Chondrule formation by collisions of planetesimals containing volatiles triggered by Jupiter's formation

Abstract

Chondrules are spherical or subspherical particles of crystallized or partially crystallized liquid silicates that constitute large-volume fractions of most chondritic meteorites. Chondrules typically range $0.1-2\,$mm in size and solidified with cooling rates of $10-1000\,{\rm K\,h^{-1}}$, yet these characteristics prove difficult to reconcile with proposed formation models. We numerically show that collisions among planetesimals containing volatile material naturally explain both the sizes and cooling rates of chondrules. We show that the high-velocity collisions with volatile-rich planetesimals first induced in the solar nebula by Jupiter's formation produced increasing amounts of silicate melt for increasing impact velocities above $2\,{\rm km\,s^{-1}}$. We propose that the expanding gas formed from volatile materials by collisional heating dispersed and cooled the silicate melt, resulting in droplet sizes and cooling rates consistent with the observed sizes and inferred cooling rates. We further show that the peak melt production is linked to the onset of Jupiter's runaway gas accretion, and argue that the peak age of chondrules points to Jupiter's birth dating 1.8 Myr after CAIs.

Figures (8)

• Figure 1: a: Snapshots of a head-on collision (impact velocity, 5 km s$^{-1}$) between $100$ and $400$ km diameter planetesimals composed of dunite. Initial porosities of the 100 and 400 km planetesimals are 0.4 and 0, respectively. From left to right, collision after $0$, $25$, $50$, and $75$ s are shown. Cylindrically symmetrical coordinates where the vertical ($z$) axis is the center of symmetry surrounded by the horizontal ($r$) axis are adopted. The color shows the volume fraction of the melt. The amount of melt reaches a maximum when $t=75$ s, at which the melt thickness is $10$ km at the central axis. b: The amount of the mass of melt normalized by the impactor mass $M_{\rm melt}/M_{\rm imp}$ as a function of the impact velocity with a fixed porosity of $0.4$. If the impact velocity is faster than $6\,{\rm km\,s}^{-1}$, the melt mass exceeds the mass of the impactor. c: The normalized amount of melt $M_{\rm melt}/M_{\rm imp}$ as a function of impactor porosity with a fixed impact velocity of $4\,{\rm km\,s^{-1}}$
• Figure 2: Temporal evolution of the collisional production rate of chondrules across the different orbital regions of the inner Solar System. The collisional melt production in each annular region is computed by integrating overall impacts that occurred within its boundary in each temporal interval over which we resolve the collisional evolution (see Methods). The left plot shows the scenario of the in situ formation of Jupiter, and the right plot shows the scenario of extensive migration of Jupiter following its formation beyond the N$_2$ snowline. The peak efficiency in melt production is achieved between 3 and 4 au in both scenarios. The insets in the plots show the cumulative production of chondrules over time, the sharp increase at about 1.8 Myr is the result of Jupiter's runaway gas growth.
• Figure 3: a: Schematic of the geometry of numerical simulation. The initial arrangement of the melt layer is approximated by the layer of thickness $L_0$ covering a planetesimal of radius $R_{\rm pla}$. b: Schematic of the melt layer expansion. Volatile material in the layer with thickness $L_0$ evaporates and expands with a velocity $v_{\rm gas}(r)$. Silicate melt is dragged by gas and has a velocity $v_{\rm melt}(r)$. The melt forms droplets of diameter $D$ determined by Weber number at which collisional equilibrium occurs.
• Figure 4: Results of melt breakup simulation using parameters of $f=0.1$, $L_0=10$ km and $m/m_{\rm H}=18$. The horizontal axis is the distance $r$ from the center of the target planetesimal normalized by the radius of the target planetesimal $R_{\rm pla}$. Snapshots of $t/t_0=27.5$, $55$, $82.5$, and $110$ s are shown. a: evolution of spatial densities of melt ($\rho_{\rm melt}$: purple) and gas ($\rho_{\rm gas}$: green) components normalized by the initial average density of melt-gas mixture $\rho_{\rm av}$. The dashed horizontal line is the breakup density, where the volume fraction of melt is $0.2$. The initial surface of the melt layer is $r/R_{\rm pla}=1.1$. b: evolution of melt ($v_{\rm melt}$) and gas ($v_{\rm gas}$) velocities. The melt component is dragged by gas and $v_{\rm gas}> v_{\rm melt}$. c: evolution of the velocity difference between gas and melt $v_{\rm gas}-v_{\rm melt}$. d: Evolution of the distribution of the melt diameter $D$. The curve starts at $r/R_{\rm pla}=1.1$ when $t=27.5$ and $55\,$s because the breakup does not proceed at these periods.
• Figure 5: a: Evolution of average droplet size for simulation using $f=0.1$, $L_0=10\,$km, and $m/m_{\rm H}=18$ case. The numerical result (solid) and analytical solution (dashed) (Eq.(\ref{['Dfit2']}) are shown. The breakup of melt occurs ($t/t_0=75$) when the melt volume fraction falls belowSparks$0.2$. b: Evolution of temperature decrease. The solid (dashed) lines are the numerical (analytical: Eq. (\ref{['DT']})) results. The horizontal dotted line is $400$ K, where the melt solidifies. Inset: evolution of the cooling rate. Solid (dashed) lines are the numerical (analytical: Eq. (\ref{['dTdt3']})) results. c: Evolution of the location of the melt layer surface normalized by the planetesimal radius $L(t)/R_{\rm pla}$. The dashed line is the least-square fitting. d: Evolution of the average melt spatial density within $L(t)$ normalized by the initial melt density $\rho_{\rm melt,av}/\rho_{\rm melt,0}$ ($\rho_{\rm melt,0}=2047\,{\rm kg\,m}^{-3}$). The dashed line is an approximated formula $3R_0^2L_0^2/L(t)^3$, where $L(t)$ is given by the least-square fitting line in panel c.