Geodynamo, Solar Wind, and Magnetopause 3.4 to

Geodynamo, Solar Wind, and Magnetopause 3.4 to 3.45 Billion Years Ago John A. Tarduno, et al. Science 327, 1238 (2010); DOI: 10.1126/science.1183445 This copy is for your personal, non-commercial use only.

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Geodynamo, Solar Wind, and Magnetopause 3.4 to 3.45 Billion Years Ago John A. Tarduno,1,2* Rory D. Cottrell,1 Michael K. Watkeys,3 Axel Hofmann,3 Pavel V. Doubrovine,1,4 Eric E. Mamajek,2 Dunji Liu,5 David G. Sibeck,6 Levi P. Neukirch,2 Yoichi Usui1,7 Stellar wind standoff by a planetary magnetic field prevents atmospheric erosion and water loss. Although the early Earth retained its water and atmosphere, and thus evolved as a habitable planet, little is known about Earth’s magnetic field strength during that time. We report paleointensity results from single silicate crystals bearing magnetic inclusions that record a geodynamo 3.4 to 3.45 billion years ago. The measured field strength is ~50 to 70% that of the present-day field. When combined with a greater Paleoarchean solar wind pressure, the paleofield strength data suggest steady-state magnetopause standoff distances of ≤5 Earth radii, similar to values observed during recent coronal mass ejection events. The data also suggest lower-latitude aurora and increases in polar cap area, as well as heating, expansion, and volatile loss from the exosphere that would have affected long-term atmospheric composition. he oldest record of Earth’s magnetic field strength, based on a thermoremanent magnetization (TRM), is from silicate crystals hosting single domain–like magnetite inclusions separated from plutons from the Kaapvaal craton, South Africa; these plutons have been dated to 3.2 billion years ago (Ga) (1). This record suggests an intensity that is within 50% of the modern field value. The geomagnetic field may be truly ancient, starting shortly after core formation, but several hypotheses suggest otherwise. A null or weak field at 3.8 to 3.9 Ga is predicted from a hypothesis seeking to explain lunar nitrogen values through transport from Earth’s atmosphere by the solar wind (2). A delayed onset of the geodynamo, to ages as young as 4.0 to 3.4 Ga, has been predicted from a model for cooling of a dense liquid layer at the base of the early Earth’s magma ocean (3). However, testing these nullfield models is difficult because of the ubiquitous metamorphism that has affected Paleoarchean terrestrial rocks. Some of the least metamorphosed Paleoarchean rocks, having experienced peak temperatures of 0.4 (0.53-0.90), typical for magmatic zircons (Hoskin and Schaltegger, 2003). The weighted average age of these 9 analyses is 3409 ± 4 Ma (MSWD=1.3), which is consistent with the intercept age and is interpreted as the crystallization age of the rock. Paleomagnetism Methods. Paleointensity measurements using unoriented quartz phenocrysts were conducted using the Thellier approach as modified by Coe (Thellier and Thellier, 1959; Coe, 1967; Cottrell and Tarduno, 2000). Temperature steps of ∼50 o C were used for the first 300 o C to 400 o C, an unblocking temperature expected to be dominated by overprints on the basis of the peak low grade metamorphic temperatures (less than or equal to 350 o C, see main text). At higher 1

Supporting Online Material Table 1: Zircon data Spot

206 Pb c

(%)

232 Th U Th (ppm) (ppm) /238 U

2

1.1 0.05 607 326 2.1• 0.01 400 321 3.1 0.15 160 83 4.1 0.12 385 293 5.1 0.00 667 298 6.1 0.08 298 140 7.1 0.08 718 357 8.1 0.24 532 277 9.1• 0.08 142 74 10.1 0.18 525 218 11.1 0.02 746 308 12.1 0.00 467 211 13.1• 0.08 471 385 14.1• 0.22 389 337 15.1 1.04 391 277 16.1• 0.15 116 60 17.1 0.64 62 29 18.1• 0.02 140 78 19.1• 0.08 96 54 19.2• 0.49 214 147 A1.1• – 217 144 A2.1 0.10 483 318 A3.1 0.16 417 223 A4.1 1.34 633 235 A5.1 1.28 1434 737 • : samples close to concordia

0.55 0.83 0.53 0.79 0.46 0.49 0.51 0.54 0.54 0.43 0.43 0.47 0.84 0.90 0.73 0.53 0.49 0.57 0.58 0.71 0.69 0.68 0.55 0.38 0.53

206 Pb∗

207 Pb

(ppm)

/206 Pb∗

232 236 66.3 199 324 140 245 147 85.7 193 256 230 265 224 141 70.5 33.7 86.6 57.4 121 127 264 189 282 287

0.2735 0.2899 0.2833 0.2881 0.2867 0.2821 0.2743 0.2689 0.2909 0.2795 0.2700 0.2868 0.2880 0.2867 0.2746 0.2893 0.2860 0.2890 0.2889 0.2875 0.2884 0.2872 0.2846 0.2702 0.2524

±%

207 Pb∗

±%

/235 U 0.29 0.30 0.64 0.33 0.26 0.60 0.29 0.51 0.50 0.33 0.75 0.31 0.28 0.31 0.62 0.64 1.0 0.52 0.63 0.49 0.37 0.25 0.31 1.60 3.30

16.73 27.40 18.83 23.85 22.35 21.22 15.01 11.86 28.21 16.48 14.84 22.67 25.98 26.45 15.67 28.05 24.78 28.67 27.83 26.03 27.05 25.21 20.67 19.06 8.01

206 Pb∗

±%

/238 U 2.7 2.6 2.8 2.7 2.6 3.0 2.6 2.6 2.7 2.6 2.7 2.6 2.6 2.6 2.7 2.9 3.1 2.7 3.2 2.7 1.7 1.6 1.6 3.3 4.3

0.444 0.686 0.482 0.600 0.565 0.546 0.397 0.320 0.703 0.428 0.399 0.573 0.654 0.669 0.414 0.703 0.628 0.719 0.699 0.657 0.680 0.637 0.527 0.512 0.230

2.7 2.6 2.7 2.6 2.6 2.9 2.6 2.6 2.7 2.6 2.6 2.6 2.6 2.6 2.6 2.9 2.9 2.7 3.1 2.6 1.6 1.6 1.6 2.8 2.8

err corr .994 .993 .973 .992 .995 .979 .994 .980 .983 .992 .959 .993 .994 .993 .973 .976 .940 .981 .980 .984 .975 .987 .981 .869 .650

206 Pb

207 Pb

/238 U

/206 Pb

Age(Ma) 2367 ±53 3366 ±67 2536 ±56 3032 ±64 2889 ±60 2807 ±66 2155 ±47 1790 ±40 3433 ±71 2295 ±50 2162 ±47 2921 ±60 3245 ±66 3302 ±67 2223 ±49 3433 ±76 3143 ±71 3494 ±72 3416 ±83 3254 ±67 3346±43 3176±39 2728 ±35 2664 ±62 1336 ±34

Discordant (%) Age(Ma) 3326.3 ±4.6 29 3416.9 ±4.6 1 3381.3±10.0 25 3407.3 ±5.1 11 3399.8 ±4.1 15 3374.4 ±9.5 17 3330.5 ±4.5 35 3299.5 ±8.1 46 3422.2 ±7.8 0 3360.4 ±5.1 32 3306.0 ±12 35 3400.4 ±4.9 14 3406.7 ±4.4 5 3399.7 ±4.7 3 3332.4 ±9.6 33 3413.8 ±10 -1 3396.0 ±12 7 3412.2 ±8.1 -2 3411.7 ±9.9 0 3403.9 ±6.0 4 3408.8 ±5.8 2 3402.5 ±3.9 7 3388.3 ±4.9 19 3307 ±25 19 3200 ±52 58

Supporting Online Material Table 2: Paleointensity parameters for BGB and NGB quartz phenocrysts. Sample da2a da2b da2h da2c da2e da2(3)c da2(3)d da2-3*† da2-6*† da2m‡ da2p‡ da2r‡ nt2b nt2-4† nt2-5† nt2a*† nt2b*† nt2f nt2h*

Method thermal thermal thermal thermal thermal thermal thermal laser laser laser laser laser thermal laser laser laser laser laser laser

Temp. (o C) 500-580 475-570 515-570 450-570 450-570 475-570 485-570 510-580 510-580 510-580 510-580 510-580 545-580 510-580 510-575 510-575 510-575 510-575 510-580

µT 17.9 27.0 28.3 24.8 29.5 23.9 30.8 33.5 33.2 28.8 29.4 29.3 19.8 20.1 16.8 19.3 19.4 15.8 16.5

R2 0.98 0.92 0.99 0.99 0.99 0.99 0.99 0.98 0.99 0.97 0.99 0.99 0.99 0.97 0.99 0.98 0.99 0.99 0.97

N 7 6 5 7 7 7 6 5 5 5 5 5 6 5 4 5 4 4 5

b -0.298 -0.450 -0.478 -0.414 -0.491 -0.398 -0.513 -0.558 -0.553 -0.961 -0.980 -0.977 -0.329 -0.335 -0.280 -0.321 -0.324 -0.264 -0.276

σb 0.030 0.095 0.022 0.010 0.019 0.010 0.020 0.070 0.056 0.067 0.048 0.011 0.014 0.048 0.064 0.034 0.010 0.007 0.042

f 0.346 0.396 0.333 0.543 0.681 0.543 0.458 0.572 0.634 0.571 0.634 0.573 0.316 0.521 0.430 0.543 0.349 0.349 0.520

g 0.716 0.756 0.705 0.810 0.791 0.810 0.801 0.591 0.672 0.600 0.672 0.733 0.504 0.681 0.595 0.738 0.590 0.590 0.681

q 2.43 1.42 5.02 18.23 13.93 19.15 9.42 2.70 4.21 4.91 8.70 37.28 3.74 2.48 1.12 3.77 7.88 7.98 2.33

Sample (“da”, BGB samples; “nt”, NGB samples), heating method, temperature range, paleofield value, regression coefficient (R2 ), number of temperature steps used in line fit (N), slope (b), standard deviation of line fit (σb ), fraction of NRM used in line fit (f), gap factor (g) and quality factor (q). Parameters after Coe et al., (1978). All samples measured with 2G 755 SQUID magnetometer except where marked (*) which were measured with 2G small bore (6.3mm) DC SQUID magnetometer. A 60 µT laboratory field was used except where noted (‡) where a 30 µT laboratory field was applied. Oriented thin sections were used for some results (denoted by †); otherwise all results are from isolated unoriented crystals. unblocking temperatures finer (e.g. 25 o C) steps were used with partial thermoremanent magnetization checks until >90% of the NRM was lost, or the magnetization was no longer stable. Typical heating times were 25-30 minutes; cooling times 30 minutes. A field of 60 µT was used for the field-on steps. Some samples were also measured with a smaller applied field (30 µT) to check for field dependence. We feel our crystal (see main text) and NRM/TRM selection criteria (see main text and below) limit the influence of MD magnetic grains. As another test, we perform the partial remanent ¨ magnetization tail test (Dunlop and Ozdemir,

2000) as implemented by Riisager and Riisager (2001). All paleointensity values are based on least squared line fits to the raw experiment data (i.e. smoothing of the data because of experimental noise relative to the signal was unnecessary). Thellier-Coe experiments were also performed using a Synrad Firestar V20 CO2 laser with calibrations as described in Tarduno et al. (2007). There are two advantages of this approach. First, the faster heating times (i.e. typical heating times were 3 minutes; cooling, 5 minutes) decreases the possibility of thermally-induced laboratory alteration. Second, the approach

3

Supporting Online Material Table 3: Summary Paleointensity Values Sample da2a da2b da2h da2c da2e da2(3)c da2(3)d da2-3*† da2-6*† da2m‡ da2p‡ da2r‡ Average

Method thermal thermal thermal thermal thermal thermal thermal laser laser laser laser laser

Intensity (µT) 17.9 ± 1.8 27.0 ± 1.5 28.3 ± 2.8 24.8 ± 0.6 29.5 ± 1.0 23.9 ± 0.5 30.8 ± 1.2 33.5 ± 3.2 33.2 ± 2.1 28.8 ± 4.1 29.4 ± 2.9 29.3 ± 1.2 28.0 ±4.3

Sample nt2b nt2-4† nt2-5† nt2a*† nt2b*† nt2f nt2h* Average

Method thermal laser laser laser laser laser laser

Intensity (µT) 19.8 ± 1.0 20.1 ± 2.9 16.8 ± 0.9 19.3 ± 2.0 19.4 ± 2.0 15.8 ± 1.9 16.5 ± 2.7 18.2 ±1.8

Uncertainties reported are 1σ. See Supporting Online Material Table 2 for definition of *, † and ** symbols.

allows the rapid heating of oriented sub-sections we use (Fisher, 1953): (i.e. portions of thin sections) containing single ) (  1 quartz phenocrysts. N − Rv 1 N−1 cosα(1−p) = 1 − −1 (1) Rv p The field-off data of some experiments alwhere Rv is vector length, N number of vectors lowed the calculation of paleodirection (and and (1 − p) is the choice of probability level (in hence paleolatitude) for some samples. A limitthis case, 0.95). For the BGB where N=2, this is ing factor in the thin-section approach (Tarduno appropriate as Rv >1.98 (McFadden, 1980). We et al., 2007) is the presence of larger magnetic determine the uncertainty in inclination from: inclusions that cannot be physically removed because they are near the glass slide used to I95 = α95 /2 × [1 + 3cos2 (Ix )] (2) hold the initial quartz phenocryst; this forced rejection of 20 oriented grains from BGB. The where Ix is the mean inclination. NGB site is from a plunging syncline (Wilson Selection Criteria and Results. Prior studand Versfeld, 1994; Hoffman and Wilson, 2007). ies have documented that magnetic inclusions in We use a trend of 250o and a plunge of 65o , and silicates have a composition that mimics that a dip of 80o and dip direction of 50o to correct seen in magnetic phenocrysts in the matrix of to horizontal. The BGB dacite sampled is from the whole rock. Our new results are fully cona plunging antiformal syncline (de Ronde and sistent with these previous findings (Cottrell and de Wit, 1994). We use a plunge (overturned) of Tarduno, 1999; Cottrell and Tarduno, 2000; Tar80o trending at 225o , and a dip of 85o and dip duno et al., 2001; 2002; Tarduno and Cottrell, direction 25o to correct to horizontal. 2005; Tarduno et al., 2006; Cottrell et al., 2008). For the calculation of uncertainty of magnetic Magnetite is found as phenocrysts in the dacite directions obtained from oriented thin sections, (Usui et al., 2009) and thermal unblocking data

4

(e.g. Figure 1) suggest a magnetite Curie tem- Supporting Online Material Table 4: Inclination perature for magnetic inclusions in the BGB and and Paleolatitude data. NGB quartz phenocrysts. Criteria used to evaluate the paleointensity data Sample Dec (o ) Inc (o ) (for unoriented and oriented quartz crystals) nt2-2† 239.2 -49.9 follow those described by Cottrell and Tarduno nt2-4† 232.0 -41.2 (2000) and Tarduno et al. (2007). However, nt2-5† 227.5 -44.0 we relax the criteria on the percentage of NRM nt2-7† 237.1 -36.9 used in the best-fit to determine paleointensity nt2-8† 239.8 -42.3 specified in Cottrell and Tarduno (2000). All nt2a*† 228.8 -37.2 BGB and NGB rocks have experienced low grade nt2b*† 228.0 -44.3 metamorphism and we expect that magnetic overprints will be dominant at low unblocking temperatures. Therefore, a smaller percentage Sample Dec (o ) Inc (o ) of the NRM is available for paleointensity da2-3*† 239.7 -49.5 determination relative to younger rocks. da2-6*† 240.7 -39.4 Seventy-two paleointensity experiments were conducted on BGB crystals (total of unoriented All directional information was obtained using and oriented crystals; 12 successful, ∼17% oriented crystals heated with a CO2 laser. Fisher success rate). Twenty-eight NGB crystals were average of stratigraphic directions: NGB, declinao o o selected for paleointensity analysis (total of tion, 233.1 ; inclination, -42.4 ; n=7; α95 = 4.5 . o o unoriented and oriented crystals; 7 successful, BGB, declination 240.2 ; inclination, -44.5 ; n=2; o ∼25% success rate). An additional 5 oriented α95 = 8.7 . See Supporting Online Material Table NGB crystals were demagnetized exclusively for 2 for definition of * and † symbols. directional studies. For the BGB results, there is a hint of a cooling rate dependence in the laboratory data (mean of values obtained with oven cooling at 30 minutes is 26.0 ± 4.3 µT, mean values obtained with laser cooling of 5 minutes is 30.8 ± 2.3 µT). However, this relationship has not been seen previously in a similar study (Tarduno et al., 2007) and a NGB paleointensity value obtained from laser heating does not differ from others obtained from oven heating (Table T2). With a factor of 2 change in applied field (Table T2), no field dependence was noted. Specifically, for BGB the critical value for 10 degrees of freedom (degrees of freedom = n-2) tc for a unpaired t-test is 2.2, whereas the calculated test statistic is t = 0.5 for a comparison of paleointensity means using a 30 µT and 60 µT field. As t < tc , the difference in the means is not significant at the 95% confidence level. Partial-thermoremanent magnetization tail checks are less than 5% at a given step, consistent with the negligible influence of MD

grains, predicted by our crystal selection criteria.

Geologic and Laboratory Cooling Rates We estimate the geologic cooling rate of our samples through field relations and modeling. Method. The NGB samples are likely from a flow or a very shallow intrusion that is 100 m thick. Our BGB samples, however, were intruded at depth; we assume the intrusion we sampled was between 100 and 200 m thick. We use Jaeger’s (1967) error function analysis to estimate the cooling rate: T /To = φ(ξ, τ ) − φ(2k − ξ, τ ) φ(ξ, τ ) =

1 2



erf

ξ+1 ξ−1 − erf 1/2 1/2 2τ 2τ

ξ = x/a, τ = κt/a2 5

(3) 

(4) (5)

Fig. S2 (A) Orthogonal vector plot of thermal demagnetization data of whole rock sample from NGB dacite in geographic coordinates. Red squares, inclination; blue circles, declination. High unblocking temperature magnetization (I=-51o , D=136o ) is isolated between 475 o C and 580 o C. (B) High unblocking temperature component of magnetization (NGB) in geographic coordinates versus potential overprint fields (the latter summarized in Tarduno et al., 2007). where a is the half thickness of the igneous unit, x is the distance between the midplane of the unit and the surface, t is time in seconds, k is a factor relating unit thickness and depth below the surface (such that x=ka), and κ is the thermal diffusivity (assumed to be 0.6 - 1.0 x 10−6 m2 /s).

where xTRM is the natural log of the ratio of the blocking temperatures in the lab and in nature and aTRM is a constant representing blocking energy (∼ 25) (Halgedalh et al., 1980). Results. For a flow or intrusion very near the surface, k=1. This is the likely scenario for the NGB samples. A 100 m thick flow will take approximately 30 years (assuming a thermal diffusivity of 0.6 × 10−6 m2 /s) to cool to a temperature below 450 o C (the approximate lower temperature bound for the high unblocking temperature component identified in our experiments). If the NGB site is a shallow sill, the temperature of the country rock at the time of intrusion is unknown. But country rock

We follow Halgedalh et al. (1980), who investigated the variation of the ratio of TRM acquisition of single domain grains with respect to geologic and laboratory cooling times, and use the approximation:

TRMancient xTRM ≈ 1+ TRMlab 2aTRM 



Hancient Hlab

(6)

6

temperatures of 50 o C and 100 o C result in only There are two important caveats. First, this relationship breaks down at t = 0.7 Gyr; a younger minor differences in cooling time. star (ξ Boo) has apparently much lower mass The BGB dacite sampled was intruded as much loss rate. Second, this empirical relationship was as 1 km below the boundary of the overlying obtained under the assumption that the stellar sediments. We assume sill thicknesses of 200 wind speed for all stars is the same irrespective of m and 100 m, k=10 and k=20 respectively, age. As discussed by Newkirk (1980), however, intruded into a 100 o C to 200 o C country the stellar wind speed is expected to decrease rock. A 200 m thick intrusion, will cool in 402 with age. years below 450 o C if it is intruded into 200 The mass loss rate is related to the stellar wind o C country rocks; it will cool in 340 years if properties by the continuity equation: it is intruded into 100 o C country rocks. A 100 m thick sill will cool below 450 o C in 104 4πR2 Psw 2 m ˙ = 4πR ρ v = (8) sw sw years if it is intruded into 200 o C country rock, vsw and 86 years if intruded into 100 o C country rocks. (The relevance of these cooling times to where R is the distance from the star (1.496 × 8 geomagnetic field averages is discussed further in 10 km for the Earth’s orbit), ρsw and vsw are the “Astrophysics and Magnetopause Standoff” the wind density and velocity at this distance, 2 ) is the wind pressure. The and Psw (= ρsw vsw section). amount of astrospheric absorption scales approximately as a square root of Psw (e.g. Wood and These geologic cooling times, when coupled Lindsky, 1998). Because Psw ∝ mv ˙ sw , the mass with the Halgedahl et al. (1980) approximation, loss inferred from models of astrospheric absorpsuggests that our paleointensity data could tion is inversely proportional to the assumed overestimate the true value by 26% to 35% wind velocity. However, the estimates of wind (table S5), assuming solely single domain pressure and mv ˙ sw are insensitive to the choice magnetic carriers. However, rock magnetic of vsw , and hence should follow the same power experiments suggest small PSD magnetic relationship regardless of whether the wind vegrains behave differently (Dunlop and Argyle, locity is assumed to be constant or not: 1997); micromagnetic modeling predicts these grains underestimate the true paleointensity Psw ∝ mv ˙ sw ∝ t−2.33±0.55 (9) value (Winklhofer et al., 1997). As noted in the main text, the net effect of these con- Normalizing by the present values (denoted by trasting cooling rate behaviors is probably small. the “0” subscript), we have: Psw mv ˙ sw = = Psw0 m ˙ 0 vsw0

Astrophysics and Magnetopause Standoff



t t0

−2.33

(10) We estimate solar mass loss, wind velocity and ram pressure following two approaches (Model A In our model, we consider magnetopause standand B) outlined below. off distance at the subsolar point (rs ) as a Model A. Wood et al. (2002) used data on H I function of the Earth’s magnetic dipole moment Lyman-α astrospheric absorption to estimate the (M ) and solar wind pressure (P ). The latter sw E mass loss rates of solar-like stars. We use these is estimated using the mass loss model described estimates to derive how the solar wind pressure above. M is estimated from our paleointensity E changed through time. In a recent compilation experimental data, presented and discussed in Wood (2006) suggests that the mass loss rate the main text. (m) ˙ approximately follows a power law: The model highlights the importance of the m ˙ ∝ t−2.33±0.55 (7) increased solar wind pressure (Figure 2) at 7

Supporting Online Material Table 5: Projected Paleointensity Overestimates Assuming Single Domain Carriers. Site (thickness) NGB (100 m) NGB (100 m) NGB (100 m) BGB (100 m) BGB (200 m) BGB (100 m) BGB (200 m)

Temp† 0 oC 50 o C 100 o C 100 o C 100 o C 200 o C 200 o C

Time to Cool 30 years 31 years 34 years 86 years 340 years 104 years 402 years

Lab Cooling Time 30 mins (5 mins) 30 mins (5 mins) 30 mins (5 mins) 30 mins (5 mins) 30 mins (5 mins) 30 mins (5 mins) 30 mins (5 mins)

Value 26 (30) % 26 (30) % 27 (30) % 28 (32)% 31 (35)% 29 (32)% 32 (35)%

†Temperature of the country rock when the dacite formed. activity (Mamajek and Hillenbrand, 2008), a solar-type star with 12-day rotation period should have a soft X-ray flux (defined here as the soft X-ray band matching the band observed by the ROSAT X-ray observatory, namely 0.1-2.4 keV) of 10−4.8 × the stellar bolometric luminosity, which for the Sun at 3.45 Ga corresponds to a soft X-ray luminosity of 1028.8 erg s−1 , and soft X-ray surface flux of 106.0 erg s−1 cm−2 .

3.4-3.45 Ga. As discussed in the main text and in the discussion of cooling rates above, our paleointensity values represent samples of the paleofield on hundreds of years (BGB) to decade (NGB) timescales. Paleointensity values from young ( 106 erg s−1 cm−2 have inferred mass-loss rates an order of magnitude or more below those of three young, active K-type stars with fX = 2-8×105 erg s−1 cm−2 ( Eri, 36 Oph, and 70 Oph). These three active stars have ages of ∼0.8, 1.0, and 1.9 Gyr, bracketing the 3.45 Ga (1.12 Gyr) Sun, so it is reasonable to assume that the Sun would be on the high mass-loss side of the discontinuity.

study predicts a maximum of stellar mass-loss rates among cool main sequence stars of ∼10× M˙ .

Considering the Wood et al. (2005) and Holzwarth and Jardine (2007) inferred mass-loss rates as bounds, the Sun’s mass-loss rate at 3.45 Ga is plausibly in the range of 10-80× M˙ = 10−12.7 to 10−11.8 M /yr. The lower value is close to our estimate discussed in Model A. We use the higher mass loss value in “Model B” to As discussed in our presentation of Model A derive standoff distances as discussed above. above, the mass-loss rates estimates of Wood et al. (2005) assume that stellar wind velocities were identical to that for the Sun (400 km s−1 ). A recent theoretical reanalysis of the Wood et Supporting Online Material References al. (2005) data by Holzwarth and Jardine (2007) predicts higher terminal wind velocities among the more active stars, and correspondingly lower mass-loss rates. Further, Holzwarth and R.A. Armstrong, W. Compston, W. J. de Wit, I. Jardine (2007) claim that the three active stars S. Williams, The stratigraphy of the 3.5-3.2 Ga previously mentioned are anomalous, since Barberton greenstone belt revisited: A zircon ion microprobe study, Earth Planet. Sci. Lett. 101, 90 their coronal densities are less than an order of (1990). magnitude larger than that observed for the Sun (Wood and Linsky, 2006), yet their wind ram L.P. Black, S.L. Kamo, C.M. Allen, J.N. Aleinikoff, pressures are nearly two orders of magnitude D.W. Davis, R.J. Korsch, C. Foudoulis, TEMORA 1: a new zircon standard for Phanerozoic UPb higher. The Holzwarth and Jardine (2007) geochronology, Chemical Geology 200, 155 (2003). 9

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