1. Signatures of formation mechanisms in the multiple-star statistics
A. Tokovinin CTIO/NOAO, Chile
Recent results & updates
on binary and multiple-star
statistics
Facts to be explained by the theory
M.Bate et al.
Toronto, May 2007

2. Orbital parameters as a fossil record of binary formation
Relevant orbital parameters [and evolution effects]
Period P (semi-major axis a)
[tides, magnetic braking, mass transfer, encounters]
Eccentricity e [tides, mass transfer]
Mass ratio q =M2/M1 (M2) [mass transfer]
Primary mass M1 [mass transfer]
Multiple (N>2) systems:
period and mass ratios, relative inclinations, etc.
Toronto, May 2007

3. Binary & multiple statistics
Observations,
selection effects
joint distribution
f (P,e,q,M1)
f (P,e,q,M1) is multi-dimensional
f (P ) is its projection
f (P )*f (e )*f (q )*f (M1) is wrong!
Statistics depends on
the environment, not universal
Physical processes
and models
N-body dynamics
Accretion & migration
Toronto, May 2007

4. Periods and companion fraction
Öpik’s law is still unexplained!
Toronto, May 2007

5. Period-eccentricity relation
Abt (2005), B0-B9.5
Udry et al. (1998), G V
Toronto, May 2007

6. Eccentricity distribution
f (e)=2e ??
Abt (2006), FGK
SBs with massive
secondaries have
higher eccentricities
0.5
e=1
Ribas & Miralda-Escude (2007)
Toronto, May 2007

7. Mass ratio Random pairing is excluded at ALL periods
There is a population of twins (q ~1) among SB and VB [accretion or… mass transfer?]
Brown dwarf desert (lack of small q) at short and long periods
2M0
5M0
Soderhjelm (2007)
Random pairing
Toronto, May 2007

8. Mass ratio distribution
f (q,P )
f (q) ~ q0
not dynamics!
Abt & Levy 1976
f (q) ~ q -1/3
Kouwenhoven et al.
Toronto, May 2007

9. Multiples (N>2) Solar-type dwarfs type % Single 56 (57) Binary
36 (38)
Triple
6 (4)
N>3
2.5 (1)
Tokovinin (2005)
vs. DM91
(15yr later)
Multiples are
still being discovered within
25 parsec!
Highest: N=6
(N=7 possible)
Up to 4 levels
of hierarchy!
GJ 225.2
Toronto, May 2007

10. Are all close binaries triple? No!
P<3d: all triple
P>10d: 35% triple
Fraction of triples
SB period [days]
Tokovinin et al. 2006: FGK-dwarfs, P=1…30 day
f (q) – same!
Toronto, May 2007

11. Period ratios in FGK multiples
PL/PS=10 000
PL/PS=5
(stability)
Plong [years]
Migration?
Gap at Pshort ~100d?
Pshort [days]
PL/PS~100
Toronto, May 2007

12. Mass ratios in multiplesq3
Plong [years]
Most massive component is preferentially in the close system (18% q3>1)
Mass ratio of the tertiary decreases with its period?
Toronto, May 2007

13. Relative orientation of orbital spins
Spin correlation
Less hierarchical
triples have
more correlated
spins
Period ratio
Sterzik & Tokovinin 2002
Spin correlation
is determined from the counts of co-rotating
and counter-rotating systems
Toronto, May 2007

14. Fact summary (I) Periods obey Öpik’s distribution f (logP) ~ const
CSF and f (P) depend on the environment and M1
Average e~0.5, f (e) same for planets and SB
SBs with larger q have larger e
f (q) depends on period, no random pairing
Twins with q~1 exist at short and long periods
Brown dwarf desert at short and long periods
Toronto, May 2007

15. Fact summary (II) Multiples with N>3 are common (~2.5%)
All P<3d binaries are multiple
Half of P~10d binaries are NOT multiple
PL/PS is 5…104 for wide multiples, but >100 for close (PS<30d) multiples
Most massive component prefers close sub-system
Tertiary mass decreases with its period
Orbital spins in triples are correlated
Toronto, May 2007

16. Challenges
Can we model f (e) from the binary-disk interaction during migration?
How many proto-binaries merged?
Are twins formed by a special mechanism?
Who will explain the Öpik’s law?
Toronto, May 2007