Justin Kasper University of Michigan PSP SWG #15

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1 Justin Kasper University of Michigan PSP SWG #15
A zone of preferential ion heating extends tens of solar radii from Sun Justin Kasper University of Michigan PSP SWG #15 Justin C. Kasper, Kris Klein, Tristan Weber, Milan Maksimovic, Stuart Bale, Tony Case, Mike Stevens, Ben Maruca, A Zone of Preferential Heating Extends Tens of Solar Radii from Sun, ApJ, accepted, in press

2 Preferential heating in corona
Zone of preferential ion heating Preferential heating in corona Landi and Cranmer, 2009 Heating mechanism has to be non-thermal Preferentially acts on certain species Sensitive to mass, charge/mass, etc Dynamical time for heating has to be faster than effects of thermalization through Coulomb relaxation 𝜈 𝑐 ∝𝑛/ 𝑇 3/2 𝑑 𝑇 𝑠 𝑑𝑡 =− 𝜈 𝑠𝑠′ T s − T s′ + n i k B Q i Non-thermal above 0.2−0.3 𝑅 𝑠 Fe IX-X (𝟔.𝟑×𝟏𝟎𝟓 K) Cranmer (2010)

3 Unequal solar wind temperatures
Zone of preferential ion heating Unequal solar wind temperatures Equal temperatures Equal thermal speeds ??? Kasper, Lazarus, and Gary (2008) Also seen with minor ions…

4 Coulomb collisions in solar wind
Zone of preferential ion heating Coulomb collisions in solar wind It has long been known that excess temperatures of ions (and other non-thermal properties of solar wind) strongly correlated with Coulomb collisions Neugebauer, 1976; Feldmen et al. 1974; Klein et al., 1985 Define Coulomb number 𝑁 𝑐 as number of Coulomb collision times the elapse as solar wind travels 1 AU, 𝑁 𝑐 ≡ 𝜈 𝑐 ∗1 𝐴𝑈/ 𝑉 𝑠𝑤 Neugebauer, 1976

5 Ratio of He2+/H+ Perpendicular Temperature
Zone of preferential ion heating Ratio of He2+/H+ Perpendicular Temperature 𝛿 𝑣 𝛼𝑝 𝑡 (3) (2) 𝛿 𝑣 𝛼𝑝 𝑐 ≃0.167 (1) (2) (3) Kasper et al., 2013

6 Three questions to answer
Zone of preferential ion heating Three questions to answer Are unequal temperatures in the solar wind maintained by ongoing local preferential heating, or are they a leftover of heating that happened close to the Sun? Is faster solar wind further from local thermodynamic equilibrium than slow wind because only fast wind experiences preferential heating in the corona resulting in non-thermal structure? How far from the Sun does preferential ion heating continue?

7 Wind measurements at 1 AU
Zone of preferential ion heating Wind measurements at 1 AU

8 Zone of preferential ion heating
Why is 𝑇 𝛼 / 𝑇 𝑝 ∝ 𝑒 − 𝑁 𝑐 ? From Spitzer (1955): 𝑑Δ𝑇 𝑑𝑡 =− 𝜈 𝑐 Δ𝑇 Ignoring local heating, adiabatic expansion, other effects for now, and rearrange 𝑑Δ𝑇 Δ𝑇 =− 𝜈 𝑐 𝑑𝑡 Integrate both sides Δ𝑇=Δ 𝑇 0 exp −∫ 𝜈 𝑐 𝑑𝑡 =Δ 𝑇 0 exp − 𝐴 𝑐 Where 𝐴 𝑐 =∫ 𝜈 𝑐 dt is the Coulomb age and 𝑁 𝑐 ≃ 𝐴 𝑐 So we get the observed dependence because 𝑁 𝑐 is an approximation for 𝐴 𝑐

9 Relaxation due to Collisional Age
Zone of preferential ion heating Relaxation due to Collisional Age So we get the observed dependence because 𝑁 𝑐 is an approximation for 𝐴 𝑐 Seems to fit all the data pretty well. Does this mean all solar wind was non-thermal close to the Sun? Look at average excess temperature ratio 𝜖≡ 𝑇 𝛼 𝑇 𝑝 −1 as a function of both 𝑁 𝑐 and 𝑉 𝑝

10 All wind was originally non-thermal!
Zone of preferential ion heating All wind was originally non-thermal! Transition at 𝑁 𝑐 ∼1, where you would expect it Coulomb Number 𝑵 𝒄 Solar Wind Speed [km/s]

11 Other ions have similar decay
Zone of preferential ion heating Other ions have similar decay Tracey et al., PRL, 2016

12 Zone of preferential ion heating
Our proposal There is a zone of preferential ion heating in the inner heliosphere where the Coulomb frequency is sufficiently low and the preferential ion heating rate is sufficiently high for sustained differences in temperature to develop. Based on spectroscopic observations this zone begins 0.2−0.3 𝑅 𝑠 above the photosphere The outer boundary 𝑅 𝑏 of this zone is unknown to date Within the zone preferential heating results in different ion temperatures, with 𝜖 reaching an asymptotic value 𝜖 𝑜 within the zone. Motivated by small spread in 𝜖 for low 𝑁 𝑐 At the outer boundary 𝑅 𝑏 the strong preferential heating falls off and quickly becomes negligible Above 𝑅 𝑏 , 𝜖 decays as a function of 𝐴 𝑐

13 Preferential heating zone and its neighbors
Zone of preferential ion heating Preferential heating zone and its neighbors

14 Steps to the derivation
Zone of preferential ion heating Steps to the derivation All we need to do is derive an expression for the expected excess helium temperature relative to hydrogen observed in the solar wind 𝜖 𝑤 as a function of the asymptotic excess temperature back in the heating zone 𝜖 𝑜 and the Coulomb age calculated between the outer boundary of the zone 𝑅 𝑏 and our spacecraft: 𝜖 𝑤 ( 𝜖 0 , 𝑅 𝑏 , 𝐴 𝑐 ) Then solve for best fit 𝑅 𝑏 and 𝜖 0 to match observations by Wind spacecraft Two major derivations Integrate an energy equation for the decay of 𝜖 0 to 𝜖 𝑤 from 𝑅 𝑏 to Wind and relate it to 𝐴 𝑐 Develop scaling for 𝜈 𝑐 with distance and integrate to develop an expression for 𝐴 𝑐 based only on measurements at the spacecraft

15 A more detailed radial energy equation
Zone of preferential ion heating A more detailed radial energy equation What changes temperature 𝑇 𝑠 of species 𝑠? 𝑑 𝑇 𝑠 𝑑𝑟 = 𝛾−1 𝑇 𝑠 𝑛 𝑠 𝑑 𝑛 𝑠 𝑑𝑟 − 𝑄 𝑠 𝑛 𝑠 𝑘 𝐵 𝑈 − 𝑠 ′ ≠𝑠 𝜈 𝑠𝑠′ 𝑈 𝑇 𝑠 − 𝑇 𝑠 ′ Coulomb relaxation with all other species s’ protons dominate Cooling from adiabatic expansion. We’re ignoring anisotropies, focusing on scalar temperature, assuming instabilities limit anisotropy Volumetric heating rate from all dissipation processes: wave damping, reconnection, turbulence, … including our unidentified preferential heating mechanism

16 Build an equation for 𝑑𝜖/𝑑𝑟
Zone of preferential ion heating Build an equation for 𝑑𝜖/𝑑𝑟 Assume both species expand at same rate and adiabatic terms cancel Assume beyond 𝑅 𝑏 the ion heating rates are similar and the 𝑄 𝑠 terms cancel Aside: If preferential heating dominates within the heating zone then the asymptotic temperature excess is related to the ratio of the heating rates per particle 𝑄 𝛼 / 𝑛 𝛼 𝑄 𝑝 / 𝑛 𝑝 = 1+ 𝜖 0

17 Zone of preferential ion heating
Expression for 𝜖 𝑤 𝐴 𝑐 Our value for 𝜖 𝑤 𝑅 𝑤 is obtained by equating the analytic solution of the left hand side of this equation to the expression for age, and then solving the resulting transcendental equation for 𝜖 𝑤 𝐸 𝜖 𝑤 𝑅 𝑤 , 𝜖 0 𝑅 𝑏 + 𝐴 𝑐 =0 Now we need an expression for 𝐴 𝑐 based on 𝜈 𝛼𝑝 𝑤 measured at Wind and scaling relations to approximate its dependence on distance. If 𝑇 𝑝 ∝ 𝑟 −𝛿 , 𝑈∝ 𝑟 −𝜎 , and 𝑛 𝑝 ∝ 𝑟 −2 𝑈(𝑟), then 𝜈 𝛼𝑝 𝑟 = 𝜈 𝛼𝑝 𝑤 𝑅 𝑤 𝑟 2+𝜎−1.5𝛿 Or integrating, 𝐴 𝑐 =− 𝜈 𝛼𝑝 𝑤 1+2𝜎−1.5𝛿 𝑅 𝑤 𝑈 𝑤 1− 𝑅 𝑏 𝑅 𝑤 −1−2𝜎+1.5𝛿

18 Zone of preferential ion heating
300−325 𝑘𝑚 𝑠 −1 ;𝛿=0.7

19 Zone of preferential ion heating
350−375 𝑘𝑚 𝑠 −1 ;𝛿=0.6

20 Zone of preferential ion heating
400−425 𝑘𝑚 𝑠 −1 ;𝛿=0.8

21 Outer boundary of preferential heating
Zone of preferential ion heating Outer boundary of preferential heating

22 Zone ion temperature and heating ratios
Zone of preferential ion heating Zone ion temperature and heating ratios Our results are in agreement with reported 𝑇 𝑠 𝑇 𝑝 =1.35 m s m p for heavy ions reported by Tracy et al. (2016) A universal ion heating mechanism?

23 What’s happening!?!? Some speculation
Zone of preferential ion heating What’s happening!?!? Some speculation Observations consistent with model where temperatures reach an asymptotic ratio determined by a preferential heating process that cuts off sharply at Rs from the Sun Alfven point could be at these heights Expect much more power in counter-propagating Alfven waves below Alfven point Perhaps collisionless data at 1 AU indicate strong heating by counter-propagating Alfven ion-cyclotron waves below the Alfven point, about Rs from Sun Beyond preferential zone weaker heating continues (2) Kasper et al., 2013

24 Three questions revisited
Zone of preferential ion heating Three questions revisited Are unequal temperatures in the solar wind maintained by ongoing local preferential heating, or are they a leftover of heating that happened close to the Sun? Predominantly a relic signature. We have possibly never seen the dissipation process responsible for strong preferential ion heating in action with a spacecraft PSP will be the first spacecraft to enter this zone Is faster solar wind further from local thermodynamic equilibrium than slow wind because only fast wind experiences preferential heating in the corona resulting in non-thermal structure? All wind will be highly non-thermal within this zone, and maybe all ions experience the same mechanism Is preferential heating and its well-defined location due to counter-propagating Alfven-ion cyclotron waves that develop below the Alfven point? How far from the Sun does preferential ion heating continue? On average about Rs from the zone Could be confirmed as soon as first perihelion

25 Zone of preferential ion heating
Backup Slides

26 Zone of preferential ion heating
With only the Coulomb terms remaining, and noting that 𝜈 𝑝𝛼 𝜈 𝛼𝑝 = 𝑛 𝛼 𝑚 𝛼 𝑛 𝑝 𝑚 𝑝 ≡𝐹 we can simplify 𝑑𝜖/𝑑𝑟 𝑑𝜖 𝑑𝑟 =− 𝜈 𝛼𝑝 𝑈 𝜖 1+𝐹 + 𝜖 2 𝐹 The temptation is to separate and integrate these equations as before but 𝜈 𝛼𝑝 is actually a function of 𝜖 𝜈 𝑠𝑠′ = 4𝜋 𝑞 𝑠 2 𝑞 𝑠 2 𝑛 𝑠′ ln Λ 𝑚 𝑠 𝜇 𝑤 𝑠𝑠′ 3 Where 𝑤 𝑠𝑠′ 2 = 𝑤 𝑠 2 + 𝑤 𝑠′ 2 and 𝜇 is the reduced mass. So define a related Coulomb collision frequency 𝜈 𝛼𝑝 that is allows us to separate out the 𝜖

27 Only interactions with protons matter
Zone of preferential ion heating Only interactions with protons matter Tracy et al., 2015