Time modulation of the flux of new Jupiter-dominated Oort cloud comets is the subject of interest here. The major perturbation of these comets during the present epoch is due to the tidal field of the relatively smooth distribution of matter in the galactic disk. A secondary source of the near-parabolic comet flux are stars penetrating the inner Oort cloud and providing impulses that create brief comet showers. Substantial stellar-induced showers occur approximately every 100 m.y. Less frequent (but stronger) impulses due to giant molecular clouds can also perturb comets from the inner cloud. These occur on timescales of approximately equal to 500 m.y. In contrast to these infrequent stochastic shower phenomena is the continuously varying tidal-induced flux due to the galaxy. As the Sun orbits the galactic center it undergoes quasiharmonic motion about the galactic midplane, which is superimposed on the small eccentricity, near-Keplerian motion in the plane having epicycle period approximately equal to 150 m.y. In the process the galactic tidal field on the Sun/cloud system will vary causing a modulation of the observable Oort cloud flux. We have created a model of the galactic matter distribution as it affects the solar motion over a time interval ranging from 300 m.y. in the past to 100 m.y. into the future. As constraints on the disk's compact dark matter component we require consistency with the following: (1) the observed galactic rotation curve, (2) today's flux distribution of new comets, (3) the studies of K-giant distributions, and (4) the periodicity found in the terrestrial cratering record. The adiabatically varying galactic tidal torque is then determined and used to predict the time dependence of the flux. We find that a model in which approximately half the disk matter is compact is consistent with these constraints. Under such circumstances the peak-to-trough flux variation will be approx. equal to 5:1 with a full width of 9 m.y. This variability will manifest in the terrestrial cratering record and is consistent with the observed cratering periodicity, if over half of the impacts on Earth are caused by comets or asteroids that originate in the outer Oort cloud

Innanen, K. A.

Matese, J. J.

Valtonen, M. J.

Whitman, P. G.

English

NASA Technical Reports Server

78
N94- 28305
:Y =L.
f
MODULATING TERRESTRIAL IMPACTS FROM OORT
CLOUD COMETS BY THE ADIABATICALLY CHANGING
GALACTIC TIDES. J. J. Matese _, P. G. Whitman I, K. A.
Innanen 2, and M. J. Valtonen 3, _Department of Physics, The
University of Southwestern Louisiana, Lafayette LA 70504-4210,
USA, 2Department of Physics, York University, Toronto ON, M3J
IP3, Canada, 3Tuorla Observatory, SF-21500, Piikki0, Finland.
Time modulation of the flux of new Jupiter-dominated Oo_
cloud comets is the subject of interest here. The major perturbation
of these cornets during the present epoch is due to the tidal field of
the relatively smooth distribution of matter in the galactic disk. A_
secondary source of the near-parabolic comet flux are stars penetrat<
ing the inner Oort cloud and providing impulses that create brief
comet showers. Substantial stellar-induced showers occur approxi- _
mately every 1130 m.y. Less frequent (but stronger) impulses due to i
giant molecular clouds can also perturb comets from the inner cloud•
These occur on timescales of _500 m.y. In contrast to these infre-
quent stochastic shower phenomena is the continuously varying _
tidal-induced flux due to the galaxy. As the Sun orbits the galactic
center it undergoes quasiharmonic (T Z- 64 m.y.) motion about the=
galactic rnidplane, which is superimposed on the small eccentric-
ity, near-Keplerian motion in the plane having epicycle period =
=150 rn.y. In the process the galactic tidal field on the Sun/cloud
sy stem will vary, causing a modulation of the observable Oort cloud
flux. We have created a model of the galactic matter distribution as
it affects the solar motion over a time interval ranging from 300 m.y. t
in the past to 100 m.y. into the future. As constraints on the disk's
compact dark matter component we require consistency with ( I) the
observed galactic rotation curve, (2) today's flux distribution of new
comets, (3) the studies of K-giant distributions, and (4) the period-
icity found in the terrestrial cratering record. The adiabatically
varying galactic tidal torque is then determined and used to predict
the time dependence of the flux. We find that a model in which
approximately half the disk matter is compact is consistent wi_h -"
these constraints. Under such circumstances the peak-to-trough flux
variation will be =,5: I with a full width of 9 m.y. This variability
will manifest in the terrestrial cratering record and is consistent with_
the observed cratering periodicity, if over half of the impacts on
Earth are caused by comets or asteroids that originate in the outer
Oort cloud.
--Analysis: The galaxy is _Toii/ded using a modified CBIP po-
tential with a nucleus, a bulge, a halo, and a disk. The analysis is
similar to that described in lnnanen et al. [1]. A central issue here
is the question of local dark disk matter. Bahcall et al. [2] have
analyzed the distribution of K giants and have concluded that there
• " " r"is "significant but not overwbelmmg evtdence for disk dark matte.
We are guided by their ISM-like model. Two of the three disk
components of the disk are fixed as having scale heights of 325 pc
and 125 pc, mass fractions of 4:1 respectively, and represent old
stellar and atomic gas contributions. The third component is com-
pact and simultaneously includes contributions of young stars, dust,
molecular H, and the dark matter. We then vary three disk param-
eters, the total disk mass, the fraction of disk matter that is compact,
and the scale height of the compact component.
The disk mass is tightly constrained by a present solar velocity,
which we fix at O = 225 km s-L The scale height and mass fraction
of the compact component are primarily limited by the K-giant
studies and the period requirement. The equations of motion of the
Sun about the galactic center are solved both backward and forward
/
in time. As initial conditions we adopt Z® - 10 pc and R® - 8 kpc
along with a Z component of velocity of 7.5 km s-_ . The scale height
and mass fraction of the compact component is then varied (keeping
the total mass fixed) and the solar motion is determined. In Fig. 1
we show the parameter range that reproduces the required plane-
crossing period. For further illustrations we choose the specific
parameter set for the compact disk component to have scale height
50 pc and mass fraction 0.50. It corresponds to total local disk
midplane density of 0.29 M o pc -3 and yields a mean plane crossing
period of 32 m.y. This is within the Io range of values (dark matter
mass fraction 0.24-0.74) given in [2] for their ISM model. In
Fig. 2 we illustrate the trajectory of the Sun as it orbits the galaxy.
The time interval considered is from I00 m.y. in the future to
300 m.y. in the past,
Results: It has been demonstrated that the galactic tidal field
dominates random stellar encounters in making Oort cloud comets
observable [3-5]. Matese and Whitman describe how the time
evolution of all orbital elements can be analytically determined if
the disk density O® (t) can be taken as adiabatically changing. The
results are expressible in terms of Jacobi elliptic functions, Of the
elements (_, £'2, i, e, and a only the last is taken tobe invariant in the
80 . , 80
_eak/trough density ratio /
70
2.5 ..... ............... : ..............
3' 0 ....... M_ 5 0
8 50
,o .o.........................Y"<'--- ..... ,o,-r. 30 30c,.} ---
"_ 5.0
0.3 0.4 0.5 0.6 0.7
Fraction of Disk Matter that is Compact
_- Fig. 1. Parameter range of the disk compact matter. Solid curves border
parameters for galactic midplane crossing intervals of 30-32 m.y. Dashed
curves illustrate the ratio of maximum to minimum disk density per oscillation
cycle.
v
O.06 +
0.06
0.04
0.02
0.00
•-0.02
-0.04
-0.06
-o.0a
7.8 8.0 6.2 8.4 8.6 8.8 9.0 9.2 9.4
Re(kpe)
Fig. 2. Solar trajectory from 300 m.y. in the past to 100 m.y. in the future.
https://ntrs.nasa.gov/search.jsp?R=19940023802 2020-06-16T15:02:17+00:00Z
LP1 Contribution No. 825 79
"i
g
E
Z
0.020 . , . , • , , ............
0.015 / today sflux/ /in situ
• includes hyperbolic
/ ["_ Jupiter dominated
t
0.010 _ // :i_ earth erossers
o
ooooJc- u,
-10 0 10 20 30 40 50 60 70 80 90
x= I/a
4O
3O
2O
I0
o
lOO
Fig. 3. Theoretical Oort cloud flux for today's density. The observed flux of
new class Icomets is shown also.
adiabatic limit. Since a typical Oort comet has a semimajor axis a =
30,000 AU (period --5 m.y.) this approximation is adequate here.
Our model of the Oort cloud includes the following assumptions.
The distribution of comet angular momenta and perihelia direc-
tions is taken to be random. For the in situ comet energy flux (shown
in Fig. 3) we adopt the predictions of Bailey [6] where x--- 106 AU/a
is a dimensionless original energy and the nominal cloud boundary
is a - 105 AU. A Monte Carlo analysis proceeds in a manner de-
tailed in [4,5] in which trajectories are evolved one period into the
future and new orbit parameter values are determined. The notion
of a "tidal efficiency," which measures the ability of the galactic tide
to overcome the loss cylinder barrier and change the perihelion
distance, was described in [5]. We use the tidal efficiency, at a time
retarded by half an orbital period, along with in situ flux density to
predict the flux of Oort comets whose perihelia leap the loss cylinder
barrier (15 AU) to the zone of Jupiter dominance in a single orbit due
to tides.
Figure 3 also shows today's predicted Earth-crossing as welt as
Jupiter-dominated flux. The results are scaled to the observed flux
of new comets today. For comparison we further show the observed
distribution [7] of class I comets that are broadened by measurement
errors and nongravitational forces. The time-dependent Jupiter-
dominated current is displayed along with the galactic density at the
solar location in Fig. 4. We have subjected the results of Fig. 4 to a
conventional regression analysis to determine the width of the
current peaks. The standard deviations are 4.0-4.5 m.y.
In Table I we list the epochs of peak Oort cloud currently
entering the solar system as well as the maximum and minimum
rates. One observes that the cycle interval, x, changes, i.e., the
"periodic" oscillations have in fact a variable period. Further, the
phase of the nearest cycle peak is 0.6 m.y. in the future with the
adopted parameters. This is consistent with the terrestrial cratering
record [8,9]. There is ample evidence from the dating of impact
structures and impact glass that suggests that the nearest flux
maximum may not have occurred as yet. The predictions are in good
agreement with the dating of impact glasses, microspherules, and
the Ir anomalies that have peaks at I, 35, and 65 m.y. ago [9].
Shoemaker and Wolfe state that the cratering record appears to
be periodic but consider it to be a statistical fluke as they can find
v
.o
L)
3.0
2.5
2.0
1.5
1.0
0.5
0.0 ..... _ • ' '
-lO0 0 100
Epoeh(Ma)
0.4
'--
......... Galactic densi Ly at Solew location ]
_a__ 0,0
200 aO0
0.3
Q.
U
o.2 .<
?
"NO.1 =
Fig.4. Time dependence of theJupiter-dominated current of comets from the
outer Oort clouddue to the adiabatically changing galactic tides. Note the small
retardationbetween the current and thedensity.
no mechanism for the periodicity. In particular they reject the
galactic oscillations model of Rampino and Stothers [8] since it
requires the impulsive perturbation of inner Oort cloud comets by
molecular clouds. As the plane-crossing epochs are too close to the
crater peak times of 2, 32, 65, and 99 m.y. ago to be due to rare
stochastic cloud impulses, the Rampino-Stothers mechanism was
rejected as a clock for this phenomena. These objections are obvi-
ated in the present model since modulation of outer Oort cloud
comet flux is the physical mechanism for the periodicity.
In comparing these results with the numerical experiments on
impact periodicity, we need to estimate the total dispersion ex-
pected from a strictly periodic sequence, i.e., we should convolve
the standard error in the mean cycle interval (=I m.y.) with the
standard deviation of the modulation about the cycle peak (=4 m.y.)
and the dating uncertainties of the most accurately dated craters
(=4 m.y.). If terrestrial cratering impact probabilities were modu-
lated as described here with dating uncertainties of this order, we
would expect a net dispersion about a strictly periodic signal to be
=5-6 m.y. Were such a signal to have a reasonable probability of
TABLE I. Oortcloud maximum [minimum] currents.*
-t,,_' (I") Earth Jupiter
-95.0 (33.8) 0.146 [0.0251 1.088 [0.199]
-61.2 (31. i) 0.168 [0.035] 1.250 [0.275]
-30.1 (29.5) 0.210 [0.043] 1.554 [0.328]
-0.6 (31.3) 0.202 I0.0331 1.501 [0.260]
30.7 (34.0) 0.160 [0.025] 1.193 [0.193]
64.7 (33.4) 0.145 [0.027] 1.085 [0.2101
98. I (30.5) 0.176 [0.038] 1.306 [0.294]
128.6 (29.7) 0.212 [0.0421 1.571 [0.323]
158.3 (31.9) 0.194 [0.031] 1.441 [0.241]
190.2 (34.2) 0.153 [0.024] I. 143 [0.189]
224.4 (32.9) 0.148 I0.029] I. 107 [0.2241
257.3 (30.0) 0.t 85 I0.0401 1.376 [0.311 ]
287.3 0.214 1.581
* Scaled to 0.2 Earth-crossers/yr today.
+ Epoch of maximum comet current, in Ma.
"Cycle interval to previous maximum, in m.y.
80 KT Event and Other Catastrophes
manifesting itself in the cratering record the steady-state main-belt
asteroidal cratering rate would have to be <50% of the total.
It is noted that the actual galactic disk matter compactness and
the past solar motion are not well known. Should it be verified that
(1) over half the disk matter is compact and of scale height =50 pc,
and (2) over half of terrestrial cratering is due to active, dormant, or
extinct comets having an origin in the outer Oort cloud, then the
solar oscillation cycle will manifest itself in the cratering record at
the marginally significant level observed. These results do not
require the dark matter to be in the form of massive objects capable
of impulsing the inner Oort cloud. Detectable modulation will exist
even in the absence of infrequent molecular cloud showers. The
observed periodicity in terrestrial cratering would then no longer be
rejectable as a statistical fluke and we would be approaching a flux
maximum from the outer Oort cloud within the next =1 m.y. We
could then say that today we are at the peak of a continuous cometary
drizzle, if not a shower.
References: [I ] Innanen K. A. et al. (1978) Astrophys. Space
Sci., 57, 511-515. [2] Bahcall J. N. et al. (1992) Astrophys. J., 389,
234-250. [3] Heisler J. and Tremaine S. (1986) Icarus, 65, 13-26.
[4] Matese J. J. and Whitman P. G. (1989) Icarus, 82, 389-401.
15] Matese J. J. and Whitman P. G. (1992) Celest. Mech. Dyn.
Astron., 54, 13-36. [6] Bailey M. E. (1986) Mon. Not. R. Astron.
Soc., 218, 1-30. [7] Marsden B. G. (1989) Catalogue of Cometary
Orbits, 6th ed. 18] Rampino M. R. and Stothers R. B. (1986) The
Galaxy and the Solar System, 241-260. [9] Shoemaker E. M. and
Wolfe R. F. (I 986) The Galaxy and the Solar System, 338-386.
A SEARCH FOR TEKTITE-RELATED STRUCTURES IN
NORTHEASTERN THAILAND: AN EXAMINATION OF
SPOT SATELLITE IMAGES, J.F. McHone Jr. 1, K. Pitak-
paivan 2, S. Bunopas 2, P. Angsuwathana 2, T. Supajanya 3, and J. T.
Wasson 4, _Arizona State University, Tempe AZ, USA, 2Geological
Survey Division, Department of Mineral Resources, Bangkok,
Thailand, 3Chulalongkorn University, Bangkok, Thailand, 4Univer-
sity of California, Los Angeles CA 90024, USA.
The dip of the magnetic remanence indicates that layered (Muong-
Nong-type) Australasian tektites formed as puddles of melt with
their layers roughly parallel to the Earth's surface [ 1,2]. Wasson [3]
concluded that, because silicate melt can only retain its heat within
the incandescent impact plume, these melts were ejected from
nearby small (kilometer-sized) craters. Several deposits of layered
Australasian tektites have been found in northeastern Thailand,
with the largest in the northeastern corner.
We obtained a set of seven high-resolution, 1:50000-scale, SPOT-
I and SPOT-2 satellite images covering parts of the southeastern
comer of northeastern Thailand and examined them for possible
impact structures. Four adjacent images and corresponding topo-
graphic maps provided location and elevation controls for the most
promising region comprising more than 3000 kmL Examination of
these yielded several sites that may be craters.
Layered tektites are found over a band 1200 km long extending
from Hainan Island in the noah-northeast to central Cambodia in the
south-southwest. Wasson [3] noted that it appears to be impossible
for a single large (5-20-kin radius) crater to produce puddles of melt
over such a large region and suggested that a cometary projectile
broke up in deep space with the fragments producing many thou-
TABLE1. Kilometer-sized circular features near Buntharik and Det
Udom, Thailand, recognized
on satellite images and topographic maps.
Site °E °N Feature
1 105.42 14.73
2 105.46 14.73
3 105.15 14.77
4 105.24 14.80
5 105.48 14.83
6a 105.07 14.98
6b 105.14 14.85
6c 105.06 14.76
6d 105.17 14.85
0e 105.32 14.63
Shallow 1.5-km-diameter basin with annular
ring at 2.5 kin.
I-km depression includes reservoir.
Bleached rim indicates grading. Airstrip.
Bull's-eye structure. Radius of outer ring
(with stream) 2.5 kin. inner ring 1 km.
Village on central mound. Annular rings at
1-kin and 4-kin radii.
Annular drainage. May be eviscerated
dome.
Small elliptical feature on topographic high.
Radius 0.15 kin.
Several ellipt ical to subrounded features.
Radii <0.3 km.
Elliptical features, some farmed. Possible
meander scars.
Elliptical feature. Bleached southern mar-
gin. Radius 0.3 km.
Numerous small, vegetated, rounded fea-
tures having radii <_0.3km
sands of small craters across the region where layered textiles have
been found. The microtektites and the tektites showing atmospheric
ablation features were launched from the largest one or more craters
whose formation deposited enough energy to produce a plume that
penetrated through the atmosphere.
Much of this 1200-kin-long field of the layered tektites is moun-
tainous and has experienced appreciable erosion during the 770 ka
since the Australasian tektites were formed [4]. Other regions,
particularly in the valley of the Mekong and some other major rivers,
have been covered by recent sediments. Particularly promising for
crater preservation is the fiat-lying Khorat Plateau of northeastern
Thailand. The southeastern comer of northeastern Thailand is within
the layered-tektite band; in fact, large deposits of layered tektites
have recently been discovered near the county-seat town of Bunthafik.
The existence of these tektites demonstrates that erosion in the
region has been minimal during the past 770 ka. The bedrock is
mainly sandstone; there seems to be little salt or limestone in the
stratigraphic column, and thus there are no solution features that
would mimic small craters.
The locations of the most promising sites are summarized in
Table I. All sites are on the four quadrangles 60381-60384 cover-
ing the region 105.0 °- 105.5°E and 14.5 °- 15.0°N. The Thai coordi-
nates listed in Table I are kilometers east of Bangkok and north of
the equator. The prime search site is the first, which shows up
prominently on aerial photos, the SPOT image, and the 1:50000
topographic sheet. All bear investigating; one, site 5, is only a few
kilometers from a region where large layered tektites are being
found today.
Site 1: Centered about 5 km south-southeast of Amphoe
Buntharik, this site was the target of a brief reconnaissance visit in
February 1989. The site is a topographic depression about 0.7 km in
radius surrounded by a discontinuous, slightly elevated rim to the
east. An isolated hill in the west may represent a large ejecta block.
A north-south road from Buntharik to Kaeng Sawang traverses the


Modulating terrestrial impacts from Oort cloud comets by the adiabatically changing galactic tides

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