[orcid = 0000-0001-5842-6985]

[1]

[1]

Conceptualization, Methodology, Software, Writing - Original Draft

1]organization=Department of Earth Sciences, addressline=University of Oxford,
South Parks Road, city=Oxford, postcode=OX1 3AN, country=UK

[orcid = 0000-0002-5675-8545] Conceptualization, Writing - Review & Editing,
Supervision

[orcid = 0000-0003-2947-5694]

Conceptualization, Writing - Review & Editing, Supervision

[cor1]Corresponding author

# Early and elongated epochs of planetesimal dynamo generation

Hannah R. Sanderson<EMAIL_ADDRESS>[  James F.J. Bryson
Claire I.O. Nichols

###### Abstract

Accreting in the first few million years (Ma) of the Solar System,
planetesimals record conditions in the protoplanetary disc and are the
remnants of planetary formation processes. The meteorite paleomagnetic record
carries key insights into the thermal history of planetesimals and their
extent of differentiation. The current paradigm splits the meteorite
paleomagnetic record into three magnetic field generation epochs: an early
nebula field ($\lesssim$5 Ma after CAI formation), followed by thermal dynamos
($\sim$5–34 Ma after CAI formation), then a gap in dynamo generation, before
the onset of core solidification and compositional dynamos. These epochs have
been defined using current thermal evolution and dynamo generation models of
planetesimals. Here, we demonstrate these epochs are not as distinct as
previously thought based on refined thermal evolution models that include more
realistic parametrisations for mantle convection, non-eutectic core
solidification, and radiogenic $\rm{}^{60}Fe$ in the core. We find thermal
dynamos can start earlier and last longer. Inclusion of appreciable
$\rm{}^{60}Fe$ in the core brings forward the onset of dynamo generation to
$\sim$1–2 Ma after CAI formation, which overlaps with the existence of the
nebula field. The second epoch of dynamo generation begins prior to the onset
of core solidification, suggesting this epoch is not purely compositionally
driven. Planetesimal radius is the dominant control on the strength and
duration of dynamo generation, and the choice of reference viscosity can widen
the gap between epochs of dynamo generation from 0–200 Ma. Overall, variations
in planetesimal properties lead to more variable timings of different
planetesimal magnetic field generation mechanisms than previously thought.
This alters the information we can glean from the meteorite paleomagnetic
record about the early Solar System. Evidence for the nebula field requires
more careful interpretation, and late paleomagnetic remanences, for example in
the pallasites, may not be evidence for planetesimal core solidification.

###### keywords:

planetary magnetic fields thermal evolution meteorite magnetism planetesimals
dynamo activity mantle viscosity

Planetesimal thermal dynamos can begin before the dissipation of the nebula
field.

Core solidification is not required to trigger a second epoch of dynamo
generation.

Planetesimal dynamos can last several 100 Ma longer than previously thought.

Planetesimal radius and reference viscosity have a strong effect on dynamo
duration.

##  1 Introduction

The strength and duration of magnetic fields generated within planetesimals
can provide unique insight into the differentiation and thermal histories of
rocky bodies in the early Solar System. For a rocky body to internally
generate a magnetic field (a dynamo), it must have a partially molten metallic
core in which flow is being driven, for example by convection. Magnetic
remanences recorded by meteorites indicate that some planetesimals met these
criteria during their thermal history, providing evidence for planetesimal
differentiation and vigorous core convection.

Three strands of investigation can be combined to allow observations of
magnetic field generation in planetesimals to constrain planetesimal
behaviour. Firstly, magnetic remanences measured from meteorites have provided
evidence for dynamos on specific parent bodies and radiometric dating of these
meteorites provide estimates for the age of dynamo activity (e.g. Maurel et
al., 2020). Secondly, thermal evolution models can be used to explore parent
body properties, such as radius and accretion time, for which the requirements
for magnetic field generation are met (e.g. Dodds et al., 2021). For undated
magnetic remanences, thermal evolution models can provide possible dynamo
timing constraints, for example based on the timing of core crystallisation
(e.g. Tarduno et al., 2012; Bryson et al., 2015; Maurel et al., 2020; Nichols
et al., 2021). Finally, thermal evolution models can also predict whether a
remanence is likely to have a dynamo or solar nebula origin (e.g. Bryson et
al., 2019a; Dodds et al., 2021). Thermal evolution models to-date include
incomplete or simplified physical descriptions of planetesimals. Here, we use
refined thermal models to re-evaluate the meteorite paleomagnetic record.

###  1.1 Meteorite paleomagnetic record

Figure 1: The meteorite paleomagnetic record. Blue and red boxes indicate
undifferentiated (chondritic) meteorite groups and green, yellow and pink
boxes indicate differentiated (achondritic) meteorite groups. Blue and black
arrows represent magnetic remanences dated using radiometric methods and
thermal evolution models, respectively. Solid arrows with filled caps indicate
magnetised samples and dashed arrows with unfilled caps indicate unmagnetised
samples. For the angrites, the time range is so short that only the arrowheads
are visible. Multiple measurements for the same meteorite group are combined,
but measurements of bulk magnetisation vs chondrules are kept separate to
distinguish between pre-accretionary and post-accretionary remanences. Unlike
the other chondrules, the CV chondrules remanence is not pre-accretionary,
because the CV chondrules have experienced aqueous alteration, thermal
metamorphism, and possibly brecciation (Fu et al., 2014a; Shah et al., 2017).
The data table shown in this plot and references for each measurement can be
found in the Supplementary Materials.

Meteorites with similar isotopic compositions are assumed to come from the
same parent body and form a group. Paleomagnetic measurements have been
recovered from both differentiated (achondritic) and undifferentiated
(chondritic) meteorites from both the outer (carbonaceous) and inner (non-
carbonaceous) Solar System (Figure 1).

Three possible sources have been proposed for these magnetisations: the nebula
field in the protoplanetary disc, which existed prior to $\sim$4–5 Ma after
calcium-aluminium-rich inclusion (CAI) formation (e.g. Fu et al., 2014a; Wang
et al., 2017; Fu et al., 2020; Borlina et al., 2021; Bryson et al., 2023;
Maurel and Gattacceca, 2024); internally generated dynamos (e.g. Tarduno et
al., 2012; Wang et al., 2017; Bryson et al., 2019b); and the solar wind
(Tarduno et al., 2017; O’Brien et al., 2020). Magnetisation from the solar
wind has been proposed to be three to four orders of magnitude too weak to
explain meteorite paleomagnetic remanences (Oran et al., 2018). Remanences
from the nebula field can be identified by randomly oriented chondrule
magnetisation directions (e.g. Fu et al., 2020).

Paleomagnetic remanences can be dated radiometrically if the closure
temperature of the radiometric system is close to the blocking temperature of
the magnetised mineral. Remanences dated to $<4$ Ma after CAI formation have
been interpreted to have a nebula origin due to the delay in the onset of
dynamo generation predicted by previous dynamo models (Dodds et al., 2021).
Meanwhile, remanences that were acquired after the dissipation of the nebula
field, $\sim$4–5 Ma after CAI formation (Weiss et al., 2021), are thought to
originate from planetesimal dynamos. For systems where radiometric dating is
not possible or extrapolation from a dated closure temperature to the Curie
temperature is required, thermal evolution models can be used to predict the
timing of dynamo generation. For example, this method was used to estimate an
age for the Main Group pallasite remanant magnetisation based on the timing of
core crystallisation (Tarduno et al., 2012).

###  1.2 Thermal evolution models

Two mechanisms of dynamo generation are considered by thermal models: thermal
dynamos, where temperature-induced density differences drive core convection;
and compositional dynamos, where density differences between solidifying pure
iron and the liquid core enriched in incompatible light elements drive
convection. For thermal dynamos, the superadiabatic portion of the core-mantle
boundary (CMB) heat flux determines the timing and strength of magnetic field
generation. Modelling compositional dynamos requires assumptions regarding the
mechanism of planetesimal core solidification. The lower pressures at their
CMB compared to planets ($\leq$0.5 GPa compared to $\geq$8 GPa) mean
planetesimal cores solidify inwards rather than nucleation occurring at the
centre of the core (Williams, 2009). Several mechanisms for inward core
solidification have been proposed, including iron snow where solid iron
particles form at the CMB and then fall to the centre of the core triggering
convection (Rückriemen et al., 2015; Scheinberg et al., 2016) and delamination
of large iron diapirs from the CMB (Neufeld et al., 2019). Due to the
complexity of these mechanisms, previous thermal evolution models of mantled
planetesimals either ended after the cessation of mantle convection but prior
to core solidification (Sterenborg and Crowley, 2012; Dodds et al., 2021) or
used the duration of eutectic core solidification as a first estimate of the
timings of compositional dynamo duration (Bryson et al., 2019a; Nichols et
al., 2021). Models of outward non-eutectic core solidification have been
attempted but either did not model the full history of the body, or only
considered cooling by mantle conduction (Nimmo, 2009; Nichols et al., 2021).

Previous thermal evolution models (e.g. Sterenborg and Crowley, 2012; Bryson
et al., 2019a; Dodds et al., 2021) that successfully generate dynamos predict
several events in the thermal evolution:

  1. [(i)]

  2. 1.

Following instantaneous accretion or during gradual accretion, planetesimals
are heated by $\rm{}^{26}Al$ decay, causing the body to differentiate into a
metallic core and silicate mantle.

  3. 2.

Following differentiation, $\rm{}^{26}Al$ preferentially partitions into the
silicate mantle. After further heating, the melt fraction in the mantle is
high enough to initiate mantle convection. The core is heated by the mantle
from above and develops a stable thermal stratification that prevents the
onset of a dynamo.

  4. 3.

Once the mantle cools below the temperature at the CMB, the core thermal
stratification is removed and the CMB heat flux becomes superadiabatic. Core
convection triggers the onset of thermal dynamo generation.

  5. 4.

As the mantle cools, it becomes more viscous until mantle convection ceases.
The cessation of mantle convection leads to a sharp decrease in CMB heat flux
and core convection drops below the critical value, terminating the dynamo.

  6. 5.

Eventually the core cools below its solidus temperature and begins to
solidify, which can lead to a compositional dynamo and a second epoch of
dynamo generation.

  7. 6.

Once the core has fully solidified, dynamo generation is no longer possible.

These previous models predict two epochs of dynamo generation: an early
thermal dynamo,and a second later compositional dynamo during core
solidification. This has led to paleomagnetic remanences $>$65 Ma after CAI
formation being interpreted as evidence of a solidifying core (Bryson et al.,
2015; Nichols et al., 2016, 2021; Maurel et al., 2021) and remanences $<$4 Ma
after CAI formation being interpreted as a record of a nebula field due to the
delay in start time of thermal dynamos caused by core thermal stratification
(Bryson et al., 2019a, 2020a; Fu et al., 2021).

The assumptions made in these earlier models are re-explored here. First,
previous models neglect heating from $\rm{}^{60}Fe$ in the core, because for
low values of primordial $\rm{}^{60}Fe$, such that
$\rm{}^{60}Fe/^{56}Fe$=$10^{-8}$ (Tang and Dauphas, 2012), only a very small
difference in core temperature ($\sim$10 K) results over the lifetime of the
planetesimal (Henke et al., 2013). However, new measurements suggest
$\rm{}^{60}Fe/^{56}Fe$ may have been as high as $6\pm 2\times 10^{-7}$ in the
formation region of carbonaceous chondrites (Cook et al., 2021). Therefore,
the role $\rm{}^{60}Fe$ on planetesimal core thermal evolution should be
explored for a wider range of values.

Second, previous thermal evolution models do not fully combine thermal and
compositional dynamo generation, mantle convection, and non-eutectic core
solidification. This limits the ability of existing thermal evolution models
to predict the full magnetic history of a body.

Third, the effect of mantle viscosity on magnetic field generation has not
been investigated in previous thermal models. CMB heat flux is limited by the
cooling rate of the mantle above and the thickness of the CMB boundary layer,
which are both governed by the mantle viscosity. Therefore, the
parameterisation of mantle viscosity as a function of temperature has a
critical role in planetesimal thermal evolution.

Sanderson et al. (2024) present a new, refined model, that accounts for all
the points discussed above. Here, we apply this new model across the full
range of realistic parameters to reassess the existing meteorite paleomagnetic
record.

##  2 Methods

This study uses the 1D spherically symmetric planetesimal thermal evolution
and dynamo generation model from Sanderson et al. (2024) to predict the
timings of dynamo generation in planetesimals with a radius up to 500 km. This
model builds on the previous planetesimal thermal evolution models of
Sterenborg and Crowley (2012), Bryson et al. (2019a) and Dodds et al. (2021)
by including radiogenic heating from $\rm{}^{60}Fe$ in the core, an adjustable
mantle viscosity law, and updated stagnant lid and CMB boundary layer
parametrisations that better reflect mantle conditions. The model includes
both convection and conduction in the mantle and models magnetic field
generation by non-eutectic core solidification. The details and complete
mathematical description of this model can be found in Sanderson et al.
(2024).

###  2.1 Thermal evolution model

All model runs begin at 0.8 Ma after CAI formation with instantaneous
accretion of the planetesimal at 200 K. The body heats up due to radiogenic
heating of $\rm{}^{26}Al$ and the Fe-FeS and silicate phases melt until the
silicate reaches its critical melt fraction, $\phi_{C}$. At this point,
differentiation is assumed to take place instantaneously, as the molten, dense
Fe-FeS sinks through the rheologically weak silicates to the centre. The model
then consists of two coupled reservoirs: the Fe-FeS core and the silicate
mantle. Sulfur is the only light element considered in the core. The surface
temperature is held constant at 200 K throughout the simulation.

In the mantle, heat is transported either by conduction or convection. Mantle
convection is assumed to occur in the stagnant lid regime with an isothermal,
convective layer between conductive boundary layers at the CMB and the
surface. These boundary layers thicken as the mantle cools and convection
ceases once the combined CMB and surface boundary layer thicknesses reach the
total mantle thickness. The temperature at the CMB is calculated by assuming
continuity of heat flux across the boundary.

The core also transports heat by conduction or convection. For the core to
convect, either the CMB heat flux, $F_{\rm CMB}$, must be superadiabatic or
the core must be undergoing non-eutectic solidification. During inward core
solidification, the density difference between the more dense, solidified pure
iron and the less dense Fe-FeS liquid drives core convection, as the solidifed
iron sinks to the centre of the core. When the core is convecting, the
combined thermal and compositional buoyancy flux can be used to calculate a
magnetic field strength (see Sanderson et al., 2024, for details). Once the
eutectic composition is reached, core solidification no longer generates a
compositional buoyancy flux. Combining buoyancy flux contributions enables the
thermal and compositional drivers of convection to be considered
simultaneously. The model ends once the whole core has solidified and dynamo
generation is no longer possible.

####  2.1.1 Dynamo generation

The vigour of convection in the liquid part of the core is characterised by
the magnetic Reynolds number, $Re_{m}$, which must be supercritical for the
core flow to be strong enough to generate a magnetic field. The analytical
estimate of the critical value is 10, while from empirical simulations this
value ranges from 40–100 (Stevenson, 2003; Aubert et al., 2009). We use a
critical $Re_{m}$ of 10 in line with previous work (Bryson et al., 2019a;
Dodds et al., 2021). However, the proportions of model runs with $10\leq\rm
Re_{m}<40$, $40\leq\rm Re_{m}<100$, and $Re_{m}\geq 100$ are also
investigated.

###  2.2 Parameter variation

Models were run for a range of mantle viscosities, planetesimal radii, initial
core sulfur contents, $\rm X_{S,0}$, and $\rm{}^{60}Fe/^{56}Fe$ ratios in the
accreted material (Table 1).

The temperature dependence of mantle viscosity is defined piece-wise (Figure
2) by five control parameters. Below the solidus, the viscosity has an
Arrhenius temperature dependence with slope $\beta$, which is proportional to
the activation energy for viscous deformation. At the solidus, the mantle has
a reference viscosity, $\eta_{0}$. Above the solidus, melt weakens the
material and the viscosity decreases with a steeper Arrhenius dependence,
quantified by the melt weakening exponent, $\alpha_{n}$ (Hirth and Kohlstedt,
2003). At the critical melt fraction, $\phi_{C}$, there is enough melt to
completely surround any remaining solid phases and the material disaggregates
with a rapid drop in viscosity. Beyond $\phi_{C}$, the viscosity tends to a
constant liquid viscosity, $\eta_{l}$, following the Krieger-Dougherty
relation (Sturtz et al., 2022b) as the melt fraction tends to one.

Each parameter was varied independently while the others were held constant at
the median value of their range, except $\phi_{C}$ where the constant value
was the experimental upper bound. The justifications for each parameter range
are detailed in the following subsections.

Figure 2: Illustration of parameters varied in the mantle viscosity model.
Reference viscosity, $\eta_{0}$=$10^{14}$–$10^{24}$ Pas, is the viscosity at
the mantle solidus. Liquid viscosity, $\eta_{l}$=1–100 Pas, is the viscosity
when the mantle is fully molten. Critical melt fraction, $\phi_{C}$ =0.2–0.5,
is the melt fraction for which all crystals become surrounded by melt, the
material disaggregates and becomes rheologically weak. Arrhenius slope,
$\beta$=0.01–0.035 $\rm K^{-1}$, determines the rate of decrease in viscosity
with increasing temperature. Melt weakening exponent, $\alpha_{n}$=25–40,
determines the additional rate of decrease in viscosity with increasing
temperature due to melting.

####  2.2.1 Reference viscosity, $\eta_{0}$

The reference viscosity, $\eta_{0}$, ranges from $10^{14}$–$10^{24}$ Pas. The
lower bound is based on experimental measurements (Scott and Kohlstedt, 2006)
while the upper bound is set by extrapolating reference viscosities used in
models of Ganymede (Rückriemen et al., 2018) to planetesimal mid-mantle
pressures (see Appendix A).

####  2.2.2 Critical melt fraction, $\phi_{C}$

Experiments suggest the critical melt fraction, $\phi_{C}$, is between 0.2–0.3
(Scott and Kohlstedt, 2006). However thermal evolution models of planetesimals
both for dynamo generation (Sterenborg and Crowley, 2012; Bryson et al.,
2019a; Dodds et al., 2021) and differentiation (e.g. Lichtenberg et al., 2019;
Monnereau et al., 2023) use a value of $\phi_{C}$=0.5. Although it is unclear
if $\phi_{C}$ =0.5 is physically reasonable, we adopted the range $\phi_{C}$
=0.2–0.5 to enable comparison with previous models and encapsulate
experimental observations.

####  2.2.3 Arrhenius slope, $\beta$

The Arrhenius slope in the viscosity law, $\beta$, is typically defined as
$\frac{E}{RT_{\text{ref}}^{2}}$, where $E$ is the activation energy, $R=8.31$
J$\rm mol^{-1}K^{-1}$ is the gas constant, and $T_{\text{ref}}$ is a reference
temperature - often taken to be the temperature at which the reference
viscosity is measured. Experimentally measured activation energies for a range
of silicate mantle compositions and strain rates range from 240–570 kJ mol-1
(Karato and Wu, 1993; Hirth and Kohlstedt, 2003). For a reference temperature
of the mantle solidus (1400 K), this corresponds to
$\beta$=0.015–0.035$K^{-1}$. Dodds et al. (2021) used $\beta=0.01\,K^{-1}$, so
to enable comparison with previous thermal evolution models, we explore
$\beta=$ 0.01–0.035 $K^{-1}$.

####  2.2.4 Melt weakening exponent, $\alpha_{n}$

The melt weakening exponent, $\alpha_{n}$, depends on whether deformation
occurs by diffusion creep ($\alpha_{n}=$ 25–30) or dislocation creep
($\alpha_{n}=$ 30–45) (Hirth and Kohlstedt, 2003). To cover both deformation
modes we consider values from 25–45.

####  2.2.5 Liquid viscosity, $\eta_{l}$

The liquid viscosity, $\eta_{l}$, is determined by mantle composition and can
range from 1–100 Pas across the compositions of all volcanic rocks commonly
encountered on Earth (Giordano et al., 2008). Increasing silica content
increases viscosity and increasing volatile content decreases viscosity
(Lesher and Spera, 2015).

####  2.2.6 Initial core sulfur content, $\rm X_{S,0}$

The initial core sulfur content, $\rm X_{S,0}$, ranges from the minimum Fe-FeS
sulfur content for which the metal phase will be fully molten before
differentiation to the eutectic composition (33 wt% for $T_{s,Fe}=1260$ K for
R=300 km). The Fe-FeS liquidus temperature is pressure dependent so the
minimum Fe-FeS changes with planetesimal radius.

####  2.2.7 Primordial $\rm{}^{60}Fe/^{56}Fe$

Estimates on the primordial $\rm{}^{60}Fe/^{56}Fe$ vary by almost two orders
of magnitude from $10^{-8}$ (e.g. Tang and Dauphas, 2012) to $6\times 10^{-7}$
(e.g. Cook et al., 2021). However, previous thermal evolution and dynamo
models neglected the presence of $\rm{}^{60}Fe$ in the core. Therefore, the
model was run for five values of $\rm{}^{60}Fe/^{56}Fe$ $=[0,1\times
10^{-9},1\times 10^{-8},1\times 10^{-7},6\times 10^{-7}]$ to cover the full
range of possible values and to compare with previous models.

####  2.2.8 Planetesimal radius, r

Models were run for planetesimal radii between 100–500 km. The lower limit is
set by previous estimates for the minimum radius for compositional dynamo
generation (Nimmo, 2009). The upper limit corresponds approximately to the
radius of Ceres, the largest known asteroid today.

Symbol | Meaning | Range of values | Constant value | Reference
---|---|---|---|---
$\eta_{0}$ | Reference viscosity |  $10^{14}$–$10^{24}$ Pas |  $10^{19}$ Pas | a, b
$\phi_{C}$ | Critical melt fraction | 0.2–0.5 | 0.3 | a, c
$\beta$ | Arrhenius slope | 0.01–0.035 $K^{-1}$ | 0.0225 $K^{-1}$ | a, d, e
$\alpha_{n}$ | Melt weakening exponent | 25–45 | 30 | f
$\eta_{l}$ | Liquid viscosity | 1, 10, 100 Pas | 10 Pas | g
$\rm X_{S,0}$ | Initial core sulfur content | 26.7–33 wt% | 29.85 wt% |
$\rm{}^{60}Fe/^{56}Fe$ |  $\rm{}^{60}Fe/^{56}Fe$ in accreting material | 0, $10^{-9}$, $10^{-8}$, $10^{-7}$, $6\times 10^{-7}$ | $10^{-8}$ | h, i, j, k
r | Planetesimal Radius | 100–500 km | 300 km | c
Table 1: Values for variable and constant parameters in simulations as
described in Section 2.2. The upper five parameters occur in the viscosity
law. The range on $\rm X_{S,0}$ is for a 300 km radius planetesimal. For [500,
400, 200, 100] km radius planetesimals the minimum and median $\rm X_{S,0}$
were [25.9, 26.3, 27.1, 27.1] wt% and [29.45, 29.65, 30.05, 30.05] wt%
respectively. The constant values are median values in their range, except
$\phi_{C}$ where the constant value was the experimental upper bound.
$\eta_{l}$ and $\rm{}^{60}Fe/^{56}Fe$vary over several orders of magnitude, so
the explored input values are stated explicitly and the constant value was the
median from this list of values. (a) Scott and Kohlstedt (2006), (b)
Rückriemen et al. (2018), (c) Bryson et al. (2019a), (d) Karato and Wu (1993),
(e) Dodds et al. (2021), (f) Hirth and Kohlstedt (2003), (g) Giordano et al.
(2008), (h) Tang and Dauphas (2012), (i) Cook et al. (2021), (j) Kodolányi et
al. (2022a), (k) Kodolányi et al. (2022b).

##  3 Results

Figure 3: Dynamo timings for a 300 km planetesimal for a range of initial
$\rm{}^{60}Fe/^{56}Fe$, mantle viscosities, and core compositions. Filled bars
indicate periods when a dynamo is active and the colour of the bar indicates
dipole magnetic field strength at the surface. The small, vertical, black line
on each bar indicates the onset of core solidification in each model run.
Magnetic field strengths between the onset of core solidification and the end
of dynamo generation are averages for this time interval to remove
oscillations in field strength due to the discretisation of the model
(Sanderson et al., 2024). The thin, vertical, white lines in some runs are
$<0.5$ Ma breaks in dynamo generation due to a rapid increase in viscosity at
$\phi_{C}$. These lines are artefacts of our viscosity and stagnant lid
parametrisation and should not be interpreted. For each parameter, the model
was run across the range of values in Table 1, while all other parameters are
held at a constant median value (except $\phi_{C}$ where the constant value
was the experimental upper bound). The constant parameter values were:
$\eta_{0}=10^{19}$ Pas, $\beta=0.0225\,K^{-1}$, $\alpha_{n}=30$, $\phi_{C}$ =
0.3, $\eta_{l}=10$ Pas, $\rm{}^{60}Fe/^{56}Fe$ = $10^{-8}$, $X_{S,0}=29.85$
wt%. Magnetic field strengths as a function of time for each combination of
parameters shown in this plot are provided in the Supplementary Materials.
Figure 4: Magnetic Reynolds number ($Re_{m}$) as a function of time for a
range of initial $\rm{}^{60}Fe/^{56}Fe$, mantle viscosities, core
compositions, and planetesimal radii. Filled bars indicate periods when the
dynamo is on and the colour of the bars indicates the magnetic Reynolds
number. Subcritical values ($<10$) are not shown. Supercritical values are
categorised according to the range of possible criticality limits: 10-40,
40-100 and $>$100 (Christensen and Aubert, 2006; Stevenson, 2003). The small,
vertical, black line on each bar indicates the onset of core solidification in
each model run. Magnetic Reynolds numbers between the onset of core
solidification and the end of dynamo generation are averages for this time
interval to remove oscillations in $Re_{m}$ due to the discretisation of the
model (Sanderson et al., 2024). The thin, vertical, white lines in some runs
are $<0.5$ Ma breaks in dynamo generation due to a rapid increase in viscosity
at $\phi_{C}$. These lines are artefacts of our viscosity and stagnant lid
parametrisation and should not be interpreted. For each parameter, the model
was run across the range of values in Table 1 and shown on Figure 3, while all
other parameters were held at a constant median value (except $\phi_{C}$ where
the constant value was the experimental upper bound). The range of values for
radius are shown explicitly. The constant parameters values are: $r=300$ km,
$\eta_{0}=10^{19}$ Pas, $\beta=0.0225\,K^{-1}$, $\alpha_{n}=30$, $\phi_{C}$ =
0.3, $\eta_{l}=10$ Pas, $\rm{}^{60}Fe/^{56}Fe$ = $10^{-8}$, $X_{S,0}=29.85$
wt%.

###  3.1 Constant radius

Firstly, we ran models with a constant radius of 300 km to identify the impact
of other parameters on thermal evolution and dynamo generation. The lowest
mantle reference viscosity, $\eta_{0}$, and lowest initial core sulfur
content, $\rm X_{S,0}$, result in a single epoch of dynamo generation, and a
single value in each of $\eta_{0}$, $\phi_{C}$, and $\alpha_{n}$ result in
three epochs of dynamo generation (see Supplementary Materials). Otherwise,
all other parameter combinations produce two periods of dynamo generation
(Figure 3). Across these two dynamo generation periods, we observe two
distinctive trends in magnetic field strength: (i) the first dynamo generation
period can have two peaks in magnetic field strength ii) in the second dynamo
generation period, magnetic field strength increases with time towards a peak
value during core solidification. The first peak in the first epoch of dynamo
generation corresponds to the onset of dynamo generation and the second peak
occurs when the base of the mantle first cools below the critical melt
fraction (Sanderson et al., 2024). The peak in field strength at the beginning
of the first epoch of dynamo generation is always the strongest because
radiogenic heating by $\rm{}^{60}Fe$ increases CMB heat flux ($F_{\rm CMB}$).
For all runs with multiple field generation periods, the final dynamo
generation period begins before the onset of core solidification. Reference
viscosity has the strongest effect on the duration of the gap in dynamo
generation and $\rm{}^{60}Fe/^{56}Fe$ has the strongest influence on the
resulting magnetic field strength. Despite the range in dynamo durations and
strengths, most $Re_{m}$ values fall between 10–40 (Figure 4).

####  3.1.1 Effect of ${}^{60}Fe$

Increasing $\rm{}^{60}Fe/^{56}Fe$ brings forward the onset of the dynamo to
1–2 Ma after CAI formation and increases peak field strength and $Re_{m}$ in
the first epoch of dynamo generation. The onset of the dynamo is earlier for
increased $\rm{}^{60}Fe$ because increased heating either erodes core thermal
stratification more rapidly or prevents its formation altogether, which brings
forward the time that $F_{\rm CMB}$ becomes superadiabatic. Radiogenic heating
by $\rm{}^{60}Fe$ also increases the temperature of the core and the
temperature difference relative to the mantle, which increases $F_{\rm CMB}$
and the strength of the dynamo. Model runs with $\rm{}^{60}Fe/^{56}Fe$ $\geq
10^{-7}$ had peak field strengths in the first period of dynamo generation 2–3
times higher than runs with $\rm{}^{60}Fe/^{56}Fe$ $=10^{-8}$. This extra heat
is removed from the core by an elevated $F_{\rm CMB}$ during the first period
of dynamo generation. As such, by the second epoch of dynamo generation the
peak field strengths, $Re_{m}$ and the onset of core solidification are
similar across all values of $\rm{}^{60}Fe/^{56}Fe$. There are similar onset
times and field strengths for the first dynamo generation period for
$\rm{}^{60}Fe/^{56}Fe$ =0 and $\rm{}^{60}Fe/^{56}Fe$ $=10^{-9}$. This
similarity suggests that when $\rm{}^{60}Fe/^{56}Fe$ $\leq 10^{-9}$ the effect
of $\rm{}^{60}Fe$ can be neglected. The onset times vary little across
variations in other parameters indicating $\rm{}^{60}Fe/^{56}Fe$ is the
dominant control on onset time for the first period of dynamo generation.

####  3.1.2 Effect of viscosity

The reference viscosity, $\eta_{0}$, has the strongest effect on the duration
of the first period of dynamo generation and the following gap. Above
$10^{21}$ Pas, the first period of dynamo generation ends after 13–14 Ma and
is followed by a gap of ¿80 Ma in dynamo generation. This results from the
rapid thickening of the surface stagnant lid shutting off convection earlier
for the highest reference viscosities. In contrast, below $10^{16}$ Pas, there
is only one epoch of dynamo generation, because the mantle viscosity is
sufficiently low that mantle convection does not cease before core
solidification. The second peak in magnetic field strength in the first epoch
of dynamo generation widens and increases in strength with decreasing
reference viscosity, because the thinner boundary layer at the CMB raises
$F_{\rm CMB}$. An elevated $F_{\rm CMB}$ increases the rate at which the core
cools, which brings forward the onset of core solidification and the end of
dynamo generation.

The viscosity parameters have very little effect on the supercriticality of
$Re_{m}$. Only the lowest $\eta_{0}$ and highest values of $\phi_{C}$ increase
$Re_{m}$ in the first 12 Ma (Figure 4). The lowest values of $\eta_{0}$ are
less physical, because they are based on the highest values from laboratory
experiments, which have not been extrapolated to planetesimal pressure values.
As such, this increase in $Re_{m}$ can be discounted. However, the highest
value $\phi_{C}$ =0.5 has been adopted in previous thermal evolution models,
despite not being supported by experimental data. The elevated $Re_{m}$ for
this value may have resulted in overestimates of field strength and dynamo
duration in previous work.

####  3.1.3 Effect of $\rm X_{S,0}$

Intial core sulfur content, $\rm X_{S,0}$, has a strong effect on the timing
of core solidification, because increasing $\rm X_{S,0}$ lowers the liquidus
temperature of the core and more cooling is required to reach this
temperature. The lowest $\rm X_{S,0}$ removes the gap in dynamo generation,
because the early onset of core solidification provides additional
compositional buoyancy flux to drive the dynamo even when mantle convection
ceases.

###  3.2 Variable radius

Figure 5: Proportion of active dynamos for variation in initial
$\rm{}^{60}Fe/^{56}Fe$, mantle viscosities, and core compositions for
planetesimals ranging from 100-500 km in radius. In an individual panel, model
runs are grouped in horizontal blocks by parameter. Yellow indicates that all
dynamos are on at a given time irrespective of the value of a parameter, dark
blue indicates no dynamos are on at a given time irrespective of the value of
a parameter. Light blue to green regions indicate a dynamo is on for a subset
of values of that parameter. White space indicates times after the last period
of dynamo generation and the end of the simulation. The constant parameters
values are: $\eta_{0}=10^{19}$ Pas, $\beta=0.0225\,K^{-1}$, $\alpha_{n}=30$,
$\phi_{C}$ =0.3, $\eta_{l}=10$ Pas, $\rm{}^{60}Fe/^{56}Fe$ =$10^{-8}$ and the
range for each parameter is given in Table 1. $\eta_{0}$ causes a wide
variation in dynamo timings, so is shown separately in Figure 6. Figure 6:
Proportion of active dynamos across a range of reference viscosity,
$\eta_{0}$, for planetesimals ranging from 100–500 km in radius. Core radius
is half planetesimal radius. Yellow indicates that all dynamos are on at a
given time irrespective of the value of $\eta_{0}$, dark blue indicates no
dynamos are on at a given time irrespective of the value of $\eta_{0}$. Light
blue to green regions indicate a dynamo is on for a subset of values of
$\eta_{0}$. White space indicates times after the last period of dynamo
generation and the end of the simulation. The vertical axis is equivalent to
one horizontal block in Figure 5 and has no physical meaning. The constant
parameter values are: $\beta=0.0225\,K^{-1}$, $\alpha_{n}=30$, $\phi_{C}$ =
0.3, $\eta_{l}=10$ Pas, $\rm{}^{60}Fe/^{56}Fe$ = $10^{-8}$, $X_{S,0}=$[29.45,
29.65, 29.85, 30.05, 30.05] wt% for [500, 400, 300, 200, 100] km radius
planetesimals. The range for $\eta_{0}$ is given in Table 1.

To identify the impact of planetesimal radius on thermal evolution and dynamo
generation we ran models with varying radii and other variables held constant
(Table 1). Core radius was assumed to be half the planetesimal radius.
Planetesimal radius has the strongest effect on dynamo timing, duration, and
width of the gap in dynamo generation (Figure 5). Larger planetesimals cool
more slowly so mantle convection ceases later, which prolongs the first epoch
of dynamo generation. Larger core size increases the lengthscale of
convection; this raises the $Re_{m}$ value for a given $F_{\rm CMB}$, which
further prolongs dynamo generation. Larger core size also increases magnetic
field strengths (Figure S1–S4). The increase in magnetic field strength is
most pronounced at the onset of the first epoch of dynamo generation for when
the highest values of $\rm{}^{60}Fe/^{56}Fe$ are considered. Bodies with
radius of 100 km only generate magnetic fields after the onset of core
solidification (Figure 4) except for the highest values of
$\rm{}^{60}Fe/^{56}Fe$. Increasing planetesimal radius from 100 km to 500 km
increases the end time of dynamo generation from $\sim$30 to $\sim$600 Ma. The
gap in dynamo generation moves later ($\sim$20–200 Ma) and increases in
duration ($\sim$20–270 Ma) for increasing planetesimal radius. For each body
size, the timings of the dynamo generation periods are consistent across
variations in the other parameters (Figure 5). An exception is $\eta_{0}$
(Figure 6), where values ¡$10^{16}$ Pas do not produce a gap in dynamo
generation. However, there is still a trend of increasing dynamo duration with
radius for $\eta_{0}$.

##  4 Discussion

Figure 7: A summary of meteorite paleointensities for the first 12 Ma after
CAI formation. Meteorites for which the cause of magnetisation is interpreted
as a nebula field (or lack of) are plotted in blue. Meteorites for which the
cause of magnetisation has been interpreted as a dynamo field are plotted in
black. Meteorites which could have a nebula or dynamo origin are plotted in
green for their possible nebula field paleointensities. The dashed grey lines
indicate the paleointensities of Winchcombe (Bryson et al., 2023) and Allende
(Fu et al., 2021) if the factor of two correction for the nebula field is not
applied. Faded grey points correspond to null or low paleointensities, which
may be due to formation of magnetite by pseudomorphic replacement which cannot
record a chemical remnant magnetisation (CRM) (Bryson et al., 2023). The blue
circles indicate pre-accretionary remanences from chondrules. The IVA irons
have not been included, because they were generated by a solidifying,
unmantled core (Bryson et al., 2017). The R chondrites have too large an age
uncertainty and the CV chondrules are too altered to provide useful
constraints, so neither are shown (Cournède et al., 2020; Shah et al., 2017).
Intensity bars with arrows indicate values with a upper/lower limit (the cap)
and for the $\rm CV_{ox,A}$ the best guess is the intersection with the time
error bar. Our new model brings forward the onset of dynamo generation (pink
box) relative to previous models (blue box). The graduated shading in the blue
and pink regions indicates the maximum paleointensity for a given planetesimal
radius (shown by ticks on the right hand vertical axis). The orange box
indicates the duration of the nebula field, which may be 1 Ma longer than
shown here if the angrite age is recalculated based on Piralla et al. (2023).
This would further increase the overlap between dynamo and nebula fields. Data
and references for this table are given in the Supplementary Materials.

###  4.1 Reevaluating the paleomagnetic record

The purpose of our model is to determine the origins (nebula field, thermal or
compositional dynamo) of magnetisations in the meteorite paleomagnetic record.
Overall, our model results suggest two key interpretations of the
paleomagnetic record should be revisited. First, the earliest recorded
magnetisations ($<$5 Ma after CAI formation), previously attributed to the
nebula field, could have been dynamo generated. This is due to inclusion of
$\rm{}^{60}Fe$ in our model bringing forward the onset of thermal dynamos to
1–2 Ma after CAI formation, which allows for thermal dynamo generation prior
to the dissipation of the nebula field (Figure 7). Second, late magnetic
remanences, previously ascribed to the second epoch of dynamo generation
during core solidification, may not have been in the second epoch and do not
require core solidification, but could instead be produced by a thermal
dynamo. Our model predicts an elongated first epoch of dynamo generation
lasting until 20–200 Ma after CAI formation (depending on radius) rather than
until 9–34 Ma after CAI formation as suggested by previous models (Dodds et
al., 2021). Additionally, in our model, the second epoch of dynamo generation
begins before the onset of core solidification. The meteorite paleomagnetic
record in light of our new model results is reassessed in detail below.

####  4.1.1 Paleomagnetic records of the nebula field

Unidirectional magnetisation within chondrules, but non-unidirectional
magnetisation between chondrules in a meteorite is only possible if the
chondrules acquired their remanence prior to accretion onto the meteorite
parent body. The nebula field is the only source of a pre-accretionary
magnetisation, therefore non-unidirectional chondrule magnetisations provide
conclusive evidence that a paleointensity can be attributed to the nebula
field. Non-unidirectional measurements of chondrules from CO (Borlina et al.,
2021), LL3 (Fu et al., 2014b) and CR chondrites (Fu et al., 2020) are
interpreted as evidence for the nebula field $\sim$1.7–4 Ma after CAI
formation with paleointensities up to $\sim\\!150\,\mu$T (Figure 7). Bulk
meteorite magnetisations from parent bodies that were too small to generate a
dynamo can also be attributed to the nebula field (e.g. Erg Chech 002, Neumann
et al., 2023; Maurel and Gattacceca, 2024).

Null remanences could indicate the dissipation of the nebula field, but there
are two other possible interpretations, which must be excluded first. First, a
meteorite parent body may have formed in a distal part of the Solar System
where the field was weak (e.g. Tagish Lake, Bryson et al., 2020b). Second, the
magnetic minerals may not have formed in a way that allowed them to record a
remanence. Many carbonaceous chondrites record magnetisation in magnetite,
which formed during aqueous alteration. If the magnetite formed by
pseudomorphic replacement of FeNi metla rather than precipitation, it may not
have recorded a new remanence during this process (Bryson et al., 2023). This
could explain the null remanence in CV chondrite Kaba (Gattacceca et al.,
2016) and the upper limit on paleointensity of $0.9\,\mu$T from the matrix of
CO chondrites (Borlina et al., 2022). For the volcanic angrites both these
interpretations can be excluded. They formed in the inner Solar System,
erupted $\sim$3.8–3.9 Ma after CAI formation111These ages were originally
reported as absolute Pb-Pb ages and may be shifted to 4.8–4.9 Ma after CAI
formation based on reevaluation of the anchor for Pb-Pb (Piralla et al.,
2023). and cooled quickly forming magnetite that should have recorded any
magnetic fields present (Wang et al., 2017). Therefore, a null remanence in
the angrites suggests the nebula field in the inner Solar System dissipated
3.8–3.9 Ma after CAI formation (Wang et al., 2017). The recovered
paleointensity of $<0.6\,\mu$T from ungrouped achondrite NWA 7325 at $\sim$4–5
Ma after CAI formation (Weiss et al., 2017) further supports the nebula field
in the inner Solar System having dissipated by this time.

####  4.1.2 Ambiguous paleomagnetic records: nebula or dynamo fields?

Interpretation of bulk chondrite paleomagnetic remanences (i.e. not individual
chondrule measurements) from the first 5 Ma after CAI formation is complicated
because these meteorites could sample the outer layer of a partially
differentiated planetesimal (Carporzen et al., 2011; Elkins-Tanton et al.,
2011; Weiss and Elkins-Tanton, 2013). In this case, a chondritic meteorite
could record a paleomagnetic remanence from a dynamo generated in the core of
their partially differentiated parent body rather than the nebula field. The
feasibility of this scenario rests on the timing of planetesimal dynamos and
evidence for partially differentiated meteorite parent bodies. Our model
demonstrates that a parent body, with $\rm{}^{60}Fe/^{56}Fe$ $\geq 10^{-8}$,
would have an early onset of a thermal dynamo before the dissipation of the
nebula field. Thermally metamorphosed chondritic meteorites could have been
heated purely radiogenically on a parent body that partially differentiated.
The interpretation of bulk remanences in the CM and CV chondrites and WIS
91600 (green points in Figure 7) is less clear than previously, in light of
the possibility they record an early dynamo. The ages of the R chondrites are
too poorly constrained (0–20 Ma after CAI formation, Cournède et al., 2020)
for the origin of their remanence to be discussed.

The CM chondrites and WIS 91600 recorded a magnetic field 2–4 Ma after CAI
formation (Cournede et al., 2015; Bryson et al., 2023) and likely 3.6–5 Ma
after CAI formation (Bryson et al., 2020a), respectively. The timing of these
remanences is consistent with either a nebula field or dynamo origin. For
example, a 500 km radius planetesimal with $\rm{}^{60}Fe/^{56}Fe$ =1–6$\times
10^{-7}$ and other constant parameters from Table 1 produces intensities that
match those recovered from Winchcombe (Figure S10). However, lack of evidence
for prolonged thermal metamorphism in the CM chondrites and WIS 91600 (Suttle
et al., 2021; Bryson et al., 2020a) argues against partially differentiated
parent bodies for these meteorites; unless they sample the topmost, coolest
layer of such a body. Further numerical modelling of partially differentiated
bodies combining gradual accretion and $\rm{}^{60}Fe$ are required to
determine whether a dynamo in a partially differentiated body or the nebula
field is the source of these remanences.

The CV chondrites are thermally metamorphosed (Carporzen et al., 2011; Elkins-
Tanton et al., 2011; Gattacceca et al., 2016) and have a complex paleomagnetic
record. CV chondrules have been modified by impacts, heating and aqueous
alteration and have a non-unidirectional magnetisation within an individual
chondrule, so their remanence cannot be attributed to the nebula field (Fu et
al., 2014a; Shah et al., 2017). Allende records a magnetisation in the iron
sulfides in the matrix from 2.5–3.5 Ma after CAI formation (Fu et al., 2021),
and has a bulk remanance dated to 5–40 Ma after CAI formation (Carporzen et
al., 2011; Elkins-Tanton et al., 2011). The CV chondrite Kaba has a null
remanence from aqueous alteration at 4–6 Ma after CAI formation, but a $\sim$3
$\mu$T remanence from prolonged metamorphism tens of Ma after CAI formation
(Gattacceca et al., 2016). The later ($>5$ Ma after CAI formation) CV
chondrite remanences, combined with evidence for thermal metamorphism, suggest
the CV chondrite parent body was partially differentiated and generated a
dynamo (Elkins-Tanton et al., 2011; Gattacceca et al., 2016). Previously,
Kaba’s null remanance, recorded during aqueous alteration, was used as
evidence for the dissipation of the nebula field before the onset of the
dynamo on the CV chondrite parent body. This supported a nebula origin for the
earliest Allende remanence (2.5–3.5 Ma after CAI formation Fu et al., 2021).
However, Kaba’s magnetite may have been unable to acquire a remanance during
formation (Bryson et al., 2023), so this null remanance may not indicate an
absence of a magnetic field on the CV parent body at 4–6 Ma after CAI
formation. Altogether, the altered interpretation of Kaba’s null remanence,
thermal metamorphism of the CV chondrite parent body and the early dynamo
onset predicted by our models suggests the earliest remanence on Allende could
be due to the early onset of a thermal dynamo.

##### Intensity of remanence

Next, we assess whether paleointensity can be used to determine if a remanence
has a dynamo or nebula field origin. As shown in Figure 7, the maximum nebula
intensities measured are stronger than the maximum intensities predicted by
our dynamo model. However, the quoted nebula intensities recorded by
Winchcombe (CM chondrite, Bryson et al., 2023) and Allende (CV chondrite, Fu
et al., 2021) are a factor of two larger than the measured paleointensities to
account for rotation of the parent body during prolonged remanence
acquisition. If these paleointensities were produced by dynamo fields this
correction would not be required, because the magnetic field is co-rotating
with the planetesimal. Removing this correction decreases their
paleointensities so they are within the range of field strengths predicted by
our dynamo models (dashed lines on Figure 7). Our upper limits on dynamo field
strengths ($>30$ $\mu$T) are for the largest planetesimals with highest values
of $\rm{}^{60}Fe$ at early times ($<3$ Ma after CAI formation). Most parameter
combinations predict weaker dynamo strengths $<3$ Ma after CAI formation
(10–30 $\mu$T, Figure 3 and S1–S4). A combination of approaches would be
required to determine if measured paleointensities, even without the factor of
two amplification, are too strong to be dynamo generated. The uncertainty on
the paleointensity measurements could be reduced, and parent body size and
$\rm{}^{60}Fe/^{56}Fe$ could be independently constrained, e.g. by thermal
models and isotopic measurements. Regardless of improved measurements, the
difficulty in converting from field strengths acquired by different mechanisms
in the laboratory compared to the parent body (factors of 2–5, Weiss and
Tikoo, 2014; Maurel and Gattacceca, 2023) and uncertainties in the ratio of
dipole field at the CMB to the internal dynamo field from dynamo scaling laws
(0.06–0.1 for Earth, Davies et al., 2022) may mean that the uncertainties of
measured and predicted paleointensities overlap. Overall, current recovered
paleointensities and modelled field intensities cannot be used to distinguish
between a dynamo or nebula field.

The possibility of the earlier onset of a thermal dynamo due to $\rm{}^{60}Fe$
reduces the number of meteorite paleomagnetic studies that provide compelling
evidence for the nebula field in the outer Solar System, because the bulk
remanences in CM and CV chondrites may not record nebula fields. This should
be considered when using this data to discuss differences in field strength
and protoplanetary disk dispersal time between the inner and outer Solar
System (Weiss et al., 2021; Borlina et al., 2022). Paleomagnetic measurements
of individual, pristine chondrules are vital to understand the nebula field,
because their non-unidirectionality can indicate conclusively if a remanence
is preaccretionary.

####  4.1.3 Paleomagnetic records of planetesimal core crystallisation

Our results argue that late remanences ($>65$ Ma after CAI formation based on
the current meteorite record) do not require the presence of a solidifying
core. The first epoch of dynamo generation can last until 20–200 Ma after CAI
formation (depending on radius) rather than until 9–34 Ma after CAI formation
suggested by previous models (Dodds et al., 2021). Additionally, our improved
core solidification model reveals the second epoch of dynamo generation can
begin prior to the onset of core solidification. As a result, the source of
buoyancy to drive a dynamo cannot be assumed purely based on timing of a
magnetic remanence. For extremes of some parameter values (low $\eta_{0}$ and
$\rm X_{S,0}$), onset of solidification is early and most of dynamo generation
is powered by a combination of thermal and compositional buoyancy. Previous
studies of the Main Group pallasites (Bryson et al., 2015; Nichols et al.,
2021) and IIE irons (Maurel et al., 2020) have used the onset of a late-stage
dynamo as an indicator for the start of core solidification. This assumption
has been used to constrain planetesimal radius, core size, thermal history,
and core composition. Our model highlights that the beginning of a second
epoch of dynamo is unlikely to be coincident with the beginning of core
solidification for any initial core sulfur content, and therefore these
studies should be re-evaluated.

####  4.1.4 Paleomagnetic constraints on primordial 60Fe/56Fe

The null paleointensities in the volcanic angrites and NWA 7325 at 3.8–5 Ma
after CAI formation (Wang et al., 2017; Weiss et al., 2017) contradicts the
early onset of a dynamo in bodies with $\rm{}^{60}Fe/^{56}Fe$ $\geq 10^{-8}$
predicted by this model. Magnetic remanences in the plutonic angrite, Angra
dos Reis at 11 Ma after CAI formation (Wang et al., 2017), indicate the
angrite parent body was differentiated and did generate a dynamo later in its
history. Explanations, such as parent body size, gradual accretion, or
$\rm{}^{60}Fe$ fractionation are unlikely to cause this delay in dynamo onset
(see Supplementary Materials). Another explanation could be
$\rm{}^{60}Fe/^{56}Fe$ was $\leq 10^{-9}$ in the formation region of the
angrites such that the time taken to erode core thermal stratification led to
a delay in dynamo generation (Bryson et al., 2019a; Dodds et al., 2021). Tang
and Dauphas (2012) measured values of $\rm{}^{60}Fe/^{56}Fe$ $=0.9\pm
0.5\times 10^{-8}$ in the angrites. Additionally, values of
$\rm{}^{60}Fe/^{56}Fe$ from silicates in non-carbonaceous chondrules are
within error of zero ($0.8\pm 1.0\times 10^{-7}$, Kodolányi et al., 2022a).
For a 300 km body accreted at 0.8 Ma after CAI formation,
$\rm{}^{60}Fe/^{56}Fe$ $<1.75\times 10^{-9}$ results in a dynamo onset time
consistent with the angrite data (see Figure S5). This limit lies within the
lower bounds of these non-carbonaceous $\rm{}^{60}Fe/^{56}Fe$ values. Current
measurements from the carbonaceous IID and IVB irons ($6\pm 2\times 10^{-7}$,
Cook et al., 2021) and carbonaceous chondrule silicates ($4\pm 2\times
10^{-7}$ Kodolányi et al., 2022a) have large uncertainties, but neither are
within error of $\rm{}^{60}Fe/^{56}Fe$ $<10^{-8}$. This suggests there could
be heterogeneity in $\rm{}^{60}Fe/^{56}Fe$ between the carbonaceous and non-
carbonaceous reservoirs (Cook et al., 2021; Kodolányi et al., 2022a).
Measurement of a paleomagnetic remanence in a carbonaceous achondrite between
the age of the volcanic and plutonic angrites could inform this discussion. If
such a carbonaceous achondrite has a null paleomagnetic remanence, this could
provide evidence for $\rm{}^{60}Fe/^{56}Fe$ $<10^{-8}$ throughout the Solar
System and constrain the timing of the dissipation of the nebula field in the
outer Solar System. If this carbonaceous achondrite is found to have acquired
a remanence at a similar time to null remanence acquisition in the volcanic
angrites (i.e., when the nebula field has dissipated), this could provide
evidence for early dynamo onset and heterogeneity in $\rm{}^{60}Fe/^{56}Fe$ in
the early Solar System.

###  4.2 Viscosity parameters in future planetesimal thermal evolution models

Mantle critical melt fraction, $\phi_{C}$, is a crucial parameter in thermal
evolution models. It determines planetesimal peak temperature and melt
fraction (see Appendix B), and defines the threshold for magma ocean formation
and convection in some models (e.g. Sturtz et al., 2022a; Neumann et al.,
2023). A lower, more realistic value of $\phi_{C}$ should be used in future
models. For models of specific parent bodies, this will affect the extent of
the magma ocean and the inferred initial location of a meteorite (e.g. Erg
Chech 002, Sturtz et al., 2022a). In two-phase flow models for planetesimal
differentiation (e.g. Lichtenberg et al., 2019; Monnereau et al., 2023),
reducing $\phi_{C}$ and planetesimal peak temperature may alter the Fe-FeS
compositions that can be molten, which will affect initial core composition.
Additionally, reducing the melt threshold for magma ocean onset in
differentiation models may decrease the time available for processes such as
differentiation via percolation.

The value of mantle reference viscosity, $\eta_{0}$, has a strong effect
planetesimal cooling rate. Future models should test multiple values in the
extrapolated range of $\eta_{0}$ when attempting to constrain a parent body
thermal history from meteorite isotope data (e.g. Bryson et al., 2019b;
Neumann et al., 2023). Future models could attempt to constrain values for
planetesimal $\eta_{0}$ (and other viscosity parameters) based on parent body
composition, water content, and observed gaps in the paleomagnetic record.

###  4.3 Validity

This work only explored variations within one parameter at a time, while all
other parameters were held at their median values (except $\phi_{C}$ where the
constant value was the experimental upper bound). Using endmember values for
multiple parameters simultaneously may result in an even wider range of dynamo
generation times. Varying a single parameter enables the effect of each
parameter to be understood and the dominant factors in dynamo generation
timing to be isolated. As demonstrated in Figure 5, even across variations in
parameters other than radius, there are large portions of time where the
planetesimal dynamo is consistently active. Therefore, even if multiple
parameters are varied, the trends in timing with radius predicted here are
likely to hold true. The choice of critical $Re_{m}$, light elements in the
core, $\rm X_{S,0}$, core radius fraction and assumptions about accretion and
differentiation are justified for the purposes of this work and do not have a
large impact on the results (for further discussion see the Supplementary
Materials).

##  5 Conclusions

Using the refined planetesimal thermal evolution model of Sanderson et al.
(2024), we explored the effects of $\rm{}^{60}Fe$, mantle viscosity, initial
core sulfur content, and planetesimal radius on planetesimal dynamo
generation. Our results suggest there is a wider range in dynamo timings and
durations than previously predicted. The meteorite paleomagnetic record
therefore cannot be split into three distinct epochs of magnetic field
generation (nebula field, thermal dynamos and compositional dynamos) and the
implications of some paleomagnetic remanences should be re-evaluated.

  * •

Inclusion of $\rm{}^{60}Fe$ in the core can bring forward the onset of thermal
dynamos to 1–2 Ma after CAI formation, extending the time at which the first
planetesimal dynamos were possible. Therefore, some meteorite remanences
recorded prior to 5 Ma after CAI formation could have a thermal dynamo origin
rather than a nebula field origin.

  * •

Null paleomagnetic remanences in the angrites contradict the early onset of
thermal dynamos caused by $\rm{}^{60}Fe$. This could provide evidence for
heterogeneous $\rm{}^{60}Fe/^{56}Fe$ in the early Solar System. Paleomagnetic
measurements of an old ($<$10 Ma after CAI formation) carbonaceous achondrite
could help inform this.

  * •

Increasing planetesimal radius (from 100 km to 500 km) greatly increases the
start time of the gap in planetesimal dynamo generation (20 to 200 Ma after
CAI formation) and final end of dynamo duration (40 to 640 Ma after CAI
formation).

  * •

The paleomagnetic record does not reflect early thermal dynamos and later
compositional dynamos during core solidification, as previously interpreted.
Variation in initial core sulfur content and mantle reference viscosity can
produce early thermo-compositional dynamos. For most parameter combinations,
there is a second thermal dynamo period prior to the onset of core
solidification.

  * •

Late magnetic remanences ($>$65 Ma post CAI formation based on the current
record) do not require a solidifying core. As a result, the planetesimal
radii, core sizes, thermal histories, and core compositions of the Main Group
pallasites and IIE irons should be re-evaluated.

  * •

A range of planetesinal radii, mantle reference viscosities, and initial
$\rm{}^{60}Fe/^{56}Fe$ ratios should be explored when attempting to constrain
parent body properties based on a meteorite paleomagnetic remanence.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

## Data availability

The dynamo and thermal evolution model and the parameter files required to
recreate the results in this paper are publicly available the Sanderson (2024)
Github repository.

## Acknowledgements

The authors would like to thank Kathryn Dodds and Chris Davies for their
helpful discussions in preparing this work. HRS acknowledges funding on a NERC
studentship NE/S007474/1 and an Exonian Graduate Scholarship from Exeter
College, University of Oxford. HRS thanks the Royal Astronomical Society for a
student travel grant that enabled this work to be presented at the American
Geophysical Union Fall Meeting 2023. JFJB acknowledges funding from the UKRI
Research Frontier Guarantee program EP/Y014375/1. For the purpose of open
access, the authors have applied a Creative Commons Attribution (CC BY)
licence to any Author Accepted Manuscript version arising.

##  Appendix A Extrapolation of reference viscosities

Viscosity is temperature and pressure dependent. Planetesimal mid-mantle
pressures lie above that of lab experiments and below that of planets,
therefore extrapolation is required when estimating planetesimal reference
viscosities. Laboratory experiments are also on shorter timescales and
lengthscales compared to planetary conditions. Therefore, geophysical
observations, such as postglacial uplift (Karato and Wu, 1993) are often used
to constrain mantle viscosity on Earth. For this reason, the full range of
$\eta_{0}$ in this paper was extrapolated from planetary values and the
experimental values were included as a lower bound. Extrapolation can be done
using an Arrhenius law

$\eta=\eta_{0}exp\left(\frac{E+pV}{RT}-\frac{E+p_{\text{ref}}V}{RT_{\text{ref}}}\right)$
(1)

or the Frank-Kamenetskii approximation (Noack and Breuer, 2013)

$\eta=\eta_{0}exp\left(\frac{E+p_{\text{ref}}V}{RT_{\text{ref}}^{2}}(T_{\text{ref}}-T)+\frac{V}{RT_{\text{ref}}}(p-p_{\text{ref}})\right).$
(2)

In these equations, $E$ and $V$ are the activation energy and volume,
$p_{\text{ref}}$ and $T_{\text{ref}}$ are the reference pressures and
temperatures, $R$ is the gas constant and $p$ and $T$ are the temperatures and
pressures being extrapolated to. To estimate planetesimal mid-mantle
viscosities extrapolations using both laws were performed on reference
viscosity values for Ganymede (Rückriemen et al., 2018) (see Table 2) using a
range in activation volumes from 2$\times 10^{-6}$–2$\times
10^{-5}\rm\;m^{3}mol^{-1}$ (Hirth and Kohlstedt, 2003) and activation energies
from 240–570 kJ$\rm mol^{-1}$ (Karato and Wu, 1993; Hirth and Kohlstedt,
2003). Assuming constant density core and mantle, planetesimal mid-mantle
pressures range from 2 MPa to 50 MPa for 100–500 km bodies.

$\eta_{0}$ /Pas |  $p_{\text{ref}}$/MPa |  $T_{\text{ref}}$ /K | Extrapolated $\eta_{0}$ /Pas
---|---|---|---
$10^{19}$–$10^{22}$ | 960 | 1600 |  $10^{19}$–$10^{24}$
Table 2: Reference parameters for viscosity extrapolations for Ganymede
(Rückriemen et al., 2018). Reference pressure is calculated in the mid-mantle
using average values for the Ganymede interior structure model in Rückriemen
et al. (2018).

These extrapolations give possible a wide range $\eta_{0}$ from
$10^{19}$–$10^{24}$ Pas due to the large uncertainties in activation volume
and activation energy. Equation 1 and 2 give values within the same order of
magnitude.

##  Appendix B Effect of $\phi_{C}$ on peak temperatures

As shown in Figure 8, peak mantle temperature is close to that of $\phi_{C}$
due to the negative feedback loop between mantle temperature and stagnant lid
thickness. At $\phi_{C}$, an increase in temperature leads to a rapid drop in
viscosity and thinning of the stagnant lid. This increases surface heat flux,
which reduces mantle temperature, increases the viscosity and thickens the
stagnant lid. This means choice of $\phi_{C}$ has direct control on the
maximum mantle temperature of a planetesimal.

Figure 8: Peak mantle temperature as a function of $\phi_{C}$ .

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