The search for inner polar disks with integral field spectroscopy: the case of NGC 2855 and NGC 7049

0.75 MB·English

by  L. Coccato

Astronomy&Astrophysicsmanuscriptno.coccato2007 c ESO2008
(cid:13)
February5,2008
The search for inner polar disks with integral field spectroscopy:
⋆
the case of NGC 2855 and NGC 7049
L.Coccato1,E.M.Corsini2,3,A.Pizzella2,andF.Bertola2
1 KapteynAstronomicalInstitute,UniversityofGroningen,Postbus800,9700AVGroningen,TheNetherlands
2 DipartimentodiAstronomia,Universita`diPadova,vicolodell’Osservatorio3,I-35122Padova,Italy
7
0
3 ScuolaGalileianadiStudiSuperiori,viaVIIIFebbraio2,I-35122Padova,Italy
0
2
February5,2008

n
a ABSTRACT
J
1 Context.Thepresenceofnon-circularandoff-planegasmotionsisfrequentlyobservedintheinnerregionsofdiskgalaxies.
1 Aims.We have measured with integral-field spectroscopy the surface-brightness distribution and kinematics of the ionized gas in
NGC2855andNGC7049.Thesetwoearly-typespiralgalaxieswereselectedtopossiblyhostakinematically-decoupled gaseous
1 componentinorthogonalrotationwithrespecttothegalaxydisk.
v Methods.Wehave modeled theionized-gas kinematics and distributionof both galaxies assuming that the gaseous component is
1 distributedeitherontwoorthogonally-rotatingdisksorinasingleandstronglywarpeddisk.
4 Results.Inbothgalaxiesthevelocityfieldanddistributionoftheinnergasareconsistentwiththepresenceofaninnerpolardisk.In
NGC2855itcorrepondstotheinnermostandstronglywarpedportionofthemaindisk.InNGC7049itisacentralandgeometrically-
3
decoupleddisk,whichisnestedinthemaindisk.
1
0 Keywords.galaxies:kinematicsanddynamics–galaxies:spirals–galaxies:structure–galaxies:individual:NGC2855,NGC7049
7
0
/
h 1. Introduction inclined anomalousorbits of a triaxial bulge or a bar, which is
p
tumblingaboutitsshortaxis,arebothviablemechanismtobuild
o- Inarecentpaperwepointedthatabout50%ofbrightunbarred a orthogonally-rotating disk. According to these different sce-
galaxiesshowa remarkablegasvelocitygradientalongthe op-
r narios, it can be either a geometrically-decoupled structure or
st ticalminoraxis(Coccatoetal. 2004).Thisphenomenonis ob- the innerportionof a stronglywarpedandlargergaseousdisk,
a servedallalongthesequenceofdiskgalaxiesfromS0’stoSm’s. respectively.Therefore,constrainingthestructuralpropertiesof
: Sinceminor-axisvelocitygradientsareunexpectedifthegasis asampleofIPDswillgivethecluestounderstandtheprocesses
v
movingontocircularorbitsinadiskcoplanartothestellarone,
i drivingtheirformation(seeSil’chenko2006forareview).
X we concluded that non-circular and off-plane gas motions are
Over the course of the last few years, we have undertaken
notrareintheinnerregionsofdiskgalaxies.Furthersupportto
r
a thispictureisgivenbytheanalysisofthevelocityfieldsoflarge aprogramaimedatdetectingIPDsindiskgalaxiesusinglong-
slit spectroscopic observations(Bertola et al. 1999;Sarzi et al.
samplesoflenticulargalaxies(Sarzietal.2006),early(Falco´n-
2000;Corsini et al. 2002,2003;Coccato et al. 2004,2005).In
Barroso et al. 2006) and late-type spirals (Ganda et al. 2006)
long-slit spectra the kinematic signature of an IPD is the pres-
observedwithintegral-fieldspectroscopy.
enceofacentralvelocitygradientalongthediskminoraxisand
The presenceof a velocitygradientalong the minoraxis is
a zero-velocity plateau along the disk major axis, respectively.
characteristicofgalaxieshostinganinnerpolardisk(IPDhere-
On the contrary, the presence of a gas velocity gradient along
after). IPDs are small disks of gas and/or stars (R 300 pc),
≈ bothmajorandminoraxisischaracteristicof gasmovingonto
which are located in the center of lenticular and spiral galax-
ellipticalorbitsinthediskplaneofatriaxialbulge(deZeeuw&
iesandarerotatinginaplaneperpendiculartothatofthemain
Franx1989;Corsinietal.2003).Ourgoalwastoidentifygalax-
disk of their host. We call them IPDs instead of inner polar
ies,whicharegoodcandidatestohostaIPD,tobefollowedup
rings(Sil’chenko2006)sincethereisnoclearcutevidencethey
with integral-fieldspectroscopyathighspatialresolutioninor-
have an anular structure. Most of these orthogonally-rotating
dertodeterminethesizeandorientationofsuchakinematically-
disks have been discovered in last few years (Corsini et al.
decoupledcomponent.
2003; Sil’chenko & Afanasiev 2004; Shalyapina et al. 2004;
Sil’chenko&Moiseev2006;Coccatoetal.2005).Theacquisi- In this paper we present the analysis of the bidimensional
tionofexternalgasviamergingoraccretiononnearlypolaror- kinematicsanddistributionoftheionized-gascomponentofthe
bitsbyapre-existinggalaxy,andthetransferofgasontohighly- twomostpromisingobjectswefoundinourinvestigation.They
arethenearbyearly-typespiralsNGC2855andNGC7049.For
Sendoffprintrequeststo:L.Coccato, both galaxies the presence of a major-axis velocity plateau to-
e-mail:[email protected] gether with a minor-axis velocity gradient is suggestive of an
⋆ Based on observations carried out at the European Southern IPD as discussed by Corsini et al. (2002, 2003). The reader is
Observatory(ESO73.B-0803). refereed to them for a summary of the main properties of the
2 Coccatoetal.:InnerpolardisksinNGC2855andNGC7049
Table1.Instrumentalsetup
Parameters Channels
1 2 3 4
Grism HR red HR red HR red HR orange
Ordersortingfilter GG475 GG475 GG475 GG435
Spatialresolution( fiber 1) 0.67 0.67 0.67 0.67
′′ −
Reciprocaldispersion(Åpixel 1) 0.58 0.58 0.58 0.62
−
Readoutnoise(e ) 4.5 3.2 3.2 3.7
−
Gain(e ADU 1) 1.9 1.8 1.7 2.0
− −
Wavelengthrange(Å) 6300–8700 6300–8700 6300–8700 5200–7600
InstrumentalFWHMatHα(kms 1) 68 68 68 70
−
Table2.Observinglog of the ESO Recipe Execution pipeline1. Cosmic rays and bad
pixelswereidentifiedandcleanedusingstandardMIDAS1rou-
tines.Wecheckedthatthewavelengthrebinningwasdoneprop-
Galaxy Date Observingblock Exposuretime
erlybymeasuringthedifferencebetweenthemeasuredandpre-
NGC2855 27Feb2004 154289 2 19min dicted wavelength for the brightest night-sky emission lines in
×
NGC2855 27Feb2004 154292 2 19min the observed spectral ranges (Osterbrock et al. 1996). The re-
×
NGC7049 13May2004 154293 2 19min
sulting accuracy in the wavelength calibration is better than 5
×
NGC7049 14May2004 154296 2×19min km s−1. The intensity of the night-skyemission lineswas used
Notes–Duringtheexecutionoftheobservingblock154293(13 to correct for the differentrelative transmission of the VIMOS
May 2004) the data of channel 4 were lost because the Grism channels. The contributionof the night-skyemission lines was
ExchangeUnitofchannel4wasoutoforder. determined from a number of spectra by fitting a Gaussian to
each line and a straightline to the adjacentcontinuum.We se-
lected spectra where the night-skyemission lines did notover-
two galaxies. The paper is organized as follows. The integral- lap with the [N II]λλ6548,6583and Hα emission lines of the
fieldspectroscopicobservationsanddatareductionaredescribed galaxy.Thennight-skyemission lines weresubtractedfromall
inSect.2.Wepresentandmodeltheionized-gaskinematicsand theavailablespectra.Itwasnotpossibletosubtractthecontribu-
distribution in Sect. 3 and 4, respectively. Our conclusions are tion of the night-skycontinuumalone since both galaxiescov-
discussedinSect.5. ered the entire field of view of the integral field unit. The pro-
cessedspectrawereorganizedinadatacubeusingthetabulated
correspondencebetween each fiber and its position in the field
2. Observationsanddatareduction
of view. From the two exposures of each observing block we
builtasingledatacube.Infact,thetwospectratakenbythesame
Theintegral-fieldspectroscopicobservationsofNGC2855and
fiberwerecoaddedaftercheckingthattherewasnopointingoff-
NGC 7049 were carried out with the Very Large Telescope
setbetweenthetwoexposures.Thiswasdonebycomparingthe
(VLT)atthe EuropeanSouthernObservatory(ESO) in Paranal
positionof the intensity peaksof the two reconstructedimages
(Chile) on February 26–27, 2004 and May 13–14, 2004. The
obtained by collapsing the datacubes along the wavelength di-
Unit Telescope 3 (Melipal) mounted the Visible Multi Object
rection. Finally, for each galaxy we coadded the two available
Spectrograph (VIMOS) in the Integral Field Unit (IFU) con-
datacubesbyusingtheintensitypeaksofthefluxmapsasaref-
figuration. The field of view of the four VIMOS channels was
erenceforthealignment.Inthiswayweproducedasingledat-
27 27 and it was projected onto a microlenses array. This
′′ ′′
× acube to be analyzed in order to derive the surface brightness
wascoupledtoopticalfiberswhichwererearrangedonalinear
andkinematicmaps.
setofmicrolensestoproduceanentrancepseudoslittothespec-
trograph. The pseudoslit was 0.95 wide and generated a total
′′
of 1600 spectra covering the field of view with a spatial reso- 3. Kinematicsanddistributionoftheionizedgas
lutionof0.67perfiber.Eachchannelwasequippedwitheither
′′
the HR red or HR orange high resolution grism and a thinned 3.1.Analysis
and back illuminatedEEV44 CCD with 2048 4096pixelsof
15 15µm2.Thedetailsoftheinstrumentalse×tuparegivenin In the coadded spectrum of the galaxy datacube we measured
× the position, full width at half maximum (FWHM), and uncal-
Table1.
ibrated flux of the Hα and [N II]λ6583 emission lines by fit-
For each galaxy we obtained 4 19-min exposures. They
× ting a Gaussian to each line and a straight line to the adjacent
were taken in service mode by executingtwo differentobserv-
continuum. This includes the contributions of both galaxy and
ingblocksoftwoexposureseach,aslistedinTable2.Different
night sky. No double-peaked emission line was observed. We
quarzandarclamp spectrawere takenaftereveryobjectexpo-
neglected the [N II]λ6548 line because it was not clearly de-
suretoensureaccurateflatfieldcorrectionandwavelengthcali-
tected in all the spectra, and we averaged the spectra of adja-
bration,respectively.DuringobservationsseeingFWHMranged
centfibersintheouterregionswheretheintensityoftheHαand
between0.8and1.0asmeasuredbytheESODifferentialImage
′′ ′′ [N II]λ6583 lines was low. We performed a 2 2 binning in
MeteoMonitor. ×
order to reach a minimum signal-to-noise ratio S/N = 10. To
For each VIMOSchannelall the spectra were traced, iden-
tified, bias subracted, flatfield corrected, corrected for relative 1 ESOREXandMIDASaredevelopedandmaintainedbytheEuropean
fibertransmission,andwavelengthcalibratedusingtheroutines SouthernObservatory
Coccatoetal.:InnerpolardisksinNGC2855andNGC7049 3
Fig.1.Mapsoftheionized-gaskinematicsofNGC2855derived Fig.2.SameasinFig.1butforNGC7049.
fromtheHα(toppanels)and[NII]λ6583(bottompanels)emis-
sionlines.Thefieldofviewofeachpanelis27 27 .Ineach
′′ ′′
×
panel the spatial coordinates with respect to the galaxy center
are given in arcsec. East is up and North is right. The ranges
are indicated at the bottom of each panel. The white color is
usedforbinswherenomeasurementwasobtainedonaccountof
a signal-to-noiseratio below the selected thresolddueto either
faintemissionlineorpoorfibertransmission.Leftpanel:Surface
brightnessin arbitrarylinear units. Central panel: Heliocentric
line-of-sightvelocityinkms 1 withoutapplyinganycorrection
−
for galaxy inclination. Isovelocity contours correspond to ve-
locitiesafterthesubtractionofthesystemicvelocity.Thezero-
velocity contour is highlighted with a thicker solid line. Right
panel:Line-of-sightvelocitydispersioninkm s 1 correctedfor
−
instrumentalvelocitydispersion.
assessthedataqualityweshowsomeexamplesoftheprofileof
the [N II]λ6583 emission line and its Gaussian fit in different
regionsofthetwogalaxies.TheyareplottedinFigs.3and4for
NGC2855andNGC7049,respectively.Thecentralwavelength
ofthefittingGaussianwasconvertedintoline-of-sightvelocity
in the optical convention. The standard heliocentric correction
Fig.5.Radialprofilesobtainedfromtheisophotalanalysisofthe
wasapplied.TheGaussianFWHMwascorrectedfortheinstru-
[N II]λ6583 surface-brightness map measured for NGC 2855.
mentalFWHMandthenconvertedintotheintrisicline-of-sight
Top panel: Surface brightness calculated adopting an arbitrary
velocity dispersion. The flux of the fitting Gaussian was con- zeropointof20magarcsec 1.Middlepanel:Ellipticity.Bottom
−
verted into surface brightnessaccordingthe fiber area. No flux
panel:Positionangle.Ineachpanelthesolidlinecorrespondsto
calibrationwasperformed.
thepredictionofthemodelwhichassumesthattheionized-gas
The result is shown in Figs. 1 and 2 for NGC 2855 and
component is distributed onto two orthogonal disks (see Sect.
NGC7049,respectively.
4.2),whilethedashedlinecorrespondstothepredictionforthe
Tostudythedistributionoftheionizedgaswefittedelliptical
singlediskmodel(seeSect.4.1).
isophotesto the [N II]λ6583surface brightnessmap by means
oftheIRAF2 taksELLIPSE.Wefirstfittedellipsesallowingthe
center to vary to test the regularity of the gas distribution. We
[NII]λ6583surface-brightnessmapareshowninFigs.5and6
found no evidence of a varying center with the fits for NGC
forNGC2855andNGC7049,respectively.
2885. The ellipse fits were then repeated with the ellipse cen-
ter fixed. This was not the case of NGC 7049. The position of
center was constant within the errorsonly for r . 4 , while it 3.2.Results
′′
changed by 2 at larger radii. The radial profiles of the sur-
′′
≈ InNGC2855theionizedgasisconcentratedinthenucleusand
face brightness, ellipticity and position angle derived from the
its distribution at larger radii follows the spiral pattern of the
2 IRAFisdistributedbyNationalOpticalAstronomyObservatories, galaxy (Fig. 1). The abrupt change of ellipticity (from 0.05 to
which is operated by Association of Universities for Research in 0.45)andpositionangle(from105◦ to155◦)oftheellipsesfit-
Astronomy,Inc.undercooperativeagreementwiththeNationalScience tingthe[NII]λ6583surface-brightnessmap(Fig.5)arethepho-
Foundation. tometricsignaturesofsuchadistributionofthegaseouscompo-
4 Coccatoetal.:InnerpolardisksinNGC2855andNGC7049
Fig.3. Centralpanel:Mapsofthesurfacebrightnessandline-of-sightvelocityfieldderivedfromthe[NII]λ6583emissionlinefor
NGC2855.Thefieldofview,orientation,rangesandisovelocitycontoursareasinFig.1.Outerpanels:The[NII]λ6583emission
lineprofile(solidline)anditsGaussianfit(dashedline)indifferentpositionsofthefieldofview.Lineprofilesarenormalizedto
thepeakintensitytoallowcomparison.
regionitshowsaregularrotationaroundthegalaxyminoraxis.
The velocity dispersion increases from the outer parts towards
thecenter.Itpeaksto 120km s 1 inHαandto 150km s 1
− −
≈ ≈
in[NII]λ6583andissystematicallysmallerforHαwithrespect
to[NII]λ6583(Fig.1).
InNGC7049the gasis mostlyconcentratedin the nucleus
and in a ring-like structure (Fig. 2). This corresponds to the
prominentdustlane,whichisvisibleintheopticalimagesofthe
galaxy(Sandage&Bedke1994,Panel74).Thephotometricpro-
filesderivedfromthe[NII]λ6583surface-brightnessmap(Fig.
6) allowstoconstrainthedifferentshapeandorientationofthe
nuclear(ǫ 0.1,PA 85 )andring(ǫ 0.3,PA 55 )regions.
◦ ◦
≈ ≈ ≈ ≈
The gas velocity field of NGC 7049 is similar to that of NGC
2855,displayingaS-shapeddistortioninthenucleusandregular
rotationaroundthegalaxyminoraxisatlargeradii.Thevelocity
dispersionissystematicallylowerinHαthanin[NII]λ6583.In
the nuclear region shows a central dip surroundedby a double
peakwhereitreaches 120kms 1 inHαand 170kms 1 in
− −
≈ ≈
[N II]λ6583.Outwardsit decreasessmoothly with radius(Fig.
2).
Fig.6.SameasinFig.5butforNGC7049. In both galaxies the line-of-sight velocities measured from
Hαand[N II]λ6583areconsistentwithinthemeasurementer-
rors. For this reason we modeled only the velocity field and
nent.Thegasvelocityfield iscomplex.Itis characterizedbya surface-brightness distribution derived from the [N II]λ6583
S-shaped zero velocity line in the nuclear region. In the outer line.Typicalerrorsontheline-of-sightvelocityandvelocitydis-
Coccatoetal.:InnerpolardisksinNGC2855andNGC7049 5
Fig.4.SameasFig.3butforNGC7049.
persionswere 10 and 20 km s 1, includingthe uncertainties thebinsizeof0.335 0.335(i.e.,asubsamplingfactorof2 2
− ′′ ′′
≈ × ×
duetowavelengthcalibration. relativetotheVIMOSpixelscale). Thisresultedthebestcom-
promise between good samplingand reasonablecomputational
time.Themodelwasrebinnedonaspatialscaleof0.67 0.67
′′ ′′
4. Analysisofthevelocityfieldoftheionizedgas and the seeing effects were taken into account by co×nvolv-
ing the model with a Gaussian kernel with FWHM = 1 .
ThefieldofviewofVIMOS/IFUallowsustomapthevelocity ′′
Finally,the modelwas comparedto the observedvelocityfield
fieldofthekinematically-decoupledgaseouscomponent,aswell
andsurface-brightnessdistribution.
as that of the gas residing in the main disk of the galaxy.As a
firststep,wefitthewholevelocityfieldbyassumingthatthegas
is moving onto circular and coplanar orbits (Sec. 4.1). To this 4.1.Singlerotatingdisk
aimwemaskedthecentralregion,wheretheS-shapeddistorsion
4.1.1. Modelcalculation
oftheisovelocitycountoursisobserved.Weadoptedtheresults
of the circular velocity model to constrain the orientation and The model of the gas velocity field is generated assuming that
inclinationofthemaindiskofthegalaxy.Thenwemodeledthe the ionized-gascomponentis movingontocircularorbitsin an
complex gas kinematics and surface-brightness distribution of infinitesimally thin disk with a negligible velocity dispersion.
theinnerregions.Weassumedthatthegaseouscomponentwas Hereafterthiswillbeconsideredasthemaindiskofthegalaxy.
distributedeitherontwodistinctandorthogonally-rotatingdisks Let(X,Y,Z) be Cartesian coordinateswith the originin the
(Sec.4.2)orontoasingleandstronglywarpeddisk(Sec.4.3). centerofthegaseousdisk,theY axisalignedalongthelineof
In our analysis we fitted iteratively a model to the ob- nodes, and the disk plane confin−ed to the (X,Y) plane. We can
served velocity field and surface-brightness distribution of the consider the gas motion in this plane by introducing the polar
[N II]λ6583 line using a non-linear least-squares minimiza- coordinates(R,φ)with origininthecenterofthegaseousdisk.
tion method. It was based on the robust Levenberg-Marquardt ItisR = √X2+Y2 (orR = (X X )2+(Y Y )2 ifthecoor-
c c
methodimplementedbyMore` etal.(1980).Theactualcompu- − −
dinatesofthekinematicandgpeometriccenterofthegaseousdisk
tation wasdoneusing the MPFITalgorithmimplementedbyC.
aredifferent)andcosφ=Y/Rwithφcountedcounter-clockwise
B. Markwardt under the IDL environment3. During each itera-
from Y axis. We assume that the gas circular velocity V at a
tion the modelwas calculated on a subsampled pixelgrid with −
givenradiusRis
3 The updated version of this code is available on 2 R
V(R)= V arctan (1)
http://cow.physics.wisc.edu craigm/idl/idl.html π max R
∼ h
6 Coccatoetal.:InnerpolardisksinNGC2855andNGC7049
whereV andR arethemaximalvelocityandascaleradius,
max h
respectively.This empiricalfunctionhas been provedto repro-
duce fairly well the shape of optical rotation curves with the
smallestnumberoffreeparameters(Courteau1997).
Wenowprojectthevelocityfieldofthegaseousdiskonthe
plane of the sky. Let (x,y,z) be Cartesian coordinateswith the
origininthecenterofthegaseousdisk,thex axispointingeast-
−
wards,they axispointingnorthwards,andthez axisalongthe
− −
lineofsightdirectedtowardtheobserver.Theskyplaneiscon-
finedtothe(x,y)plane.Inthereferenceframeofthesky(x,y,z),
thegaseousdiskisinclinedbythezenithalandazimuthalanglei
andθ,respectively.Theseanglescorrespondtotheinclinationof
thedisk(withi=0 correspondingtotheface-oncase)andposi-
◦
tionangleofitslineofnodes(withθcountedcounter-clockwise
fromthe y axisandθ = 0 correspondingto the case with the
◦
−
lineofnodespointingnorthward).Thetransformationoftheco-
ordinatesof the main disk from its reference frame (Z = 0) to
thereferenceframeofthesky(x,y,z)isgivenby
Fig.7.ModelofthevelocityfieldofNGC2855(upperpanels)
x X
y =R Y (2) and NGC 7049 (lower panels) with a single rotating disk. The
    field of view, orientation, ranges and isovelocity contours are
z  0  asinFig. 1. Leftpanel:Observedvelocityfield. Centralpanel:
where Model.Rightpanel:Residuals.
cosθcosi sinθ cosθsini
R= sinθcosi cosθ sinθsini . (3) Table3.Modelwithasinglerotatingdisk
− − 
whichlea−dssitnoitheus0ualequactoisoinsintheskyplane(x,y): Parameter NGC2855 NGC7049
x = Xcosθcosi+Ysini Xc[pixel] −0.4±0.5 −0.2±0.3
Y [pixel] 0.4 0.6 0.6 0.3
y = Xsinθcosi+Ycosθ Vc [kms 1] 189±3 6 −223±0 5
− sys − ± ±
θ[ ] 116.6 0.8 58.1 0.7
Theionized-gasvelocitymeasuredalongthelineofsightat ◦ ± ±
i[ ] 42 4 60 2
agivenskypoint(x,y)is V◦ [kms 1] 344 ±22 459 ±13
max − − ± − ±
v(x,y)=V(R)sinicosφ+Vsys (4) Rh[′′] 3.9±0.7 3.5±0.4
where the circular velocity V is given in Eq. 1, and V is the
sys
systemicvelocityofthegalaxy.
Intherestofthepaperweadoptaspositionangleandincli-
TheparametersofourmodelarethemaximalvelocityV ,
max nationof themaingaseousdisksofNGC2855andNGC7049
scaleradiusR ,inclinationiandpositionangleθofthegaseous
h thevalueswederivedfromthekinematicmodel.
disk,andthesystemicvelocityV ofthegalaxy.Thebest-fitting
sys
modelwasobtainedbymaskingtheregionofthe observedve-
locityfieldcharacterizedbytheS-shapeddistorsionoftheisove- 4.2.Orthogonally-rotatingdisks
locitycountours.Theareaofthemaskedregionwas9 11pixels
× 4.2.1. Modelcalculation
and7 8pixelsinNGC2855andNGC7049,respectively.
×
The model of the gas velocity field is generated assuming that
therearetwodifferentionized-gascomponentswhicharemov-
4.1.2. Results
ingontocircularorbitsintwoorthogonally-rotatingdisks.They
Thevelocityfieldsofthebest-fittingdiskmodelsarecompared are the main galactic disk studied in Sect. 4.1 and an inner or-
to observedones in Fig. 7. Best-fitting parametersare given in thogonal disk. Both disks have the same center, are infinitesi-
Table3. mallythin,andhaveanegligiblevelocitydispersion.
For the gaseous disk of NGC 2855, the position angle and Let (X ,Y ,Z ) be Cartesian coordinates with the origin in
′ ′ ′
inclination measured at large radii with the isophotal analysis thecenteroftheorthogonaldisk,theY axisalignedalongthe
′
−
(Sec. 3.1) are not consistent with that derived from the kine- lineofnodes(definedastheintersectionbetweentheplaneofthe
matic model(Tab.3). We explainsuch a discrepancyas due to orthogonaldiskandthatofthemaindisk),andtheplaneofthe
the presence of the patchy spiral arm pattern, which character- orthogonaldisk confined to the (X ,Y ) plane. In the reference
′ ′
izes the surface brightness distribution of the [N II]λ6583 line frameofthemaindisk(X,Y,Z),the orthogonaldiskisinclined
at r & 4 . This makes the photometricparameters not reliable bythezenithalandazimuthalangleδandγ,respectively.These
′′
todescribethegeometryofthedisk.Thecoordinatesofthedisk anglesaretheinclinationoftheinnerdisk(withδ = 90 corre-
◦
centersderivedinthephotometricandkinematicanalysis(Tab. spondingto the case of an orthogonaldisk) and position angle
3)coincidewithinapixel. ofitslineofnodes(withγcountedcounter-clockwisefromthe
The position angle, inclination and center derived from the Y axis and γ = 0 corresponding to the case with the line of
◦
−
photometricandkinematicanalysisofthegaseousdiskofNGC nodes of the orthogonaldisk pointing in the same direction as
7049areconsistentwithintheerrors. the line of nodesof the main disk). A sketch of the orthogonal
Coccatoetal.:InnerpolardisksinNGC2855andNGC7049 7
diskinthereferenceframes(X,Y,Z)and(X ,Y ,Z )isshownin The line of nodesof the orthogonaldisk, defined as the in-
′ ′ ′
Figure8. tersectionbetweenthediskplaneandtheskyplane,is
Weassumedthatthecircularvelocityofthegaseouscompo-
Z =R x+R y+R z=0 (14)
nentinthemaindiskandintheorthogonaldiskaregivenbyEq. ′ ′3,1 ′3,2 ′3,3
1and whereR denotestheinverseofR.Intheskyplaneitis
′
2 R
VOD(R′)= πVm′axarctanR′, (5) R′3,1x+R′3,2y=0 (15)
′h
and therefore the position angle θ of the apparent major axis
′
respectively.Vm′ax andR′h arethemaximalvelocityandscalera- of the orthogonal disk with respect to the y axis is given by
diusofthe orthogonaldisk.ItisR′ = √X′2+Y′2 andcosφ′ = tanθ′ =−R′3,2/R′3,1.Thisis −
Y /R withφ countedcounter-clockwisefromY axis.
′ ′ ′ ′
− sinθ(sinδcosγcosi+cosδsini)+cosθsinδsinγ
Thefluxradialprofileofthemaingaseousdiskwasassumed tanθ = (16)
tobeexponential ′ cosθ(sinδcosγcosi+cosδsini) sinθsinδsinγ
−
FMD(R)= F0+F1e−R/RF. (6) Theionized-gasvelocitymeasuredalongthelineofsightat
agivenskypoint(x,y)is
For the flux radialprofile of the orthogonaldisk we assumeda
v (x,y)f (x,y)+v (x,y)f (x,y)
truncatedexponentialfunction v(x,y)= MD MD OD OD (17)
f(x,y)
FOD(R′)=(0F0′ +F1′e−R′/R′F ffoorrRR′′ >≤RR′0′0 (7) where
v (x,y) = V (R)sinicosφ+V (18)
MD MD sys
where R correspondsto the radialextensionof the orthogonal
′0 f (x,y) = F (R)/cosi (19)
gaseouscomponent. MD MD
We now project the velocity field of the two gaseous disks aretheline-of-sightvelocityandsurfacebrightnessofthemain
ontheplaneofthesky.Thetransformationofthecoordinatesof disk,
the inner polar disk from its reference frame (X ,Y ,Z ) to the
′ ′ ′
referenceframeofthemaindisk(X,Y,Z)isgivenby vOD(x,y) = VOD(R)sini′cosφ′+Vsys (20)
f (x,y) = F (R)/cosi (21)
X X OD OD ′
′
Y =R1Y′  (8) are the line-of-sight velocity and surface brightness of the or-
Z  Z′  tshuorfgaocneablrdiigshkt,naensds.f(x,y)= fMD(x,y)+ fOD(x,y)istheobserved
where
Forthemain diskwe adoptedthe inclinationi andposition
cosγcosδ sinγ cosγsinδ angleθderivedinSect.4.1andweassumedtheinnerdisktobe
R1= sinγcosδ cosγ sinγsinδ . (9) orthogonalwith respect to the main one within 1◦. Therefore
− −sinδ 0 − cosδ  tmheaipnadraismk,etVem′rsaxo,fRo′hu,rFm0′,oFd1′e,lRar′Fe,VRm′0,axi,′R(wh,itFh08,9F◦1,≤±a|ni′d−RiF|≤for9t1h◦e)
Thetransformationofthecoordinatesofthemaindiskfrom andθ fortheorthogonaldisk,andthesystemicvelocityV of
′ sys
its reference frame (X,Y,Z) to the reference frame of the sky thegalaxy.
(x,y,z)isgivenby Westartedfittingamodelonlytotheobserved[NII]λ6583
surface-brightenessdistribution (Fit #1 hereafter).Then we fit-
x X tedamodelonlytotheobservedvelocityfieldadoptingforthe
y =R2Y  (10) maindiskthemaximalvelocityVmaxandscaleradiusRhderived
whzere Z  isnitiSoencat.n4g.l1eaθn′ddeforirvtehdeinorFthito#g1on(Falitd#is2khtehreeainftcelri)n.aFtiionnalil′y,anwdepfiot--
tedsimultaneouslyboththevelocityfieldandsurface-brightness
cosθcosi sinθ cosθsini distribution(Fit#3hereafter).
R2= sinθcosi cosθ sinθsini . (11)
− − 
 −sini 0 cosi  4.2.2. Results
Thetransformationofthecoordinatesoftheorthogonaldisk
The surface-brightness distribution of the best-fitting models
fromitsreferenceframe(X ,Y ,Z )tothereferenceframeofthe
′ ′ ′ built in Fit #1 are shown in Fig. 9. The radial profiles of the
sky(x,y,z)isgivenby
surface brightness, ellipticity, and position angle derived from
themodelarecomparedto thosefromthe isophotalanalysisin
x X
′ Fig. 5 and Fig. 6 for NGC 2855 and NGC 7049, respectively.
y =R Y (12)
   ′  The velocity field of the best-fitting models built in Fit #2 are
whzereR=RZ′2R1. isthyofiwenldinofFtihge.1b1e.stT-fihettisnugrfmacoed-eblrsigbhutinlteisnsdFiistt#ri3buartieocnoamnpdavreeldotco-
The inclinationi ofthe orthogonaldisk withrespectto the observationsinFig.12and13.
′
skyplaneisgivenbythedirectioncosinebetweenthez axisof The surface-brightness distribution and velocity field of
thelineofsightandtheZ axisoftheorthogonaldisk − NGC2885cannotbeinterpretedasduetopresenceoftwodif-
′
− ferentorthogonally-rotatingdisksofgas.Thelargestdeviations
cosi =R =cosδcosi sinδcosγsini. (13) intheresidualmapsareobservedinthenuclearregion.
′ 3,3
−
8 Coccatoetal.:InnerpolardisksinNGC2855andNGC7049
Fig.9. Model of the surface-brightness distribution of NGC
2855 (upper panels) and NGC 7049 (lower panels) with two
orthogonally-rotatingdisks (Fit #1).The field of view, orienta-
tion,rangesandisovelocitycontoursareasinFig.1.Leftpanel:
Observedsurface-brightnessdistribution.Centralpanel:Model.
Rightpanel:Residuals.
Fig.8. Panel A: Orientation of the plane (X,Y) of the main
diskof thegalaxywith respectto thesky plane(x,y).PanelB:
Orientationoftheplane(X ,Y )oftheorthogonaldiskwithre-
′ ′
specttotheplane(X,Y)ofthemaindisk.
For NGC 7079 the surface-brightness distribution of the
modelbuiltinFit#1isconsistentwithobservationssuggesting Fig.10. The velocity field of the orthogonal-rotating disk of
thepresenceofaninnergaseouscomponentwhichisorthogonal NGC 7049, as obtained from Eq. 22 The field of view of the
withrespecttothemaingaseousdiskofthegalaxy.However,as panelis9′′ 9′′.EastisupandNorthisright.Therangeisindi-
×
in the case of NGC 2855, the observations are not reproduced catedatthebottomofthepanel.Isovelocitycontourscorrespond
bythemodelsbuiltinFit#2and#3.Weconcludethatthecircu- tovelocitiesafterthesubtractionofthesystemicvelocity.
larvelocitycurveoftheorthogonaldiskdiffersfromEq.5.We
derivethevelocityfieldoftheorthogonaldiskas Table4.Modelwithtwoorthogonally-rotatingdisks(Fit#1)for
NGC7049
v(x,y)f(x,y) v (x,y)f (x,y)
v = − MD MD (22) Parameter
OD
f
OD
F 0.01 0.01
0 ±
F 1.6 0.2
1 ±
andshowit inFig. 10. We tested differentparametricprescrip- RF [′′] 15±2
tions(Brandt1960;Freeman1970;Bertolaetal.1991;Persicet F0′ 0.01±0.01
F 22 1
al.1996)tofitthevelocityfieldassumingtheionizedgasison 1′ ±
R [ ] 1.13 0.08
circularorbitson a plane.But noneof them gave better results ′F ′′ ±
γ[deg] 23 4
than that obtained adopting Eq. 5. This suggests that proba- ±
δ[deg] 91 1
blythegaskinematicsplottedinFig.10isnotcharacterized ±
R [ ] 3.6 0.1
by circular motions. The limited radial extension of the re- ′0 ′′ ±
giondoesnotallowustoadoptmorecomplicatedfunctions
as well as a larger number of free parameters to take into
accountfornon-circularmotions.
Coccatoetal.:InnerpolardisksinNGC2855andNGC7049 9
Fig.11.ModelofthevelocityfieldofNGC2855(upperpanels) Fig.13.SameasinFig.12butforNGC7049.
and NGC 7049 (lower panels) with two orthogonally-rotating
disks (Fit #2). The field of view, orientation,rangesand isove-
sky(x,y,z)isgivenbyEq.12,whereδandγarereplacedbyδ
locity contours are as in Fig. 1. Left panel: Observed velocity n
andγ ,respectively.Similarly,theinclinationi andtheposition
field.Centralpanel:Model.Rightpanel:Residuals. n ′n′
angle θ of the apparentmajor axis of the n th wire are given
n′′ −
by
cosi =cosδ cosi sinδ cosγ sini. (23)
′n′ n − n n
and
sinθ(sinδ cosγ cosi+cosδ sini)+cosθsinδ sinγ
tanθ = n n n n n.(24)
n′′ cosθ(sinδ cosγ cosi+cosδ sini) sinθsinδ sinγ
n n n n n
−
Weassumedthatthecircularvelocityofthegaseouscompo-
nentinthewarpeddiskandisgivenby
2 R
V (R )= V arctan ′n′, (25)
WD ′n′ π m′′ax R
′h′
whereV andR arethemaximalvelocityandscaleradiusof
m′′ax ′h′
the warped disk. It is R′n′ = Xn′′2+Yn′′2 and cosφ′n′ = Yn′′/R′n′
withφ′n′countedcounter-clockpwisefromYn′′−axis.
Theionized-gasvelocityandfluxmeasuredalongthelineof
sightatagivenskypoint(x,y)where M wiresareobservedare
givenrespectivelyby
Fig.12.Modelofthesurface-brightnessdistribution(upperpan-
els) and velocity field lower panels) of NGC 2855 with two v(x,y)= nM=1vn(x,y)fn(x,y) (26)
orthogonally-rotatingdisks (Fit #3). The field of view, orienta- P M f (x,y)
tion,rangesandisovelocitycontoursareasinFig.1.Leftpanel: n=1 n
Observeddata.Centralpanel:Model.Rightpanel:Residuals. and P
f(x,y)= Mf (x,y), (27)
n
4.3.Warpeddisk where
4.3.1. Modelcalculation v (x,y) = V (R )sini cosφ +V (28)
n WD ′n′ ′n′ ′n′ sys
The modelofthe gasvelocityfield is generatedapproximating is the line-of-sightvelocity and f (x,y) is the line-of-sightflux
n
thewarpedgasdistributionwithaseriesofconcentricandcircu- of the n th wire. Eq. 27 implies that all the wires observed at
larwires. a given−position on the sky give the same contribution to the
Let(X ,Y ,Z )beCartesiancoordinateswiththeoriginin observed surface brightness. This is supported by the fact that
n′′ n′′ n′′
the centerof the n th wire, the Y axisalignedalongthe line all the wiresobservedat a givenpositionare supposedto have
− n′′−
of nodes defined as the intersection between the plane of the similar radii, warping and twisting. Moreover, this choice al-
wire(X ,Y )andthatofthe maindisk(X,Y).Inthe reference lowed to better reproduce the inhomogeneous distribution of
n′′ n′′
frameofthesky(x,y,z),thewireisinclinedbythezenithaland surfacebrightnessduetothespiralarmsofNGC2855andring-
azimuthalangleδ andγ ,respectively. like structureof NGC 7049.The attemptto modelthe surface-
n n
Thetransformationofthecoordinatesofthen thwirefrom brightnessdistributionadoptinganexponentialradialprofilewas
−
its reference frame (X ,Y ,Z ) to the reference frame of the notsuccessful.
n′′ n′′ n′′
10 Coccatoetal.:InnerpolardisksinNGC2855andNGC7049
Table5.ModelwithawarpeddiskforNGC2885
Parameter
V [kms 1] 373 16
max − − ±
R [ ] 4.3 0.6
h ′′ ±
k [ ] 3.4 0.1
0 ′′ ±
k [ ] 0.82 0.03
1 ′′ ±
k [deg] 79.0 2
2 − ±
c [deg] 85.7 0.7
c0[deg/ ] 10.11 ±0.07
V1 [km′′s 1] − 18±85 3
sys − ±
We evaluatedthewarpingandtwistingofthegaseouscom-
ponentfrom the radial profiles of ellipticity and position angle
obtained from the isophotal analysis of the surface-brightness
mapofthe[NII]λ6583lineinSect.3.1.Wefoundthatthefol-
lowingempiricalfunctions
Fig.14. Model of the velocity field of NGC 2855 (upper pan-
k R k k els)andNGC7049(lowerpanels)withawarpeddisk.Thefield
δn(R′n′)= −π2 arctan ′n′k− 0!+ 22 (29) of view, orientation, ranges and isovelocity contours are as in
1 Fig.1.Leftpanel:Observedvelocityfield.Centralpanel:Model.
and Rightpanel:Residuals.
γ (R )=c +c R (30)
n ′n′ 0 1 ′n′
reproducedfairlywelltheradialprofilesofδ andγ wederived
n n
from Eq. 23 and Eq. 24 by adopting for i and θ the values of
the main disk fitted in Sect. 4.1. This constraints the warped
structuretobeconfinedintheinnerregionofthegalaxy.
Thereforethe parametersof ourmodelare V andR for
m′′ax ′h′
the circular velocity, k , k , and k for warping, c and c for
0 1 3 0 1
twisting, and V for systemic velocity. Forty wires were used
sys
tobuildthewarpedstructureandcoverthewholevelocityfield
withatleastonewireforeachpixelbin. Fig.15. Model of the surface-brightness distribution of NGC
2855with a warpeddisk.The field ofview,orientation,ranges
and contours are as in Fig. 1. Left panel: Observed surface-
4.3.2. Results
brightness distribution. Central panel: Model. Right panel:
Thevelocityfieldsofthebest-fittingmodelsandtheirresiduals Residuals.
are are shown in Fig. 14. Best-fitting parameters are given in
Table5.
The warped model is able to reproduce the S-shaped zero in a ring-like structure. The ionized-gas velocity field of both
velocity line we observed in the nuclear region of NGC 2855 galaxiesis characterizedby a S-shapedline of zero velocity.It
withvelocityresidualslowerthanafewtensofkms−1.Atlarge isalignedwiththediskminoraxisintheinnerregions(r . 8′′)
radii the position angle and inclination of the warped disk are andwiththediskmajoraxisatlargerradii.Thisremarkablemis-
consistent with those of the main disk of the galaxy. At small alignement between the kinematical and photometrical major
radii,thewarpeddiskisalmostorthogonaltothemaindisk(Fig. axesgivesrisetothecentralvelocitygradientandzero-velocity
15). plateau observed along the disk minor and major axis, respec-
The velocity field of NGC 7049 can not be interpreted as tively.Thesekinematicalfeaturescannotbeexplainedasdueto
due to presenceof a single gaseouscomponentdistributedin a non-circulargasmotionsintheprincipalplaneofthediskcaused
warpeddisk.Infact,thedeviationsoftheresidualmaparelarger bythetriaxialpotentialofthebulgeorabar(deZeeuw&Franx
thanthosewefoundforthemodelswithbothasinglediskand 1989;Corsinietal.2003).
twoorthogonally-rotatingdisks.
Asafirst stepwe modeledthevelocityfield,exceptforthe
inner region where the S-shaped distorsion of the isovelocity
countoursisobserved.Weassumedthatthegasismovingonto
5. Conclusions
circular orbits in an infinitesimally thin disk with a negligible
Wehavemeasuredwithintegral-fieldspectroscopythesurface- velocitydispersion.Thisallowedustoconstraintheorientation
brightness distribution and kinematics of the ionized gas in andinclinationofthemaindiskofthegalaxy.Thenwemodeled
NGC2855andNGC7049.Thesetwoearly-typespiralgalaxies theionized-gaskinematicsanddistributionofboththeinnerand
wereselectedtopossiblyhostanIPDonthebasisoftheanalysis outer regions. We assumed that the gaseous component is dis-
oftheirlong-slitspectra(Corsinietal.2002,2003). tributed either on two orthogonally-rotating disks or in a sin-
In NGC 2855 the ionized-gas distribution peaks in the nu- gleandstronglywarpeddisk.Inbothgalaxiesthevelocityfield
cleus and follows the patchy spiral pattern of the galaxy. In anddistributionoftheinnergasareconsistentwiththepresence
NGC 7049 the gas is mostly concentrated in the nucleus and of an IPD, which is in orthogonal rotation with respect to the