Something about the structure of the Galaxy

22 Pages·1999·0.93 MB·English

Mon.Not.R.Astron.Soc.000,000{000 (1994) Printed26July1999 (MNplainTEXmacrosv1.5)
Something about the structure of the Galaxy
Maartje N. Sevenster1,2
1Sterrewacht Leiden, POBox 9513, 2300 RA Leiden, The Netherlands
2Presently at : RSAA/MSSSO, Private Bag Weston Creek PO, Weston2611 ACT, Australia ([email protected])
Accepted xx.Receivedxx
ABSTRACT
We analyse a sample of 507 evolved (OH/IR) stars in the region (10◦ > (cid:96) >
−45◦),(jbj < 3◦). We derive average ages for subsets of this sample and use those
sets as beacons for the evolution of the Galaxy. In the Bulge the oldest OH/IR stars
in the plane are 7.5 Gyr (1.3 M(cid:12)), in the Disk 2.7 Gyr (2.3 M(cid:12)). The vertical dis-
tribution of almost all AGB stars in the Disk is found to be nearly exponential, with
< >
scaleheight increasing from 100 pc for stars of (cid:24)1 Gyr to 500 pc for stars of (cid:24)5 Gyr.
There may be a small, disjunct population of OH/IR stars.The radialdistribution of
AGBstarsisdictatedbythemetallicitygradient.Unequivocalmorphologicalevidence
ispresentedfortheexistenceofacentralBar,butparameterscanbeconstrainedonly
foragivenspatial–densitymodel.Usingavarietyofindicators,weidentifytheradiiof
the inner ultra–harmonic(2.5 kpc) andcorotationresonance(3.5 kpc). We show that
the 3–kpc arm is likely to be an inner ring, as observed in other barred galaxies, by
identifying a group of evolved stars that is connected to the 3–kpc HI filament. Also,
using severalobserved features, we argue that an inner–Lindblad resonance exists, at
(cid:24)1–1.5 kpc. The compositions of OH/IR populations within 1 kpc from the galactic
Centre give insight into the bar–driven evolution of the inner regions. We suggest
that the Bar is (cid:24)8 Gyr old, relatively weak (SAB) and may be in a final stage of its
existence.
Key words: Galaxy: structure – Galaxy:evolution– Galaxy:stellar content– Stars:
AGB and post–AGB.
1 INTRODUCTION will attempt to do so.
Theaimofthisarticleistodescribetheoverallformof
It has become widely accepted that our Galaxy is barred, thestellardistributionin,andtheevolutionofvariousgalac-
as evidence accumulated over the last (cid:12)ve years from star tic components (disk, bulge, spiral arms etc), based mainly
counts,gas{dynamicalstudiesandstellarthree{dimensional on its content of evolved stars and focussing mainly on the
kinematics and especially from the analysis of the COBE{ inner Galaxy. To a lesser extent, we attempt to constrain
DIRBE integrated{light data (Dwek et al.1995; for a re- the free parameters of these stellar distributions. The goal
viewon thegalactic Bar see Gerhard 1996). Theimportant is a schematic, rather than comprehensive, picture of the
parameters of a barred potential are the semi{major{axis Galaxy.
length, a, the in{plane axis ratio, q, the pattern speed, Ω , We restrict ourselves largely to the stellar distribution
p
andthestrengthrelativetotheaxisymmetricpartofthepo- anddiscussthedistributionofthegasonlysuper(cid:12)cially.As
tential,A.Fromtheobserver’spointofview,anotherquan- starsareprobablythesourceandthecleanesttracersofthe
tity is the major axis’ orientation with respect to the line barred potential, such a study of only the stellar compo-
of sight, the viewing angle φ. Due to the awkward view we nentoftheGalaxyisnecessary.Obviously,thegas{andthe
haveof theGalaxy,thevaluesof thoseparameters areeven stellardistributionsshouldultimatelybeexplainedsimulta-
harder to determine than in external galaxies. They are of- neously in one coherent picture. In fact, the (cid:12)rst evidence
ten inferred from the influence the barred potential has on for non{axisymmetry of the inner Galaxy came from the
the other parts of the galaxy. Helpful, albeit crude and not neutral{gas kinematics (see review by Oort 1977). It was
completelyunderstood,diagnosticsarethe\resonantrings" exactly the drive for coherence that has shifted the atten-
andspiralfeaturesthatariseatradiiwhereorbitsareinres- tiontothestars, becausetheirdistribution showednoclear
onancewiththefrequencyofrotationofthebar.Theuseof deviation from axisymmetry. Neither of the prevailing ex-
these structures is especially di(cid:14)cult in our Galaxy, where planations for the origin of the observed radial gas motions
we see only tangent points to rings and spiral arms, but we -centralexpansionorelongationofthepotential-weresup-
2 M. Sevenster
portedbystellarobservations.OncetheBarhadbeenfound 2 PROPERTIES OF THE DATA SET
in the stellar surface density (Blitz & Spergel 1991; Dwek
The stellar density and the gravitational potential of the
et al.1995), questions remained. For instance, why are the
Galaxy arebesttraced byintermediate{mass, evolvedstars
stellarkinematicsexplainedsowellbyaxisymmetricmodels
as they constitute the largest fraction of the total stellar
(Kent 1992; Ibata & Gilmore 1995) and why is the micro{
massandaredynamicallyrelaxed(Frogel1988). Good can-
lensing optical depth toward Baade’s window incompatible
didates for this are the so{called OH/IR stars; oxygen{rich
withdensitymodelsderivedfromsurface{densitymaps(eg.
objects on the asymptotic giant branch (AGB; see for in-
Nikolaev & Weinberg 1997) ?
stance Habing 1993; Sevenster, Dejonghe & Habing 1995).
The stellar data used in this paper (Sevenster et We use an unbiased, homogeneous sample of 507 OH/IR
al.1997a,b) were collected speci(cid:12)cally to form the optimal starsinthegalacticPlane,theAOSPsample(Australiatele-
sample to address such issues and to complement existing scope Ohir Survey of the Plane), acquired in a systematic
data. The sample consists of OH/IR stars: intermediate{ survey of the region between longitudes 10(cid:14) > (cid:96) > −45(cid:14)
mass, oxygen{rich, far{evolved asymptotic{giant{branch and latitudes jbj<3(cid:14) in the 1612 MHz (18 cm) OH{maser
(AGB)stars.Theseareexcellenttracersofthegeneralstel- line (Sevenster et al.1997a,b). The positional accuracy is
larpopulation,as starswith initialmasses between roughly 00.05, the line{of{sight velocities (with respect to the local
1M(cid:12) and6M(cid:12) gothroughthisphase.Theyarealsotracers standard of rest) are accurate to 1 kms−1.
ofthegalacticpotentialastheyformafairlyrelaxedpopula- In Fig.1(a) we show the surface density of the AOSP
tion,withtypicalages ofseveralgigayears. Verystrongand sample, smoothed with an adaptive{kernelalgorithm (Mer-
characteristicmaseremissionat1612MHzfromtheground{ ritt & Tremblay 1994). With the initial kernel size that re-
stateOHmolecule allows forradio{interferometric observa- tains best the steepness of the central density pro(cid:12)le with-
tions, combining extinction{free coverage of the plane and out showing individual stars (1(cid:14)) many local maxima are
fastsamplingouttolargedistanceswithpositionsandveloc- revealedinthedistribution(R−1,R−2 andR−3).Themax-
ities with negligible errors (compared to modelling errors). imum at (cid:96) = +9(cid:14) is likely to be a spurious edge e(cid:11)ect. We
Theemployabilityofthissampleingalactic{structurestud- will not discuss any asymmetries in the vertical direction,
ies is clearly demonstrated in Sevensteret al.1999. such as a tilt, because the data quality is slightly latitude{
dependent (Sevenster et al.1997a,b). First, in this section,
Thestructureofthispaperisasfollows.Inthe(cid:12)rstpart, we will assess some astrophysical properties of the sample.
wediscussthelarge{scalespatialdistributionoftheOH/IR{ The OH emission comes from an optically{thick, ex-
starsample.WedescribethesampleofOH/IRstarsinmore panding circum{stellar envelope. Because the expansion is
detail in Sect.2. In Sect.3 we analyse the structure of this radiation{pressure driven, the unobservable intrinsic stel-
sample and estimate the scaleheights and {lengths for the lar luminosity L(cid:3) is related to the outflow velocity of the
galactic Bulge and galactic Disk. Variations of those expo- circum{stellar envelope, V , and its gas{to{dust ratio, µ,
exp
nentialscaleswithpositionarecombinedwithscalesderived (related to metal abundance Z; µ / Z−1 for oxygen{rich
from similar samples and interpreted as age dependencies. stars, Habing, Tignon & Tielens 1994). According to van
InSect.4,wegivemorphological evidenceforagalactic Bar derVeen (1989):
thatcannotbeexplainedbyaphysicallopsideddistribution
(see Blitz & Spergel 1991; Sevenster 1996). By comparing L(cid:3) /µ2Ve4xp. (1)
some parametrized models to the observations, a flavour of
ThisequationisderivedanddiscussedinmoredetailinAp-
the values of the relevant parameters is obtained. Most im-
pendixA.Separatingtheobjectsaccordingtooutflowveloc-
portantly, we derive an approximate distance limit for the
ity(Fig.1(b,c))henceresultsinaseparationroughlyaccord-
sample. The kinematic type of the galactic Bulge in terms
ing to stellar luminosity, or age, without knowledge of the
of its anisotropy parameter and ellipticity is found.
distances to the objects. This results, as expected, in very
In the second part of the paper we discuss the influ- di(cid:11)erentapparentscaleheightsofthesubsamples(Fig.2,see
ence of the bar{shaped potential on the inner Galaxy. In discussion in Sect.3).
Sect.5 we interpret various patterns found in the sample as OH/IR stars can span a wide range of ages, of 0.1 Gyr
>
resonant patterns and identify resonant radii. New insight to (cid:24)10 Gyr. From the IRAS two{colour diagram, one can
into thenatureof the so{called 3{kpc arm is provided bya determine a \turn{over" [25]{[60] colour R3f2, of sources
small group of OH/IR stars that follows the 3{kpc arm’s leaving the evolutionary track (van der Veen & Habing
longitude{latitude{velocity structure. In Sect.6 we give a 1988). This R3f2 is related to the initial mass (Garcia Lario
description of theinnerGalaxy based on thepresented evi- 1991);thisrelationisdiscussedinAppendixB.Wecanthus
dence and we speculate on its evolution in Sect.7. We con- (cid:12)nd the initial mass of a star that has reached the end of
clude in Sect.8. theOH/IR{starphase(thethermally{pulsingAGBphase).
Sincethisphaseitself isshort((cid:24)105yr,Tanabeetal.1997)
Throughout this article, we will use the term \Bulge" compared to the ages of the AGB stars, we can use the
to denote the galactic component we see in the general di- value for the AGB{tip ages by Bertelli et al.(1994) to ob-
rection of j(cid:96)j <(cid:24)10(cid:14), without being interested in its actual tain, for an assumed abundance, the age of the star from
form. If we use the term \Bar" we denote speci(cid:12)cally the itsinitial mass. Theminimum Rf forasamplehencegives
32
prolateortriaxialcomponentoftheBulge.Unlessexplicitly the maximum age of the stars in that sample. We deter-
stated otherwise, stellar velocities are given with respect to mined this for the Bulge region (Rf > −0.4, Sevenster et
32
the local standard of rest (see Sevenster et al.1997a,b for al.1997a,b) and the Disk region (Rf > +0.2, Sevenster et
32
theused Dopplercorrections) and R(cid:12) (cid:17)8 kpc. al.1997a,b)separately.We(cid:12)ndminimuminitialmassesand
Something about the Galaxy 3
Figure1ThesurfacedensityoftheAOSPsample(Sect.2),inlongitudeversuslatitudeindegrees.Theobservationsweresmoothedwith
anadaptive{kernelalgorithm(initialkernelof1(cid:14)).TheupperpanelisforallOH/IRstars(507),themiddleforoutflowvelocitieshigher
than 14 kms−1 and the lowest panel for outflow velocities lower than 14 kms−1(and higher than 1 kms−1). Panels b, c represent
younger and older stars, respectively, with an abundance e(cid:11)ect (Sect.2). Both subset{plots are based on (cid:24)210 stars. Note the o(cid:11)set
toward negative longitudes in for the young sample (see Sect.4.1). The local maxima at (cid:24) −10(cid:14),−20(cid:14),−30(cid:14) { R−1, R−2 and R−3,
respectively{willbediscussedinSect.5.Theunmarkedverticaldashedlinesindicatemaximaintheobserved2.4GHzdistribution(see
Sect.5,Fig.11).Themaximumat(cid:96)=+10(cid:14) isnotreliable.Contoursarespacedattwentyevenintervalsbetweenzeroandthemaximum
ofeachparticularplot.
maximum ages of 1.3M(cid:12)& 7.5 Gyr and 2.3M(cid:12)& 2.7 Gyr,
respectively,bothforsolarabundance.Theratioofthemean
initial masses (3.3/2.3 with an IMF /M−2.5, almost inde-
pendentlyofZ usedtoderivetheages)andofmeanoutflow
velocities(15/14 kms−1)arecompatiblewith asimilar av-
erageabundanceforDiskandBulgestars,Z =0.9{0.95Z ,
b d
accordingtoequation(1).ThenumberofstarsintheAOSP
<
sample with ages (cid:24)0.5 Gyr is negligible.
Thesevaluesaremeanttogiveanindication only,with
a likely uncertainty of about 15% in the derived ages and
about10%intheinitialmasses.TheR3f2−Mirelationisnot
yetfullyestablished andshouldbeusedonlyforensembles,
notforindividualobjects. Besides,notallAOSPstarshave
a (reliable) IRAS identi(cid:12)cation (Sevenster et al.1997a,b),
althoughthosethatdomustberepresentativeofthosethat
don’t, as the identi(cid:12)cations are hampered mainly by the
Figure 2 The cumulative{number distribution over latitude for
the two subsamples of the AOSP sample (Fig.1(b,c)). The (ap- confusion{limited spatial resolution of IRAS.
parent) scaleheights di(cid:11)erbyafactorof2,whichisindicativeof TheagesareinfluencedbythefactthattheAOSPsam-
theagedi(cid:11)erencebetweenthesamples. ple covers only low latitudes. The fraction of (sub{) solar{
mass OH/IR stars is apparently smaller than 1% at low
latitudes. Out of the plane, van der Veen & Habing (1990)
(cid:12)ndthemassesofoxygen{richAGBstarstorangeto<1.0
4 M. Sevenster
M(cid:12), and the corresponding ages to well over 10 Gyr. How-
ever, with their mass-loss parameter (cid:15) =1.5 instead of (cid:15)
M˙ M˙
=1.0 (both values are equally likely to be right), the mass
rangewouldbe1.2{2.2 M(cid:12),which(cid:12)tsinverywellwithour
derivations. Correspondingly, the ages of their stars would
belower,especiallywhenusingZ =0.02insteadofZ =0.04
astheyadvocate.Weconcludethatourresultsarecompat-
ible with theirs.
3 EXPONENTIAL SCALES OF THE DISK
AND THE BULGE
The latitude distribution of the AOSP sample is steeper
than a (projected) exponential (exp(−z)) at all longitudes
and irreconcilable with flatter functional forms (sech2(z)
or exp(−z2)). The same was found recently by de Grijs &
Peletier (1997) for a large number of spiral galaxies; Kent,
Dame & Fazio (1991) found from NIR observations of the
Galaxy that the pro(cid:12)le is closer to exponential than to
sech2(z).Toobtainestimatesofthevaluesofthescalelength
andscaleheight ofthespatialdensity,wehenceuseddouble
exponentials (ρ / exp(−R/hR)exp(−z/hz)). We estimated Figure 3 The local apparent exponential scaleheights hzb and
thosevaluesinvariousregionsofthesky,toassessvariations hR(cid:96) of the AOSP sample, from (cid:12)ts to the cumulative distribu-
of the scales with radius and height (age). Note, however, tions in latitude and longitude separately. The symbols are for
thatwearenottryingtomodeltheGalaxyasasetofdouble 0 < jbj < 1 (closed) and 1 < jbj < 3 (open), respectively. The
exponentials. bars along the abscissa indicate the longitude bins (A,B,C,D)
We (cid:12)tted cumulative{number densities with single ex- usedforthedetermination ofthe (cid:12)ts;the datapoints areatthe
ponentials, in latitude (in R(cid:12)tanb); R(cid:12) (cid:17) 8 kpc) and lon- middlevaluesofthesebins.Alllongitudebinscontainabout100
gitude(inR(cid:12)sin(cid:96))separately. Thisyielded apparentscales stars over the fulllatitude range (jbj<3(cid:14)); the formalerrorson
hzb andhR(cid:96) ofthelocalsurface{densitydistributionatvari- (cid:12)thtetemdetaosluorwem{oeunttflsoawrest(cid:24)a1rs5%(c.f.TFhieg.t1w(oc)c)irocnlleys.aFroertAhetshceaaleplepnagrethnst
ouslongitudes and latitudes(Fig.3). Duetothenon{trivial
scaleheightisverysmallduetothepresenceofthegalactic{centre
angles between lines of sight, the scales are not invariant
population (seeSect.3.2). Verylargeapparent scalelengths, such
for projection, even though the Galaxy is seen edge{on.
asinlongitudebinC,areequivalenttoanin(cid:12)nitescalelengthor
Thismeanswehavetodeprojecttheapparentscalesto(cid:12)nd a(locally)flatdistribution(Sect.3.1).
the true scales h and h . By projecting analytic double{
z R
exponentialdistributionswith arangeofhR andhz,weob- column7vs.9;Fig.3(circles)).Thisregionaround(cid:96)=−18(cid:14)
tained a range of apparent scales at the same ((cid:96),b) as the will be treated in more detail in Sect.5, where we (cid:12)nd that
datameasurements.Wecouldthusretrievetheintrinsic(hz, the distribution in that direction is probably dominated by
hR)thatwouldyieldameasuredpair(hzb,hR(cid:96)).Projection a ring structure.
e(cid:11)ectscausetherelationbetweenthetrueandtheapparent
scalestodependuponlongitudeandlatitude,andalsoupon
3.2 Central disk
each other, thusjeopardizing a uniquedeprojection.
However, for all our measurements, except those at C A deciparsec{scale, flat, rapidly{rotating flat population of
(Fig.3),thistechniquegaveuniqueresults(Table1,columns OH/IR stars is present in the galactic Centre (Lindqvist,
3{6),withinthecontextofusingdoubleexponentials.InTa- Habing & Winnberg 1992; Sevenster et al.1995). Even
ble1thedeprojectedscalesarealsogivenforthehigh{and though the AOSP sample contains only 19 out of the 134
low{outflow sources separately, determined over the whole known OH/IRstars in thisregion (Lindqvistet al.1992; 52
latituderangeofthesurvey.Forthegalacticdisk(j(cid:96)j<(cid:24)15(cid:14)), more were discovered by Sjouwerman et al.1998a), we can
most references (see Sackett 1997) give h =2.5{4.5 kpc stillresolveitsverylowscaleheightwithrespecttootherre-
R
andh =250{400pc(\thin")andh =750{1500pc(\thick" gions(Table1,column5).Aswasknownbefore,thecentral
z z
disk). disk is seen primarily in the high{outflow sources (Table 1,
column 10).
However,thescalelength of 250pc(Table1,column 3)
3.1 Ring ?
isunlikelytorepresentthissmall centraldisk.Indeed,ifwe
The very large apparent scalelength at (cid:96)(cid:24)−18(cid:14) (C; Fig.3) applyourmethodtothefullsampleofLindqvistetal.(1992)
indicates a flat distribution in longitude. With this valueof we(cid:12)ndh =20pcandh =40pc,thesamevaluesasthey
z R
themeasurement,thedeprojectionisnotunique.Neverthe- (cid:12)ndthemselves (Table 1, columns 3,5 between brackets).
less,ourtestsshowedthatprojectione(cid:11)ectsalone,although
being largest at these longitudes, can not explain the ex-
3.3 Outer Galaxy
treme apparent scalelength and we conclude it is intrinsic.
The flat distribution is formed mainly by the high{outflow Hardly any OH/IR stars are known outside the solar cir-
(and single{peaked) sources, ie. theyounger stars (Table 1, cle. Carbon{rich AGB stars, on the other hand, are hardly
Something about the Galaxy 5
Table 1. Deprojected exponential scales for the squares and triangles in Fig.3 (columns 3{6) and for low{ (\o",
columns7,8)andhigh{outflow(\y",columns9,10)sources(jbj<3(cid:14)).Thevaluesbetweenbracketsarefromanother
sampleatj(cid:96)j=0(cid:14) (seetext)orconceivablyunreliablebecause ofthein(cid:12)nitevalueofhR atj(cid:96)j=18(cid:14).
j(cid:96)j hR(jbj<1(cid:14)) hR(1(cid:14)<jbj<3(cid:14)) hz(jbj<1(cid:14)) hz(1(cid:14)<jbj<3(cid:14)) hR(o) hz(o) hR(y) hz(y)
(cid:14) kpc kpc pc pc kpc pc kpc pc
A 0 0.25(0.04) 0.25 10(20) 150 0.2 200 0.35 30
B 6 0.95 0.75 90 350 0.75 250 0.75 100
C 18 1 1 (100) (300) 10.0 350 1 (10)
D 35 3.5 5.5 100 250 10.0 200 1.5 100
mass for which a star will reach the AGB in turn becomes
lower with lower abundance (see Bertelli et al.1994). The
upperlimittotheoutflowvelocitieswilldecreaseevenmore
noticeably(equation(1));thisexplainsthesmallscalelength
forthehigh{outflowsources(Table1).Theabundancemay
decreaserathersuddenlyaroundR=6kpc,asobservedby
Simpsonetal.(1995). Theyexplainthisbyassumingthisis
the outer edge of the zone{of{influence of the Bar. As we
will see later (Sect.6), the Bar’s outer{Lindblad resonance
(OLR, Binney & Tremaine 1987 (BT) Ch.6) may indeed
havea radius of 6{7 kpc.
3.4 The Arecibo sample
With respect to an otherwise equivalent sample (te Lintel
Figure 4 The cumulative{number distributions of outflow ve- et al.1991), the Arecibo sample has twice as many sources
locities fordouble{peaked OH/IR stars fromvarious samples: 1. at outflow velocities <(cid:24)9 kms−1 (Fig.4, see left{most ar-
DiskAOSPsample;2.Arecibosample(Chengaluretal.1993);3. row ). This di(cid:11)erence is signi(cid:12)cant to 99.8% (Kolmogorov{
Outer Galaxy (Blommaert et al.1993); B. Bulge AOSP sample; Smirnov). The apparent scales of the subset with outflow
GC. galactic{centre sample (Sjouwerman et al.1998a). The me- velocities < 10 kms−1 (Fig.6) are hzb = 1.1 kpc and
ditisandeocuretflasoewwvietlhocliatyrgecrormreelaatnesrawdiituhsm(ientaolrlidceitry:((eGquCa,tBio)n1,(21,)3)); hR(cid:96) !1(Fig.5).Again,thenearly{in(cid:12)niteapparentscale-
length makesuniquedeprojection impossible, butwefound
reflects mainly the galactic metallicity gradient. The small dif-
that the apparent scaleheight is most probably close to the
ferencebetween \1"and \B"ismainlyduetoamean{mass dif-
true scaleheight in this case. These stars might be part of
ference, however. The arrows indicate deviant sub{populations
of distribution \2" (thick disk; discussed in Sect.3.4) and \GC" the1{kpcthickdiskclaimedbyotherauthors(Habing1988;
(star burst; Sect.7). Except sample \3" that consists of 9 stars, Gilmore&Reid1983,Ojhaetal.1996),althoughBlommaert
allsamplescontainmorethan200stars. et al.(1993) conclude that true AGB stars do not partake
in the thick disk and there is no sign of this population in
seen in the inner Galaxy (see the (cid:12)gures in Blanco 1965). theteLintel(etal.1991)sample.InFig.6,weseethatthese
Blommaert,vanderVeen&Habing(1993)(cid:12)ndthatthefew low{outflow stars are not concentrated toward the plane.
OH/IR stars in the outer Galaxy have initial masses of at This may be a selection e(cid:11)ect as the Arecibo sample was
least 2{3 M(cid:12),similar totheAOSPdiskstars (Sect.2).The acquired in a detection experiment toward IRAS{selected
low outflow velocities of the sample (the median is 3 km/s point sources, but this is also true for the te Lintel (et
lower than for the Disk AOSP sample, Fig.4) indicate low al.1991) sample. Moreover, when we select stars from the
metallicity(equation(1)),aswasobservedbyBlommaertet Arecibo sample in the same latitude range as the AOSP
al.(1993).Atintermediatelongitudes((cid:96)(cid:24)50(cid:14)),theOH/IR sample a small excess is still present (Fig.7).
stars from the Arecibo survey (Chengalur et al.1993) have So, in the Arecibo sample we see an extra population
initial masses and ages similar to the Bulge AOSP sample with low outflow velocities and a gap in the latitude distri-
(Sect.2) and slightly lower median outflow velocity. bution.Thelatterbringstomindtheintriguing\levitation"
The decrease in outflow velocities with higher longi- process(Sridhar&Touma1996a,b),avertical{to{radialres-
tudeistheresultofdecreasingmetallicity.Thegalactic{disk onance. This would not explain an excess of sources, how-
metallicity gradient (−0.07 dexkpc−1 from oxygen,Smartt ever. If the excess sources have low metallicity, rather than
& Rolleston 1997) corresponds, for constant mass, to an only low masses (equation (1)), this population could have
outflow{velocitygradientof(cid:24)1 kms−1 kpc−1(for V (cid:24)14 been accreted anytime duringthelast 10 Gyr from a dwarf
exp
kms−1, equation (1)). such as Fornax ([Fe/H] < −0.7). With the observational
At the same time, at lower metallicity, the limiting limit of less than (cid:12)vesuch moremetal{rich dwarfs accreted
massabovewhichstarsremainoxygen{richandbelowwhich in the last 10 Gyr (Unavane,Wyse & Gilmore 1996) this is
carbon{rich stars form increases. The upper limit to the a possibility.
6 M. Sevenster
Figure5Thecumulative{latitudedistributionofallArecibostarswithoutflowvelocity<10 kms−1 (solid,cf.Fig.4,6).The(cid:12)t(dashed)
is a projected double{exponential distribution with apparent scaleheight hzb =1.1 kpc. For comparison, the dot{dashed lines give the
distributionforhzb=800pcand1kpc,respectively.Theintrinsicscaleheight isprobablycloseto1.1kpcaswell.
Figure 7 As Fig.4,for the BulgeAOSP sample(\B", 250 stars
intheplot),theDiskAOSPsample(\1",165stars)andthestars
of the Arecibo sample with jbj < 3(cid:14) (\2P", 160 stars). There is
still an excess of sources below Vexp=10kms−1 for \2P". Note
thatthedistributionofhigheroutflowvelocitiesof\2P"ismuch
morelike\B"thanlike\1".
Figure6ThedistributionoftheArecibostarsoverlatitudeand
outflowvelocity.Thereisadi(cid:11)erenceintheconcentrationtoward
around thegalactic Centresince their formation and there-
the plane at low latitudes between stars with outflow velocities
higherandlowerthan10 kms−1,respectively.Below10 kms−1 forephasemixing,let alone radial mixing,hasnotyet been
e(cid:11)ective.Thereseemtobenosuddentransitionsinthedis-
there is also a clear excess of sources (50%)in the Arecibo sam-
tribution; except that from the flat distribution (h ! 1)
ple with respect to the other samples in Fig.4. These stars form R
possiblyathickdisk. totheouterdisk(hR =1.5kpc)forthehigh{outflowsources
thatisratherabrupt.Aswewillseelater(Sect.5),thismay
bearoundtheradiusofcorotationwiththepatternspeedof
thecentralBar. Theradial scale derived(viathesame pro-
cedure described earlier) from the Arecibo sample (using
3.5 Radial and vertical variations
only jbj > 8(cid:14) because of it’s incompleteness in the plane)
Clearly, one double{exponential cannot describe the distri- and from a sample of carbon{rich AGB stars (j(cid:96)j (cid:24) 60(cid:14),
butionofOH/IRstars.Theolderdiskstars(fewGyr)seem jbj < 15(cid:14), Loup et al.1993), is (cid:24) 10 kpc; the same as from
to trace an exponential disk with rather large scalelength the low{outflow OH/IR stars. So, except for the massive
plus a central component with similar vertical scale (Table oxygen{rich objects, the scalelength is found to be similar
1).Theyoungerstars(<1Gyr)followamorecapriciouspat- for all AGB stars. The very di(cid:11)erent radial distributions of
tern and havevarying,but small vertical scales. This is not C{rich and O{rich AGB stars, respectively, is governed by
unexpected since they have completed only a few rotations themetallicity gradient only.
Something about the Galaxy 7
Outside the AOSP{survey window, we also derived maps calculated by Evans (1994). The strength of this ef-
scaleheightsfromtheArecibosubsampleandtheLoupsam- fect obviously depends upon the parameters of the density
ple, and found h (cid:24) 500 pc for both. The full sample of distribution of thebar.
z
outer{Galaxy AGB (not only OH/IR) stars of Blommaert We will try to (cid:12)nd this e(cid:11)ect in our Bulge AOSP
etal.(1993)hash <(cid:24)400pc.Theverticalscaleappearstoin- sample. The double{peaked OH/IR stars are divided into
z
crease with latitude from (cid:24)100 pc to (cid:24)500 pc, irrespective two equally{sized samples by outflow velocity, at V =14
exp
of the longitude range. The increase in scaleheight within kms−1, with average V of 11.3 (sample I) respectively
exp
the Disk AOSPsample agrees with thedi(cid:11)usion models by 18.3 (sampleII) kms−1 (cf.Fig.1(e,d)). Thisgivesafactor
Wielen (1977) for age increasing from <(cid:24)1 Gyr to >(cid:24)2 Gyr. of 1.7 di(cid:11)erence in stellar luminosity L(cid:3), even if we assume
The scaleheight of 500 pc for the oldest AGB stars is the µ = 2µ (equation (1)). Blommaert et al.(1997) (cid:12)nd a
I II
sameasthatforwhitedwarfsasgiveninMihalas&Binney rangeinµof(cid:24)2intheGCwithIRobservations.Therange
(1981). of masses in theBulge (Sect.2) makes a factor of 1.7 di(cid:11)er-
ence in L(cid:3) ((cid:24)1.5 in Mi) very well possible. Since the OH
masers are saturated, the OH luminosity L increases, on
3.6 In short OH
average,linearlywithL(cid:3).Thelowerlimittothefluxdensity
Insummary,theAGBstarsaredistributedinthethin(old) S is the same for both samples, so the average limiting
OH
diskwithascaleheightof100pcfortheyoungestAGBstars distanceofsampleIIisafactor (cid:24)1.3larger thanofsample
<
((cid:24)1 Gyr). The scaleheight increases continuously to 500 pc I. We can thus use the two samples to mimic the di(cid:11)erent
>
for AGB of (cid:24)5 Gyr. The scaleheights for the Disk and the integration limits in Fig.8 (see also Sect.2).
Bulgearethesame.Thecarbon{rich andoxygen{richAGB The e(cid:11)ect of skewed distributionsshould be clearest in
stars form one population; the di(cid:11)erences between the dis- the inner regions of the Galaxy (see Fig.8(b,c)). The ratios
tributions of the two groups are governed mainly by the of the number of stars with 0(cid:14) < (cid:96) < 4(cid:14) to the number of
metallicity gradient. There seems to be a small population stars with 0(cid:14) > (cid:96) > −4(cid:14) are 39/35 (sample I) and 22/35
that has a distinctly large scaleheight. (sample II). These ratios are in accordance with the theo-
AlltrendsintheAOSPsamplecanbeseeninFig.1ina retical results shown in Fig.8. To de(cid:12)ne these trends in a
pictorial fashion. The exact numbersfor thescales in Table moresophisticatedway,wesortedbothsamplesonabsolute
1shouldbeusedwithcare,sinceourdeprojectionmethodis longitudeand(cid:80)calculated thecumulativesumsof thesign of
indirect.Nevertheless,frommodellingdistributionfunctions the longitude ((cid:96)/j(cid:96)j); we add or subtract 1 for each star
forvariousofthesamplesusedherethesametrendsnumbers (Fig.9). Anaxisymmetricdistributiongivesalinethathov-
emerge(Sevenster1997).Also,thescalesintheBulgeregion ers around zero. If negative (positive) longitudes are ‘over-
agree verywell with thoserecentlyfoundfrom DENISdata populated’ the sum will steadily decay (rise). This sum is
(Gilmore priv.comm.). shown in Fig.9 for the two data sets and for the bar model
shown in Fig.8(c), as well as for an N{body model (Fux
1997) found to represent the AOSP sample well (Sevenster
4 THE BAR etal.1999).Thedottedcurvesgivethe95%con(cid:12)dencelimits
fordeviationfromaxisymmetry.SampleI(solidcurve)never
4.1 Surface density
deviatessigni(cid:12)cantly from axisymmetry,although thereare
Inthissection,wecompareparametrized barmodelstothe local trends similar to those of the models with the inter-
surfacedensityoftheAOSPsample.Wedonotoptimize(cid:12)ts mediate cut-o(cid:11). Sample II (dashed curve) , however, lies at
quantitatively,sincethechoiceofaparametrizedbarmodel oroutsidethe5%con(cid:12)dencelevelandcoincidesremarkably
isalreadyanarbitraryone.Rather,wetakebarmodelsthat well with the models without distance cut-o(cid:11). The set of
areknowntogivegoodapproximationstootherobservations stars with low V would have an average distance cut-o(cid:11)
exp
and see how well they agree with ours. of 9{9.4 kpc according to these models, the set with high
TheviewingangleφistheanglebetweentheBar’sma- V of around 12 kpc, beyond which thereis no signi(cid:12)cant
exp
jor axis and the line of sight toward the galactic Centre contributionfromthebartotheintegrateddensityanymore.
(Fig.8(a)). In Fig.8(b,c) we show the surface density distri- This agrees very well with the di(cid:11)erence of a factor 1.3 in
bution as a function of longitude, N((cid:96)), for two flat (two{ averagedistancederivedfromtherelationbetween V and
exp
dimensional) elliptical bars with gaussian density distribu- stellar luminosity.
<
tion (cf. G2 model in Dwek et al.1995). The viewing an- Weestimatethediskcontaminationtobe(cid:24)20%within
gles are takento be20(cid:14),as suggested bysome observations 5(cid:14) of longitude from the GC (Sect.2; Sevenster 1997). If an
(Dweketal.1995).TheformofN((cid:96))dependsuponthedis- axisymmetriccomponentcontributessigni(cid:12)cantlyinthein-
tance out to which we integrate or, in observational terms, nerdegrees,theevidencefor(cid:80)theexistenceoftheBarwould
thedistance d out to which the data sample the Galaxy, so only become stronger. The ((cid:96)/j(cid:96)j) distribution would not
N((cid:96)) = N((cid:96);d). For values of d (cid:24)R(cid:12), N((cid:96);d) essentially change with the subtraction of a projected axisymmetric
looks like the distribution arising from an m = 1 distor- distribution of any relative density, but N((cid:96) < (cid:96)lim) would
tion(lopsided;seeFig.8(a)), withitsmaximumtowardpos- becomelower.Thiswouldmaketheprobabilityofthedevi-
itive longitudes. With d = 1, however, the distribution is ation coming from a binomial distribution even smaller. In
skewed toward negative longitudes. This is the result of the otherwords,thedottedcurvesinFig.9would shifthorizon-
line of sight through the m = 2 distortion being longer on tally to the right, but the data{lines would remain in place
the far side than on the near side, for small values of abso- on average.
lutelongitudes (Fig.8(a)). This e(cid:11)ect was (cid:12)rst predictedby Theevidencepresentedhereisthe(cid:12)rstlarge{scalemor-
Blitz&Spergel(1991) andisalsoseen inthemicro{lensing phological evidence for a galactic Bar that cannot also be
8 M. Sevenster
3 s2
s1
GC
2 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
1
f
Sun
Figure 8 a (left) Schematic view of the Bar from the galactic North pole. The viewing angle φ is indicated; the near end of the Bar
is most certainly at positive longitudes. The lines of sight (s1 and s2) at equal but opposite longitudes di(cid:11)er in length. The dotted
arcs show schematically possible observation limits. The shaded circlerepresents a lopsided distortion, that would project to a similar
surface{density distribution as the Bar for an observation limit of R(cid:12) (dotted arc 1). In b and c we show the total number of stars
(arbitrarily normalized) along the line of sight in a two-dimensional elliptical barmodel with gaussian density distribution for three
di(cid:11)erent integration limits(8 kpc (1), 9kpc (2) and 1(3); R(cid:12) (cid:17)8kpc). The integration limitscorrespond to the observational limits
shown in a. For reference a gaussian is shown (dashed). Note the o(cid:11)set of the maximum toward negative longitudes for the largest
integrationlimit.b(middle)Axisratioq=0.6,semi{majoraxisa=3.5kpc(=3σgaus).c(right)Axisratioq=0.4,semi{majoraxisa=2.5
kpc (=3σgaus). The viewing angle φ is 20(cid:14) inboth panels b and c. The model inc is based on the K{band G2 model for Rmax =2.4
kpcofDweketal.(1995).
(cid:80)
Figure 9a(left)Thecumulativesum ((cid:96)/j(cid:96)j)versusj(cid:96)jaftersortingonj(cid:96)jforthetwosamples(thicksolidanddashedlines)andfor
theG2{bar modelfromFig.8(c)withdi(cid:11)erentintegrationcut-o(cid:11)s(shortdashedlines,seeFig.8).Thedottedcurvesindicatethevalues
for which the probability of the sum arising in a binomial distribution being larger (or smaller for negative values) than that value is
5% (ie. single{sided). For j(cid:96)j < 0.5(cid:14) and j(cid:96)j > 5(cid:14) contributions by additional features influence the distribution (see Fig.1; Sect.5). b
(right) Same as a, but for a bar model consisting of two exponential elliptical{bar pro(cid:12)les with major{axis scalelengths of 200 pc and
1kpc (central{density contrast 8.5), withviewingangleof 45(cid:14) and axisratioof 0.5.The pro(cid:12)leisanapproximate (cid:12)t tothe density in
the plane of an N{body bar and the viewing angle of 45(cid:14) optimizes the (cid:12)t between the AOSP data and the N{body model (Sevenster
etal.1999;Fux1997).
explained by a physical lopsided density distribution (Sev- the asymmetries one is after. Unavane & Gilmore (1998)
enster 1996). The e(cid:11)ect is also clearly visible in Fig.1(b,c) (cid:12)ndthat theDwek models (E2, G3) give too large a devia-
(sampleII,I)inaqualitativeway.Thesametrendinthelon- tionfrom axisymmetry,whereastheG2modelgivesagood
gitudedistributionisreportedbyUnavane&Gilmore(1998) representation of our data (Fig.9(a)). The results in Fig.9
who use L{band data in the plane. However, the necessary demonstratethatonlyforagivendensitymodeltheparam-
extinction corrections are estimates and of similar order as etersofabarcanbeoptimized (Zhao1997), asbothrather
Something about the Galaxy 9
di(cid:11)erent models give good representations of the data. spiral{armbifurcationsorlocaldecreasesinthedensity(eg.
Elmegreen1996).Aflatpartoftherotationcurvemayout-
line roughly the region between the inner{ultra{harmonic
4.2 The Bulge’s kinematic type
resonance (IUHR) and CR (Wozniak & Pfenniger 1997).
The anisotropy parameter (Binney 1976) is a measure of This is observed in the edge{on S0{galaxy NGC4570 (van
the rotational support of a system. It is the ratio of the denBosch&Emsellem1998).Similarly,theorbitalstochas-
maximum rotational velocity of a bulge (Vm) to its central ticityinthisregion(Contopoulos&Grosb(cid:28)l1986)willcause
velocity dispersion (σ0). In combination with the flatten- e(cid:14)cient radial mixing, smearing out the density gradient
ing(cid:15),itprovidesawaytodistinguishbetweenrotationally{ (seealsoFux1997).Aneasilyobservedresultofthedynam-
supported, dispersion{supported and streaming{dominated icsinthisregionare\innerrings"thatareprominentinthe
systems(Illingworth1977).Themaximumrotationvelocity majority of barred galaxies (see Buta 1996).
of the Bulge occurs at (cid:96) (cid:24) −18(cid:14), where the mean{velocity AllthesefeaturesareinfactpresentintheGalaxy.The
curve levels out (Fig.10), so Vm = 140(cid:6)20kms−1. For σ0, narrow gap between the so{called 3{kpc and Norma arms
weuse153 kms−1 (Blum1996),whichismorereliablethan (Fig.11),alsoseeninothertracers(eg.CO,Bronfman1992),
our determination of this second{order moment (135(cid:6)20 couldwell indicateCR.Ingood agreement with thisisthat
kms−1, Fig.10(b)). This gives a value of Vm/σ0 of 0.9(cid:6)0.1 theflatpartoftherotation curvefoundfortheAOSPsam-
. Together with an ellipticity of (cid:15) (cid:24) 0.4 (Table 1; Dwek ple (Fig.10) stretches from (cid:96) (cid:24) −18(cid:14) to (cid:96) (cid:24) −25(cid:14). Those
et al.1995, G0-model; Kent 1992), this locates the galac- longitudeswould,accordingtoWozniak&Pfenniger(1997),
tic Bar in the Vm/σ0 { (cid:15) diagram between the oblate and indicate IUHR and CR, respectively. The very flat density
the SAB bulges (Kormendy 1993), governed by somewhat{ foundforthisregioninSect.3furtherreinforcesthispicture
more{than{rotational support. The Galaxy (cid:12)ts well in the (Contopoulos & Grosb(cid:28)l 1986). It also rules out the pos-
relation as an average SABgalaxy. sibility that the rotation curve is flat due to a logarithmic
EarliervaluesfortheBulge’sdispersion,frommeasure- potential (density /R−2).
ments toward Baade’s window, were much lower (113+−65 Most importantly, we argue that the 3{kpc arm is the
kms−1; Sharples, Walker & Cropper 1990). Adopting this projection not of a spiral arm but of an inner ring, such
asσ0,theBulgewouldbelocatedintheregionofextremely as mentioned above, for the following reason. A subsample
triaxial bulges in the Vm/σ0 { (cid:15) diagram. Baade’s window of the AOSP sample follows exactly the longitude{velocity
(b = −4(cid:14)) is too far from the plane to sample the central structure of the 3{kpc (cid:12)lament (Fig.12). A group of nine
Bar dispersion. We conclude that the Bar is so flat that it young (high{outflow) stars, that trace the kinematic struc-
cannot be assumed to be the dominant contributor to the turebetween 0(cid:14) >(cid:96)>−10(cid:14), stands out in the left panel of
distribution along the line of sight toward Baade’s window Fig.12. These nine stars are at very low latitudes and have
(Table 1; see also Sevenster et al.1999). Paradoxically, us- a very high median outflow velocity of 17.5 kms−1. If the
ing the dispersion in Baade’s window one would obtain an metallicity is the same as in the rest of the disk, the initial
anisotropy parameter indicative of a strong bar. massesofthis3{kpcsamplewouldbe(cid:24)6 M(cid:12) andtheages
(cid:24)600Myr(AppendixA).Asthosestarsremainclosetothe
gas for several galactic years, their trajectories must follow
5 RESONANT STRUCTURES
closelythatofthegas,Inotherwords,thegas(cid:12)lamentmust
In this section, we will concentrate on local features in the outlineclosedorbitsinsteadofa(temporary)spiraldensity{
distributionsofvarioustracers.FortheAOSPsample,these wave maximum. With proper motions for these stars one
structures are seen in Fig.1, marked as R−1, R−2 and R−3. couldconstrainthemotionalongthe3{kpcarmcompletely,
We complement our own evolved{stellar data set with 2.4{ something that is impossible to achieve with gas.
GHz{continuum observations (Duncan et al.1995) and a In Fig.13(a), we show longitude{velocity trajectories
sample of star{forming regions (Comeron & Torra 1996). constructed by Mulder & Liem (1986). They solved gas{
Thesynchrotronradiationdominatingthecontinuumat2.4 dynamical equations in a weakly{barred potential, using
GHz, is found to be a good tracer of the current locations a (cid:12)nite{di(cid:11)erence, hydrodynamic grid code. The gas is
of density waves (eg. Tilanus & Allen 1989). described by the inviscid Euler equations. The curves in
Duncan et al.(1995) present their data separated in Fig.13(a)representtheirpreferredmodelforthe3{kpcarm,
a small{scale{ (sub{degree) and large{scale distribution the main feature used to constrain the scales of their mod-
(Fig.11). The small{scale emission arises largely in super- els. The viewing angle is φ =20(cid:14) and RCR = 0.98R(cid:12). In
novae;thelarge{scaleemissiontracesthemoleculargasand Fig.13(b), the model spiral is seen face{on. Although this
density waves. For theuninitiated, an introduction to non{ spiralreproducesthe3{kpc(cid:12)lamentaround(cid:96)=0(cid:14) verywell,
axisymmetric galactic dynamics can be found in Binney & thetangentpointtothe3{kpcarmisatmuchtoohighlongi-
Tremaine(Ch.6),andanintroductiontoterminolgyandlit- tude,(cid:96)=−27(cid:14) (Fig.13(a)).Mulder&Liem(1986)showthe
erature in Sevenster(1997). longitude{velocity diagram for another model, for φ =40(cid:14)
and RCR = 0.56R(cid:12). In this diagram the tangent point is
much closer to the observed point (see Fig.12) and also the
5.1 The corotation region
central CO{disk’s velocity signature is matched much bet-
The only direct method to (cid:12)nd corotation (CR), via the ter.ThetrajectoriesofbothILRarmsremainsimilarinthe
pattern speed, is in most cases inapplicable (see Tremaine innerregions.Unfortunatelytheydonotgivetrajectoriesfor
& Weinberg 1984; Merri(cid:12)eld & Kuijken 1995). However, this model but they note that the arms are \more concen-
a number of indirect indicators can be used. A signa- trated around CR". This would be in agreement with our
ture of CR is often observed in the form of dust lanes, inner ring, discussed above. The Mulder{Liem models are
10 M. Sevenster
Figure 10The mean line{of{sight velocity (dash) inthe inertial frame(for VLSR(cid:17)200 kms−1) smoothed data (double{peaked stars
only)atb=0(cid:14) (a)andb=2(cid:14) (b).Thegridsizeis1(cid:14) by6 kms−1,theinitialkernelsizesare1(cid:14) and30kms−1,respectively.Weshow
errorsderivedviabootstrapping (Presset al.1992, seeSevenster 1997) forthe features that wediscussinthetext. (The meanvelocity
isthe50%valueanddispersionishalfthedi(cid:11)erenceofthe83%andthe17%valuesofthesmoothedvelocitypro(cid:12)les.)
Figure 11 The observed surface{density distribution at 2.4 GHz due to Duncan et al.(1995). The features R−1, R−2 and R−3 are
indicated(seeFig.1)aswellasthe\Normaarm"(tangent point−32(cid:14))andthe\3{kpcarm"(tangent point−22(cid:14)).Forthelarge{scale
(> 1(cid:14))distribution,the tendashed contours arespacedlinearlybetween 10%and 100% ofthemaximum (large{scale) density. Forthe
small{scale (< 1(cid:14)) distribution, the ten solid contours are spaced logarithmically between 3% and 95% of the maximum (small{scale)
density.Thelarge{scaleemissionisagoodtracerofdensitywaves.
forced to be quasi steady. Therefore, gas flows around CR the intricate streaming and di(cid:11)usion processes around CR
wouldnotberepresentedcorrectlyanditcouldwellbethat (Roberts,Huntley&vanAlbada1979;Kenney&Lord1991;
thetwo arms in Fig.13(b) connect in reality to form a ring. Vogel et al.1993; Tilanus & Allen 1989), but it is virtually
Binney et al.(1997) (cid:12)nd, deprojecting the COBE map impossible to draw conclusions from them.
with imposed eight{fold symmetry, two density enhance-
ments on the minor axis at 3 kpc from the Centre ((cid:96) =
+17(cid:14),−22(cid:14)). They suggest these are the L4,5 points. With 5.2 The inner{Lindblad resonance
four{fold symmetry, however, they (cid:12)nd a, leading, spiral. Otherthanacorotationresonanceandouter{Lindbladreso-
The longitude (cid:96) = −22(cid:14) of their feature coincides with the nances,theexistenceof aninner{Lindblad resonance(ILR)
maximaintheOH/IRstarsandthe2.4 GHzemission used in a galaxy is dependent on its exact potential. If it exists,
inthissection.AsBinneyetal.(1997) note,theremaybea ismayshowviaaavarietyofindicators.TheILRisusually
signi(cid:12)cantcontributionofyoungstarstotheK{bandsurface outlinedbya"nuclearring",often accompanied bymassive
density(Rhoads1996).Wearguethattheirdensityfeatures starformation(seeeg.Buta1996;Phillips1996).Aso{called
areincorrectdeprojectionsoftheinnerring.Inanycase,the double{wave feature in the stellar rotation curve (Bettoni
derived loci for CR are very similar. 1989) may exist as a result of orbits trapped around the
The maxima R−2 and R−3 interestingly border those the retrograde x4 orbit family inside ILR (Pfenniger 1984;
of the 2.4 GHz emission (Fig.1). Also, the locations of the Wozniak & Pfenniger 1997; Contopoulos & Papayannopou-
maximaintheolderandyoungerOH/IRstars,respectively, los1980).Finally,ifanILRexists,thegasflowingtowardthe
are slightly di(cid:11)erent.Suchdisplacements may becaused by centre, following bar{induced instabilities, will follow o(cid:11)set