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FIP Enhancement by Alfvén Ionization D A Diver ([email protected]), L Fletcher ([email protected]) and H E Potts ([email protected]) Department of Physics and Astronomy, Kelvin Building, University of Glasgow, Glasgow G12 8QQ, Scotland Abstract. Alfvén ionization is offered as a possible mechanism underlying the enhanced population of low First Ionization Potential(FIP) species in the solar corona. In this process, the photospheric flow impinging on the magnetic structure of a coronal flux tube collides and displaces ions in the magnetised plasma within the flux tube. This leads to pockets of charge imbalance that persist due to the impeded electron transport perpendicular to the magnetic field. The localised electric field then energises electrons to the impact ionization energy threshold of low FIP components in the surface flow. Such species then remain trapped in the plasma, and drift up the magnetic structure, causing a localised population enhancement compared to photospheric levels. 1. Background motivation Recent reviews( Feldman & Widing (2002), Peter (2002)) confirm that there is yet no widely accepted single cause of the enhanced population in the solar corona of low first ionization potential (FIP) species compared with their relative abundances in the photosphere. This enhancement is often referred to as the FIP effect. Low FIP species such as atomic sodium, aluminium, calcium, chromium, nickel, magnesium etc that are present in the solar atmosphere are observed to be at least three times more abundant in the chromosphere and corona than in the photosphere (Mohan et al (2000), Phillips et al (2003), Schwadron, Fisk & Zurbuchen (1999)) with all the concomitant implications for the solar wind. Table 1 presents a selected list of solar photospheric elements, using data from Asplund, Grevesse & Sauval (2005). Notice that the elements are ordered in terms of their critical Alfvén velocity, rather than first ionization potential. The significance of this ordering will become clear in the following section. Despite the lack of a single cause of low FIP enhancement, there are a variety of sophisticated physical processes that have been identified by various experts in the field, each of which may contribute to the overall FIP effect. For example, Laming (2004) most recently suggests that, under simplified assumptions of geometry and wave energy density, field gradients arising from chromospheric Alfén waves may c 2005 Kluwer Academic Publishers. Printed in the Netherlands. ° fipsfinalrev.tex; 13/01/2005; 16:46; p.1 2 cause fractionation consistent with the FIP effect, neglecting ambipolar forces. However, Wang (1996) uses only ambipolar flows generated by transient coronal heating to recover the same FIP bias, based on the collisional selective dragging of neutrals by protons. In Vauclair (1996), a magnetic skimmer model uses an erupting magnetic field to elevate neutral material, again based on proton drag. We offer here a simple mechanism based on Alfvén ionization which will complement those already existing, but which introduces the ionisation bias at a very early stage. The basic premise is that the surface flow on the photosphere will be sufficient, near strong, perpendicular magnetic features, to ionize preferentially components of the neutral gas for which the ionization energy is equal to, or less than, the bulk kinetic energy of the flow. In this way the lower FIP components are ionized simply by the flow kinetics, creating automatically a fractionation of the solar surface gas. The next section explains the physical mechanism in more detail. 2. Alfvén Ionization Where a constant stream of neutral gas flowing with speed v0 impinges on a low-density stationary, magnetised plasma of similar chemical composition, the gas will diffuse through, and be scattered by, the plasma without significant alteration, unless the kinetic energy of the neutrals (in the frame in which the plasma is seen to be stationary) exceeds the ionization energy of the gas, in which case the gas will be efficiently ionized (Alfvén, 1960). The mechanism at work can be expressed in simple terms as follows: atoms from the impinging gas collide with plasma ions and displace them; the local charge imbalance cannot be rectified immediately by electron motion because the magnetic field, oriented perpendicular to the flow, inhibits electron transport. The resulting electrostatic field continues to increase until the potential difference limits the further escape of ions, meaning that the potential barrier is now equivalent to the maximum energy of an ion as a result of a collision, namely 12 mg v02 , where mg is the mass of a neutral particle. The persistent electric field then accelerates the local electron population to this energy. These pockets of energetic electrons will then ionize those incoming neutrals with an electron-impact ionization threshold that is less than this energy. This mechanism was verified experimentally as an efficient plasma ionization method (Wilcox, 1959; Anderson et al, 1959; Fahleson, 1961), irrespective of fipsfinalrev.tex; 13/01/2005; 16:46; p.2 3 Table I. Table of selected components of the solar photosphere. The ionization potential φI is given in electron volts, and the critical ionization speed vc is in km s−1 using Eq. (1). Relative abundances are taken from Asplund, Grevesse & Sauval, 2005. element symbol Xenon Potassium Chromium Nickel Vanadium Cobalt Manganese Iron Titanium Scandium Calcium Krypton Aluminium Sodium Silicon Magnesium Sulphur Phosphorus Chlorine Argon Boron Lithium Oxygen Fluorine Carbon Beryllium Nitrogen Neon Helium Hydrogen Xe K Cr Ni V Co Mn Fe Ti Sc Ca Kr Al Na Si Mg S P Cl Ar B Li O F C Be N Ne He H Z atomic weight Rel abundance φI vc 54 19 24 28 23 27 25 26 22 21 20 36 13 11 14 12 16 15 17 18 5 3 8 9 6 4 7 10 2 1 131.3 39.1 52 58.69 50.94 58.93 54.94 55.85 47.88 44.96 40.08 83.8 26.98 22.99 28.09 24.3 32.07 30.97 35.45 39.95 10.81 6.94 16 19 12.01 9.01 14.01 20.18 4.0026 1.0079 1.86E-10 1.20E-07 4.37E-07 1.70E-06 1.00E-08 8.32E-08 2.45E-07 2.82E-05 7.94E-08 1.12E-09 2.04E-06 1.91E-09 2.34E-06 1.48E-06 3.24E-05 3.39E-05 1.38E-05 2.29E-07 3.16E-07 1.51E-06 5.01E-10 1.12E-11 4.57E-04 3.63E-08 2.45E-04 2.40E-11 6.03E-05 6.92E-05 8.51E-02 1.00E+00 12.13 4.34 6.77 7.64 6.75 7.88 7.43 7.9 6.83 6.56 6.11 14.0 5.99 5.14 8.15 7.65 10.4 10.5 13 15.8 8.3 5.39 13.6 17.4 11.26 9.32 14.5 21.6 24.6 13.6 4.22 4.63 5.01 5.01 5.06 5.08 5.11 5.22 5.25 5.31 5.42 5.68 6.54 6.57 7.48 7.79 7.91 8.09 8.41 8.74 12.17 12.24 12.81 13.29 13.45 14.13 14.13 14.37 34.43 51.02 fipsfinalrev.tex; 13/01/2005; 16:46; p.3 4 whether the moving neutral gas encountered stationary magnetised plasma, or a moving plasma encountered stationary neutrals; it is only the relative speed that counts. The conditions required are that: (i) the stationary plasma is strongly magnetized, so that transport perpendicular to the magnetic field is significantly hampered and (ii) the neutral gas speed reaches vc , given by à vc = 2eφI mg !1/2 (1) where φI is the ionization potential of a neutral gas particle. Values of vc for low FIP photospheric elements are given in the last column of Table 1. Clearly there are restrictions on the flow and magnetic field strengths that will allow such a mechanism to operate. The neutral gas flow must establish the local charge imbalance faster than the electron transport can neutralise it. Suppose that plasma ions are displaced, by collisions with the flowing neutrals, over a scale length equal to the ion Larmor radius RL . Then the typical set-up time τs for collisions to establish a charge imbalance across RL is given by τs ≈ RL v0 (2) The characteristic time τe for electron transport to eliminate this charge imbalance must depend on the electron drift-diffusion speed vde for perpendicular transport across the magnetic field: τe ≈ RL vde (3) If Alfvén ionization is to work, then condition (i) means that νe ¿ ωce (4) where νe is the collision frequency for electron-neutral particle encounters, and ωce is the electron cyclotron frequency. This ensures that the electron diffusion coefficient perpendicular to the magnetic field is much smaller than that parallel to the field. Consider now the ratio of timescales vde µ⊥e E τs ≈ = τe v0 v0 (5) fipsfinalrev.tex; 13/01/2005; 16:46; p.4 5 where µ⊥e = ≈ eνe 2 ) me (νe2 + ωce (6) eνe 2 me ωce (7) is the component of electron mobility perpendicular to the magnetic field that is independent of E × B drift, and E is the magnitude of the electric field. (Recall that E × B drift is charge-independent, and so cannot rectify charge imbalance.) Using Poisson’s equation to balance the maximum gas particle energy with the electric potential caused by ejection of ions, mg v02 2eRL (8) v0 ≈ RL ωi (9) τs ¿1 τe (10) E≈ and taking yields eventually thus ensuring that a potential barrier can be set up faster than the charge equilibration time from electron motion. Stated another way, (10) means that RLe ¿ λmfp (11) where RLe is the electron Larmor radius, and λmfp is the mean free path for electron-neutral collisions. Note that (10) allows a pocket of unbalanced charge to be created, (1) places a further restriction on how large the associated potential must be before ionization can take place. 3. Application to solar abundances The solar photospheric flow of neutral gas encounters a strong, verticallyaligned magnetic structure containing predominantly ionized plasma. Depending on the actual magnitude of the flow speed, some atomic species in the flow may be moving faster than the critical speed for ionization; others will not (in accordance with Table 1). Strong flows fipsfinalrev.tex; 13/01/2005; 16:46; p.5 6 near concentrated magnetic fields could reach the photospheric sound speed, approximately 7 km s−1 , and so satisfy the ionization threshold for Alfvén’s process. Supersonic horizontal flows have been observed in active regions; for example, Meunier and Kosovichev (2003) detected long-lived supersonic horizontal flows of the order of 7.7 km s−1 , and Yang et al (2003) also observed peak horizontal flow speeds of 5.68 km s−1 in pores. Chae et al (2000) report observations of horizontal flows up to 20.6 km s−1 . In order to have the plasma sufficiently magnetized, we need to guarantee that (10) holds. From Vauclair, 1996, we can take the collision frequency ν for electrons with neutrals in the lower chromosphere to be νe ≈ 1.1 × 106 s−1 . Comparing this with the electron cyclotron frequency ωce ≈ 1.8 × 1010 × B s−1 where B is the magnitude of the magnetic flux density in Tesla, we have νe 6 × 10−5 ≈ ωce B (12) and so (10) is satisfied for field strengths B ≥ 10−2 T, which is reasonable at the base of magnetic loops. Vauclair’s data pertains to mid-chromospheric conditions. To be sure that (10) is satisfied at the upper photospheric levels, the electronneutral collision frequency νe can be modelled (Cravens, 1997) approximately by νe ≈ ken nn ≈ (10−8 cm−3 s−1 ) × nn (13) where nn is the neutral number density, per cubic centimetre. Taking nn ≈ 1016 cm−3 gives a value for νe that is 100 times larger than the chromospheric parameter. However, (10) is still reasonable for magnetic field strengths greater than 0.01 T. Selective Alfvén ionization is also consistent with the evolution of bias as a function of time in regions of emergent coronal loops (Widing & Feldman, 2001), since the perpendicular magnetic field component at the photospheric surface is also evolving, and the flow imposes a natural time for the cumulative bias to appear. Even in the case of a static magnetic structure, the photospheric flow will continue to deliver low-FIP material to the footpoints where it may be ionized. Supposing the flow continues to be above the critical threshold for some species. Let us assume a very simple picture, ignoring all subsequent collisional processes, in which the low-FIP neutral, having been ionized by Alfvén ionization, is now caught in a magnetic trap formed by the magnetic loop with highest field strengths at the base. We can consider the characteristic time τb for one transit of the loop fipsfinalrev.tex; 13/01/2005; 16:46; p.6 7 (the bounce-time) as a useful indicative timescale for the FIP evolution. Now τb ≈ Z L ds 0 vq (s) ds (14) where L is the path length along the loop, parametrised by s, and vq is the speed along the major axis of the loop. Treating the magnetic structure as a trap, we have that 2 1 2 m(vq 2 + v⊥ ) = Wq + W⊥ = constant W⊥ = constant B (15) (16) where k refers to the direction of the local magnetic field, ⊥ is orthogonal to k, and Ws is the kinetic energy. Assuming that the newly ionized neutral has negligible parallel velocity, since it originates from the photospheric flow, we can take its kinetic energy to be entirely in the form of W⊥ , and use this as the mirror condition. This means we can write τb as τb ≈ v0−1 Z L 0 µ 2L = v0 (1 − B(s)/B0 )1/2 ds R R−1 (17) ¶1/2 (18) where R = Bmin /B0 is the mirror ratio, that is, the ratio of the magnetic field strength at the loop top, Bmin , (weakest) to that at the footpoint, B0 , (strongest), and where we have taken a simple linear behaviour · B(s) ≈ B0 ¸ 2(R − 1) 1− s , RL s ≤ L/2 (19) With indicative values of L ≈ 2 × 108 m, R ≈ 4 (Nakariakov & Ofman, 2001) and v0 ≈ 7 × 103 ms−1 (modest in comparison with Winebargeret al (2002) who show flows in the range 15-40 km s−1 in coronal loop structures) we have τb ≈ 6.6 × 104 s ≈ 43 day (20) The ionized low-FIP species are then trapped in the magnetic loop, and their numbers continue to increase as more neutral flow at the footpoint delivers a continuous supply of freshly ionized material. This result compares favourably with the analysis of Widing & Feldman, 2001, in which FIP bias is observed to increase linearly with time, fipsfinalrev.tex; 13/01/2005; 16:46; p.7 8 taking approximately a day to augment the FIP bias by unity for Mg in active region plasmas. We could improve the sophistication of our model by taking account of weakly collisional processes in the loop. This would alter the loop transit time, and change the FIP evolution timescale in a involved way, since although diffusion will lengthen the transit time compared to τb , the density enhancement of newly ionized low-FIP material may well increase faster as a result. 4. Concluding Discussion In this article we present a simple physical process that may account for the enhanced abundance of low-FIP elements in the upper solar atmosphere. Alfvén ionization has the merit of converting the kinetic energy in the photospheric flow into ionizing energy selectively for the lowFIP elements where such a flow impinges on a pre-existing magnetised plasma. In this way, we have a simple mechanism that delivers up to 10 eV (generated from modest photospheric flows) to selected neutrals in order to ionize them, consistent in part with the ethos of McKenzie & Feldman (1994), who conclude that a mechanism that could impart a small amount of energy only to selected particles could account for the discrimination, albeit they were discussing ions, rather than neutrals. Having ionized our neutrals by Alfvén ionization, we invoke a magnetic bottle description to show how the increased abundance evolves with time, with the newly ionized low-FIP neutrals moving up the magnetic loop as a result of a magnetic gradient near the footpoint. This is consistent with the physical picture of Schwadron, Fisk & Zurbuchen (1999), in which the greatest low-FIP bias is seen in the slow solar wind, assumed to originate from material stored in large coronal loops and released sporadically via reconnection. The ‘magnetic skimmer’ model (Vauclair, 1996) uses the magnetic field too, in that an erupting field raises ionised material from the photosphere up into the chromospheric plateau where any neutrals dragged up in the process can be ionized. Our Alfvén ionization model is complementary to this, in that we use the vertical magnetic elements to generate the FIP enhancement; however, if the initial loop eruption is sufficiently fast, then the horizontal field could also ionize, since it is only the relative motion between magnetized plasma and neutral gas that is important. Vauclair also notes that small dense loops acquire a FIP bias in their footpoints as the loops grow; this is consistent with both our treatments. fipsfinalrev.tex; 13/01/2005; 16:46; p.8 9 FIP enhancement fraction 12 Feldman et al (1998) Reames (1995) Mohan et al (2000) Laming (2004) Wieler et al (1995) 10 8 6 4 2 0 0 5 10 15 20 25 30 35 40 45 50 Critical Alfven velocity /km s−1 12 FIP enhancement fraction 10 8 6 Xe 4 2 0 0 5 10 15 Ionisation energy /eV 20 25 Figure 1. Observational data on FIP bias for a variety of elements, from a range of sources.Top graph shows the bias as a function of vc ; lower graph shows the same data as a function of FIP. Multiple data points for the same value on the horizontal axis reflect the diversity in observation for particular elements. Mohan et al (2000) note that the FIP bias for K seems to be greater than all the other low-FIP elements; in our treatment, K has the lowest critical flow speed of all the low-FIP elements, and so is the most readily ionized by photospheric flows. Their observation of spatial structure in the FIP bias is also in agreement with our model, where the bias itself is generated at the footpoints, and enhanced by storage in magnetic loops. Although comparisons between FIP bias observations are difficult, the elements which show the greatest relative bias are in accord with those having the smallest vc (as shown in Table 1). Notice that Xe has the lowest vc of all the quoted elements, yet has an ionization potential of 12.3 eV, and so should not fall into the category of low FIP bias. fipsfinalrev.tex; 13/01/2005; 16:46; p.9 10 Studies of solar noble gas abundance however (Wieler & Baur, 2001) reveal that Xe abundance in the solar wind is greater than photospheric abundance by a factor similar to the standard low FIP bias. This is also partly true of Krypton, which also has a sufficiently small vc for Alfvén ionization to be possible. A compendium of observational results is presented in the graphs of Figure 1. The top graph shows relative abundance as a function of FIP; the lower graph presents the same data re-ordered to show bias as a function of vc . The second graph accommodates the anomalous Xe result more satisfactorily than the first. Multiple points for the same value on the horizontal axis reflect the diversity of data for the same element; given that the data spread partly reflects the source type, and partly the date of the observation, it may be that FIP bias is also a function of the solar cycle. References Alfvén, H.: 1960 Rev. Mod. Phys. 32 710 Anderson, O., Baker, W.R., Bratenahl, A., Furth, H.P. and Kunkel, W.B.: 1959 J. Appl. Phys. 30 188 Asplund, M., Grevesse, N. & Sauval, A. J.: 2005 Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis ASP Conference Series Vol XXX arXiv:astro-ph/0410214 v2 Chae, J., Denker, C., Spirock, T. J., Wang, H. and Goode, P. R.:2000 Solar Physics 195, 333 Cravens, T. E. Physics of Solar System Plasmas, CUP, ISBN 0-521-35280-0 Fahleson, U.V.:1961 Phys. Fluids 4 123 Feldman, U. and Widing, K. G.: 2002, Physics of Plasmas 9, 629 Feldman, U., Schüle, U., Widing, K.G. & Laming, J.M.: 1998, Ap.J. 505 999 Laming, J.M.:2004: Ap.J. 614 1063 McKenzie, D. 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