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CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

Study of Stellar Flares

A thesis submitted in partial fulfillment of the requirements

For the degree of Master of Science in Physics

Masoumeh Rousta

August 2014

This thesis of Masoumeh Rousta is approved by:

Jan J. Dobias, Ph. D. Date

Damian J. Christian, Ph.D. Date

Debi Prasad Choudhary, Ph.D., Chair. Date

California State University, Northridge

Acknowledgments

I would like to express my special appreciation and thanks to my advisor Professor Dr.

Debi Prasad Choudhary, you have been a tremendous mentor for me. I would like to thank you for encouraging my research. Your advice on both research as well as on my education and career path have been priceless. I would also like to thank my committee members, Professor Dr. Damian J. Christian, and Professor Dr. Jan J. Dobias, for serving as my committee members even at hardship.

A special thanks to my family. Words cannot express how grateful I am to you for all of the sacrifices that you’ve made for me. Your prayer for me was what sustained me thus far.

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Table of Contents

Signature page ...... ii Acknowledgments ...... iii ABSTRACT ...... vi 1. Introduction ...... 1 1.1 Star properties ...... 1 1.2 Main sequence stars ...... 4 1.3 Flares ...... 5 1.4 Stellar flares ...... 8 2. Data and observation ...... 11 2.1 Kepler ...... 11 2.1.1 System Characteristics ...... 11 2.1.2 Mission Characteristics...... 13 2.2 G- type main sequence stars data ...... 14 2.3 Kepler light curve flux ...... 17 2.4 Kepler light curve time ...... 18 3. Data analysis ...... 19 3.1 Data log...... 20 4. Results ...... 23 4.1 Initial results ...... 23 4.2 Revised data results ...... 24 4.3 Dips ...... 29 5. Discussion and Conclusion ...... 37 References ...... 40

List of Figures

Figure1: An HR diagram showing many well known stars in the Milky Way galaxy. (http://science.nasa.gov/astrophysics/focus-areas/how-do-stars-form-and-evolve/) ...... 4 Figure2: The positions of some flaring objects in the HR- diagram. Dots are Main- sequence stars, crosses are young stars and circles are (sub) giants and supergiants at various stages of stellar evolution. (A review of stellar flares and their characteristics, B. R. Pettersen, Solar Physics ,1989, Volume 121, Issue 1-2, pp 299-312) ...... 10 Figure3: Kepler Spacecraft and Photometer. (http://kepler.nasa.gov/Mission/QuickGuide/) ...... 12 Figure4: Contrast mean value versus number of flares...... 23 Figure5: Contrast standard deviation versus number of flares...... 24 Figure6: Kepler ID 3100568...... 25 Figure7: Kepler ID 6034120...... 25 Figure8: Contrast mean value versus number of flares...... 26 Figure9: Contrast standard deviation versus number of flares...... 27 Figure10: Flux log vs number of flares...... 28 Figure11: Flux standard deviation log vs number of flares...... 28 Figure12: Kepler Id 4245449- quarter 3 light curve...... 30 Figure13: Kepler Id 4245449- quarter 7 light curve...... 30 Figure14: Kepler Id 4245449- quarter 8 light curve...... 31 Figure15: Kepler Id 4245449- quarter 14 light curve...... 32 Figure16: Kepler Id 4830001- quarter 6 light curve...... 33 Figure17: Kepler Id 8143783- quarter 2 light curve...... 33 Figure18: Kepler Id 8143783- quarter 12 light curve...... 34 Figure19: Kepler Id 8226464- quarter 6 light curve...... 35 Figure20: Kepler Id 10000785- quarter 8 light curve...... 35 Figure21: Kepler Id 10000785- quarter 9 light curve...... 36 Figure22: Flare amplitude vs pre- flare...... 36

ABSTRACT

STUDY OF STELLAR FLARES

Masoumeh Rousta

Master of Science in Physics

Kepler observations revealed that many sun-like stars produce flares that are much greater strength in terms of total luminosity visual wavelengths compared to solar flares.

It is well known that energy released in solar flares is stored in the magnetic field structures which are anchored to sun through sunspots. Powerful flares that are produced at locations of greater energy storage that often manifest in more light output. As such, relation between the sunspot area and flare productivity have been observed since long.

Since the flares occur at the locations of flux emergence, it is possible to relate the fluctuation in spot area with flare productivity. Assuming that the stellar flares occur due to similar processes as solar flares, we have investigated superflares data that are taken from the Kepler catalog in order to find relationship between the flare frequencies with spot activity. We measured the flare frequencies by counting the number of flares produced by the star during an observing quarter. The amplitude of the light curve is estimated by computing the contrast, which is due to the passage of star spot on stellar disk. Larger mean contrast would be produced by bigger star-spots, which is a measure of surface magnetic field. The standard deviation of mean contrast is used as a measure of fluctuating field resulting from flux emergence. We examine the relationship between the

amplitude of the light curve and its change with the flare frequency. Our results show that the flare frequency of a star increase with the contrast of the light curve observed with

Kepler instrument. This shows that the large stellar flares are produced at the locations of greater magnetic field reserve. Dependence of flux emergence in flare frequency is less obvious.

In the second part of our research, we investigated Kepler IDs pre- flare dips. We observed ten stellar flares with pre- flare dip on Kepler device. We found that the flare amplitude increase with the pre- flare dip flux, however, this is not a reliable result as relativity we do not have enough data.

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1. Introduction

A star is a massive, luminous sphere of plasma held together by its own gravity. For at least a portion of its life, a star shines due to thermonuclear fusion of hydrogen into helium in its core, releasing energy that traverses the star's interior and then radiates into outer space. In the end some stars end by supernova explosion once the hydrogen in the core of a star is nearly exhausted. Almost all naturally occurring elements heavier than helium are created by stellar nucleosynthesis during the star's lifetime. Near the end of its life, a star can also contain degenerate matter. Astronomers can determine the mass, age, metallicity (chemical composition), and many other properties of a star by observing its motion through space, luminosity, and spectrum respectively. The total mass of a star is the principal determinant of its evolution and eventual fate. Other characteristics of a star, including diameter and temperature, change over its life, while the star's environment affects its rotation and movement.1

1.1 Star properties

Most stars are between 1 billion and 10 billion years old. The more massive a star is, the shorter its lifespan. The most massive stars last an average of a few million years, while stars of minimum mass (red dwarfs) burn their fuel very slowly and can last tens to hundreds of billions of years. When stars form in the present Milky Way galaxy they are composed of about 71% hydrogen and 27% helium, as measured by mass, with a small fraction of heavier elements. Typically the portion of heavy elements is measured in terms of the iron content of the stellar atmosphere, as iron is a common element and its absorption lines are relatively easy to measure. Because the molecular clouds where stars

form are steadily enriched by heavier elements, a measurement of the chemical composition of a star can be used to infer its age.2

The magnetic field of a star is generated within regions of the interior where convective circulation occurs. This movement of conductive plasma functions like a dynamo, generating magnetic fields that extend throughout the star. The strength of the magnetic field varies with the mass and composition of the star, and the amount of magnetic surface activity depends upon the star's rate of rotation. This surface activity produces starspots, which are regions of strong magnetic fields and lower than normal surface temperatures. Coronal loops are arching magnetic fields that reach out into the corona from active regions. Stellar flares are bursts of high-energy particles that are emitted due to the same magnetic activity. Young, rapidly rotating stars tend to have high levels of surface activity because of their magnetic field. The magnetic field can act upon a star's stellar wind, functioning as a brake to gradually slow the rate of rotation with time. Thus, older stars such as the Sun have a much slower rate of rotation and a lower level of surface activity.3

The combination of the radius and the mass of a star determines the surface gravity. Giant stars have a much lower surface gravity than main sequence stars, while the opposite is the case for degenerate, compact stars such as white dwarfs. The surface gravity can influence the appearance of a star's spectrum, with higher gravity causing a broadening of the absorption lines. The most dependable method for weighing a star relies on Newton’s version of Kepler’s third law. The law can be apply to measure masses only in binary star systems, systems in which two stars continually orbit one another. Most stars are much

too small in angular size to be observed with current ground-based optical telescopes, and so interferometer telescopes are required to produce images of these objects. Another technique for measuring the angular size of stars is through occultation. The star's angular diameter can be computed by precisely measuring the drop in brightness of a star as it is occulted by the Moon (or the rise in brightness when it reappears).

The surface temperature of a main sequence star is determined by the rate of energy production at the core and by its radius, and is often estimated from the star's color index.

The temperature is normally given as the effective temperature, which is the temperature of an idealized black body that radiates its energy at the same luminosity per surface area as the star. Note that the effective temperature is only a representative value, as the temperature increases toward the core. The temperature in the core region of a star is several million Kelvin. The stellar temperature will determine the rate of ionization of various elements, resulting in characteristic absorption lines in the spectrum. The surface temperature of a star, along with its visual absolute magnitude and absorption features, is used to classify a star.4

The luminosity of a star is the amount of light and other forms of radiant energy it radiates per unit of time. It has units of power. The luminosity of a star is determined by the radius and the surface temperature. However, many stars do not radiate a uniform flux

(the amount of energy radiated per unit area) across their entire surface. The rapidly rotating star Vega, for example, has a higher energy flux at its poles than along its equator. Surface patches with a lower temperature and luminosity than average are known as starspots. Small, dwarf stars such as our Sun generally have essentially

featureless disks with only small starspots. Larger, giant stars have much larger, more obvious starspots, and they also exhibit strong stellar limb darkening. That is, the brightness decreases towards the edge of the stellar disk. The apparent brightness of a star is expressed in terms of its apparent magnitude, which is the brightness of a star and is a function of the star's luminosity, distance from Earth, and the altering of the star's light as it passes through Earth's atmosphere.5

1.2 Main sequence stars

A plot of the temperature of many stars against their luminosities, known as a

Hertzsprung–Russell diagram (H–R diagram), allows the age and evolutionary state of a star to be determined.

Figure1: An HR diagram showing many well known stars in the Milky Way galaxy.

(http://science.nasa.gov/astrophysics/focus-areas/how-do-stars-form-and-evolve/)

The Hertzsprung–Russell diagram is a scatter graph of stars showing the relationship between the stars' absolute magnitudes or luminosities versus their spectral types or classifications and effective temperatures.

A G-type main-sequence star (G V), often (and imprecisely) called a yellow dwarf, or G dwarf star, is a main-sequence star (luminosity class V) of spectral type G and has about

0.8 to 1.2 solar masses and surface temperature of between 5,300 and 6,000 K. The Sun is the best known (and most visible) example of a G-type main-sequence star. A G-type main-sequence star will fuse hydrogen for approximately 10 billion years, until it is exhausted at the center of the star. When this happens, the star expands to many times its previous size and becomes a red giant. Eventually the red giant sheds its outer layers of gas, which become a planetary nebula, while the core cools and contracts into a compact, dense white dwarf.6

1.3 Flares

A solar flare is a sudden brightening observed over the Sun's surface or the solar limb, which is interpreted as a large energy release of up to 6 × 1025 joules of energy. They are often, but not always, followed by a colossal coronal mass ejection also known as a

CME. The flare ejects clouds of electrons, ions, and atoms through the corona of the sun into space. These clouds typically reach Earth a day or two after the event. The term is also used to refer to similar phenomena in other stars, where the terms stellar flare applies.7.8.9

Flares affect all layers of the solar atmosphere (photosphere, chromosphere, and corona), when the plasma medium is heated to tens of millions of Kelvin, the electrons, protons,

and heavier ions are accelerated to near the speed of light. They produce radiation across the electromagnetic spectrum at all wavelengths, from radio waves to gamma rays, although most of the energy is spread over frequencies outside the visual range and for this reason the majority of the flares are not visible to the naked eye and must be observed with special instruments. Flares occur in active regions around sunspots, where intense magnetic fields penetrate the photosphere to link the corona to the solar interior.

8Flares are powered by the sudden (timescales of minutes to tens of minutes) release of magnetic energy stored in the corona. The same energy releases may produce coronal mass ejections (CME), although the relation between CMEs and flares is still not well established. Flares occur when accelerated charged particles, mainly electrons, interact with the plasma medium. Scientific research has shown that the phenomenon of magnetic reconnection is responsible for the acceleration of the charged particles.10

It has been observed that when sunspot area increases, the flare occurrence rates and probability noticeably increase, especially for major flares. This is because of the fact that large spots store more magnetic energy that can become unstable by small perturbations.

This means that when sunspot area is larger, then the flare probability becomes higher.11

During the emergence, both the positive and negative sunspots in the bipole show translational as well as rotational motion. Solar flares are one of the transient phenomena of magnetic energy release in the solar atmosphere. The magnetic energy stored in the twisted/sheared complex magnetic fields of active regions is converted into thermal and kinetic energies, as well as the acceleration of energetic particles via magnetic reconnection. The emergence/activation of twisted flux tubes/ropes can lead to magnetic instabilities, interacting with the overlying fields and eventually result in the flare.

Associated eruption rotating sunspots may be one of the most likely candidates to inject magnetic helicity into the solar atmosphere, which may cause the flare energy build-up.

Many pieces of observational evidence of sunspot rotation have been reported (e.g. several hundred degrees around their umbral centers over a few days) prior to the occurrence of strong flares. The rapid rotation of the sunspots can cause the formation of sigmoid loop that can erupt to produce flares and coronal mass ejections .The recent theories/model suggest that sunspot rotation can be caused by a pre-twisted magnetic flux tube emerging from below the photosphere .12The energy for solar flares is believed to derive from magnetic fields in the solar corona. The assumptions of one model are that flares are powered by a coronal energy source and flares are the dominant mechanism for depleting these energetic sources. Moreover, there is a characteristic time-scale for flares to release the available free energy. The time-scale is the response time for the flaring corona. Solar flares are strongly related with sunspot number as they generally occur in active regions lying over the sunspot regions.12. 13

Large active regions have more large flares than small ones and also tend to be more complex.14

A solar flare is a result of the effect of reconnection of magnetic fields, the magnetic reconnection. The principal flare process is contingent on the accumulation of the free magnetic energy in the corona. By ‘free’ we mean the surplus energy above that of a potential magnetic field. This field has the sources (sunspots, background fields) in the photosphere. The free energy is related to electric currents in the corona. A flare corresponds to rapid changes of the currents. It is of principal importance to distinguish the currents of different origin because they have different physical properties and, as a

consequence, different behaviors in the pre-flare and flare processes a slow accumulation of energy and its fast release, a flare. An interaction of magnetic fluxes (and an excess of energy) appears as a result of slow changes of the field sources. The changes are an emergence of a new flux from below the photosphere and other flows of photospheric plasma, in particular the shear flows along the neutral line of the photospheric magnetic field.14

1.4 Stellar flares

Solar flares are caused by the sudden release of magnetic energy stored near sunspots.

They release1029 to 1032 ergs of energy on a timescale of hours. Similar flares have been observed on many stars, with larger ‘superflares’ seen on a variety of stars, some of which are rapidly rotating and some of which are of ordinary solar type. Here there is a report of observations of 365 superflares, including some from slowly rotating solar-type stars, from about 83,000 stars observed over 120 days.15 Quasi-periodic brightness modulations observed in the solar-type stars suggest that they have much larger starspots than does the Sun. The maximum energy of the flare is not correlated with the stellar rotation period, but the data suggest that superflares occur more frequently on rapidly rotating stars. It has been proposed that hot Jupiter may be important in the generation of superflares on solar-type stars, but none have been discovered around the stars that we have studied, indicating that hot Jupiter associated with superflares are rare. Stellar flares have 102 to 107 times more energy than the largest solar flare have and they have durations of hours to days and are visible from at least X-ray to optical frequencies.

Short duration flares are well known to occur on cool main-sequence stars as well as on many types of ‘exotic’ stars. The core of the star may collapse into a few solar mass black

hole accretion into which powers the GRB flow. Alternatively, a millisecond period protomagnetar may form at the stellar core. In this model, magnetic fields extract the rotational energy of the magnetar launching the GRB flow. From the theoretical perspective, fast rotation and very strong fields appear to be needed for a successful magnetar model for GRBs Galactic magnetar can release a substantial fraction of their magnetic energy during powerful flare. The distance out to which a flare from a GRB magnetar can be observed depends on both luminosity and spectrum.16

Stellar flares are generally regarded as the stellar analogues of solar flares and their X-ray emission often only differs from their solar counterparts in magnitude and duration.

Stellar flare peak temperatures and emission measures can be orders of magnitude greater than what is seen on the Sun. The durations of the longest lived stellar flares significantly exceed the longest durations seen in solar flares17. Stellar flares can involve the release of

106 times more energy in total than solar flares, suggesting substantially higher magnetic fields and larger flaring volumes. Flares are observed in all types of stars with convective envelopes, including from M dwarfs, solar analogs, RS CVn stars, and also giants. Flare emission emerges in the optical and near-UV, as well as X-rays and radio. There are also flares showing much more exotic X-ray light curves, with dips and multiple peaks, and it is conceivable that these could be used to deduce spatial information about stellar flares, which is at a premium. It probably has large starspots which can store a large amount of magnetic energy enough to give rise to superflares.

Stars are considered to show much higher coronal activity than that of the Sun. They probably have large starspots which can store a large amount of magnetic energy enough to give rise to superflares.18

Short duration flares are well known to occur on cool main-sequence stars as well as on many types of ‘exotic’ stars. Ordinary main-sequence stars are usually pictured as being static on time scales of millions or billions of years. Our sun has occasional flares involving up to ∼ 1031ergs which produce optical brightening too small in amplitude to be detected in disk-integrated brightness. However, nine cases of superflares has been detected involving 1033to 1038ergs on normal solar-type stars. That is, these stars are on or near the main-sequence, are of spectral class from F8 to G8, are single (or in very wide binaries), are not rapid rotators, and are not exceedingly young in age. This class of stars includes many those recently discovered to have planets as well as our own Sun and the consequences for any life on surrounding planets could be profound. For the case of the

Sun, historical records suggest that no superflares have occurred in the last two millennia.

Stellar flares are known to come from many types of stars ranging from faint red dwarfs to many types of ‘exotic’ stars. 19

Figure2: The positions of some flaring objects in the HR- diagram. Dots are Main- sequence stars, crosses are young stars and circles are (sub) giants and supergiants at various stages of stellar evolution. (A review

of stellar flares and their characteristics, B. R. Pettersen, Solar Physics ,1989, Volume 121, Issue 1-2, pp

299-312)

2. Data and observation

2.1 Kepler

The Kepler Mission, NASA Discovery mission #10, is specifically designed to survey a portion of our region of the Milky Way galaxy to discover dozens of Earth-size planets in or near the habitable zone and determine how many of the billions of stars in our galaxy have such planets.

Results from this mission will allow us to place our solar system within the continuum of planetary systems in the Galaxy.

2.1.1 System Characteristics

 Space based Photometer: 0.95-m aperture

 Primary mirror: 1.4 meter diameter, 85% light weighted

 Detectors: 95 mega pixels (21 modules each with two 2200×1024 pixel CCDs)

 Band pass: 430-890 nm FWHM

 Dynamic range: 9th to 16th magnitude stars

 Fine guidance sensors: 4 CCDs located on science focal plane

 Attitude stability: <9 milli-arcsec, 3 sigma over 15 minutes

 Avionics: Fully block redundant

 Science data storage: >60 days

 Uplink X-band: 7.8125 bps to 2 kbps

 Downlink X-band: 10 bps to 16 kbps

 Downlink Ka-band: Up to 4.33125 Mbps

 Photometric One-Sigma Noise Designed Performance

 No mechanisms other than a one-time ejectable cover and three focus mechanism

for the primary mirror

 Flight segment and instrument mass: 1071 kg, maximum expected (10/06)

 Flight segment and instrument power: 771 W, maximum expected (10/06)

 Flight Segment labeled

Figure3: Kepler Spacecraft and Photometer. (http://kepler.nasa.gov/Mission/QuickGuide/)

2.1.2 Mission Characteristics

 Point continuously out at a single star field in Cygnus-Lyra region except during

Ka-band downlink

 Roll the spacecraft 90 degrees about the line-of-sight every 3 months to maintain

the sun on the solar arrays and the radiator pointed to deep space

 Monitor more than 100,000 main-sequence stars for planets

 Mission lifetime of 3.5 years extendible to at least 6 years (The spacecraft was

launched on March 7, 2009 )

 D2925-10L (Delta II) launch into an Earth-trailing heliocentric orbit

 Scientific Operations Center and Project management (operations) at Ames

Research Center

 Project management (development) at Jet Propulsion Laboratory

 Flight segment design and fabrication at Ball Aerospace & Technologies Corp

 Mission Operations Center at Laboratory for Atmospheric and Space Physics

(LASP)University of Colorado

 Data Management Center at Space Telescope Science Institute

Deep Space Network for telemetry

 Routine contact

 X-band contact twice a week for commanding, health and status

 Ka-band contact once a month for science data downlink20. 21

2.2 G- type main sequence stars data

We searched for stellar flares on solar-type stars (G-type main-sequence stars) using data collected by NASA’s Kepler mission during the period from April 2009 to December

2009. The effective temperature (Teff) and the surface gravity (log (g)) available from the

Kepler Input Catalog have been used to select solar-type stars. The selection criteria are as follows: 5,100 K ≤ Teff < 6,000 K, log (g) ≥ 4.0. The total numbers of solar-type stars are 9,751 for quarter 0 of the Kepler mission (the length of observation period is about

10 d), 75,728 for quarter 1 (33 d), 83,094 for quarter 2 (90 d) and 3,691 for quarter 3

(90 d).

There has been found 365 superflares (flares with energy >1033 erg) on 148 solar-type stars. The durations of the detected superflares are typically a few hours, and their amplitudes are generally of order 0.1–1% of the stellar luminosity. The bolometric luminosity and total bolometric energy of each flare were estimated from the stellar radius, the effective temperature in the Kepler Input Catalog, and the observed amplitude and duration of the flare by assuming that the spectrum of white-light flares can be described by blackbody radiation with an effective temperature of 10,000 K (ref. 10). We considered the spectral response of the Kepler photometer in doing our luminosity and energy calculations. The bolometric luminosity of superflares on G-type main-sequence stars ranges from 9 × 1029 to 4 × 1032 erg s−1, and the total bolometric energy of superflares ranges from 1033 to 1036 erg (hereafter the luminosities and energies of flares given are the bolometric values). The uncertainties in the luminosities and energies of flares are estimated to be about ±60%.

The average occurrence frequency of superflares can be estimated from the number of observed superflares, the number of observed stars and the length of the observation period. For example, in the case of slowly rotating G-type main-sequence stars with surface temperatures of 5,600 K ≤ Teff < 6,000 K, 14 superflares were detected from the data on about 14,000 stars over 120 d. Hence, the occurrence frequency of superflares is

2.9 × 10−3 flares per year per star, which corresponds to a superflare occurring on a star once every 350 yr. The occurrence frequency distribution of superflares on solar-type stars can be fitted in the energy range ≥4 × 1034 erg using a simple power law. The frequency distribution function of superflares on solar-type stars is similar to those of solar flares and stellar flares on red dwarfs. The power-law index of the distribution of superflares (−2.0 to −2.3) is nearly equal to that of the distribution of solar flares. The occurrence frequency of superflares on slowly rotating G-type main-sequence stars is about ten times lower than the average occurrence frequency. The occurrence frequency also depends on the surface temperature of the star, and is higher for lower-temperature

(5,100 K ≤ Teff < 5,600 K) G-type main-sequence stars than for higher-temperature

34 (5,600 K ≤ Teff < 6,000 K) stars. The superflares of 10 erg on Sun-like stars (that is, slowly rotating G-type main-sequence stars with surface temperatures of

35 5,600 K ≤ Teff < 6,000 K; occurrence every 800 yr, and those of 10 erg occur once every

5,000 yr, although accurate statistics are difficult to obtain because only 14 superflares have been observed on Sun-like stars.

The maximum energy of a superflare does not show any clear correlation with the period of stellar rotation, assuming that the period of brightness modulation corresponds to the rotational period of the star. If the flare energy can be explained by the magnetic energy

stored near the starspot, this result suggests that the maximum magnetic energy stored near the spot does not have a strong dependence on the period of rotation. This result also implies that superflares can occur on slowly rotating solar-type stars like the Sun.

The frequency of superflares tends to decrease as the period increases to periods longer than a few days. The frequency of superflares on the slowly rotating stars (rotational period, >10 d) is only 1/20 of that of superflares on rapidly rotating stars. The rotation period correlates with the chromospheric activity, which is known to be an indicator of the magnetic activity of the stars, and the more rapidly rotating stars have higher magnetic activity. According to the dynamo theory of magnetic field generation, magnetic activity results from the interaction between rotation and convection, and the rapid rotation can cause the high magnetic activity. Our result implies that rapidly rotating stars with higher magnetic activity can cause more frequent superflares. The frequency distribution of superflares saturates for periods of less than a few days. A similar saturation is known for the relationship between the coronal X-ray activity and the rotation period.

The rotation period of a star is also known to be related to the star’s age, with younger stars rotating more rapidly. Our findings suggest that superflares occur more frequently on the solar-type stars younger than the Sun. Moreover, on solar-type stars similar in age to the Sun, superflares occur less frequently but are nearly equal in energy to the superflares on the younger stars.

It has been pointed out that there is no record of solar superflares over the past 2,000 yr.

According to the measurement of the impulsive nitrate events in polar ice, the largest

proton flare event during the past 450 yr is the Carrington event, which occurred on 1

September 1859. The total energy released in this flare was estimated to be of order

1032 erg, which is only 1/1,000 of the maximum energy of flares on slowly rotating Sun- like stars. It has also been proposed that hot Jupiters have an important effect on stellar magnetic activity and that superflares occur only on solar-type stars with hot Jupiter.

However, there is no hot Jupiter in the Solar System. For these reasons, it was suggested that a superflare on the Sun is extremely unlikely. Although the Kepler mission has discovered 1,235 exoplanet candidates around 997 host stars from a survey of 156,453 stars, no exoplanet has been found around the 148 G-type main-sequence stars with superflares. For a solar-type star with a hot Jupiter, the probability of a transit of the planet across the star is about 10% averaged over all possible orbital inclinations. If the superflares on all 148 stars were caused by hot Jupiter, then Kepler should detect 15 of them from transits. However, the Kepler planetary-transit search is almost complete for hot Jupiter, and the non-detection of planetary transits therefore suggests that hot Jupiter associated with superflares is rare.

2.3 Kepler light curve flux

The light curves of these 365 superflares on 148 solar type stars have been plotted by

PDSSAP flux and SAP flux in which are two types light curves. The Simple Aperture

Photometry (SAP) light curve is a pixel summation time- series of all calibrated flux falling within the optimal aperture. Data archive users need to be aware that a SAP light curve can be contaminated by astrophysics from neighboring sources. There are many astrophysical targets that are less likely to benefit from direct employment of SAP data.

These include any science relying on more subtle light curve structures and periods longer than a few days, in which case systematic are more likely to be significant.

Investigation of magnetic activity, gyro chronology, binary stars and long period variables must scrutinize the SAP data with great care before proceeding. One artifact mitigation methods is PDCSAP photometry. Pre- search Data Conditioning Simple

Aperture Photometry (PDCSP) data included within the archived light curve files produced by a pipeline module that remains under continuing development.

2.4 Kepler light curve time

Julian day is the continuous count of days since the beginning of the Julian Period used primarily by astronomers. The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Greenwich Mean Time, with

Julian day number 0 assigned to the day starting at noon on January 1, 4713 BC, proleptic

Julian calendar (November 24, 4714 BC, in the proleptic Gregorian calendar).

The Modified Julian Day (MJD) is an abbreviated version of the old Julian Day (JD) dating method which has been used for plotting the Kepler light curve in this research.

The Modified Julian Day is defined as:

MJD = JD - 2400000.5

The Epoch of MJD is 0h Nov 17, 1858; Epoch refers to the point in time used to set the origin.23

3. Data analysis

In this research we benefits from PDCSAP light curves. By using Kepler data search software, the light curve of each 365 G- type main sequence stars listed by their Kepler

IDs has been plotted. Each light curve is plotted based on Flux versus time. The unit of time in which applied here is Modified Julian Date (MJD). Each Kepler ID includes of certain number of quarters, quarter is a sequential number indicating the quarter in which the exposure was made that range from zero to greater than fourteen. In this research we have investigated the number of flares which exists in sunspot by using the light curve plots for 100 G- type main sequence stars. We’ve measured the peak of each flare. Large spot means large flare. We find the max and min of each plot and the time that they occur. We found the contrast of flux and also difference of max and min time.

Then we investigate the number of flares of each plot, also their amplitude of light curves, and the time that they occur. So we can find out the frequency of occurrence of flares of each plot. In the next step, we calculate the mean value of contrast and also standard deviation of contrast.

3.1 Data log

Standard Number KPID Mean Deviation of Flare 2158047 0.014775 4.21E-06 8 2303352 0.004228 1.12E-05 3 2860579 0.031216 0.00139 18 3100568 0.107355 0.003253 11 3118883 0.048954 0.002647 18 3217974 0.003519 1.45E-06 1 3239219 0.030137 0.002138 7 3425756 0.035516 0.00313 38 3557532 0.027179 0.000294 13 3626094 0.006241 0.000116 10 3749062 0.084668 0.001096 0 3852071 0.026591 0 0 3869649 0.051575 0.000195 0 3939069 0.027513 0.000585 2 4045215 0.001297 2.71E-07 1 4138557 0.002452 7.23E-07 2 4245449 0.00886 1.32E-06 8 4449749 0.03012 9.44E-05 3 4742436 0.005065 3.31E-06 18 4749912 0.002813 9.16E-05 2 4750938 0.007866 4.04E-06 7 4830001 0.011561 7.46E-05 8 4831454 0.00976 4.32E-05 6 5179841 0.006272 1.92E-06 7 5350447 0.001594 4.22E-07 10 5427641 0.039446 1.16E-04 0 5445334 0.006267 1.63E-06 1 5474356 0.002141 3.49E-07 4 5522535 0.000604 9.42E-07 0 5528061 0.012313 7.66E-05 28 5529084 0.025434 4.04E-05 7 5616432 0.009764 6.77E-06 1 5729515 0.01255 1.32E-05 1 5896387 0.007499 1.51E-05 3 6032920 0.002389 2.90E-07 20 6034120 0.011969 7.56E-06 63 6127565 0.002675 4.98E-07 10

6196021 0.001138 8.61E-08 26 6277018 0.001649 2.24E-08 3 6292596 0.005163 1.09E-06 1 6347656 0.002821 3.00E-08 2 6503434 0.00197 6.29E-07 0 6507334 0.011837 3.67E-06 6 6633602 0.001204 1.10E-06 8 6691930 0.030438 4.35E-05 38 6697041 0.02182 2.12E-05 22 6836589 0.047856 9.50E-05 3 6848592 0.006741 3.86E-06 14 6865416 0.049461 3.16E-04 15 6865484 0.007761 2.49E-06 6 7093547 0.003372 1.35E-06 0 7133671 0.002683 6.15E-06 0 7174505 0.048786 1.99E-03 0 7256548 0.011826 8.02E-06 8 7264976 0.027211 3.01E-05 21 7287601 0.006592 2.43E-06 3 7368914 0.005794 5.52E-08 2 7532880 0.045506 3.41E-04 10 7667812 0.001755 2.80E-07 9 7902097 0.009154 3.66E-06 5 8009474 0.029567 5.18E-05 1 8074287 0.019454 1.84E-05 5 8076634 0.026188 5.24E-05 2 8091757 0.001744 3.88E-07 6 8143783 0.031571 9.37E-05 8 8162830 0.029148 8.99E-05 4 8212826 0.000699 2.31E-05 1 8226464 0.016129 2.13E-05 11 8302223 0.07556 3.10E-05 0 8359398 0.015684 1.65E-05 3 8479655 0.028594 1.29E-04 17 8480296 0.002834 6.31E-08 0 8482482 0.021664 4.59E-05 6 8491470 0.0217 2.11E-05 5 8547383 0.006159 1.49E-06 27 8604805 0.033192 9.88E-05 4 8613466 0.016053 2.25E-05 4 8621739 0.012792 1.70E-05 5 8802001 0.059791 4.77E-02 2 8848528 0.006279 5.23E-06 6

8935644 0.005983 2.81E-06 9 9146690 0.001828 5.27E-07 14 9149986 0.031484 3.60E-05 5 9150539 0.041413 3.31E-04 10 9410906 0.00469 9.28E-07 3 9412514 0.000405 2.55E-08 1 9459362 0.024246 8.06E-04 4 9583493 0.014719 1.23E-05 4 9630984 0.008311 3.35E-07 0 9652680 0.04678 1.45E-04 5 9653110 0.026234 8.29E-05 7 9655134 0.007734 1.10E-05 8 9764192 0.024695 3.66E-05 4 9764489 0.015639 1.38E-05 0 9786953 0.012394 7.98E-06 0 9838078 0.009307 1.10E-05 8 9897464 0.021798 2.38E-05 8 9934388 0.032059 8.45E-05 3 10000785 0.12074 6.70E-02 6 10120296 0.023163 6.00E-05 15

Table 1: List of G- type main sequence stars showing superflares.

4. Results

4.1 Initial results

We used our data to plot the mean value of contrast versus flare frequency. Our preliminary results show that the mean value versus number of flare is a straight line

(Fig~4). However, we observed that there are some data points that deviate from the general path of data.

70 y = 4.1663x + 7.6366 60 R² = 9E-05

Flare frequency Flare 20

0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Contrast

Figure4: Contrast mean value versus number of flares.

Then, we plotted standard deviation of contrast versus flare frequency (Fig~5). We observed that this plot is a straight line two, while still we have three odd data points.

70 y = -40.656x + 7.7751 60 R² = 0.0012

Flare frequency Flare 20

0 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02 8.00E-02 Standard deviation of contrast

Figure5: Contrast standard deviation versus number of flares.

4.2 Revised data results

In each plot, we’ve observed some odd data points with significant difference with the rest of the data points. After reviewing the light curves of these data, we’ve noticed that the light curve of these data points are not a periodic curve with maximum flux and minimum flux, which is in contrast with the other light curves, so we decided to remove them from our data. For the mean value of flux, the data of Kepler IDs 3100568 (Fig~6),

3749062, 6034120 (Fig~7), 8302223, 8802001, and 10000785 has been removed.

Figure6: Kepler ID 3100568.

Figure7: Kepler ID 6034120.

Our new results show that mean value of contrast increase with the flare frequency

(Fig~8).

40 y = 82.487x + 5.9881 35 R² = 0.0221

Flare frequency Flare 10

0 0 0.01 0.02 0.03 0.04 0.05 0.06 Contrast

Figure8: Contrast mean value versus number of flares.

For the standard deviation of flux the data of Kepler IDs 6034120, 8802001, and

10000785 has been removed. The new results show that the standard deviation is increasing with the number of flares (Fig~9).

70 y = 3235.3x + 7.1113 R² = 0.0422 60

Flare frequency Flare 20

0 0.00E+00 5.00E-04 1.00E-03 1.50E-03 2.00E-03 2.50E-03 3.00E-03 3.50E-03 SD of Contrast

Figure9: Contrast standard deviation versus number of flares.

As our plots show concentration in the area with less number of flares, we calculate the logarithm of our data to have better observation of our result. The plots agreed with our preliminary results.

y = 2.4442x + 12.257 40 R² = 0.0249 35

Flare frequency Flare 10

0 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 Contrast log

Figure10: Flux log vs number of flares.

y = 0.7216x + 11.311 70 R² = 0.0095 60

Flare frequency Flare 20

0 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 SD of Contrast

Figure11: Flux standard deviation log vs number of flares.

4.3 Dips

Pre- flare dips have been rarely observed on several flare stars and in different spectral bands but observed duration has been comparatively short from tens of seconds to a few minutes. The explanation of pre- flare dips is still unsettled. The dip could be due to a starspot coincidentally appearing on any of the star just before flare. They could be mirror image of the optical flares and simultaneous to them. The model proposed by

Mullan explains the red dips in terms of an increased Hα, while Grinin’s model is based on increase H- continuum opacity due to impulsive heating of the chromospheres caused by a down flow of material, which cause the optical flare upon reaching the photosphere.

This model predicts characteristic time scales of the order of seconds, tied to the relaxation time needed by the atmosphere to restore the thermal equilibrium perturbed by a weak impulsive heating. These models predict only time scale and spectral dependence of the short duration negative flares. 22

We observed and analysis10 stellar flares with pre- flare dip on Kepler device. We observed that the flux light curve is approximately periodic except for the part with flare.

For each curve, we divided the path with flare by general path.

For the Kepler ID 4245449, we found four pre- flare dip. For the third quarter (Fig~12), the division gives us 1.01 which related to the pre- flare dip and flare area. The elapsed time for the dip was 0.55 MJD.

Figure12: Kepler Id 4245449- quarter 3 light curve.

For the seventh quarter (Fig~13) the division of two curves is 1.01 and the elapsed time

0.57 MJD.

Figure13: Kepler Id 4245449- quarter 7 light curve.

The eighth quarter (Fig~14) gives 1.06 for division, and the elapsed time is 0.45MJD.

Figure14: Kepler Id 4245449- quarter 8 light curve.

For the fourteen quarter (Fig~15) the division of two curves is 1.01 and the elapsed time is 0.67MJD.

Figure15: Kepler Id 4245449- quarter 14 light curve.

The next Kepler ID that we observed the pre- flare dip is 4830001 (Fig~16). We divided the curve with flare by general path and the result was 1.01, and the elapsed time for pre- flare dip was 0.29MJD.

Figure16: Kepler Id 4830001- quarter 6 light curve.

For Kepler ID 8143783 we found two pre- flare dip on quarter two and twelve (Fig~17,

Fig~18). The light curves divisions for these two were 1.02, and 1.03, and the elapsed time was 0.14, and 0.21 respectively.

Figure17: Kepler Id 8143783- quarter 2 light curve.

Figure18: Kepler Id 8143783- quarter 12 light curve.

The quarter sixth of Kepler ID 8226464 (Fig~19) has light curves division of 1.01 and pre- flare dip elapsed time of 0.66MJD.

Figure19: Kepler Id 8226464- quarter 6 light curve.

The last Kepler ID in our data that has been observed with pre- flare dip was 10000785, with dips on quarters eighth (Fig~20) and nineth (Fig~21). The light curves division for them were 1.12, and 1.10, and the elapsed time were 0.10, and 1.12MJD respectively.

Figure20: Kepler Id 10000785- quarter 8 light curve.

Figure21: Kepler Id 10000785- quarter 9 light curve.

For ten pre- flare dips, we found the average of light curves division of 1.038. The average flux depth for these ten dips was 245.486e/sec and the average elapsed time for them 0.476MJD. Also, we plotted flare amplitude versus the pre- flare dip (Fig~22).

4.00E+05

3.50E+05

3.00E+05

/sec) - 2.50E+05 2.00E+05

1.50E+05 y = 142.89x + 64782

1.00E+05 R² = 0.6268 Flare Amplitude Amplitude Flare (e 5.00E+04 0.00E+00 0.00E+00 5.00E+02 1.00E+03 1.50E+03 2.00E+03 2.50E+03 Pre- flare dip flux (e-/sec)

Figure22: Flare amplitude vs pre- flare.

5. Discussion and Conclusion

We have examined the light curve and flare frequency of 100 solar like stars. Our results show that the flare frequency increase with the mean value of the contrast of the light curve of a star observed with Kepler instrument. The mean value shows the size of starspot, so we conclude that bigger spot has more flares. Furthermore, our results show that the flare frequency increase with the standard deviation of the contrast of the light curve of a star. The standard deviation correspond the fluctuation of flux emergence.

However, the number of flares does not increase in a convincing manner as standard deviation of flux increase which indicates that the fluctuation (or flux emergence) is not the only trigger mechanism. Flares are observed in all types of stars with convective envelopes, including from M dwarfs, solar analogs, RS CVn stars, and also giants. The

RS CVn stars are binary stars which typically flare 35%–40% of the time (Osten &

Brown 1999). A binary star consists of two stars orbiting around their common center of mass. The more massive star is called the primary and the other companion star, or secondary. In binary systems the stars orbit their common center of mass under the influence of their mutual gravitational force, but evolve independently.

The rotation period of stars correlates with the chromospheric activity, which is known to be an indicator of the magnetic activity. The rapidly rotating stars have higher magnetic activity and brightness of these stars show quasi- periodic variation. The brightness variation can be caused by several mechanisms such as rotation of a star with starspots, orbital motion of a binary system, eclipse by an accompanying star or stellar pulsation.

Following Maehara et al (2012), here we assumed that the period of quasi- periodic modulation corresponds to the period of stellar rotation.

Our results can be compared with RS CVn stars. RS CVn stars are class of detached binary typically composed of a chromospherically active G or K type stars. The system generally rotates fast with typical orbital period from a few days to 20 days. Tidal forces between the close components have locked their rotational period s to the orbital period.

The RS CVn binaries display a high level activity with strong chromospheric line emissions. One of the striking aspects of these systems is their propensity to flare. These stars show rotational modulation of photospheric spots and are also magnetically active.

It is known that RS CVn systems show large flares and they are thought to be caused by magnetic reconnection mediated by the close companion star. Although our sample of stars appears to be isolated stars, further moderate resolution optical spectroscopy is needed to confirm these stars are not also in a binary system.

Our results confirm that when sunspot area increases, the flare occurrence rates and probability noticeably increase, especially for major flares. This means that when sunspot area is larger, then the flare probability becomes higher (Lee, K.; Moon, Y. J. 2010).

Large starspots can store a large amount of magnetic energy enough to give rise to superflares (Maehara, 2012).

We do not find that bigger starspots result in bigger flares. Although sometimes it is true, in most cases flare magnitude do not depend on the light curve contrast. This would mean, only a small fraction of the magnetic energy in star spots are used in flare.

We observed ten pre- flare dips. Our results show that the flare amplitude increases for deeper negative flare. However, we cannot certainly manifest this result, as for four dips we measure the depth approximately zero.

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