Hyades
log t = 8.90
d = 45 pc
[Fe/H] = +0.17 dex
Width of Main Sequence
about 1.8 mag in MV
NO
Observational error
What are the reasons?
Haffner & Heckmann, 1937, VeGeo, 55, 77
MV
B-V
„color“
Absolute magnitude:
MV = -2.5 log (L1 + L2)
Maximum at L1 = L2 =>
MV = -0.753 mag
The maximal width of the main
sequence due to binary systems is
0.753 mag
x = a(CAB – CA) + VA – VAB
q
Vertical distance from the main
sequence
Praesepe: Fossati et al., 2008, A&A, 483, 891
Fe: -4.28 to -4.62dex; 0.34 dex
Metallicity => different opacity
Isochrones for 10 Myr
Von Zeipel theorem (1924,
MNRAS, 84, 665)
Energy generation rate
From the rotational velocity => e => Teff and L (log g)
Slettebak et al., 1980, ApJ, 242, 171 Rotation
Vega
Hill et al., 2010, ApJ,
712, 250
Collins & Smith, 1985, MNRAS, 213, 519
p … Degree of differential rotation
Collins & Smith, 1985, MNRAS, 213, 519
Conclusions – Width of the Main
Sequence
• Differential reddening: k.DE(B-V)
• Spectroscopic Binaries: 0.753 mag
• Metallicity: up to 1.2 mag for MV, but
only 0.2 mag for (U – B) versus (B – V)
• Rotation: 1 mag for MV, 0.2 (?) mag for
(U – B) versus (B – V)
Binary fraction
• Important for the formation and
evolution of star clusters
• Critical parameter for the IMF
• Needed for N-body numerical
simulations
• Observations are biased in many
respects
• Many different types of binary systems
Lower metallicities seem to favour binary formation
Machida, 2008, ApJ, 682, L1
How to observe the binary
fraction?
• Photometric observations of star clusters
1. “Cluster main sequence”
2. Eclipsing binaries
3. Positions (astrometric binaries)
• Spectroscopic observations
1. Radial velocity variability
2. Direct detection in spectrum (SB2)
Hurley & Tout, 1998, MNRAS, 300, 977 Haffner & Heckmann, 1937, VeGeo, 55, 77
Simulation with randomly distributed
mass ratios
Observations of Praesepe with
known binary systems
Observed binaries with the Gaia
DR2
Cantat-Gaudin et al., 2018, A&A, 618, A93
Observed binaries with the Gaia
DR2
Cantat-Gaudin et al., 2018, A&A, 618, A59
Bin size of one day
Bin size of one hundred days
Bin size of ten thousand days
Results for open clusters
• Sollima et al., 2010, MNRAS, 401, 577
– NGC 188 (9.63): 21 – 58%
– NGC 2204 (9.20): 12 – 36%
– NGC 2243 (9.58): 34 – 70%
– NGC 2420 (9.08): 17 – 51%
– NGC 2516 (8.52): 25 – 66%
• Sana et al., 2009, MNRAS, 400, 1479
– NGC 6611 (6.50): 44 – 67%
• Sana et al., 2008, MNRAS, 386, 447
– NGC 6231 (6.50): 63% - ?
⚫ Bica & Bonatto, 2005, A&A, 431, 943
– IC 4651 (9.26): 50 +- 11%
– NGC 2287 (8.20): 48 +- 45%
– NGC 2447 (8.60): 21 +- 9%
– NGC 2548 (8.56): 48 +- 23%
– NGC 2682 (9.51): 39 +- 16%
– NGC 3680 (9.20): 25 +- 5%
– NGC 5822 (9.00): 16 +- 8%
– NGC 6208 (9.11): 54 +- 30%
– NGC 6694 (7.85): 18 +- 12%
• Sandhu et al., 2003, A&A, 408, 515
– NGC 2099 (8.60): ~30%
– King 5 (9.00): ~30%
– King 7 (8.80): ~20%
Davis et al., 2008, AJ, 135, 2155
Globular clusters