Symmetries and Dynamics of Star Clusters

92 Pages·2014·4.525 MB·English

by  Jaroslav Haas (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Jaroslav Haas
Symmetries
and Dynamics
of Star Clusters
Springer Theses
Recognizing Outstanding Ph.D. Research
For furthervolumes:
http://www.springer.com/series/8790
Aims and Scope
The series ‘‘Springer Theses’’ brings together a selection of the very best Ph.D.
theses from around the world and across the physical sciences. Nominated and
endorsed by two recognized specialists, each published volume has been selected
for its scientific excellence and the high impact of its contents for the pertinent
fieldofresearch.Forgreateraccessibilitytonon-specialists,thepublishedversions
includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor
explaining the special relevance of the work for the field. As a whole, the series
will provide a valuable resource both for newcomers to the research fields
described, and for other scientists seeking detailed background information on
specialquestions.Finally,itprovidesanaccrediteddocumentationofthevaluable
contributions made by today’s younger generation of scientists.
Theses are accepted into the series by invited nomination only
and must fulfill all of the following criteria
• They must be written in good English.
• ThetopicshouldfallwithintheconfinesofChemistry,Physics,EarthSciences,
Engineering andrelatedinterdisciplinaryfieldssuchasMaterials, Nanoscience,
Chemical Engineering, Complex Systems and Biophysics.
• The work reported in the thesis must represent a significant scientific advance.
• Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis
must be gained from the respective copyright holder.
• They must have been examined and passed during the 12 months prior to
nomination.
• Each thesis should include a foreword by the supervisor outlining the signifi-
cance of its content.
• The theses should have a clearly defined structure including an introduction
accessible to scientists not expert in that particular field.
Jaroslav Haas
Symmetries and Dynamics
of Star Clusters
Doctoral Thesis accepted by
the Charles University in Prague, Czech Republic
123
Author Supervisor
Dr. JaroslavHaas Dr. LadislavŠubr
Faculty ofMathematics and Physics Faculty ofMathematics and Physics
Astronomical Institute Astronomical Institute
Charles Universityin Prague Charles Universityin Prague
Prague Prague
Czech Republic Czech Republic
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-319-03649-6 ISBN 978-3-319-03650-2 (eBook)
DOI 10.1007/978-3-319-03650-2
Springer ChamHeidelberg New YorkDordrecht London
LibraryofCongressControlNumber:2013956344
(cid:2)SpringerInternationalPublishingSwitzerland2014
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor
informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodology now known or hereafter developed. Exempted from this legal reservation are brief
excerpts in connection with reviews or scholarly analysis or material supplied specifically for the
purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe
work. Duplication of this publication or parts thereof is permitted only under the provisions of
theCopyright Law of the Publisher’s location, in its current version, and permission for use must
always be obtained from Springer. Permissions for use may be obtained through RightsLink at the
CopyrightClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt
fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
While the advice and information in this book are believed to be true and accurate at the date of
publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor
anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with
respecttothematerialcontainedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Supervisor’s Foreword
Inanattempttounderstandnaturethatsurroundsus,theory,thatencodesthelaws
of nature into mathematical formulae and experiment that discovers behaviour of
therealworld,needtogohandinhand.Wefindourselvesinasomewhatspecific
situation when dealing with processes that occur on scales exceeding our labo-
ratories. This is the case of astronomy, which provides us usually with just short
snapshots of systems vastly exceeding our local means of measure of space and
time. The role of the theoretical part—the astrophysics—is then quite often to
make a movie from a single snapshot, i.e. to deduce evolution of the observed
systems on timescales of millions of years.
Galaxies are huge structures, several tens of thousands of parsecs across,
formed by gas and hundreds of billions of stars. Only the innermost regions of
radii up to few parsecs are usually called the galactic nuclei. Considering their
spatial extent and enclosed mass, they represent just a tiny seed in comparison to
their host systems. However, they are remarkable due to extreme physical con-
ditionsinthem—theyhostcentralsupermassiveblackholesofmassrangingfrom
millions to billions of Solar masses which are surrounded by star clusters with
densities exceeding million times the stellar density in the Solar neighbourhood.
The unique conditions of galactic nuclei definitely deserve attention by them-
selves. Nevertheless, they also play an important role in a wider context. It is
known that galactic nuclei keep imprints of the galactic evolution and, therefore,
they are a kind of tracers of the evolution of the Universe. They are not only
passive tracers; from time to time, when a sufficient amount of gas is pushed
towards the supermassive black hole, an episode of so-called active galactic
nucleus is triggered. The hot gas falling onto the black hole overshines the host
galaxy by no less than an order of magnitude and this radiation strongly affects
even the outer parts of the galaxy.
The centre of our Galaxy—The Milky Way—is the nearest galactic nucleus
which can be observed with by far the best resolution. In spite of that it does not
belongtothecategoryofactivegalacticnuclei,ithostsallcomponentstypicalfor
them: a supermassive black hole, very dense star cluster and a considerable
amountofgas.Recentobservationsthatallowedustofollowmotionsofstarsand
gasinthevicinityoftheblackholein‘realtime’revealedseveralmysteriousfacts
about the Galactic Centre. In particular, discovery of several hundreds of very
youngstarswhichorbitaroundthesupermassiveblackholeindistancesbetweena
v
vi Supervisor’sForeword
few milliparsecs to about one-half of parsec was a big surprise and their origin is
still unclear.
The Ph.D. thesis of Jaroslav Haas addresses the mystery of young stars in the
Galactic Centre from a theoretical point of view. He stresses that their current
kinematic state is definitely different from the initial one and, therefore, it can be
used for determination of their origin only with caution. The non-trivial link
between initial and current state of the young stars lies in their dynamical and
internalevolutionfromthetimeoftheirbirth,severalmillionsyearsago,tillnow.
NumericalmodellingofthedynamicsofyoungstarsintheGalacticCentrewhich
isdrivenbymutualgravitationalinteractionofvariousconstituents(supermassive
black hole, dense star cluster and massive molecular torus) is the key subject of
Mr.Haas’thesis.Heextendsandfurtherdevelopsoldermodelswhichassumethat
the young stars have been born in a single gaseous disc. Then, their orbital evo-
lution has been considerably affected by gravity of a massive molecular torus,
which encircles the region under consideration. Both direct N-body simulations
andsemi-analyticapproachareusedtoshowthatsuchasetupmayleadtothestate
observednowadays.Theoriginaldisctendstobepartiallydestroyedbythegravity
of the molecular torus, while mutual gravitational interaction of individual young
starskeepsthe‘core’ofthedisctogether.Italsoshowsthattheresidualdisctends
tochangeitsorientationtowardsperpendicularwithrespecttothemoleculartorus.
Such an orientation is consistent with current observations and, therefore, it may
be considered an indirect proof of quality of the model.
Yet another effect, which has been discussed in the thesis, is mutual gravita-
tional interaction of young stars and a much numerous population of late-type
stars. In spite of that the role of this interaction is not fully understood yet, the
general message from the thesis is correct at high confidence level: the disc-like
stellarstructureembeddedinasphericalstellarclusterleadstoformationofglobal
lopsidedmode—akindofperturbationtothemeanpotential—whichiscapableto
affectindividualstellarorbitsinasubstantialway.Themostapparentconsequence
is secular growth of their eccentricities which may lead to tidal disruptions of the
stars by the supermassive black hole.
The Ph.D. thesis of Jaroslav Haas represents an important step forward in our
understandingofevolutionoftheGalacticnucleus,sheddingnewlightontherole
of gravitational interactions among its different constituents.
Prague, 25th June 2013 Ladislav Šubr
Preface
Over the past decades, both theoretical and observational efforts have led to a
commonviewthatmostgalacticnucleihostamassivecentralbody,presumablya
supermassive black hole (hereafter SMBH). It has been further accepted that
galacticnucleicontainextremelydensestarclustersthatbelongtotheveryoldand
onlyslowlyevolvingstellarpopulationfromthemoredistantpartsofgalaxies.In
the first approximation, these star clusters may be considered roughly spherically
symmetric. Their dynamical evolution in the potential of the central SMBH has
been studied by various authors in the past, starting with the series of papers by
Peebles (1972a, b) and Bahcall and Wolf (1976, 1977).
Onespecifictargetofsuchinvestigationshasalwaysbeen,duetoitsproximity,
the centre of our own Galaxy. Surprisingly, the observations of this region that
havebeencarriedoutduringthelast20yearshaveestablishedthat,inadditionto
theoldsphericalcluster,theclosestvicinityofthecentralSMBHisalsooccupied
byveryyoungstars(Allenetal.1990;Genzeletal.2003;Ghezetal.2003,2005;
Paumard et al. 2006; Bartko et al. 2009, 2010). Moreover, it has also turned out
that the spatial configuration of a substantial subset of these young stars is rather
unexpected, in particular, many of them appear to belong to a coherently rotating
disc-like structure identified for the first time by Levin and Beloborodov (2003).
The dynamical evolution of such a stellar disc has been analysed by Alexander
et al. (2007) and Cuadra et al. (2008) by means of numerical modelling. These
works, however, are based on several simplifications. Among others, the most
limiting one seems to be the approximation of an isolated stellar system, i.e. a
systemthatisnotinfluencedbyanyothersourcesofgravityexceptforitsownand
the central SMBH. Other works include the perturbative influence of a possible
second stellar disc (Nayakshin et al. 2006; Löckmann et al. 2008; Löckmann and
Baumgardt 2009; Löckmann et al. 2009) or the old spherical star cluster (Kocsis
and Tremaine 2011).
A stellar disc similar to the one detected in the Galactic Centre has also been
reportedin the central parts ofour neighbouringgalaxy M31 (Benderet al. 2005;
Lauer et al. 2012). Hence, it appears that such structures might represent generic
component of galactic nuclei. In this thesis, we thus attempt to broaden the pre-
viousanalysesandfurtherinvestigatetheevolutionoftheinitiallythinstellardiscs
around the SMBH. By means of numerical N-body modelling, we include the
perturbativeinfluenceofanextendedsphericallysymmetricstarcluster(Chap.2).
vii
viii Preface
Wediscussthecasewhentheclusterisemulatedbyapredefinedanalyticpotential
incontrasttothecasewhenitistreatedinthefullN-bodyway,asalargenumber
of gravitating stars. In the later one, our results reveal a significant impact of the
clustergravityupontheevolutionoftheembeddeddisc.Furthermore,weconsider
the perturbative gravitational influence of a distant axisymmetric source which
approximates massive gaseous torus, another widely expected component of the
active galactic nuclei. We develop a simple semi-analytic model for this setting
(Chap.3)andapplythismodeltotheyoungstellarsystemintheGalacticCentre,
confronting the results with direct numerical N-body calculations (Chap. 4).
Before we start with the scientific part of this thesis, there are a few people I
would like to thank. First of all, I thank my supervisor Ladislav Šubr for having
patience with me, which might have not been always easy. I thank Marek Wolf,
the director of the Astronomical Institute of the Charles University, for providing
me a chair, a table and other necessities; David Vokrouhlicky´ for his invaluable
help with the research presented in this thesis; Hana Mifková, the Institute’s
secretary, for feeding me with a tremendous amount of homemade cakes; Attila
Mészáros for all the ‘PŠMs’, political discussions and jokes; Petr Pokorny´ and
Josef Hanuš for unplugging and hiding my laptop battery, dismantling my chair,
continuouslydisplacingorhidingallofmystuffandotherpleasantriesandMichal
ŠvandaforscaringmeintheInstitute’scorridors.IwouldliketothankalsoPavel
KroupafromtheArgelanderInstituteforAstronomyoftheUniversityofBonnfor
beingakindhostduringmystaythereandgivingmemuchusefulscientificadvice
and Sverre J. Aarseth from the Institute of Astronomy of the University of
Cambridge for all the delicious Scottish cookies and the optimized version of his
NBODY6codewithoutwhichthisthesiswouldneverexist.Butmostofall,Iwish
to thank my future wife, Jana, for being my future wife.
Inthisbookversionofmythesis,Ihavecorrectedseveraltyposandmisleading
expressions and sentences.
References
AlexanderR.D.,BegelmanM.C.,ArmitageP.J.,2007,ApJ,654,907
AllenD.A.,HylandA.R.,HillierD.J.,1990,MNRAS,244,706
BahcallJ.N.,WolfR.A.,1976,ApJ,209,214
BahcallJ.N.,WolfR.A.,1977,ApJ,216,883
BartkoH.etal.,2009,ApJ,697,1741
BartkoH.etal.,2010,ApJ,708,834
BenderR.etal.,2005,ApJ,631,280
CuadraJ.,ArmitageP.J.,AlexanderR.D.,2008,MNRAS,388,L64
GenzelR.etal.,2003,ApJ,594,812
GhezA.M.etal.,2003,ApJ,586,L127
GhezA.M.,SalimS.,HornsteinS.D.,TannerA.,LuJ.R.,MorrisM.,BecklinE.E.,Duchêne
G.,2005,ApJ,620,744
KocsisB.,TremaineS.,2011,MNRAS,412,187
LauerT.R.,BenderR.,KormendyJ.,RosenfieldP.,GreenR.F.,2012,ApJ,745,121
Preface ix
LevinY.,BeloborodovA.M.,2003,ApJ,590,L33
LöckmannU.,BaumgardtH.,KroupaP.,2008,ApJ,683,L151
LöckmannU.,BaumgardtH.,2009,MNRAS,394,1841
LöckmannU.,BaumgardtH.,KroupaP.,2009,MNRAS,398,429
NayakshinS.,DehnenW.,CuadraJ.,GenzelR.,2006,MNRAS,366,1410
PaumardT.etal.,2006,ApJ,643,1011
PeeblesP.J.E.,1972a,Gen.Rel.Grav.,3,63
PeeblesP.J.E.,1972b,ApJ,178,371