Introduction – Star Clusters II
Distance:V0-MV
AV
k.AV
Turn-off
Gaia – before and after
Location of Star Clusters
Credit:
Pearson
Education Inc.
Galactic Distribution
+- 20 degree Galactic latitude
Location of Globular Clusters
• Globular Clusters are found in
1. Galactic Halo – formed there
2. Galactic Bulge –
formed there
3. Galactic Disc – path
Star Clusters – tricky to analyze
NGC
7789
Diameters of open clusters
• How could we determine the diameter of a star
cluster?
1. The determination, for example inspection by eye,
should be no problem. Be careful, most open clusters
show no real concentration
2. Count the number of stars (members) in concentric
rings around the cluster center
3. If the derived distribution is not symmetric => go to 1.
and shift the coordinates of the center
• This procedure could be easily done via a computer
program
Pietrukowicz et al., 2006, MNRAS, 365, 110
III 2 m
II 2 m
Galactic field
Ferreira et al., 2019, MNRAS, 483, 5508
Gaia data
Diameters of open clusters
Pre - Gaia
Radii of open clusters
Gaia DR2
Janes et al., 1988, AJ, 95, 771
all
young
Why do Star Clusters dissipate?
Differential Galactic Rotation
Total Mass of the Milky Way:
Gravitational acceleration of the complete star
cluster 𝑔 𝑂𝐶𝐿 and the individual member 𝑔∗ :
The difference of these two values, is the
force, of which “the Milky Way” tries to pull away
a star from the cluster
𝑀 𝑀𝑊 = 2 ∙ 1011M⨀
𝑔∗ =
𝐺 ∙ 𝑀 𝑂𝐶𝐿
𝑅 𝐺𝐶 − 𝑟 2
𝑅 𝐺𝐶 … Distance of the
star cluster’s centre to the
Galactic centre
𝑟 … Distance from star to
the star cluster’s centre
𝑔 𝑂𝐶𝐿 =
𝐺 ∙ 𝑀 𝑀𝑊
𝑅 𝐺𝐶
2
On the other side we have the gravitational force of
the star cluster. The stability radius 𝑟𝑠 is defined as:
For 1000 M⨀ => Diameter 20 pc
𝑔 𝑀𝑊,∗ =
2 ∙ 𝐺 ∙ 𝑀 𝑀𝑊 ∙ 𝑟
𝑅 𝐺𝐶
3 for 𝑟 ≪ 𝑅 𝐺𝐶
2 ∙ 𝐺 ∙ 𝑀 𝑀𝑊 ∙ 𝑟
𝑅 𝐺𝐶
3 =
𝐺 ∙ 𝑀 𝑂𝐶𝐿
𝑟𝑠
2 ⇒ 𝑟𝑠 = 𝑅 𝐺𝐶 ∙
𝑀 𝑂𝐶𝐿
2𝑀 𝑀𝑊
ൗ1
3
𝑟𝑠 = 10.9 ∙
𝑀 𝑂𝐶𝐿
1000
ൗ1
3
for 𝑅 𝐺𝐶 = 8 kpc in units of M⨀, pc
Common proper motion
Van Bueren, 1952, BAN, 11, 385
Hyades
After the correction of
the solar motion
Well known but high
accuracy especially for
distant clusters is
needed
Klein Wassink, 1927, Publications of the Kapteyn Astronomical Laboratory Groningen, Vol. 41, 1
Praesepe
d = 190 pc
Field stars
Common proper motion
Credit: Tristan
Cantat-Gaudin
Dramatic improvement by Gaia even for
overlapping star clusters
Kinematical membership criteria
• Members follow the motion of the cluster
center of gravity
• Internal velocity distribution
• From best to …
1. Radial velocity and proper motion
2. Radial velocity
3. Proper motion
Clemens, 1985, ApJ, 295, 422
Determination of the kinematical
membership
• Three possibilities:
1. Observation of the position at two
difference times (= epochs), with a very
large time basis. First photographic plates
around 1860, largest time scale about 160
years
2. Proper motions of stars in the direction of
the Declination a and Right Ascension d
3. Radial velocity measurements
• Calculate the absolute distance in X and Y for both
epochs and each star individually
• Plot the histograms of the differences of the
absolute distances
• The distributions are fitted with Gaussian functions
• The probability p, if a star is member of the star
cluster is defined as
Javakhishvili et al. (2006, A&A,
447, 915) for Collinder 121
From these diagrams, the
membership probability can
be exactly determined