Lunar chronology model with the Chang’e-6 farside samples and implications for the early impact history

Abstract

The radiometric ages of the returned samples are the cornerstone of lunar cratering chronology models. However, all the previous samples were from the lunar nearside and the radiometric ages of those samples that can be associated with particular surfaces are <4.0 billion years. On 25 June 2024, Chang’e-6 successfully returned 1.935-kilogram samples from the lunar farside. The samples included local basalts with an age of 2807 ± 3 million years and the norites with an age of 4247 ± 5 million years likely corresponding to the age of the South Pole–Aitken basin. With these radiometric ages, we refined the lunar chronology function (CF) and verified that it is still consistent with a combination of an exponential decrease and a linear rate. We further derived the impacting rate and found it supports a smooth decay instead of abrupt changes of the impactor flux at early times. The refined lunar CF can be used to obtain more reliable ages for unsampled lunar areas and provide critical constraint for the lunar early impact history.

Ages of Chang’e-6 farside samples refine lunar cratering chronology model and indicate a smooth decline in early impact rate.

INTRODUCTION

Absolute ages are crucial for understanding the evolution of solar system bodies, but direct radiometric dating has thus far been extensively applied only to Earth. For unsampled regions on the Moon, absolute model ages (AMAs) are usually estimated by the crater size–frequency distribution (CSFD) method, e.g., refs. (1–4). As the core component of the CSFD method, the lunar chronology model [i.e., chronology function (CF)] depicts the relationship between the radiometric ages of the returned samples and the corresponding crater distribution densities at the sampling sites, e.g., refs. (1, 5–7). The cornerstone of lunar chronology model is the measured radiometric ages of the returned lunar samples. However, the samples used in the current lunar CF are all from the Moon’s nearside (1, 8). Samples from the lunar farside are essential to validate the CF’s applicability across the entire Moon. Moreover, the oldest samples currently used to establish the lunar CF are subject to considerable controversy (Supplementary Note 1). Thus, there is an urgent need for samples from the lunar farside and old geologic unit to determine whether the current model is applicable throughout the Moon and accurately represents the earlier lunar impacts.

As the first sample return mission in the human history from the lunar farside, China’s Chang’e-6 (CE-6) was launched on 3 May 2024, and it landed in the Apollo basin within the South Pole–Aitken (SPA) basin on the Moon on 2 June 2024 (figs. S1 and S2). The SPA basin is the largest and oldest impact basin on the Moon, and numerical simulations of the formation of the SPA basin suggest that extensive molten mantle material emerged and was redistributed across the impact basin floor (9, 10). The subsequent differentiation process likely resulted in an upper layer of noritic composition (11), aligning with spectral analyses of materials ranging from noritic (12) to mafic (13). The landing site (153.9856°W, 41.6383°S) is located in the southern basalt unit within the Apollo basin (fig. S1). Previous remote sensing studies have divided this basalt area into different units according to the mineral compositions (14–17), and CE-6 landed on the west part of the basalt unit (fig. S2). After landing on the Moon, CE-6 began scooping surface samples using a robotic arm and drilling subsurface samples. As a result, 1935.3-g samples were collected and were successfully returned to Earth on 25 June 2024 (18).

RESULTS

Refined lunar chronology model

We have conducted mineral and radiometric dating analyses of the scooped surface samples immediately after they were allocated by the China National Space Administration. Radiometric measurements using the Pb-Pb dating technique were made on both Zr-rich minerals and phosphates of the basalt samples and revealed the absolute age of the basalt unit where CE-6 landed was 2807 ± 3 million years (Ma) (19). This result is consistent to that reported in ref. (20). In addition, the norite samples plausibly represent the differentiated products of the SPA impact melt pool and they have been radiometrically dated to be 4247 ± 5 Ma (21). The corresponding crater frequencies are described in detail in Supplementary Note 1. It is worth noting that, when calculating the crater frequency for SPA basin, basaltic regions within the SPA basin should be excluded because their ages are notably younger than the SPA impact event. Larger craters should be preferentially used to minimize the influence of secondary craters, and a buffered non–sparseness correction method should be applied to account for the erosion of earlier craters by later-formed ones. These radiometric ages and their corresponding crater frequencies were then used to update the currently widely used lunar CF with the crater densities of the corresponding geological units.

Neukum (1) first fitted the lunar CF between the radiometric ages of Apollo and Luna samples and the crater frequencies N(1) in the corresponding areas, i.e., the total number of craters with diameter ≥ 1 km/km². However, more modern calibration points were derived with recently acquired high-resolution images, e.g., refs. (8, 22–25), in which both the sample ages and the corresponding N(1) values are updated. We carefully reviewed the relevant progresses and selected the most reliable results for use in this study (Supplementary Note 1). Table 1 lists the calibration points used by Neukum (1) and this research.

Table 1. Calibration points used in the Neukum model and this research.

The references for the calibration points are explained in Supplementary Note 1.

Site and mission	Chronology calibrations		Chronology calibrations in this study
	N(1) (km−2)	Age (Ga)	N(1) (km−2)	Age (Ga)
Highland (Terrae)	(3.6 ± 1.1) × 10−1	4.35 ± 0.10
Nectaris Basin (A16)	(1.2 ± 0.4) × 10−1	4.10 ± 0.10
Apennines (A15)	(3.5 ± 0.5) × 10−2	3.91 ± 0.10
Descartes Formation (A16)	(3.4 ± 0.7) × 10−2	3.90 ± 0.10
Fra Mauro Formation (A14)	(3.7 ± 0.7) × 10−2	3.91 ± 0.10	(3.82 ± 1.07) × 10−2	3.922 ± 0.012 (U-Pb dating)
Taurus Littrow Mare (A17)	(1.0 ± 0.3) × 10−2	3.70 ± 0.10	(1.06 ± 0.21) × 10−2	3.752 ± 0.007 (Pb-Pb dating)
Mare Tranquillitatis (old) (A11)	(9.0 ± 1.8) × 10−3	3.72 ± 0.10
Mare Tranquillitatis (young) (A11)	(6.4 ± 2.0) × 10−3	3.53 ± 0.05	(6.64 ± 0.561) × 10−3	3.578 ± 0.009 (Pb-Pb dating)
Mare Imbrium (A15)	(3.2 ± 1.1) × 10−3	3.28 ± 0.10	(2.23 ± 0.12) × 10−3	3.281 ± 0.012 (Pb-Pb dating)
Oceanus Procellarum (A12)	(3.6 ± 1.1) × 10−3	3.18 ± 0.10	(2.34 ± 0.05) × 10−3	3.242 ± 0.013 (Pb-Pb dating)
Mare Fecunditatis (L16)	(3.3 ± 1.0) × 10−3	3.40 ± 0.04	(4.32 ± 0.01) × 10−3	3.382 ± 0.014 (Ar-Ar dating)
Mare Crisium (L24)	(3.0 ± 0.6) × 10−3	3.30 ± 0.10	(2.54 ± 0.08) × 10−3	3.328 ± 0.021 (Ar-Ar dating)
Copernicus (A12)	(1.3 ± 0.3) × 10−3	0.85 ± 0.2	(6.68 ± 0.048) × 10−>4	0.80 ± 0.015 (Ar-Ar dating)
Tycho (A17)	(9.0 ± 1.8) × 10−5	0.109 ± 0.004	(7.12 ± 0.063) × 10−5	0.109 ± 0.004 (Kr-Kr dating)
North Ray (A16)	(4.4 ± 1.1) × 10−5	0.0500 ± 0.0014	(3.90 ± 0.043) × 10−5	0.0503 ± 0.0008 (Kr-Kr dating)
Cone (A14)	(2.1 ± 0.5) × 10−5	0.0260 ± 0.0008	(2.1 ± 0.5) × 10−5	0.0260 ± 0.0008 (Kr-Kr dating)
Phanerozoic craters (North America + Europe, lunar equivalent)	(3.6 ± 1.1) × 10−4	0.375 ± 0.075
Northern Oceanus Procellarum (CE-5)			(1.74 ± 0.022) × 10−3	2.030 ± 0.004 (Pb-Pb dating)
Mare Apollo (CE6)			(2.08 ± 0.13) × 10−3	2.807 ± 0.003 (Pb-Pb dating)
SPA basin (CE6)			(3.69 ± 0.48) × 10−1	4.247 ± 0.005 (Pb-Pb dating)

Figure S2 shows the two radiometric ages and corresponding N(1) values from the farside are within 95% confidence region of the lunar CF that were derived from the nearside data (Table 1). This suggests that the farside impact flux is similar to that of the nearside, which is consistent with previous theoretical analyses, e.g., refs. (6, 26, 27). The CE-6 samples supported the impact symmetry between the lunar nearside and farside, which provides a foundation to establish a universal crater CF cross the whole Moon. Therefore, the two radiometric ages and corresponding N(1) values along with previous datasets from Apollo, Luna, and Chang’e-5 missions (Table 1) are used to update the lunar CF through least-squares fitting. The resultant lunar cratering CF is as follows

$$N(1,t)=3.885\times {10}^{-15}(e^{7.595t}-1)+7.377\times {10}^{-4}t$$ (1)

Figure 1A shows the fitted model with all the data points. Figure 1B illustrates the model age differences between the refined model and the most widely used Neukum (1) model (i.e., refined model–Neukum model) with respect to the age derived from the Neukum (1) model. Compared with the Neukum (1) model, the refined model with the CE-6 samples gives older ages in most of the geologic ages regarding to the same crater frequency, whereas the case is reverse when the ages are >4.05 billion years (Ga). The maximum difference is 0.34 Ga at 2.58 Ga, which is well within the uncertainties of crater chronologies. It is noteworthy to observe that all of the datasets are within the 95% confidence interval of the refined lunar CF, indicating the good performance of the fitting. In addition, we also used the lunar meteorite age of 4.33 Ga (28) as the SPA basin age to fit the lunar CF, and there is not too much difference between them (the maximum difference is about 0.09 Ga; fig. S6).

Fig. 1. Refined lunar chronology model and comparison with a previous model.

(A) Refined lunar chronology model and 95% confidence interval along with all the radiometric ages. (B) Model age difference of the refined model with respect to the Neukum (1) model.

From the refined lunar cratering chronology model (1), the derived impact rate for D ≥ 1 km is as follows

$$\mathrm{\varphi }(1,t)=2.951\times {10}^{-14}{e}^{7.595t}+7.377\times {10}^{-4}$$ (2)

The result is shown in Fig. 2A in comparison with the model by Neukum (1). The frequency of impact events that produce craters 1 km or larger likewise exhibits an exponential decline before ~3.0 Ga and attains an almost invariant value afterward. The disparity in the impact rates yielding craters 1 km and larger between the two models is clearly illustrated in Fig. 2B. Before 3.91 Ga, the cumulative cratering rate derived from the refined model consistently surpasses that of the Neukum (1) model, with the divergence intensifying toward earlier epochs. Since 3.91 Ga to the present, the refined model presents a slightly lower cumulative impact rate and the maximum difference appears at 3.78 Ga. However, from 3.78 Ga to the present, the difference between the two models quickly diminishes until they are almost identical.

Fig. 2. Cratering rate and the difference between the refined model and the Neukum model.

(A) Cumulative cratering rates with respect to the model age of the refined model (red) and Neukum (1) model (blue). (B) Difference of the cumulative cratering rates between the two models [refined model–Neukum (1) model].

DISCUSSION

Implication for lunar early impact history

The oldest sample from CE-6, assumed to represent the SPA impact event (21), was used in fitting the refined CF model, providing a unique opportunity to constrain the early lunar impact history. Now, there are several hypotheses on the early impact history of the Moon, including the monotonically decreasing impact flux (1, 29–31), the Late Heavy Bombardment (LHB) at about 3.9 Ga (32–35), a sawtooth-like uptick impact flux earlier than about 4.1 Ga (36), etc. The hot debate on the early impact history of the Moon has further extended to the dispute over the source of lunar impactors, e.g., refs. (37–39). The reason for this controversy is that there were very few samples dating impacts before 4.0 Ga ago and a widespread signature of isotopic disturbance in the samples of ~3.9 Ga ago (39). CE-6 has arguably returned samples from the SPA basin, plausibly providing an important “anchor point” to address this issue. Figure 3 shows the comparison between the crater CF calibrated with the proposed SPA age and others (Table 1). The blue solid line is the sawtooth-like model (36), and the blue dashed line is translated to the refined model according to the cumulative cratering rate between 3.5 and 4.1 Ga (see Materials and Methods). It can be observed that the SPA age obviously deviates from the sawtooth-like model. Substantial deviations also appear from the LHB model, and similar situations also appear in the samples of the Fra Mauro Formation (3.922 Ga). Therefore, the new observations do not support these theoretical models with abrupt changes. If we adopt the 4.33 Ga age of the lunar meteorite for the SPA basin (28), the result also does not support the LHB model (fig. S7).

Fig. 3. Comparison of the cumulative crater frequency N(>20 km) between previous models and the result in this study.

The red solid line represents the result obtained using Eq. 1 in this paper, as well as the relationship between N(20) and N(1); the blue solid line is the result from ref. (36), and the blue dashed line represents the result normalized to this study based on the cumulative impact rate between 3.5 and 4.1 Ga; the cyan dashed line shows the results for the LHB from ref. (31). The black dots indicate measurements from Apollo samples, whereas the red cross represents the result from the potential SPA sample returned by the CE-6 mission.

In summary, a refined lunar cratering chronology model based on the radiometric ages of CE-6 samples is presented, assuming one of them represents the time of the SPA impact. The result indicates that a summation of an exponential equation and a linear equation is applicable to describe the chronology model, and correspondingly the impact rate rapidly decreased before about 3.0 Ga and then gradually slowed down to its current level. No clear evidence from the newly returned samples was found to support that the impact flux on the Moon sharply increased around 3.9 Ga ago. Overall, the refined lunar chronology model is not substantially different from the widely used Neukum (1) model, which was based solely on samples from the nearside of the Moon. This suggests that the impact flux on the lunar nearside does not differ substantially to that on the farside. The refined model will enhance the reliability when estimating ages with the CSFD method, and we suggest that they be used in lunar surface dating in the future.

MATERIALS AND METHODS

Lunar crater CF fitting

Like the previous lunar crater CF proposed by Neukum (1), the current model is also expressed as the sum of an exponential equation and a linear equation. The coefficients of the CF were solved iteratively using the nonlinear least-squares fitting algorithm (40, 41), with the coefficients of the Neukum (1) model being the initial values. The residual function used in the nonlinear fitting is expressed as follows

$$\mathit{err}=1-\frac{f\left(x_i\right)}{y_i}$$ (3)

where $f\left(x_i\right)$ represents the ith N(1) value obtained from the fitting function, and $y_i$ is the ith observed N(1) value. The errors obtained from the above function follow a normal distribution according to the Shapiro-Wilk test (42), indicating that the above nonlinear fitting algorithm has good performance. The fitting result is shown in Fig. 1, and the comparison of the fitting result with other models can be seen in figs. S3 and S4.

To analyze whether the datasets related with the two samples on the lunar farside is consistent with the lunar CF only with the lunar nearside samples, we first calculated the 95% confidence interval of the fitted lunar CF and it can be expressed as follows

$$\frac{f\left(x_i\right)}{1+1.96\mathrm{\sigma }}<y<\frac{f\left(x_i\right)}{1-1.96\mathrm{\sigma }}$$ (4)

where $\mathrm{\sigma }$ is the SE during the fitting, and $f\left(x_i\right)$ is the calculated N(1) value according to the fitting function. The above result, along with the datasets from CE-6 samples, is shown in fig. S1. The CE-6 data points fall within the 95% confidence interval of the lunar crater CF curve obtained using only samples from the lunar nearside, indicating a high degree of consistency between the impact flux on the farside of the Moon and that on the nearside.

Translation of the sawtooth-like model

There is a systematic offset between the sawtooth-like model provided in ref. (36) and the refined model obtained in this paper. To facilitate comparison of the impact flux predictions for the early Moon, it would be best to translate the sawtooth-like model so that the curves align roughly within the time period less than 4.1 Ga. The specific method to achieve this translation is based on the systematic offset between the two models since 4.1 Ga. The approach is to find an optimal factor that, when multiplied by the entire curve, achieves the translation.

Generally, if two CFs [denoted as $N_s\left(t\right)$ and $N_n\left(t\right)$] overlap at only one age $t_1$, the $N_n\left(t\right)$ CF can be translated to $N_s\left(t\right)$ CF by simply multiplying a scaling factor $c=\frac{N_s\left(t_1\right)}{N_n\left(t_1\right)}$. The CFs of $N_s\left(t\right)$ and $N_n\left(t\right)$ overlap over many ages, and the goal is to find the optimal factor so that the two CF curves coincide as closely as possible after translation. In this study, the sawtooth-like model and the refined model are considered to be consistent since 4.1 Ga. Therefore, the optimal factor $\overline{c}$ should satisfy the following condition: After translating the sawtooth-like model, the sum of the squared differences between the two CFs at the same ages should be minimized. This is the residual function, based on which the optimal factor is expressed as follows

$$\overline{c}=\frac{{\displaystyle \sum _{i=1}^m}[N_s\left(t_i\right)·N_n\left(t_i\right)]}{{\displaystyle \sum _{i=1}^m}{\left[N_n\left(t_i\right)\right]}^2}$$ (5)

where m represents the total number of ages used for the translation.

Supplementary Materials

The PDF file includes:

Supplementary Note 1

Figs. S1 to S7

Legend for code S1

References

Other Supplementary Material for this manuscript includes the following:

Code S1