Statistics of Visual Binaries and Star Formation History Oleg Malkov Institute of Astronomy Rus. Acad. Sci. (INASAN) Faculty of Physics, Moscow State University malkov@inasan.ru MSA-2017

Contents Introduction Initial distributions Evolutionary stages Observational data for comparison Results of comparison Conclusions MSA-2017

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. MSA-2017

Initial distributions MSA-2017

Spatial distribution Uniform Barometric: GALACTIC_DISC_VERTICAL_SCALE_PC = 200 Barometric: GALACTIC_DISC_VERTICAL_SCALE_PC = 50 for mass>10, 10-0.832*log(mass)+2.531 for 1<=mass<=10, 340 for mass<1, (Gilmore and Reid 1983, Kroupa 1992, Reed 2000) No radial gradient MSA-2017

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 0.12-0.14 stars per cubic pc MSA-2017

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) MSA-2017

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 MSA-2017

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 MSA-2017

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) MSA-2017

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) MSA-2017

Eccentricity distribution f(e) = 2e f(e) = δ(0) f(e) = 1 MSA-2017

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 MSA-2017

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 MSA-2017

Evolution MSA-2017

Evolution stage (mass, age) BD Pre-MS MS RG WD NS BH MSA-2017

Evolution stage (mass, age) MSA-2017

Evolution stage (mass, age) MSA-2017

HR diagram MSA-2017

Observational data for comparison: WDS+CCDM+TDSC binaries with TGAS parallaxes MSA-2017

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 MSA-2017

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“) MSA-2017

An example: TPP (m1+m2, m1), Kroupa IMF, f(a) ~ a-1.5, f(e) = 1 ρ” An example: TPP (m1+m2, m1), Kroupa IMF, f(a) ~ a-1.5, f(e) = 1 V2-V1 V1 π" MSA-2017

Results of comparison MSA-2017

Resume. 1 Results weakly depend on eccentricity distribution. It is difficult to make conclusions on mass ratio (q) distribution. MSA-2017

Scenario, IMF f(a) ~ aλ MSA-2017

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. MSA-2017

Acknowledgments Co-authors RFFR 15-02-04053 Audience for your attention MSA-2017