HI shells in the Leiden/Argentina/Bonn HI survey

1.1 MB·English

by  S. Ehlerova

Astronomy&Astrophysicsmanuscriptno.shell cESO2013
(cid:13)
January18,2013
HI shells in the Leiden/Argentina/Bonn HI survey
S.EhlerováandJ.Palouš
AstronomicalInstitute,AcademyofSciences,BocˇníII1401,Prague
e-mail:[email protected]
ReceivedSeptember6,2012;acceptedNovember9,2012
ABSTRACT
3
1 Aims.Weanalysetheall-skyLeiden/Argentina/BonnHIsurvey,whereweidentifyshellsbelongingtotheMilkyWay.
0 Methods. We used an identification method based on the search of continuous regions of a low brightness temperature that are
2 compatiblewithgivenpropertiesofHIshells.
n Results.Wefound333shellsinthewholeGalaxy.ThesizedistributionofshellsintheouterGalaxyisfittedbyapowerlawwiththe
a coefficientof2.6correspondingtotheindex1.8inthedistributionofenergysources. Theirsurfacedensitydecreasesexponentially
J withascalelengthof2.8kpc. Thesurfacedensityofshellswithradii 100 pcinthesolarneighbourhoodis 4kpc−2andthe2D
porosityis 0.7. ≥ ∼
7 ∼
1 Keywords. ISM:bubbles–Galaxy:structure–radiolines:ISM

]
A
1. Introduction nalgalaxies,wherewehavetoconsidertheorientationrelativeto
G
thelineofsight. IntheMilkyWay,therearemanyobservations
h.Theneutralinterstellarmedium(ISM)ingalaxiesisfullofstruc- of individual shells and several papers dealing with the global
ptures. Some of them are turbulent, wildly changing structures, picture(Heiles1979;McClure-Griffithsetal.2002;Daigleetal.
-othersaremorestable,whileHIinparticularshowsverypromi- 2007;Ehlerová&Palouš2005),buteventhesedonotcoverthe
onentstructures.Weseeroughlyellipticalobjectswithsizesfrom wholeGalaxy.
r
tafewpctomorethan1kpc,whichmayexpandintotheambient
smedium.IntheMilkyWaytheywereidentifiedforthefirsttime
a
by Heiles (1979) and since then they have been discovered in
[
many externalgalaxies, both spiral and irregular, including the Since2005theall-skyLeiden/Argentina/BonnHIsurveyhas

1LMCandSMC(foramorecompletereviewsee,e.g.,Bagetakos beenavailable(LAB;Kalberlaetal. 2005). Surveysof thesky
vetal.2011). availablefromtheParkestelescope(GASS;Kalberlaetal.2010)
3 andtheEffelsbergtelescope(EBHIS;Kerpetal.2011)existor
0 ShellsmaybetheresultsofdifferentprocessesintheISM.It
will exist in the near future and have a higher resolution than
0isachallengetodistinguishbetweenshellscreatedbytheenergy
LAB. There are other surveys with a higher resolution (The
4insertedbystellarwinds,stellarradiation,andsupernovaeexplo-
Southern Galactic Plane Survey, the Canadian Galactic Plane
.sions;andstructurescreatedbyotherdrivingmechanisms,such
1 Survey, the VLA Galactic Plane Survey), but they cover only
as the infalling high-velocity clouds, gamma ray bursts, or the
0 theregionalongtheGalacticequator.
3turbulencedrivenbygalacticdifferentialrotation.Wallsofshells
1maydevelopRayleigh-Taylor,Vishniac,Jeans,orotherinstabil-
:ities,therebycreatinghigh-densityandlow-temperatureregions,
v
whichbecomesitesofsecondarytriggeredstarformation.Dense
i Identificationofshellsisusuallydonebyeye. Humaneyes
Xcondensationsof cold gas along the edgesof shells, secondary
areverygoodatconnectingpartiallydisconnectedpartsofshells
star formation, and compact HII regions of second-generation
r and using some software tools (e.g.some routines in KARMA
astars have been observed by Zavagno et al. (2006), Deharveng
Gooch 1997) may help. Still, an objective method is prefer-
et al. (2010), and others (see also review by Elmegreen 2012).
able. There are a few attempts at an automatic identification
However,manydetailsonthestarsvs. shellsconnectionremain
processforshells:Thilkeretal.(1998)comparedahydrodynam-
unknown,e.g.,thenumberofshellsperassociation,theenerget-
ical model with observations; Daigle et al. (2007) based their
icsinvolved,andthefractionofshellswithnonstellarorigins.
methodonfindingsimple dynamicalcharacteristicsin HI data;
Due to our position inside the Milky Way, observations of andEhlerová&Palouš(2005)(Paper1)locatedcontinuousre-
shells in the Galaxy present special problems: unlike observa- gionsof low brightnesstemperature. The first attempt was not
tionsofexternalgalaxies,anobserverhastoprocessasubstan- followedanyfurther,probablybecauseitisverydifficulttocon-
tial part, ideallyall, of the skyto coverthe wholeGalaxy. The structa satisfactory and universalhydrodynamicalmodelcom-
structures do not lie at almost the same distance as in external parabletotherealdata. Thesecondapproachisaimedatsmall
galaxies, therefore results are more dependent on the distance bubbles (typically 10 pc) and was used for a portion of the
∼
ofobjectsfromthe Sun. Anotherdifferenceis theshapeof the CanadianGalacticPlaneSurveydata,whichfound 7000bub-
∼
shells perpendicular to the galactic symmetry plane. It is di- bleswithradiir < 40pc. Thethirdapproachisdevelopedin
sh
rectlyobservableintheMilkyWay,whilenotsoclearinexter- thiscommunication.
Articlenumber,page1of19
2. Dataandmethods p,wemayartificiallyconnecttwoormorephysicallyunrelated,
butneighbouring,structures,whileforahighvalueof pwemay
2.1.Leiden-Argentine-Bonnsurvey
divideonephysicalstructurewithanirregularshapeintoseveral
The Leiden-Argentine-Bonn HI survey (LAB, Kalberla et al. smallerpieces.
2005) is an all-sky survey, a combination of the Leiden- Connecting2Dstructuresinto3Donesmayincreasethean-
Dwingeloosurvey(Hartmann&Burton1997)andtheInstituto gularsizesofstructures,sotheycanexceedthevaluedpixmax.
ArgentinodeRadioastronomíasurvey(Bajajaetal.2005),with
angularresolution36arcmin(thepixelsize30arcmin)andve-
2.2.3. PropertiesofHIshells
locity resolution1 kms 1 (the channelwidth is 1.0306kms 1).
− −
Weusedthedatacubelimitedinv to( 250,+250)kms 1. WedonotprescribeanydesiredshapeforanHIshell, weonly
lsr −
− requestthat structures, which we call shells, span a certain ve-
locity extent and that their shapes do not change significantly
2.2.Identificationprocess betweenconsecutivevelocitychannels.
The first condition is simple. We demand that the velocity
Theidentificationprocessisdividedintothreesteps:1)wetrace
extentofthestructure∆visgreaterthanagivenvalue. Theve-
continuousregionsaroundlocalminimain2Dchannelmaps;2)
locityextentis
we construct3Dstructuresfrom2Didentificationsfromstep 1
byconnectingconsecutiveoverlappingregions;3)weeliminate ∆v=v v , (1)
max min
structuresthatarenotcompatiblewiththegivenpropertiesofHI −
shells. where vmin and vmax delimit the interval in which the structure
exists.
To estimate how much the shape of the structure changes
2.2.1. Definitionofa2Dstructure
betweenthevelocitychannelswecalculatetheparameterP
2
Inchannelmapswe searchforregionswith locallylow bright- N (iv,iv+1)
nesstemperatures. Theregionhastobecontinuous,i.e. allpix- P2(iv)= max(Nbot(hiv),N (iv+1)), (2)
elsthatbelongtoitmustbeconnectedbytheiredges,notonlyby pix pix
touchingtheircorners,andtheirbrightnesstemperaturesmustbe whereN (iv)isthenumberofpixelsbelongingtothestructure
pix
lowerthanorequalto a certain levelof brightnesstemperature in the channeliv, N (iv,iv+1) is the numberof overlapping
both
T . All neighbouringpixels, whichare notmembersof the pixels,i.e. thosepixelswithpositionsil,ib,whichbelongtothe
Blevel
identified region, have to have brightness temperatures higher structureinbothchannelsivandiv+1.
than T . These conditions allow embedded clouds with a If P has a low value, it means that the lb-size or the lb-
Blevel 2
highertemperature. position in subsequent velocity channels are very different. It
Foreachchannelmap,therangeofT isexamined,start- mayalso mean thatthe 3D shape ofthe structure changessub-
Blevel
ing ata levelofnoise and growingto the maximumbrightness stantiallybetweenthetwoneighbouringchannels. Itservesasa
temperature in the map. For the LAB processing we used the warning that the structures might not be compact or uniform.
squarerootscaleforthebrightnesstemperature(i.e. weworked Since an ideal expanding shell, viewed in velocity channels,
with √T ,notdirectlywithT ),thelowestT weprocessed startssmall, reachesits maximumsize, andthen shrinksagain,
B B Blevel
was0.64K, √T wasincreasedbystepsof0.2. we determinethe average P andthe minimumvalue P ,
Blevel 2,ave 2,min
The identified regionhas sizes in l and b directions. These notinthe wholevelocityrangeofthestructure, butonlyinthe
sizeshavetobewithinlimits(d ,d ). Foreachregion limited range of velocity channels between the two local max-
pixmin pixmax
we find the highest T for which it is fulfilled. We used imain P ,thefirstafterthelowestvelocitychannel,thesecond
Blevel 2
d =3,whicheliminatedsinglepixelsandverysmallstruc- thelastbeforethehighestvelocitychannel.
pixmin
turesandsetstheminimumsizeofastructureto1.5◦. Thevalue ThecalculationofP2 issimilar,butnotidentical,tothecal-
omfedapnixinmgax,,bsuettwtoe9fi0n(de.ogu.t4t5h◦a)t,ihtagsivneoscgloeoardprhesyuslitcsa;lworenwuemreeraibclael cduifflaetrieonncoefitshtehoatv1er)lahpepreinwgepcaorammpeatreertpheinntuhmebperervoifouovsesrtelapp.pTinhge
to identify a whole range of structures under many conditions pixelswiththelargerofthesetwochannelstructures(itwasthe
occurring in the data. A lower value of d would prevent smalleronepreviously),and2)inthisstepwealreadyevaluatea
pixmax
identification of angularlylarge shells. Very few 2D structures structureconstructedfromseveraloriginallyindividual2Dparts.
have sizes larger than d = 90, only a few identifications Thespectrumthroughthecentreoftheshellshouldbeseen
in the solar neighbourhopioxdm,axwhere such angularly large shells asanoticeable,smoothdepressioninthebrightnesstemperature
mightoccur. profile compared to the profile outside the shell. We construct
therelativeprofile
2.2.2. Creatinga3Dstructure ∆TB(iv)= Tin(iv) Tout(iv), (3)
| − |
Foreach2Dregionidentifiedinthepreviousstepwecheckthat whereTinistheaveragebrightnesstemperatureinpixelsbelong-
ithasacounterpartinsubsequentchannelmaps.Wemeasurethe ing to the structure in a given velocity channel and Tout is the
overlapbetweentheneighbouring2Dstructures,andifitislarge averagevalue of TB in pixelsjust outside the structure. Which
enough, we connect them in one 3D structure. This continues pixelsareoutsideisdeterminedforeachvelocitychannelsepa-
forallvelocitychannelsandforallstructures,untilallpossible ratelytoaccountforthechanginglb-sizeofthestructure. Then
connectionsaremade. wedefine
Theoverlapconditionisthatatleastafraction pofthearea
P =max (∆T ), (4)
ofthesmalleroneofthesetwostructuresisoverlapped.Weused 3 v B
avalue p = 0.5,butresultswerenotverysensitivetothisvalue i.e., the maximum difference in average values of brightness
(we also tested values 0.1 and 0.9). If we use a low value of temperature inside and outside the shell in all channels where
Articlenumber,page2of19
S.EhlerováandJ.Palouš:HIshellsintheLeiden/Argentina/BonnHIsurvey
Fig.1. RelativenumberofstructuresidentifiedinLABasafunctionoftheirvelocityextent(leftpanel);therelativenumberofstructuresthat
fulfilltheP criterion(hatched),P criterion(cross-hatched),P criterion(empty),andallthree(solid)asafunctionoftheextentofvelocity
2,min 2,ave 3
(rightpanel).
the given structure exists. Clearly visible shells have high P . d = 90 as a minimum and a maximum size of the struc-
3 pixmax
Low P is connected with poorly visible shells, but also with turesandtheoverlappingparameterp=0.5,weidentified17535
3
shellsinaregionwithhighT gradients. 3Dstructures. Themajorityofthesestructuresspanonlyafew
B
The3DstructureisclaimedtobeanHIshellifitfulfillsthe velocity channels (see Fig. 1, left panel): 2152 structures (12
followingthreeconditions: %)haveavelocityextentgreaterthanorequaltofourchannels
(4.1kms 1), 775structures(4.4%) have an extentgreaterthan
∆v ∆v ; P ; P ; (5) −
≥ min 2,min ≥P2,min 2,ave ≥P2,ave orequaltoeightchannels(8.2kms−1). Weeliminatedirregular
withapossibleauxiliary“visibility”parameter, structuresbyadoptingparameters = 0.2and = 0.5
2,min 2,ave
P P
(seeFig.1,rightpanel,showingthefractionofstructures,which
P , (6)
3 3
≥P fulfill the requiredcriteria). Geometrical conditions and
2,min
wstrhiecrtneetshseovfatlhueesseoafrc∆hv.min, P2,min, P2,ave, and P3 determine the vPe2l,oavceiteylimexitneantte).feAwsesrhtohwann∼in4F0i%g.o1f,tthheesmheolsltsr(edsetrpiecntiPdvseopnarthameir-
eteristhevisibilityparameter :onlyabout40 50%ofshells
3
P −
haveparameterP greaterthan4K.Thevalueof =4K will
2.3.Anewversionoftheidentifyingalgorithm 3 3
P
bejustifiedinthenextsection.
Thenumericalcodedescribedinthispaperisasuccessortothe Themostimportantcriterionineliminatingshellsisthemin-
codedescribedandusedinEhlerová&Palouš,2005. Themain imum required velocity extent ∆v . The lowest acceptable
min
differencesfollow. valueisprobably∆v = 4kms 1,andthesafeoptioniscloser
min −
1. The currentversion deals with the whole datacube at once, to∆vmin = 8kms−1. Thisparameterisrelatedtothedispersion
whiletheoldversionhadtocutthebigdatacubeintosmaller velocityintheISM.Avalueof∆vmin lowerthanthetypicalve-
subcubesandthenconnectthembacktogether. locitydispersionleadstoidentificationofsomefalsestructures,
Cutting the big datacube into smaller ones led to artificial whilethehighervaluemayeliminatesomerealstructures. The
edgeproblems(mostimportanttodistortionsintheshapeof dispersionvelocityinISMvariesgreatly,dependingonthecon-
identifiedstructuresandthefailureofsomeidentifications). ditionsinISM,butitstypicalvaluefortheHIemissionisaround
2. Thelaststepintheidentification,“PropertiesofHIshells”, 7kms 1.
−
wascompletelychanged. Theoldversionusedtheanalysis
oftheT (v)spectrumthroughthecentralpixelofthestruc-
B
tures, the current version used the geometrical parameters 3.2.ComparisonstopreviouslyknownHIshells
P and P , and an auxiliary visibility parameter P .
2,min 2,ave 3 We compared our LAB identifications to two previous papers
Bothversionsusedtheconditionwiththe∆v ,whichwas
min on HI shells in the Milky Way: Heiles (1979) and McClure-
setinthepreviousversionto∆v =4kms 1.
min − Griffithset al. (2002),whichcontainthe majorityof knownHI
The spectrum analysis worked well for small structures in
supershells. Heiles’s list is divided into two parts: stationary
smooth surroundings. For larger structures and a more vi-
shells, which do not change their size with velocity; and ex-
olent medium, it was sensitive to the exact position of the
pandingshells, which show differentsizes in differentvelocity
studiedspectrumandtothedefinitionofthebackgrounden-
channels.
hancingthepossibilityof false identifications. Geometrical
Table1showsacomparisonof82supershellsfromthetwo
parametersfromthecurrentversionaremorerobust.
paperswithourLABidentificationsforthewholedatacube(the
middle section of the table) and separately for the second and
3. Results thirdquadrants(the rightsection of the table). We chose these
two quadrants, because they contained only the outer Galaxy,
3.1.LAB
where structuresare less crowded, which makes identifications
We used the LAB survey with v 250 kms 1 as an input more accurate. We distinguish whether the shells have similar
lsr −
| | ≤
datacube for our identifying algorithm. Using d = 3 and sizes(“volumerestricted”)ornot(“volumeunrestricted”).
pixmin
Articlenumber,page3of19
Fig.2. RegionofGS242-02+37,oneoftheexpandingshellsinHeiles(1979),asseenintheLABsurvey.Theoriginalidentificationisshownby
theblackcross(lengthofitsarmscorrespondstopublishedsizes),ournewidentification(thestructureGSH243.5-02.5+043.3inappendedtables)
isshownbythebox.Leftpanelisthelb map,rightpanelisthelv diagram.
− −
Fig.3. RegionofGS228-05+47,oneofthestationaryshellsinHeiles(1979),asseenintheLABsurvey.Theoriginalidentificationisshownby
theblackcross(lengthofitsarmscorrespondstopublishedsizes),ournewidentification(thestructureGSH226.5-09.5+031.9inappendedtables)
isshownbythebox.Leftpanelisthelb map,rightpanelisthelv diagram.
− −
Table1.ComparisonofidentificationswithHIsupershells:thewholeGalaxy(themiddlesection),the2ndand3rdquadrants(therightsection).
num vol. restr. vol. unrestr. num vol. restr. vol. unrestr.
Q2+3
Heiles1979,stationary 46 14(30%) 33(72%) 18 6(33%) 15(83%)
Heiles1979,expanding 17 7(41%) 9(53%) 7 4(57%) 4(57%)
McClure-Griffithsetal2002 19 10(53%) 17(89%) 4 3(75%) 4(100%)
Notes.Theleftsectiondenotessources,fromwhichpreviouslyknownHIshellsweretaken. Themiddleandrightsectionsgivethetotalnumber
ofshells(inthewholeGalaxyorinthe2ndand3rdquadrant,respectively)andthenumberofshells,whichwereidentifiedagainbyourmethod
(percentageofthetotalisinparentheses). Wedistinguishtwocases: thefirst,wherewedemandthatsizesofthecomparedstructuresaresimilar
(vol.restr.),andthesecond,wherewedonotputanyrestrictionsonsizesofthestructures(vol.unrestr.).
Articlenumber,page4of19
S.EhlerováandJ.Palouš:HIshellsintheLeiden/Argentina/BonnHIsurvey
1. ∆v = 4 kms 1 (designated as delv4 in Fig. 4, an unde-
min −
mandingcondition);
2. ∆v =4kms 1,P 0.2,P 0.5(designatedC2_4
min − 2,min 2,ave
≥ ≥
inFig. 4);
3. ∆v = 8 kms 1, P 0.2, P 0.5 (designatedas
min − 2,min 2,ave
≥ ≥
C2_8inFig. 4);
4. ∆v = 8 kms 1, P 0.2, P 0.5, P = 4 K
min − 2,min 2,ave 3
≥ ≥
(designatedasC3_8inFig. 4,thestrictestsetofconditions).
Furthermore,wedemandedthatsizesofshellsweresimilar
(“volumerestricted”). Correspondingfractionswere 61 %(the
1stset ofconditions),54%(2nd),33%(3rd),and26%(4th).
Eachstructureinthepreviousversionhadavisualquality,which
describes how good it looked (a purely subjective criterion: a
shell with q = 1 is clearly visible in velocity channels and is
probablysphericalorelliptical;ashellwith q = 4isinconspic-
Fig. 4. Comparisons between previous and current versions of the
searchalgorithms. Differentsymbolsdenotedifferent setsofparame- uousinvelocitychannels,withalowcontrasttoitssurrounding
tersputonnewidentifications(seethetextfortheexactexplanationof and probably fragmented and irregular). The comparison was
delv4,C2_4,C2_8,andC3_8).They-valueshowswhatfractionofold performedseparatelyforshellswithdifferentqualities(Fig. 4),
identificationsisalsoobservedwiththenewalgorithm. andthebest-lookingshells(visualquality1)hadcorresponding
fractionsrangingfrom80 % to 55 %. Fractionsof reidentified
shells for volume-unrestrictedcomparisonswere 88 % (the 1st
ThebestagreementwasfortheMcClure-Griffithsshells(in setofconditions),81%(2nd),76%(3rd),and72%(4th).
allcasesmorethan50%ofsupershellswerere-identified),the Wealsocomparedwhatfractionofthoseshellsthatfulfilled
worstagreementforHeiles’stationaryshells. Thisisduetothe the given set of conditionswere also classified as shells by the
quality of data used in the different searches. Stationary shells previousmethod (Fig. 4). The fractions are 25 % for the first
were re-identifiedwith differentsizes more frequentlythan ex- setofconditions,29%(2nd),48%(3rd),and74%(4th). That
pandingshells:thetraceofastationaryshellinadatacubeisless means that three fourths of shells fulfilling the strictest set of
sharplydefined,lesspronounced,andnotasspecificasthetrace conditionswere also defined as shells by the previousmethod.
ofanexpandingshell,andthereforeitiseasilymistakenbyboth Onefourtharenew: theseshellswererejectedbecauseofedge
humaneyesandnumericalmethods. Figures2and3showone effectsinherenttothepreviousversionofthecode(describedin
expandingandonestationaryshellfromthelistbyHeiles(1979) theSect. 2.3).
andthecorrespondingLABidentifications. Comparisonsinthe The summary of these results follows. The less strict the
outerGalaxyweremorefavourable.Thisis,webelieve,because setofconditionsusedforthenewidentifications,thebetterthe
theISMintheinnerGalaxyisveryviolent,andthereisanover- agreementwegetwiththepreviousversionofthesearchingal-
lapfromnearandfarregionsalongthelineofsight, leading to gorithm. Visuallyniceshellsaremuchlesssensitivetothepre-
problemsin artificialconnectionsof unrelatedstructures, all of cisechoiceofconditionsandmethods. Differencesariseforthe
whichmakeidentificationsintheinnerGalaxylessreliable. lesspronouncedandnotveryregularstructures.
We concludethat our methodis reliable in the outerMilky By using the fourth set of conditions (∆v = 8 kms 1,
min −
Way,becauseweareabletoidentifythemajorityofknownex- P 0.2, P 0.5, P = 4 K), we chosestructuresthat
2,min 2,ave 3
pandingHIsupershellsandapartofknownstationaryHIsuper- havere≥gular,notwil≥dlychangingshapesthatarenoticeableand
shellsagain.However,evenintheouterMilkyWaytheexistence have a large velocity extent. All previously known supershells
ofsomeofthesepublishedshellsisdoubtful.Ourmethodisless belongtothisgroup,andthemajorityofshellsfromthisgroup
reliableintheinnerMilkyWay. werealsoidentifiedbythepreviousmethod. Thisisthedefault
All LAB identificationsconnectedto the previouslyknown settingforanyfurtherdiscussion.
HIsupershellshad∆v 9kms 1,P 0.2,P 0.7,and
− 2,min 2,ave
≥ ≥ ≥
P 4.0K.
3
≥
4. Discussion
3.3.Comparisontothepreviousversionofthesearch 4.1.Skydistributionofidentifiedshells
algorithm
We identify 333 shells in the LAB data, which fulfill the fol-
Thepreviousversionofthesearchalgorithmwasappliedtothe lowing criteria : ∆v = 8 kms 1 (the minimum velocity
min −
Leiden-Dwingeloo HI survey (only the northern sky, Ehlerová span); P 0.2, P 0.5(geometricalparameters); and
2,min 2,ave
&Palouš2005).WecomparedcurrentLABidentificationswith P = 4K (the≥visibilitypa≥rameter). Theirpositionsonthesky
3
ourpreviousidentifications. We restrictedourselvestothesec- andinvelocityspaceareshowninFigs. 5and6. EllipsesinFig.
ondquadrant,whichwasfullyobservedinthepreviousversion 6correspondtosizesofshells. Angularsizesofshellsareshown
andwhichdidnotsufferfromshellcrowdingintheinnerGalaxy. inFig. 7. Themajorityofstructuresareelongatedintheldirec-
Wecomparedwhatfractionofshellsidentifiedbytheprevi- tionratherthanin b,whichmaybeexplainedasaconsequence
ousmethod(277in totalin the 2ndquadrant)wasre-identified ofthelowershellcolumndensitiesinhighbdirections.
by the new method with various values of search parameters OnlineTableA.1,availableattheCDS, containsthenames
∆v ,P (theaverageoverlap),P (theminimumoverlap), andpositionsofallidentifiedstructures: thenamewithcoordi-
min 2,ave 2,min
andP (visibilityparameter).InFig. 4weshowthecomparison natesofthecentre;andtheminimumandmaximuml,bandv ,
3 lsr
for wherethestructureisvisible.
Articlenumber,page5of19
Fig.5. Distributionof333identifiedshellsonthesky.Leftpanel:lb-map;rightpanel:lv-map.
Fig.6. IdentifiedHIshells,Hammer-Aitoffprojection,centeredonl=0◦,b=0◦.
4.2.Galacticdistributionofshells of sizes in l and b directions), the expansionvelocity v (cal-
exp
culated as half of the measured velocity extent), the estimated
The kinematic distances of identified HI shells are derived us-
energyinput L neededto create the shell based on the solution
ingtherotationcurveofBrand& Blitz (1993),assuming R =
ofWeaver etal. (1977),assumingthe densityfromKalberla &
8.5 kpc, V = 220 kms 1. We consider only shells in⊙the
− Dedes (2008), and the approximateage of the shell t (based
outer Galax⊙y. We exclude shells found at very low velocities exp
onthesolutionofWeaveretal.1977).
v < 10 kms 1, since identifications at these low velocities
lsr −
| | Figures 8 and 9 show galactic coordinates of shells and
are heavily influenced by the local emission. We also disre-
theirpositionsinthegalacticplane. Atgalactocentricdistances
gardshellsclosetothecentreandanticentredirections(l<20◦,
greaterthan19kpc,thereareshellsonlyinthesecondquadrant,
l > 340◦, 170◦ < l < 190◦)andshellswithveryhighbcoordi-
othersarenearlyempty. Thisisespeciallystrikingforthe third
nates(b > 50◦),sincenoncircularmotionsmaybecomparable
| | quadrant,whichis, fromthegeometricalpointofview,equiva-
toprojectedrotationalmotions. Theseselectioncriteriaconcern
lenttothesecondone.
thefollowinganalysesandfiguresfromFig. 8onwardsonly.
OnlineTableA.2,availableattheCDS,containsthefollow- Figure10 showsthe rv diagram,i.e. the dependenceofthe
ing information about these shells: the galactocentric distance expansionvelocityoftheshellonitsradius. Theexpansionve-
R, the radius of the shell r (calculated as a geometricalmean locityoftheshelliscalculatedas0.5∆v,andtheradiusisthege-
sh
Articlenumber,page6of19
S.EhlerováandJ.Palouš:HIshellsintheLeiden/Argentina/BonnHIsurvey
Fig.7. Angularsizesofidentifiedshells.
Fig. 10. rv diagram of supershells. Evolutionary lines (Weaver
et al. 1977) for three luminosities are overlaid (dotted lines), as well
as three lines of different times (dashed lines), for the density n =
0
0.3cm 3. Differentsymbolsdenoteestimatedenergyinputstoshells,
−
whenrealdensitiesaretakenintoaccount(seetextfortheexplanation):
crosses for L < 0.1 SNMyr−1, open circles for 0.1 SNMyr−1 L
1.0SNMyr−1,trianglesforL>1.0SNMyr−1. ≤ ≤
Calculatedenergyinputsaregivenbydifferentsymbolsin Fig.
10.
The analytical solution (Weaver et al. 1977, lines in
Fig. 10) is overlaid for three different luminosities
(0.1SNMyr 1,1.0SNMyr 1,10.0SNMyr 1),assumingtheISM
− − −
densityn = 0.3cm 3 (whichisanoverestimateforthemajor-
0 −
ity of shells) and forthree differentevolutionarytimes (1 Myr,
10Myr, and100Myr). Thissolutionservesasa guideline,es-
pecially for ages, since the evolutionary age in Weaver et al.
(1977)doesnotdependondensityandluminosity,whilethecal-
Fig.8. Positionsofidentifiedsupershells: thegalactocentricdistance
RandthedistancefromtheGalacticplanez. culatedluminositydependslinearlyonthedensity. Wedetecta
fewshellswithagesbelow5Myr,whichisgivenbytheresolu-
tionofthesurveyandconstraintsonthesizes. Thereisonlyone
shellwithagegreaterthan100Myr. Thislackofoldshellsmay
be explained by dissolution due to random motions and turbu-
lence ordue to destructionby spiralarms, differentialrotation,
andothergalacticforces.
4.2.1. Sizedistributionofshells
Weassumeapower-lawdistributionforsizesofshells
dN(r )
sh = r α. (7)
sh−
dr A
sh
Wecanthencalculatetheaveragesizeofshellsr (d )atagiven
sh hc
heliocentric distance d using observed minimum and maxi-
hc
mumsizesr (d )andr (d ):
min hc max hc
oFfigth.e9.SunDiisstsrihbouwtinonanodftswupoecrsirhcellelsswinitthhegaGlaacltaocctiecntprliacndei.stTahnecepsoosifti8o.n5 r (d ) = RrrmminaxN(rsh)rshdrsh
kpcand15kpcareoverlaid. sh hc RrrmminaxN(rsh)drsh
= α−1r (d )1−(rrmmainx((ddhhcc)))α−2. (8)
ometricmeanofsizesinlandbdirections. Usingtheanalytical α 2 min hc 1 (rmin(dhc))α 1
solution forthe shell evolution(Weaveret al. 1977), we derive − − rmax(dhc) −
the required energy inputs for individual shells and their ages, Since we restrict the minimum and maximum angular size
usingthedensitybasedonthedistributionofKalberla&Dedes on identified shells, r and r must depend on the distance
min max
(2008)andthewarpparametersofLevineetal.(2006).Wefind (seeFig. 11,leftpanel). With knownorassumed r , r , and
sh min
that 11 shells require energyinputs higherthan 1 SNMyr 1. r (assumptionsareconnectedtorestrictionsonangularsizes
− max
∼
Articlenumber,page7of19
1
Q2D 0.1
0.01
8 10 12 14 16 18 20 22
R (kpc)
Fig.12. 2DporosityoftheouterMilkyWay.
Fig.11. Dependenceofminimum(dash-dottedline),average(solid
line),andmaximum(dashedline)radiusoftheshellr asafunctionof
sh
theheliocentricdistanced .
hc calculateσ . WeapplythesamemethodasinPaper1,briefly
gsh
described in the Sect. 4.2.1. It is based on selecting subsets
of detectedstructures),we cancalculate α. Solutionslie in the thatcontaininformationforachosenintervalofheliocentricdis-
interval(2.2,3.1),thebestsolutionisfor2.6.Thisvaluemightbe tancesandsizes. Theradialdistributionoftheshellsurfaceden-
artificiallyflatterthantherealvalue,sinceouridentifyingalgo- sityΣ(R)isbasedonthenumberofshellswiththegalactocentric
rithmformsonebigshellfromtwosmallshellsmorefrequently distanceRcorrectedforthelimitationscausedbyafiniterange
thanviceversa,producingaflattersizespectrum. ofheliocentricdistances.Resultsdependontheselectedinterval
Analternativemethodtocalculatethecoefficientα,usedin ofdistances, butin a particularway: results, whichare consis-
Paper 1, is to take such a subset of identified shells, which in tent with the assumed exponential decrease (i.e. show a high
a certain range of distances contains shells in a given range of correlation between observed numbers of shells with numbers
sizes. Resultsofthismethodcoveranintervalofαandinclude predictedfrom Eq. 11) form a distinct group, while the others
thevalue2.6calculatedhere. Uncertaintiesinthedetermination form another one with a wide spread in values of σ . Good
gsh
ofαarefairlylarge,probablybecauseouridentifyingalgorithm solutionsforσ havetheaveragevalueof(2.8 0.5)kpc.
gsh
±
isbetteratlocalizingstructuresthanatdeterminingtheirprecise After extrapolating solutions for the size distribution of
sizes. shellsandtheradialdependenceoftheshellsurfacedensity,we
Theaveragevalueofαinexternalgalaxies(Bagetakosetal. canestimate thetotalnumberofshells andalsothe porosity of
2011)is 2.9, which is a slightly steepervalue than ours. Their theGalaxy. Theseextrapolationsarenottooprecise,since they
valueisanaveragethroughseveraltypesofgalaxiesandthereis combineallinaccuraciescomingfromerrorsinthederivationof
adependenceofthecoefficientαonthegalaxytype(earlytype αandσ , andtheyalsoincludetheeffectofselectioncriteria
gsh
spiralstendtohavesteeperslopes). AccordingtotheirFig. 28, described in the Sect. 3. Taking the minimum size of a shell
ourvalueof2.6correspondstoScgalaxies. to be 100 pc and the maximum size to be 1 kpc, we come to
The coefficient α is connected to the power-law coefficient theconclusionthatthereshouldbesomethinglike400to1000
βoftheluminosityfunctionofsourcescreatingshells, e.g. OB shellsintheouterGalaxy,andabout2000to5000suchshells
associations inthewholeGalaxy.
The number surface density of HI shells with radii r
Φ(L) L−β. (9) 100 pcinthesolarneighbourhoodisabout4+1 shellsperkshpc2≥.
∝ 2
Apartfromuncertaintiesconnectedwithextra−polating,thereare
AccordingtoOey&Clarke(1997)αandβareconnectedas
intrinsicvariationsinthesurfacedensity(seee.g. Fig. 9),most
α=2β 1. (10) probablyconnectedtospiralarms. Thederivedvalueofsurface
− densityishigherthan—thoughnotincomparableto—theaver-
Therefore,β 1.8,whichissomewhatflatterthantheexpected agevalueofthesamequantityforanumberofexternalgalaxies
luminosity fu∼nctionof OB associations in the Milky Way (2.0; (THINGSgalaxies,Bagetakosetal.2011). Thetypicalvalueis
seee.g.McKee&Williams1997). (0.1-1)shellsperkpc2,thoughtherearesomegalaxiesinthatpa-
perthatreachhighervalues. Thisdiscrepancymaybecausedby
eitherthelessstrictconditionsputontheidentificationmethod
4.2.2. Radialdistributionofshells forHIshellsonoursideandstricterconditionsontheirs(among
others,Bagetakosetal.(2011)demandedquiteahightempera-
Weassumethattheshellsurfacedensityfollowsanexponential
turecontrastfortheirshellsandregularellipticalshapes),orby
distribution
adifferentpointofview:frominsideintheMilkyWayandfrom
Σ(R)=Σ0e−(R−R⊙)/σgsh (11) outsideforexternalgalaxies.Theinsideviewismuchmoresen-
sitivetoshellsthatdidnotyetbreakthroughtheHIdisc. Onthe
whereΣ(R)isthesurfacedensityofHIshells. other hand, the surface density of OB associations in the solar
Typicalsizesofshells,hencetherelativeproportionofiden- neighbourhoodis about7 perkpc2 (McKee & Williams 1997),
tified to total number of shells, change with heliocentric dis- which is comparable to our value: we would instead expect a
tance, and therefore to get intrinsic values of Σ(R) we have to higher number of shells than OB associations, since the typi-
correct the observed values. With the corrected value we can callifetime of a shellis longerthan foran OB association, but
Articlenumber,page8of19
S.EhlerováandJ.Palouš:HIshellsintheLeiden/Argentina/BonnHIsurvey
clustering of OB associations may decrease the numberof OB Ehlerová,S.&Palouš,J.2005,A&A,437,101,paper1
associationspershell. Elmegreen,B.G.2012,inIAUSymposium,Vol.284,IAUSymposium,317–
Theporosity Q, whichis a ratioof thesurfaceoccupiedby 329
Gooch,R.E.1997,PASA,14,106
shellstothetotalsurface(the2Dporosity)orthevolumeoccu-
Hartmann,D.&Burton,W.B.1997,AtlasofGalacticNeutralHydrogen
piedbyshellstothetotalvolume(the3Dporosity),isderived.In Heiles,C.1979,ApJ,229,533
theinnerGalaxytheporosityascalculatedfromderiveddistribu- Kalberla,P.M.W.,Burton,W.B.,Hartmann,D.,etal.2005,A&A,440,775
tions,islarge,muchlargerthan1,whichpredictsthesignificant Kalberla,P.M.W.&Dedes,L.2008,A&A,487,951
Kalberla,P.M.W.,McClure-Griffiths, N.M.,Pisano,D.J.,etal.2010,A&A,
overlappingofshells.TheporosityoftheouterGalaxyissmaller
521,A17
(see Fig. 12), where values lower than 0.01 are reached at
Kerp, J., Winkel, B., Ben Bekhti, N., Flöer, L., & Kalberla, P. M. W. 2011,
∼
galactocentricdistances of 20 kpc. Local valuesat the solar AstronomischeNachrichten,332,637
∼
neighbourhoodareQ =0.7andQ =0.4(assumingacylin- Levine,E.S.,Blitz,L.,&Heiles,C.2006,ApJ,643,881
2D 3D
derwith height1 kpc)forshells with radii r (0.1,1.0)kpc. McClure-Griffiths,N.M.,Dickey,J.M.,Gaensler,B.M.,&Green,A.J.2002,
sh ∈ ApJ,578,176
Error boxes are similar to those in the case of number surface
McKee,C.F.&Williams,J.P.1997,ApJ,476,144
density. Porosity (especially Q3D) is mostly dependent on the Oey,M.S.&Clarke,C.J.1997,MNRAS,289,570
maximumsize of the shell, which we assume to be 1 kpc, and Thilker,D.A.,Braun,R.,&Walterbos,R.M.1998,A&A,332,429
thereforevaluesquotedhereapproachtherealvalues,sincethe Weaver,R.,McCray,R.,Castor,J.,Shapiro,P.,&Moore,R.1977,ApJ,218,
377
contributionofsmallbubblesisnegligible.
Zavagno,A.,Deharveng,L.,Comerón,F.,etal.2006,A&A,446,171
Daigle et al. (2007) calculate the partial porosity of shells
with radii r (5,40) pc in the region of the Perseus arm
sh
Q =0.007+0.0∈25. We can do the same thing by extrapolating
3D 0.003
our solutions−to small shells and get the result Q = 0.003.
3D
Thisissurprisinglygoodagreement.Ifthisisnotacoincidence,
itmeansthatwebothdetectthesametypeofobjects-indifferent
evolutionaryphases-eventhoughweusesubstantiallydifferent
approaches. Our somewhat lower value could mean that some
ofthesmallobjectswillnotevolveintolargestructures(suchas
bubblescreatedbysinglesupernovaexplosions).
5. Conclusions
We haveidentified333HIshellsintheLeiden/Argentina/Bonn
HIsurveyoftheMilkyWayusinganautomaticsearchingalgo-
rithm. Theadvantageofthisapproachistheuniformityofcon-
ditionsthroughouttheMilkyWay. Ourmethodisquitesensitive
forlocating“somethinginteresting”,while itis notaseffective
formeasuringtheprecisesizesoftheshells.
Wediscoveredtheasymmetrybetweenthesecondandthird
Galactic quadrants in the distribution of shells at large galac-
tocentric distances. At distances greater than 19 kpc there are
shells only in the second quadrant. The third quadrant, which
isanequivalenttothesecondonefromthegeometricalpointof
view,containsnoshellsatthesegalactocentricdistances.
Because of crowding and distance ambiguity in the Milky
Way, we base the following conclusions on shells in the outer
Galaxy. We foundthattheirradialdistributiondecreasesexpo-
nentially on a scale length of 2.8 kpc, and their size distribu-
tion is a power law with the coefficient of 2.6 (correspond-
∼
ingtoapower-lawcoefficientoftheluminosityfunctionofOB
associations 1.8). The surface density of shells with radii
<0.1,1.0>k∼pcinthesolarneighbourhoodis 4kpc 2.
−
∼
Acknowledgements. ThisstudyhasbeensupportedbytheCzechScienceFoun-
dation grant 209/12/1795 and by the project RVO: 67985815. This research
madeuseofNASA’sAstrophysicsDataSystem.Theauthorswouldliketothank
theanonymousrefereeforhelpfulproposalsandJimDaleandtheA&Alanguage
editorJoliAdamsforthehelpwiththemanuscript(anyremainingineleganceis
purelyourown).
References
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Brand,J.&Blitz,L.1993,A&A,275,67
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A&A–shell,OnlineMaterialp10
AppendixA: Onlinetables
TableA.1containsobservedpropertiesofHIshells.Column1is
arunningnumberofthestructure,Col.2isthenameofstructure
(GSH +galacticcoordinatesofthecentreandtheradialveloc-
ity). Theremainingcolumnsdescribetherangesincoordinates,
wherethestructureisvisible: Col. 3 andCol. 4the longitude,
Col. 5 and Col. 6 the latitude, Col. 7 and Col. 8 the radial
velocity.
TableA.2containsderivedpropertiesofHIshells. Column
1isarunningnumberofthestructure,Col. 2isthenameofthe
structure(GSH+galacticcoordinatesofthecentreandtheradial
velocity). Col. 3 is the galactocentricdistance of the structure
(usingtherotationcurveofBrand&Blitz1993),Col.4isthera-
diusoftheshell(calculatedasthegeometricmeanofdimensions
inlandb),Col. 5istheexpansionvelocity(calculatedasahalf
ofthevelocityextentofthestructure).Columns6and7areesti-
matesoftheneededenergyinputintotheshellandtheevolution-
ary time based on the modelof Weaveret al. (1977). Shellsin
theinnerGalaxyareexcludedfromthistable,asareshellsfound
atverylowvelocities v <10kms 1,shellsclosetothecentre
lsr −
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andanticentredirections(l < 20◦, l > 340◦, 170◦ < l < 190◦),
andshellswithveryhighbcoordinates(b >50◦).
| |