interstellar turbulence driven by magneto-rotational instability - AIP

98 Pages·2005·2.03 MB·English

Astrophysikalisches Institut Potsdam
Arbeitsgruppe “Magnetohydrodynamik”
INTERSTELLAR TURBULENCE DRIVEN BY
MAGNETO-ROTATIONAL INSTABILITY
Dissertation
zur Erlangung des akademischen Grades
“doctor rerum naturalium”
(Dr. rer. nat.)
in der Wissenschaftsdisziplin Astrophysik
eingereicht an der
Mathematisch-Naturwissenschaftlichen Fakulta¨t
der Universita¨t Potsdam
von
Natalia Dziourkevitch
Potsdam, im Februar 2005

Contents
Introduction 1
1 Magneticfieldsofspiralgalaxies 3
1.1 Globalmagneticfields . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Magneticpitchanglesandfieldstrength . . . . . . . . . . 7
1.1.2 Axisymmetry . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.3 Questionswaitingtoanswer . . . . . . . . . . . . . . . . 12
1.2 Thegalacticdynamo . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.1 Mean-fielddynamotheory . . . . . . . . . . . . . . . . . 14
1.2.2 Successandlimitationsofthegalacticdynamotheory . . 21
1.3 Magneticturbulence . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4 Interstellarturbulence . . . . . . . . . . . . . . . . . . . . . . . . 24
1.5 MRIforgalaxies? . . . . . . . . . . . . . . . . . . . . . . . . . 30
2 Abouttherotationlaws 32
3 Magneto-RotationalInstability 38
3.1 IntroductiontoMRI . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 MRIforaccretiondisks: turbulencecharacteristics . . . . . . . . 47
4 ZeusMP3Dcodeandmodeldescription 49
4.1 Modeldescription . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Boundaryconditions . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.1 Perfectconductor . . . . . . . . . . . . . . . . . . . . . . 55
4.2.2 Pseudo-vacuum . . . . . . . . . . . . . . . . . . . . . . 55
4.3 HDandMHDtests . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 3DglobalsimulationsofMRIforgalaxies 59
5.1 MRIwithpurelyverticalinitialmagneticfields . . . . . . . . . . 59
5.1.1 Uniformdensity . . . . . . . . . . . . . . . . . . . . . . 60
5.1.2 Nonuniformdensity . . . . . . . . . . . . . . . . . . . . 64
5.2 Influenceofturbulentdiffusivity . . . . . . . . . . . . . . . . . . 76
5.3 MRIwithflux-freeinitialmagneticfield . . . . . . . . . . . . . . 80
3
6 Conclusions 83
Appendix 85
A.1 Derivativeoperatorsincylindricalcoordinates . . . . . . . . . . 86
A.2 Basicelectrodynamicequations . . . . . . . . . . . . . . . . . . 86
A.3 MRIwithinitialfree-decayingturbulence . . . . . . . . . . . . . 87
Acknowledgments 93
Introduction
Galaxiesareamongthemostfascinatingobjectsinthesky. Strongemissionfrom
structures built early in the history of the universe, such as quasi-stellar objects
(QSO), give us some hints about the physical processes shaping young galaxies.
Galaxiesclosertousandevolvedoveralongertimescaleshowavarietyofforms,
interactions and active regions, resulting from long internal evolution and galaxy
collisions. To obtain detailed observational information, huge investments went
into powerful telescopes. But the more detailed these observations become, the
morequestionsappeartobeansweredbytheory. Thereisalsoapermanentgrowth
of computingpower fornumericalexperiments. Thisallows to includea growing
numberofphysicalprocessesactingonanextendedrangeofscales.
There are no two identical spiral galaxies in the sky - every one shows us a
different face and has its own individual history. It therefore becomes more and
moredifficultforanindividualtheoreticianstoincorporateallthedetectedeffects
anddetailsintoonecoherentlargescalepicture. Thus,apersonalscientificcontri-
butionisjustasmallstoneinthehugepuzzleoftheUniverse.
ObservationsdetectmagneticfieldsinsideandoutsidetheMilkyWay,starting
with globules ( 1 parsec), filaments, clouds, superbubbles, spiral arms, nearby
(cid:24)
galaxies,superclusters,andendingwiththeCosmologicalUniverse’sBackground
Surfaceat 8Teraparsecs(Vallee´ 1997). Thisworkisconcernedwithacommon
(cid:24)
property of every galaxy – the galactic global magnetic field. It was observed
to be of the same strength for both young and old galaxies. The magnetic fields
are coupled to the interstellar matter (ISM) and may be one of the causes for the
turbulencedetectedintheISM.
InthefirstchapterIshallgiveabriefoverviewofthegalacticglobalmagnetic
field properties. The dynamo mechanism (a well-known theoretical explanation
of the global magnetic fields) will be briefly described. The success of dynamo-
amplificationofthemagneticfieldsdependsonthepropertiesofISM.ISMphases
andtheirdistribution inagalacticdisk,aswellasthereportaboutobserved prop-
ertiesoftheturbulentdensity, velocityandmagneticfieldsarethereforegiven. As
a summary of the first chapter we shall formulate the motivation for a magneto-
rotationalinstability(MRI)investigationinthegalacticdisk.
Chapter2isdevotedtothedescriptionofobservedrotationlawsforthegalax-
ies. Thetopicdeservesourattentionasfarastheradialvariationofgalacticrotation
is a causefor existenceof MRI. Many years of galacticrotationlaw studiesleave
1
2 Introduction
neverthelessmanyquestionsopen,theywillbediscussedinthiswork.
In Chapter 3 we explain the physical mechanism of the magneto-rotational
instability. We give thesimplestderivation of an instabilitycriterionfortheMRI.
Most of the previous results have been obtained for Keplerian disks. A summary
ofbothlinearstudyandlocalsimulationsisgiven.
InChapter4wegivethenumericalcodedescription. Themagneto-hydrodynamical
code ZeusMP has been used for 3D global simulations of the gaseous galactic
disks. Thereareplentyofalternativecodes,thereforewehavetojustifyourchoice
forZeusMP.Thedescriptionofthemodel,boundaryconditionchoiceandnumer-
icaldifficultiesarediscussedaswell.
Chapters5and6containthemainresultsandthesummary.
Chapter 1
Magnetic fields of spiral galaxies
1.1 Global magnetic fields
Eachspiralgalaxyhasbothuniquefeaturesandothersthatarecommonwithmost
other galaxies. Therefore, we shall distinguish between the features driven by a
veryspecific(foragivengalaxy)processandfeaturescreatedbyacommonphys-
icalmechanism. Thecommonfeaturesare:
magneticfieldstrengthis 10(cid:22)G,
(cid:15) ’
magnetic spiral arms are parallel to optical ones (if the latter are clearly
(cid:15)
present),
magneticfieldlineshavepitchanglesfrom10o to40o (inplane),
(cid:15)
magnetic fields have mixed spiral structure (MSS) or axisymmetric spiral
(cid:15)
structure(ASS)(bisymmetricstructureisreportedonlyforM81),
evidenceforthemagneticquadrupole(orthemixtureofitwithadipole),
(cid:15)
magneticfieldsareconcentratedinthemidplane,
(cid:15)
significantmagneticfieldsexistintheveryyounggalaxies.
(cid:15)
We derive most of the listed features from the radio observation data for nearby
spiral galaxies, which are presented in Table 1.1 and Table 1.2 (R. Beck 2000).
Themagneticfieldstructuresaregivenbothforface-onandedge-onobjects.
A theoretical finding of the physical mechanism for the fast magnetic field
amplification is requested not only for nearby spiral galaxies. Magnetic fields of
about1(cid:22)Gareobservedinextremelyyounggalaxies(Kronbergetal. 1992,Lesch
& Hanasz 2003). The magnetic fields are required to be strongly amplified on
short time-scales because of the observed magnetization of very young (0.5 Gyr)
galaxies.
The amplitude of the magnetic field is a derived and not directly observed
value. We use the fact that the energetic charged particles (cosmic rays) emit a
3
4 CHAPTER1. MAGNETICFIELDSOFSPIRALGALAXIES
Table1.1: Radiopolarizationobservationsandmagneticfieldstructuresofnormal
galaxieswithlowormoderateinclination(Beck2000). Instruments: E:Effelsberg
100m; A: Australia Telescope Compact Array; V: Very Large Array; P: Parkes
64m; W: Westerbork Synthesis Radio Telescope. Notations: ASS: axisymmetric
spiralstructure(m=0dynamomode)dominates;BSS:bisymmetricspiralstructure
(m=1dynamomode)dominates;MSS:mixedmodes
galaxy wavelength[cm] fieldstructure
M33 E21,18,11,6,2.8 spiral
M51 W21,6
E6,2.8 MSS,magneto-ionichalo,
V20,18,6 inter-armfields
M81 E6,2.8 BSS+weakerASS,
V20,6 inter-armfields
M83 E6,2.8 MSSand bar
k
V20,6,A13 magneticarms
M101 E11,6 spiral
NGC1097 V22,18,6,3.5 gasflow,nuclearspiral
k
NGC1365 V22,18,6,3.5 gasflow
k
NGC1566 A20,13,6 spiral,inter-armfields
NGC1672 A20,13,6 spiral,inter-armfields
NGC2276 V20,6 spiral,BSS?
NGC2442 A13,6 spiral, bar
k
NGC2903 E6,2.8,V18,20 spiral
NGC2997 V20,6,3.5,A13 spiral,ASSininnerregion
NGC3521 E2.8 spiral
NGC3627 E2.8 dustline
k
V6,3.5 anomalousmagneticarm
NGC4254 E6,2.8V20,6,3.5 spiral, compressionregion
k
NGC4258 W+V21E6,2.8 anomalousarm
k
V20,6,3.5 planarspiraljet?
NGC4414 V6,3.5 spiral,MSS?
NGC4449 E6,2.8 opticalfilament
k
V6,3.5 spiral
NGC4535 V22,18,6,3.5 spiral
NGC5055 E2.8 spiral, dustfilaments
k
NGC6822 E6 isolatedpatches
NGC6946 E11,6,2.8 spiral,
V22,18,6,3.5 MSS,magneticarms
NGC7479 V22,18,6,3.5 extra-planarspiral‘jet’?
NGC7552 A6 spiral, bar
?
IC10 E6 localcompressionregion
k
IC342 E11,6V20,6,3.5 ASS,magneticspiralarms
1.1. GLOBALMAGNETICFIELDS 5
Table1.2:Radiopolarizationobservationsandmagneticfieldstructuresof(almost)
edge-ongalaxies(Beck2000). (E,P,V,ASS,BSS:seeTable1.1)
galaxy wavelength[cm] fieldstructure
M31 E21,11,6 ASS(+weakerBSS),
V20,6 spiral(innerregion)
M82 V6,3.6 halo,radialfield
M104 V20,6 disk
k
NGC55 V20
NGC253 P6
V20,6 plane,ASS
k
E6,2.8 spursinclinedtoplane
NGC891 V20,6 spursinclinedtoplane
k
E6,2.8
W49
NGC1808 V20,6 spurs plane
?
NGC3079 V6 extra-planarjet?
NGC3628 V20,6 plane
k
E6,2.8 spursinclinedtoplane
NGC4565 V20,6 plane
k
E6,2.8
NGC4631 E6,2.8 plane(outerregion)
k
V20,6 plane(innerregion)
?
V22,18 halo,dipolarfield
NGC4666 V20,6 halo,fieldinclinedtoplane
E6,2.8
NGC4945 P6 extensions plane
?
NGC5775 V6 plane
k
NGC5907 V20
E6 plane
k
NGC7331 V20,6
E6,2.8 almost plane
k
Circinus A13,6 northernplume
?
6 CHAPTER1. MAGNETICFIELDSOFSPIRALGALAXIES
lot of energy while spiraling around the magnetic lines within a galaxy. An in-
tensity of the synchrotron emission j is measured directly and related to the
sync
strengthofthemagneticfield,j E B2. Ifthecosmicrayscanbeassumed
sync CR
(cid:24)
tobeinanequipartitionwiththemagneticfields,thenbydefinitionthecosmicray
energy density, E ,isproportionaltoB2. Therefore,themagneticfieldstrength
CR
isassumedtobeproportionaltotheintensityasB j(cid:0)4 .
(cid:24) sync
TheenergydensityofthemagneticfieldE (estimatedfromanequipartition
mag
withCR)isfoundtobeinanequipartitionwiththeturbulentkineticenergydensity
E . Therefore,forspiralgalaxiesweemploythewidelyacceptedequipartition
T;kin
condition,
E E E : (1.1)
T;kin mag CR
’ ’
Usually, itisjustifiedtoestimatetheequipartitionmagneticfield
B = p(cid:22) (cid:26)u ; (1.2)
eq 0 T
usingtheobserved gasdensity(cid:26)andthevelocitydispersionu = u02 ,which
T
h i
can be measured for a galaxy. For example, for uT = 10km=s anqd density (cid:26) =
10(cid:0)24g=cm3 theequipartitionfieldis3:5 10(cid:0)6G. Obviously,themagneticfields
(cid:2)
are too weakto affect thegalacticrotation, whereasthe dynamicalimportance on
theturbulencescalescannotbeneglected.
Synchrotron emission in a purely regular magnetic field should be totally po-
larized. Inreality, thegalacticmagneticfieldshavebothmeanandturbulentcom-
ponents, B = B + B . The degree of the synchrotron emission polariza-
reg T
tion is telling us about the contribution of the turbulent magnetic fields. Usually,
B =B 2. Typically, the turbulent magnetic fields are dominating in the op-
T reg
(cid:24)
tical spiral arms, whereas the regular component is typically concentrated in the
inter-armregions(withrareexceptions).
The interpretation of the radio-polarization data of spiral galaxies reveals the
existenceoflarge-scalemagneticfieldswithveryspecificproperties. Theirexpla-
nationisofconsiderableinterest. Inparticular, thereisaproblemofunderstanding
the relation between the particle flow and the magnetic fields. We are looking
forward to the next generation of radio telescopes, with 100 times increased sen-
sitivity, whichwillpresenttousthefullwealthofmagneticstructuresingalaxies.
Fortunately, the power of supercomputers allow us to start already with the nu-
merical simulations, in an attempt to explain some of the problems mentioned or
even to predict some features to be observed in future with better resolution and
sensitivity.
In spite of many similarities, each galaxy shows individual traits and compli-
cation of magnetic fields patterns (spurs, spiral arms, blobs, cross-arms and axial
flows). Radiomapswithhigherresolutionshownowmoredetailsofthemagnetic
structures,whichseemedtobemuchmorecoherentandregularonpreviousmaps
withlessresolution.