Very long solar periods and the radiocarbon record

The ∼ 200‐year periodicity in the time variations of atmospheric radiocarbon is shown to extend over the entire 8500‐year La Jolla record and appears to be associated with a longer period between about 1500 and 2000 years via amplitude, frequency, or phase modulation, or some combination of these; but the statistical certainty of the source and form of the modulation is hampered by the low signal/noise ratio of the two periods. Autocorrelations of the La Jolla sequence show that the record violates even weak stationarity; although the 200‐year period is well ordered in time, the appearance of other periods may be more sporadic. Significant cross correlation between the very long period and the modulation envelope about the neighborhood of the 200‐year line suggests an identity between the two manifestations of the long period, and modulation by a nonlinearity satisfying the rule that it have at least one nonvanishing derivative of odd order and n > 2. Commensurate segments of the La Jolla, Belfast, and Groningen radiocarbon records confirm the existence between 3900 B.C. and 3200 B.C. of other periods, particularly 150 and 300 years. A likely source of these periodic changes in the radiocarbon record is the sun because the source of the variations is time dependence of the cosmic ray flux on the atmosphere. Further evidence is the recently reported correlation of radiocarbon and bristlecone pine growth ring variations and the lack of observational evidence to support the very large change in the earth's main field required for a geomagnetic explanation, especially of the ∼200‐year period. If it can be confirmed that the sun is the source, the very long periods suggest as one possibility that the core of the sun is the ultimate source, though multiple convective zone dynamo eigenmodes are an equally conjectural possibility. An alternate source for the longer period is pressure variations of the local arm of the galaxy, but this model is not favored.