OB STARS IN THE SOLAR NEIGHBORHOOD. II. KINEMATICS
F. Elias
Facul ad de Fı´sica, Depa amen o de Fı´sica A o
´mica, Molecula , y Nuclea , Uni e sidad de Se illa, Apa ado 1065, 41080 Se illa, Spain
E. J. Al a o
Ins i u o de As o ı´sica de Andalucı´a, CSIC, Apa ado 3004, 18080 G anada, Spain
and
J. Cab e a-Can˜o
Facul ad de Fı´sica, Depa amen o de Fı´sica A o
´mica, Molecula , y Nuclea , Uni e sidad de Se illa, Apa ado 1065, 41080 Se illa, Spain; and
Ins i u o de As o ı´sica de Andalucı´a, CSIC, Apa ado 3004, 18080 G anada, Spain
Recei ed 2006 Feb ua y 24; accep ed 2006 May 17
ABSTRACT
Using he spa ial classi ica ion me hod and he s uc u al pa ame e s es ima ed o he Gould Bel (GB) and he
local Galac ic disk (LGD) om a p e ious pape , we ha e e alua ed spa ial membe ship p obabili ies o a sample o
O and B s a s om he Hippa cos ca alog (Pe yman and cowo ke s) wi h a ailable p ope mo ions and adial e-
loci y da a. Thus, being able o s udy he space eloci y ields o bo h sys ems, we conclude ha he GB and he LGD
p esen di e en s a is ical dis ibu ions, bo h in eloci y space and in phase space. In ligh o hei possible exis ence
as dis inc sys ems, we analyze di e en kinema ic aspec s in he icini y o he Sun, and we ind he GB o be e-
sponsible o he highly nega i e e ex de ia ion ound o he OB s a s in he sola neighbo hood. We also ind ha
he GB no iceably al e s he es ima ion o he Oo cons an s in he Galac ic disk; hus, in o de o es ablish com-
pa isons wi h o he kinema ic s udies based on olde s ella popula ions, a ca e ul p uning o he GB membe s mus be
pe o med. Fu he analysis o he GB eloci y ield and he mo ing g oups ha con ibu e o i sugges he possibili y
ha he GB can be he esul o a chance supe posi ion o mo ing g oups. We p opose o u u e in es iga ions he
dynamical analysis o hese mo ing g oups in o de o p obe he o igin o he GB.
Key wo ds: sola neighbo hood — s a s: ea ly- ype — s a s: kinema ics
1. INTRODUCTION
Since he disco e y o he Gould Bel (GB) as a sys em o
b igh s a s o ming an angle o abou 20wi h he Galac ic disk
(Gould 1879; He schel 1847), many e o s ha e been de o ed o
un a eling i s complex s uc u e o s a s and he associa ed in e -
s ella medium. When s udies o i s kinema ics began o appea
in he second hal o he pas cen u y, he peculia i ies o i s be-
ha io made he global pic u e o he GB e en mo e puzzling.
The mos s iking disco e y was he expansion o he s ella
componen (Bonneau 1964; Lesh 1968; F icke & Tsioumis 1975;
F ogel & S o he s 1977; Wes in 1985; Come o
´n e al. 1994), which
canno be sa is ac o ily explained by a single explosi e e en (Lesh
1968; Mo eno e al. 1999), making i di icul o ace back o he
o igin o he GB by e e sing his mo emen . Models conside ing
Galac ic densi y wa es gene a ed by pe u ba ions om he spi-
al a ms canno accoun o his expansion ei he (Wes in 1985;
Come o
´n & To a 1991). Also, he shell o gas associa ed wi h he
GB p esen s e idence o expansion acco ding o he wo ks o
Lindblad (1967), Olano (1982), Elmeg een (1982), and Mo eno
e al. (1999).
Because he age o he GB (be ween 20 and 90 My ; see To a
e al. 2000 o a de ailed discussion) is a conside able ac ion o
he pe iod o e ical oscilla ion o he s a s o e he Galac ic plane
unde he in luence o he g a i a ional po en ial o he Galaxy, he
spa ial cohe ence o he GB mus co espond o a kinema ical co-
he ence ha p e en s he dissolu ion o he s uc u e in o he Ga-
lac ic plane. Come o
´n (1999) and Pe o & G enie (2003) ind a
global oscilla ion o he GB a ound an axis di e en om he spa ial
line o nodes whe e he GB and he Galac ic plane c oss each o he .
All his leads Elmeg een e al. (2000) o include he GB as pa
o he hie a chy o s ella complexes wi hin he Milky Way, as a
second-le el s uc u e subo dina ed o he local a m ( he O ion-
Cygnus spu ). Thus, he GB would be he s a o ma ion complex
closes o us, so he s udy o i s global p ope ies will help shed
ligh on he possible o igin and e olu ion o hese complexes.
In a p e ious a icle (Elias e al. 2006, he ea e Pape I) we
had de eloped a h ee-dimensional spa ial classi ica ion me hod
o sepa a e he GB s a s om he local Galac ic disk (LGD) s a s.
Ha ing ob ained he s uc u al pa ame e s o bo h sys ems ex-
clusi ely h ough spa ial conside a ions, we now classi y a sample
o Hippa cos (Pe yman e al. 1997) OB s a s wi h space eloc-
i ies, in o de o compa e he kinema ics o bo h s uc u es.
Thus, in x2 we i s build a sample o OYB6 Hippa cos s a s
wi h p ope mo ions and adial eloci y da a ha we hen analyze
in o de o s udy he kinema ic p ope ies o he young Galac ic
disk. We begin (x3) wi h he iden i ica ion o he mo ing g oups
in he eloci y ield, and hen (x3.1) we sepa a e he GB om he
LGD s a s, choosing a membe ship o ei he sys em o he de-
ec ed mo ing g oups. The nex s ep o enhance ou analysis o
he young disk eloci y ield is he elimina ion o he sys ema ic
e ec s on he eloci ies o sola mo ion and Galac ic di e en ial
o a ion. We ob ain he esidual eloci ies, he analysis o which
also yields di e en kinema ic beha io s o he GB and he LGD
(x4). The s udy o he eloci y ellipsoids con i ms such a di e -
ence (x4.1). The e ec o he GB on he de e mina ion o he
Oo cons an s is add essed in x5. Finally, some conclusions a e
gi en in x6.
2. STAR SAMPLE
We selec a sample o 1156 s a s o spec al ypes OYB6
and luminosi y classes III, IV, and V om he Hippa cos ca a-
log (Pe yman e al. 1997). Pho ome ic da a om he Hauck &
1052
The As onomical Jou nal, 132:1052Y1060, 2006 Sep embe
#2006. The Ame ican As onomical Socie y. All igh s ese ed. P in ed in U.S.A.
Me milliod (1998) ca alog, as well as adial eloci y da a om he
Ba bie -B ossa & Figon (2000) and G enie e al. (1999) ca alogs,
ha e been added when a ailable. Thus, he compila ion includes
1. HIP, he Hippa cos iden i ie numbe .
2. Spec al ype.
3. V, he Johnson isual magni ude.
4. T igonome ic pa allax (millia cseconds).
5. S anda d e o in igonome ic pa allax (millia cseconds).
6. Righ ascension o he epoch J1991.5 in he In e na ional
Celes ial Re e ence Sys em (ICRS) (deg ees).
7. Declina ion o he epoch J1991.5 in he ICRS (deg ees).
8. P ope mo ion in igh ascension, cos (mas y 1).
9. S anda d e o in p ope mo ion in igh ascension (mas y 1).
10. P ope mo ion in declina ion, (mas y 1).
11. S anda d e o in p ope mo ion in declina ion (mas y 1).
12. Radial eloci y (km s1) om Ba bie -B ossa & Figon
(2000).
13. Quali y o adial eloci y om Ba bie -B ossa & Figon
(2000).
14. Radial eloci y (km s1) om G enie e al. (1999).
15. E o in adial eloci y (km s1) om G enie e al. (1999).
16. The u bypho ome y da a om Hauck & Me milliod
(1998).
Fo he dis ance es ima ion we ha e used Hippa cos igono-
me ic pa allaxes only i he ela i e e o is lowe han o equal
o 10%. O he wise, u byS o¨mg en pho ome y has been used
o es ima e he dis ance h ough he Balona & Shobb ook (1984)
MV() calib a ion. I no da a we e a ailable, spec opho ome ic
dis ances om he appa en isual magni ude Vand he Schmid -
Kale (1982) calib a ion o spec al ypes we e chosen. We ha e
compa ed he h ee di e en dis ance es ima ions, looking o any
possible sys ema ic biases among hem. Wi h his pu pose, we
ha e selec ed 950 s a s om he ini ial ca alog wi h S o¨mg en pho-
ome y da a.
Se e al au ho s (A enou & Lu i 1999; Maı´z-Apella
´niz 2001,
2005; Sch o¨de e al. 2004), s udying he dis ance calib a ion com-
pa isons wi h he dis ances ob ained om igonome ic pa allaxes,
ha e deal wi h he p oblem o analyzing he biases ha he sample
selec ion e ec s in oduce. The es ima ion o hese biases is e y
complex because i depends, among o he a iables, on he spa-
ial dis ibu ion o he sample. Maı´z-Apella
´niz (2005) demons a es
ha he eal dis ance p obabili y dis ibu ion o indi idual s a s
will always be ill-beha ed when ha dis ance ends o in ini y and
a cons an unde lying spa ial dis ibu ion has been assumed o
he sample. This idea had al eady been sugges ed by A enou &
Lu i (1999), who p oposed ha —in o de o a oid any unca ion
biases— o compa ison pu poses one should use a sample no se-
lec ed by any limi in he ela i e e o o he igonome ic pa -
allax, including he nega i e pa allaxes. We use his me hodology
o he compa ison be ween igonome ic, pho ome ic, and spec-
oscopic pa allaxes, using he comple e sample wi h spec al ypes
up o B6.
The esul s o he analysis demons a e ha he S o¨mg en pho-
ome ic pa allaxes (S ) a e e y simila o he Hippa cos ig-
onome ic pa allaxes, as Kal che a & Knude (1998) had al eady
demons a ed, bu he o me p esen , in compa ison wi h he spec-
oscopic pa allaxes (SK , de i ed om he Schmid -Kale cali-
b a ion), a unc ional ela ionship in he o m o S /SK 1:21.
Ne e heless, a ecen s udy o O s a s (Maı´z-Apella
´niz 2005) dem-
ons a es ha he Hippa cos igonome ic pa allaxes and he spec-
oscopic pa allaxes a e e y simila o his spec al ype. Whe e
does his di e ence ha we ind in hei alues come om? We
ha e o conside ha ou spec oscopic calib a ion is based on
h ee s eps: (1) spec al classi ica ion, (2) calib a ion o he absolu e
magni ude o each spec al ype; and (3) e alua ion o he ed-
dening om he in insic colo alues.
The spec al classi ica ion o he Hippa cos ca alog comes om
di e en sou ces and hus is a om being uni o m. On he o he
hand, he ca alog o O s a s (Maı´z-Apella
´niz e al. 2004) used by
Maı´z-Apella
´niz (2005) o he compa ison o he pa allaxes was
de i ed om a g oup o homogeneous and p ecise s ella spec a.
Thus, i mus no be in e ed om ou esul ha he Schmid -Kale
calib a ion has sys ema ic biases bu ha he spec oscopic pa -
allaxeso heOYB6 s a s om he Hippa cos ca alog—acco ding
o he spec al classi ica ion wi hin he ca alog—show a sys em-
a ic e o when we compa e hem wi h he S o¨mg en pho ome ic
pa allaxes (which, as we said, show no signi ica i e di e ences
om he Hippa cos igonome ic pa allaxes).
In his wo k we do no in end o pe o m an exhaus i e s udy
o he p oblems ha he di e se me hodologies o ob aining dis-
ance calib a ions p oduce. We ha e only uni ied o he pu pose
o his wo k he di e en dis ance calib a ions used o ou sam-
ple. To do his, we ha e ied he spec oscopic pa allaxes o hose
de i ed om S o¨mg en pho ome y, applying a co ec ion o 21%
o he o me . We wan o s ess ha he compa ison be ween he
di e en dis ance calib a ions has been made s ic ly h ough hei
espec i e pa allaxes.
We ha e also chosen he Ba bie -B ossa & Figon (2000) adial
eloci y and quali y da a when a ailable; o he wise, adial eloc-
i ies and e o s om G enie e al. (1999) ha e been used. Finally,
a dis ance limi o 1 kpc has been imposed, hus educing he sam-
ple o 881 s a s.
While he Hippa cos ca alog is comple e down o V7:9,
and o V7:5 o OYB6 s a s, in Figu e 1 we can see om a his-
og am ha ou sample is comple e only down o a magni ude o
V6:5. This is caused by he necessi y o ha ing adial eloc-
i y da a a ailable o he s a s in ou sample, as is also obse ed
in Fe na
´ndez (2005); in ha wo k, he comple eness o he sam-
ple o O and B s a s om he Hippa cos ca alog alls down om
V7:9 o6 when he s a s wi hou adial eloci y da a a e
emo ed.
3. IDENTIFICATION OF MOVING GROUPS
IN THE SAMPLE AND THEIR MEMBERSHIP
We ha e calcula ed he space eloci ies om he p ope mo ions
and adial eloci ies (Johnson & Sode blom 1987) o he s a s in
ou sample. Thei densi y ield is ep esen ed in he h ee con ou
plo s o Figu e 2. We no e in his image ha he eloci y ield is
domina ed by se e al maxima ha may co espond o associa ions
o s a s (no necessa ily bound) wi h a small eloci y dispe sion,
known as mo ing g oups (e.g., P oc o 1869; Eggen 1963).
The i s and mos p ominen maximum, loca ed a ound (U;
V;W)¼(6:5;19;7) km s1, is ce ainly associa ed wi h
he Pleiades mo ing g oup. The exac si ua ion o he peak may
di e sligh ly om he es ima ion gi en by o he au ho s, bu we
mus conside ha he mo ing g oup always appea s as a maximum
in he eloci y space wi h a ce ain wid h. Fo ins ance, Chen e al.
(1997), wo king wi h a sample o B, A, and F s a s om he
Hippa cos Inpu Ca alogue (Tu on e al. 1992) and u bypho-
ome y, ind ha he maximum is loca ed a (U;V;W)¼(10;
19;8:1) km s1, he s anda d de ia ions o he h ee compo-
nen s being, espec i ely, 7.9, 8.6, and 5.8 km s1.
The second mos p ominen peak in Figu e 2 is loca ed a ound
(U;V;W)¼(17;11;5) km s1. We ha e iden i ied i as
he mo ing g oup ela ed o he supe clus e IC 2391. I s posi ion
OB STARS IN SOLAR NEIGHBORHOOD. II. 1053
in eloci y space is es ima ed by Chen e al. (1997) a (U;V;W)¼
(15:9;13:1;4:5) km s1, wi h he s anda d de ia ion being
(U;
V;
W)¼(4:1;6:2;3:0) km s1.
The hi d maximum, cen e ed a ound (U;V)¼(11;8:5)
km s1, is mo e di use and di icul o iden i y. We ha e decided
o ollow he c i e ia o Asiain e al. (1999), who, based on he s ud-
ies by Come o
´n (1992), ule ou he possibili y o linking his e-
gion in eloci y space wi h he Coma Be enices clus e , in a o
o a p obable bond wi h he Cassiopeia-Tau us associa ion, a
(U;V)¼(9:9;6:1) km s1. This associa ion has an age be-
ween 50 My , as he p obable expansion age es ima ed by Blaauw
(1956) om a sample o s a s o spec al ype B5 o ea lie , and
90 10 My , as de e mined om he li hium deple ion bounda y
by S au e e al. (1999). In he de ailed s udy o he nea by OB
associa ions by de Zeeuw e al. (1999) he au ho s ind a physical
ela ion be ween he Cas-Tau g oup and he Pe sei clus e . The
main-sequence u no age o his clus e is abou 50 My (Meyne
e al. 1993), so he age o bo h Cas-Tau and Pe sei could be he
same (e.g., B own 2002). No e ha in Pape I we ound ha
Pe sei is loca ed well wi hin he spa ial bounda ies o he GB.
3.1. Classi ica ion o he Sample
In o de o obse e how hese mo ing g oups con ibu e o he
wo sys ems in s udy, we classi y he sample and de e mine he
membe ship o he s a s in ei he he GB o he LGD. In Pape I
we ob ained se e al es ima ions o he pa ame e s ha cha ac e ize
bo h sys ems in ou model. We wo k wi h he solu ion o he ull
OYB6 sample o Pape I wi h an exponen ial model o he s ella
dis ibu ion in he di ec ion pe pendicula o he mean planes.
Thus, using ha es ima ion as he ue alue o he GB and he
LGD mean planes, we simply apply ou sepa a ion algo i hm o
ou cu en s a sample wi h kinema ic da a. No i e a ion in o de
o ee alua e he mean planes is pe o med; we jus assign mem-
be ship p obabili ies o he s a s acco ding o he planes es ima ed
in Pape I. Also, spa ial ou lie s a e elimina ed acco ding o he
p ocedu e explained in ha pape ; he emaining sample has 776
s a s. We ob ain a sepa a ion be ween he GB and he LGD based
exclusi ely on he spa ial posi ions o hese s a s. Ye we can see
in Figu e 3 how a di e ence in hei eloci y ields is ob ained as
a esul .
The mos s iking di e ence is ha in he U-Vp ojec ion (Fig. 3,
op panels) he h ee mo ing g oups ha we had ound in he ull
sample (Fig. 2, op) now dis inc ly belong o ei he he GB o he
LGD. The wo maxima associa ed wi h he Pleiades and IC 2391
appea only in he GB eloci y ield (Fig. 3, op le ), while he Cas-
Tau peak emains isible only in he LGD ield (Fig. 3, op igh ).
This is no su p ising, i we conside ha he Pleiades mo ing
g oup is spa ially ela ed o he Sco-Cen associa ion, which is one
o he main componen s o he GB (Mo eno e al. 1999). Also,
we know ha IC 2391 is a young clus e , i s age being abou 30 My
(S au e e al. 1997). In a ecen s udy o angen ial eloci ies,
Piskuno e al. (2006) concluded ha he kinema ic p obabili y
o i s belonging o he GB is 73%. No e ha we ha e a i ed a a
simila conclusion by a p ocess based solely on he spa ial posi ions
o he s a s, and hus independen o he esul in he ci ed pape .
We mus also no e ha a la e- ype popula ion o young s a s
has been associa ed wi h bo h he Pleiades and IC 2391 by Mon es
e al. (2001). In ha pape hese mo ing g oups a e desc ibed
as cen e ed a ound (U;V;W)¼(11:6;21;11:4) and (U;
V;W)¼(20:6;15:7;9:1) km s1, espec i ely, wi h a dis-
pe sion o abou 8 km s1a ound he cen al posi ions. No
Fig. 1.— His og ams o he Vmagni ude in he Johnson sys em o he OYB6
s a s in he Hippa cos ca alog ( Pe yman e al. 1997) and o ou s a sample.
Fig. 2.—Dis ibu ion o space eloci ies o he s a sample.
ELIAS, ALFARO, & CABRERA-CAN
˜O1054
Fig. 3.—Dis ibu ion o space eloci ies o he GB (le panels) and he LGD ( igh panels)s a s.
su p isingly, a la e- ype componen o s a s o abou 30Y80 My
o age had al eady been associa ed wi h he GB disk s uc u e
by Guillou e al. (1998) when s udying he X- ay sou ces in he
ROSAT All-Sky Su ey.
Finally, we also obse e ha in he U-Wp ojec ion (Fig. 3, mid-
dle igh ) a new maximum clea ly ises ha has a co espondence
wi h a small p o ube ance a ound U¼11 km s1in he U-Vp o-
jec ion (Fig. 3, op igh ). I was also p esen , al hough weak, in
he eloci y densi y ield o he ull sample (Fig. 2, op and middle).
We ha e no ound an exac co espondence o his possible mo -
ing g oup among he s uc u es in he sola neighbo hood, bu he
posi i e alue o he U-componen makes us hink ha i may be
ela ed o he Si ius supe clus e (e.g., Eggen 1996; Dehnen 1998;
Asiain e al. 1999).
4. ANALYSIS OF THE RESIDUAL VELOCITIES
I we wan o imp o e ou s udy o he kinema ic di e ences
be ween he GB and he LGD, we mus wo k wi h esidual e-
loci ies. In his way, he sys ema ic e ec s o he Galac ic kinema -
ics do no in e e e wi h ou compa ison. Thus, we now co ec he
space eloci ies o he s a s in ou sample o sola mo ion (using
he classical es ima ion o Delhaye [1965]: U;V;W
½¼
9;12;7½km s1) and o Galac ic di e en ial o a ion using he
alues gi en by Ke & Lynden-Bell (1986).
In o de o e ine he analysis o he eloci y dis ibu ions, we
mus also elimina e ou lie s o kinema ic na u e ha may be p esen
in he sample. Tha is, we elimina e he s a s loca ed in he egions
o e y low densi y in eloci y space o ou sample unde s udy.
We achie e his by unning he OUTKER algo i hm (Cab e a-
Can
˜o & Al a o 1985), which educes he sample o a inal numbe
o 752 s a s. We hen again sepa a e he sample in o GB and
LGD membe s. Now we wan o compa e bo h dis ibu ions in
an N-dimensional space, whe e N¼6 (phase space) o N¼3
( eloci y space). In o de o achie e his, we employ a mul i-
dimensional, nonpa ame ic wo-sample es : he C ame es
(Ba inghaus & F anz 2004). The es s a is ic is he di e ence
o he sum o all he Euclidean in e poin dis ances be ween he
andom a iables om he wo di e en samples:
T¼mn
mþn"2
mn X
m;n
i;j
XiYj



2

1
m2X
m
i;j¼1
XiXj



2

1
n2X
n
i;j¼1
YiYj



2

#;ð1Þ
whe e Xiand Yia e he poin ec o s o each sample membe , m
and na e he espec i e sizes o he samples, and is a ke nel
unc ion; o his pa icula case we ha e used he C ame ke nel
implemen ed by F anz (2004) in he R s a is ical en i onmen
(R De elopmen Co e Team 2005).
Thus, an analysis o he h ee-dimensional eloci y space (U;
V;W) yields ha he GB and he LGD dis ibu ions a e di e en
wi h a 99% con idence le el. Simila ly, he C ame es o he
six dimensions o he phase space (X;Y;Z;U;V;W) ejec s he
possibili y ha he GB and he LGD dis ibu ions a e he same
wi h a con idence o 99%.
Thus, we con i m ha he GB and he LGD a e wo di e en
s ella sys ems in he sense ha hey show a clea s a is ical sep-
a a ion be ween hei dis ibu ions in he phase space. I is un-
a oidable o ake in o conside a ion he con ibu ion o he GB
when he young disk is unde s udy, because, as we ha e demon-
s a ed, he eloci ies o he OB s a s in he sola neighbo hood
a e no s a is ically independen o hei spa ial posi ions.
4.1. Veloci y Ellipsoids
A mo e in ui i e isualiza ion o he di e ences be ween he
GB and he LGD esidual eloci y dis ibu ions is in he con ou
densi y plo s o he h ee di e en eloci y planes (see Fig. 4).
Thei dispa a e shapes and o ien a ions al eady show ha he e-
loci y ellipsoids clea ly e lec he dis inc kinema ic beha io o
bo h s ella sys ems.
We ha e es ima ed he main geome ic pa ame e s o he eloc-
i y ellipsoids o he whole sample and o he GB and he LGD
membe s sepa a ely. The esul s a e displayed in Table 1. Two
main esul s a ise om his analysis:
1. The e ex de ia ion o he GB is highly nega i e, while
ha o he LGD is posi i e.
2. The e is he sugges ion ha he hi d axis o he eloci y
ellipsoid o he GB is il ed wi h espec o he Galac ic plane.
The es ima ion o he e ex de ia ion in he sola neighbo -
hood om di e en s a samples has p oduced di e en alues de-
pending on he na u e o he sample and on he kinema ic a iables
used in he calcula ion (see Mo eno e al. [1999] o a compila ion
o p e ious esul s). In b ie , he gene al conclusion has been ha
he e ex de ia ion becomes mo e nega i e as he s a sample
ge s younge . In ac , one o he classic es ima es based on space
eloci ies o OB s a s (Filin 1957) yielded a alue close o l ¼
50 o he Galac ic disk. Fo yea s, his esul has emained a
puzzling issue ha has been gi en se e al and a ied explana-
ions. Mos o hem can be classi ied in o wo classical ypes: na-
u e o nu u e, we could say. Some au ho s claim ha hese young
s a s ha o med om a molecula cloud show he same kinema -
ics as he pa en cloud a he ime o he s a o ma ion. In his
way, he ini ial eloci y and la e expansion de ine he eloci y
ellipsoid o he p esen s ella sys em. O he au ho s, howe e , a -
gue ha he e ec s o di e en singula e en s (such as passing
h ough a spi al a m) could also be he cause o he peculia e-
loci y ellipsoid obse ed in he young s ella componen .
Wha we conclude om ou analysis is ha he classic p ob-
lem o he nega i e e ex de ia ion o young s a s in he sola
neighbo hood is a consequence o he p esence o he GB. I we
elimina e he s a s ha belong o he GB, he emaining sample o
only LGD s a s p esen s a posi i e e ex de ia ion (lLGD
¼18).
Mo eno e al. (1999), wo king wi h a sample o dwa OYB5.5
s a membe s o he GB, ound ha he nega i e e ex de ia ion
(l 64) was caused by he Pleiades mo ing g oup. Once his
g oup was emo ed, Mo eno e al. ob ained a posi i e e ex de-
ia ion (l ¼22) o he emaining s a s in he GB. We now dem-
ons a e ha he OB s a s o he LGD also ha e a posi i e e ex
de ia ion, simila o ha ound by Mo eno e al. (1999) o he
GB s a s a e elimina ing he ones belonging o he Pleiades mo -
ing g oup. So when we wo k wi h samples (o ei he GB o LGD
s a s) in which a single mo ing g oup clea ly domina es o e he
o he s, he e ex de ia ion is posi i e and close o l 20, which
is he alue expec ed om he dynamic equa ions o he sys-
em o his age g oup. The nega i e e ex de ia ion o he GB
seems o o igina e om he ela i e posi ions o he cen oids o
he wo mo ing g oups a he han om he dis ibu ion o he e-
sidual eloci ies as a whole. We mus no e ha he analysis o he
young s a s, especially hose belonging o he GB, based on he
Schwa zschild dis ibu ion om which he eloci y ellipsoid is
ailo ed, is no he bes sui ed o desc ibe he eali y o he sys-
em. The eloci y ield is domina ed, as we ha e seen, by he p es-
ence o mo ing g oups, and hus, i is a om he hypo hesis o a
homogeneous and s a iona y sys em. The p oblem hus lies in ha
he classical analysis o he eloci y ellipsoid is applied o a se o
ELIAS, ALFARO, & CABRERA-CAN
˜O1056

Fig. 4.—Con ou densi y plo s o he esidual eloci ies o he GB (le ) and he LGD ( igh )s a s.
mo ing g oups. Mihalas & Binney (1981) ha e al eady poin ed
ou ha he cause o he e ex de ia ion was he exis ence o mo -
ing g oups in he Galac ic eloci y ield. Bu e en hough he e-
loci y ellipsoid does no s ic ly co espond o a physical eali y in
ou case, ha does no in alida e ou esul , ha is, he undamen al
con ibu ion o he GB o he nega i e e ex de ia ion o he O
and B s a s.
Thus, he di e en alues o he e ex de ia ion ound in he
li e a u e can be explained acco ding o he di e en p opo ions
o GB s a s p esen in he espec i e samples. This ansla es he
ques ion abou he o igin o he nega i e e ex de ia ion o he in-
es iga ion o he o igin o he mo ing g oups. Al hough he la e
is ou o he scope o his pape , we wan o s ess ha he mo e we
s udy in de ail he na u e o he GB, he mo e we ind indica ions
ha we mus p obe bo h i s na u e and o igin as a se o mo ing
g oups.
Ano he s iking esul is he inclina ion o he GB’s eloci y
ellipsoid o abou 1012wi h espec o he U-Vplane, al-
hough his alue does no ha e a g ea s a is ical signi icance.
While he hi d axis (W0) o he LGD ellipsoid me ely shows an
inclina ion o 2, he GB’s ellipsoid inclina ion (10) esembles
ha o he spa ial sys em wi h espec o he Galac ic plane (iGB 
14as we ound in Pape I). Some au ho s ha e poin ed ou ha
he GB could be oscilla ing as a whole a ound he Galac ic plane
(Come o
´n 1999; Pe o & G enie 2003). Bu ou esul does no
p e en a di e en in e p e a ion in e ms o a jux aposi ion o mo -
ing g oups: his links back o he idea ha a desc ip i e pa ame e
o he GB, such as he inclina ion o he mino axis o he ellipsoid,
can be in e p e ed in e ms o he ela i e posi ion (in he eloci y
space) o wo mo ing g oups.
5. ESTIMATION OF THE OORT CONSTANTS
Al hough ou sample has no been ideally compiled wi h he
in en ion o calcula ing he Oo cons an s, i is wo h pe o ming
a basic es ima ion o ob ain in o ma ion abou he GB’s con ibu-
ion o hei alue. Thus, wi hin he axisymme ic app oxima-
ion o Oo ’s model in i s o de , and including a Kexpansion
e m, we sol e he condi ion equa ions (Sma 1968; Clube 1972;
F ogel & S o he s 1977) o he adial and angen ial eloci ies:
¼u0coslcosbþ 0sin lcosbþw0sinbþA sin2lcos2bþK;
ð2Þ
l¼u0sin lþ 0cos lþA cos 2lcos bþB cos b;ð3aÞ
b¼u0coslsinb 0sinlsinbþw0cosbA sin2lcosbsinb;
ð3bÞ
whe e is he adial eloci y, l¼4:74057l and b¼
4:74057b a e he angen ial eloci ies in Galac ic longi ude (l)
and la i ude (b), wi h land b he espec i e p ope mo ions and
he heliocen ic dis ance, and (u0; 0;w0)¼(U;V;W)a e
he e lex o he sola mo ion.
In p inciple, i would only make sense o es ima e he Oo
cons an s o he LGD, elimina ing he GB membe s om he sam-
ple. As we ha e seen om he s udy o he mo ing g oups and he
eloci y ellipsoid, he eloci y dis ibu ion o he GB clea ly de i-
a es om he axisymme ic hypo hesis; hence, he Oo cons an s
would no co espond o a physical eali y in his case. Ye we ha e
sol ed he equa ions in o de o es ablish a compa ison and hus ob-
se e he e ec s ha he p esence o he GB in oduces in he ki-
nema ics o he LGD.
The solu ions o he p ope mo ions and o he adial e-
loci y alone a e lis ed in Table 2. The sola mo ion o he LGD
p ope mo ion solu ion is in good ag eemen wi h he IAU s an-
da d, (U;V;W)¼(9;12;7) km s1(Ke & Lynden-Bell
1986). Bu he Oo cons an s di e no iceably om he IAU
ecommended alues o A¼14:41:2kms
1kpc1and B¼
12:02:8kms
1kpc1, and ins ead we ha e a la o a ion
TABLE 1
Veloci y Ellipsoids
Axis

(km s
1)
l
(deg)
b
(deg)
Full Sample
U0................... 10:70:4529 6 4
V0................... 10:20:48529 24
W0.................. 6:90:6 153 115 84 3
Gould Bel
U0................... 9:80:347 22 10 8
V0................... 8:90:34322 1 12
W0.................. 7:10:8 141 92 80 12
Local Galac ic Disk
U0................... 12:20:61811 24
V0................... 10:20:572 11 0 5
W0.................. 7 12766 88 5
No es.— The quan i ies U0,V0,andW0 ep esen he p incipal
axes o he ellipsoids, which de ia e om he (U;V;W) e e ence
ame. The e o s we e es ima ed by boo s ap.
TABLE 2
Oo Cons an s
Sample
U
(km s
1)
V
(km s
1)
W
(km s
1)
A
(km s
1kpc1)
B
(km s
1kpc1)
K
(km s
1)
Solu ion om P ope Mo ions
FS ......................... 9:80:413:00:66:60:314118 1...
GB........................ 9:90:513:00:66:70:311220 1...
LGD ..................... 9:40:812:60:96:30:316216 1...
Solu ion om Radial Veloci y
FS ......................... 8:70:815:00:6112132... 0:60:4
GB........................ 10 21518492... 0:40:6
LGD ..................... 9 114185163... 21
No es.—FS is he ull sample.
ELIAS, ALFARO, & CABRERA-CAN
˜O1058 Vol. 132
cu e wi h A¼B¼16 km s1kpc1. Ye he alue p o ided
by Ke & Lynden-Bell (1986) is a mean o e he esul s ob ained
by se e al au ho s, so i is mo e e ealing o compa e ou es-
ima ion wi h ha o a s udy simila o ou s.
F ogel & S o he s (1977), wo king wi h a sample o OYB5 s a s,
sepa a ing he GB om he LGD, and conside ing a ixed alue
o A¼15 km s1kpc1, es ima ed he alue o B o bo h sys-
ems, as well as o he whole unclassi ied sample. Fo he la e
hey ound a la o a ion cu e o A¼B¼15 km s1kpc1; o
he LGD, B¼12 km s1kpc1; and o he GB, B¼19 km
s1kpc1, a alue simila o ou es ima ion. Bu ega dless o he
nume ical esul s, we can also conclude ha he global kinema ics
o he GB di e s g ea ly om he kinema ics o he LGD, and ha
he p esence o his s ella sys em a ec s he es ima ion o he pa-
ame e s desc ibing he kinema ics o he sola neighbo hood.
On he o he hand, he K e m is gene ally lowe in absolu e
alue han he es ima ion by F ogel & S o he s (1977). We ha e
checked ha when sol ing he equa ions wi hou his e m, he
esul s o he Oo cons an s do no change signi ican ly. Thus,
we do no conside i wise o conclude any hing abou he possible
expansion mo emen s o he sys em om hese esul s.
The de ailed s udy o he local i egula i ies in he kinema ics
o young s a s by To a e al. (2000), om a sample o O and B
Hippa cos s a s, e eals ha o heliocen ic dis ances lowe han
600 pc and age g oups unde 90 My (i.e., o a sample wi h a high
p opo ion o GB membe s), he alue o he Oo cons an Bis
much g ea e in absolu e alue han expec ed o he LGD:
13:62:0kms
1kpc1<B<20:71:4kms
1kpc1:
On he o he hand, hey ind qui e a small alue o he Oo
cons an A:
10:52:1kms
1kpc1<A<5:71:4kms
1kpc1:
Bo h es ima ions a e pe ec ly compa ible wi h ou esul o
(A;B)¼(11 2;20 2) km s1kpc1 o he GB, which is
undoub edly con amina ing hei sample.
Some o he ecen s udies ind alues o Aand Bin good
ag eemen wi h ou s. Uemu a e al. (2000), o a sample o OYB5
Hippa cos s a s, es ima e ha A¼14:00:7kms
1kpc1and
B¼15:80:7kms
1kpc1. Zhu (2000), wo king wi h OYB5
s a s wi h Hippa cos p ope mo ions, inds ha A¼16 1km
s1kpc1and B¼15:60:8kms
1kpc1.Olling&Dehnen
(2003), o a sample o young main-sequence s a s, ind ha (A;
B)¼(9:6;11:6) km s1kpc1, while o a sample o ed gian s,
wi h no signi ican con ibu ion om he GB, he disk o a ion cu e
is almos la , (A;B)¼(15:9;16:9) km s1kpc1, in e y good
ag eemen wi h ou esul s o he OB s a s o he LGD.
Ou es ima ion o he ci cula o a ion speed, conside ing ha
he Sun’s dis ance o he Galac ic cen e is 8.5 kpc (Ke & Lynden-
Bell 1986), is ¼272 km s1 o he LGD om p ope mo ions.
I is a high alue bu in ag eemen wi h ecen s udies o OYB5 s a
samples om he Hippa cos ca alog by Miyamo o & Zhu (1998),
¼268:711:9kms
1; Uemu a e al. (2000), ¼255:52 
8:33 km s1; o B anham (2002), ¼258:734:29 km s1.A
simila esul (¼270 km s1) is also eached by Me
´ndez e al.
(2000) using da a om he Sou he n P ope Mo ion Ca alog
(Pla ais e al. 1998); hus, hei esul is ob ained om measu es o
he p ope mo ions independen o hose om Hippa cos.
6. CONCLUSIONS
In Pape I we concluded ha in he young Galac ic disk he e
a e wo spa ially di e en sys ems, he GB and he LGD. Now we
ha e classi ied using only spa ial c i e ia a sample o OYB6 s a s
om he Hippa cos ca alog and ha e ound ha he GB’s global
kinema ics is essen ially di e en om he kinema ics o he LGD.
No only ha , mul idimensional wo-sample es s p o e ha he
GB and he LGD a e sepa a ed sys ems in phase space. This does
no necessa ily imply ha he GB is a cohe en s uc u e bo n om
a single sou ce such as a gian molecula cloud. We jus no e ha
in i s p esen s a e, he GB is a local sys em (whose size is well ep-
esen ed by ou sample) showing e y di e en kinema ic p ope -
ies han he la ge sys em in which i is embedded, he Galac ic
disk. The ac ha he GB is mainly composed o ce ain mo ing
g oups challenges he idea o his sys em coming om a single o i-
gin, and aises he ques ion o whe he we a e wi nessing a phys-
ical en i y wi h cohe en s uc u e o a e jus obse ing a ansi o y
pic u e o se e al smalle sys ems wi h no common o igin a all.
The answe o his ques ion can only be sough in he dynamical
s udy o he mo ing g oups ha o m he GB (which would equi e
a deep knowledge o he Galac ic po en ial and i s asymme ies),
in o de o ace hei ajec o ies back o he pas and disco e
whe he hey come om a single p o os ella cloud o a e he an-
si o y esul o some dynamical aps.
We ha e also p o ed ha he classic p oblem o he nega i e
e ex de ia ion o young s a s in he sola neighbo hood is caused
by he con ibu ion o he GB. This e ec disappea s once his s el-
la sys em is emo ed om he sample, lea ing he LGD, de ined
by i s spa ial dis ibu ion, as he only emaining s uc u e.
Finally, we ha e obse ed how he p esence o wha is called
he GB in oduces dis u bances in he es ima ion o he Oo con-
s an s ha desc ibe he kinema ics o he young Galac ic disk, mak-
ing i necessa y o disca d i s con ibu ion by iden i ying and
emo ing he GB membe s. Once he young disk is p uned by elim-
ina ing he GB membe s, we es ima e a la o a ion cu e wi h a
local eloci y e y close o he alues calcula ed by se e al au-
ho s in he las decade o a wide ange o ages.
Thus, al hough we ind ha a kinema ic analysis is no enough
o deciphe he o igin o he GB, i is indeed undamen al o cha -
ac e izing he complexi y o he young Galac ic disk and o be e
unde s anding he di e en mo ing g oups ha o m he bulk o
he GB s ella componen . A comp ehensi e explana ion o he
o igin o he GB will equi e a dynamical analysis o hese mo -
ing g oups.
F. E. wan s o hank he Depa amen o de Fı´sica A o
´mica, Mo-
lecula , y Nuclea o he Uni e sidad de Se illa o i s suppo du -
ing his wo k. We would also like o acknowledge he unding om
MCEyD o Spain h ough g an s AYA 2004-05395, and AYA 2004-
08260-C03-02, and om he Conseje ı´a de Educacio
´n y Ciencia
(Jun a de Andalucı´a) h ough TIC-101.
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