Physics of Solar and Stellar Flares

Kazunari Shibata

Kwasan and Hida Observatories,

Kyoto University, Kyoto, Japan

ICPP 2016 (Kaohsiung, Taiwan) July 1 (35+5 min)

contents

• Introduction

• Solar flares - What is the Mechanism ?

• Superflares on Solar Type Stars

Kojiki and Universe(古事記と宇宙）

Kitaro and Shibata

Special entertainment

Let’s enjoy Various movies ofSolar flares and Eruptions withKitaro-san’s Music Kojiki : Orochi

(7 min)Orochi is 8 headed dragon monster

What is the Mechanism of Solar Flares ?

Shibata and Magara (2011) Living Reviews in Solar Physics

Simultaneous Halpha and X-ray view of a flare Magnetic

reconnecitonHα X-ray

Plasmoid ejections are ubiquitous

impulsive flares~ 10^9 cm

LDE(Long DurationEvent) flares~ 10^10 cm

CMEs(Coronal Mass Ejections) from Giant arcades~ 10^11 cm

Unifiedmodel

Plasmoid-Induced-Reconnection(Shibata 1999)

• Yohkoh/SXT discovered X-ray jets from microflares(Shibata et al. 1992, Strong et al. 1992,Shimojo et al. 1996)

Jets from very small flares (microflares)

Summary of observations ofvarious “flares”

“flares” Size (L) Lifetime

(t)

Alfven

time (tA)

t/tA Mass

ejection

microflares 103 -

104 km

100-

1000sec

1-10 sec ~100 jet/surge

Impulsive

flares

(1-3) x

104 km

10 min –

1 hr

10-30

sec

~60-100 X-ray

plasmoid/

Spray

Long duration

(LDE) flares(3-10)x

104 km

1-10 hr 30-100

sec

~100-300 X-ray

plasmoid/

prom.

eruption

Giant

arcades

105 -

106 km

10 hr – 2

days

100-1000

sec

~100-300 CME/prom.

eruption

speed)(Alfven

4

/

BV

VLt

A

AA

Unified model(plasmoid-induced

reconnection model)(Shibata 1996, 1999)

(a,b)： large scale flares,

Coronal mass ejections

(c,d) ：small scale flares,

microflares, jets

Energy release rate＝2

222

2

410

4LV

BLV

B

dt

dEAin

Plasmoid

superflare

nanoflare

microflare

solar flare

statistics of occurrence frequency of solar flares, microflares, nanoflares

1000 in 1 year100 in 1 year10 in 1 year1 in 1 year1 in 10 year

C M X X10 X1000 X100000

Largest solar flare

Basic Puzzles of Reconnection

1. What determines the Reconnection Rate ?

Recent magnetospheric observations and collisionless plasma theory suggest that fast reconnection occurs if the current sheet thickness becomes comparable with

ion Larmor radius or ion inertial length(either with anomalous resistivity or collisionlessconductivity)

Huge gap between micro and macro scale in solar flares

• Ion inertial length

• Ion Larmor radius

• Mean free path

• Flare size

2/1

310,10

300

cm

ncm

c

pi

ionin

2/1

6

1

1010100

K

T

G

Bcm

eB

vcmr iLi

1

310

2

6

7

2

2 101010

1

cm

n

K

Tcm

e

kT

nmfp

cmrflare

910

Basic Puzzle of Reconnection

1. What determines the Reconnection Rate ?

Recent magnetospheric observations and collisionless plasma theory suggest that fast reconnection occurs if the current sheet thickness becomes comparable with

ion Larmor radius or ion inertial length(either with anomalous resistivity or collisionless conductivity)

2. How can we reach such small scale to lead to anomalous resistivity or collisionless reconnection in solar flares ?

Plasmoid-Induced-Reconnection

and Fractal Reconnection

Shibata and Tanuma (2001)Earth, Planet, Space 53, 473

Shibata and Takasao (2016) “Fractal Reconnectionin Solar and Stellar Environment”, In a book “Magnetic Reconnection” (ed. By Gonzalez and Parker, Springer)

Various ways of plasmoid formation in flare current sheets

Ohyama & Shibata (1997)

1. Plasmoid starts to be ejected long before the impulsive phase.

2. The plasmoidacceleration occurred during impulsve phase.

(Ohyama and Shibata1997)

X ray Observationsshow

Height of plasmoid

time

HXR intensity

Laboratory experiment(Ono et al. 2003 )

What is the Role of

Plasmoid Ejections ?

(Shibata-Tanuma 2001)

MHD simulations show plasmoid-induced reconnection

in a fractual current sheet(Tanuma et al. 2001, Shibata and Tanuma 2001)

Tanuma et al. (2001)

Vin/VA

plasmoid

Reconnection rate

timeSee also Bhattacharjee＋2009, Loureiro+2009, Barta+ 2010, Shibayama+ 2016, many

Observation of hard X-rays and microwave emissions show fractal-like time variability, which may be a result of fractal

plasmoid ejections

(Ohki 1992)

(Tajima-Shibata 1997)

Benz and Aschwanden 1989Zelenyi 1996, Karlicky 2004 , Barta, Buechner et al. 2010

Aschwanden 2002

This fractal structure enable to connect micro and macro scale structures and dynamics

Fractal current sheet Lazarian and Vishniac 1998

Bhattacharjee＋2009, Loureiro＋2007, Ji and Daughton 2011

Multiple plasmoids are ubiquitousin the universe (Ji and Daughton 2011)

Lamda = L/rho_s (ion sound gyroradius)

Plasmoid speed, acceleration and reconnection rate

Shibata and Tanuma 2001Analytical model

Qiu, Chen+ 2004, Chen,Choe+ 2003Observations

Ohyama and Shibata 1997Observations Magara, Shibata + 1997

MHD simulation

Plasmoid Acceleration ~ Reconnection electric field

Electric field

Acceleration Electric fieldAcceleration

Remaining Questions

• What is 3D structure of plasmoid dominated fractal current sheet ?

• What is flare triggering mechanism ?

• How and where particle acceleration occurs ?

temperature

density

Emission measurefor X-ray images

Nishida, Nishizuka, Shibata, 2013 ApJL 775, 39

(400x400x400)

3D MHD simulations (Nishida+ 2013)

Fragmented Current sheetCurrent density

prominence

Current sheet

・Multiple plasmoids are formed in a current sheet.

・3D plasmoid with a finite length.

・Strong E-field■ is enhanced between plasmoids.

Nishida+ 2013

Fractal Reconnection & Particle Acceleration by plasmoids colliding with fast shocks [Nishizuka & Shibata 2013, Phys. Rev. Let. . 110, 051101]

cf) Fermi Acceleration at the fast shock: Somov & Kosugi (1997), Tsuneta & Naito (1998)

Shock at the loop-top

Plasmoid collide with

Fast shock (MA~1.5)

Shock at the bottom of a large plasmoid

Time slice image of small plasmoid ejections

1) Particles are trapped in a plasmoid.2) Multiple plasmoids collide with fast shock.3) Particles are reflected due to magnetic

mirror effect. 4) Reflection length becomes shorter and

shorter. 5) Particles are accelerated by Fermi process, until reflection length becomes comparable to ion Larmor radius.

Loop top structure: full of shocks

Density

MHD simulations by Takasao+ 2015, 2016 ApJ

Loop top structure: full of shocks

Density

Blue: Compressed regions (~ Shocks)

MHD simulations by Takasao+ 2015, Takasao-Shibata 2016 ApJ

Observations of multiple plasmoids in a flare current sheet (Takasao+ 2012)

Superflares on Solar Type Stars

Maehara et al. (2012) Nature, 483, 478

superflare

nanoflare

microflare

solar flare

statistics of occurrence frequency of solar flares, microflares, nanoflares

1000 in 1 year100 in 1 year10 in 1 year1 in 1 year1 in 10 year

C M X X10 X1000 X100000

Largest solar flare

superflare

nanoflare

microflare

solar flare

statistics of occurrence frequency of solar flares, microflares, nanoflares

1000 in 1 year100 in 1 year10 in 1 year1 in 1 year1 in 10 year1 in 100 year1 in 1000 year1 in 10000 year

C M X X10 X1000 X100000

？

Largest solar flare

superflares

Questions

• Previously, it has been believed that the Sun does not produce superflares (> 10^33 erg), because the Sun is old and is slowly rotating.

• However, Schaefer et al. (2000) discovered 9 superflares on ordinary solar type stars with slow rotation.

• Schaefer et al. argued that the Sun would never produce superflares, because they believed that hot Jupiter is a necessary condition to produce superflares.

• Are superflares really occurring on ordinary solar type stars ?

• Are hot Jupiters necessary condition for superflares ?

• Hence we searched for superflares on solar type stars using Kepler satellite data, which include data of 83000 solar type stars

• Since the data are so large, we asked 1st year undergraduate students to help analyzing these stars, because students have a lot of free time (2010 fall)

• Surprisingly, we (they) found 365 superflares on 148solar type stars (G-type main sequence stars)

Superflares on Solar Type Stars :Our study (Maehara et al. 2012)

Superflares on Solar type stars

H. Maehara, T. Shibayama, S. Notsu, Y. Notsu, T. Nagao, S.

Kusaba, S. Honda, D. Nogami, K. Shibata

Published in Nature (2012, May)

Undergraduate students

typical superflare observed by Kepler

Brightnessof a starand a flare

Time (day)

Total energy~ 10^35 erg

Maehara et al. (2012)

typical superflare observed by Kepler

Brightnessof a starand a flare

Time (day)

Total energy~ 10^36 erg

Maehara et al. (2012)

What is the cause of stellar brightness variation ?

It is likely due to rotation of a star with a big star spot

Flare energy vs rotational period

Stars with period longerthan 10 days

cf solar rot period ~ 25days

Maehara+(2012), Notsu+ (2013)

Fast rotation(young)

Slow rotation(old)

There is no hot Jupiter in these superflare stars against previous prediction (Schaefer+ 2000)

Are these indirect measurement of rotational period correct ? => Need spectroscopic obs

with Subaru (Notsu+2015)• We performed high-dispersion

spectroscopy of 50 superflare stars with Subaru telescope (34 are single stars)

• Photometric periods of each star are consistent with rotation velocities .

Notsu et al. 2015.

superflare

nanoflare

microflare

solar flare

Comparison of statistics between solar flares/microflares and superflares

？

Largest solar flare

superflare

nanoflare

microflare

solar flare

Comparison of statistics between solar flares/microflares and superflares

1000 in 1 year100 in 1 year10 in 1 year1 in 1 year1 in 10 year1 in 100 year1 in 1000 year1 in 10000 year

C M X X10 X1000 X100000

Largest solar flare

Superflares of 1000 times more Energetic than the largest solar flares occur once in 5000 years !

Stellar Flare duration vs. flare energy

• Observation: e-folding time of flare ∝ (flare energy)0.39

• Flare energy ∝Magnetic energy∝ volume × B2

• Timescale of impulsive phase of flare ∝ Alfvén time scale∝ (scale length)/(Alfvén velocity)

𝐸 ∝ 𝐿3𝐵2, 𝜏 ∝ 𝐿/𝑣𝐴 → 𝜏 ∝ 𝐸1/3

𝜏 ∝ 𝐸0.39±0.03

Maehara et al. (2015)

Indirect observational evidence of reconnection in stellar flares

Fundamental Question

• Why and how can superflares occuron Sun-like stars (i.e., present Sun) ?

• Superflares occur because of the presence of large spots.

=>

• Why and how can large spots be generated on Sun-like stars (i.e., present Sun) ?

Necessary time to generate magnetic flux producing superflares (Shibata et al. 2013)

yearsHzMxMx

t

rRBdt

d

pt

pppt

1

7

1

2224 106.5101040

222

only 8 years (< 11 years) to generate2x1023 Mx producing superflares of 1034 erg

The necessary time to generate magnetic flux of 1024 Mx that can produce superflares of 1035 ergare 40 years （<< 5000 years) (but > 11 years)

Is it possible to store such huge magnetic flux below the base of convection zone ?

=> big challenge to dynamo theorist !

=> easily occur !?

Why and how can large spots be generated on the present Sun ? (Shibata et al. 2013)

Okayama 3.8m New Technology Telescope of Kyoto Univ

(under construction)

courtesy of Prof. Nagata (Department of Astronomy , Kyoto University)

High speed photometricand spectroscopicobservation of Transient objects

Gamma ray burstsExoplanetsStellar flares

(superflares)Will be completed ~ 2017

Spectroscopic Observations of Solar type stars causing superflares will be extremely important

New Technology1. Making Mirrors with

Grinding 2. Segmented mirror3. Ultra Light mounting

Budget for operationIs still lacking.Please support us !

Summary

• Recent observations show unified view of solar flares, prominence eruption, coronal mass ejections, microflares, jets, and nanoflares (Shibata and Magara 2011).

• Plasmoid-induced-reconnection and fractal reconnection have been proposed (Shibata and Tanuma 2001), which explain coupling between micro and macro plasma dynamics and particle acceleration (Nishizuka and Shibata 2013).

• Kepler data revealed superflares of 10^34-10^35 erg occur on Sun-like stars with frequency of once in 800 - 5000 years (Maehara et al. 2012). Hence there is a possibility that superflares of 10^34 – 10^35 erg might occur on our present Sun with similar frequency (Shibata et al. 2013). => dangerous for our civilization and society

Thank you for your attention

Backup Slides

Stellar Flares

Observations of Stellar Flares

• In 1924, Hertzsprung first noticed a stellar flare in Carina

• After that, many flares have been observed on M-type red dwarfs (flare stars) using visible light photometric observations(e.g., Luyten (1949),Joy and Humason (1949),

see review by Gershberg(2005)).

• Similar to white light flareon the Sun

(Hawley and Petterson 1991)

10min

a flare of AD Leo

X-ray Observations of Stellar FlaresSolar Flare

X-rayIntensity(3-24keV)

time

10 hours

Stellar Flare of Prox Cen (Haisch et al. 1983)

Protostellar Flare of YLW15 (Monmerle,Tsuboi + 2000)

time

X-rayIntensity(~ 1 keV)

time

X-rayIntensity(2-10 keV)

Can stellar flares be explained by magnetic reconnection ?

• Yes !

• Indirect evidence has been found in empirical correlation between

Emission Measure ( )

and Temperature from soft X-ray obs

(Shibata and Yokoyama 1999, 2002)

32LnEM

Emission Measure （ＥＭ＝ｎ２Ｖ） of Solar and Stellar Flares increases with Temperature （Ｔ）

（n：electron density、Ｖ： volume）(Feldman et al. 1995)

soft X-ray observations

ＥＭ－Ｔ relation of Solar and Stellar Flares

Log-log plot

of Feldman

etal (1995)’s

figure

Shibata and Yokoyama, 1999, 2002

ＥＭ－Ｔ relation of Solar and Stellar Flares

microflare

(Shimizu 1995)

Shibata and Yokoyama, 1999, 2002

young-star and protostellar flares

Tsuboi (1998)Pallavicini(2001)

Koyama(1996)

Class I protostar

Shibata and Yokoyama (1999) ApJ 526, L49

2D MHD Simulation of Reconnection with Heat

Conduction and Chromospheric Evaporation

7/27/6 LBT

Yokoyama and Shibata (1998) ApJ 494, L113

------------------------------- (2001) ApJ 549, 1160

What determines Flare Temperature ?

• Reconnection heating＝conduction cooling（Yokoyama and Shibata 1998)

(radiative cooling time is much longer)

LTVB A 2/4/ 2/72

7/27/6 LBT

• Emission Measure

• Dynamical equilibrium (evaporated plasma must be confined in a loop)

• Using Flare Temperature scaling law, we have

Flare Emission Measure(Shibata and Yokoyama 1999)

32LnEM

2/175TBEM

8/2 2BnkT

EM-T correlation for solar/stellar flares

Shibata and Yokoyama (1999, 2002)

Magnetic field strength（Ｂ）＝constant

Magnetic field strengths of solar and stellar flaresare comparable ~ 50-100 G

2/175TBEM

Shibata and Yokoyama (1999, 2002)

Total energy of stellar flares

Superflares

Their energy= 10-10^6times thatofthe largestsolar flares

Solar flares

Solar microflares

Stellar flares

Their host starsare young starsand binary starswith fast rotation

Q: What determines flare total energy ? A: loop length (because magnetic field strength is

roughly constant)

The reason why stellar flares are hot => loop lengths of stellar flares are large

Shibata and Yokoyama (2002)

Cf Isobe et al. 2003, Aulanier et al. 2013

Why young stars produce superflares ?

• Answer：young star’s rotation is fast

（so dynamo is active and total magnetic flux is large =>

loop is large）

Young stars

Stellar X-rayLuminosity

Stellar rotational velocity

Young stars

Aged stars (Sun)）

Aged stars (Sun)

Relation between flare energy and spot size

10^35 erg X10000

su

10^34 erg X1000

10^33 erg X100

10^32 erg X10

10^31 erg X

10^30 erg M

10^29 erg C

0.0001 0.001

0.01

Flare energy vs sunspot area

Once in 1000 years

Once in 10 years

Once in 100years

Once in 1 year

10 in 1 year

100 in 1 year

1000 in 1 year

Sunspot area(in unit of solar surface area)

Solar flare

Superflares on solar type stars

Sammis et al. 2000

Flare Energy

10^35 erg X10000

su

10^34 erg X1000

10^33 erg X100

10^32 erg X10

10^31 erg X

10^30 erg M

10^29 erg C

Flare energy vs sunspot area

Once in 1000 years

Once in 10 years

Once in 100years

Once in 1 year

10 in 1 year

100 in 1 year

1000 in 1 year

Sunspot area(in unit of solarSurface area)

Superflares on solar type stars

Sammis et al. 2000

0.0001 0.001

Solar flare

0.01

Flare Energy

Solar flares

Flare energy vssunspot area

(magnetic flux)

2/3

219

2

3

32

2/3232

103101.0][107

88

cm

A

G

Bferg

AB

fLB

ffEE

spot

spotmagflare

Shibata et al. (2013)

?

Solar flares

Stellar flares

Indirect Measurement of Rotational Period and Spot Area

are True ?=> Spectroscopic Observations of

Superflare Stars

Notsu et al. (2015) PASJ

Projected rotation velocity (v sin i)

※Measurement methods

Takeda et al.(2008etc)

Line of sight

i

Rotation Axis

Fast rotators ⇒ wide line profile

Slow rotators ⇒ narrow line profile

We can estimate projected rotation velocity (v sin i) from

the Doppler broadening of absorption lines.

Rotation Period ⇔Brightness variation period ?

Most of the data points locate below the line of i=90°

⇒“Brightness variation≒Rotation” is OK!!

P

Rv star

lc

2

※Sun: Vrot～2 [km s-1]

Velocity estimated from brightness

variation period (Vlc[km s-1])

v sin i

[km s-1]

Pole-on view

pole-on view

Edge-on view(sin i =1)

Line of Sight

i

RotationAxis

Flare energy vs. area of starspots

low inclination angle

Notsu, Y. et al. (2015)

Spectroscopic rotational velocity (Subaru obs)

Photometric rotational velocity

Solar flares

Stellar flares

Strong magnetic field area around starspotsshow strong Ca II emission!!

We can indirectly investigate the existence of large

starspots by using the intensity of Ca II lines.

The Sun with visible light The Sun with Ca II K line(BigBear Solar Observatory data)

The core depth

becomes shallow.

Indirect estimation of starspot coverage with Ca II lines

Large

starspots

• As the magnetic activity enhanced, the core depth become shallow because

of the greater amount of the emission from the chromosphere.

• Chromospheric activity⇒These stars have large starspots !

18Sco

(Solar-twin)

Superflare

stars

Superflare

stars

Superflare

stars

Starspot coverage vs Ca II 8542 intensity

Brightness Variation Amplitude≒ starspot coverage

All the stars that are expected to have large starspots

(from large brightness variation amplitude)

show high (Ca II) magnetic activities.

↑ Sun

r0 (8542)

r0: Normalized intensity

of Ca II 8542

NotsuY+ (2015)

Hypothetical image In visible light(photosphere)

Hypothetical imageIn CaII line

(chromosphere)

Superflare stars have large spots

Using spectroscopic observations, the rotational period of two

superflare stars (Eflare = 10^34 erg) has been determined as

KIC 9766237 P_rot = 21.8 d KIC 9944137 P_rot = 25.3 d

Two Sun-like Superflare

Stars Rotating as Slow

as the Sun

(Nogami et al. 2014)

=> very similar to the Sun !

Can Superflares Occur on Our Sun ?

Shibata et al. (2013) PASJ, 65, 49

(theoretical paper)

Mechanism of superflare occurrence

Big starspot is necessary

32

3

32

2/3232

04.0101.0][10

88

R

L

G

Bferg

AB

fLB

ffEE

spot

spotmagflare

ergE

RLIf

flare

spot

3534 1010

,4.02.0

][1010 24232MxBLspot

Basic mechanism of superflare is the same as that of solar flares (i.e. reconnection) because MHD (magnetohydrodynamics) is scale free

How to make big star spot ?

pt BBrrotBVrot

t

B

)()(

)/( dzdz

][106.5 7 Hz

Rotation is fast near equator

Rotation is slow near poles

Necessary time to generatemagnetic flux producing superflares

yearsHzMxMx

t

rRBdt

d

pt

pppt

1

7

1

2224 106.5101040

222

only 8 years (< 11 years) to generate2x1023 Mx producing superflares of 1034 erg

The necessary time to generate magnetic flux of 1024 Mx that can produce superflares of 1035 ergare 40 years （<< 5000 years) (but > 11 years)

Is it possible to store such huge magnetic flux below the base of convection zone ?

=> big challenge to dynamo theorist !

=> easily occur !?

Evidence of superflares on the Sun

Evidence of a superflare ?

Corresponding to 10^34 erg superflareIf this is due to a solar flare

(Miyake et al. Nature , 2012, June, 486, 240)

Another evidence ?

Another event!

Miyake 2012

Miyake 2013

AD993

AD775

From Miyake et al. (2013)Nature Communications 2783

Short time cadense dataof superflares observed by Kepler

Maehara et al. (2015) Earth, Planets, and Space

Superflares (short cadence data)

Maehara et al., EPS 67, 59 (2015)

Superflares (short cadence data)

Maehara et al., EPS 67, 59 (2015)

Superflares on Sun-like stars (P>10d, Teff=5600-6300K)

Flare frequency vs. flare energy

Maehara et al. (2015)

~ 1 in 100 years

~ 1 in 800 years

~ 1 in 5000 years

Flare energy vs. area of starspots

• Flare energy is consistent with the magnetic energy stored near the starspots.

->Large starspots are necessary.

• Flares above the line may occur on the stars with low-inclination angle (or stars with polar spots?)

superflares

Solar flares

E∝Aspot3/2

f=0.1, B=3000Gf=0.1, B=1000G

Maehara et al. (2015)

Stellar Flare duration vs. flare energy

• Observation: e-folding time of flare ∝ (flare energy)0.39

• Flare energy ∝Magnetic energy∝ volume × B2

• Timescale of impulsive phase of flare ∝ Alfvén time scale∝ (scale length)/(Alfvén velocity)

𝐸 ∝ 𝐿3𝐵2, 𝜏 ∝ 𝐿/𝑣𝐴 → 𝜏 ∝ 𝐸1/3

𝜏 ∝ 𝐸0.39±0.03

Maehara et al. (2015)

Indirect observational evidence of reconnection in stellar flares

Flare Triggering Mechanism

Flare Triggering Mechanism

• Break Out Model (Antiochos)

• Tether-Cutting Model (Moore)

• Catastrophe Model (Forbes, Lin)

Two-step Reconnection Model

(Wang-Shi, Chen-Shibata, Kusano)

Moore and Roumeliotis 1992

Tether-cutting

Antiochos et al. 1999

breakout

Two step reconnection model(Wang-Shi 1993, Chen-Shibata 2000,

Kusano et al. 2012)

Emerging flux

reconnection (cancellation) associated with emerging flux

sudden decrease in magnetic tension

expansion of flux rope more energetic reconnection

X

emerging flux triggering model

• Feynmann and Martin (1995) --Obs

• Chen-Shibata (2000) --- 2D

• Lin+ (2001) -- analytic• Toroek and Schmieder

(2008) –3D • Nagashima et al.

(2007) -- Obs• Kusano+ (2012)—3D

Multi-step reconnection as Triggering mechanism of flares

• Janvier, Kishimoto, Li (2011) PRL

– Structure Driven Nonlinear Instability in Resistive Double Tearing Mode

– Extension of Ishii et al. (2002)

Other slides

Lamda = L/rho_s (ion sound gyroradius)

Plasmoid-dominated reconnection becomes fast (rec rate ~ 0.01) for S > 10^4

Loureiro et al. (2012) Phys Plasma 19, 042303

Bhattacharjee et al. 2009

abstract