Keith A. Holsapple

1
Does melt volume give the signature of the
impactor?

• Keith A. Holsapple
• University of Washington
• holsapple_at_aa.washington.edu

2
The Premise

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

3
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?

4
The solution lies in good scaling laws

• Crater sizeF1(impactor size, impactor velocity)
• Melt VolumeF2(impactor size, impactor velocity)
• Given the craer size and melt volume, Solve for
  impactor size and velocity.

5
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)

6
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.
7
Code studies of melt scaling

• Ahrens and OKeefe, 1977 Energy scaling, VmeltE
  holds (above a threshold)
• Bjorkman and Holsapple, 1987
• (Ahrens and OKeefe were wrong)
• Pierazzo, Vickery and Melosh, 1997
• (Bjorkmann and Holsapple were wrong)
• Today, 2003
• Pierrazo et al. were wrong)

(Well, partially)
8
So, what can we expect to learn form a suite of
code calculations to determine the amount of melt
volume?
9
First, some features of hypervelocity impact
problems
10

• 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

11
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)

12
Point-source measures a single scalar measure of
all sources in a given material
Radius a Velocity U Mass density d
Energy KE Momentum H Mass m
or
Combines to
aUmdn
KE(3m-1)H(2-3m)d(3n-1)
or
13
So We can only determine the value of the
combination aUmdn of the source from any measured
far-field quantity of the result.
14
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??

15
The Pierazzo et al. (1997) data
Slope1.05
16

• 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 Ugt 50 km/s found
  by Bjorkman and Holsapple"
• (Bjorkman and Holsapple actually report energy
  scaling for U2/Em lt100, which is Ult30 km/s, and
  that VmeltU1.83 above that.)

17
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.
18
So what, you might ask, 2.1 or 1.83, who cares?
19
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?
20
If crater diameter and melt volume is known, then

• Crater Size scaling

Melt Volume Scaling (Pierazzo et al.)
21

• But if

Then
And if the same exponent m determines both, then
And the impact velocity cannot be determined
22
Accuracy required to determine U within 50,
assuming m0.55
Melt Scaling" Ua On Vmelt/Kmelt On Emelt On Dcrater/Kc
a2.1 20 20 5
a1.8 6 6 2
A1.68 1 1 0.3
23

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

24
The determination of the impact velocity and size
from field measurements is essentially hopeless.
The end, thank you.