chondrule formation - jeremiah horrocks · stammler & dullemond (2014) impossible to melt the...

Chondrule FormationShock Model vs. Impact ModelChondrule Formation

Shock Model vs. Impact Model

Sebastian Markus Stammler1

Cornelis Petrus Dullemond1, Daniel Harsono1, Anders Johansen2

1 Center for Astronomy, Institute of Theoretical Astrophysics, Heidelberg University2 Lund Observatory, Sweden

Disc Dynamics & Planet Formation Cyprus, 29 June – 3 July

Credit: E. Moser

Credit: E. Moser

Credit: Jürgen Otto & Norbert Classen

1 mm

Constraints on chondrule formation:

● Flash heating

● Cooling rates

● Chondrule size distribution

● Chondrule-matrix complementary

● Chondrule age

● ...

Constraints on chondrule formation:

● Flash heating

● Cooling rates

Energy argument

Required energy:

35 300 J/g (Wasson 1996)

Estimated chondrule mass:

~1027 g (Morris & Desch 2009)

Total energy needed:

3.5 x 1031 J = 9.8 x 1024 kWh

in 2011: 4.77 x 109 kWh

2.1 x 106 Gyr

data.worldbank.org

Cooling rates

Desch et al. (2012)

The shock model

Boley & Durisen (2008)

The shock model

● 1-D, stationary hydro model

● Decelleration by drag force

● Frictional heating

● With radiative transfer

The shock model

Stammler & Dullemond (2014)

Tpeak

Tpost

The shock model

Stammler & Dullemond (2014)

Impossible to melt the chondrule completely AND sustain a lowpost-shock temperature simultaneously

solidus

liquidus

The shock model

Estimation of energy loss by radiative diffusion

0.01 HP

0.02 HP

0.04 HP

∞

Diffusive length scale

Even with unrealistically short diffusion length scalesThe particles stay hot for too long.

Credit: NASA/JPL-Caltech

The impact model

The impact model

Dullemond, Stammler & Johansen (2014)

Three main parameters: M cloud , T 0 , v exp

Optical depth from center to surface: τ ( t)=3

4 π

M cloud κ

vexp2

1t 2

Opacity: κ =34

1ξ chon achon

The impact model

Dullemond, Stammler & Johansen (2014)

In the center of the cloud:

T (t< t cool) = T 0

T (t> t cool) = T 0[ 35

tt cool

+25 ]

−5/3

t cool ∝ M cloud2 /5 T 0

−3/5 v exp−4 /5

The impact model

Dullemond, Stammler & Johansen (2014)

The impact model – the future

SPH simulation by Daniel Harsono

Summary

The shock model

The impact model

● Difficult to cool the particles in a large scale shock

● Cooling rates do not match laboratory experiments

● Possible volatile loss

● Even in a simple approach the cooling rates can match the requirements for a wide parameter range

● Volatile loss can be prevented by saturation in high density regions

● SPH simulations are performed for more detailed calculations