Ob stars in the solar neighborhood. II. kinematics
Abstract
Using the spatial classification method and the structural parameters estimated for the Gould Belt (GB) and the local Galactic disk (LGD) from a previous paper, we have evaluated spatial membership probabilities for a sample of O and B stars from the Hipparcos catalog (Perryman and coworkers) with available proper motions and radial velocity data. Thus, being able to study the space velocity fields of both systems, we conclude that the GB and the LGD present different statistical distributions, both in velocity space and in phase space. In light of their possible existence as distinct systems, we analyze different kinematic aspects in the vicinity of the Sun, and we find the GB to be responsible for the highly negative vertex deviation found for the OB stars in the solar neighborhood. We also find that the GB noticeably alters the estimation of the Oort constants in the Galactic disk; thus, in order to establish comparisons with other kinematic studies based on older stellar populations, a careful pruning of the GB members must be performed. Further analysis of the GB velocity field and the moving groups that contribute to it suggest the possibility that the GB can be the result of a chance superposition of moving groups. We propose for future investigations the dynamical analysis of these moving groups in order to probe the origin of the GB.
Full text
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 20wi 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 s1) 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 s1) om G enie e al. (1999).
15. E o in adial eloci y (km s1) om G enie e al. (1999).
16. The u bypho 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 byS 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 V7:9,
and o V7:5 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
V6:5. 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
V7:9 o6 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 s1, 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 bypho-
ome y, ind ha he maximum is loca ed a (U;V;W)¼(10;
19;8:1) km s1, 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 s1.
The second mos p ominen peak in Figu e 2 is loca ed a ound
(U;V;W)¼(17;11;5) km s1. 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 s1, wi h he s anda d de ia ion being
(U;
V;
W)¼(4:1;6:2;3:0) km s1.
The hi d maximum, cen e ed a ound (U;V)¼(11;8:5)
km s1, 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 s1. 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 s1, espec i ely, wi h a dis-
pe sion o abou 8 km s1a 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 s1in 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
½¼
9;12;7½km s1) 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
XiYj
2
1
m2X
m
i;j¼1
XiXj
2
1
n2X
n
i;j¼1
YiYj
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 1012wi 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
14as 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
l¼u0sin lþ 0cos lþA cos 2lcos bþB cos b;ð3aÞ
b¼u0coslsinb 0sinlsinbþw0cosbA sin2lcosbsinb;
ð3bÞ
whe e is he adial eloci y, l¼4:74057l and b¼
4:74057b 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 s1(Ke & Lynden-Bell
1986). Bu he Oo cons an s di e no iceably om he IAU
ecommended alues o A¼14:41:2kms
1kpc1and B¼
12:02:8kms
1kpc1, 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................... 10:70:4529 6 4
V0................... 10:20:48529 24
W0.................. 6:90:6 153 115 84 3
Gould Bel
U0................... 9:80:347 22 10 8
V0................... 8:90:34322 1 12
W0.................. 7:10:8 141 92 80 12
Local Galac ic Disk
U0................... 12:20:61811 24
V0................... 10:20:572 11 0 5
W0.................. 7 12766 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
1kpc1)
B
(km s
1kpc1)
K
(km s
1)
Solu ion om P ope Mo ions
FS ......................... 9:80:413:00:66:60:314118 1...
GB........................ 9:90:513:00:66:70:311220 1...
LGD ..................... 9:40:812:60:96:30:316216 1...
Solu ion om Radial Veloci y
FS ......................... 8:70:815:00:6112132... 0:60:4
GB........................ 10 21518492... 0:40:6
LGD ..................... 9 114185163... 21
No es.—FS is he ull sample.
ELIAS, ALFARO, & CABRERA-CAN
˜O1058 Vol. 132
cu e wi h A¼B¼16 km s1kpc1. 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 s1kpc1, 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 A¼B¼15 km s1kpc1; o
he LGD, B¼12 km s1kpc1; and o he GB, B¼19 km
s1kpc1, 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:
13:62:0kms
1kpc1<B<20:71:4kms
1kpc1:
On he o he hand, hey ind qui e a small alue o he Oo
cons an A:
10:52:1kms
1kpc1<A<5:71:4kms
1kpc1:
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 s1kpc1 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 A¼14:00:7kms
1kpc1and
B¼15:80:7kms
1kpc1. Zhu (2000), wo king wi h OYB5
s a s wi h Hippa cos p ope mo ions, inds ha A¼16 1km
s1kpc1and B¼15:60:8kms
1kpc1.Olling&Dehnen
(2003), o a sample o young main-sequence s a s, ind ha (A;
B)¼(9:6;11:6) km s1kpc1, 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 s1kpc1, 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 s1 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),
¼268:711:9kms
1; Uemu a e al. (2000), ¼255:52
8:33 km s1; o B anham (2002), ¼258:734:29 km s1.A
simila esul (¼270 km s1) 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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ELIAS, ALFARO, & CABRERA-CAN
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