1. Statistics of Visual Binaries and Star Formation History
Oleg Malkov
Institute of Astronomy Rus. Acad. Sci. (INASAN)
Faculty of Physics, Moscow State University
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2. Contents Introduction Initial distributions Evolutionary stages
Observational data for comparison
Results of comparison
Conclusions
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3. Introduction
Most stars formed as part of a binary or multiple systems.
In order to understand the star formation process, it is vital to characterize distributions of physical parameters in the history of the Galaxy.
In the solar neighborhood limit, few hundred parsec of distance, most of the binary systems are visual binaries.
We begin from the assumption that all stars born in a binary system.
Evolutionary stage is calculated as a function of system age and component masses.
Observational selection effects are involved.
Thus, we modeled visual binaries in the solar neighborhood and compare our calculations with observations.
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4. Initial distributions
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5. Spatial distribution Uniform
Barometric: GALACTIC_DISC_VERTICAL_SCALE_PC = 200
Barometric: GALACTIC_DISC_VERTICAL_SCALE_PC =
50 for mass>10,
*log(mass) for 1<=mass<=10,
340 for mass<1,
(Gilmore and Reid 1983, Kroupa 1992, Reed 2000)
No radial gradient
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6. Number of pairs simulated
Sphere radius = 500 pc
Pairs are simulated until their number in a 100-pc-sphere reaches 500,000
It corresponds to the observed stellar density in the solar vicinity, about stars per cubic pc
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7. Pairing scenarios: masses. 1
Select (two) fundamental parameters among m1, m2, m1+m2, m2/m1, m1-m2, m1*m2, …
The following scenarios are used
m1, m2 (RP, random pairing)
m1, m2/m1 (PCP, primary constrained pairing)
m1+m2, m2/m1 (SCP, split-core pairing)
m1+m2, m1 (TPP, total and primary pairing)
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8. Pairing scenarios: masses. 2
Select method of treating low-mass companions (m2<mmin):
Accept (even stars with a planetary companion are considered to be in a binary system)
Reject (the primary star becomes a single star)
Redraw (it is rejected, and a new companion star is drawn)
Method of treating low-mass companions (m2<mmin): Accept
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9. Mass distribution
Masses are distributed according to a power-law function N(m) ~ mα from 0.08 to 100 msun
Salpeter IMF: α=-2.35
Kroupa IMF:
α=-1.3 for m<0.5 msun
α=-2.3 for m≥0.5 msun
Later: vary slopes and inflection points of Kroupa IMF
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10. Total mass and mass ratio distributions
m1+m2 (strictly speaking, it does not precisely equal protobinary cloud mass): is distributed like masses of individual stars
f(q) ~ qβ, where β = 0, -0.5, +0.5
Later: add twins (q=1)
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11. Semi-major axis distribution
f(a) ~ aλ, where λ=-1, -1.5, -2
Lower limit is 10 Rsun, upper limit is 106 Rsun
λ = -1: uniform logarithmic distribution along five orders of magnitude
Later:
lower limit depends on stellar mass, amin=amin(RocheLobe(m))
upper limit amax=amax(height scale z, mass, eccentricity)
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12. Eccentricity distribution
f(e) = 2e
f(e) = δ(0)
f(e) = 1
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13. Star formation rate
Constant star formation rate from 0 to DISCAGE = 14 Gyr
Declining star formation rate from 0 to DISCAGE = 14 Gyr: SFR(t)=15e-(t/τ), where τ=7Gyr
Verification: the function produces
current SFR = 3.6 msun/yr, which is correct
integral mass 8*1010 msun, which is equal to Galaxy mass
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14. Other parameters
Metallicity: normal Fe/H distribution with mean=-0.1 and dispersion 0.3
Random distributions for: mean anomaly, sin(inclination), position angle, periastron longitude
Interstellar extinction Av=0
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15. Evolution
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16. Evolution stage (mass, age)BD
Pre-MS MS RG WD NS BH
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17. Evolution stage (mass, age)
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18. Evolution stage (mass, age)
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19. HR diagram
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20. Observational data for comparison: WDS+CCDM+TDSC binaries with TGAS parallaxes
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21. Selection criteria Main component belongs to MS
Secondary component is not degenerate
Separation ρ > 1 arcsec
Primary brightness V1 < 10m
Secondary brightness V2 < 11m
Brightness difference (V2-V1) < 4m
Distance d < 500 pc (π > 2 mas)
Altogether 1028 systems
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22. Numbers/distributions for comparison
Number of selected stars
Distributions over V1, V2, V2-V1, ρ”, ρRsun, π“ (χ2 test)
Overall χ2 value, based on distributions of independent, original parameters (V1, V2-V1, ρ”, π“)
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23. An example: TPP (m1+m2, m1), Kroupa IMF, f(a) ~ a-1.5, f(e) = 1ρ”
An example: TPP (m1+m2, m1), Kroupa IMF, f(a) ~ a-1.5, f(e) = 1
V2-V1 V1
π"
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24. Results of comparison
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25. Resume. 1 Results weakly depend on eccentricity distribution.
It is difficult to make conclusions on mass ratio (q) distribution.
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26. Scenario, IMF
f(a) ~ aλ
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27. Resume. 2
PCP (m1, q), RP (m1, m2) and SCP (m1+m2, q) scenarios show a good agreement with observations.
Kroupa IMF is slightly more preferable than Salpeter IMF.
Semi-major axis distributions f(a) ~ aλ, where λ=-1 and -1.5, look very promising, and will be analyzed in detail. Distribution with λ=-2 should be omitted from further consideration.
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28. Acknowledgments Co-authors RFFR 15-02-04053
Audience for your attention
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