Spins and Satellites: Probes of Asteroid Interiors

Alan W. Harris and Petr Pravec

Sixth Catastrophic Disruption Workshop

Cannes, 9-11 June 2003

Probes to Asteroid Interiors

• Fast rotation barrier - rubble piles

• Small super-fast rotators - monoliths

• Tumbling rotation - damping time scale

• Shapes - required internal strength

• Binaries - implications for internal structure

• Very slow rotation - escaped binaries?

Asteroid Rotation Rates vs. Diameter988 astero ids tota l

0.01

0.1

1

10

100

1000

Spi

n R

ate

(rev

/day

)

0.1 1.0 10.0 100.0 1000.0

D iam eter (k m )

1000

100

10

1

0.1

Period (hours)

0.1 1.0 10.0 100.0 1000.0

Fast rotation barrier

0.01

0.1

1

10

100

1000

Spi

n R

ate

(rev

/day

)

0.1 1.0 10.0 100.0 1000.0

D iam eter (k m )

1000

100

10

1

0.1

Period (hours)

0.1 1.0 10.0 100.0 1000.0

Small super-fast rotators – “monoliths”

0.01

0.1

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100

1000

Spi

n R

ate

(rev

/day

)

0.1 1.0 10.0 100.0 1000.0

D iam eter (k m )

1000

100

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0.1

Period (hours)

0.1 1.0 10.0 100.0 1000.0

Main monoliths-rubble piles transition

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n R

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0.1 1.0 10.0 100.0 1000.0

D iam eter (k m )

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0.1

Period (hours)

0.1 1.0 10.0 100.0 1000.0

Slow rotators excess988 astero ids tota l25 astero ids w ith f < 0.16<f> , D >0.15 km

0.01

0.1

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n R

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/day

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0.1 1.0 10.0 100.0 1000.0

D iam eter (k m )

1000

100

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0.1

Period (hours)

0.1 1.0 10.0 100.0 1000.0

Running Box Mean Spin vs. Size

1

10

Spi

n R

ate

(rev

/day

)

251 252 253 254 255 256 257 258 259 25

1 10 1 00

D iam eter (k m )

1 10 1 00

Spin Rate Distribution of Large Asteroids

0 .0 1 .0 2 .0 3 .0

N o rm alized sp in ra te

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0N

umbe

r

Large asteroids (D > 40 km )

Collisional equilibrium, Gravitational and Material Strength Regimes

0.01

0.1

1

10

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1000

0.01 0.1 1 10 100 1000

Material strength regime

Gravitational regime

file: d:\rot\mar01\rot.pltfile: d:\rot\mar01\rot.plt

Diameter, km

Rot

atio

n pe

riod,

hou

rs

Rotation rate vs. Diameter

Rubble Pile Speed Limit

Centrifugal force = Gravity

ellipsoid prolate afor

sphere afor 3

abaGm

o

o

Rubble Pile Speed Limit (spherical)

0.01

0.1

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Spi

n R

ate

(rev

/day

)

0.1 1.0 10.0 100.0 1000.0

D iam eter (k m )

1000

100

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0.1

Period (hours)

0.1 1.0 10.0 100.0 1000.0

Rotation Rate Limit vs. Shape

0.0

0.5

1.0

1.5

2.0

Lig

htcu

rve

Am

plit

ude

(mag

)

C ritica l b u lk d e n sity :1 .0 g /ccm

2.0 g/ccm

3.0 g /ccm

4.0 g /ccm

5.0 g /ccm

D >0.15 km

D <0.15 km

2001O E84

2002TD 60

176 N EAs + M ars-crossers

0.1 1.0 10.0 100.0 1000.0

S p in R ate (rev /d ay )

Non- principal Axis Rotation

)/( 3223 rKQ

The damping time scale to principal-axis rotation is:

where is mechanical rigidity, Q is the energy dissipation factor, is density, K3

2 is a shape factor with a possible range from 0.01 (near spherical) to 0.1 (highly elongate). r and are asteroid radius and rotation rate, respectively. For values of , Q, , and K3

2 appropriate for “rubble piles”, rotation period P in hours, and diameter D in km, the damping time scale in billions of years is:

2

3

5000DP

Observed Tumbling Asteroids990 astero ids tota l950 astero ids w ith f from 0.16<f> to 11.5 /d , D >0.15 km

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0.1

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1000

Spi

n R

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(rev

/day

)

0.1 1.0 10.0 100.0 1000.0

D iam eter (k m )

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100

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0.1

Period (hours)

Tum bling astero ids

"rubble p iles"30x m ore rig id

0.1 1.0 10.0 100.0 1000.0

Strength Implied from ShapesAverage slope is 11.5, maximum is 49. Thus shape could be maintained by loose regolith.

The asteroid shape hugs the Roche lobe within ~1 km average, coming as close as 0.09 km.

Similar profiles probably apply to Ida, and even Kleopatra.Figure from Miller, et al., Icarus 155, 3-17 (2002)

Binary AsteroidsName Method D, km r/R a/R e Rot. P. Orbit P. Density

Main Belt/Trojan 22 Kalliope AO 181 0.10 11.7 4.15 3.6d 2.30.4 45 Eugenia AO 215 0.06 11.1 0 5.70 112.6 1.20.4 87 Sylvia AO, HST 271 0.05 10.1 5.18 3.6d 1.60.3 90 Antiope AO 85 1.0 4.0 0 16.51 16.51 1.30.4 107 Camilla HST 237 0.04 ~8 4.84 121 Hermione AO 209 0.06 >6 243 Ida SC 31 0.05 7.0 4.65 37 2.60.5 617 Patroclus (T) AO 105 0.9 11.6 81.8 81.8 1.30.5 762 Pulcova AO 140 0.14 11.6 5.84 96 1.80.8 1509 Esclangona AO 12 0.3 >25 3749 Balam AO 6 0.2 ~100 ? months 3782 Celle LC 6 0.43 6.8 3.84 36.57 2.3 TNO Pluto DI 2300 0.26 16.6 0 6.387d 6.387d 1.8 1997 CQ29 HST 300 ~1 35 26308 1998 SM165 HST 450 0.42 25 7.98h 1998 WW31 DI, HST 170 0.8 260 0.8 570d 0.6? 1999 TC36 AO, HST 740 0.36 22 2000 CF105 HST 170 0.6 270 2001 QT297 DI 580 0.7 70 2001 QC298 HST 350 (large) >30 2001 QW322 DI 200 1.0 1250 ~1 1500d NEA 3671 Dionysus LC 0.9 >0.28 5.2 (0) 2.7053 27.72 5381 Sekhmet RA 1.5 few h 5407 1992 AX LC 4.0 0.30 3.4 <0.05 2.5488 13.52 31345 1998 PG LC 0.9 0.30 3.4 (0) 2.5162 14.01 35107 1991 VH LC 1.2 0.40 5.4 0.07 2.6238 32.69 1994 AW1 LC 0.9 0.53 4.6 <0.05 2.5193 22.40 1996 FG3 LC 1.4 0.31 3.4 0.05 3.5942 16.16 1998 ST27 RA 0.4 <0.3 ~20 ? ? ? 1999 HF1 LC 3.5 0.24 4.0 ? 2.3191 14.02 1999 KW4 RA, LC 1.2 0.3 4.2 <0.03 2.765 17.45 2.61.6 2000 DP107 RA, LC 0.8 0.38 6.6 0.01 2.7755 42.2 1.71.0 2000 UG11 RA, LC 0.23 0.6 3.6 0.12 (4.44) 18.4 1.50.7 2001 SL9 LC 1.0 0.31 3.6 (0) 2.4003 16.40 2002 BM26 RA 0.6 ~0.2 ~10 ? ~2.7 ~72 2002 KK8 RA 0.5 0.2

Binary primaries – Spin vs. Size990 astero ids tota l950 astero ids w ith f from 0.16<f> to 11.5 /d , D >0.15 km

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n R

ate

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/day

)

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D iam eter (k m )

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Period (hours)

M B + Tro jan b inariesNEA binaries

0.1 1.0 10.0 100.0 1000.0

Binary primaries – Amplitude vs. Spin

0.0

0.5

1.0

1.5

2.0

Lig

htcu

rve

Am

plit

ude

(mag

)C ritica l b u lk d e n sity :

1 .0 g /ccm

2.0 g /ccm

3.0 g /ccm

4.0 g /ccm

5.0 g /ccm

D >0.15 km

D <0.15 km

B in a ry p rim a rie s:N EAM BA

176 N E As + M ars-crossers

0.1 1.0 10.0 100.0 1000.0

S p in R ate (rev /d ay )

NEA vs. MB binaries

• Fast rotation of primaries (relatively to similarly sized single asteroids) in both groups (except for 90 Antiope which is a synchronous double asteroid)

• Lower amplitudes (i.e., elongations) of primaries of NEA binaries than those of MB binaries – related to size, primary spin rate, size ratio, or orbital class ??

Some points for discussion

• Greater abundance of NEA binaries may be the result of tidal disruptions. Argues for rubble pile structure.

• MB/Trojan binaries are likely collision products. Near equal-mass binaries may be nature’s only way to solve an angular momentum excess of a gravitationally bound blob of matter.

• Time scale of tidal evolution sets constraints on internal properties of primary and secondary, and time of formation.

• Near-unstable shape/spin configurations of some asteroids (Ida, Eros) suggest very easy formation of satellites from ejecta.

Very Slow Rotation

1

10

100

0.01 0.1 1

N(<f ) f 3

N(<f ) = 45f + 27f 3

±N1/2

Observed N(<f )

file: d:\rot\mar01\slow2l.plt

(b)

file: d:\rot\mar01\slow2l.pltfile: d:\rot\mar01\slow2l.pltfile: d:\rot\mar01\slow2l.pltfile: d:\rot\mar01\slow2.pltfile: d:\rot\mar01\roty.out

f, rev/day

N(<f

)

0

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300

0 0.5 1.0 1.5 2.0

N(<f ) = 45f + 27f 3

±N1/2

Observed N(<f )

file: d:\rot\slowrot\fig1a.pltfile: d:\rot\mar01\slow2.pltfile: d:\rot\mar01\slow2.plt

(a)

file: d:\rot\mar01\slow2.pltfile: d:\rot\mar01\slow2.pltfile: d:\rot\mar01\roty.out

f, rev/day

N(<f

)

Slow Rotation by Satellite Escape

Characteristics of an initially contact binary that would leave the primary with no spin upon escape of the secondary:

r ab

Well, maybe not...

The distribution of despun primaries should be uniform in residual rotational energy. Since rotational energy is proportional to f 2, one would expect the resulting distribution of spins to be N(<f ) f 2

instead of the observed N(<f ) f .

Stay tuned….

Concluding Remarks

• The main transition between “rubble piles” and “monoliths” is around D=0.15 km. Fraction of monoliths among asteroids with D=0.2-1 km is on the order of a few percent. (Are there rubble piles below D=0.15 km?)

• Tumblers suggest that “monoliths” may be a few ten times more rigid (longer damping time scales) than “rubble piles”.

• NEA binary primaries’ rotations/amplitudes are consistent with rubble pile structure.

The Cruelty of Nature

• If MB binaries had the average characteristics of TNO binaries the first would probably have been discovered in the 1800’s, by visual observation.

• If MB binaries had the average characteristics of NEA binaries, they would likely have been found by lightcurves decades ago.

• Of all the ways to find a binary, the only method that has yet to yield a confirmed discovery is by stellar occultation.