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이학석사학위논문

An Analysis of the Ellerman Bomb

Spectra Observed by the FISS

고속영상태양분광기로 관측한 엘러먼 폭탄 스펙트럼 분석

2018년 8월

서울대학교 대학원

물리 ·천문학부 천문학 전공

서 민 주

An Analysis of the Ellerman BombSpectra Observed by the FISS

by

Minju Seo(astrosmj@astro.snu.ac.kr)

A dissertation submitted in partial fulfillment of the requirements for

the degree of

Master of Science

in

Astronomy

in

Astronomy Program

Department of Physics and Astronomy

Seoul National University

Committee:

Professor Yongsun Park

Professor Jongchul Chae

Professor Sungchul Yoon

One must live the way one thinks or end up thinking the way one has lived.

Paul Bourget

Abstract

Ellerman bombs (EBs) are small, transient brightening features that were

firstly found in the solar Balmer lines, and later observed in other spectral

lines. They are considered to be produced when the magnetic reconnection

occurs in the low solar atmosphere, and heat the area. Many studies have been

conducted to identify the effects of EBs on the solar atmosphere by comparing

the observed line profiles with the synthetic profiles obtained from the non-LTE

radiative transfer computations using a model atmosphere. The previous studies

had limitations in the observational data due to poor resolution. In the present

work, we use the data taken by the Fast Imaging Solar Spectrograph (FISS),

which provides both Hα and Ca II 8542A line spectral data with temporospatial

resolution high enough for the advanced study of EBs.

We aim to construct the model atmosphere of an EB that can best explain

the observed profiles of the two lines simultaneously. As the first attempt, we

have built model atmospheres by adding a Gaussian temperature enhancement

function specified by temperature (∆T ), width (W ), and height (h) to the one-

dimensional model atmosphere of the solar quiet region where the width W is

set to vary from 80 to 240km. With this approach, however, we could not find

any model atmosphere which successfully explains both the Hα and the Ca II

lines at the same time. The Ca II synthetic profile obtained from the model

that best describes the Hα line shows much higher wing intensities than the

observational data, while the Hα synthetic profile from the Ca II line best model

has much weaker wings than the observations. To resolve the discrepancy, we

have introduced a temperature increasing function with a much narrower width

i

(W ∼ 20km). Using this new function, we could obtain the model atmosphere

that can simultaneously explain both the observed Hα and Ca II lines. We

have found that the temperature excess in this model occurs at a height (h

= 120km) that is much lower than the previously-thought formation height of

EBs. In addition, we observed the rapid increase and decrease of intensities in

both wings of the Hα and the Ca II lines, which indicates that the atmospheric

structure changed because of heating and cooling. In fact, it was found from

the non-LTE modeling that the temperature rapidly increased and decreased.

Our results indicate that the EB occurs in the photosphere, whereas the

previous studies suggesed the low chromosphere as the site of EBs. The forma-

tion of the wings of Hα and Ca II lines is limited to very narrow layers. Next,

the sudden change in brightness over a lifetime of the EB suggests that the

heating and cooling of the EB is done in a very short time. Further studies with

more EBs will be needed to generalize these results.

Keywords: The Sun: Active Region, Photosphere, Ellerman Bombs, Radiative

Transfer, Spectral Analysis

Student Number: 2015-22603

ii

Contents

Abstract i

List of Figures iv

List of Tables vi

Chapter 1 Introduction 1

1.1 The Ellerman Bombs . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Non-LTE Modeling of the Ellerman Bombs . . . . . . . . . . . . 5

1.3 Purpose of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Chapter 2 Observations 8

Chapter 3 Modeling 11

Chapter 4 Results 17

4.1 Results From the Conventional Modeling . . . . . . . . . . . . . 17

4.1.1 The First Modeling . . . . . . . . . . . . . . . . . . . . . . 17

4.1.2 Two-hump Modeling . . . . . . . . . . . . . . . . . . . . . 22

4.2 The Narrow Hump Modeling . . . . . . . . . . . . . . . . . . . . 29

4.2.1 Results From The Narrow Hump Modeling . . . . . . . . 29

iii

4.2.2 Additional Results From Another EB . . . . . . . . . . . 33

4.3 Temporal Evolution of EBs . . . . . . . . . . . . . . . . . . . . . 36

Chapter 5 Summary & Discussions 40

5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2 Comparison with the Previous Studies . . . . . . . . . . . . . . . 41

5.3 Implications of Our Results . . . . . . . . . . . . . . . . . . . . . 42

Bibliography 44

초록 48

iv

List of Figures

Figure 1.1 Line profiles of the EB on the Hα and the Ca II 8542A

lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Figure 1.2 EB triggering model from the magnetic reconnection . . . 4

Figure 1.3 General non-LTE modeling procedure . . . . . . . . . . . 6

Figure 2.1 Multiwavelength raster images of the Ellerman bombs . . 10

Figure 3.1 Comparison between the observed profiles and the syn-

thetic profiles of the solar quiet region . . . . . . . . . . . 12

Figure 3.2 Temperature structure of the EB model atmosphere . . . 14

Figure 3.3 Changes in the synthetic profiles with respect to the Line-

of-Sight angle . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 4.1 The best result of the modeling for the Hα line . . . . . . 19

Figure 4.2 The best result of the modeling for the Ca II 8542A line 20

Figure 4.3 The figure which draws the best results from each line in

one graph . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 4.4 Temperature structure of the two-hump model atmosphere 25

v

Figure 4.5 The best result from the two-hump modeling for the Hα

line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Figure 4.6 The best result from the two-hump modeling for the Ca

II 8542A line . . . . . . . . . . . . . . . . . . . . . . . . 27

Figure 4.7 The figure which draws the best results of two-hump models 28

Figure 4.8 Temperature structure of the narrow hump model atmo-

sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Figure 4.9 The best result from the narrow hump model . . . . . . . 32

Figure 4.10 Multiwavelength raster images of an another EB . . . . . 34

Figure 4.11 The best narrow hump model results of an another EB . 35

Figure 4.12 Temporal evolution of the EB intensity . . . . . . . . . . 37

Figure 4.13 Temporal evolution of the EB wing intensities . . . . . . 38

Figure 4.14 Temporal evolution of the EB best model temperature . . 39

vi

List of Tables

Table 3.1 Grid of model atmospheres . . . . . . . . . . . . . . . . . . 13

Table 4.1 The best models in each lines . . . . . . . . . . . . . . . . 18

Table 4.2 Grid of model atmospheres for two-hump model . . . . . . 23

Table 4.3 The best models from the two-hump modeling . . . . . . . 24

Table 4.4 Grid of model atmospheres for the narrow hump model . . 29

Table 4.5 The best results from the narrow hump modeling . . . . . 31

Table 4.6 The best narrow hump model results of an another EB . . 33

vii

Chapter 1

Introduction

1.1 The Ellerman Bombs

In 1917, Ferdinand Ellerman from the Mount Wilson Observatory reported

sudden brightening events observed in the solar Hα line (Ellerman 1917) under

the name ‘Solar Hydrogen Bombs’. As to these features, he initially quoted them

as “seemed hardly real”. Nonetheless, after observing the same features and

finding the previous report before his observation (Mitchell 1909), he accepted

that they are the parts of the solar activities. Later, Severny (1956) observed

these features using higher spectral resolution than Ellerman’s observations and

found that the wings of the Hα line became very bright when they occurred.

He reported that when these phenomena occurred, brightening appeared to the

extent of 15A away from the center of the line, and he called them “moustaches”.

Early researchers called them as “moustaches” or “Ellerman’s solar hydrogen

bombs”, but since the word “bomb” proposed by Ellerman reflected the short

and intense characteristics of them well, the name of these phenomena became

1

fixed as the Ellerman Bombs (EBs).

EBs are observed in active regions, and they have size of about 1′′ and

lifetime less than 30 minutes (Nelson et al. 2013; Rutten et al. 2013). For this

reason, although the first report of the EB was made over 100 years ago, full-

fledged research on EBs could be done in recent years with the development at

the temporospatial resolution of the observational instruments.

Although the presence of EB was first reported in the solar Hα line, subse-

quent studies have shown that EBs are also observed in spectral lines other than

the Hα line. The lines that reported the observations of EBs are the 1600A (Qiu

et al. 2000) & 1700A (Vissers et al. 2013) UV continuum, the G band (Herlen-

der & Berlicki 2011), the He I D3 & 10830A lines (Libbrecht et al. 2017), the Ca

II H & K (Matsumoto et al. 2008) lines and the Ca II 8542A (Fang et al. 2006;

Yang et al. 2013) lines. Since these various lines show different environments

and characteristics in the solar atmosphere, studying EBs through various lines

have been widely used to study EBs.

From the research of EBs in the Hα line spectra, the emission core in the

form of a Gaussian is observed in the near wings. Moving toward the far wings,

the emission in the wings decreases like a form of the power-law function (Kitai

1983). Also, these wing changes were observed not only in the Hα line but also

in the Ca II 8542A line (Yang et al. 2013, 2016). The changes described above

can be found in Figure 1.1.

It is widely accepted that the magnetic reconnection which occurs in the

lower chromosphere is responsible for EBs as depicted in Figure 1.2. At that

time, energy is released near the reconnecting region and the temperature in

the area increases (Hashimoto et al. 2010).

2

Figure 1.1: Top: Center-to-wing line profiles of the EB on the Hα line.Where

∆λ on x-axis means that the distance from the central wavelength, ∆I is the

enhanced emission profile of the EB compared to the quiet region profile, and I0

means that the continuum intensity. (Image reproduced from Kitai 1983) Down:

Profile of the EB on the Ca II 8542A line. A thick solid line is the line profile

of the EB, and the thin solid line is the quiet region profile. (Image reproduced

from Yang et al. 2016)

3

Figure 1.2: The model of EBs triggered by the magnetic reconnection. (Image

reproduced from Hashimoto et al. 2010)

4

1.2 Non-LTE Modeling of the Ellerman Bombs

The temperature enhancement in an EB can be determined from the non-LTE

modeling of the line profiles. (Berlicki & Heinzel 2014; Grubecka et al. 2016).

The modeling process is generally as follows. First, the temperature structure

of the solar quiet region is set as the base. Then, the temperature enhancement

function of a Gaussian form is added to the base temperature structure to

construct the modified model atmosphere. The temperature enhancement is

fully specified by the choice of height (h), width (W ), and peak excess (∆T ).

Finally, the non-LTE radiative transfer computations is carried out using the

modified model atmospheres and as a result the synthetic profiles are obtained

and compared with the observed profiles.

Figure 1.3 shows an example of the EB modeling. The graphs on the left

show the modified model atmospheres produced by the method mentioned

above and the right graphs are the synthetic profiles of the Hα lines. The dotted

lines represent the quiet atmosphere model, and the solid lines represent the EB

models. By comparing the observed profiles of EBs with the synthetic profiles,

one can estimate the temperature structure of the atmosphere perturbed by EBs

from the model which produces the profiles that have the smallest difference

from the observations.

1.3 Purpose of Thesis

As we explained before, obtaining the observational data with a high spectro-

spatial resolution is essential to make the non-LTE modelling be more reliable.

However, we found that the previous EB modeling studies were subject to ob-

servational limitations. Some studies were conducted using from the filtergrams,

or some studies used fixed spectrographs which cannot correctly track the EB.

5

Figure 1.3: General non-LTE modeling procedure. Left: Model atmospheres

Right: synthetic Hα profiles. In each graph, dotted lines represent the tempera-

ture of the quiet region atmosphere and corresponding line profiles of the region,

and solid lines represent. (Image reproduced from Berlicki & Heinzel 2014)

6

The present research aims to develop improved models by using the high-

spectral resolution data. Our observational data have spectrospatial resolution

high enough to study the fine structures of EBs. Also, we use the spectral data

from two lines which were obtained at the same time for the same region. We

use the Hα and the Ca II 8542A lines. As we mentioned before, these lines

show clear features on the spectral lines when EBs occurred. We expect that

the usage of these two lines can help to determine the structure of the solar

atmosphere disturbed by EBs better than when only one line is used. Also, the

accurate modeling of the temperature structure of EBs can help us to estimate

the energy released by EBs more precisely.

7

Chapter 2

Observations

Our observational data for this research were obtained with the Fast Imaging

Solar Spectrographs (FISS), which is installed on the 1.6m Goode Solar Tele-

scope (GST) in Big Bear Solar Observatory (BBSO) (Chae et al. 2012). The

FISS is an imaging spectroscopy instrument that acquires spatial and spectral

information of a target area. The FISS is designed to study fine-scale structures

and provides data with high temporal (< 20 seconds), spatial (0.′′3), and spec-

tral (30mA) resolutions. Also, the FISS can simultaneously observe the same

region using the Hα line and the Ca II 8542A line. The coverage of each spectral

band is 9.7A for the Hα and the 12.9A for the Ca II 8542A lines, and it is broad

enough for the study of EBs.

The area of our interest is the active region NOAA AR 12080, observed on

June 5, 2014. During our observation time, the region was located at (-520′′,

-200′′) in the solar disk and the angle between our line-of-sight and the radial

direction was 33◦. In this observation, the field of view was 18′′ × 40′′ and

the cadence between images is 16 seconds. We observed several solar activities

8

during the observing time, including the EB that is the main feature of our

study. The EB showed up at 17:24:26 UT and disappeared at 17:43:32 UT.

During its lifetime, we obtained 52 FISS scans of the region.

Figure 2.1 is the multiwavelength raster images of the region observed at the

time when the EB occurred. The areas indicated by the circles are the region

where the EB found. The EB is visible in the photospheric images, but cannot

be seen in the chromosphere.

9

Figure 2.1: Multiwavelength raster images of the active region which EB occurred, Up: From the center of the Hα

line, -1.3A, -0.5A , 0A, 0.5A, 1.3A, respectively. Down: From the center of the Ca II 8542A line, -0.75A, -0.25A ,

0A, 0.25A, 0.75A, respectively.

10

Chapter 3

Modeling

Next, we perform the modeling of EBs to compare with the FISS observa-

tional data. Here, we use the RH code (Uitenbroek 2001; Pereira & Uiten-

broek 2015) to perform the non-LTE radiative transfer computations for one-

dimensional model atmospheres. This code can solve the non-LTE radiative

transfer equations in a short time by using the multilevel accelerated lambda

iteration (MALI) method (Rybicki & Hummer 1991, 1992). Therefore, it is quite

suitable for our research requiring the calculation of many model atmospheres.

As the basis of EB models, we use FALC model (Fontenla et al. 1993) which

described the average solar quiet region. Figure 3.1 shows the comparison be-

tween the FISS observational data of the solar quiet region and the synthetic

profile from the model. Results from the figure show that there are little dif-

ferences between profiles, and we conclude that we can use this model for our

research.

To perform the radiative transfer calculations, the model should contain

data as follows: temperature, electron density, turbulent velocity, hydrogen pop-

11

Figure 3.1: Up: Comparison of the quiet region FISS Hα profile at the disk

center and the synthetic profile obtained from FALC model. The red line is the

synthetic profile, and the black line is the FISS observed profile. Down: Same

for the Ca II 8542A line.

12

ulations from n = 1 to n = 5 level and proton densities for the height. In our

modeling, we use these parameters from FALC model as the base, and we make

different models by only changing the temperature. The first reason why we fix

other parameters is that we want to focus our research on the effect caused by

the heating from EBs which is mainly the change of the temperature structure.

Also, previous research reported that a change of models on density does not

make a significant difference in results (Berlicki & Heinzel 2014).

Table 3.1: The range of the grid of model atmospheres in our modeling.

Parameters Range Gap Steps

∆T (K) 50 < ∆T < 5000 100 100

h (km) 50 < h < 850 50 17

W (km) 80 < W < 240 100 3

Our modeling follows the method described in Section 1.2. We make the

grid of models which have three parameters: height of an EB center (h), the

Full Width at Half Maximum (FWHM) of a heating function (W ), and the

maximum temperature of the heating (∆T ). We set the ranges for each param-

eter as listed in Table 3.1. With varying three parameters, we produce a total

of 5100 EB models. Figure 3.2 shows an example of the model atmosphere that

we produce.

When we set the range of parameters, things that we consider for each pa-

rameter are as follows. First, ∆T , the temperature enhancement due to EBs has

been reported from 600K to 5000K (Kitai 1983; Fang et al. 2006; Bello Gonzalez

et al. 2013; Berlicki & Heinzel 2014; Li et al. 2015; Kondrashova 2016; Hong

et al. 2017a). As we focus this research on the temperature change, we have

set up a wide range of temperature changes to cover all reported temperature

13

Figure 3.2: The red line shows the temperature structure of the EB model

atmosphere that we produced. The black line is the temperature structure of

FALC model atmosphere.

14

enhancements. Second, we set the range of the height (h) from the photosphere

to the lower chromosphere. As we mentioned in Section 1.1, the magnetic re-

connections which trigger EBs occur at the lower chromosphere, and it seems

unnecessary to consider the area higher than 1000km from the photosphere.

Last, about the width W , previous research of the EB modeling that we re-

ferred was modeled only for 160km width (Berlicki & Heinzel 2014). While we

design the modeling of the research, we think that we need to check the pos-

sibility of other widths as well. For this reason, we added 80km and 240km

width.

Now, we performed the radiative transfer calculations for the model ob-

tained above. Before calculating, we had to consider the position of the target

EB in the solar disk. Intensities of line profiles decrease when moving from the

center toward the limb, and we needed to consider the difference caused by the

position for accurate comparison between the synthetic data and the observed

data. The observational data we have described in Section 2 is obtained from

the angle with cos(θ) = µ = 0.81. Figure 3.3 shows differences concerning the

angle. We can see differences between the lines become larger at the far wings.

In this respect, considering the µ value is very important for the research of EB

modeling, and therefore we consider the µ value of the observed area while we

perform the computation. Also, we performed the normalization for both the

computed data and the observed data, since they are given with different units.

For example, the profiles from the RH code is given for the unit of the intensity

[J m −2 s−1 Hz−1 sr−1], and the FISS data are given in the unit of ADU; hence

it is unable to compare these two data directly. Thus, we normalize our data by

setting the continuum intensity as the unity and obtain the normalized profiles

for both data.

15

Figure 3.3: Graphs show changes in the synthetic profiles of the Hα (up) and the

Ca II 8542A (down) from FALC atmosphere with respect to the Line-of-Sight

angle.

16

Chapter 4

Results

4.1 Results From the Conventional Modeling

4.1.1 The First Modeling

In this chapter, we explain our findings from the conventional modeling research

where the width W is set to vary from 80 to 240km. We found the best model

atmosphere by performing the χ2 tests with normalized intensities of the syn-

thetic profiles with the observed profiles for both the Hα and the Ca II 8542A

lines. We selected the model which produces the lowest χ2 profiles as the best

model atmosphere for each line. From the test, we excluded the wavelengths

near the line core (Hα: -0.5A to 0.5A, Ca II 8542A: -0.25A to 0.25A from

the center of each line), that’s because we cannot find any particular spectral

changes caused by EBs in those wavelength areas.

As a result, we found the best model atmosphere which produces the syn-

thetic profile that matches well with the observed EB. However, our synthetic

profiles could not fit both observed Hα and Ca II lines simultaneously. We

17

draw the data from the Hα line best model in Figure 4.1. The left graph shows

temperature structures of the EB model and the quiet region model, and the

right ones are comparisons between the results from the best model and the

observed profiles. The upper graph is for the Hα, and the lower one is for the

Ca II 8542A. For the Hα, there is little difference between the synthetic and the

observational profiles. However, in the Ca II 8542A line, the synthetic profile

shows much stronger wings than the observation at near wings. On the con-

trary, in Figure 4.2, the Hα synthetic profile from the Ca II 8542A best model

shows much lower intensities than the observed line. We have listed parameters

of the best models for each line in Table 4.1.

The remarkable information in the table is the difference in the peak tem-

perature of the two best models. Our result shows that the Hα best model has

a peak temperature of 2450K, which is more than twice 950K; the Ca II 8542A

best model peak temperature. As for the cause of such a substantial tempera-

ture difference, we speculate that the difference in the line formation mechanism

of two lines affects them. According to Cauzzi et al. (2009), the source function

of the Ca II 8542A line is temperature-sensitive so that the intensity of the Ca

II 8542A line increases even by a slight temperature enhancement.

Table 4.1: The best models

Line ∆T (K) h (km) W (km) χ2

Hα 2350 300 160 0.58

Ca II 8542A 850 250 160 0.46

18

Figure 4.1: Left: The temperature structures of the best EB model for the Hα line (red) and the quiet region model

(black). Right: Comparison of profiles between the Hα best model result and the FISS observed profiles. The upper

one is for the Hα line, and the lower one is for the Ca II 8542A.

19

Figure 4.2: Left: The temperature structures of the best EB model for the Ca II 8542A line (red) and the quiet

region model (black). Right: Comparison of profiles between the Ca II 8542A best model result and the FISS

observed profiles. The upper one is for the Hα line, and the lower one is for the Ca II 8542A.

20

Figure 4.3: Left: The temperature structures of the best EB models for both the Hα line (red) and the Ca II 8542A

line (green) and the quiet region model (black). Right: Comparison of profiles between two best model result (Hα:

red, Ca II 8542A: green) and the FISS observed profiles. The upper one is for the Hα line, and the lower one is for

the Ca II 8542A.

21

We conjecture two possibilities which cause the discrepancy that we men-

tioned above. The first possibility is that there will be an unknown parameter

which we do not take into account in our computation. Hong et al. (2017b) per-

formed the radiative hydrodynamics computation for the formation of the EB

in both the Hα and the Ca II 8542A lines. The synthetic profiles are changed

when the non-thermal energy such as energies from high energy electron added

into the atmosphere. Thus, if we can calculate the influence of non-thermal en-

ergy on the generation of two lines, then we can reinterpret our results in this

respect. However, they conducted their study by using the RADYN (Carlsson &

Stein 1992, 1995, 1997, 2002) code, which is not available to other researchers.

The code can calculate the radiative hydrodynamics equation including non-

thermal energy components, which cannot be dealt with the RH code. For this

reason, we decide to stop further research about the non-thermal effect on EBs.

The next possibility we consider is that the difference in the formation

height. For the Hα and the Ca II 8542A line, the source function of line wings are

known to be the highest in the photospheric height. However, if the formation

height of each line is at a different level of the photosphere, and also if the

height difference is too narrow to catch from our previous model, then we need

to consider another form of modeling. In this regard, we create a new method

of modeling that is different from the previous model.

4.1.2 Two-hump Modeling

Our next model has a feature with two temperature enhancement functions;

hereafter we call this model a two-hump model. We produce two-hump models

in the following order. First, we add a hump with half values of the Hα best

model (W = 80km, ∆T = 1200K, h = 300km) to FALC model. The reason for

setting this hump is that h = 300km is the height at which near wings of the

22

two lines are supposed to be generated. Also, we already find that the previous

Hα best model produces too enhanced near wings at the Ca II 8542A line.

Therefore, if we add a lower temperature enhancement than our previous Hα

best model, then near wings of the resulted Ca II 8542A profile could achieve

the low intensity as the observed one shows. Then, we added one more hump

with varying parameters to the model above. An example of this model is in

Figure 4.4, and settings for the moving hump are in Table 4.2. We fix the width

of humps as 80km since we assume that the formation height difference between

two line wings is not as large as the width of the photospheric height.

Table 4.2: The range of the moving hump

Parameters Range Gap Steps

∆T (K) 1200, 500 < ∆T < 2500 50 41

h (km) 300, 10 < h < 400 10 40

W (km) 80, 80 - 1

However, the conclusion is that we still cannot obtain a model that can

simultaneously explain two observed lines. From Figure 4.4 to 4.6, we draw the

same graphs as shown in Section 4.1.1. Problems that we found from this new

modeling are almost not different from the previous modeling. Table 4.3 is the

result of the best model.

The Hα best model has a similar form with a single Gaussian function

which has a narrower and hotter hump than the single hump model. The only

improvement in this new modeling is that the decline of χ2 values. Also, for

the Ca II 8542A line, there doesn’t seem any particular improvement when

compared with the single hump model. Moreover, if we look at the tempera-

ture structure, we can see that the temperature increases at two points in the

23

atmosphere. We have tried to find out if any studies have existed for this kind

of temperature change, yet we could not find any similar type of report.

If we go further with the two-hump modeling research, we can carry out the

modeling by moving both humps. However, in this case, the number of models

to be computed increases exponentially, although there is no certainty that the

improved results will be obtained. Also, as a result of the Ca II 8542A line, it

would be difficult to explain how such a model atmosphere exists, and if so,

what mechanism causes the temperature to change in the solar atmosphere.

Therefore, we have stopped the further research for the two-hump modeling.

Table 4.3: The best models from the two-hump modeling

Line ∆T (K) h (km) W (km) χ2

Hα 1200, 2000 300, 240 80, 80 0.36

Ca II 8542A 1200, 250 300, 60 80, 80 1.41

24

Figure 4.4: The red line shows the temperature structure of the two-hump model

atmosphere that we produced. The black line is the temperature structure of

FALC model atmosphere.

25

Figure 4.5: Left: The temperature structures of the best two-hump model for the Hα line (red) and the quiet region

model (black). Right: Comparison of profiles between the Hα best model result and the FISS observed profiles. The

upper one is for the Hα line, and the lower one is for the Ca II 8542A.

26

Figure 4.6: Left: The temperature structures of the best EB model for the Ca II 8542A line (red) and the quiet

region model (black). Right: Comparison of profiles between the Ca II 8542A best model result and the FISS

observed profiles. The upper one is for the Hα line, and the lower one is for the Ca II 8542A .

27

Figure 4.7: Left: The temperature structures of the best two-hump models for both the Hα line (red) and the Ca

II 8542A line (green) and the quiet region model (black). Right: Comparison of profiles between two best model

result (Hα: red, Ca II 8542A: green) and the FISS observed profiles. The upper one is for the Hα line, and the

lower one is for the Ca II 8542A.

28

4.2 The Narrow Hump Modeling

4.2.1 Results From The Narrow Hump Modeling

As we mentioned in Section 4.1, we failed to explain the observation using

the two models. While seeking another breakthrough, we happened to hear

about the research of Quintero Noda et al. (2016). Their research focuses on

the response of the Ca II 8542A line profile to the perturbed solar atmosphere.

Their analysis reported that there is a specific width of height in the solar

atmosphere where the Ca II line is not very sensitive to the temperature so that

the line intensities not changed much. To apply their result on our research, we

get an idea of the high-temperature change confined in a narrow width of height.

The width would be much thinner than our previous results, even for two-hump

models. Table 4.4 shows our grids. We shorten the width of humps within 20km.

Figure 4.8 is an example of a model atmosphere. We have produced a total of

2700 narrow hump model atmospheres.

Table 4.4: The range of the narrow hump model parameters

Parameters Range Gap Steps

∆T (K) 100 < ∆T < 3000 100 30

h (km) 10 < h < 300 10 30

W (km) 10 < W < 20 5 3

Additionally, we apply the FALC model atmosphere by interpolating the

height from 500km to 0km at intervals of 5km. In the existing FALC model,

the height from -50km to 2200km was divided into 82 grids, and the height of

0 ∼ 500km, which is the height of the photosphere and the lower part of the

chromosphere was given as a step of 50km. At this interval, we can not apply

29

Figure 4.8: The red line shows the temperature structure of the narrow hump

model atmosphere that we produced. The black line is the temperature struc-

ture of FALC model atmosphere.

30

the above-mentioned atmospheric change, so we use the improved FALC model

to implement this idea. The only drawback by applying this model atmosphere

is that the computational power and the calculation time required for the com-

putation are more than doubled, making it very challenging to calculate the

grid of models just as we did in Section 4.1.1. Therefore, we minimize the grid

than in Section 4.1.1.

Table 4.5: The best results from the narrow hump modeling

∆T (K) h (km) W (km) χ2

1700 120 20 0.82 (Hα), 2.64 (Ca II 8542A)

The best results from our narrow hump modeling are in Table 4.5 and Figure

4.9. Before describing our results, we mention that there seems little difference

between the Hα best model and the Ca II 8542A best model in both χ2 values

and parameters of the best models. For this reason, we can only consider the

Hα best model for the best narrow model.

The temperature structure of the best narrow hump model is in Figure 4.9.

There are two interesting results in the model; the first is the height where the

heating occurred and the second is the width. In Section 5, we cover what they

mean in detail.

Results show that the Hα synthetic profile is almost similar to the observed

one. Also, we can see that the Ca II 8542A synthetic profile explains far wings

of the FISS observed line. Nevertheless, there are some discrepancies at near

wings, the χ2 value drastically decreases than the previous modeling results. It

seems that if we modify the model by giving asymmetry on the temperature

hump with increasing temperature on the upper half of the hump, then we can

compensate the insufficient intensities of the synthetic profile.

31

Figure 4.9: Left: The temperature structures of the best narrow hump model (red) and the quiet region model

(black). Right: Comparison of profiles between the results from the best narrow hump model (red) and the FISS

observed profiles (black). The upper one is for the Hα line, and the lower one is for the Ca II 8542A.

32

4.2.2 Additional Results From Another EB

In the previous section, we explained the line profile of the EB that we observed

by the FISS with using the narrow hump model. The result is entirely different

from the temperature structure of the existing EB model. Still, it was very

different from the known one, so we wondered whether the results from this

model were general or not. In this regard, we analyzed an another EB with

using the same narrow hump model.

The EB that we additionally analyzed was in the active NOAA AR 12079,

taken on June, 3rd 2014 21:46:21., During the observation, the region was lo-

cated at (-696′′, 51′′) in the solar disk and the µ value was 0.67. The other

observational properties such as bandwidths are the same as we used at the

first analyzation. Figure 4.10 shows multiwavelength raster images of the re-

gion observed at that time when the EB occurred.

The results obtained from this figure are shown in Table 4.6 and Figure

4. 11. As we presented in previous sections, these results from this hump also

showed good fitting results with the observation. Therefore, we can suppose

that our model can describe a general EB rather than a specific case.

Table 4.6: The best narrow hump model results of an another EB

∆T (K) h (km) W (km) χ2

1700 130 20 1.09 (Hα), 1.53 (Ca II 8542A)

33

Figure 4.10: Multiwavelength raster images of the active region where EB occurred, Up: From the center of the Hα

line, -1.3A, -0.5A , 0A, 0.5A, 1.3A, respectively. Down: From the center of the Ca II 8542A line, -0.75A, -0.25A ,

0A, 0.25A, 0.75A, respectively.

34

Figure 4.11: Left: The temperature structures of the best narrow hump model (red) and the quiet region model

(black). Right: Comparison of profiles between the results from the best narrow hump model (red) and the FISS

observed profiles (black). The upper one is for the Hα line, and the lower one is for the Ca II 8542A.

35

4.3 Temporal Evolution of EBs

Also, we track the change of the EB within its lifetime. In the previous studies

of the temporal evolution of EBs, Bello Gonzalez et al. (2013) and Yang et al.

(2013) reported that the rapid increase and decrease of the wing intensities of

EBs during their lifetime (Figure 4.12). Then, we also track the change of the

EB with time.

Figure 4.13 is the result of our target EB during the lifetime. We find the

intensity fluctuations for both lines at the same time (800∼950s). Notably,

during 850∼900s, the most rapid intensity increase appeared within one raster

scan time (∼20s) for two lines. Also, we find the decrease of intensities in a

short time(1000∼1200s). After the decrease, the EB becomes extinct.

We also check the temporal evolution for the best model temperature. Figure

4.14 shows the temporal evolution of the temperature of the EB best model

obtained from the narrow hump model. We find that the increase (800∼950s)

and the decrease (1000∼1200s) of the EB temperature at the same time.

36

Figure 4.12: Graphs show varying intensities of EBs at 1700A continuum (left), and at line wings of the Hα line

(right) during the lifetime of the EB. (Left: Image reproduced from Bello Gonzalez et al. 2013, Right: Image

reproduced from Yang et al. 2013))

37

Figure 4.13: Temporal evolution of the EB wing intensities during the lifetime.

The black line shows wing intensity of Hα line at -1.0A from the center. The

red line is that of the Ca II 8542A line at -0.5A from the center. We normalize

intensities of each line by using intensities from the quiet region at -1.0A and

-0.5A from the center.

38

Figure 4.14: Temporal evolution of the EB best model temperature during the

lifetime. The best model temperature obtains from the result of the narrow

hump model.

39

Chapter 5

Summary & Discussions

5.1 Summary

The main results of our study are summarized as follows.

1. We have performed the EB modeling to diagnose the temperature struc-

ture of the solar atmosphere perturbed by the EB.

2. With the existing modeling method, we failed to obtain any result which

explains both the Hα and the Ca II 8542A line profiles simultaneously.

3. We have applied new modeling characterized by a narrow temperature

hump. This model better explains both the line profiles than the previous mod-

els, and even it still cannot fit the near wing of the Ca II line.

4. We investigated the evolution of the EB over time. We found the increase

and decrease of the wing intensities of the Hα and the Ca II 8542A lines. By

repeatedly applying the non-LTE modeling, we determined the time variation

of temperature excess, and as a result, we found the increase and decrease of

temperature excess, corresponding to those of the intensities.

40

5.2 Comparison with the Previous Studies

Our results may be compared with the three previous studies; Kitai 1983; Fang

et al. 2006; Berlicki & Heinzel 2014. These three papers explained their non-LTE

EB modeling, and hence they served as a good guideline for our research. We

think that our research results are better than these studies as will be explained

below.

Kitai (1983) performed the non-LTE modeling for EBs using the Hα line

only. He reconstructed the model atmospheres by adding constant temperature

enhancement (∆T ) or multiplying density (ρ) by a factor of 5 or 10 in a specific

height range of width 500km or 800km on the quiet region atmosphere model

(Vernazza et al. 1981). By this kind of reconstruction, he produced 11 model

atmospheres. He then performed the non-LTE calculation and obtained the best

model characterized by ∆T of 1500K and ρ = 5ρ0 in the heights ranging from

700 to 1200km.

It seems that Kitai’s model atmospheres are too simple to be realistic. If

heating occurs somewhere in the solar atmosphere, then temperature enhance-

ment would be peaked at the location of heating and would decrease with the

distance from it. Kitai’s model atmospheres, however, did not take into account

such a pattern and adopted constant temperature enhancement.

Also, the modifications of the physical parameters in his models were made

in the much higher region than the photosphere with some being in the range

of 700 to 1200km and others being in the range of 400 to 1200km. It is much

contrasted with our result that the modification of the model atmosphere in

the lower atmosphere, mostly in the photosphere, can explain the observed line

profiles of the EB. His model did not consider the lower atmosphere below the

temperature minimum, not to speak the photosphere, at all.

41

Fang et al. (2006) used the Hα and the Ca II 8542A lines for their study,

the same lines that we used. Still, their observational data had a limited spatial

resolution of about 2′′. Thus the EB profiles they used may have been subject

to the contamination of the surrounding quiet region profiles. On the contrary,

our spectral data have a spatial resolution of about 0.′′3, so the profiles of

surrounding regions did not contaminate our EB profiles, and therefore our

result is more reasonable than them.

Berlicki & Heinzel (2014) used the observational data from the filtergram,

so the wavelengths that used for modeling were the Hα center and ± 0.7A,

and the Ca II H line center and -2.35A only. Their modeling resulted in ∆T =

5000K, h = 1000km, which seems to be much different from the results of other

studies.

5.3 Implications of Our Results

Our results have several physical implications.

First, the height where the EB occurred is remarkably lower than the re-

ported heights from the previous studies. Our results indicate that the EB

occurred at the photospheric height, the area which has high density. Because

of higher density, a temperature excess in the photosphere corresponds to a

higher density of thermal energy than that in an upper region.

Second, we need to consider the meaning of the narrow hump model. The

width of our model is about 1/8 of those used the previous research (e.g.,

Berlicki & Heinzel 2014). In earlier studies of EBs, it was expected that the

thickness (width) should be similar or even thinner than the observed diameter

of EBs (∼ 1′′). From the simultaneous observations of EBs with the Hα line

wings and 1600A continuum, Georgoulis et al. (2002) suggested that the vertical

42

extent of EBs should be at least more than 100km, considering the difference in

the formation heights of these two lines. However, considering that the formerly

known formation height of EBs is a relatively low-density region such as the

lower chromosphere, the order of the total energy emitted by the EB may

not be different with our model. In this respect, if we perform the quantitive

calculation for the total energy emitted by the EB, then we can make our model

more persuasive.

The last is about the temporal evolution of the EBs. Our results show sudden

changes in wing intensities and the best model temperature. Since it is likely

that the brightness of EBs is related to the energy release, we can regard the

sudden change of intensities and temperature as the manifestation of explosive

events like magnetic reconnection in the solar atmosphere.

We conclude that for the generalization of results from this paper, further

investigations for other EBs are required.

43

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47

초록

엘러먼폭탄은태양활동영역에서관측되는작은크기와짧은수명을가지는현상

이다. 엘러먼 폭탄은 최초로는 태양 발머선에서 발견되었으나, 이후 여러 스펙트

럼선에서발견되었다.엘러먼폭탄은태양대기하부에서자기재연결이발생할때

생성되는 것으로 받아들여지는데, 이때 그 현상이 발생한 영역 주위를 가열한다.

엘러먼폭탄으로인해변화된태양대기를확인하기위해,관측된엘러먼폭탄의선

프로파일과 모형 대기에 대한 non-LTE 복사전달 계산을 통해 얻은 합성 프로파일

을 비교하는 방식의 연구가 진행되어 왔다. 기존 연구에서는 관측 데이터의 낮은

해상도로 인해 연구의 한계가 있었다. 본 연구에서, 우리는 고속영상태양분광기

(FISS)로부터 얻은 데이터를 이용하였는데, FISS는 Hα와 Ca II 8542A 양쪽 선으

로부터 엘러먼 폭탄을 연구하기에 충분할 정도로 높은 시공간분해능의 데이터를

제공한다.

우리는 관측된 두 선을 동시에 설명할 수 있는 엘러먼 폭탄의 대기 모형을 제

작하는 것을 목표로 하였다. 첫 번째 시도로서, 우리는 다양한 온도 변화 (∆T ), 폭

(W ), 높이(h)를 가지는 가우스 함수 형태의 온도 증가 함수를 태양 정온 지역에

대한 1차원 모형 대기에 첨부하는 방식으로 모형 대기를 제작하였으며, 폭 W는

80km 에서 240km까지 변화시켰다. 그러나, 이와 같은 접근법으로는 우리는 관

측된 Hα와 Ca II선을 동시에 설명하는 어떠한 대기 모형도 찾을 수 없었다. Hα

를 가장 잘 설명하는 대기 모형으로부터 얻은 Ca II 합성 프로파일은 선 날개에서

관측 데이터에 비해 매우 높은 밝기를 나타냈고, Ca II 선 최적 모형으로부터 얻은

Hα 합성 프로파일은 관측 데이터에 비해 매우 약간 날개를 가졌다. 이 불일치를

해결하기위해,우리는기존의모형에비해매우좁은폭의 (W ∼ 20km)온도증가

함수를 가지는 새로운 모형을 만들었다. 이 새로운 모형을 통해, 우리는 관측된

Hα선과 Ca II 선을 동시에 설명할 수 있는 대기 모형을 얻었다. 우리는 이 모형

48

의 온도 증가가 기존에 알려진 엘러먼 폭탄의 생성 높이보다 매우 낮은 지점에서

(h = 120km) 생성된다는 것을 발견했다.추가적으로, 우리는 Hα선과 Ca II 선

양쪽 날개에서 밝기의 빠른 증가 및 감소를 관찰하였는데, 이는 대기 구조가 가열

과 냉각으로 인해 변화하였다는 것을 나타낸다. 사실, 온도의 빠른 증가와 감소는

non-LTE 모형 제작으로부터 발견되었다.

우리의 결과는 엘러먼 폭탄이 기존 연구에서 추측했던 것처럼 채층 하부에서

발생하는 것이 아니라 광구에서 생성된다는 것을 나타낸다. Hα선과 Ca II선 날

개의 생성은 매우 좁은 영역에 한정되어 있다.다음으로, 엘러먼 폭탄의 수명 동안

관측되는 급격한 밝기의 변화는 엘러먼 폭탄의 가열과 냉각이 매우 짧은 시간 내

에 이루어진다는 것을 암시한다.이 결과들을 일반화시키기 위해서는 다른 엘러먼

폭탄에 대한 추가적인 연구가 필요할 것이다.

주요어: 태양: 활동 영역, 광구, 엘러먼 폭탄, 복사 전달, 스펙트럼 분석

학번: 2015-22603

49