The Milky Way is a barred spiral galaxy. As a consequence, the solar system revolves around the galaxy and carries out a small oscillation in the direction perpendicular to the dense galactic disk, with a period much shorter than its orbital period1. For very small amplitudes of oscillation, the disk-crossing period P 1/2 depends solely on the density ρ 0 in the galactic plane, via (with G being the gravitational constant, assuming a constant density disk, otherwise the period may be somewhat larger2). Previous determinations of the half-period range between 30 and 42 Ma2,3,4. The methodologies for measuring the density of the galactic disk can be classified into three categories. In the first approach, the known components are simply summed up, giving the total baryonic mass density at the galactic plane of about 0.09 to 4,5. The second approach is based on the vertical kinematics of stars6. Assuming that a given tracer population of stars is kinematically relaxed, there is then a relation between the vertical density of the tracer stars and their dispersion velocity. This enables derivation of the underlying vertical dependence of the gravitational potential and from it the density, yielding values from 0.07 to 2,3. These two approaches are often used to estimate the amount of dark matter (DM) in the disk. It was argued that the stellar kinematics are inconsistent with a higher end estimate of the central mass density7, implying that DM in the disk may account for the deficient mass. Since the Hipparcos data set is presently the most extensive astrometric data available, analyses based on it should be considered the most reliable. They appear to converge towards lower values of 0.10 to 2,3, suggesting that the unobserved DM in the disk is at most the amount expected from a spherical or oblate DM halo, around 0.01 to . The DM density is important because its exact value is essential for searches of weakly interacting massive particles8.

The third approach to derive the density of the galactic disk is based on the periodicity of the solar systems vertical oscillation (VO). The periodic perturbation of the Oort cloud should increase the population of comets crossing the Earth pathway, potentially leaving an imprint in the terrestrial cratering record. Estimates for cratering periodicity range from 26 to 36 Ma (e.g., ref. 9), but the sparse statistics are disputed10.

Paleo-climatic records could serve as alternative chronometers if a physical mechanism exists to link the solar system's vertical motion to the terrestrial climate. Several suggested mechanisms could potentially do so: 1) perturbation of comets in the Oort cloud that, after disintegration into dust, could potentially cool the climate11, 2) collision with interstellar gas clouds12, 3) climate modulation via cosmic rays13,14,15. In the latter case, the VO would translate into an oscillatory variation in the cosmic ray flux, because the cosmic rays density depends on the distance from the galactic plane16. In addition, the lower interstellar pressure would allow the heliosphere to puff up and increase the cosmic ray energy loses as they propagate into the solar system17.

Since the cosmic ray mechanism can potentially explain climate variations on longer time scales18, we will assume that the link does indeed operate and with it construct in what follows a model for the average climate. However, two points should be noted. First, any VO/climate correlation by itself does not prove that the climate link is through any particular mechanism. Second, the cosmic ray climate link is controversial and it should therefore not be taken for granted. For example, various criticisms were raised on the validity and implications of the long time scale correlations19, the cloud cover cosmic-ray correlation on the decade time scale20 and during Forbush decreases21, or whether the observed link between atmospheric ionization and the nucleation of small particles can affect the number density of cloud condensation nuclei22.

Here we use a new database of δ18O values over 488 Ma, which covers almost the entire Phanerozoic and that transcend the aforementioned limitations. We will show that it exhibits a very clear 32 Ma periodicity.