Obtaining solar flare footpoint densities from Hinode/EIS Oxygen V diagnostics

David Graham, Lyndsay Fletcher, Nicolas Labrosse

SUPA School of Physics and Astronomy University of Glasgow

Motivation

HXR emission

Energy transport

Released magnetic energy is observed as non-thermal hard X-Ray emission in the lower atmosphere. Accelerated electrons heat local plasma through collisions heating > ionisation > dynamics

Motivation Energy transport

Released magnetic energy is observed as non-thermal hard X-Ray emission in the lower atmosphere. Accelerated electrons heat local plasma through collisions heating > ionisation > dynamics Problem - how is the energy transported? - where is the energy deposited?

HXR emission

Motivation Footpoint heating depth

HXR emission

Strongly stratifed atmosphere Density diagnostics specify both temperature and density Compare to a model atmosphere to estimate the depth of emitting plasma Essential to making constraints on flare energy transport mechanisms

Background Observations of high densities during the flare impulsive phase

Skylab slit spectrograph (Feldman et. al. 1977) O IV (1401 Å) and O V (1218 Å) lines

ne = 1012 cm-3

Skylab spectroheliograph (Widing 1982) 192.904Å / 220.350Å ratio

ne = 3 x 1012 cm-3

Hinode EUV Imaging Spectrometer (Del Zanna et. al 2010, Watanabe et. al. 2010, Graham et. al. 2011)

Fe XII, Fe XIII, Fe XIV ratios ne > 1011 cm-3

Skylab S082a - December 22nd 1973

EIS Diagnostics Determining the density at transition region temperatures

Diagnostic ratio of Oxygen V 192.904 Å to 248.460 Å

Sensitive up to 1012 cm-3 Formation temperature – 2.5 x 105 K

Flare Footpoints Impulsive Phase Observations – 14 December 2007

A medium sized flare – impulsive phase lasts around 4 minutes Good EIS spectral coverage (X-Band EIS era) Identify the footpoints from RHESSI HXR imaging and spectroscopy (Milligan & Dennis 2009) CAM_ARTB_RHESSI_b_2 study 2” slit - 10s exposure time

Spectra and Fitting

5x O V lines - estimated from CHIANTI ne = 1011 cm-3 Fe XI 192.813 - 20% of Fe XI 188.213 Fe XI 192.627 – fitted Ca XVII 192.0285 – fitted

O V 192.904 Å * O V 248.460 Å

Ar XIII - fitted Al VIII – 10% of O V 248

* ne sensitive transition

Footpoint Densities Obtained from 192.904 Å / 248.460 Å ratio

Densities from ±1 pixel averaged spectra (black cross) Footpoint (1) I192/I248 = 2.94 ± 0.25 log ne > 12.71 cm-3

Footpoint (2) I192/I248 = 1.24 ± 0.03 log ne = 10.80 ± 0.08 cm-3

Densities from 3x6 pixel average (white box) Footpoint (1) I192/I248 = 2.83 ± 0.06 log ne > 13.63 cm-3

Footpoint (2) I192/I248 = 1.47 ± 0.03 log ne = 11.06 ± 0.07 cm-3

1 2

1 2

Footpoint Densities Diagnostic Limits

Rmax = 2.8

Densities from ±1 pixel averaged spectra (black cross) Footpoint (1) I192/I248 = 2.94 ± 0.25 log ne > 12.71 cm-3

Footpoint (2) I192/I248 = 1.24 ± 0.03 log ne = 10.80 ± 0.08 cm-3

Densities from 3x6 pixel average (white box) Footpoint (1) I192/I248 = 2.83 ± 0.06 log ne > 13.63 cm-3

Footpoint (2) I192/I248 = 1.47 ± 0.03 log ne = 11.06 ± 0.07 cm-3

Assumptions

Is the footpoint plasma out of ionisation equilibrium? τcollision < τionisation (in optically thin conditions)

i.e - if the plasma is heated rapidly the Ionisation state can lag behind the plasma temperature Can recalculate diagnostic curves for higher plasma temperatures

Ionisation Equilibrium

Assumptions

For a ratio of I192/I248 = 2.9

Density must be at least log ne = 12.4 cm-3

Ionisation Equilibrium log ne minimum = 12.4

Note that at densities ne > 1012

cm-3 the plasma should remain in equilibrium (Bradshaw 2009)

Assumptions Optical Depth

(Mihalas 1978, Kulinova 2010)

Calculated optical depth at line centre for Machado F1 model atmosphere τ < 1 for both lines –very little attenuation, or no change to the observed ratio However, cases exist where lines can be enhanced by optical depth effects (see Kerr 2004, Keenan et al 2014 )

Interpretation Preflare and Flare Atmospheres

Where is the O V emission coming from? O V formation temperature – 2.5 x 105 K

Measured density ne = 1012.5 cm-3

Places the emission at a height of 200-300 km

How do you heat dense plasma from an ambient temperature of < 10,000 K to 250,000 K ?

Electron beam heating

RHESSI HXR parameters (from Milligan 2009) Fp = 5 x 1010 ergs cm-2 s-1 Ec = 13 keV δ = 7.6 For ne = 1012.5 cm-3

Collisional heating rate (per particle) FNT = 10-9 – 10-10 ergs s-1 Radiative loss rate (per particle) FR = 10-9 ergs s-1

Input energy is balanced by radiation - no energy to heat plasma at these depths?

Non-thermal electron energy depostion

Heating rate per particle (VAL-E)

Solution?

EMDs of these events were found to have a gradient T1 (Graham et al 2012) Consistent with conduction from a directly heated slab at 10 MK – balanced by radiative losses in the lower atmosphere (Widing 1982, Syrovatskii & Shmeleva 1973) Here, the flare energy source may not need to penetrate to deeper layers to produce the required emission

Conductive Heating

Conductive Heating

Assume conductive flux is balanced by radiative losses

Heating from a hot 10 MK slab

Scale of the region between heated slab and dense O V emission

S > 90 km

Conduction along one dimension along field line / loop (Spitzer conductivity)

Constant gradient between 107 K and 105.4 K plasma

Conclusions • Observe plasma at >1012.5 cm-3 heated to 250,000 K in flare footpoints

• Deviations from local ionisation equilibrium cannot account for the large intensity ratio and optical depths in both lines are low – although this should be carefully investigated

• From a simple collisional thick target approach it may be difficult to heat this plasma – although we are not accounting for compression/dynamics

• Conductive flux from a directly heated 10 MK upper source can heat at these depths – requires relatively steep temperature gradient

• The extremely high line ratios are still a puzzle - reproduce result using IRIS O IV and Si IV diagnostics