1. B. L. Alterman & Justin C. Kasper July 18, 2019
Helium Variation Across Two Solar Cycles Reveals A Speed-Dependent Phase Lag
B. L. Alterman & Justin C. Kasper
July 18, 2019

2. Solar Wind Helium Abundance & Sunspot Number (SSN)
Definitions
Published Observations
Hydrogen (Protons)
95 % by number density
Fully Ionized Helium (Alphas)
4% by number density
Helium Abundance
𝐴 𝐻𝑒 =100 × 𝑛 𝛼 / 𝑛 𝑝
𝐴 𝐻𝑒 & SSN Cross Correlation
𝜌( 𝐴 𝐻𝑒 , 𝑆𝑆𝑁)
𝜌( 𝐴 𝐻𝑒 ,𝑆𝑆𝑁)
Strongest in slow wind ( 𝑣 𝑠𝑤 ≲ 550 km/s)
Falls off for 𝑣 𝑠𝑤 >426 km/s
Helium vanishing speed
𝑣 0 =259 km/s
Within 1𝜎 of min observed 𝑣 𝑠𝑤
Possibly indicates helium essential to solar wind formation

3. Data Sources Wind/SWE FCs Solar cycles 23 & 24; end of cycle 22
Solar Wind Ions
SSN
Wind/SWE FCs
Solar cycles 23 & 24; end of cycle 22
> 23 years
Covers one Hale cycle
Long-term stability of SWE/FC system essential to this study
13 month smoothed SSN
Solar Information Data Center (SIDC)

4. 𝐴 𝐻𝑒 ( 𝑣 𝑠𝑤 , 𝑡) & SSN
Trailing end of cycle 22 through decline of cycle 24.
SSN in black, dashed
𝐴 𝐻𝑒 𝑣 𝑠𝑤 ,𝑡 colored lines.
10 𝑣 𝑠𝑤 quantiles
Color & symbol
Covers 312 km/s to 574 km/s
Take 250 day averages of all data
Legend
𝑣 𝑠𝑤 −𝜌( 𝐴 𝐻𝑒 ,𝑆𝑆𝑁)

5. 𝐴 𝐻𝑒 ( 𝑣 𝑠𝑤 , 𝑡) & SSN
Present drop in 𝐴 𝐻𝑒 indicates entering minimum 25
𝜌 𝐴 𝐻𝑒 ,𝑆𝑆𝑁
peaks at 355 km/s
Meaningful (>0.6) up to 488 km/s
Highly significant (≥0.7) up to 426 km/s
Phase offset between 𝐴 𝐻𝑒 and SSN
𝐴 𝐻𝑒 returns to same value at Max 23 & 24, even though different cycle amplitudes

6. Time-Lagged Cross Correlation
Calculate 𝜌 𝐴 𝐻𝑒 ,𝑆𝑆𝑁 for delay times -200 days to 600 days, steps of 40 days
Delay time is time for which 𝐴 𝐻𝑒 peaks as function of delay.
Plot Observed (open) and Delayed (filled) 𝜌(𝑣)
Error bars are repeat of procedure for 225 to 275 day averages

7. Time-Lagged Cross Correlation
Delayed 𝜌 𝐴 𝐻𝑒 ,𝑆𝑆𝑁 ≥0.7 for all 𝑣 𝑠𝑤
Observed & Delayed 𝜌( 𝐴 𝐻𝑒 ,𝑆𝑆𝑁) peak at 355 km/s Δ𝜌
Largest in fast wind
Most significant in slow wind

8. Phase Delay: 𝐴 𝐻𝑒 𝑆𝑆𝑁 (Top) Observed (Bottom) Delayed
Hysteresis present
Time is counter clock (color bar)
(Bottom) Delayed
Larger 𝑅 2 indicates spread of 𝐴 𝐻𝑒 about trend decreases
𝑋 𝜈 2 indicates linear model better in Delayed case
As expected, fit parameters are identical.

9. 𝜏 Delay of Peak 𝜌 𝐴 𝐻𝑒 ,𝑆𝑆𝑁 Positive delay = SSN precedes 𝐴 𝐻𝑒
Speed of instantaneous response
𝑣 𝑖 =200 km/s OR
Two delays
𝜏 𝑠𝑙𝑜𝑤 =150 days
𝜏 𝑓𝑎𝑠𝑡 >300 days
Either case, time lag is present

10. 𝐴 𝐻𝑒 𝑣 𝑠𝑤 Robustness 𝐴 𝐻𝑒 𝑣 =1.62 × 10 −2 (𝑣− 𝑣 0 ) 𝐴 𝐻𝑒 SSN=0
𝐴 𝐻𝑒 𝑣 =1.62 × 10 −2 (𝑣− 𝑣 0 )
Helium vanishing speed 𝑣 0
𝑣 0 =259 km/s
Kasper+ (2007), black dashed
𝐴 𝐻𝑒 SSN=0
Low solar activity 𝐴 𝐻𝑒 across Hale cycle
Suitable for comparison to Kasper+ (2007)

11. 𝐴 𝐻𝑒 𝑣 𝑠𝑤 Robustness All SSN (Unfilled)
SSN<25 selects solar activity conditions similar to Min 25
𝐴 𝐻𝑒 SSN=0
Consistent in both cases
Better agreement for SSN<25
Discrepancy for 𝑣 𝑠𝑤 =542 km/s expected

12. Helium Filtration Phase offset w/rt SSN observed in many solar indices
Lyman-alpha 𝐿 𝛼
Measures chromosphere & transition region activity
125 day
Soft x-ray flux (SXR)
Measures active regions (ARs)
> 300 day
Speed-dependent phase lag suggests processes above the photosphere modify 𝐴 𝐻𝑒

13. Helium Filtration Two slow wind sources If two delays FIP effect
Streamer belt
Weak B
Magnetically closed
Long-lived loops
ARs
Strong B
Higher latitudes than Streamer Belt
More open flux
If two delays
𝜏 𝑠𝑙𝑜𝑤 =150 days is streamer belt
𝜏 𝑓𝑎𝑠𝑡 >300 days is ARs
𝜏 reflects extent B is open
FIP effect
First Ionization Potential (FIP)
Ion abundances differ from photospheric value
Low FIP (< 10 eV) increase
High FIP show apparent depletion
Strongest in upper chromosphere & transition region
Weakens with B
Increases with loop length and age
Gravitational settling
interchange reconnection
Not mutually exclusive