Download Lecture 6: Multiple stars

VI
Multiple stars
6.1 Multiple systems
We have made a hidden assumption in all of our previous discussion that stars form individually. This is probably very wrong...
Observations of the Solar Neighbourhood show that many stars are in binary and multiple systems. The binary fraction is defined as
where S is the number of single stars, B the number of binaries, T the number of triples etc.
Fbin is the fraction of 'systems' that are multiples.
6.1 MS multiples: binary fraction
Fbin in the field is a strong function of primary mass
field
6.1 Multiple systems
There are a number of properties of binary systems that it is important
for star formation to reproduce:
Binary fraction: the number of 'systems' that are multiple (and their Binary fraction:
multiplicities).
Separation/period distribution: the distributions of the semi­major axes Separation/period distribution:
(related to the period by the generic form of Kepler's third law)
Mass ratio distribution: the distribution of secondary mass to primary Mass ratio distribution:
mass (q). Eccentricity distribution: the distribution of orbital eccentricities (actually
Eccentricity distribution:
this is by far the least important).
6.1 Multiple systems
There are three common ways of finding binaries:
Spectroscopic binaries: radial velocity variations (cf. planets) ­ Spectroscopic binaries:
tend to be close and high­mass ratio
Visual binaries: observe two stars close to each other – tends Visual binaries:
to find wide, high­mass ratio systems, also statistical (unless a common proper motion pair)
Photometric binaries: star in the “wrong” Photometric binaries:
place on the HR diagram (redder and brighter) – tends to find high­mass ratio
systems.
(Also rare eclipsing binaries)
eclipsing binaries
6.2 MS multiples: separation/period
Most multiples are binaries, but 15­25% are triples, with a small number of quadruples and higher­order systems. The distribution of periods (equivalently semi­major axes) is very wide and flat...
6.2 MS multiples: mass ratio & eccentricity
6.3 PMS multiples
The fraction of PMS stars in multiples seems to be far higher than in the field (MS stars). In particular there is an excess at around 100au.
6.3 Why 100au?
Our understanding of the thermodynamics of core collapse predicts that the favoured length­scale for fragmentation should be about 100au ­ exactly where we see an excess.
This is at least some evidence that our understanding of core collapse is correct.
(A similar argument can be applied from disc fragmentation which should occur only at >100au.)
6.3 Low­mass PMS multiples
The observations of PMS multiplicity tend to be of approximately Solar mass T Tauri stars. The evidence for high multiplicity in young low­mass stars is very inconclusive.
6.4 Why are the MS and PMS different?
Amongst Solar­type stars the PMS binary fraction is around 100%, compared to about 60% for MS G­dwarfs. Massive stars have a binary fraction of about 100% (they must be young).
Low­mass PMS stars may have a high binary fraction, but it is low (~40%) in the field, they may have an excess at ~100au as well.
Why are the MS and PMS different?
6.4 Why are the MS and PMS different?
Presumably the PMS binary fraction evolves to the MS fraction ­ therefore binary systems are destroyed when they are still young. There are two mechanisms that would do this:
Decay: higher­order (N>2) systems can be unstable and will decay on Decay
short timescales: an N=3 triple will decay into a binary and a single, so
reducing the binary fraction.
Dynamical destruction: an interaction between two binaries will tend Dynamical destruction
to destroy one binary leaving a binary plus two singles. This requires a dense environment in which encounters are common: a dense star cluster.
6.4 The Heggie­Hills law
Binaries in a star cluster can be divided into three classes:
Hard: if the orbital velocity of the binary is >> than the velocity dispersion
Hard
of the cluster the binary should survive and encounters will tend to make the binary even harder.
Soft: if the orbital velocity is << than the velocity dispersion of the cluster Soft
the binary will probably be destroyed by encounters (get softer)
Active: if the orbital velocity is of order the velocity dispersion of the cluster
Active
then the binary might survive, or might be destroyed, depending on the number and severity of encounters.
Hard binaries get harder, soft binaries get softer.
6.4 The Heggie­Hills law
The crucial factor in determining the frequency of interactions is the stellar density.
A typical cluster has 102 – 104 stars pc­3 (compared to <1 for the field) meaning that encounters are at least 102 – 104 more frequent
as the collision time goes as (see also later, r is the radius of a star or stellar system):
or stellar system
6.4 The Heggie­Hills law
The crucial factor in determining if a binary is hard or soft is the velocity dispersion of the surrounding stars. If a cluster is virialised then the velocity dispersion is
For a small cluster this will be about 1 km/s, up to 10 km/s for the largest clusters (105 Msun).
6.4 Binary destruction
In the diffuse Taurus star forming region almost all stars (>0.3 Msun) are found in binaries. In Orion the fraction is far closer to that of the field.
The commonly held view is that almost all stars form in multiples (mainly binaries). Taurus is so diffuse that we still see the birth population. In Orion (which is a far more typical region) many of the binaries have been destroyed by interactions leaving the field population.
Destruction is mass­dependent: low­mass binaries are more easily destroyed resulting in the strong primary­mass vs. binary fraction relationship.
(I disagree with this commonly held view.)
But it is not clear if low­mass stars need to form in binaries... 6.4 Dynamical destruction of binaries
Final distribution Initial distribution
Summary
The MS binary fraction is a strong function of primary mass.
High­mass PMS stars (>0.5 Msun) are observed to have a high binary fraction, close to unity.
Low­mass PMS stars might... it's very unclear.
It is thought that the PMS binary fraction evolves into the MS binary fraction due to decay and destruction.
Binary destruction requires the dense environment of a star cluster to be efficient.
References
For an review of observations of multiple systems and the differences between MS and PMS multiples see Duchene & Kraus (2012) and Goodwin et al. (2007) in 'Protostars and Planets V', Goodwin (2010) in Phil.Trans.A, soon Reipurth et al. (2014) in 'Protostars & Planets VI'.
The classic papers on MS multiplicity are Duquennoy & Mayor (1991, for G­dwarfs), and Fischer & Marcey (1992, for M­dwarfs).
If you ever need to know lots about disruption, Heggie (1974) is a monster paper that covers everything. Binney & Tremaine's 'Galactic Dynamics' is a good book on all dynamics.