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the dynamics of star cluster formation
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The Dynamics of Star Cluster Formation Juan Pablo Farias Jonathan Tan (Chalmers, U. Virginia), Sourav Chatterjee (TATA Institute), Madeline Gyllenhoff (U. Virginia) How is gas transformed into a star cluster? What is the star formation

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The Dynamics of Star Cluster Formation

Juan Pablo Farias

Jonathan Tan (Chalmers, U. Virginia), Sourav Chatterjee (TATA Institute), Madeline Gyllenhoff (U. Virginia)

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How is gas transformed into a star cluster?

  • What is the star formation rate? (and its evolution)
  • What is the primordial stellar population?

–

Binary fraction and properties

–

Mass segregation

  • Can this population be signifjcantly processed during cluster

formation?

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What is the timescale of formation?

  • Fast formation models:

(e.g. Elmegreen 200,2007; Hartmann & Burkert 2007)

○ Short timescales ~1 or 2 free fall times ○ Cloud is collapsing quickly

  • Slow formation models:

(e.g. Tan, Krumholtz & Mckee 2006, Nakamura & Li 2007,2014)

○ several free fall times ○ cloud is in approximate equilibrium.

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Dynamical Timescales

It is important to note that star cluster’s dynamical evolution timescales scales with density

  • Free fall time: “The time a cloud of gas need to

collapse under its own weight if no forces support it”

  • Crossing time: “The time a typical star in a star

cluster needs to cross the system”

Formation rate:

(Krumholtz & McKee 2005)

Star formation effjciency per free fall time

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Stellar Dynamics

e.g. Baumgardt & Kroupa (2007), Smith+(2011,2013), Farias et al. (2015)

Hydrodynamicse.g. Nakamura & Li (2007,20014), Bate+(2005,2014),Wu+(2017,2018),

Stages of star cluster formation

Proszkow & Adams(2009)

Stellar dynamics cons:

  • Sink particles
  • Not so accurate N-body codes
  • Small samples

Our Approach:

  • Study the formation stage from a

dynamical perspective.

  • Make assumptions for the gas behaviour

and star formation.

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  • 𝝑fg = 0.01, 0.03, 0.1, 0.3, 1, ∞
  • Uniform SFE ( =

𝝑

0.5 fjducial case)

  • Stars follow the mass and velocity profjle of the parent clump
  • Star cluster is isolated
  • Gas is exhausted and expelled as the stars form
  • Star formation rate is constant with time

The Star Cluster formation model:

Gradual formation of Stars

(Farias, Tan, Chatterjee 2017,2019)

Nbody6++SF

Aarseth (2003), Wang+(2015), Farias+(2019)

see estimates from DaRio+(2014) in the ONC

T u r b u l e n t C

  • r

e C l u m p M

  • d

e l

Mckee & Tan (2003)

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Sample simulation: Fiducial case:

  • Σcl = 0.1 g cm-2
  • 50% binaries
  • Stellar evolution
  • 𝝑fg = 0.03
  • 𝝑 = 0.5

Gas (shown as red area) decrease with time as stars are created according to the assumed star formation effjciency

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Sample simulation: Fiducial case:

  • Σcl = 0.1 g cm-2
  • 50% binaries
  • Stellar evolution
  • 𝝑fg = 0.03
  • 𝝑 = 0.5

Gas (shown as red area) decrease with time as stars are created according to the assumed star formation effjciency

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AONC = 2.0 (DaRio et al. 2014)

Perturbing the Model: Elliptical Clouds

  • Star clusters are do not form in spherical

systems. Next Step: Perturbing the model ..

  • Stretch it

A= Z R

Z R

Madeline Gyllenhofg University of Virginia

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Perturbing the Model: Elliptical Clouds

Sample simulation: Fiducial case (instant. Formation):

  • Σcl = 0.1 g cm-2
  • 50% binaries
  • Stellar evolution
  • 𝝑fg = 0.03
  • 𝝑 = 0.5
  • Ai = 3
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Perturbing the Model: Elliptical Clouds

Sample simulation: Fiducial case (Gradual Formation):

  • Σcl = 0.1 g cm-2
  • 50% binaries
  • Stellar evolution
  • 𝝑fg = 0.03
  • 𝝑 = 0.5
  • Ai = 3
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Perturbing the model: Turbulence

  • Star clusters are do not form in spherical

systems. Next Step: Perturbing the model ..

  • Stretch it
  • Apply turbulence
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Perturbing the model: Turbulence

  • Perturbing the model

Turbulent Core Model Scale free Turbulent Box Simulation

Turbulent background with the density and velocity profjle of the TCM

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Perturbing the model: Turbulence

  • Perturbing the model

Turbulent Core Model Scale free Turbulent Box Simulation

Turbulent background with the density and velocity profjle of the TCM

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Results

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Results

Expansion Rates Relaxation timescales Bound Fractions Velocity dispersion profiles Mass segregation Stellar age gradients Dynamical Ejections Brown Dwarf distributions

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Results

Expansion Rates Relaxation timescales Bound Fractions Velocity dispersion profiles Mass segregation Stellar age gradients Dynamical Ejections Brown Dwarf distributions

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Formation timescales:

Formation time (Myr)

𝝑ff 𝝑ff /𝝑

0.01 50 0.03 16.6 0.1 5 0.3 1.6 1.0 0.5

𝝑 = 0.5 Number of Dynamical times

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  • We test our fjducial model under

difgerent values of 𝝑fg.

  • Difgerent formation timescales

defjnes how long number densities remains high

Different formation timescales

The density starts low as there are less stars but raises and stays high for some “physical” time. But, how long is that time in crossing times?

Number Density (stars/pc3)

fastest slowest

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Dynamical Ejections

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Dynamical Ejections

Probability Velocity

Low Density Case

Probability Energy

fastest slowest

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Dynamical Ejections

  • We look for massive

runaway stars at difgerent velocity cuts.

  • Low forming clusters

produce more runaway stars than fast forming clusters. Observations*

* e.g. Gies 1987; Stone 1991; De Wit et al. 2005

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Stellar Ages

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Stellar Age gradients

Standardized ages and distances

Getman et al. 2018

  • Observations suggest that star

clusters tend to have positve age gradients (Getman et al 2018)

  • i.e. In general, younger stars are

in the center and older stars in the outskirts.

MYStIX clusters (Kuhn et al. 2014) SfjNCs cluters (Getman et al. 2018)

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Stellar Age gradients

  • Our methods enable us to study the evolution of stellar systems with difgerent

stellar ages Standardized ages and distances

fastest slowest

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Stellar Age gradients

  • Our methods enable us to study the evolution of stellar systems with difgerent

stellar ages Standardized ages and distances

fastest slowest

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Stellar Age gradients

  • Our methods enable us to study the evolution of stellar systems with difgerent

stellar ages Standardized ages and distances

fastest slowest

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Brown Dwarfs

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Brown Dwarfs

Slopes

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Summary and Future Work

  • The formation of a cluster may take several dynamical times, and considerable

dynamical processing may happen during formation.

  • Longer formation time increases chances for energetic dynamical ejections.
  • We have developed a method for testing any star cluster formation model from

the Stellar Dynamics perspective.

  • Next steps:

Test the consequences of the difgerent levels of substructure in the stellar population dynamics. Include the ability of using an arbitrary background potential in Nbody6++SF. In the models In the code Compute synthetic observation in order to compare our models with the JWST and Gaia. In the analysis

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