Superdiffusion of magnetic elements
in the quiet Sun
Dr. Fabio Giannattasio
INAF - Osservatorio Astronomico di Roma
email: [email protected]
2nd Solarnet Meeting
Palermo, February 2-5, 2015
Motivations
Why are we interested in small-scale magnetic fields (magnetic elements, MEs)?
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Ubiquitous on the solar surface (Trujillo Bueno et al. 2004)
●
Host magnetohydrodynamics waves → Talk of Stangalini
●
Dynamic properties of MEs → Evolution and scales of organization (De Rosa & Toomre 2004;
Del Moro et al. 2007; Martìnez Gonzàlez & Bellot Rubio 2009; Ishikawa & Tsuneta 2009; Manso
Sainz et al. 2011; Abramenko et al. 2011; Giannattasio 2013, 2014a)
●
Recover the rate of interaction → Magnetic reconnection → Talk of Del Moro
●
Motion of MEs → Dynamics of the underlying flow (Lepreti et al. 2012, Giannattasio 2014b)
Motivations
Why are we interested in small-scale magnetic fields (magnetic elements, MEs)?
●
Ubiquitous on the solar surface (Trujillo Bueno et al. 2004)
●
Host magnetohydrodynamics waves → Talk of Stangalini
●
Dynamic properties of MEs → Evolution and scales of organization (De Rosa & Toomre 2004;
Del Moro et al. 2007; Martìnez Gonzàlez & Bellot Rubio 2009; Ishikawa & Tsuneta 2009; Manso
Sainz et al. 2011; Abramenko et al. 2011; Giannattasio 2013, 2014a)
●
Recover the rate of interaction → Magnetic reconnection → Talk of Del Moro
●
Motion of MEs → Dynamics of the underlying flow (Lepreti et al. 2012, Giannattasio 2014b)
Dynamics of magnetic elements
Passive transport
B
FB
Fd >> FB
Fd : drag force
FB: magnetic force
Fd
●
Tracking MEs = tracking photospheric plasma motions
●
Motion of MEs may be described in terms of a diffusion process.
Dynamics of magnetic elements
Random Walk
Dynamics of magnetic elements
displacement
spectrum
γ: efficiency of diffusion
γ=1
random walk (normal diffusion)
γ≠1
anomalous diffusion
γ>1
superdiffusion
γ<1
subdiffusion
K = K (s , τ) = d (< Δs2 >) / dτ
Example of superdiffusion
Dynamics of magnetic elements
Displacement spectrum ← Tracking MEs
G-band images
Magnetograms
-
Berger et al. (1998)
-
Hagenaar et al. (1999)
-
Cadavid et al. (1998, 1999)
-
Manso Sainz et al. (2011)
-
Lawrence et al. (2001)
-
Sanchez Almeida et al. (2010)
-
Abramenko et al. (2011)
Dynamics of magnetic elements
Previous studies in literature
●
Superdiffusive regime γ ≥ 1 changing with the scales (e.g., Manso Sainz et al. 2011, Abramenko
et al. 2011)
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Very different values of diffusivity
Observational limitations
●
Relatively small range of scales investigated
●
Low number of tracked MEs
Dynamics of magnetic elements
The data set
●
Hinode quiet Sun magnetograms
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FoV 51 x 53 Mm2
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Spatial resolution 0”.3
●
25-hr without interruption
●
90-s cadence
-
seeing-free
“direct” magnetic field detection
-
wide range of spatial scales
high statistics
-
wide range of temporal scales
Dynamics of magnetic elements
The data set
●
Hinode quiet Sun magnetograms
●
FoV 51 x 53 Mm2
●
Spatial resolution 0”.3
●
25-hr without interruption
●
90-s cadence
-
seeing-free
“direct” magnetic field detection
-
wide range of spatial scales
high statistics
-
wide range of temporal scales
Dynamics of magnetic elements
The data set
●
Hinode quiet Sun magnetograms
●
FoV 51 x 53 Mm2
●
Spatial resolution 0”.3
●
25-hr without interruption
●
90-s cadence
-
seeing-free
“direct” magnetic field detection
-
wide range of spatial scales
high statistics
-
wide range of temporal scales
Dynamics of magnetic elements
Tracking MEs (Del Moro 2004)
20145 MEs tracked
Dynamics of magnetic elements
Displacement spectrum in all the FoV
< Δr2 > ∝ τγ
●
●
Giannattasio et al. 2013, ApJ 770 L36
superdiffusive regime
-
2 slopes, changepoint at
~2000 s
-
augmented magnetic inertia at
longer time-scales
-
velocity field renewal
increasing diffusivity
-
cooperation of small-scale
fields allows field aggregation
Dynamics of magnetic elements
Internetwork VS Network
NW
IN
Dynamics of magnetic elements
Displacement spectrum: Internetwork (IN) VS Network (NW)
●
IN spectrum → single slope
●
NW spectrum → 2 slopes,
changepoint at ~600 s
Comparison with all FoV → at small
(large) scales IN (NW) MEs
dominate the field dynamics
●
IN → increasing diffusivity
(aggregation at small scales)
●
NW → lower and lower diffusivity
Giannattasio et al. 2014, ApJ 788 137
Dynamics of magnetic elements
Main conclusions
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Displacement spectrum in all FoV → superdiffusion with 2 slopes → a changing regime
-
augmented inertia
renewal of the underlying velocity field
●
IN → MEs transported efficiently at all scales
●
NW → -
●
Weak-field regime in IN and strong-field regime (reduced convection) in NW (Cattaneo et al.
2003)
stronger flux lowers the diffusivity at smaller scales
MEs in velocity sinks → after the decorrelation time MEs move according the
underlying velocity pattern along more random paths
Thank you
References
Abramenko et al. 2011, ApJ, 743, 133
Manso Sainz et al. 2011, A&A, 531, L9
Berger et al. 1998, ApJ, 506, 439
Martìnez Gonzàlez & Bellot Rubio 2009, ApJ, 700, 1391
Cadavid et al. 1998, ApJ, 509, 918
Sanchez Almeida et al. 2010, ApJL, 715, L26
Cadavid et al. 1999, ApJ, 521, 844
Trujillo Bueno et al. 2004, Nature, 430, 326
Cattaneo et al. 2003, ApJ, 588, 1183
Del Moro 2004, A&A, 428, 1007
Del Moro et al. 2007, A&A, 472, 599
De Rosa & Toomre 2004, ApJ, 616, 1242
Giannattasio et al. 2013, ApJL, 770, L36
Giannattasio et al. 2014a, ApJ, 788, 137
Giannattasio et al. 2014b, A&A, 569, A121
Hagenaar et al. 1999, ApJ, 511, 932
Ishikawa & Tsuneta 2009, A&A, 495, 607
Lawrence et al. 2001, PRL, 86, 5894
Lepreti et al. 2012, ApJ, 759, L17