Untitled Document
## The relevance of parametric U-uptake models in ESR
age

Rainer Grün

* Research School of Earth Sciences, The
Australian National University, Canberra, ACT 0200,
Australia*

*Figure
1. Compilation of p-values from cave sites*

A: p-values from dentine

B: p-values from enamel

C: Relationship between p(EN), p(CE) and p(DE).

Ever since the inception of ESR dating of tooth enamel, it was clear
that the unknown uranium uptake history has to be addressed in dose rate
calculations. Various parametric models have been proposed for the reconstruction
of U-uptake in dental tissues, notably early (EU), linear (LU) and very
recent (RU) uptake. The EU model has some physical meaning, it presents
the closed system and provides the minimum age. The RU model is physically
less meaningful, but provides the maximum age. The main virtue of these
parametric models lies mainly in their reasonable simple computability.
Nevertheless, many publications have either favoured a particular U-uptake
model, for the convenience of being able to explain a dating result,
or claimed that the correct age of the sample lied somewhere between
the EU and LU results. However, without any knowledge of the U-uptake
history, it is only safe to assume that the correct age of a sample lies
somewhere between the EU and RU calculations. Depending on the contribution
of the U in the dental tissues to the total dose rate, this difference
ranges between negligible and utterly enormous.

U uptake can be modelled by combining ESR and U-series
data. Although the explicit U-uptake in nature may occur in multiple
phases, two models can bracket virtually all possible scenarios, as long
as no U-leaching occurs. Grün et al. (1988) used a smooth diffusion function: U(t)
= U_{m} (t/T)^{p+1}, where U(t) is the uranium concentration
at the time t, U_{m} the measured, present day U-concentration,
T the age of the sample and p the uptake parameter. This system provides
minimum age estimates for given ESR/U-series data sets. A delta function,
where U_{m} is accumulated instantly at the apparent closed system U-series
age of the dental tissue, provides the maximum age. For younger samples,
the differences between these two models are relatively small, which
means that the explicit U-uptake history has little effect on the age
calculation. For older samples (> 700 ka), with larger differences
between the closed system U-series and ESR age estimates, the differences
may be large (by more than a factor of 2).

To get more general insights into the general behaviour of U-uptake,
published p-values were compiled and separated into two groups, from
cave sites (and rock shelters) and open air sites. For the cave sites,
most of the p-values of the dentine fall between about -1 and 1, but
still a significant number give higher values (Figure 1A). All enamel
values fall within -1 and 0.5 (Figure 1B). Note, however, that many of
the teeth with high p-values in the dentine had not their enamel analysed
(partly because of low U-concentrations). Most of the measured p-values
in cement, p(CE), indicate a more rapid accumulation in cement than dentine
(Figure 1C). This is expected, as the cement is located on the outside
of the tooth. The relationship between p(EN) and p(DE) is random, most
values lying in a band of 0.5 around the 1:1 line. The results on the
open air sites are markedly different (Figure 2). Most p(DE) and p(EN)
lie outside the -1 to 0 range (Figures 2A and B). A large number of results
show p-values of > 2. There is no trend whether enamel or dentine
experienced a faster uptake (Figure 2C). The p(CE) values are reasonably
close to p(DE). For open air sites it is impossible to define a range
of p-values that could be used for general approximations. It is even
not possible to claim that the correct uptake is somewhere between EU
and RU, because there is a significant number of sites where model violations
have been observed (the closed system U-series age is older than the
corresponding ESR age) or U-leaching (with ^{230}Th/^{234}U ratios lying outside
the isotope evolution diagram).

In the former case it is not unequivocally
clear whether U-leaching has occurred of whether the ESR results underestimate
the correct age because of problems with the distributions of the orientated
and non-orientated CO_{2}^{-} radicals (Grün et al. 2008a), thermal transfer
processes (Joannes-Boyau and Grün, submitted), reworking of samples,
or the usual vagrancies in dose rate estimation. Leaching has been observed
in a range of sites (Grün et al. 2008b, Grün, unpublished data).

*Figure 2.Compilation
of p-values from open air sites*

A: p-values from dentine

B: p-values from enamel

C:Relationship between p(EN), p(CE) and p(DE).

The differences between cave and open air sites can
probably be explained through the different sedimentological histories
of the sites. Caves are systematically excavated because archaeologists
know that ancient humans preferred to live in rock shelters and caves.
Until excavated, the sedimentary stack is usually undisturbed. In contrast,
many open air sites are discovered because erosion, starting at some
time in the past, had provided an indication that a site was present.
Erosion causes changes in the hydrological environment, e.g., by re-activation
of drainage and changing the ground water table. This is accompanied
with renewed U-mobilisation. Not surprisingly, many U-series age estimates
of open air sites seem to reflect this change in the hydrology rather
than the age of the sample.

To conclude, the statement that the correct
ESR age of a sample probably lies somewhere between the EU and LU uptake
age calculations is incorrect. It is not even true that the correct age
lies always somewhere between the EU and RU model calculations, because
there have been occasions of model violations and U-leaching. Any ESR
dating study on teeth with substantial U concentrations in the tissues
requires U-series age estimates. Anything else is simply a tenesmic approach
to dating.

Grün, R., Aubert, M., Joannes-Boyau, R., Moncel, M.H. (2008a) High
resolution analysis of uranium and thorium concentrations as well as
U-series isotope distributions in a Neanderthal tooth from Payre using
laser ablation ICP-MS. Geochimica Cosmochimica Acta 72: 5278-5290.

Grün, R., Joannes-Boyau, R., Stringer, C. (2008b) Two types of CO_{2}^{-} radicals threaten the fundamentals of ESR dating of tooth enamel. Quaternary
Geochronology 3: 150-172.

GrĂ¼n, R., Schwarcz, H.P. and Chadam, J.M. (1988) ESR dating of
tooth enamel: Coupled correction for U-uptake and U-series disequilibrium.
Nuclear Tracks and Radiation Measurements 14: 237-241.

Joannes-Boyau, R., Grün, R. (submitted). Thermal behaviour of orientated
and non-orientated CO_{2}^{-} radicals in tooth enamel. Radiation Measurements.