Planetary perturbations for Oort clouds comets

Marc FouchardHans RickmanChristiane FroeschléGiovanni Valsecchi

Lille workshop, 27th-30th September 2011

  

Our modelEach time a comet is at barycentric distance smaller than r

s, the planetary perturbation is 

applied at its perihelion. 

The perturbation is computed using a barycentric restricted and circular 6 bodies problem (Sun, Jupiter, Saturn, Uranus, Neptune, comet). 

The computation of the perturbation starts with the comet placed at a barycentric distance d

bary and ends when either the comet passes again the distance d

bary, or reaches its 

aphelion or hits a planet or the Sun. 

The initial (t=0) mean anomaly of the planets corresponds to their actual mean anomaly.

Before and after each perturbation one has to shift from Galactic coordinates to barycentric ones. 

The equatorial coordinates of the north Galactic pole are :

= 192.8595°, = 27.128336°

The equatorial coordinates of the Galactic centre, taken as origin for the Galactic longitude are :

= 266.4051°, = ­ 28.936175°

We consider these coordinates as independent of time!

  

rs and d

bary

How to choose rs and d

bary ? 

We have integrated 300(q)x36(i)x9()x10(t) comets initially on parabolic orbits.  The initial q, i and  are taken on regular grids whereas the time of perihelion is taken at random.

For each comet we record the barycentric distances d

8, … ,d

4 at which the variation of the barycentric  

orbital energy (taken equal to ­1/a) becomes greater than  10­8, … ,10­4 (AU­1) respectively.

For each grid point in (q,i,) we consider the mean, max and min of the 10 d

k values obtained with the 

different t.

  

Evolutions of dk

15 au

32 au

75 au50 au

100 aud

7 (mean)

min

max

d6 (mean)

min

max

d5 (mean)

min

max

d8 (mean)

min

max

d4 (mean)

min

max

In the following results we have retained rs=37 AU and d

bary=100 AU.

  

Simulations with only the planetary perturbations

We initially have 106 Oort cloud comets randomly chosen with uniform distribution in cos i (in        [­1,1]) ,, M (in [0°,360°]) and q (in [0, 32 AU]) and a=20,000 AU (those are elements with respect to the Ecliptic and the Solar System barycentre).

Each comet is integrated for a maximum of 1 Gyr or 1000 perihelion passages, or if a < 1000 AU or the comet hits the Sun or a planet.

  

Comparison with Fernandez (1981)

Comparison of the strandard deviations of the energy changes during the first passage at perihelion of our Oort cloud comets (colored lines) with the results obtained by Fernandez (1981) (black lines).

  

Transparency factorBehaviour of the transparency factor P versus the initial orbital elements q, cos i. P is defined as the proportion of comets that have z

final<-10-4 AU-1 or

zfinal

> -5x10-6 AU-1 after the first

planetary kick.

PP for z

final<-10-4 AU-1 only

P for zfinal

> -5x10-6 AU-1 only

  

The flux of comets with respect to the number of perihelion passages

  

Full simulationsInitial thermalized Oort cloud with 106 comets with 

energy distribution similar to DQT 87.

Each comet is integrated for a maximum of 5 Gyr. 

The other end states are:

Impact with a planet or the Sun

Ejection from the Solar­System

If no planetary perturbations are modelled, injection into the loss cone (heliocentric distance smaller than 15 AU)

Attention if given to comets that are observable (heliocentric distance smaller than 5 AU) for the first time

  

Injection scenarii with planets

q (UA)

-1/a

Galactic and stellar effect Planetary perturbations

0

15

5

0

Creepers True-Jumpers

Jupiter-Saturn barrier

Kaib&Quinn-Jumpers

  

Flux of observable comets for different models

TidesTides+StarsTides+PlanetsTides+Stars+Planets

Number of comets that come at heliocentric distance smaller than 5 AU for the first time per period of 50 Myr versus time.

  

Oort peak for different models I

Tides Stars, Tides

Tides

Planets, Tides

zorig

(before PP)

zinit

(at t=0)

Relative distribution of z=-1/a, wrt the total number of injected comets, for quiescent comets which come at heliocentric distance smaller than 5 AU for the first time. The last 3 Gyr are considered except for the Tides only model for which the first 2 Gyr were considered

n=2902

n=6204 n=7411

n=2142

  

Oort peak for different models II

Tides Stars,Tides

Tides

Planets, Tides

zorig

(before PP)

zinit

(at t=0)

Relative cumulative distribution of z=-1/a for quiescent comets which come at heliocentric distance smaller than 5 AU for the first time. The last 3 Gyr are considered except for the Tides only model for which the first 2 Gyr were considered

Finit

(2x104 au)= 0.00

Finit

(2x104 au)=0.67 Finit

(2x104 au)=0.70

Finit

(2x104 au)=0.30

  

Preliminary ConclusionsThe Solar System seems to be more transparent than it is usually 

thought, with a transparency factor always smaller than 60%, and smaller than 50% for q<5 AU, and 20% for q<10 AU.

This allows comet to make several perihelion passages even inside Jupiter orbit (several tens for few retrograde orbits with q<0.5 AU)

 The flux of observable comets is almost doubled when all perturbations are taken into account wrt simulations with Tides+Stars or Tides+Planets

The distribution of semi­major axis for the Tides+Planets model is consistent with Kaib&Quinn (2009) results.

  The addition of stellar perturbations results in a shift to smaller semi­major axis of the Oort peak

Results need to be disentangle