Strengthen core formation evidence in lecture 4 notes and slides

The magma ocean paragraph now makes the argument in plain terms for second-year students: while the mantle is liquid, iron sinks and a core forms in weeks; once the mantle is solid, the iron is trapped, which is why chondritic asteroids never formed cores.

The partitioning figure now shows Ni and Co only, with the required partition-coefficient band at the correct level (D of about 26 and 24 from core-mantle mass balance) and the 40-60 GPa window of Siebert et al. (2013) and Fischer et al. (2015), who place single-stage equilibration at 54 +/- 5 GPa. A new script regenerates the figure, and a second new script draws a two-panel schematic of Hf-W chronometry whose curves follow the two-stage model of the worked example. Both figures have matching slide frames.

Oxygen fugacity is now defined qualitatively, with the iron-wuestite buffer as the reference scale, for readers who have not met geochemical redox notation.

The quoted Hf-W ages for Earth now follow Nimmo and Kleine (2015) and Kleine and Walker (2017): the two-stage age of about 30 Myr is a strict lower limit, and core formation probably finished within about 100 Myr. This replaces the earlier 30-60 Myr window, which matched neither source.

The Mars hemispheric dichotomy passage now includes the MOLA topography map, and the slides get a button macro that links a frame to the animated version of its figure.

Author: timlichtenberg

book/04_differentiation_magnetospheres/differentiation_magnetospheres.md

@@ -514,6 +514,38 @@ @article{Rubie2015
     url           = {https://ui.adsabs.harvard.edu/abs/2015Icar..248...89R/abstract}
 }
 
+@article{Hirose2021,
+    author  = {Hirose, Kei and Wood, Bernard and Vo{\v c}adlo, Lidunka},
+    title   = {Light elements in the {Earth's} core},
+    journal = {Nature Reviews Earth \& Environment},
+    volume  = {2},
+    number  = {9},
+    pages   = {645--658},
+    year    = {2021},
+    doi     = {10.1038/s43017-021-00203-6}
+}
+
+@article{Shahar2026,
+    author  = {Shahar, Anat and Young, Edward D. and Hirose, Kei and Yokoo, Shunpei},
+    title   = {The Compositions of Planetary Cores},
+    journal = {Annual Review of Earth and Planetary Sciences},
+    volume  = {54},
+    number  = {1},
+    pages   = {559--584},
+    year    = {2026},
+    doi     = {10.1146/annurev-earth-040722-094945}
+}
+
+@article{Fischer2015,
+    author  = {Fischer, Rebecca A. and Nakajima, Yoichi and Campbell, Andrew J. and Frost, Daniel J. and Harries, Dennis and Langenhorst, Falko and Miyajima, Nobuyoshi and Pollok, Kilian and Rubie, David C.},
+    title   = {High pressure metal--silicate partitioning of {Ni}, {Co}, {V}, {Cr}, {Si}, and {O}},
+    journal = {Geochimica et Cosmochimica Acta},
+    volume  = {167},
+    pages   = {177--194},
+    year    = {2015},
+    doi     = {10.1016/j.gca.2015.06.026}
+}
+
 @article{Siebert2013,
     author  = {Siebert, Julien and Badro, James and Antonangeli, Daniele and Ryerson, Frederick J.},
     title   = {Terrestrial Accretion Under Oxidizing Conditions},
@@ -719,6 +751,29 @@ @article{Kleine2009
     url           = {https://ui.adsabs.harvard.edu/abs/2009GeCoA..73.5150K/abstract}
 }
 
+@incollection{NimmoKleine2015,
+    author    = {Nimmo, Francis and Kleine, Thorsten},
+    title     = {Early Differentiation and Core Formation: Processes and Timescales},
+    booktitle = {The Early Earth: Accretion and Differentiation},
+    editor    = {Badro, James and Walter, Michael},
+    series    = {Geophysical Monograph Series},
+    volume    = {212},
+    pages     = {83--102},
+    publisher = {American Geophysical Union and John Wiley and Sons},
+    year      = {2015},
+    doi       = {10.1002/9781118860359.ch5}
+}
+
+@article{KleineWalker2017,
+    author  = {Kleine, Thorsten and Walker, Richard J.},
+    title   = {Tungsten Isotopes in Planets},
+    journal = {Annual Review of Earth and Planetary Sciences},
+    volume  = {45},
+    pages   = {389--417},
+    year    = {2017},
+    doi     = {10.1146/annurev-earth-063016-020037}
+}
+
 @article{ElkinsTanton2012,
     author  = {Elkins-Tanton, Linda T.},
     title   = {Magma Oceans in the Inner Solar System},

book/04_differentiation_magnetospheres/figures/hf_w_schematic.avif

@@ -0,0 +1,120 @@
+"""Generate Fig. (`fig:hf-w-schematic`).
+
+Two-panel explanatory schematic of Hf-W chronometry:
+
+(a) Why the system dates core formation: 182Hf is lithophile and stays
+    in the mantle, W is siderophile and is extracted into the core, so
+    core formation separates the parent from the daughter reservoir.
+(b) Mantle 182W excess vs time for early, Earth-like, and late core
+    formation. Curves follow the two-stage model of Eq. eq:hfw-age in
+    the notes: eps(t) = A0 * exp(-lambda t_cf) * (1 - exp(-lambda (t -
+    t_cf))) with A0 = Q * (f - 1) * (182Hf/180Hf)_0 = 1e4 * 17 *
+    1.02e-4 = 17.3 for Earth's mantle Hf/W enrichment, so the 28-Myr
+    case plateaus at the measured mantle value of +2 epsilon units,
+    reproducing the worked example.
+
+Caption / figure id : `fig:hf-w-schematic`
+Markdown source     : book/04_differentiation_magnetospheres/differentiation_magnetospheres.md
+Citation key        : Kleine2009
+"""
+from __future__ import annotations
+
+from pathlib import Path
+
+import matplotlib.pyplot as plt
+import numpy as np
+from matplotlib.patches import Circle, FancyArrowPatch
+
+from scripts.figures._shared.style import apply_style, save_figure
+
+
+REPO_ROOT = Path(__file__).resolve().parents[3]
+OUT_AVIF = (REPO_ROOT /
+            "book/04_differentiation_magnetospheres/figures/hf_w_schematic.avif")
+
+HALF_LIFE = 8.9                      # Myr
+LAM = np.log(2.0) / HALF_LIFE
+AMP0 = 1e4 * 17.0 * 1.02e-4          # Q * (f - 1) * (182Hf/180Hf)_0, Earth Hf/W
+EPS_EARTH = 2.0                      # measured mantle excess, epsilon units
+T_EARTH = 28.0                       # two-stage model age from Eq. eq:hfw-age
+
+CASES = [
+    (10.0, "#d62728", "early (10 Myr)"),
+    (T_EARTH, "#1f77b4", "Earth-like (28 Myr)"),
+    (100.0, "#2ca02c", "late (100 Myr)"),
+]
+
+
+def eps_curve(t: np.ndarray, t_cf: float) -> np.ndarray:
+    """Mantle 182W excess vs time for core formation at t_cf."""
+    amp = AMP0 * np.exp(-LAM * t_cf)
+    out = np.where(t > t_cf, amp * (1.0 - np.exp(-LAM * (t - t_cf))), 0.0)
+    return out
+
+
+def draw_cartoon(ax: plt.Axes) -> None:
+    ax.set_xlim(0, 10)
+    ax.set_ylim(0, 10)
+    ax.set_aspect("equal")
+    ax.axis("off")
+
+    ax.add_patch(Circle((5, 5.4), 3.4, facecolor="#f5deb3",
+                        edgecolor="0.4", lw=1.2, zorder=1))
+    ax.add_patch(Circle((5, 5.4), 1.5, facecolor="0.55",
+                        edgecolor="0.3", lw=1.2, zorder=2))
+
+    # W droplets sinking from the mantle into the core
+    rng_pts = [(3.4, 7.4), (6.7, 7.2), (2.9, 4.6), (7.2, 4.9)]
+    for (x, y) in rng_pts:
+        ax.plot(x, y, "o", color="0.25", ms=5, zorder=3)
+        dx, dy = (5 - x) * 0.35, (5.4 - y) * 0.35
+        ax.add_patch(FancyArrowPatch((x, y), (x + dx, y + dy),
+                                     arrowstyle="-|>", mutation_scale=10,
+                                     color="0.25", lw=1.0, zorder=3))
+    ax.annotate("W (siderophile)\nsinks into the core", xy=(5, 0.6),
+                fontsize=9.5, ha="center", color="0.2")
+
+    ax.annotate("mantle: Hf (lithophile) stays", xy=(5, 9.5), fontsize=9.5,
+                ha="center", color="#8a6d1a")
+    ax.annotate("$^{182}\\mathrm{Hf} \\rightarrow\\, ^{182}\\mathrm{W}$\n"
+                "$t_{1/2} = 8.9$ Myr", xy=(5, 7.6), fontsize=9.5,
+                ha="center", color="#8a6d1a", zorder=4)
+    ax.annotate("core", xy=(5, 5.3), fontsize=10, ha="center",
+                color="white", zorder=4)
+    ax.set_title("(a) parent and daughter separate", fontsize=11)
+
+
+def draw_curves(ax: plt.Axes) -> None:
+    t = np.linspace(0.0, 130.0, 600)
+    for t_cf, color, label in CASES:
+        ax.plot(t, eps_curve(t, t_cf), color=color, lw=2.2, label=label)
+        ax.axvline(t_cf, color=color, lw=0.8, ls=":", alpha=0.6)
+
+    ax.axhline(0.0, color="0.4", lw=1.0)
+    ax.annotate("chondrites (never differentiated)", xy=(64, 0.12),
+                fontsize=8.5, color="0.35")
+    ax.axhline(EPS_EARTH, color="0.2", lw=1.0, ls="--")
+    ax.annotate("Earth's mantle today ($+2\\,\\varepsilon$)",
+                xy=(64, EPS_EARTH + 0.12), fontsize=8.5, color="0.2")
+
+    ax.set_xlim(0, 130)
+    ax.set_ylim(-0.4, 9)
+    ax.set_xlabel("Time after CAI condensation (Myr)")
+    ax.set_ylabel(r"mantle $\varepsilon^{182}\mathrm{W}$ (parts per $10^4$)")
+    ax.legend(title="core formation", loc="center right", fontsize=9)
+    ax.set_title("(b) earlier core formation, larger excess", fontsize=11)
+
+
+def make_plot() -> Path:
+    apply_style()
+    fig, (ax_a, ax_b) = plt.subplots(1, 2, figsize=(10.4, 4.6),
+                                     gridspec_kw={"width_ratios": [1, 1.35]})
+    draw_cartoon(ax_a)
+    draw_curves(ax_b)
+    fig.tight_layout()
+    return save_figure(fig, OUT_AVIF, avif_quality=80)
+
+
+if __name__ == "__main__":
+    out = make_plot()
+    print(out)

book/04_differentiation_magnetospheres/figures/mola_mars_topography.avif

@@ -0,0 +1,87 @@
+"""Generate Fig. (`fig:partitioning-pressure`).
+
+Schematic pressure dependence of the metal-silicate partition
+coefficients of Ni and Co, the two elements that anchor the
+deep-magma-ocean equilibration argument:
+
+    log10 D = a + b * P    (Eq. eq:d-parameterisation at constant T, fO2)
+
+The lines are schematic fits chosen to reproduce the behaviour
+established experimentally (Siebert et al. 2013 Science; Fischer et
+al. 2015 GCA): D(Ni) and D(Co) decrease with pressure, converge
+toward each other, and reach the values required by the bulk silicate
+Earth (D_Ni ~ 26, D_Co ~ 24 from core/mantle mass balance with the
+McDonough 2003 compositions; Fischer et al. 2015 place single-stage
+equilibration at 54 +/- 5 GPa) at pressures near 40-60 GPa.
+
+Caption / figure id : `fig:partitioning-pressure`
+Markdown source     : book/04_differentiation_magnetospheres/differentiation_magnetospheres.md
+Citation keys       : Siebert2013, Rubie2015
+"""
+from __future__ import annotations
+
+from pathlib import Path
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+from scripts.figures._shared.style import apply_style, save_figure
+
+
+REPO_ROOT = Path(__file__).resolve().parents[3]
+OUT_AVIF = (REPO_ROOT /
+            "book/04_differentiation_magnetospheres/figures/"
+            "siebert2013_partition_coefficients.avif")
+
+# Schematic linear fits in log10 D vs P (constant T ~ 3500 K, fO2 ~ IW-2).
+# Anchors: low-pressure D(Ni) ~ 10^4, D(Ni)/D(Co) ~ 5 at low P, and both
+# elements reaching their BSE-required values at ~55 GPa.
+NI = dict(a=4.0, b=-0.0472, color="#d62728", label="Ni")
+CO = dict(a=3.3, b=-0.0380, color="#ff7f0e", label="Co")
+
+# D required by core/mantle mass balance (mantle Ni 1960 ppm, Co 105 ppm,
+# McDonough & Sun 1995; core Ni 5.2 wt%, Co 0.25 wt%, McDonough 2003):
+# D_Ni ~ 26, D_Co ~ 24. Band spans D = 20-32.
+BAND_LO, BAND_HI = np.log10(20.0), np.log10(32.0)
+
+# Equilibration pressure window inferred from the experiments.
+P_LO, P_HI = 40.0, 60.0
+
+
+def make_plot() -> Path:
+    apply_style()
+    p = np.linspace(0.0, 75.0, 200)
+
+    fig, ax = plt.subplots(figsize=(7.2, 5.0))
+
+    ax.axvspan(P_LO, P_HI, color="#1f77b4", alpha=0.10, zorder=0)
+    ax.axhspan(BAND_LO, BAND_HI, color="0.55", alpha=0.30, zorder=1)
+
+    for el, p_lab, dy in ((NI, 22.0, 0.12), (CO, 22.0, -0.30)):
+        d = el["a"] + el["b"] * p
+        ax.plot(p, d, color=el["color"], lw=2.2, zorder=3)
+        ax.annotate(el["label"], xy=(p_lab, el["a"] + el["b"] * p_lab + dy),
+                    color=el["color"], fontsize=11, fontweight="bold",
+                    ha="center", va="center")
+
+    ax.annotate("$D$ required to match the\nmantle's Ni and Co content",
+                xy=(4, (BAND_LO + BAND_HI) / 2), fontsize=9.5,
+                color="0.25", va="center")
+    ax.annotate("inferred equilibration\npressure 40–60 GPa",
+                xy=(50, 3.55), fontsize=9.5, color="#1f77b4",
+                ha="center", va="top")
+
+    ax.set_xlim(0, 79)
+    ax.set_ylim(0, 4.3)
+    ax.set_xlabel("Pressure (GPa)")
+    ax.set_ylabel(r"$\log_{10}\, D^{\mathrm{met/sil}}$")
+    ax.set_title("Metal–silicate partitioning of Ni and Co vs pressure\n"
+                 r"(schematic, at $T \approx 3500$ K, $f_{\mathrm{O_2}} \approx$ IW$-$2)")
+
+    fig.tight_layout()
+    return save_figure(fig, OUT_AVIF, avif_quality=80)
+
+
+if __name__ == "__main__":
+    out = make_plot()
+    print(out)

book/04_differentiation_magnetospheres/figures/siebert2013_partition_coefficients.avif

@@ -15,6 +15,7 @@
 \definecolor{ipsText}{HTML}{2D3748}       % dark gray — body text
 \definecolor{ipsLightFill}{HTML}{EDF2F7}  % light gray — boxes, highlights
 \definecolor{ipsOrange}{HTML}{DD6B20}     % orange — alerts, key results
+\setbeamercolor{button}{bg=ipsAccent, fg=white}
 
 % ── Apply colors to Beamer elements ────────────────────────
 \setbeamercolor{normal text}{fg=ipsText, bg=ipsBackground}

book/references.bib

@@ -20,3 +20,8 @@
 
 % ── Constants ───────────────────────────────────────────────
 \newcommand{\kB}{k_{\mathrm{B}}}
+
+% ── Media links ─────────────────────────────────────────────
+% Clickable button that opens the animated or video version of a
+% figure, e.g. \mediabutton{https://...gif}{Play animation}
+\providecommand{\mediabutton}[2]{\href{#1}{\beamergotobutton{#2}}}