SH31C-08: The Photospheric Poynting Flux and Coronal Heating Some models of coronal heating suppose that convective motions at the photosphere shuffle the footpoints of coronal magnetic fields and thereby inject sufficient magnetic energy upward to account for observed coronal and chromospheric energy losses in active regions. Using high-resolution observations of plage magnetic fields made with the Solar Optical Telescope aboard the Hinode satellite, we investigate this idea by estimating the upward transport of magnetic energy --- the vertical Poynting flux, S z --- across the photosphere in a plage region. To do so, we combine: (i) estimates of photospheric horizontal velocities, v h, determined by local correlation tracking applied to a sequence of line-of-sight magnetic field maps from the Narrowband Filter Imager, with (ii) a vector magnetic field measurement from the SpectroPolarimeter. Plage fields are ideal observational targets for estimating energy injection by convection, because they are: (i) strong enough to be measured with relatively small uncertainties; (ii) not so strong that convection is heavily suppressed (as within umbrae); and (iii) unipolar, so S z in plage is not influenced by mixed-polarity processes (e.g., flux emergence) unrelated to heating in stable, active-region fields. In this plage region, we found that the average S z varied in space, but was positive (upward) and sufficient to explain coronal heating, with values near (5 +/- 1)?10 7 erg /cm 2 /s. We find the energy input per unit magnetic flux to be on the order of 10 5 erg /s /Mx. This is consistent, within order of magnitude, with luminosities per unit magnetic flux observed in soft X-ray emission. We also found upward fluxes to predominate in most other plage regions, indicating that upward energy flux is a generic property of plage fields, and suggesting this is a manifestation of the energy required for coronal heating. Brian T. Welsch Space Sciences Laboratory, University of California, Berkeley

If I’ve seemed a little fuzzy minded for the past few days, there’s a reason... I apologize for not functioning at full capacity! Owen, age 4.5 months

What heats the chromosphere & corona to 10 4 & 10 6 K? Dissipation of magnetic energy is powers heating. This energy probably enters the corona from the interior as waves or via convectively driven footpoint shuffling: Parker 1983Marsh et al wave heating (“AC”?) “DC” heating

The Poynting flux of magnetic energy across the photosphere into the corona is given by: dU/dt = ∫ dA (cE ph x B ph ) z /4 π B ph is the photospheric magnetic field, and E ph is the photospheric electric field. Parker (and others) convincingly argued that E ph is ideal, i.e., E ph = -(v ph x B ph )/c Q: If magnetic energy powers the heating, can we see any flux of magnetic energy across the photosphere?

dU/dt = ∫ dA S z =∫ dA (B ph x [v ph x B ph ]) z /4 π =∫ dA (v z B h 2 – [v h ⋅ B h ]B z )/4 π In fact, both terms involve the transport of magnetized plasma into the corona – so emergence of fields! – But they do differ: “emergence” increases total unsigned flux. “emergence”“shearing” v Assuming an ideal Ohm’s law, cE ph = -(v ph x B ph ), the Poynting flux can be written in terms of photospheric velocities, v ph :

Plage magnetic fields are mostly-vertical fields in active regions, where “shearing” term should dominate. Emergence of new flux is not observed in plage. So S z plage ≈ - f [v h ⋅ B h ]B z /4 π In this box, inclinations were ~20 o from vertical. Estimating S z plage requires\ estimating v h & B h 0.32’’ pix, so ~100 Mm must include fill fraction!

7 We used Fourier local correlation tracking (FLCT) to get v h ( x, y) by correlating LOS magnetograms’ subregions. * = = = B LOS cadence = 2 min. ;  t = 8 min.; window parameter σ = 4 pix.

Vector B is measured by relatively slow rastering – 45 minutes to scan across the entire active region! So we co-registered the (tracked) B LOS with B from the vector magnetogram in our plage region. Aligned B los & B z Correlation ≈ 0.8

Flows & fields are combined to make Poynting flux maps. Withbroe & Noyes (1977) estimated coronal & chromospheric energy demands to be 1 x 10 7 erg cm -2 s -1 and 2 x 10 7 erg cm -2 s -1, resp. There are regions of positive & negative Poynting flux, but mean is positive, about (5 ± 1) x 10 7 erg cm -2 s -1 – enough power to heat both!

Flows & fields

Poynting flux map

We checked our flow estimates with another LCT code: Velocities agreed in many regions, disagreed in others. Correlation coefficients were ≈ 0.7 The mean is again upward, but ~10% larger, at 5.5 x 10 7 erg cm -2 s -1 – so uncertainties on the order of ~10% (or more) from tracking.

Poynting flux is upward in the one region we study in detail. Is the Poynting flux also upward elsewhere? We defined all pixels with filling-factor-weighted 100 Mx cm −2 <|B z |< 1500 Mx cm −2 and inclination < 30 o from vertical as “plage-like.”

To construct a flow map simultaneous with the rastered B( x, y) map, we sampled near-simultaneous columns in velocity maps, v h ( x, y, t). Again, both upward and downward Poynting fluxes, but mostly up! Blue is histogram of upward Poynting fluxes. Red is histogram of downward Poynting fluxes. Poynting flux is upward in the one region we study in detail. Is the Poynting flux also upward elsewhere? (cont’d)

Physically, magnetic energy travels both up & down -- BUT the corona “extracts” a small but significant “heating tax!” LMSAL/TRACE Does the energy propagate along B? Or is it (mostly) reflected – up & back down? Would this lead to waves, -- and non-thermal broadening in IRIS lines? Coronal dissipation & heating should drive intensity variations on moss above footpoints – correlated with Poynting flux?

Is this is a “DC” Poynting flux? Autocorrelation of v x & v y in this plage region ==> lifetime ~500 sec. Alfvén transit times for coronal portion of loops are ~100 sec. Photosphere-to-corona transit times are ~ sec. each way (van Ballegooijen et al. 2011) ==> Footpoint motions evolve on loops’ approximate global relaxation timescale – coronal B never relaxes!

The energy flux we find can be expressed as a luminosity per unit magnetic flux, L Poynt ≈10 5 erg/s/Mx. Pevtsov et al. (2003) “Pevtsov’s law:” magnetic fields like to radiate in soft X-rays In soft X-rays, luminosities per unit flux are L x ≈10 3 erg/s/Mx; matches rule of thumb that L x ≈ 0.01 L heat, the total input from heating.

What type of flows produce this upward energy flux? No clear twisting & braiding; correlation of Poynting flux with flow vorticity was weak. Mismatch between structure in v h & B h produces bipolar Poynting flux

Main Idea: studies of the Poynting flux can help understand energy input for coronal heating. We see enough energy to heat both the corona & chromosphere -- - about 50% more than Withbroe & Noyes (1977) said is needed. There must be some scales below which the flux decreases (so no ultraviolet catastrophe) – higher-res observations are needed. Additional studies with Hinode/SOT can address these questions. – Comparisons with IRIS and AIA observations are planned. Poynting flux studies are a “Critical Science” item for DKIST!