Keith A. HolsappleUniversity of Washington

holsapple@aa.washington.edu

Keith A. HolsappleUniversity of Washington

holsapple@aa.washington.edu

Does melt volume give the signature of the

impactor?

Does melt volume give the signature of the

impactor?

Higher impact velocity => more melt..

Therefore, a study of melt volume in the field can give information about the impact velocity.

Higher impact velocity => more melt..

Therefore, a study of melt volume in the field can give information about the impact velocity.

The Premise:

This is an example of an inverse problem of Impacts:

This is an example of an inverse problem of Impacts:

Given a result, what was the problem??

Given the crater, what was the impactor size and velocity?

Given the melt volume, what was the impactor size and velocity?

Given a result, what was the problem??

Given the crater, what was the impactor size and velocity?

Given the melt volume, what was the impactor size and velocity?

The solution lies in good scaling laws:

The solution lies in good scaling laws:

Crater size=F1(impactor size, impactor velocity)

Melt Volume=F2(impactor size, impactor velocity)

Given the craer size and melt volume, Solve for impactor size and velocity.

Crater size=F1(impactor size, impactor velocity)

Melt Volume=F2(impactor size, impactor velocity)

Given the craer size and melt volume, Solve for impactor size and velocity.

But, the scaling laws have limits:

But, the scaling laws have limits:

• For Crater Size:• Small scale experiments• Numerical Calculations• + Theoretical scaling arguments

• For melt volume• Cannot get experimental data in lab

experiments• Therefore, we must rely on codes (or

theoretical estimates)

• For Crater Size:• Small scale experiments• Numerical Calculations• + Theoretical scaling arguments

• For melt volume• Cannot get experimental data in lab

experiments• Therefore, we must rely on codes (or

theoretical estimates)

Code calculations give a way to estimate the answers to such problems, by performing a suite of calculations to see how the outcome depends on the input.

Code calculations give a way to estimate the answers to such problems, by performing a suite of calculations to see how the outcome depends on the input.

This problem is much simpler than the entire impact problem, it is governed by the Hugoniot, and an assumed value for the energy (or pressure) that must be reached to eventually give melt when unloaded.

Code studies of melt scaling:

Code studies of melt scaling:

Ahrens and O’Keefe, 1977: Energy scaling, Vmelt~E holds (above a threshold)

Bjorkman and Holsapple, 1987 (Ahrens and O’Keefe were wrong)

Pierazzo, Vickery and Melosh, 1997(Bjorkmann and Holsapple were wrong)

Today, 2003 Pierrazo et al. were wrong) (Well, partially)

So, what can we expect to learn form a suite of code calculations to determine the amount of melt volume?

So, what can we expect to learn form a suite of code calculations to determine the amount of melt volume?

First, some features of hypervelocity impact

problems:

First, some features of hypervelocity impact

problems:

Scaled Pressure Decay Assuming a Point-Source

0.01

0.1

1

10

100

0.1 1 10 100

Scaled Range=(r/a)(c/U) μ

= /(Scaled Pressure P

ρc2)

101 =80 /run U km s

101 =40run b U/km s

101 =20run a U/km s

Self Similar

- , -Point Source Self similar regime

- , -Point Source Not-Self Similar

“Close-in” or “initially”, the impactor size, velocity, mass, and other details such as shape, impact angle, material, color, and so on affect the process

“Close-in” or “initially”, the impactor size, velocity, mass, and other details such as shape, impact angle, material, color, and so on affect the process

However, by the time the shock has traveled about 2 impactor radii, those individual features do not matter.

However, by the time the shock has traveled about 2 impactor radii, those individual features do not matter.

Instead there is a single product measure that determines all subsequent aspects of the process.

(Well approximately)

Instead there is a single product measure that determines all subsequent aspects of the process.

(Well approximately)

Point-source measures: a single scalar measure of

all sources in a given material

Point-source measures: a single scalar measure of

all sources in a given material

Radius aVelocity UMass density

Energy KEMomentum H

Mass m

aUμ

or

Combines to

KE(3μ-1)H(2μ1or

So: We can only determine the value of the combination aUμ of the source from any measured “far-field” quantity of the result.

So: We can only determine the value of the combination aUμ of the source from any measured “far-field” quantity of the result.

In that case measurements of two different "far-field" quantities cannot be used to separately estimate size and velocity, both are determined by the same combination.

In that case measurements of two different "far-field" quantities cannot be used to separately estimate size and velocity, both are determined by the same combination.

But is Melt volume “Near field”, or “far field?”??

i.e. Does it scale differently from crater size??

But is Melt volume “Near field”, or “far field?”??

i.e. Does it scale differently from crater size??

The Pierazzo et al. (1997) data

0.1

1

10

100

1000

10000

10 100 1000 10000

U^2/Emelt

Vmelt/Vimpactor

granitedunitealuminumB-H MeltIceIronPierazzo et al FitIce fit

Slope=1.05

Their conclusion is that, except for the ice data, the melt volume scales as U2.1 , slightly above energy scaling, which scales as U2.

They conclude that: "We see no evidence for the 'less than energy' scaling for U> 50 km/s found by Bjorkman and Holsapple"

(Bjorkman and Holsapple actually report energy scaling for U2/Em <100, which is U<30 km/s, and that Vmelt~U1.83 above that.)

Their conclusion is that, except for the ice data, the melt volume scales as U2.1 , slightly above energy scaling, which scales as U2.

They conclude that: "We see no evidence for the 'less than energy' scaling for U> 50 km/s found by Bjorkman and Holsapple"

(Bjorkman and Holsapple actually report energy scaling for U2/Em <100, which is U<30 km/s, and that Vmelt~U1.83 above that.)

But, fitting only this same data for velocities above 30 km/s gives, for each material, a dependence of U1.8, below the energy-scaling result, consistent with point-source scaling, and the same as the Bjorkman-Holsapple result.

But, fitting only this same data for velocities above 30 km/s gives, for each material, a dependence of U1.8, below the energy-scaling result, consistent with point-source scaling, and the same as the Bjorkman-Holsapple result.

Point-Source Fits to Pierazzo et al Melt Dataw/ μ=0.6, 0 / km s and higher

10

100

1000

100 1000 10000

^2/U Emelt

/Vmelt Vproj

granitedunitealuminumIceIron

Pierazzo et al Fit Aluminum Fit

granite fit dunite fit

iron fit Ice fit

So what, you might ask, 2.1 or 1.83, who

cares?

So what, you might ask, 2.1 or 1.83, who

cares?

The difference is important when we look at field data, which is not in terms of the impactor (which is unknown) but is in terms of the crater volume.

Do size and melt scale differently, or the same?

The difference is important when we look at field data, which is not in terms of the impactor (which is unknown) but is in terms of the crater volume.

Do size and melt scale differently, or the same?

Crater Size scaling: Crater Size scaling:

Melt Volume Scaling (Pierazzo et al.):€

Dcrater =Kcratera0.78U 0.43g−0.22

€

Vmelt =Kmelta3 U

2

Em

⎛

⎝ ⎜

⎞

⎠ ⎟

1.05

If crater diameter and melt volume is known, then:

€

aU 0.55 =K1

€

aU 0.70 =K2

€

U =K2Vmelt

0.33

K1Dcrater1.28

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1

0.15

∝Vmelt

2.22

Dcrater8.53

But if: But if:

€

Vmelt =Kmelta3 U

2

Em

⎛ ⎝ ⎜

⎞ ⎠ ⎟

0.9

Then:

And if the same exponent μ determines both, then

€

Vmelt =Kmelta3 U

2

Em

⎛ ⎝ ⎜

⎞ ⎠ ⎟

0.825

And the impact velocity cannot be determined

€

U =K2Vmelt

0.33

K1Dcrater1.28

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1

0.05

∝Vmelt

6.66

Dcrater25.6

€

U =K2Vmelt

0.33

K1Dcrater1.28

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1

0.00

∝Vmelt

∞

Dcrater∞

Accuracy required to determine U within 50%, assuming

μ=0.55:

Accuracy required to determine U within 50%, assuming

μ=0.55:

Melt Scaling"

Ua

On Vmelt/Kmelt

On Emelt On Dcrater/Kc

a=2.1 20% 20% 5%

a=1.8 6% 6% 2%

A=1.68 1% 1% 0.3%

Conclusions:

If the two scaling laws have a different combination aUm, then, in principle crater size and melt volume can be used to unfold the impactor size and velocity.

1. However, if the same exponent governs both, the calculation degenerates, and no solution is possible.

2. In any case, small differences in melt volume or crater size lead to very different solutions, because the measured quantities are being raised to a very large power.

Conclusions:

If the two scaling laws have a different combination aUm, then, in principle crater size and melt volume can be used to unfold the impactor size and velocity.

1. However, if the same exponent governs both, the calculation degenerates, and no solution is possible.

2. In any case, small differences in melt volume or crater size lead to very different solutions, because the measured quantities are being raised to a very large power.

The determination of the impact velocity and size from field measurements is essentially hopeless.

The determination of the impact velocity and size from field measurements is essentially hopeless.

The end, thank you.