Why do Star Clusters dissipate?
Collisions
Virial Theorem:
Kinetic Energy:
Potential Energy:
yielding:
2𝐸 𝑘𝑖𝑛 = −Ω
2𝐸 𝑘𝑖𝑛 = 𝑛 ∙ 𝑚𝑖 ∙ 𝑣
2
= 𝑀 ∙ 𝑣
2
𝑣 … mean velocity of the members
relative to the cluster centre
Ω = −
1
2
∙
𝐺 ∙ 𝑀2
𝑅
2
𝑣
2
=
𝐺 ∙ 𝑀
2𝑅
2
Escape Velocity:
Collisions:
Density r and cross section s:
Example of a typical Open Cluster:
𝑡 𝑐𝑜𝑙𝑙= 1025 s => Collisions play no role
𝑣∞
2
= 4 ∙ 𝑣
2
𝑡 𝑐𝑜𝑙𝑙 ≈
1
𝜌 ∙ 𝜎 ∙ Δ𝑣
𝜌 =
𝑁
𝑅
3 𝜎 = 4𝜋 ∙ 𝑅∗
2
⇒ 𝑡 𝑐𝑜𝑙𝑙 =
𝑅
3
4𝜋∙𝑁∙𝑅∗
2∙Δ𝑣
𝑁 = 1000, Δ𝑣 = 10 km/s, 𝑅∗ = 2.5R⨀, 𝑅 = 5 pc
Even in the most inner core parts, collisions are
highly improper, but could occur
Conclusions:
1.Binary and Multiple systems are not results
of collisions in later stages but form already
at the very beginning
2.Members do, in general, not escape due to
collisions (swing-by effect), but their
peculiar velocity component is part of the
cluster formation or due to SNs
Why do Star Clusters dissipate?
Crossing time - escaping
Crossing Time:
Members can escape from a Star
Cluster on a relatively short time scale
Reason: Velocity dispersion caused by
the cluster formation and SN events
𝑡 𝑐𝑟𝑜𝑠𝑠 =
ത𝑅
Δ𝑣
Δ𝑣 = 10 km/s, 𝑅 = 5 pc ⇒ 𝑡 𝑐𝑟𝑜𝑠𝑠 = 4.9 ∙ 108
yr
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
Summary
• Star Cluster dissipate because of
1. Differential Galactic Rotation
2. Internal Velocity Dispersion
3. Collisions in the first few Myrs
4. SN Explosions and corresponding Shock
Waves
5. ( Collisions with “Field Stars”)
• Explanations of the existence of Globular
Clusters?
• Valid for all Spiral Galaxies
Tidal Forces due to Differential
Galactic Rotation
• Star Clusters lose members on their way
following the Galactic rotation due to
differential rotation and internal velocity
distribution as well as “SN kicks”
• These stars become “Galactic field stars”
• For some Star Clusters, also tidal tails were
found. These are former members still very
weakly bound to the Star Cluster following its
path
Why do Star Clusters dissipate?
Tidal tails
• Stars leaving in the path around the Galactic
centre
Distance about 45 pc from the Sun
2021, A&A, 647, A137
Why do Star Clusters dissipate?
Tidal tails
Simulation of tidal tails
True orbit
Why do Star Clusters dissipate?
Tidal tails
Simulation of tidal tails
Why do Star Clusters dissipate?
Tidal tails
11 000 field stars in the Hyades’s field
Why do Star Clusters dissipate?
Tidal tails
Selected candidates
Why do Star Clusters dissipate?
Tidal tails
Still many field stars among
the selected candidates
Tidal Trails - Coma Berenices
Tang et al., 2019, ApJ, 877, 12 Open Cluster, age about 400 Myr
Tidal Trails – Palomar 5
Bonaca et al., 2020, ApJ, 889, 70
Globular Cluster, age about 11 Gyr
Why do Star Clusters dissipate?
“Coronae”
2021, A&A, 645, A84
Why do Star Clusters dissipate?
“Coronae”
Why do Star Clusters dissipate?
“Coronae”
Never list such values without errors
Reddening? Objects below the zero age main sequence?
Why do Star Clusters dissipate?
“Coronae”