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Radial migration of stars, measured in N-body simulations

Mikkola, Daniel LU (2017) In Lund Observatory Examensarbeten ASTM31 20171
Lund Observatory
Department of Astronomy and Theoretical Physics
Abstract
The purpose of Galactic archaeology is determining the history of the Milky Way (MW) Galaxy. To do this one uses observational data from stellar populations in terms of properties such as
kinematics, chemistry, ages, and evolution. In this context a population means stars with similar characteristics and the most notable population is “the Solar Neighbourhood” (SN). Stars orbit with a ‘guiding radius’ defined as R g ∼ L z /V c where L z is the angular momentum in z-direction (perpendicular to the disc of the Galaxy) and V c the circular velocity in the potential. If we make the two assumptions that (1) stars do not significantly change their radius over time and (2) the Galactic disc is axisymmetric, we can view populations like the SN as... (More)
The purpose of Galactic archaeology is determining the history of the Milky Way (MW) Galaxy. To do this one uses observational data from stellar populations in terms of properties such as
kinematics, chemistry, ages, and evolution. In this context a population means stars with similar characteristics and the most notable population is “the Solar Neighbourhood” (SN). Stars orbit with a ‘guiding radius’ defined as R g ∼ L z /V c where L z is the angular momentum in z-direction (perpendicular to the disc of the Galaxy) and V c the circular velocity in the potential. If we make the two assumptions that (1) stars do not significantly change their radius over time and (2) the Galactic disc is axisymmetric, we can view populations like the SN as representative samples of the history of the Galaxy at their given radius. With these assumptions the content at one radius is isolated, so using it to make assumptions about the past history for a certain radius is a powerful approach.

If the assumptions hold true, we can use the age-metallicity relation (AMR) and the metallicity distribution function (MDF) of stars to find out the entire history of the MW disc at a given radius. The metallicity of stars and interstellar medium (ISM) should increase with time as metals are created predominantly in supernovae, so newer stars are more metal rich. Thus, we can predict that metallicity decreases with age. Considering only this, we expect the distribution of stellar metallicity to have a peak. This is because fewer very metal-poor stars should be left alive and conversely
not so many very metal-rich stars have been born so far as have in the peak. However with basic modelling of this kind the “G-dwarf problem” arises in which the number of metal-poor stars are too many compared to observations (Searle & Sargent 1972). A proposed solution revolves around gas in- and outflow (Larson 1974). In such a suggestion it is recognised that different regions of the Galaxy are not isolated and can undergo mixing. Also, more recent observations (e.g. Holmberg et al. 2009) suggest that the observed AMR is flat and has a large scatter in metallicity at a given age.

Kinematic properties of stars can usually tell us a lot about stars. Stars move in various ways and can have eccentric orbits in which case they can spend some time on radii different from their present one. The eccentricity of a star’s orbit can be identified from the velocity of the star at different times. This might tells us that the star has had a dynamical interaction with something in the past. Instead consider the more devious case where a star’s orbital radius is changed while the orbit remains as circular as before. It would end up in a region with different typical metallicity content while having a metallicity indicative of its own birthplace. We would be unable to identify a kinematic difference between this star and one that has been born and remained in the same region throughout its lifetime in contrast to the eccentric star.

The first idea of a process of diffusion through the disc comes from Wielen (1977) but only regards diffusion through interaction with giant molecular clouds (GMCs) which is insufficient at changing the radius of stars enough for mixing. Two ways of changing the radius of a star are called blurring and churning. The former, blurring, is when stars have non-circular orbits. No star has a truly circular orbit, but the degree to which they are eccentric varies. Because of the eccentric motion stars trace out what is called epicyclic orbits and visit radii up to a kiloparsec different than their mean radial distance. Coupled with the fact that observations show clear radial
metallicity gradients in the disc (e.g. Vila-Costas & Edmunds 1992; de Jong 1996) it is clear that this effect would cause chemical mixing in the Galaxy.

Regarding churning, it was shown in a paper by Sellwood & Binney (2002) that resonant interaction with spiral arms in the Galaxy should be taken into account as well and is in fact the principal driver of what we call radial migration. Churning is also a process which arises naturally within the Galactic disc if there are spiral arms and can move stars across much greater distances than blurring and does it without changing the star’s eccentricity, leaving no dynamical trace of occurrence.

The Milky Way has complicated structure and content with different populations, thick and thin discs, flaring, a halo, and more (Bland-Hawthorn & Gerhard 2016) and not everything observed in these parts is explainable or likely due to radial migration. But behaviour involving more than one part of the disc can be investigated to ascertain if radial migration is part of the solution. A feature long noted in the Milky Way is the existence of, as stated above, two separate discs, the thin and the thick discs. We can identify their differences through properties such as velocity
dispersion, metallicities, and ages with some small overlap (Haywood 2008).

There has been explanations beyond radial migration given to account for differences between the discs (see e.g. Chiappini et al. 1997; Bensby et al. 2005) but the duality of the discs is one of the cases where radial migration offers a solution. Schönrich & Binney (2009) performed simulations of Galactic chemical evolution and included radial mixing. They were able to produce a thick and thin disc from radial migration and showed that it can be used to explain some of the observations found in the Galaxy.

Over recent years, a large number of numerical simulations of Galaxies with radial migration have been performed and analysed (see e.g. Sellwood & Binney 2002; Solway et al. 2012; Roškar et al. 2012; Vera-Ciro et al. 2014; Halle et al. 2015). A good example of other more comprehensive studies is a series of papers lead by Michael Aumer and James Binney (Aumer et al. 2016a,b; Aumer & Binney 2017; Aumer et al. 2017) where they perform a large N -body study of galaxies with live dark matter halos and include the effects of combined spirals/bar and GMCs. They study the growth and evolution of thick and thin discs under different conditions. Studies such as these have increased the understanding of radial migration which is a topic still not completely understood. This is where the work of this thesis comes into play.

The work presented in this thesis differs from those previously stated in that they have mostly focused on individual, or in other ways somewhat limited, simulations while this work is intended to have a broad scope of investigation. A large number of different N -body simulations have been performed where different initial conditions have been used. By investigating the positions and velocities of the stars the radial migration of each simulation can be gauged. The nature of radial migration depends strongly on the conditions of the galaxy in which it transpires. The effect of
conditions that will be investigated are the varying halo mass, the subsequent effect on spiral arms in terms of strength and quantity, the stability of the disc in terms of dynamics, and the robustness to numerical alterations regarding number of bodies, duration, and seed numbers. This will provide a greater understanding of radial migration and provide a basis for future work in analytical models or other N -body simulations. (Less)
Popular Abstract (Swedish)
Galaktisk arkeologi kallas det forskningsfältet inom astronomin som undersöker Vintergatans historia i termer av stjärnors kemi, ålder, utveckling, och inte minst deras kinematik. Vintergatan började som ett band av dimma över natthimlen innan människan förstod att det var våran egen Galax, som vi själva satt inuti. Sedan dess har vi försökt förstå allt vi kan om Vintergatan. Galaktisk arkeologi är forskningen om Galaxens olika komponenter, deras ursprung och deras utveckling.

Vi är dock väldigt begränsade i hur djupt in i Vintergatan vi kan se. Rymdteleskopet Hipparcos kunde upplösa objekt ner till en millibågsekund. Det motsvarar ungefär att kunna upplösa en människa på månens yta. Den nya satelliten Gaia kan nå ner till en... (More)
Galaktisk arkeologi kallas det forskningsfältet inom astronomin som undersöker Vintergatans historia i termer av stjärnors kemi, ålder, utveckling, och inte minst deras kinematik. Vintergatan började som ett band av dimma över natthimlen innan människan förstod att det var våran egen Galax, som vi själva satt inuti. Sedan dess har vi försökt förstå allt vi kan om Vintergatan. Galaktisk arkeologi är forskningen om Galaxens olika komponenter, deras ursprung och deras utveckling.

Vi är dock väldigt begränsade i hur djupt in i Vintergatan vi kan se. Rymdteleskopet Hipparcos kunde upplösa objekt ner till en millibågsekund. Det motsvarar ungefär att kunna upplösa en människa på månens yta. Den nya satelliten Gaia kan nå ner till en mikrobågsekund, vilket motsvarar att upplösa en pennspets på månen. Gaia har precis börjat ge resultat dock och vi kan för tillfället inte nå längre än Solens ‘kvarter’ i Vintergatan.

Men även i denna begränsade sfär har vi kunnat skapa många teorier och modeller om hur stjärnor rör på sig, hur de formas och hur de utvecklas. Oftast har man börjat med de enklaste approximationerna och hur stjärnor rör sig i Galaxen är inget undantag. Den enklaste bilden är att de rör sig i nästan cirkulära banor kring Galaxens center. Men detta tillsammans med ett antagande om att den enda kemiska berikning som sker är genom stjärnors explosiva död leder till ett förutsägande att varje del av Galaxen borde utvecklas separat från de andra. Med modeller som visar att mängden metaller i stjärnor minskar desto längre ut man kommer i Vintergatan så blir varje radie unik och borde ha en rätt strikt definierad relation mellan åldern på en stjärna och dess kemiska komposition. Detta är dock inte vad vi ser.

När vi pratar kemisk komposition av en stjärna pratar vi gärna om metallicitet, som skrivs [Fe/H], och är relaterat till mängden järn gentemot väte i en stjärna. När metallicitet och ålder jämförs hade de enkla antaganden som beskrevs ovan gett en nära relation. Men observationer visar att varje ålder har en spridning i metallicitet. En av förklaringarna till detta är att stjärnor inte rör sig i nästan cirkulära banor utan kan oscillera i radie från en plats till en annan, eller till och med migrera radiellt och hamna på en helt ny plats i Galaxen. Alltså sker en hel del blandning av stjärnorna. Oscillerande radie är ett fenomen som kallas ‘blurring’ och radiell migrering genom interaktion med spiralarmar kallas för ‘churning’. Fenomenet churning beskrevs först för galaxer av Jerry Sellwood och James Binney i en artikel år 2002. De visade också att den främsta processen för att skapa spridningen, churning, kan ske utan att lämna några dynamiska fotspår i stjärnan. Detta betyder att dess omloppsbana inte behöver bli mer elliptisk när den interagerar med en spiralarm.

För att undersöka radiell migrering använder man sig av simulering eftersom det kan ta flera hundra miljoner år. Många olika studier har genomförts men har i stor utsträckning varit begränsade i vad de tittar på för sorts galax eller hur många olika galaxer de simulerar. I detta arbete ska jag och min handledare göra en storskalig studie av hur radiell migrering är annorlunda från galax till galax genom att genomföra flera olika simuleringar. Vi kommer dessutom kolla på stjärnors vertikala egenskaper för att se vad dessa spelar för roll. Vertikala egenskaper har varit i fokus i tidigare artiklar där det varit debatt om en stjärna migrerar mindre eller ej om den är vertikalt långt ifrån galaxdisken. (Less)
Please use this url to cite or link to this publication:
author
Mikkola, Daniel LU
supervisor
organization
course
ASTM31 20171
year
type
H2 - Master's Degree (Two Years)
subject
keywords
N-body, simulations, galaxies, radial migration, stars
publication/series
Lund Observatory Examensarbeten
report number
2017-EXA128
language
English
id
8924746
date added to LUP
2017-09-05 13:32:36
date last changed
2017-09-05 13:32:36
@misc{8924746,
  abstract     = {The purpose of Galactic archaeology is determining the history of the Milky Way (MW) Galaxy. To do this one uses observational data from stellar populations in terms of properties such as
kinematics, chemistry, ages, and evolution. In this context a population means stars with similar characteristics and the most notable population is “the Solar Neighbourhood” (SN). Stars orbit with a ‘guiding radius’ defined as R g ∼ L z /V c where L z is the angular momentum in z-direction (perpendicular to the disc of the Galaxy) and V c the circular velocity in the potential. If we make the two assumptions that (1) stars do not significantly change their radius over time and (2) the Galactic disc is axisymmetric, we can view populations like the SN as representative samples of the history of the Galaxy at their given radius. With these assumptions the content at one radius is isolated, so using it to make assumptions about the past history for a certain radius is a powerful approach.

If the assumptions hold true, we can use the age-metallicity relation (AMR) and the metallicity distribution function (MDF) of stars to find out the entire history of the MW disc at a given radius. The metallicity of stars and interstellar medium (ISM) should increase with time as metals are created predominantly in supernovae, so newer stars are more metal rich. Thus, we can predict that metallicity decreases with age. Considering only this, we expect the distribution of stellar metallicity to have a peak. This is because fewer very metal-poor stars should be left alive and conversely
not so many very metal-rich stars have been born so far as have in the peak. However with basic modelling of this kind the “G-dwarf problem” arises in which the number of metal-poor stars are too many compared to observations (Searle & Sargent 1972). A proposed solution revolves around gas in- and outflow (Larson 1974). In such a suggestion it is recognised that different regions of the Galaxy are not isolated and can undergo mixing. Also, more recent observations (e.g. Holmberg et al. 2009) suggest that the observed AMR is flat and has a large scatter in metallicity at a given age.

Kinematic properties of stars can usually tell us a lot about stars. Stars move in various ways and can have eccentric orbits in which case they can spend some time on radii different from their present one. The eccentricity of a star’s orbit can be identified from the velocity of the star at different times. This might tells us that the star has had a dynamical interaction with something in the past. Instead consider the more devious case where a star’s orbital radius is changed while the orbit remains as circular as before. It would end up in a region with different typical metallicity content while having a metallicity indicative of its own birthplace. We would be unable to identify a kinematic difference between this star and one that has been born and remained in the same region throughout its lifetime in contrast to the eccentric star.

The first idea of a process of diffusion through the disc comes from Wielen (1977) but only regards diffusion through interaction with giant molecular clouds (GMCs) which is insufficient at changing the radius of stars enough for mixing. Two ways of changing the radius of a star are called blurring and churning. The former, blurring, is when stars have non-circular orbits. No star has a truly circular orbit, but the degree to which they are eccentric varies. Because of the eccentric motion stars trace out what is called epicyclic orbits and visit radii up to a kiloparsec different than their mean radial distance. Coupled with the fact that observations show clear radial
metallicity gradients in the disc (e.g. Vila-Costas & Edmunds 1992; de Jong 1996) it is clear that this effect would cause chemical mixing in the Galaxy.

Regarding churning, it was shown in a paper by Sellwood & Binney (2002) that resonant interaction with spiral arms in the Galaxy should be taken into account as well and is in fact the principal driver of what we call radial migration. Churning is also a process which arises naturally within the Galactic disc if there are spiral arms and can move stars across much greater distances than blurring and does it without changing the star’s eccentricity, leaving no dynamical trace of occurrence.

The Milky Way has complicated structure and content with different populations, thick and thin discs, flaring, a halo, and more (Bland-Hawthorn & Gerhard 2016) and not everything observed in these parts is explainable or likely due to radial migration. But behaviour involving more than one part of the disc can be investigated to ascertain if radial migration is part of the solution. A feature long noted in the Milky Way is the existence of, as stated above, two separate discs, the thin and the thick discs. We can identify their differences through properties such as velocity
dispersion, metallicities, and ages with some small overlap (Haywood 2008).

There has been explanations beyond radial migration given to account for differences between the discs (see e.g. Chiappini et al. 1997; Bensby et al. 2005) but the duality of the discs is one of the cases where radial migration offers a solution. Schönrich & Binney (2009) performed simulations of Galactic chemical evolution and included radial mixing. They were able to produce a thick and thin disc from radial migration and showed that it can be used to explain some of the observations found in the Galaxy.

Over recent years, a large number of numerical simulations of Galaxies with radial migration have been performed and analysed (see e.g. Sellwood & Binney 2002; Solway et al. 2012; Roškar et al. 2012; Vera-Ciro et al. 2014; Halle et al. 2015). A good example of other more comprehensive studies is a series of papers lead by Michael Aumer and James Binney (Aumer et al. 2016a,b; Aumer & Binney 2017; Aumer et al. 2017) where they perform a large N -body study of galaxies with live dark matter halos and include the effects of combined spirals/bar and GMCs. They study the growth and evolution of thick and thin discs under different conditions. Studies such as these have increased the understanding of radial migration which is a topic still not completely understood. This is where the work of this thesis comes into play.

The work presented in this thesis differs from those previously stated in that they have mostly focused on individual, or in other ways somewhat limited, simulations while this work is intended to have a broad scope of investigation. A large number of different N -body simulations have been performed where different initial conditions have been used. By investigating the positions and velocities of the stars the radial migration of each simulation can be gauged. The nature of radial migration depends strongly on the conditions of the galaxy in which it transpires. The effect of
conditions that will be investigated are the varying halo mass, the subsequent effect on spiral arms in terms of strength and quantity, the stability of the disc in terms of dynamics, and the robustness to numerical alterations regarding number of bodies, duration, and seed numbers. This will provide a greater understanding of radial migration and provide a basis for future work in analytical models or other N -body simulations.},
  author       = {Mikkola, Daniel},
  keyword      = {N-body,simulations,galaxies,radial migration,stars},
  language     = {eng},
  note         = {Student Paper},
  series       = {Lund Observatory Examensarbeten},
  title        = {Radial migration of stars, measured in N-body simulations},
  year         = {2017},
}