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
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