Dark Matter in the Universe
Reuven Opher
InstitutoAstron^omioeGeofsio-USP
Av. Miguel Stefano,4200,04301-904, S~aoPaulo,SP,Brazil
Reeivedon22February,2001
Wetreat herethe problemof darkmatteringalaxies. Reentartiles seemto implythat we are
entering into the preision era of osmology, implyingthat all of the basiphysis of osmology
is known. However, we show here that reent observations question the pillar of the standard
model: thepreseneofnonbaryoni\darkmatter"ingalaxies. UsingNewton'slawofgravitation,
observations indiatethatmost ofthe matteringalaxies isinvisibleor dark. Fromthe observed
abundanesoflightelements,darkmatteringalaxiesmustbeprimarilynonbaryoni. Thestandard
modelanditsproblemsinexplainingnonbaryonidarkmatterwillrstbedisussed. Thiswillbe
followedbyadisussionofamodiationofNewton'slawofgravitationtoexplaindarkmatterin
galaxies.
I Introdution
The matter produing the visible light in galaxies is
only0:1%oftheamountofmatterneessaryto
pro-due the approximate atuniverse, whih present
ob-servations indiate. While part of thedark matter in
galaxies is baryoni, the major partis assumed to be
nonbaryoniin the standard model. Present
observa-tions indiate that this analysis ofthe darkmatter in
galaxiesmaynotbetrue. InsetionIIwedisussdark
matteringalaxiesasunderstoodinthestandardmodel,
aswellasthediÆultieswithsuhaninterpretation. A
modiationofNewton'slawofgravitationinorderto
explainthedarkmatteringalaxiesistreatedinSetion
III.Finally,in setionIV,wepresentouronlusions.
II The standard model of dark
matter in galaxies and its
problems
A. The standard model
Aordingto thestandardmodel, earlyin the
uni-verse, there ourred an epoh of expansion that was
exponentialintime. Thisexponentialexpansionis
gen-erally attributed to bedue to asalar(inaton) eld.
Quantumutuationsofthesalareldeventually
re-ated utuations in the density (i.e., adiabati
u-tuations). Due to the expansion of the universe, the
relativisti partiles, suh as photons and neutrinos,
ooled faster then the non-relativisti partiles, suh
as baryons and WIMPS (weakly interating massive
partiles, whih are alled old dark matter (CDM)).
Whennon-relativistipartilesbeganto dominatethe
universe(i.e.,thematter-dominatedepoh),the
utu-ations of CDM began to grow. At the reombination
epoh,whenhydrogenatomsformedandtheosmi
mi-rowavebakground(CMB)wasreated,baryons(i.e.,
hydrogen, helium, et.) beganto fall into the
gravita-tionalpotentialwellsreatedbythegrowingCDM
u-tuations. Thesmallestmassutuationsthatollapsed
had masses 10 6
M
. They eventually oalesed to
form the observed galaxies ( 10 12
M
) and lusters
ofgalaxies(10 15
M
). Thismodelfortheformation
ofgalaxiesandlustersofgalaxiesinvolves,however,a
numberofproblems, whih wedisussin thefollowing
sub-setions.
B.Smoothrotation urves of galaxies
The dark matter ontent of spiral galaxies is
pri-marily determined from their rotation urves. We
andeterminethe veloities ofhydrogenatoms in
dis-tant parts from the enter of aspiral galaxyby their
Doppler-shifted 21 m lines, observed by radio
tele-sopes. FromNewton's lawofgravitation, theamount
ofmatterwithinaradiusRfromtheenterdetermines
theirularveloityofahydrogenatom. Wendfrom
observationsthattheirularveloity,V
,risesinitially
with radius, as expeted, but then beomes
approxi-mately onstant with radius, whih is unexpeted. If
matter were indeed onned to within a radius R
m ,
weshould expet V 2
R =Constantfor R >R
m , from
Newton'slaw.
In the standard model, a spiral galaxy onsists of
CDMandbaryonimatter. Thebaryonimatter,
sub-jettoeletromagnetidissipationproesses,ollapsed
andformedthediskofthegalaxy. Wethereforeexpet
tohaveallofthebaryonimatter(primarallyonned
toadisk)intheinnerpartofthegalaxy,andtheouter
partofthegalaxy(thehalo)tobedominatedbyCDM
(weaklyinteratingmatter)whihisnotsubjetto
ele-tromagnetidissipationproesses. FromNewton'slaw,
we haveV 2
R = GM
R
, where M
R
is the mass within
theradius R and G is thegravitationalonstant. We
expet a \break",or disontinuity, in the urve V
vs
R when R passes from the disk to the halosine the
baryoni density of the disk has little to do with the
CDMdensityofthehalo. Howevertheexpetedbreak
does notexist. This wasrst notied by Bahall and
Casertano[1℄,whoalleditthe\disk-haloonspiray".
CasertanoandvanGorken[2℄notedthatwhatever
fea-turedoes exist,itis lessthan 10%. Blumenthalet al.
[3℄ noted that if CDM dominated at all radii, then a
featurelessV
vsRurveshouldbeseen. Observations,
however, indiate that for small radii, at least in our
galaxynear thesun, CDMdoesin fat,not dominate
thematterontent. Theseobsevationsappeartoimply
that CDM interats strongly with the baryoni
mat-ter(e.g.,eletromagnetially),whereasaordingtothe
standardmodel,theyshouldonlyinteratweakly(i.e.,
gravitationally).
C. Surfae brightnessof galaxies
Galaxies have the same asymptoti irular
velo-ity, V
1
(for agivenluminosity)whether theyhave a
high orlow surfaebrightness. This peuliar fat was
notedbyZwanet al. [4℄, Sprayberryet al. [5℄ andM
Gaugh et al. [6℄. In the standard model, we require
thatthemasstolightratioinreases(i.e.,moreCDM)
in order to ompensatefor the lowsurfae brightness
andpreservethesameLuminosityvsV
1
dependeny.
Itis,thus,impliedthattheCDMsomehowknowswhat
thebaryonimatter is doing,whih isnot thease in
thestandardmodelsinethereisnegligibleinteration
betweenCDMandbaryonimatter.
D. Evidenefor CDM
It is generally observed that evidene for CDM
only exists in regions with gravitational aelerations
< 10 8
ms 2
[7℄, [8℄. There is, however,no
hara-teristi aelerationa
0 10
8
ms 2
in the standard
model.
E. Parametersto desribe rotationurves
Thestandardmodelrequirestwoparametersto
de-sribetheurvesV 2
=RvsR . Thetwoparameters
fre-quentlyused areV
1
,theasymptotiirularveloity,
andR
e
,theeetiveradiusofthespiralgalaxy,where
However,theurves,anbeshowntobeverywell
de-sribedbytherelationV 2
=R=a
N (1+x
2
) 1=2
=x,where
a
N =GM
R =R
2
,x=a
N =a
0 ,anda
0 =10
8
mse 2
. a
0
istheonlyparameterrequired. Inthestandardmodel,
withthebaryonimatterandCDMfairlyindependent,
itis reasonablethatweshouldrequiretwoparameters
to desribe rotation urves: one for baryoni matter
ontent and the seond for CDM. Sine only one
pa-rameter,isin fat required(a
0
),thematterontentof
thespiralgalaxydoesnotappeartohavetwo
indepen-dentomponents.
F. Galatidiss
The standard model predits galati diss whih
are too small ompared to observations. In the
stan-dardmodel,theangularmomentumofthedissreated
bynumerialsimulations,isabout10%ofwhat is
ob-served[9℄. Afeedbaksenario,inwhihstar-formation
helps preventbaryonimatter tolose angular
momen-tum to the CDM halo, does not resolve the problem
[10℄.
G. Centers ofgalaxies
Aording to the standard model, CDM interats
onlyweakly(i.e.,gravitationally). FromLiouville's
the-oremandthe fatthat in thepast,thedistributionof
CDMwasapproximatelyhomogeneous,alltheenters
of CDM objets (i.e., the enters of galaxies) should
havethe samemaximum phasespae. This, however,
isnotobserved[11℄.
H. Cusps in the enters ofgalaxies
SimulationswithCDMpreditsingularentral
den-sities (\usps") in galaxies, whih, however, are not
observed [12℄, [13℄. Desribing the entral density by
an index of onentration, the index is found to vary
greatlyfromgalaxytogalaxy[14℄. Ingeneral,rotation
urvesindiateentralgalatidensities(inludingthe
MilkyWay)whiharemuhlessthanpreditedbythe
standardmodel[15℄.
I. L vs V
1
Numerialalulationswith CDM predita
Lumi-nosity vsV
1
whihis notinagreementwith
observa-tions. ThepreditedLvsV
1
urveswithCDMpredit
toohigh aV
1
,asomparedwithobservations[15℄.
J. Dwarfgalaxies
The number of dwarf galaxies is predited by the
standardmodel to be10 timesmorethanis observed.
This has been notedby Klypin et al. [16℄ and Moore
K. L vs V 4
1
Numerial alulations with CDM indiate L vs
V 3
1
, however, what isobserved is L vsV 4
1
, asnoted
byDalantonetal. [17℄andMoetal.,[18℄.
L. Surfae density ofgalaxies
Observationsindiate aut-oof highsurfae
den-sity diss in spiral galaxies (Freeman Law) as well
as a ut-o of high density elliptial galaxies (Fish
Law). The ut-o ours for a surfae density
'
10 8
ms 2
. The standard model does not predit
these ut-os.
M. Aousti peaks of osmi mirowave
bak-ground (CMB)
The standard model with CDM predits a seond
aousti peak muh higher than observed. There is,
however, no obvious explanation for this in the
stan-dardmodel.
N. Self-interatingCDM
In order to help with the large number of dwarf
galaxies that thestandardmodelpredits, a
modia-tion ofthe standardCDMsenariohasbeenmade by
assumingthattheWIMPShavealargesatteringbuta
small annhilationrosssetionamongthemselves
[19℄-[21℄. Although this modiation helps with the
num-berofdwarfgalaxies[22℄-[24℄,theotherproblemsited
above,suh asformingusps,remain[25℄.
III Modiation of Newton's
law of gravitation in order
to explain the dark matter
in galaxies
We disuss herethe evidene indiating that asimple
modiation of Newton's law of gravitation for small
aelerations,g<a
0 =10
8
ms 2
,isinbetter
agree-ment with observations than the standard model
em-ployingCDM.SuhamodelwassuggestedbyMilgrom
[26℄ who named it MOND (Modied Newtonion
Dy-namis).
Ifg
N
istheaelerationpreditedbyNewton'slaw,
MOND suggeststhat thetrueaelerationisgivenby
g = g
N
=(x), where (x) is a monotoni funtion of
x and x = g=a
0
. The funtion (x) has the
proper-ties (x) ' 1 for x >> 1 and (x) ' x << 1. In
partiular,Milgrom[26℄suggestedthefuntion (x)=
x=(1+x 2
) 1=2
,whihisgenerallyusedin theliterature
A.The rotation urvesin our galaxy
Lepine and Leroy [27℄ studied the rotation urve
(irularveloityV
)data(V
vsR )inourgalaxy.From
themassdistributionofthediskandthebulge,thesum
wasfoundto giveaV
vsR urvein verygood
agree-mentwiththeobserveddata. Inpartiular,theyfound
that \... there is no need for a dark matter
ompo-nent". Thedata wasanalyzedfor R <10kp. Thus
thegravitationalaelerationsresponsibleforthe
rota-tionurveare >3:210 8
ms 2
. These results are
in agreementwith MOND, where x >1 andg 'g
N ,
whihpreditsnoCDM.
B.Spiral galaxies
Sanders and Verheijen [28℄ studied the rotation
urvesof30galaxiesinanearbylusterofgalaxies,ata
distaneof15Mp. Theyfoundverygoodagrrement
withtheMONDpredition.
C. Low surfae brightness galaxies
Alowsurfaebrightnessgalaxyhasasurfae
bright-ness1=2thatofanormalgalaxy. However,itsatomi
hydrogenontentisnormal. Thegalaxiesarenotdwarf
galaxies,buthavemassesontheorderofnormal
galax-ies. de Blok & M Gaugh [29℄ studied the rotation
urvesof 15suhgalaxies andfoundthattheywerein
agreementwith MOND.
D.Stability ofgalati diss
Normally a massive CDM halo is invoked as the
soure of stability of a Newtonian dis. However,
MONDpreditsgreaterstabilityofgalatidissthan
doesNewtoniantheoryand,thus,doesnothavetorely
onCDM. Bradaand Milgrom [30℄ found that the
ex-trastabilityintheMONDtheorywasequivalenttothe
preseneofamassivehalowithamassthreetimesthat
ofthedis.
E.Galati warps
Thedissofspiralgalaxies arenotompletelyat,
butarewarpedattheiredges. Theoriginofthewarps
of these galaxies annotbe understood using
Newto-niandynamis. ThetidalforeoftheMagellaniloud
ating on our galaxyis not enough to reate the
ob-sevedwarp. BradaandMilgrom[31℄showedthatusing
MOND,theMagellaniloudreatestheobservedwarp
inourdis.
F.Dwarfgalaxies
Our galaxy has many nearby dwarf galaxies.
predi-proportionalto thedistaneto ourgalaxyandits
sur-fae density,proportionaltothis distane. Mullerand
Opher [33℄ made the predition, that stellar orbits in
dwarfgalaxiesaremorestableiftheyareperpendiular
totheline-of-sighttotheMilkyWay. Thesepreditions
shouldbeabletobeveried(orshowntobeinorret)
inthenearfuture.
G. Groups ofgalaxies
Milgrom[34℄appliedMONDtothestudyofgroups
of galaxies in the Las Campanas Redshift Survey
(LCRS)[35℄,theCfA1survey[36℄,andtheCfA2survey
[37℄. Thenumberofgroupsstudiedwere394in LCRS,
166 in CfA1, and 406 in CfA2. Using the standard
modelforthesegroups,theaveragemasstolightratios
found(insolarmasstolightunits)were115forLCRS,
198 for CfA1, and 180, for CfA2. Using MOND, the
massto lightratiosfoundwere3:7 forLCRS,2:4
for CfA1, and 8:6 for CfA2. Whereas onsiderable
CDM is indiated for the groups using the standard
model, littleornoCDMisindiatedusingMOND.
H. (CDM) vs (NOCDM) in theCMB
One of the most important soures of information
on the early universe is the osmi mirowave
bak-ground(CMB).TheintensityoftheCMBismeasured
indegreesKelvinofaneetiveblakbodythatould
produetheCMB.Theutuationsofthetemperature
T over the sky an be expanded in Legendre
poly-nomials(i.e.,theCMBmaybestudiedbydetermining
amplitudes of the Legendre polynomialsasa funtion
of l, theorder of theLegendre polynomial). A plotof
T vsl,whihdependsontheinputphysis,anbe
ob-tainedfromapublidomainode,CMBFAST[38℄. The
standardmodelpreditsaoustipeaksatl220and
l440. Thevaluesfortheserstandseond aousti
peaksare T 65K andT 50K, respetively.
What is observed, however, is a muh smaller seond
aoustipeak. MGaugh[39℄,[40℄showedthatifthere
werenoCDM,andonlybaryonimatter,theorywould
thenbein agreementwithobservations.
I. Creating inhomogeneitieswith MOND
Sanders [41℄ investigated the reation of
inhomo-geneities aording to MOND. The simplied theory
that wasused was: ifthe Newtoniangravitational
a-eleration g
N
isgreater thana
0
('1:210 8
ms 2
);
it is unaltered, whereas if the Newtonian aeleration
is less than a
0
, it is inreased to the value p
(g
N a
0 ).
This value for the aelerationis obtained taking the
extreme MOND limit, when (x) ! x for x < 1and
(x)=1forx>1.
The surfaes of small spheres have small
gravita-tionaldeaelerationswithrespettotheentersofthe
spheres. These spheres are thus in the MOND limit.
the MOND limit is R
= a
0 =G
M
(4=3), where
M is
thematter densityof thesphere. The ritialmassof
thissphereisM
=(4=3)R 3
M .
In the standardmodel, the epoh of equipartition
(whenthematterdensityisequaltotheradiation
den-sity) ours at a redshift z 10;000. If there is no
CDM,however,andonlybaryonimatter,theepohof
equipartitionours ataredshift z222. Theritial
massatthisepohisM
=3:710 9
M
.
Aftertheepohofequipartition,theradiation
pres-sureisnegligible. Athighredshifts,theeetofa
os-mologial onstant is also negligible. If R
i (< R
i ) is
the radius of asphere at the equipartition epoh, the
deaeleration of the surfae is proportional to R 1
.
WhenR
i >R
,thenthedeaelerationisproportional
to R 2
. The veloity of the surfaehas a logarthmi
dependene on R for R
i < R
, whereas it has a R 1
dependeneforR
i >R
.
Starting at the equipartition epoh, a sphere
ini-tially expands with the Hubble ow, reahes a
max-imum radius, and then ollapses. The equipartition
epoh redshift,z =222, ours at atime 10 7
years
aftertheBigBang. Asphereof10 5
M
reahesits
max-imumradiusataredshiftz150,whereasasphereof
galati mass 10 11
M
reahes its maximum radius
at z 25. Presentobservationsindiate that galaxies
formed at a redshift z 25, in agreement with this
model whihdoesnotinludeCDM.
IV Conlusions
Thearmationthatweareenteringinto\thepreision
era of osmology" appears in various reent artiles.
Thisphraseimpliesthatweunderstandallofthebasi
physisandthatallweneedtodonowistomeasurethe
important parametersto several deimalplaes. This
is reminisent of the way that physiists talked when
entering the 20 th
entury a hundredyears ago,before
quantum mehanis and relativity were disovered. I
hopetohaveshown insetionsII andIII thatpresent
observationsquestiontheexisteneofoneofthepillars
of thestandardmodel,thepresene ofCDMin
galax-ies. AmodelsuhasMOND,whihassumesthatCDM
doesnotexist,seemstottheobservationsofgalaxies
betterthandoesthestandardmodel.
Ihavenottriedto argueherethat CDMdenitely
does not exist nor that MOND is denitely the true
lawofgravitation. Ionlywishtoshowherethatweare
definitelynotin \thepreisioneraofosmology"and,
on theontrary, are still strugglingto understand the
formationofgalaxies.
Itisonthesaleofgalaxiesthat alargeamountof
observationaldataisavailableandwheretheproblems
with thestandardmodel have,onsequently,been
notevident.
Aknowledgments
The author would like to thank the brazilian
agenies FAPESP, CNPq and PRONEX/FINEP (no.
41.96.0908.00)forpartialsupport.
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