temperature of the CME core remains almost constant despite
expected adiabatic cooling due to the expansion of the CME core, which
suggests that the CME core plasma must be heated as it propagates. In previous
studies based on in-situ observations of ICMEs, the polytropic index
($\gamma$) of ICME plasma is also found to be close to unity implying the
isothermal expansion of ICME plasma. $\gamma$ of ICME plasma was suggested to
be of the order of 1.1 to 1.3 from 0.3 and 20 au (Liu et al. 2005, 2006),
indicating local heating of ICME plasma. Furthermore, in few MHD models of CME
have also used $\gamma$ close to unity. Gibson and Low 1998 constructed a
theoretical MHD model describing the ejection of a 3-D CME out of the solar
corona by making an assumption $\gamma$ $\sim$ 4/3. Odstrcil et al. 2002 have
used $\gamma$ = 1.05 in a coronal 2-D MHD model to simulate the disruption of
a sheared helmet streamer launching a CME. Chen 1996 $\&$ Krall et al. 2000
have used $\gamma$ = 1.2 in their theoretical treatment describing the
initiation, propagation, and driving mechanisms of ICMEs. Thus, we can infer
that the expansion of July 20, 2017, CME core behaves more like an isothermal
than an adiabatic process during its evolution in the inner corona from 1.05 -
1.35 Rsun. It may also be possible that the thermal force is the internal
driver of CME expansion, as highlighted in the study by Mishra and Wang 2018.
The presence of plasma heating processes occurring during the CME expansion is
also reported in many studies in the literature (Akmal et al. 2001; Ciaravella
et al. 2003; Lee et al. 2009; Landi et al. 2010; Murphy et al. 2011; Bemporad
2022). The candidate heating mechanisms are briefly discussed in studies by
Kahler and Reames 1991; Kumar and Rust 1996; Murphy et al. 2011; however,
there is no widely accepted heating mechanism. Moreover, the above conclusion
that the CME core is not a filament/prominence and the CME core is continually
heated during its early expansion has an important inference on the initiation
mechanism of CMEs. Currently, the existing theories of CME initiation fall
into two categories: one is based on the ideal MHD instability of magnetic
flux rope ( Török and Kliem 2005; Kliem and Török 2006; Fan and Gibson 2007;
Aulanier et al. 2010; Kliem et al. 2014; Amari et al. 2018), which often
contains a filament, and the other is based on magnetic reconnection
(Antiochos et al. 1999; Moore et al. 2001; Wyper et al. 2017; Jiang et al.
2021b, a), which does not require a pre-existing flux rope or filament. In the
reconnection model, the core of the CME is formed by reconnection, and thus it
is continually heated by the reconnection. On the other hand, in the ideal
instability-based model, the CME core is the pre-existing flux rope; thus, no
heating can be provided during the ideal expansion. Hence, July 20, 2017, CME
event supports the reconnection model.

Our work demonstrates the potential of the CoMP and the K-Cor and future
multi-channel coronagraphs upgraded-CoMP (UCoMP) at MLSO and Visible Emission
Line Coronagraph (VELC: Prasad et al., 2017; Banerjee et al., 2017) onboard
Aditya-L1 to study the thermodynamic evolution of CMEs in the inner corona.
The UCoMP has the capability to perform simultaneous 2-D imaging and high-
resolution spectroscopy in the inner corona. It has a FOV of 1.03 - 1.95 Rsun
and a spatial resolution of 6 arcsecs (3 arcsecs/pixel). The UCoMP has seven
coronal emission lines (FeXIV 530.3 nm, FeX 637.4 nm, ArXI 691.8 nm, FeXV
706.2, FeXI 789.4 nm, FeXIII 1074.7 nm, and 1079.8 nm) covering a wide range
of temperature (log Teff $\sim$ 5.80 - 6.63). A similar analysis can be
applied to the observations of CMEs that will be acquired simultaneously by
MLSO/UCoMP and MLSO/K-Cor. In addition, FeX 637.4 nm and FeXI 789.4 nm are
temperature-sensitive lines, and FeXIII 1074.7 & 1079.8 nm are density-
sensitive lines. The ratio of these lines, together with the help of atomic
spectral line databases (Dere et al. 1997), it is possible to infer the 2-D
distribution of plasma temperatures and densities inside the CMEs. This study
is a testing bed for VELC/Aditya-L1, which will perform both spectroscopy and
imaging of the CMEs in the inner corona in three visible (one continuum
centered at 500 nm and two emission lines; FeXIV 530.3 nm & FeXI 789.2 nm )
and one infrared (FeXIII 1074.7 nm) passbands (Patel et al. 2021).

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

JS led the analysis and carried out the image processing and spectroscopic
based investigations. VP and RP planned the analysis and identified the case
for analysis. VP and DB assisted in the interpretation of the results. JS
prepared the manuscript. All authors took part in the discussion.

## Funding

JS is supported by funds of the Council of Scientific $\&$ Industrial Research
(CSIR), India, under file no. 09/0948(12550)/2021-EMR-I.

## Acknowledgments

We would like to thank ARIES for providing the computational facilities.
Courtesy of the Mauna Loa Solar Observatory, operated by the High Altitude
Observatory, as part of the National Center for Atmospheric Research (NCAR).
NCAR is supported by the National Science Foundation. The SECCHI data used
here were produced by an international consortium of the Naval Research
Laboratory (USA), Lockheed Martin Solar and Astrophysics Lab (USA), NASA
Goddard Space Flight Center (USA), Rutherford Appleton Laboratory (UK),
University of Birmingham (UK), Max-Planck-Institut for Solar System Research
(Germany), Centre Spatiale de Li$\grave{e}$ge (Belgium), Institut d’Optique
Th$\acute{e}$orique et Appliqu$\acute{e}$e (France), Institut d’Astrophysique
Spatiale (France). We also acknowledge SDO team to make AIA data available.

## Data Availability Statement

The MLSO/CoMP, MLSO/K-Cor, SDO/AIA, and STEREO/SECCHI data sets analyzed for
this study can be found in their respective data archives under the open data
policy. The data sets generated in this study can be made available upon
request.

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