Quantitative description of stellar radial migration from N-body to semi-analytical

simulations Maxime KUBRYK , IAP, Ph.D student

advisors: Nikos PRANTZOS, IAP Lia ATHANASSOULA, OAMP

LIA-ORIGINS, May 2012

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Introduction: radial migrationStellar orbits = churning + blurring *

Churning : change in angular momentum change in guiding radius Blurring : increase in star’s epicycle amplitude

Time (Gyr)

Radius evolution of two star particles in an N-body/SPH simulation.

* Schönrich & Binney, 2008, MNRAS 000,1-22

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Introduction Thanks to the joined study of N-body and semi-analytical simulations, the stellar

radial migration is now known to possibly have a strong impact on the evolution of disk galaxies : both dynamical and chemical evolution are modified.

But at the moment, our knowledge of the phenomenon cannot be used to reproduce the evolution of a specific galaxy, because we have not a general quantitative description of radial migration, depending on some physical properties of galaxies.

We need a method to find a proper description of the radial migration of stars in a given galaxy.

We will study an existing N-body simulation, and try to reproduce it with our semi-analytical code. To do so we will need to introduce a simple semi-analytic law in our code to reproduce the radial migration of stars.

The semi-analytical code compute detailed chemical evolution. Therefore it is complementary to the N-body simulations.

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Outline

The N-body/SPH simulationBuilding a quantitative empirical law for

migrationRadial migration of gas Results in semi-analytical vs. N-body/SPHConclusion

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Simulation with GADGET2 of the evolution of a disk galaxy made of stars and gas, in a dark matter halo, in 10 Gyr, without infall. The final result is an early type (Sb0) galaxy.

Initial composition in % of the total mass, and number of particles: Dark matter : 83,2% , N = 1 000 000 Gas : 12,6% , N = 750 000 Old stars : 4,2% , N = 200 000

Final composition in % of the total mass: Dark matter : 83,2% , N = 1 000 000 Gas : 1,0% , N = 58 290 Old stars : 4,2% , N = 200 000 New stars : 11,6% , N = 691 710

The used N-body/SPH simulation

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The used N-body/SPH simulation

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In our semi-analytical code, a disk galaxy is described as concentric rings evolving independently.

We need a law describing how much stellar masses of stellar populations are exchanged between the rings.

We guess this law have to be a distribution function like : ΔR : difference between birth and a given radius Δt : elapsed time since birth

where F is a fraction of mass.

We guess the distribution’s time dependence is the time elapsed since birth and not the time of birth.

So we separated stars in birth radius and birth time. For each of the obtained group of stars, we get a position distribution on the disk, which evolve with time.

Building a quantitative empirical law

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and 2Gyr and 4Gyr and 7Gyr

We fit the distributions above with Gaussian curves.

On the left: the FWHM of the Gaussians fitting the distributions

And we fit the FWHM with a function

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Brunetti et al, (2011) made the hypothesis that stellar migration can be modeled by a diffusion process in the disk.

In their model, the distribution of a single stellar population over the disk is a Gaussian, centered on the birth radius of the population (when far from the edges of the disk):

The standard deviation σ of these distributions evolve with time like:

Where D: is a diffusion coefficient , which should depend on some physical parameters.

Δt : time elapsed since birth of stellar population.

In the results of our analysis, we find the same time dependence in

Building a quantitative empirical law

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The radial position of the gas particles, in the disk, do not change strongly :

Then we will study the radial migration of the stars, and consider that the gas do not migrate in the disk.

Treatment of the gas:

At 10 Gyr Mean every 2 Gyr

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Final density profiles of stars and gas in semi-analytic simulation compared to N-body results:

Final profiles of star formation rate in semi-analytic simulation compared to N-body results :

Results in semi-analytical vs. N-body:

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We can look at the birth place of the stars at each radius at the final time of the simulations (10 Gyr), in both N-body and semi-analytic:

We cannot reproduce the effects of the central bar in the semi-analytical code.

Results in semi-analytical vs. N-body:

N-body result Semi-analytical result

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We can integrate at the final time, at each radius, the amount of stars which come from the internal, external, or same radius:

Results in semi-analytical vs. N-body:

N-body result Semi-analytical result

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Compared results in the semi-analytical code, when radial migration is enabled and disabled.

The SNIa rate is modified by migration and then the Fe56

Some effects on chemical evolution

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Conclusion We analyzed a N-body simulated disk galaxy, and get a quantitative law to describe radial

migration of stars in it.

We inserted this law in our semi-analytical code: it allows to reproduce the N-body galaxy with semi-analytical simulation.

With a N-body/SPH-simulated galaxy similar to the Milky Way, we could use this method, and work both with N-body/SPH and semi-analytical simulations to get more insight about Milky Way formation and evolution.

Works in progress : Inserting a detailed chemical evolution in the N-body/SPH code GADGET2

N-body and semi-analytical simulations are complementary.

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Thank You!

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On all the disk:

We got a law which can be applied in the semi-analytic code:

Then this formula is inserted in Gaussian expression to compute the distribution of single star populations on all the disk at each time.

Building a quantitative empirical law

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Stellar orbits = churning + blurring * Churning : change in angular momentum change in guiding radius Blurring : increase in star’s epicycle amplitude

Difficulties about radial migration

* Schönrich & Binney, 2008, MNRAS 000,1-22

Radius and angular momentum evolution of a star particle in the N-body simulation.

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Difficulties about radial migration

Radius and angular momentum evolution of a star particle in the N-body simulation.

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In the semi-analytical simulation, we compute the specific evolution of a set of chemical elements.

This is not done in the N-body simulation GADGET2, the quantity we call “metallicity” is only the evolution of Oxygen, which is the most abundant heavy element.

We get a fine agreement between semi-analytical and N-body simulations concerning the shape of the disk, and the stellar moves due to radial migration. Therefore the chemical evolution of the elements computed in the semi-analytical code should

In the N-body simulation GADGET, there is no specific computation for chemical elements. Therefore the “metals” represent only the Oxygen

Results in semi-analytical vs. N-body: