A numerical check of the

Collisional Resurfacing scenario

Philippe Thébault & Alain Doressoundiram

Observatoire de Meudon

Color Dispersion within the Kuiper Belt

Color Dispersion within the Kuiper Belt

- Correlated to orbital parameters

¤ inclination

¤ eccentricities (?)

¤ periastron

¤ Vrms = (e2 + i2)1/2 Vkep

Possible explanations

• Intrinsic physical differences within the early KB

•Coexistence of 2 distincs populations

¤ Excited objects originating from the a < 30 AU region

¤ indigenous « Cold » objects

•Collisional resurfacing

Unlikely because of too weak physical gradients in KBO region

- Surface Reddening by space wethearing

(sun radiative processing, sun or galactic cosmic rays,…)

-Mutual Collisions

resurfacing by fresh « gray » material

The collisional resurfacing scenario

• Competing effect between

Requires both mechanisms to act on comparable timescales

The collisional resurfacing scenario

While space weathearing should act ~homogeneously throughout the KB, the level of collisional resurfacing should strongly depend on KBO’s excitations and positions

Collisional resurfacing should leave a signature that might be tracked

Could it explain the observed correlation with orbital parameters?

To a first approximation:

Search for a link between color-index and objects’ excitation

Vrms=(e2+i2)1/2.VKep

But it’s more complicated than this …

Problems with a local Vrms analysis…

Need for a more complete study, taking into account spatial distributions and mutual interactions

GOAL:

¤ Numerically estimate the relative spatial distribution of kinetic energy received by collisions within the KB

¤ search for similarities with the relative distribution of color-index

do the regions of « bluer » KBOs match the regions of higher collisional activity ?…

Deterministic code following the evolution of test particles under the gravitational pull of Sun+4giant-planets.

2 populations:

¤ 500 test target bodies in the 38-55 AU region placed in the identified stable regions

embedded in a swarm of

¤ 2500-5000 test impactors bodies

Close encounter search algorithm => estimate <dv>coll and Ecin for each impact on a target

At the end of the run, we compare Ecin for each target and derive a spatial map of the relative amount of kinetic energy received by collisions within the numerical system.

Numerical Procedure

The target population

The impactor population

a) cut-off at 48 AU

The impactor disc

b) extended excited disc

c) extended « cold » disc

The impactor population

The impactor population

d) SKBO only (academic)

¤ moderate correlation with e

¤ Weak correlation with i

¤ Strong correlation with q

¤ Vrms correlation with large dispersion

¤ « bluer » plutinos

Results / case 1

¤ Weak correlation with e

¤ Weak correlation with i

¤ moderate correlation with q

¤ Vrms correlation with large dispersion

¤ « bluer » plutinos

Results / case 2

¤ moderate correlation with e

¤ Weak correlation with i

¤ moderate correlation with q

¤ Vrms correlation with large dispersion

¤« bluer » outer disc bodies

Results / case 3

No significant correlations

Results / case 4

eccentricity inclination qCase 1: 48 AU cutoff 0.33 (3.10-2) 0.12 (0.05) 0.48 (4.10-25)

Case 2: exicted outer disc 0.27 (8.10-8) 0.14 (0.015) 0.28 (5.10-8)

Case 3: « cold » outer disc

0.41 (2.10-15) 0.16 (4.10-3) 0.38 (4.10-2)

Case 4: SKBO only 0.12 (4.10-3) 0.06 (0.55) -0.07 (0.24)

Correlations between Ecin and orbital parameters

(Spearman’s rank correlation coefficient)

Similarities with color-index distribution in the « real » belt

Global statistical correlations

with e, i, q and Vrms

but…

¤ Stronger correlation with e than with i

BUT other features strongly contradict the observed correlations:

¤ tendency towards highly impacted (« bluer ») plutinos

-« out of plane effect »

- more structure in e than in i

Possible explanations

• simplicity of the numerical model?

• better understanding of the physical processes at play

Long range effect of the space weathering

continuous reddening or formation of a neutral mantle?

different collisional environment in the plutino region?

too academic impactor discs ?

• give up the C.R. scenario in favour of an alternative explanation

Can these contradictions be explained within the frame of the C.R. scenario?

• but problems with the spatial localisation of

highly collisional regions “gray” KBOs localisation

Conclusions

• general statistical correlations with e,q, Vrms… ( i )

c.f. color indexes in the« real » belt

numerical estimations of inhomogeneities of the collisional activity within the KB