Science - USA (2019-08-30)

This term modulates the amplitude of eccen-

tricity and, e.g., the interval between consecutive

minima in a 2-Myr filter of eccentricity (Fig. 3).

Other solutions such as La10c ( 33 )alsoshow

a resonance transition around 50 Ma. How-

ever, the pattern for ZB18a is different before

55 Ma, which is critical for its better fit with

the data record from 58 to 53 Ma (smaller

RMSD; Table 1 and Fig. 1). For example,P 43 ≈

2 and ~1.6 Myr at ~59 and ~56 Ma in La10c but

is rather stable at ~1.5 to 1.6 Myr across this

interval in ZB18a. Briefly, to explain the geologic

record, our astronomical solution requires that

the Solar System is (i) chaotic and (ii) underwent

a specific resonance transition pattern between

~60 and 50 Myr BP.

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Zeebeet al.,Science 365 , 926–929 (2019) 30 August 2019 3of4

Fig. 2. Wavelet analysis of astronomical solution.Wavelet analysis ( 34 )of(A)h¼esinπand
(B)p=sin(I/2) sinWfrom our astronomical solution ZB18a (see text).g’sands’s indicate fundamental
frequencies of the Solar System’s eigenmodes (multiple frequencies are expressed in the spectrum
of a single planet). For example,g 3 andg 4 are loosely related to the perihelion precession of Earth’s and
Mars’orbits.The wavelet amplitude (red, peaks; blue, valleys) in, e.g., theg 3 andg 4 frequency band is
modulated by the period 1/(g 4 – g 3 )≈2.4 Myr for ages younger ~45 Ma, whereg 3 ≈1/74.61 kyr–^1 and
g 4 ≈1/72.33 kyr–^1 ( 6 ). Correspondingly, 1/(s 4 – s 3 )≈1.2 Myr. However, in our solution, the period
associated withg 4 – g 3 switches from ~1.5 Myr to ~2.4 Myr across the resonance transition around
50 Ma (arrow).The ratio (g 4 – g 3 ):(s 4 – s 3 )≈1:2 after ~45 Ma and closer to 1:1 before but appears irregular.

Fig. 3. Resonance
transition in selected
astronomical solutions.
Interval between consecu-
tive minima (Dtmin) in 2-Myr
Gaussian filter (±60%) of
Earth’s orbital eccentricity
for selected solutions
( 6 , 33 ). The rise ofDtmin
around 50 Ma in ZB18a and
La10c indicate resonance
transitions. However, note
distinct pattern of ZB18a
before 55 Ma. Hence our
solution ZB18a (closest
agreement with the data
record, Fig. 1) requires that
the Solar System underwent
a specific chaotic resonance
transition pattern between
~60 and 50 Myr BP.

30 35 40 45 50 55 60

Age (Ma)

1

1.5

2

2.5

3

3.5

Interval between min in 2-Myr ecc filter (Myr)

Resonance

Transitio

n

ZB18a

ZB17b

La10c

RESEARCH | REPORT