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Understanding Links Between the Solar Interior and Atmosphere. Brian Welsch, George Fisher*, and Bill Abbett Space Sciences Laboratory, UC Berkeley. *NB : much material presented here was borrowed from George!. Links between the interior and atmosphere?!.
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Brian Welsch, George Fisher*, and Bill Abbett
Space Sciences Laboratory, UC Berkeley
*NB: much material presented here was borrowed from George!
Are you kidding?? There are too many!
And CMEs! And flares!
Well, not driving them.
Waves, current sheets, however --- it’s
all from the convection!
But at least their ultimate source.
And maybe a trigger.
Oh, yeah, and solar wind
Links, links, everywhere…
an interior conspiracy!
And streamer structure,
What about the grassy knoll?!
Call in Glenn Beck!
From T.G. Forbes, “A Review on the Genesis of Coronal Mass Ejections”, JGR (2000)
dU/dt = ∫ dASz= c ∫dA (E x B)z /4π= ∫dA (B x[vx B])z /4π
Q: What would happen if all photosphericflows ceased?
(For this exercise, ignore the fact that the Sun needs these flows to expel the heat it produces!)
Partial answers, I believe:
tB = x (xtBz) +xtJztBz= h2(tB)
h·(tBh) = h2(z(tB))
B = x ( xB z) +xJz
Bz = -h2B,
Left: the full vector field B in AR 8210. Right: the part of Bh due only to Jz.
tBh also depends upon vertical derivativesin Eh, which single-heightmagnetograms do not fully constrain.
But most importantly:
Faraday’s law only relates tB to the curl of E, not E itself; a “gauge electric field” ψis unconstrained by tB.
==> Even multiple-height magnetograms won’t fix this!
Ohm’s law is one additional constraint. What about others?
Important magnetodynamics is not always apparent in ΔBz/Δt -- e.g., flux emergence!
Schematic illustration of flux emergence in a bipolar magnetic region, viewed in cross-section normal to the polarity inversion line (PIL).
But Doppler measurements can detect vertical flows along PILs!
Note the strong signature of the field change at the edges of the region, while the field change at the PIL is zero.
Generally, Doppler shifts cannot distinguish flows parallel to B (red), perpendicularto B(green), or in an intermediate direction (blue).
With v estimated another way & projected onto the LOS, the Doppler shift determines v|| (Georgoulis & LaBonte2006).
Doppler shifts are only unambiguous along polarity inversion lines (PILs), where Bn changes sign (Chaeet al. 2004, Lites 2005).
The total electric field is given by
where we used the iterative scheme of Fisher et al. (2010) to determine the scalar potential ψ,
so that E⋅B=0, as implied by the ideal Ohm’s law,
E = -(v x B)/c.
Validation is essential before use with real data! Use MHD simulation with known magnetic field evolution, electric fields, and velocity fields:
Our test case is an ANMHD simulation of a bipolar magnetic region rising through a convecting medium.
The simulation was performed by Bill Abbett.
Welsch et al. (ApJ 2007) used this same simulation for a detailed evaluation and comparison of velocity/electric-field inversion techniques.
Top row: The three components of the electric field E and the vertical Poyntingflux Sz from the MHD reference simulation of emerging magnetic flux in a turbulent convection zone.
2nd row: The inductive components of E and Szdetermined using the PTD method.
3rd row: E and Szderived by incorporating Doppler flows around PILs into the PTD solutions. Note the dramatic improvement in the estimate of Sz.
See Fisher et al., Sol. Phys, in press, and
Left: A comparison of the vertical component of the Poynting flux derived from the PTD method alone with the actual Poynting flux of the MHD reference simulation.
Right: A comparison between the simulated results and the improved technique that incorporates information about the vertical flow field around PILs into the PTD solutions.
Poyntingflux units are in
[105 G2 km s−1]
See Fisher et al., Sol. Phys, in press, and
Hudson (2000): coronal fields should “implode” in flares and CMEs.
Wang & Liu (2010) report that photospheric fields often become “more horizontal” during flares.
A sudden field change can produce a Lorentz “jerk” on the interior:
See Fisher et al., Sol. Phys., in revision, http://arxiv.org/abs/1006.5247
At the surface, strong downflows in strong-field concentrations (turbulent pumping!) imply a downward Poynting flux.
Abbett & Fisher “find a… positive… Poynting flux… along the edges of overturning granules above the surface where the field is being compressed.”
The surface is a special place: flows do work on the magnetic field!
Steiner et al. (2008) refer to the visible surface as “a separatrix for the vertically-directed Poynting Flux”
See Abbett & Fisher, Sol. Phys., in press, http://arxiv.org/abs/1102.1035
Long-term: What process removes all the flux from active regions over a solar cycle?
Every solar cycle, ~3000 ARs emerge, each with ~1022Mx of unsigned flux.
And every cycle it must be removed from the photosphere ---somehow!
Which model more accurately describes the Sun?
Several models of cancellation have been proposed, including emergence of U-loops, and submergence of Ω loops.
Because rising plasma is (1) brighter (it’s hotter), and (2) occupies more area, there’s an intensity-blueshift correlation (talk to P. Scherrer!)
S. Couvidat: line center for HMI is derived from the median of Doppler velocities in the central 90% of the solar disk --- hence, this bias is present!
Punchline: HMI Doppler shifts are not absolutely calibrated!
(Helioseismology uses time evolution of Doppler shifts, doesn’t need calibration.)
From Dravins et al. (1981)
Here, an automated method (Welsch & Li 2008) identified PILs in a subregion of AR 11117, color-coded by Doppler shift.
Ideally, the change in LOS flux ΔΦLOS/Δt should equal twice the flux change ΔΦPIL/Δtfromvertical flows transporting Bhacross the PIL (black dashed line).
Abias velocity v0 implies
:= “magnetic length” of PIL
NB: v0 should be the SAME for ALLPILs==> solve statistically!
Error bars on v0 were computed assuming uncertainties of ±20 G on BLOS, ±70G on Btrs, and ±20 m/s on vDopp.
- The two main paramsare PIL “dilation” d and threshold |BLOS|.
The radial component of SDO’s orbital velocity (dashed line) varies on a similar time scale.
Asplund & Collet (2003) used radiative MHD simulations to investigate bisectors in Fe I lines similar to HMI’s 6173 Å line, and found convective blueshifts of a few hundred m/s.
From Gray (2009): Solar lines formed deeper in the atmosphere, where convective upflows are present, are blue-shifted.
Dots indicate the lowest point on the bisectors.
Snodgrass (1984), Hathaway (1992, 2002), and Schuck (2010) fitted center-to-limb Doppler velocities.
But such fits only yield the difference in Doppler shift between the center and the limb; they don’t fit any “DC” bias!