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Physical properties of components in multiple stars and their dynamics
V.V. Orlov (St. Petersburg State University), R.Ya. Zhuchkov (Kazan Federal University), O.V. Kiyaeva (Pulkovo Observatory), E.V. Malogolovets (Special Astrophysical Observatory), Yu.Yu. Balega (Special Astrophysical Observatory), I.F. Bikmayev (Kazan Federal University)


Overview
1. Classification 2. Hierarchy and stability 3. Stability criteria for triple systems 4. Systems with weak hierarchy 5. Effect of errors (Monte Carlo approach) 6. Dynamical simulations 7. New observations 8. Physical properties (spectra and masses) 9. New simulations 10. Conclusions


Classification

I. Methods of observations:
1. 2. 3. 4. Astrometry Photometry Spectroscopy Speckle interferometry

II. Structure:
1. Non-hierarchical (Orion Trapezium) 2. Hierarchical ( Lyrae) Note: apparent configuration may be another than actual one (projection effect)


Hierarchy and stability
Systems of strong hierarchy are probably stable (superposition of few weakly perturbed Keplerian orbits). Non-hierarchical systems are dynamically unstable. Rare exclusions may be in vicinity of stable periodic orbits

Systems with weak hierarchy - ???


Stability criteria
Analytical (so far are derived only for n = 3). Semi-analytical (only for n 4). Numerical simulations (it is possible for arbitrary n).

Note: One needs to take into account the external perturbations (regular field of the Galaxy and GMC)


Analytical stability criteria for triple stars: 1. Golubev's criterion (1967, 1968)

where c and H are angular momentum and total energy of triple system, G is gravity constant, M1 M2 are masses of inner pair components, M3 is mass of distant component. Critical value sc depends on mass ratio and it is derived by solution of algebraic equation of the 5-th degree.


2. Aarseth's criterion (2003)

3. Valtonen's criterion (2007)


Sample of multiple systems with known orbital elements for all subsystems Methods to study dynamics 1. Stability criteria for triple systems. 2. Numerical simulations for all systems. Error effect Monte Carlo approach - variation of orbital elements and component masses assuming Gaussian distribution of uncertainties (1001 trials for each system).


Preliminary results
1) Evidently, hierarchical systems are probably stable (escape probability during 106 years is less than 10%). 2) Several low-hierarchical systems may be unstable (escape probability during 106 year is greater than 90%). The detailed study was made for systems: HD 40887 (GJ 225.2), HD 76644 ( UMa = ADS 7114), HD 136176 (ADS 9578), HD 217675/6 ( And), HD 222326 (ADS 16904) HD 284419 (T Tau).


Possible reasons of appearance of unstable systems with low hierarchy
1. Errors of observations. 2. Temporary capture due to encounter of binary (multiple) system and single star or two binary (multiple) systems. 3. Stability loss due to encounter of stable multiple system and massive object (GMC, black hole, star of field etc.). 4. Product of dissipation of star cluster or stellar group. 5. Effect of component's merging. 6. Physical young components. Expected number of unstable systems within the sphere of 200 pc around the Sun for scenarios 2-4: ~ 1 В 102 for systems with Pout < 103 years.


Additional observations of the systems with weak hierarchy
1.

6-m telescope (BTA) SAO RAS ­ speckleinterferometry (SI) of close pairs. 2. 1.5-m Russian-Turkish telescope (RTT) ­ spectroscopy of components with high and moderate resolution. 3. Direct images using VLT.


The results for selected systems with weak hierarchy (physical properties of components)
System HD 40887 AB+CD HD 76644 AB+CD HD 217675 AB+CD HD 222326 A?+BC HD 284419 A+BC Spectral types K5V, M0V, K4V, ??? F0V, WD?, M3V, M4V B6III, ???, A0V, ??? Masses, MSun 0.69, 0.25, 0.65, 0.25 1.70, 1. ?, 0.35, 0.30 6.8, 2.3, 2.9, 3.7

G0III, ???, F3III, sdO-BVIII 1.2, ???, 1.3, 0.7 PMS, Ae, ??? 2.0, 2.73, 0.61


More accurate results for selected systems
HD 40887 (Gliese 225.2) The system is quadruple. Orbital elements (Tokovinin et al. 2005)

Pair AB Pair -

We need to make - orbit.


More accurate results for selected systems

HD 217675/6 ( And)
Quadruple system


More accurate results for selected systems

HD 217675/6
Pair B1B
2


More accurate results for selected systems

HD 217675/6

(Zhuchkov et al. 2010) Pair

Pair B


More accurate results for selected systems
HD 222326 (ADS 16904)
Triple(?) system (Zhuchkov et al. 2008) -

The system is probably stable. Possibly, it is quadruple.


More accurate results for selected systems
HD 284419 (T Tau) Triple system (Zhuchkov et al. 2010) NS pair Sab pair

We have derived the family of orbital solutions of outer subsystem. The system is probably stable, however there are the instability regions too.


More accurate results for selected systems
HD 76644 ( Uma = ADS 7114) Quadruple system. (Zhuchkov et al. 2006, 2011 (in prep.))

The system is unstable with probability 0.98.


Conclusions
For a few multiple stars, which were classified as preliminary unstable, we have derived more accurate physical parameters of components and orbital solutions of the subsystems. We have made more definite conclusions on their dynamical stability.


Thank You for Your attention!


Stability storage due to i-th criterion (i = 1,2,3):

where ki is observable value of i-th stability parameter, kic is its critical value. For stable system i > 0. Different criteria may give different results for systems with weak hierarchy. Error effect

Here i ic are the uncertainties of the i-th stability parameter and its critical value.