Transcript Spins and Satellites: Probes to Interiors Alan W. Harris, JPL

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
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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. Diameter
0.1
1.0
10.0
100.0
1000.0
988 asteroids total
1000
0.1
1
10
10
1
Period (hours)
Spin Rate (rev/day)
100
100
0.1
1000
0.01
0.1
1.0
10.0
Diameter (km)
100.0
1000.0
Fast rotation barrier
0.1
1.0
10.0
100.0
1000.0
1000
0.1
1
10
10
1
Period (hours)
Spin Rate (rev/day)
100
100
0.1
1000
0.01
0.1
1.0
10.0
Diameter (km)
100.0
1000.0
Small super-fast rotators – “monoliths”
0.1
1.0
10.0
100.0
1000.0
1000
0.1
1
10
10
1
Period (hours)
Spin Rate (rev/day)
100
100
0.1
1000
0.01
0.1
1.0
10.0
Diameter (km)
100.0
1000.0
Main monoliths-rubble piles transition
0.1
1.0
10.0
100.0
1000.0
1000
0.1
1
10
10
1
Period (hours)
Spin Rate (rev/day)
100
100
0.1
1000
0.01
0.1
1.0
10.0
Diameter (km)
100.0
1000.0
Slow rotators excess
0.1
1.0
10.0
100.0
1000.0
988 asteroids total
25 asteroids with f < 0.16<f>, D>0.15 km
1000
0.1
1
10
10
1
Period (hours)
Spin Rate (rev/day)
100
100
0.1
1000
0.01
0.1
1.0
10.0
Diameter (km)
100.0
1000.0
Running Box Mean Spin vs. Size
1
10
100
Spin Rate (rev/day)
10
1
925
825
1
725
10
Diameter (km)
625
525 425
325
225
125
100
25
Spin Rate Distribution of Large Asteroids
90
Large asteroids (D>40 km)
80
70
Number
60
50
40
30
20
10
0
0.0
1.0
2.0
Normalized spin rate
3.0
Collisional equilibrium, Gravitational and
Material Strength Regimes
Rotation rate vs. Diameter
0.01
Rotation period, hours
0.1
Ma
ter
i al
str
e
ng
th
reg
im
e
1
Gravitational regime
10
100
1000
0.01
0.1
1
10
Diameter, km
100
1000
Rubble Pile Speed Limit

Centrifugal force = Gravity
Gm
 o 
for a sphere
3
a
b
   o    for a prolate ellipsoid
a

Rubble Pile Speed Limit (spherical)
0.1
1.0
10.0
100.0
1000.0
1000
0.1
1
10
10
1
Period (hours)
Spin Rate (rev/day)
100
100
0.1
1000
0.01
0.1
1.0
10.0
Diameter (km)
100.0
1000.0
Rotation Rate Limit vs. Shape
176 NEAs + Mars-crossers
Critical bulk density:
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
Lightcurve Amplitude (mag)
2.0
1.5
2002TD60
1.0
2001OE84
0.5
0.0
0.1
1.0
10.0
Spin Rate (rev/day)
100.0
1000.0
Non- principal Axis Rotation
The damping time scale to principal-axis rotation is:
  Q /( K 32 r 2 3 )
where  is mechanical rigidity, Q is the energy dissipation
factor,  is density, K32 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 K32 appropriate for “rubble
piles”, rotation period P in hours, and diameter D in km,
the damping time scale in billions of years is:
P3

5000D 2
Observed Tumbling Asteroids
0.1
1.0
10.0
100.0
1000.0
990 asteroids total
950 asteroids with f from 0.16<f> to 11.5/d, D>0.15 km
1000
Tumbling asteroids
"rubble piles"
30x more rigid
0.1
1
10
10
1
Period (hours)
Spin Rate (rev/day)
100
100
0.1
100
m.y
.
4.5
b.y.
1000
0.01
0.1
1.0
10.0
Diameter (km)
100.0
1000.0
Strength Implied from Shapes
Average 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.
Figure from Miller, et al., Icarus 155, 3-17 (2002)
Similar profiles probably
apply to Ida, and even
Kleopatra.
Binary Asteroids
Name
Main Belt/Trojan
22 Kalliope
45 Eugenia
87 Sylvia
90 Antiope
107 Camilla
121 Hermione
243 Ida
617 Patroclus (T)
762 Pulcova
1509 Esclangona
3749 Balam
3782 Celle
TNO
Pluto
1997 CQ29
26308 1998 SM165
1998 WW31
1999 TC36
2000 CF105
2001 QT297
2001 QC298
2001 QW322
NEA
3671 Dionysus
5381 Sekhmet
5407 1992 AX
31345 1998 PG
35107 1991 VH
1994 AW1
1996 FG3
1998 ST27
1999 HF1
1999 KW4
2000 DP107
2000 UG11
2001 SL9
2002 BM26
2002 KK8
Method
D, km
r/R
a/R
e
Rot. P.
Orbit P.
Density
AO
AO
AO, HST
AO
HST
AO
SC
AO
AO
AO
AO
LC
181
215
271
85
237
209
31
105
140
12
6
6
0.10
0.06
0.05
1.0
0.04
0.06
0.05
0.9
0.14
0.3
0.2
0.43
11.7
11.1
10.1
4.0
~8
>6
7.0
11.6
11.6
>25
~100
6.8
4.15
5.70
5.18
16.51
4.84
3.6d
112.6
3.6d
16.51
2.30.4
1.20.4
1.60.3
1.30.4
4.65
81.8
5.84
37
81.8
96
2.60.5
1.30.5
1.80.8
3.84
months
36.57
2.3
DI
HST
HST
DI, HST
AO, HST
HST
DI
HST
DI
2300
300
450
170
740
170
580
350
200
0.26
~1
0.42
0.8
0.36
0.6
0.7
(large)
1.0
16.6
35
25
260
22
270
70
>30
1250
6.387d
6.387d
1.8
0.8
570d
0.6?
~1
1500d
LC
RA
LC
LC
LC
LC
LC
RA
LC
RA, LC
RA, LC
RA, LC
LC
RA
RA
0.9
1.5
4.0
0.9
1.2
0.9
1.4
0.4
3.5
1.2
0.8
0.23
1.0
0.6
0.5
>0.28
5.2
(0)
0.30
0.30
0.40
0.53
0.31
<0.3
0.24
0.3
0.38
0.6
0.31
~0.2
0.2
3.4
3.4
5.4
4.6
3.4
~20
4.0
4.2
6.6
3.6
3.6
~10
<0.05
(0)
0.07
<0.05
0.05
?
?
<0.03
0.01
0.12
(0)
?
0
0
?
0
7.98h
2.7053
few h
2.5488
2.5162
2.6238
2.5193
3.5942
?
2.3191
2.765
2.7755
(4.44)
2.4003
~2.7
27.72
13.52
14.01
32.69
22.40
16.16
?
14.02
17.45
42.2
18.4
16.40
~72
2.61.6
1.71.0
1.50.7
Binary primaries – Spin vs. Size
0.1
1.0
10.0
100.0
1000.0
990 asteroids total
950 asteroids with f from 0.16<f> to 11.5/d, D>0.15 km
1000
MB + Trojan binaries
NEA binaries
0.1
1
10
10
1
Period (hours)
Spin Rate (rev/day)
100
100
0.1
1000
0.01
0.1
1.0
10.0
Diameter (km)
100.0
1000.0
Binary primaries – Amplitude vs. Spin
176 NEAs + Mars-crossers
Critical bulk density:
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
2.0
Binary primaries:
Lightcurve Amplitude (mag)
NEA
MBA
1.5
1.0
0.5
0.0
0.1
1.0
10.0
Spin Rate (rev/day)
100.0
1000.0
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 equalmass 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
300
(a)
(b)
3
100
N(<f )  f
3
N(<f ) = 45f + 27f
N(<f ) = 45f + 27f
1/2
±N
1/2
3
Observed N(<f )
±N
Observed N(<f )
N(<f )
N(<f )
200
10
100
1
0.01
0.1
f, rev/day
1
0
0
0.5
1.0
f, rev/day
1.5
2.0
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
a
b
b/a
r/a
m/M
P, hrs
1/1
0.577
0.192
3.63
2/3
0.456
0.214
4.38
1/2
0.394
0.245
5.13
2/5
0.355
0.280
5.86
1/3
0.328
0.317
6.56
1/4
0.290
0.391
7.89
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.