D. Fujimura and S. Tsuneta- Properties of Magneto- Hydrodynamic Waves in the Solar Photosphere with...

8/3/2019 D. Fujimura and S. Tsuneta- Properties of Magneto- Hydrodynamic Waves in the Solar Photosphere with Hinode

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Properties of Magneto-Hydrodynamic Waves in the Solar

Photosphere with Hinode

D. Fujimura (NAOJ, Tokyo University)

S. Tsuneta (NAOJ)

Hinode Team

2009/10/06 US - Japan reconnection workshop


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Unresolved issues in solar physics

-Solar wind acceleration-Coronal heatingThe energy source of these twophenomena has not been identified yet.


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Alfvn waves as candidate of the energy source(Suzuki and Inutsuka, 2005)

-Solar wind is accelerated to 800 km/s and the corona isheated to 106 K caused by the footpoint fluctuation ofmagnetic field at the photosphere.

- The outgoing Alfvn waves may generate slow shock and

dissipate, but no observational evidence has been reported.


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Transverse waves detected with Hinode

Transverse oscillations are detected in prominences(Okamoto et al., 2007) and in spicules (De Pontieu et al.,2007) but these studies could not rule out the possibility

that the observed fluctuations are standing waves.

Ca II movie, Okamoto et al. (2007)

108

217


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10854

Fine magnetic structures observed withSolar Optical Telescope aboard Hinode

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(2) Inter-Granular

Magnetic Structure (IMS)

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(1) Pores around sunspot


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Detection of MHD waves in the photosphere

- High spatial resolution of SOT/SP (~0.32) allows usto detect the fluctuations in small-scale flux tubessuch as pores and inter-granular magnetic structures.

- Stable observations from space allow us to detect clearfluctuations in the intensity , as well as in themagnetic field and in the velocity.

We obtained the phase relations between thefluctuations in the magnetic field, in the velocity, andin the intensity, and determined the mode of the MHDwaves in the flux tubes.


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Detection of transverse MHD

waves at the limb Rough estimation (substituting the observed values)B0=2 KG, VA=20 km/s, v=0.1 km/sB=10 G

Detection limit of Hinode/SOTLine-of-sight (LOS) :1-5 GPerpendicular to LOS:30 - 50 G

We intentionally choose target

region far away from disk center,to detect transverse fluctuations inthe LOS magnetic field, in the LOSvelocity, and in the intensity.


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Stokes Profiles and Dataset

Our target: (1) pore(2) Inter-granular Magnetic Structure (IMS)

Region:25 - 49 west away from disk center Time resolution: 67 s

we can detect waves with period of 134 s (Nyquist criticia)

Duration: 1 hour or 3 hours


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Time profiles


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Power spectrum

-We detect 20 clear strong peaks in the magnetic flux, inthe velocity, and in the intensity with common periods.

-There are 8 cases for pores and 12 cases for IMSs. Wefound common strong peaks in 14 flux tubes out of 29(48%).


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Phase relation and period


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mode of MHD waves and intensity fluctuation

kink modeis dominant

sausage modeis dominant


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Phase relation of propagating

kink waves-Phase difference between thefluctuations in the magnetic

field and the velocity -vshould have been 0 or 180,

depending on the direction ofwave propagation.

-The propagating kink wavescould not explain the observedphase difference B v ~ -90.


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Phase relation of standing kink wave

-When ascending anddescending kink wave reflectedat a boundary coexist in theline formation layer, Thesuperposed wave has aproperty of a standing wave.

-phase difference B v is90

or -90

, which is consistentwith our observation.


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Standing kink wave

Phase difference between the fluctuations in the magneticfield and the velocity B v is 90 (a,c) or -90 (b,d).


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Residual upward Poyning flux of kink wave - We can estimate the residual (upward downward) Poyningflux with observables. The residual Poynting flux is

proportional to cos(B v),

- In one case with low intensity fluctuation (dI/I=0.3%), wesubstitute the observables (f=0.73, B0=1.7x10

3 (G), Bs,rms21(G), vs,rms=0.059(km/s), Bv=96) into the equation,and obtain F=2.7x106 (erg/s/cm2) for the residual upward

Poynting Flux.

- The coronal energy losses required in the active region is about106-107 erg cm-2 s-1 (Withbroe and Noyes, 1977)


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Phase relation for the sausage modePhase difference between the magnetic field anddensity (in-phase with intensity) is 0 for fast sausagemode and 180 for slow sausage mode, which isconsistent with our observation IB~180.

Phase difference B v:180 (left), 0(right)

Phase difference B v:90 or 90


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Slow sausage standing wave

Phase difference between the fluctuations in the magneticfield and the velocity B v is 90 (a,c) or -90 (b,d),

which is consistent with our observation.


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Phase relation and type of MHD wavesB v

Observation -90 propagating kink wave 0 or 180 Not consistent

standing kink wave 90 or -90 Consistentpropagating slow sausage wave 0 or 180 Not consistentstanding slow sausage wave 90 or -90 Consistent

Although the two types of waves may coexist in a fluxtube, we separate these two for the following discussion.


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Seismology of photospheric flux tubesObservables- magnetic field amplitude (B)- velocity amplitude (v)- vertical magnetic field (Bi)- fluctuation period (P)

Calculated physical parameters- mass density inside (i) and

outside (e) a flux tube- plasma beta ()- Alfvn velocity (VA)- wavelength (L)- distance between a boundaryand a line formation height (d)

Phase difference B v:90 (a) 90 (b)


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Plasma density of flux tubes withkink waves

The dispersion relation for kink mode is

(e.g. Edwin & Roberts, 1983)

Giving transverse component for the magnetic field and assuming

Be=0, we obtain the relation between the amplitude in themagnetic field and the velocity.

Since flux tubes with kink waves are in pressure equilibrium, wehave

Thus we can estimate internal and external plasma densities (iand e) substituting the observables (B, v, Bi).


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We consider only the components longitudinal to the magneticfield. The equation of energy conservation is,

Taking the derivative of the equation, we obtain the relationbetween the amplitude between the magnetic field and thevelocity.

The phase speed for the sausage mode is (e.g. Edwin & Roberts,1983)

We can estimate the mass density inside the flux tube (i)substituting the observables (B, v, Bi)

Plasma density of flux tubes with slowsausage waves


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Other physical parametersThe plasma beta and the Alfvn velocity are derived

substituting i,

Substituting the Alfvn velocity, we can estimate thephase speed for both the kink wave and the sausagewave,

We can also obtain the wavelength (L) and the distance

between the boundary and the line formation layer (d).


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Result of the photospheric seismology

i 6.3x10-8 g cm-3e 2.4x10-7 g cm-3 0.22vA 21 km s-1d 4.9x103 km

-The detection of clear strongfluctuations allows us to estimatethe physical parameters

(especially i, , VA) from theobservables (v, B, B0).-Magnetic field can be measuredby inversion of the Stokesprofiles, but the plasma densityhas not been measured yet.-This estimation can be the gateto photospheric seismology.


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Conclusion (1)- Performing spectro-polarimetric observation of the flux

tubes in the photosphere, we detect clear strongfluctuations in the magnetic flux, in the velocity, and inthe intensity with common periods in both pores and

the IMSs.

Peaks Pore8(all flux tubes) IMS12 (1/3 of flux tubes)Amplitude 4-17 G (0.3-1.2%) 0.03-0.12 km/s

Fluctuation Period Pore36 min IMS49 minPhase difference -90 (Bv) -90 (v- I)

180 (I - B) 10 (I(core) -I(cont))Intensity Fluctuation 0.11.0%


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Conclusion (2)

- The residual upward Poyning flux is estimated to be2.7x106 (erg/s/cm2) for a case of kink mode, enough toheat the corona and accelerate the solar wind.

- Seismology of the magnetic flux tubes in the photosphereis possible to obtain various physical parameters fromthe amplitudes in the magnetic field and the velocity, andthe vertical magnetic field strength, and so on.

B vObservation -90

propagating kink wave 0 or 180 Not consistentstanding kink wave 90 or -90 Consistent

propagating slow sausage wave 0 or 180 Not consistentstanding slow sausage wave 90 or -90 Consistent


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Thank you!


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Backup slides


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Opacity effect- Opacity effect is caused by the opacity

fluctuation due to the temperatureand/or density perturbation.

- Magnetic field fluctuation withoutMHD waves take place because of themagnetic field gradient.

- The phase difference between themagnetic field and the intensitywould not be consistent with thatfrom our observation (IB~180),if we assume

(1)dB/dz is negative towards theobserver.

(2)The magnetic field is fixed. (i.e. itdoes not move upward nor downward)

dB/dz


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Location of SP field-of-view


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Method to select region for analysis


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d- Diagram

We found a solution with d=4.9x103 km, which is consistentwith the separation between the chromospheric/coronal

boundary and the line formation layer.

D. Fujimura and S. Tsuneta- Properties of Magneto- Hydrodynamic Waves in the Solar Photosphere with...

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