Title: Flare-related color effects in UV Ceti stars
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 Material Information
Title: Flare-related color effects in UV Ceti stars
Physical Description: x, 140 leaves : ill. ; 28 cm.
Language: English
Creator: Flesch, Terry Ralph, 1950-
Copyright Date: 1975
 Subjects
Subject: Stars -- Color   ( lcsh )
Astronomy thesis Ph. D   ( lcsh )
Dissertations, Academic -- Astronomy -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Terry Ralph Flesch.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 135-139.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00098309
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000171196
oclc - 02952160
notis - AAT7619

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FLARE-RELATED COLOR EFFECTS IN UV CETI STARS


By

TERRY RALPH FLESCH










A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY






UNIVERSITY OF FLORIDA

1975
































To my late Grandpa Homan,

who, some 20 years ago, first turned my gaze to
the stars.








ACKNOWLEDGEMENTS


To try and acknowledge everyone who helped make this
dissertation a reality is futile, since, like all acknowl-
edgements, it is doomed to be incomplete. However, there
are some who have had a more immediate and direct influence
upon me and my work and whom, in particular, I would like
to thank:

Frank B. Wood, the chairman of the dissertation
committee;

John P. Oliver, who introduced me to the subject of flare
stars and read over my preliminary attempts at making sense
of my research. His aid was invaluable not only as a col-
league and instrumentationalist, but as a much needed friend
when the going wasn't so smooth;

Howard L. Cohen, who also perused the preliminary
pages and was always ready and willing to talk and help in
any way he could;

Thomas D. Carr, who agreed to submit himself to the
rewarding experience of being on my committee;

Stanley S. Ballard, who, like Dr. Carr, couldn't wait
to be included on my committee;

Eli Graves, who machined the three-channel photometer;

Woody Richardson, who helped by supplying drafting
materials and much needed advice;

my fellow astronomy grad students, for their helpful
discussions and comments;

Sue, who helped in typing the thing and who supplied
love and patience in listening to my ravings; and

my family, whose support was as important to the com-
pletion of this task as was my own effort.









TABLE OF CONTENTS


Acknowledgements . . . . .

List of Tables . . . . . .

List of Figures . . . . . .

Abstract . . . . . . .

CHAPTER

I INTRODUCTION AND HISTORY . .

Introduction . . .

History . . . . .

II INSTRUMENTATION AND TECHNIQUES
AND DATA REDUCTION . . .

Observing Technioues .

Data Reduction . . .

III THE OBSERVATIONS . . . .

IV THEORETICAL CONSIDERATIONS .

The Nebular Model . .

Fast Electron Model . .

Fitting The Observed Ligh


Conclusions . . . .

FLARE COLORS . . . . .

CONCLUSIONS AND FUTURE RESEARCH:

Conclusions . . . .

Future Research . . .


Page
iii

vi

vii

ix


OF OBSERVATION





















H . . .
t Curves





























APPENDIX 1. TIMES OF COVERAGE OF PROGRAM STARS . 103

APPENDIX 2. TABULATION OF OBSERVED CHANGES IN
INTENSITY FOR FLARES OF EV LAC AND AD LEO 107

REFERENCES ................... 135

ADDITIONAL REFERENCES . . . . . . 138

Biographical Sketch ............... .. 140












LIST OF TABLES


TABLE PAGE

la. OBSERVED PARAMETERS FOR FLARES OF EV LAC . 17

lb. OBSERVED PARAMETERS FOR FLARES OF AD LEO . 18

2. THEORETICAL PARAMETERS AND MAXIMUM FLARE
AMPLITUDES FOR FAST ELECTRON THEORY .... 52

3. TABULATION OF THE FITTED PARAMETERS IN THE
FAST ELECTRON THEORY FOR A TEMPERATURE OF
2800 K . . . . . . . .... . 57

4. TABULATION OF THE FITTED PARAMETERS IN THE
FAST ELECTRON MODEL FORtL = 10 . . . 58

5. DIFFERENTIAL COLOR INDICES (FLARE LIGHT -
QUIET STAR) AT TIME OF MAXIMUM LIGHT FOR
OBSERVED EVENTS ON EV LAC AND AD LEO . . 93

6. AVERAGED DIFFERENTIAL COLOR INDICES (FLARE
LIGHT QUIET STAR) FOR OBSERVED EVENTS ON
EV LAC AND AD LEO . . . . . ... 94









LIST OF FIGURES


FIGURE

1 Spectral response of the three-channel photo-
metric system used in flare star monitoring

2 Spectral response of the standard UBV system
in use at RHO . . . . . . . .

3 Schematic diagram of the three-channel photo-
meter including Fabry lenses(F) and
photomultiplier tubes(PM) . . . . .

4 Three-color light curve for event 26AU3 . .


PAGE


9


. 10


Three-color light curve for event 3SE3 . . .

Two-color light curve for event 7003 . . .

Three-color light curve for event 90C3A . .

Three-color light curve for events 90C3B,C . .

Three-color light curve for event 90C3D . .

Three-color light curve for event 19AU4 . .

Three-color light curve for event 21SE4 . .

Three-color light curve for event 21FE . ..

Three-color light curve for events 26FE4A,B .

Three-color light curve for event 27FE4 . .

Three-color light curve for event 25AP4 . .


16 Three-color light curve for event 18AP5


A fast electron model "best

A fast electron model "best

A fast electron model "best


fit"

fit'

fit"


for even

for even

for even


t 7003

t 90C3C

t 90C3D




















20 A fast electron model "best fit' for event 21FE4 72

21 A fast electron model "best fit" for event 26FE4A 74

22 A fast electron model 'best fit" for event 26FE4B 76

23 A fast electron model "best fit" for event 25AP4 78

24 A fast electron model "best fit" for event 21SE4 80

25 Instrumental color indices of flare light for
event 90C3A . . . . . . ..... 82

26 Instrumental color indices of flare light for
events 90C3B,C . . . . . . . . 84

27 Instrumental color indices of flare light for
event 90C3D . . . . . . . ... 86

28 Instrumental color indices of flare light for
event 26FE4B . . . . . . . ... 88

29 Instrumental color indices of flare light for
event 21SE4 . . . . . . . ... .90

30 Plot of observed differential color indices of
flare light for flares of AD Leo and EV Lac . 95









Abstract of Dissertation Presented to the
Graduate Council of the University of Florida
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



FLARE-RELATED COLOR EFFECTS IN UV CETI STARS

By
Terry Ralph Flesch

December, 1975

Chairman: Frank B. Wood
Major Department: Astronomy

The UV Ceti flare stars YZ CMi, BD+1602708, EV Lac,

and AD Leo were monitored photoelectrically for flare activity

with the 76 centimeter reflecting telescope of the University

of Florida's Rosemary Hill Observatory. Observations were

carried out from January, 1973 to April, 1975. The instru-

mentation allowed simultaneous readings to be taken at 3500,

4632, and 6496 R with a time resolution of 2 seconds. A
total of 15 major events were observed, with 14 of these

being observed in all three colors. All events showed the

classical fast rise and slower decline that is typical of

this type of activity. One event showed peculiar behavior

in the red bandpass that may indicate strong dependence of

the flare light in some cases on line emission.

The data were applied to the fast electron model of

flare activity proposed by Gurzadyan. Several serious






inconsistencies in the theory were found that would not have

been evident in single-channel monitoring. No event could

be fitted in all three colors using consistent values of the

unknown parameters in the theory. The most serious deficien-

cies in the theory were the wavelength dependence of the

optical depth of the electron cloud and the lack of treatment

of line emission behavior.

Differential color indices for flare light are calculated

and are shown to be essentially constant throughout the

entire event for the stronger flares. A color-color plot

of the flare light at maximum reveals that 11 of the flares

show a linear relation. This relation indicates that the

smaller the u-b index, the larger is the b-r index. This

is probably directly involved with line emission during

flare events.

Future research possibilities are discussed, with

spectroscopic studies and simultaneous multicolor obser-

vations being stressed.









CHAPTER I


INTRODUCTION AND HISTORY



Introduction

UV Ceti flare stars comprise one of a number of types

of eruptive variable stars, including supernovae, novae,

U Gem stars and others. The outbursts of flare stars are

the least energetic and have the shortest duration of all

the various types of eruptive phenomena in nonstable stars.

The class is comprised predominantly of red dwarf stars of

spectral class M, and therefore are among the most intrin-

sically faint stars in the Galaxy, occupying a place on or

near the faintest portion of the main sequence (Gershberg

1967; Lippincott 1953; Morgan 1938).

Because of their intrinsic faintness, the vast majority

of known flare stars lie within 20 parsecs of the sun. In

fact, flare stars constitute an appreciable percentage of

stars within 20 parsecs of the sun. The fact that our sample

is fairly complete in this region implies that UV Ceti stars

may represent one of the most numerous types of variable

stars in the Galaxy.

The outbursts seen in flare stars have durations of a

few minutes and probably originate from only a portion of










the star's surface. The energies involved in flare activity

are comparable to those of solar flares, releasing about

1031 ergs in the optical part of the spectrum (Gurzadyan 1971;

Gershberg 1973).

The flare light itself is much bluer than the radiation

from the quiet star. Line emission and photometric colors

of flare light indicate temperatures at the flare site in

excess of 10,000 K. Since the photospheric temperatures of

flare stars are in the neighborhood of 3000 K, the relative

change in the brightness of the star is much greater at the

shorter wavelengths. For this reason, the ultraviolet is

the best region of the spectrum in which to look for flare

activity (Joy 1960; Kunkel 1967; 1970). However, due to

the late spectral class and the apparent faintness of these

stars (especially in the ultraviolet), photometry in this

band is difficult and prone to large uncertainties.

Optically, flares are characterized by a very rapid

rise to maximum intensity. The time required for this rise

is typically only tens or hundreds of seconds. The peak of

the light curve is usually sharp and the quasi-exponential

decay is more gradual than the rise, taking several minutes.

Very rarely will the decline be more rapid than the rise to

maximum. The light curve may also exhibit secondary peaks,

periods of constant brightness, and sudden drastic changes

in slope. Less frequently, the maximum is very rounded and

indistinct, making the measurement of the time of maximum










difficult. Occasionally the intensity of the star will

increase or decrease a small amount before the rapid rise

to maximum begins.

Flares are also distinctive spectroscopically. The

spectrum of the quiet star typically shows several emission

features, most common of which are the hydrogen Balmer

lines and the Ca II H and K lines (Roques 1955). During a

flare, the emission lines are enhanced and many of the

absorption lines at the blue end of the spectrum can be

completely washed out. Other emission lines may appear in

the spectrum, most frequently those of helium. The enhance-

ment of the emission lines can last much longer than the

enhancement observed in the wide-band photometry observations,

being conspicuous in many cases long after the photoelectric

light levels return to normal. Bopp and Moffett (1973)

have found that the Balmer lines can contribute 16 per cent

of the flare intensity in the B bandpass, and Flesch and

Oliver (1974) have reported an event that may indicate that

HG in some cases dominates the stellar intensity near 6500O

(Mullan 1974). However, the increase in intensity in typical

broad-band photometry is primarily due to enhancement in the

continuum radiation (Joy 1954; 1957; Struve 1959; Oskanian

1968; Ambartsumian and Mirzoyan 1971).

At least some flare stars show slow quasi-periodic

variations of a few hundreths of a magnitude in addition

to their flare activity (Kron 1952; Roques 1958; Torres,










Mello, and Ouast 1972; Bopp and Evans 1973; Torres and

Mello 1973; Martins 1974; Mullan 1974). These spots are

very possibly associated with stellar flares in much the

same way as sunspots are with solar flares. This idea is

supported by observations of ultraviolet excesses when these

secondary variations are at a minimum light phase.

Presumably the activity associated with the spot region is

visible at these times.



History



The intrinsic faintness of flare stars and the rapid

nature of the events have made the study of these stars a

comparatively recent endeavor in astronomy.

In 1924 Hertzsprung noted a dramatic increase in bright-

ness on one of a series of photographs of the star later to

become known as DH Carinae. The rate of increase in inten-

sity was too great for the star to be a nova or an RR Lyrae

star, so Hertzsprung postulated that an asteroid had fallen

into the star, causing the increase in brightness. We now

know that this was one of the first observations of a stellar

flare, though it would take about 25 years from the time of

Hertzsprung's observation for the astronomical community to

officially recognize the existence of stellar flares.

Observations of flares were so infrequent during the

next few decades that each observation warranted a publication.









Indeed, not until 1950 did the International Astronomical

Union officially recognize UV Ceti stars as a separate

class of variable star (Bateson 1971).

One of the more important early observations of a

stellar flare was made late in 1948. The faint red star

L-726-8 had been found to have a large proper motion,

thereby being a good candidate for parallax measurements.

Page and Struve obtained spectra of the star and determined

its spectral class to be M6 with hydrogen and calcium in

emission. Joy and Humason (1949) found the star to be double

with a separation of about 1.5 arc seconds. Carpenter

took parallax plates on December 7, 1948 and found that one

of the five images of the star was much brighter than the

other four. The conclusion was reached that the fainter

component of the system had undergone a flare. In three

minutes the star had increased in brightness by about 3

magnitudes. The star was consequently named UV Ceti and

became the prototype for this class of variable (Luyten 1949).

Beginning in 1949, photoelectric light curves of flares

have provided much information about the general character-

istics of these events. Unfortunately, the vast majority of

this monitoring has been done in only one spectral region.

While this provides information as to the frequency and

strength of the outbursts, it provides little insight into

the physics involved. Several observatories have recently

begun using photometers equipped with filter wheels which

allow rapid interchanging of filters, resulting in multicolor























observations of flare events. However, several problems are

present in this type of monitoring. The major difficulty

lies in the fact that if three filters are employed in such

a system, then at best only 1/3 of the observing time is spent

in any one color. This effectively cuts down the amount of

flux which defines each observation by at least a factor of

three. Also, since the measures are not really simultaneous,

it becomes necessary to interpolate or extrapolate on the

light curve to obtain the observed color of the flare light

at any particular epoch. Truly simultaneous multicolor

observations were needed, and it was with this in mind that

the flare star program at the University of Florida was

planned.









CHAPTER II

INSTRUMENTATION AND TECHNIQUES OF
OBSERVATION AND DATA REDUCTION



The accurate investigation of flare-related color

effects in UV Ceti stars puts restrictions on the type of

equipment used that are not encountered in most photoelectric

programs. Because of the short duration of the events and

the rapid changes that occur in the light curve, high time

resolution is essential. The observations must also be

truly simultaneous, since interpolations and extrapolations

over the rapidly changing light curve would introduce a

major source of uncertainty. These considerations neces-

sitate a multichannel photometer rather than one using

interchangeable filters. Also, due to the low light levels

inherent in the study of dMe stars, especially in the ultra-

violet, the light beam must be split into the various bands

in the most efficient way possible.

The apparatus designed and built to meet these con-

siderations consisted of a three-channel photometer using

ultraviolet reflection filters and two interference filters

as dichroic mirrors. The reflected beam from an Optics

Technology interference filter #621 was used to isolate the

ultraviolet band. This beam was then reflected from three









Schott-Mainz UV-R-347 reflection filters to cut down on the

side lobes. This particular ultraviolet bandpass was chosen

in order to isolate as much as possible the region of the

spectrum to the short wavelength side of the Balmer discon-

tinuity. The transmitted beam from the #621 filter was

split using the Optics Technology interference filter #4540.

The reflected portion of this beam was used in defining the

blue band and the transmitted portion the red band.

EMI 6256B photomultiplier tubes were used for the

ultraviolet and blue bands. An EMI 9658B photomultiplier

tube was used for the red band. This combination of filters

and tubes defined the three bandpasses shown in Figure 1.

This system allows simultaneous readings to be made in

three separate spectral regions. It therefore enjoys a

great advantage over the interchanging filter technique,

since 100 per cent of the monitoring time is spent in all

colors. In addition, the use of the interference filters

as dichroic mirrors gives very high efficiencies in separat-

ing the star light into the three spectral regions. This

increase in efficiency can be seen by comparing the quantum

efficiencies of the three-channel system with those of the

UBV standard system shown in Figure 2. The photometer

system is schematically shown in Figure 3.

All observations were made with the 76 centimeter

reflecting telescope of the University of Florida's Rosemary

Hill Observatory (RHO). The telescope was used at the f/16

Cassegrain focus. Data consisting of the Julian Day number,


























8- -8




S-6

z
w
H

U_
4- -4











300 400 500 600 700 800 900

X (nm)

Figure 1 Spectral response of the three-channel

photometric system used in flare star

monitoring.

























O


O
X

>- 4





U-
o
z









14
H
D


2


I-
Z

0


300 400 500 600 700
X (nm)


Figure 2 Spectral response of the

in use at RHO.


standard UBV system





























uv
Reflection
Filter


blue


Reflection .. 7 Rer.
FilterI 7f Filter


uv


II
Main I1 Beam


II


uv Dichroic
/I I Kirror


blue+red
II

i ichroic
S Mirror

II
S I

Hired

I
I
I I


T


Figure 3 Schematic diagram of the three-channel photometer
including Fabry lenses(F) and photomultiplier

tubes(PM).


I -


- L---- YB-Pm~-~U~U---- I--~- II U~









intensity readings, length of integration, Universal Time,

and other coded information were recorded on magnetic tape

using a DigiData 7 track 200 BPI magnetic tape unit. A

Honeywell chart recorder was used to monitor the ultraviolet

channel during observation.



Observing Techniques



The data-taking system used in the observing program

allowed a series of readings to be taken continuously with

a dead time between integration of approximately 0.1 second.

The integration times used were typically 2 to 3 seconds

because of the high noise level in the ultraviolet signal.

Star readings were taken continuously except for breaks

for sky readings at intervals of about 30 minutes and checks

on the centering of the star in the diaphragm every 5 to 10

minutes. Few if any observations were made of comparison

stars, the quiet level of the stellar intensity being used

as a reference for all activity. This procedure was chosen

to maximize the time of coverage on the variable because of

the unpredictability of flare activity. With this type of

monitoring, 90 to 95 per cent of the time was spent in

actual observation of the variable.

All data were recorded by the magnetic tape unit. The

chart recorder was used only as a visual check on activity.

Chart readings were not used in the reduction of the data.

The photomultiplier tubes were operated at 1000 volts.











The ultraviolet and red channels were maintained at dry ice

temperatures, whereas the blue channel was cooled by an EMI

ZD-50 thermoelectric chamber to a temperature of approximately

0 C. The signal from each tube was fed to a separate

standard RHO electrometer amplifier (Oliver 1975).

A 23.6 arc second diaphragm was used in the photometer

for all observations. The three amplifiers were calibrated

at the beginning and end of each observing session.



Data Reduction



The magnetic tape containing the data was fed to an IBM

1401 computer where the data were transformed from 7 track

200 BPI to 9 track 800 BPI format. This enabled the data

to be fed into an IBM 370-65 computer which was used for most

of the data reduction. Computer reductions consisted of

printer plots of the raw data (star less sky) versus time

for the entire night. In addition, intensity changes and

system colors for flare events were calculated so that plots

of intensity and color versus time and color-color plots

could be made. These plots were also constructed with the

use of the printer plot routines and later with the use of

the Gould 5100 on-line plotter. The matching of the flare

events to theoretical models was done with both the IBM 370-65

and a Hewlett Packard 9810A calculator.









CHAPTER III


THE OBSERVATIONS

The observing program consisted of the monitoring of

four UV Ceti flare stars; YZ CMi, BD+1602708, AD Leo, and

EV Lac. A total of 44 observing runs were made, with the

majority of time being spent on AD Leo and EV Lac. These

two stars were emphasized because of their level of activity,

apparent brightness, and accessibility from the latitude

of the Rosemary Hill Observatory (+300). The complete list

of the monitoring times is presented in Appendix 1.

The effective wavelengths at which the observations

were made were found by convolving the response curves of

the apparatus (Figure 1) with the energy distribution of the

star. The relation used was


X = X R(X) S(X) dX

R(X) S(X) dX

where

Xe is the effective wavelength

R(X) is the ultraviolet, blue, or red response

curve plotted in Figure 1,

and S(X) is the energy distribution of the star.

The energy distribution for a dM4.5 star (assumed for both








EV Lac and AD Leo) was obtained by linearly interpolating

between the dM4 and dM5 energy distributions given in Straizys

and Sviderskiene (1972). The resultant effective wavelengths

were 3500, 4632, and 6496 R for the ultraviolet, blue, and

red bandpasses respectively.

Only brightness variations substantial enough to provide

color data were reduced and noted as "flare activity."

Though no strict criteria were applied to the strength of

the events, activity treated as a flare typically exhibited

a maximum in the uv bandpass at least three standard devi-

ations above the quiet level of the star. The quiet levels

and noise levels of the intensity of the star in the various

bandpasses were found by obtaining the average value and

standard deviation of a 2-to 3-minute segment of data imme-

diately preceding the onset of the event.

A total of 107 hours 41 minutes was spent monitoring

EV Lac and AD Leo, resulting in 15 major flares. No flare

activity was observed on either YZ CMi or BD+1602708. As

mentioned above, some events were not reduced due to their

small amplitudes. However, there were only about 6 of these

events. Of the 15 major flares, several were obviously not

isolated. In particular, the events observed on AD Leo on

26 February, 1974, and on EV Lac on 7 and 9 October, 1973

show several outbursts occurring within minutes of each other.

Considering the typical time interval between flares for UV

Ceti stars, it is highly unlikely that events could occur

on the same star in such rapid succession and not be physi-

cally related in some way.









Tables la and Ib contain the parameters for the observed

flare activity of EV Lac and AD Leo respectively. Column 1

contains the UT date of the event. Column 2 gives the name

of the event by which it will be referred to hereafter. The

initial number in the name indicates the day of the month

on which the flare was observed. The following 2 letters

give the month of the year. The final number is the last

digit of the year. The final letter, if any, denotes the

first (A), second (B), etc. event on the given date. For

example, 90C3B refers to the second event observed on October

9, 1973. Column 3 gives the time of the maximum intensity
of the flare. Column 4 lists the bandpass of the obser-

vations; and the integrated intensity, P, is given in units

of minutes in column 5. P is defined to be fIf(t) dt,

where If is the intensity of the flare light alone in terms

of the quiet level of the star. Column 6 gives the maximum

relative change in intensity of the star in terms of the quiet

level (i.e. If max), column 7 the noise level of the signal

in the same units, and column 8 the airmass at which the

observations were made. This airmass was computed for the

time of maximum light for the event.

EV Lac is a visual binary with the companion, signifi-

cantly bluer than the variable, located about 5 arc seconds

from the primary. Both components were included in the 24

arc second diaphragm used for the observations. However,

measures of the individual components enable the parameters

of the flare to be related to the variable only. The measures













Table 1a


OBSERVED PARAMETERS FOR FLARES OF EV LAC


ID UT of Max


Band P(min)


5 59 40 uv
blue
red

7 24 50 uv
blue
red


70C3 2 04 41


90C3A 4 04 50 uv
blue
red

90C3B 4 12 54 uv
blue
red


90030 4 15 44


uv
blue
red


90C3D 5 30 19 uv
blue
red


19 Aug 1974



21 Sep 1974


19AU4


21SE4


6 26 17 uv
blue
red


4 55 50


uv
blue
red


3.24
0.35
0.16

3.80
0.12
0.14


1.50
0.12
0.07

1.78
0.17
0.07


0.31
0.03
0.02

0.35
0.04
0.02


uv 32.00 7.16 0.31
red 1.40 0.26 0.01


3.04
1.14
0.16

17.10
1.30
0.60


3.51
1.25
0.49

2.08
0.18
0.09


* 3.98
0.45
0.16


6.25
0.58
0.24

1.33
0.14
0.01

6.04
0.66
0.20


6.47
0.65
0.23

1.27
0.18
0.05

6.06
0.78
0.11


26 Aug 1973



3 Sep 1973


7 Oct 1973


9 Oct 1973


1.034


1.129



1.065


1.057


1.064



1.066


1.182



1.034



1.044


* The value of P given for 90C3B is the combined value
for 90C3B and 90C3C, since the two events overlapped.


Date


26AU3



3SE3


0* X


0.35
0.04
0.02

0.35
0.04
0.02

0.35
0.04
0.02

0.46
0.04
0.02

0.21
0.06
0.01

0.15
0.05
0.01


















Table lb


OBSERVED PARAMETERS FOR FLARES OF AD LEO


Date


21 Feb 1974



26 Feb 1974


ID UT of Max Band


21FE4



26FE4A


5 07 12



4 49 09


uv
blue
red

uv
blue
red


26FE4B 4 52 57 uv
blue
red


27 Feb 1974



25 Apr 1974



18 Apr 1975


27FE4



25AP4



18AP5


7 22 18 uv
blue
red

4 59 33 uv
blue
red

2 40 52 uv
blue
red


P(min)


0.90
0.17
0.06

72.40
8.60
2.90


If

2.12
0.35
0.08

8.65
1.50a
0.27


b 9.51
1.69
0.31


1.34
0.22
0.02

1.18
0.10
0.01

1.03
0.21
0.07


1.00
0.14
0.03

1.45
0.24
0.04

0.85
0.14
0.05


The value of I in the blue band is estimated due to
saturation of the amplifier before the gain could be changed.

The value of P given for 26FE4A is the combined value
for 26FE4A and 26FE4B, since the two events overlapped.


07 X


0.09
0.01
0.01

0.12
0.02
0.01

0.12
0.02
0.01

0.13
0.01
0.01

0.15
0.02
0.01

0.06
0.02
0.01


1.025



1.024



1.022



1.142



1.452


1.023









were obtained by placing the binary close enough to the edge

of the diaphragm to exclude one of the components. Readings

were taken first with one star excluded then the other. The

brighter component of the system is known to be the flare

star, so its brightness relative to the entire flux of the

system could be computed. The measures indicated that the

variable is responsible for 51, 77, and 87 per cent of the

total flux of the system in the ultraviolet, blue, and red

bandpasses respectively. Using these values, the observed

intensities of the events and the noise levels quoted in

Table la are relative to the flux of the variable component

of the system only.

Figures 4 through 16 show the three-color light curves

for the observed events except for Figure 6, a plot of event

70C3 which was observed in only 2 colors. A tabulation of

the observed changes in intensity for all events is given

in Appendix 2. For events tabulated for EV Lac, the listed

changes in intensity are relative to the total light of the

system.

For all events the relative change in the brightness of

the star increased toward shorter wavelengths. It is inter-

esting to note that in many cases, the greatest change in

brightness relative to the noise level occurred in the blue

bandpass. That is, for these flares, the peak intensity

in the blue rose above the quiet level of the star by a

greater number of standard deviations than in the other

bands. This is not surprising if, as suggested by Kunkel (1973),

























20


the measurement of the "quiet" level of the star in the

ultraviolet is constantly polluted with contributions from

"microflare" activity, thereby causing the signal to seem

noisier than if the star were really quiet between major

flare activity. In most cases the red band is relatively

insensitive to flare activity, and so does not show this

microflaring disturbance of the quiet intensity.






























Figure 4 Three-color light curve for event 26AU3.






EV LRC AUG 26, 1973


I~,.113! 1


TIME (UT)


('f)u


(If)b






























Figure 5 Three-color light curve for event 3SE3.































Figure 6 Two-color light curve for event 70C3.






























Figure 7 Three-color light curve for event 90C3A.































Figure 8 Three-color light curve for events 90C3B,C.






























Figure 9 Three-color light curve for event 90C3D.
































Figure 10 Three-color light curve for event 19AU4.
































Figure 11 Three-color light curve for event 21SE4.
































Figure 12 Three-color light curve for event 21FE4.








RD LEO FEB 21, 1974





1.50 1 I


(I )
TU
0.50-




0.36



o.se^ \ -
0.22-


(If)b











0.021.-M'1^


50800
TIME WUT)































Figure 13 Three-color light curve for events 26FEfA,B.































Figure 14 Three-color light curve for event 27FE4.






























Figure 15 Three-color light curve for event 25AP4.







RD LEO APR 25, 1974


TIME (UT)


(If)b

0.




0,




(I,)o,































Figure 16 Three-color light curve for event 18AP5.








CHAPTER IV


THEORETICAL CONSIDERATIONS


Like most other discoveries in science, the rapid

increase in the brightness of certain red dwarf stars has

stimulated a large number of possible explanations. Every-

thing from Hertzsprung's asteroid hypothesis to the involve-

ment of starspots and intense magnetic fields have been or

are now being used to try and explain the outbursts (see

Gershberg 1970 for summary of theories.)


The Nebular Model


The nebular model of Gershberg (1968) and Kunkel (1967;

1970) poses problems for the direct analytic application of

observed data to the theory. The model represents flare light

as recombination radiation from an isothermally expanding

cloud of ionized hydrogen. The light curve is given by


I(t) Q

Imax JK _KA K
Im [ {K +(K -1)> -


where
t
Q = 1 + t being measured from time of maximum
A light;

A = R/v = the expansion time scale of a cloud with
an initial radius, R, expanding with a
velocity, v;








B = the characteristic time scale of recombination
as a function of the electron density and
temperature;

and K = 1, 2, or 3 for the different geometries of
expansion.

There are serious problems encountered in attempting to

apply data to the equation since the problem is overdetermined.

The unknown quantities A, B, and K cannot be solved for

analytically. In the past, the theory has been fitted to

observed light curves by choosing values for the unknowns and

matching the resulting curves with the observations by trial

and error. Unfortunately, the light curves produced by the

theory are not independent of each other. For example, the

family of curves produced by varying K and keeping A and B

constant can be closely approximated by holding K constant

and varying A or B. Obviously, this provides little in the

way of practical insight into the flare phenomenon.

The theory itself has been losing favor recently as more

and better observations have become available. For these

reasons, the nebular model will not be quantitatively treated

here.


Fast Electron Model


The fast electron model proposed by Gurzadyan explains

flare light as the result of inverse Compton scattering of

infrared photons by a cloud of electrons having energies that

are suprathermal but not relativistic. The energies of the

electrons are assumed to be identical and in the range of

10 10 eV. If = E/mc2 = the energy of the fast electron








in terms of its rest energy, Gurzadyan finds that the photon

scattered from a fast electron will have its frequency
2
increased by a factor of 2. That is, it will become bluer.

So, the appearance of a cloud of fast electrons above the

surface of the star is accompanied by a sudden increase in

the radiation originating in the blue end of the spectrum.

The theory also predicts that an increase in intensity at the

blue end of the spectrum will be accompanied by a decrease in

the intensity beyond about 7000A (the exact wavelength depends

on the temperature and the electron energy). This results

since, presumably, these are the photons which undergo the

inverse Compton scattering. The number density of the electrons

reaches a maximum at flare maximum and then begins to diminish.

This decrease in the optical depth of the cloud causes the

decrease in flare light. The origin of the cloud of electrons

is unknown.

Several points need to be kept in mind with regard to

the fitting of data to the theory. First, as it is used in

the theory, optical depth is a measure of the number density

of electrons; and, as such, it is wavelength-independent.

This means that the value for the optical depth at any time

during a flare should be identical in all three colors.

Secondly, the theory predicts a constant color for the flare

light. This is implied in the form of the expression for the

decay in the optical depth. According to the theory, the

optical depth, T, is represented by


T = ro(tr/t)n









where

To = the maximum value of the optical depth,
t = the time elapsed since maximum light,

tr = the rise time of the flare,

and n = a dimensionless quantity which indicates the
number of dimensions in which the cloud is
expanding as it dissipates.

A spherical expansion is denoted as n = 2. If 1
expansion is like a slab which is increasing in thickness.

The theory states that n is also wavelength independent.

Thus, two of the most important points to look for are whether

or not To and n are identical for all three colors.

The light curve of a flare is represented by the fast

electron theory according to the equation,


f = (1 + A)eT 1 (2)

=AI/Io

where

A = A(4L,T,X)
1 exp(C2/XT) -1

=4 exp(C24/2XT) -1

C2= hc/k = 1.439 cm K,

UL= the electron energy as mentioned above,
and T= the instananeous value of the optical depth
of the electron cloud as given in equation (1).

The parameters solved for from the data are To and n. All

others are known. The value of tr is gotten from the light

curve, is the effective wavelength of the photoelectric

bandpass, and T is the temperature of the star.








At flare maximum, T= To, and


If = (1 + A-o)e- 1

For a given value of A, the largest possible If that the theory

predicts is obtained by setting



= 0 = -e T+ AeT ATe-T
br
1
This reduces to T = 1 -- (4)
A

This represents the optical depth of the electron cloud at

which the maximum possible value of If in a given bandpass

is attained. In other words, for a given A, all flare events

observed on the star must have maxima that are less than or

equal to the value of If when equation (4) is substituted into

equation (2). Thus, the value of the maximum for a flare is

related to the temperature, T, of the star and the energy

of the electron cloud. If>Tmax, the cloud will absorb

sufficient radiation from the photosphere so that the observed

If will be less than the maximum If possible. Since A is

always positive, T m<1, and from physical considerations,
max
Tmust be greater than zero for an increase in intensity to

occur. Table 2 gives the values for A and the maximum allow-

able values of If for various values of T and the electron

energy. The wavelengths used were the effective wavelengths

of the three-channel photometer (3500, 4632, and 6496A).

Columns 6-8 are the maximum possible values of If at the three

effective wavelengths. Note that for 2 = 10 and T = 3100 K,

A(r)<1. This means that ax<0. It follows that at this
max





















Table 2

THEORETICAL PARAMETERS AND MAXIMUM FLARE
AMPLITUDES FOR FAST ELECTRON THEORY*

T(K) L2 A(u) A(b) A(r) u b r
3100 5 138.839 11.558 1.271 50.4 3.6 .027
10 165.460 10.386 0.967 60.2 3.2
3000 5 196.486 14.428 1.516 71.7 4.7 .079
10 242.524 13.767 1.172 88.6 4.4 .012
2900 5 284.990 19.010 1.832 104. 6.4 .163
10 365.340 18.626 1.441 134. 6.2 .061
2800 2 30.728 5.125 1.059 10.7 1.3 .002
5 424.765 25.567 2.246 156. 8.8 .290
10 567.288 25.778 1.800 208. 8.9 .154
20 437.348 17.667 1.118 160. 5.9 .006
2700 5 652.526 35.180 2.798 239. 12.3 .472
10 911.061 36.589 2.288 335. 12.8 .303
2600 5 1036.790 49.657 3.549 381. 17.6 .731
10 1519.250 53.420 2.968 558. 19.0 .529

* Tabulated amplitudes are in intensity units.









temperature, an increase in intensity is impossible at

X= 6496R; so a flare on this star (if 2 = 10) would

produce a decrease in the intensity of the star in the

r band.

Several characteristics of the theory can be found

from an investigation of the table and equations (1) and

(2).

(A) For a given temperature, the larger the value of

A, the faster the light curve will decay. In this case, the

parameter n in the optical depth equation decreases.
2
(B) For a given value of 2 the lower the temperature,

the smaller is n.

(C) For given values ofp 2 and T, an increase in n makes

the curve decay faster.

(D) The larger the temperature, the smaller are the
2
possible flare amplitudes for the same values of p2.


Fitting the Observed Light Curves


The procedure used to fit the light curves was the follow-

ing. The rise time, tr, was obtained from the light curve

directly, as was the maximum value of If. Through his match-

ing of observed light curves, Gurzadyan (1970) found that

U2 = 10 is the best value for the electron energy. The
temperature was assumed to be 2800 K for both EV Lac and

AD Leo. This along with the effective wavelength of a band-

pass defines a value of A. At maximum, T= To so

If = (1 + ATr)e-o -1.









If at maximum is obtained from the light curve and To is

found by iteration using Newton's iterative procedure for

finding roots. The value of To is analytically found in this

way and is the exact value consistent with the theory. The

approximation used by Gyrzadyan (1969) was not used even for

<1. After maximum, equation (2) is iterated using the

observed values of If to find a series of values for T(t).

Each value of T(t) is assumed to depend on T according to

equation (1), so n can then be calculated by,

In(T/To)
n =- (5)
In(t /t)

This procedure gives values of Tand n for each observation.

The values obtained for n were then averaged to get a value

with which to describe the entire curve. A curve can then

be plotted from the substitution of the value for T and n
0
into equtiori (2).

When this procedure was used on the data, it was found

that the values 2 = 10 and T = 2800 K could not be used to

describe all of the observed light curves. Comparison of

Tables 1 and 2 shows that flares 70C3, 90C3A,C,D, and 26FE4A,B

all have If maxima that can be fitted in the u and b bands, but

are too large in the r band. The theory was not applied to

90C3A because of its obviously anomalous character. There

are at least three possible explanations for the large ampli-

tude in the red bandpass. Either f2 had to be decreased,

T had to be decreased, or the excess radiation in the r band

was due to Ha emission strong enough to affect the total flux









in the band to the extent that it was too great for p = 10

and T = 2800 K. The theory does not treat lineemission.

However, these stars show emission lines in their quiet

spectrum, and the lines are greatly enhanced during a flare.

The effective wavelength of the red bandpass lies close to

the Ha line, so excess line emission is a possible explanation.

From the convolution of the response curve of the r bandpass

with the energy distribution of the quiet photosphere, it

was found that approximately 1.1 per cent of the total signal

in the r band for the quiet level of the star is due to Ha

emission. For the theory to be applied to the data, the

excess radiation must be subtracted out of the total observed

If. A value for AHa could be arrived at if the change in the

intensity of the continuum could be estimated. Since T

should be the same for all wavelengths, the To found from the

uv and b curves could be used in equation (2) to give Ifmax

for the r band. This then could be used to find theAHa from

AIobs 0.98941c

0.011

where AIc is the value of If max in the r band found by

substituting the value of T into equation (2). Aobs

is the observed maximum value of If. The constants 0.989

and 0.011 result from the convolution procedure mentioned

above. However, there is a problem with this procedure,

since, as will be discussed later, the values of T were not

as predicted by the theory. In fact, To for the uv band was

typically an order of magnitude smaller than in the r band.









So the value of To could not be estimated for the r band by

this method. The other possibility is to assume the AI was

the maximum allowed (i.e. 0.154) and attribute the excess to

the change in the strength of HQ. This procedure leads to

values of AHQ at maximum of 9.8, 30.7, 1.5, 11.0, 21.6, and

14.3 for the 6 events mentioned above. These results are

obviously subject to large uncertainties and are listed here

only as possible considerations.

The first procedure used in this study for flares which

showed to large an increase in r was to change the value of

L2 while keeping T at 2800 K. As can be seen from Table 2,

U2 is reduced to allow for larger amplitudes in If. Reducing

L2 to 5 allowed all the events to be fitted except for 26FE4B

(and 90C3A which was not fitted as,mentioned above). It was

discovered that for T = 2800 K, there existed no value of A

large enough to allow a value of If great enough to fit the

observed maximum in the red bandpass for event 26FE4B. The

second procedure was to force 2 to equal 10 and vary T in

steps of 100 K until the flare light curve could be fitted.

Except for 26FE4B, this necessitated only a decrease in T

of 100 K. For 26FE4B, T had to be reduced to 2600 K. As is
2
obvious from Table 2, if a flare could be fitted with .2 = 10

and T = 2800 K, it could also be fitted with a lower temper-

ature. In these cases, only the first fit was made. The

final values for the parameters are given in Tables 3 and 4.

Table 3 lists the parameters for the temperature of 2800 K.

Table 4 contains the values of the parameters when T was




















Table 3

TABULATION OF THE FITTED PARAMETERS IN THE FAST
ELECTRON THEORY FOR A TEMPERATURE OF 2800 K

Event /2 Band n TO tr(sec)

70C3 5 uv 1.50 .0172 118
red 1.50 .3542

90C3C 5 uv 1.46 .0095 104
blue 2.17 .0190
red 2.23 .1689

90C3D 5 uv 1.09 .0155 23
blue 1.14 .0266
red 1.24 .2729
21FE4 10 uv 1.03 .0038 9
blue 1.04 .0143
red 0.62 .1170
26FE4A 5 uv 0.73 .0208 16
blue 0.80 .0653
red 0.97 .3895
25AP4 10 uv 0.83 .0026 9
blue 0.98 .0098
red 0.89 .0547
21SE4 10 uv 1.00 .0108 17
blue 1.13 .0323
red 1.00 .2098


















Table 4

TABULATION OF THE FITTED PARAMETERS IN
THE FAST ELECTRON THEORY FOR k= 10

Event T(K) Band n To tr(sec)

70C3 2700 uv 1.50 .0079 118
red 1.50 .3255

90030 2700 uv 1.30 .0044 104
blue 1.90 .0131
red 2.03 .0612

90C3D 2700 uv 1.10 .0072 28
blue 1.18 .0182
red 1.23 .2568

21FE4 2800 uv 1.03 .0038 9
blue 1.04 .0143
red 0.62 .1170
26FE4A 2700 uv 0.72 .0096 16
blue 0.79 .0441
red 0.93 .3529
26FE4B 2600 uv 0.93 .0063 104
blue 1.05 .0333
red 1.11 .2050
25AP4 2800 uv 0.83 .0026 9
blue 0.98 .0098
red 0.89 .0547

21SE4 2800 uv 1.00 .0108 17
blue 1.13 .0323
red 1.00 .2098








allowed to vary. An examination of the table shows that no

one temperature could be used with Y2 = 10 to produce a

satisfactory fit to the light curves. A temperature of 2700 K

fits all the events except 26FE4B, for which T had to be

2600 K. The photospheres of these stars are not believed to

show overall variations in temperature, so another explanation

must be found for the discrepancies in T that seem to be

present in Table 4. A possible explanation stems from the

studies in recent years of the slow semiperiodic variations

in these and other stars. The mechanism invoked to explain

these low-amplitude variations in brightness is, as mentioned

in Chapter 1, the existence of spots on the surface of the

stars. It has been suggested (Mullan 1973; 1974) that the

sizesof the spots are proportional to the depth of the

convective zone in the star. If this is true, flare stars

should exhibit the most pronounced spot activity, since M

stars are the most convective of all spectral classes.

Assuming that the spot region is facing the earth at the time

of a flare, the difference in temperatures in Table 4 may

be explained by the existence of these spots on the star.

Assuming the stellar and spot energy distributions to be

blackbody, if a spot is visible on the surface of the star

and a Planck curve is fitted to the observed flux distribution,

the effective temperature arrived at would be less than that

of the actual photospheric temperature. In particular, if

/ represents the flux per unit area of a blackbody at a

certain wavelength and temperature,

q 3p(1 -S) +qS = (6)









where

4p is the flux as defined above for the true
P photospheric temperature of the star,

s is the flux from a blackbody at the tempera-
ture of the spot,

s represents the fitted curve to the combined
effects of the photosphere and spot for the
"observed" temperature,

and S is the fraction of the visible disk of the
star occupied by the spot region.

The visible disk of the star is here taken to have an area

of 1. This equation was used substituting 6496A for the

wavelength in the Planck equations. The temperature of the

star was assumed to be 2800 K in order to get *p. A tempera-

ture can be assumed for the spot so that is can be calculated

and S can be found by substituting a temperature for the

combined photosphere + spot observed flux. Mullan (1974)

found that spots on YY Geminorum could take up 19 per cent of

the total surface area of the star and have temperatures of

from 1590-1890 K. Bopp and Evans (1973) found areas of 20

per cent and temperatures of 2000 K for star spots also on

YY Gem. If the photospheric temperature is really 2800 K,

and 2700 K is the temperature needed to fit the fast electron

theory (the "observed" temperature), then some ideas can be

gotten as to the size of the spots if a temperature is assumed

for the spot region. Several temperatures in the range 1600-

2000 K were used for the temperature of the spot. At T = 1750 K

and 2700 K for the temperatures of the spot and observed tem-

perature respectively, \p/ls = 115 and gps//s = 86. Thus,








equation (6) becomes

115(1 S) + S = 86,

so that S = 0.25.

This means that a spot at a temperature of 1750 K would

reduce the observed temperature of the star from its true

photospheric temperature of 2800 K to 2700 K if the spot

covered 25 per cent of the visible disk. However, in this

temperature region, the radiation of the spot at 6496R is

negligible when compared to that of the star. Thus, S = 0.25

is a lower limit in this temperature range. In other words,

if the temperature of the spot is less than about 2000 K, the

spot must cover at least 25 per cent of the visible stellar

disk in order to decrease the observed temperature by 100 K.

For a reduction to 2600 K (as for event 26FE4B), the size of

the spot needed is 45 per cent of the visible disk. These

sizes correspond to 12.5 and 22.5 per cent respectively of the

total surface area. Larger spots would result in a greater

reduction in the observed temperature. However, as mentioned

above, a cooler spot would still need to cover 25 per cent of

the disk since it is already essentially black when compared

to the photosphere. However, it should be emphasized that the

observing program was not conducted in such a way as to make

these results definitive. They have been presented only as a

possible explanation for the necessity of allowing the temp-

erature of the star to vary in the tables. It should be noted

that the temperature changes occur in Table 4 for the stronger

events. This would be expected if flares are associated

with the spot regions. The larger the spot region, the more








and stronger is the expected activity and the lower the

observed temperature would be.


Conclusions


How well does the fast electron model for flare activity

explain the observed events? As mentioned earlier in the

chapter, the wavelength independence of T and n is the most
0
important thing to look for when attempting to fit the theory

to the observations. However, as can be seen from Tables 3

and 4, the values of T proved to be very dependent on

wavelength. The value of T for the blue band was typically

3 to 5 times that for the uv band. An even greater discrepancy

is found when the values for the red band are compared to

those for the uv. In this case the values are 15 to 40 times

as great for the red band as they are in the uv. In all cases

the value of T increased toward longer wavelengths. This

must be considered a serious objection to the theory. The

values of n for most of the events were fairly consistent

with the theory. It was found that the theoretical curve is

not extremely sensitive to changes in n of 0.1. The fact that

n was found to be essentially wavelength-independent means

that the flare light was fairly constant in color. However,

for a light curve in a single color, the value of n needed

to fit the data was not time-independent.

Figures 17-24 are the observed light curves with a "best

fit" theoretical curve drawn from the observed points. For
2
events that were fitted with two different values of2 and T,

it was found that even though the values of n and T differed
0









for the two fits, the theoretical curves were indistinguishable

in appearance from one another. For example, Table 3 shows

that 90C3D was fitted for L2 = 5 and T = 2600 K. Table 4

shows that the same event was fitted using = 10 and T = 2700 K.

However, the plots of the theoretical curves obtained from the

two different fits were essentially identical. Thus, from the

fit of the curves to the observed data, a choice between the
2
two sets of values for and T was impossible. For event

90C3D, the value of n used in obtaining the curve fits the

observations well throughout the curve. However, for other

events (e.g. 21SE4) the value of n needed to describe the

shape of the curve immediately following maximum is signifi-

cantly larger than that needed for the later portions of the

curve. This is exemplified by the observed curve dropping

below the theoretical curve. This is not as serious an

objection as that for the T values or if the values of n
0
in the 3 colors were very different. The value of n being

a function of time means that the cloud does not expand in

the same way during the later stages of the flare as it did

immediately following maximum. Values of n immediately after

maximum sometimes reached 3 or 4 for short portions of the

curve and decreased as time went on. There were no cases

where n became larger for the later parts of the curve. A

few flares (e.g. 21FE4 and 90C3C) had values of n that showed

significant differences for the different colors. This effect

is not readily explained in the context of the theory. The

event 21FE4 might possibly be explained as a long-lived























enhancement of Ha causing the red curve to decrease at a slower

rate than uv or blue. However, 90C3C shows the red band de-

creasing faster. Though the theory was not applied to event

90C3A, as can be seen from Figure 25, the color of the flare

light changed drastically during the event. This type of

activity is totally unexpected in the context of the theory.

Thus it seems as if the fast electron theory falls short

in its attempt to explain the phenomenon of stellar flares.

The question of the different values of To for the various

bandpasses needs to be answered. Also, treatment of the

emission lines and how they are affected during a flare should

be considered. Last but not least, where does the cloud of

suprathermal electrons come from?































Figure 17 A fast electron model "best fit" for event 70C3.































Figure 18 A fast electron model "best fit" for event 90C3C.











EV LRC OCT 9, 1973







,3.00-

.*' .
v. *,.\.

*4 .4 4:

,, ** *, *.. *4
4 **s .. 't ** '
4 4* .4*

*













4*
,\,,




















fb * *+ .
So *w l *
0.10- 4. 4 ** .*
.. .C .4_ *.
.. a- .*
* *

*, .I: -
*44


0. ia




r. ..

(I ) **C . .. ,


TIME (UT)































Figure 19 A fast electron model "best fit" for event 90C3D.











7.00





L.50-


0.75





0.45-



b

0.15-






n.,s.


(If)r012-


EV LRC OCT 9, 1973
I I


0 eGGS i

1 ~ S


4 1-


Ic






s C


-~ I-


I
530M0


I
?:I230
TIME (13')


a a I





1


I I I II -I -r


%, .
































Figure 20 A fast electron model "best fit" for event 21FE4.






























Figure 21 A fast electron model "best fit" for event 26FEI;A.

The maximum value of If in the blue bandpass was

not observed due to amplifier saturation. A

value of 1.50 was assumed.
































Figure 22 A fast electron model "best fit" for event 26FE4B.






























Figure 23 A fast electron model "best fit" for event 25AP4.
































Figure 24 A fast electron model "best fit" for event 21SE4.
































Figure 25 Instrumental color indices of flare light

for event 90C3A.






























Figure 26 Instrumental color indices of flare light

for events 90C3B,C.































Figure 27 Instrumental color indices of flare light

for event 90C3D.































Figure 28 Instrumental color indices of flare light

for event 26FE4B.
































Figure 29 Instrumental color indices of flare light

for event 21SE4.




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