Are spiral galaxies optically thin or thick?

13 Pages·0.46 MB·English

by  E. M. Xilouris

A&A manuscript no.
(will be inserted by hand later) ASTRONOMY
AND
Your thesaurus codes are:
ASTROPHYSICS
03(11.16.1; 11.19.2; 11.09.4; 09.04.1) 1.2.2008
Are spiral galaxies optically thin or thick?
E. M. Xilouris1,2, Y. I. Byun3, N. D. Kylafis4,2, E. V. Paleologou4,2, and J. Papamastorakis4,2
1 University of Athens,Department of Physics, Section of Astrophysics, Astronomy & Mechanics, 157 83 Athens,Greece
2 Foundation for Research and Technology-Hellas, P.O. Box 1527, 711 10 Heraklion, Crete, Greece
3 Center for Space Astrophysics & Department of Astronomy,Yonsei University,Seoul 120-749, Korea
4 University of Crete, Physics Department,P.O. Box 2208, 710 03 Heraklion, Crete, Greece
9 Received date / Accepted date
9
9
1
Abstract. The opacity of spiral galaxies is examined by Galactic extinction law, indicating a universal dust be-

n modellingthedustandstellarcontentofindividualgalax- haviour.
a ies.The threedimensionalmodelthat weuse assumesex-
J
ponential distributions for the dust and the stars in the
3 disk, while the R1/4 law is used to describe the bulge. In
1
thismodel,bothabsorptionandscatteringbythedustare

Key words: galaxies: photometry – galaxies: spiral –
1 taken into account. The model is applied to five late-type
galaxies: ISM – ISM: dust, extinction
v spiralgalaxies(NGC4013,IC2531,UGC1082,NGC5529
8 and NGC 5907) using their optical (and near infrared for
5
IC 2531) surface photometry. For these galaxies we have 1. Introduction
1
determined the scalelengths and scaleheights of the stars
1 The amount and the way that dust is distributed within
0 and the dust in the disk, the bulge characteristics, the
spiralgalaxiesaswellasitsextinctioneffectsonthegalac-
9 inclination angle and the face-on optical depth. Compu-
tic starlighthas been a matter ofdebate overthe last few
9 tation of the dust masses, as well as the extinction as a
/ years.SinceDisney,DaviesandPhillipps(1989)proposed
h function of the wavelength, are also reported.
thatspiralgalaxiesmaybeopticallythick,alongseriesof
p
Havinganalyzeda totalof sevengalaxiesthus far, the papershasbeenpublishedbydifferentauthors(seee.g.the
-
o five galaxies mentioned above plus UGC 2048 and NGC introduction ofXilouris et al.1997)with conclusionsthat
r 891 presented in (Xilouris et al. 1997, 1998), we are able oftendifferwidely.Recentpaperstendtosupporttheidea
t
s to draw some general conclusions, the most significant of of optically thin/moderately opaque spiral galaxies. This
a
: which are: means that galaxies are either optically thin throughout
v
1) The face-on central optical depth is less than one in their disks or that they are optically thin in the outer re-
i
X all optical bands, indicating that typical spiral galaxies gionsandmoderatelyopaqueatthecenter(e.g.Giovanelli
r like the ones that we have modelled would be completely et al. 1994, 1995; Kodaira & Yamashita 1996; Ro¨nnback
a transparent if they were to be seen face-on. & Shaver 1997; Domingue et al. 1998; Moriondo et al.
2) The dust scaleheight is about half that of the stars, 1998;Kuchinskietal.1998;Gonz´alezet al.1998).Onthe
which means that the dust is more concentrated near the otherhand,recentfarinfrared/submillimeterobservations
plane of the disk. of spiral galaxies give a direct picture of the dust distri-
3)Thedustscalelengthisabout1.4timeslargerthanthat bution and a good estimate of the total amount of dust
of the stars and the dust is more radially extended than (e.g. Alton et al. 1998a, 1998b; Haas et al. 1998; Bianchi
the stars. et al. 1998; Kru¨gel et al. 1998). These observations indi-
4) The dust mass is found to be about anorderof a mag- cate that the cold dust component (∼ 10−20 K) that is
nitude more than previously measured using the IRAS now detected, boosts the dust masses about an order of
fluxes, indicating the existence of a cold dust component. magnitude higher than previouslyestimated by IRAS ob-
Thegas-to-dustmassratiocalculatedisclosetothe value servations. On the other hand, a more radially extended
derived for our Galaxy. dustdistributioncomparedto thatofthe starsis derived.
5) The derived extinction law matches quite well the In our studies we perform detailed modelling of spiral
galaxies, aiming at the determination of the parameters
that describe the three-dimensional dust distribution in
Send offprint requests to: [email protected] these galaxies. For the three dimensional distribution of
2 E. M. Xilouris et al.: Arespiral galaxies optically thin or thick?
stars and dust we use simple and smoothgeometries (e.g. UGC 1082 is an Sb Hubble type spiral galaxy with
axisymmetricexponentialsforthestarsandthedustinthe a redshift of 0.009353 ± 0.000017 (Giovanelli & Haynes
disk and the R1/4 law for the bulge). There is no doubt 1993). Using the formulae given by Zombeck (1990), we
that in reality spiral galaxies are clumpy with small and derive a distance of 37 Mpc (assuming a value of H0 =
largescalestructure(e.g.spiralarmswiththedusttrailing 75 km s−1 Mpc−1) for this object. The B luminosity is
the armsinapatchyway).Onehastokeepinmindthose M = -18.4 mag. Visual inspection of this galaxy (see
B
oversimplifications. The edge-on picture though that we Fig.1)showsanedge-onconfigurationofarelativelyfaint
use cancels out most of the variation along the line of galacticdiskandabrightbulgewithanobviousdustlane
sight and allows us to use simple mathematical functions passing through the disk.
in order to get a mean description of the galaxies. We NGC 5529 is an Sc Hubble type spiral galaxy at a
have verified this with detailed computations (Misiriotis distance of 29.6 Mpc (Shaw et al. 1990) with M = -
B
et al. in preparation) which take into account the spiral 19.6mag.Visualinspectionofthis systemshowsagalaxy
structure. which is not quite edge-on. Despite this geometry, a dust
The two galaxies (UGC 2048 and NGC 891) that we lane is very well revealed and thus our axisymmetric
have already modelled (Xilouris et al. 1997;hereafter Pa- model, which is able to deal with any inclination angle,
per I and Xilouris et al. 1998; hereafter Paper II) us- can be applied.
ing the radiative transfer model of Kylafis & Bahcall NGC 5907 is a well studied Sc galaxy at a distance of
(1987; hereafter KB87), show low values of the optical 11Mpc(vanderKruit&Searle1982).It’sBluminosityis
depth in the face-on orientation, indicating low opacities M = -19.1 mag. Several photometric studies have been
B
for these galaxies, while the predicted dust masses and reportedaboutthisgalaxyandthestellardistributionhas
the dust distributions are now supported by the far in- been obtainedinseveralbands.InvanderKruit&Searle
frared/submillimeter observations mentioned above. Our (1982),U,JandFbanddatawerefittoatruncatedexpo-
aimistocontinuethiskindofstudywithasmanygalaxies nential disk in the R direction and a sech2 type function
as possible in various orientations and thus improve the in the z direction. The inclination angle was reported to
statistics. In this paper we do the analysis of the edge-on be 87◦, while the scalelength and scaleheight were found
late-type spiral galaxies NGC 4013, IC 2531, UGC 1082, to be 5.7 kpc and 0.43 kpc respectively in the J-band.
NGC 5529 and NGC 5907 (see Fig. 1). Barnaby and Thronson (1992) used H-band data to fit
NGC 4013 is an Sbc Hubble type spiral galaxy at a the stellar distribution of this galaxy. The disk was fitted
distance of 11.6Mpc (Bottema 1995)and a B-band lumi- with an exponential in the R direction with a scalelength
nosityM =-18.1mag.Photometricpropertiesofthe2D of4.0kpc andasechtypefunctioninthez directionwith
B
stellardistributionofthisgalaxycanbefoundinBottema ascaleheightof0.43kpc.Thebulgewaswelldescribedby
(1995), where a disk with exponential scalelength of 2.3 amodifiedHubble profile.Morrisonetal.(1994)obtained
kpcandasech2 scaleheightof0.7kpcisreportedtofitthe good quality R-band data and fitted the disk with expo-
F-banddata.Barnabyetal.(1993)presentbulgeanddisk nential (in both directions) functions with a scalelength
decomposition ofan H-band image,where anexponential of 4.81 kpc and a scaleheight of 0.43 kpc. The inclination
◦
diskwithscalelength2.5kpcandscaleheight0.2kpcanda angle was reported to be 86.7 .
modified-Hubble type bulge witheffective radius0.24kpc In Sect. 2 we describe the observations and the data
arefitted.Observationsofthisgalaxyinthe21cmneutral reduction, in Sect. 3 we briefly discuss the model and in
hydrogenline(Bottema1995;1996)showahighlywarped Sect.4wepresentthemodelresultsforthefivegalaxies.A
gas disk, while the optical image of this galaxy (also pre- discussionfollowsinSect.5withsomegeneralconclusions.
sentedin Fig.1) showsthat the stellardistribution in the A quick summary is presented in Sect. 6.
disk is not warped, at least not to the degree that should
affecttheaxisymmetricmodellingthatwedo[seealsothe
2. Observations and data reduction
optical warp curves presented in Florido et al. (1991)].
IC 2531 is an Sb Hubble type spiral galaxy at a dis- Observations of the four galaxies NGC 4013, UGC 1082,
tance of 22 Mpc (Shaw et al. 1990)andM = -18.8 mag. NGC 5529 and NGC 5907 were made at Skinakas obser-
B
Two attempts at modelling IC 2531 have been reported vatory in Crete, using the 1.3 m telescope. The detector
(Wainscoat et al. 1989; Just et al. 1996). The model used that was used was a Thomson 1024 × 1024 CCD camera
wasalongthelinesofKB87,butinamoresimplifiedform, with19µmpixels,installedattheprimefocusofthef/7.7
dealing with absorption by dust and neglecting multiple Ritchey-Cretien telescope. This arrangement corresponds
′ ′
scattering effects. Also, only a local fit was made in sev- to 0.39 arcsec/pixel and a field of view of 6.7 ×6.7. For
eral strips parallel to the disk’s minor axis. Furthermore, the observations of NGC 5907 we used a focal reducer
a bulge component was not included in the model. Our that is installed on the telescope in order to increase the
work presents a global fit to the observed data using the field of view. This arrangementproduced a larger field of
′ ′
full radiative transfer model described in KB87 and more view (∼ 13 ×13) and a scale of 0.75 arcsec/pixel (us-
realistic (bulge included) distributions. ing the same camera as above). The chip was run with
E. M. Xilouris et al.: Arespiral galaxies optically thin or thick? 3
Table 1. Observational data.
′′ ∗
Galaxy Pixel size Observing seeing ( ) rms (mag) Total exposuretime (min)
′′
(pc) nights B V I B V I
NGC4013 0.39 (22) 20 Jun 95 1.3 0.04 0.02 0.02
0.39 (22) 21 Jun 95 1.0 0.03 0.02 0.02 140 40 25
UGC1082 0.39 (70) 09 Sep 94 1.4 0.04 0.03 0.03 60 50 20
NGC5529 0.39 (56) 04 Aug97 1.2 0.03 0.03 60 40
NGC5907 0.75 (40) 07 May 97 1.8 0.03 0.03 0.02 30 20 10
∗
rms deviations from theleast squares fit between catalogue magnitudes and calibrated magnitudes for the standard stars.
a gain of 3.33 e−/ADU and showed a readout noise of +L exp(−7.67B1/4)B−7/8, (1)
b
−
5.6e .Exposureswere made throughB,V, I broadband
filters. The B and V passbands are comparable to those with hs and zs being the scalelength and scaleheight of
of Johnson’s photometric system, while the I passband is the disk and
comparable to that of Cousin’s photometric system. The
R2+z2(b/a)2
effective wavelength of the system (filter and camera) in B = , (2)
p R
each passband is 0.443µm, 0.564µm and 0.809µm for the e
B, V and I bands respectively. In order to calibrate the with R being the effective radius of the bulge and a and
e
images, we used standard stars and a photometric proce- b the semi-major and semi-minor axis respectively. Here
dure described in detail in Paper I. In Table 1 we present L and L are the normalization constants for the stel-
s b
some data concerning these observations. lar emissivity of the disk and the bulge respectively. The
The optical observations of IC 2531 were made in relations
March, 1991 with the 1m Australian National University
(ANU)telescopeattheSidingSpringObservatory(SSO). I =2L h , (3)
s s s
The CCD system was equipped with an EEV CCD of
576 × 380 giving a pixel size of 0.56 arcsec at the f/8 and
Cassegrain focus. Graham’s (1982) standard stars were
I =5.12L R , (4)
observedforcalibration.Observationsweremadethrough b b e
B, V and I broad band filters with exposure times of
givethecentralvalueforthesurfacebrightnessofthedisk
1000, 600, and 500 seconds respectively. The seeing was
and the bulge respectively, if the model galaxy is seen
′′
estimated to be 2 . The near-infraredobservations of the
edge-on and there is no dust.
same galaxy were made in February, 1995 with the 2.3 m
Fortheextinctioncoefficientweuseadoubleexponen-
ANU telescope at SSO using CASPIR (Cryogenic Array
tial law, namely
Spectrometer/Imager). The instrument was installed at
thef/18CassegrainfocusandwasequippedwithanSBRC R |z|
κ (R,z)=κ exp − − , (5)
InSb256×256detectorgivingapixelsizeof0.5arcsecfor λ λ (cid:18) h z (cid:19)
d d
itsfastcameramode.ThestandardJ filterandamodified
K filter (Kn), whose long wavelength edge is tailored to where κλ is the extinction coefficient at wavelength λ at
exclude much of the thermal emission, were used for the thecenterofthediskandhdandzdarethescalelengthand
imaging observations. The observation sequence included scaleheight respectively of the dust. The central optical
asmanyskyexposuresasthegalaxyinordertofollowthe depth of the model galaxy seen face-on is
fast changing sky emissions. Several standard stars were
τf =2κ z . (6)
observed during the same night. λ λ d
For a more detailed description of all the parameters,
3. Model the reader is referred to Sect. 4 of Paper I.
Theradiativetransfermodelthatwehaveusedisthat
The stellar emissivity (luminosity per unit volume) that described in KB87 (see also Paper I). For computational
we use consists of an exponential (in both radial and ver- reasons,asinPapersI&II,theradiativetransferwasper-
tical directions) disk and a bulge described by the R1/4 formedinsideacylinderwithradiusR =3max(h ,h )
max s d
law, namely andhalfheightof6max(z ,R ),sothatpracticallyallthe
s e
galactic light as well as the dust are included. A Henyey-
R |z| Greensteinphasefunctionhasbeenusedforthescattering
L(R,z)=L exp − −
s (cid:18) h z (cid:19) of the dust (Henyey & Greenstein 1941). The values for
s s
4 E. M. Xilouris et al.: Arespiral galaxies optically thin or thick?
Table 2. Global model fit parameters for NGC 4013.
Parameter Units I band V band B band
Is mag/arcsec2 17.29 ±0.05 19.08 ±0.04 19.60 ±0.06
zs kpc 0.20 ±0.01 0.22 ±0.01 0.19 ±0.01
hs kpc 1.76 ±0.1 1.94 ±0.1 2.55 ±0.1
I mag/arcsec2 10.49 ±0.13 11.73 ±0.11 12.60 ±0.14
b
Re kpc 1.61 ±0.06 1.42 ±0.04 1.46 ±0.05
b/a – 0.42 ±0.01 0.44 ±0.01 0.41 ±0.01
τf – 0.48 ±0.01 0.67 ±0.01 0.89 ±0.01
λ
z kpc 0.11 ±0.01 0.13 ±0.01 0.13 ±0.01
d
h kpc 2.60 ±0.1 2.45 ±0.1 2.62 ±0.3
d
θ degrees 89.6 ±0.1 89.7 ±0.1 89.9 ±0.1
Table 3. Global model fit parameters for IC 2531.
Parameter Units K band J band I band V band B band
Is mag/arcsec2 16.49 ±0.12 17.45 ±0.35 18.24 ±0.04 19.48 ±0.05 20.34 ±0.07
zs kpc 0.45 ±0.02 0.44 ±0.10 0.43 ±0.01 0.40 ±0.01 0.43 ±0.01
hs kpc 5.04 ±0.1 4.96 ±0.3 5.05 ±0.1 5.22 ±0.1 6.78 ±0.1
I mag/arcsec2 10.39 ±0.37 10.97 ±0.40 11.00 ±0.20 11.85 ±0.20 13.40 ±0.30
b
Re kpc 2.00 ±0.24 1.97 ±0.10 1.57 ±0.08 1.23 ±0.08 1.96 ±0.15
b/a – 0.68 ±0.03 0.69 ±0.02 0.65 ±0.02 0.65 ±0.02 0.63 ±0.02
τf – 0.02 ±0.01 0.06 ±0.02 0.22 ±0.01 0.30 ±0.01 0.40 ±0.01
λ
z kpc 0.22 ±0.03 0.20 ±0.07 0.21 ±0.01 0.23 ±0.01 0.27 ±0.01
d
h kpc 8.00 ±0.3 8.08 ±0.6 8.43 ±0.2 8.18 ±0.2 8.88 ±0.3
d
θ degrees 89.6 ±0.2 89.7 ±0.2 89.6 ±0.2 89.6 ±0.2 89.6 ±0.2
Table 4. Global model fit parameters for UGC 1082.
Parameter Units I band V band B band
Is mag/arcsec2 19.02 ±0.11 20.50 ±0.07 21.29 ±0.09
zs kpc 0.44 ±0.02 0.47 ±0.02 0.44 ±0.03
hs kpc 4.13 ±0.2 4.43 ±0.1 4.57 ±0.2
I mag/arcsec2 9.42 ±0.08 10.98 ±0.10 12.17 ±0.09
b
Re kpc 1.34 ±0.12 1.30 ±0.14 1.44 ±0.16
b/a – 0.59 ±0.01 0.64 ±0.01 0.63 ±0.01
τf – 0.17 ±0.01 0.27 ±0.02 0.34 ±0.02
λ
z kpc 0.29 ±0.02 0.27 ±0.02 0.27 ±0.03
d
h kpc 5.47 ±0.4 5.78 ±0.3 5.55 ±0.4
d
θ degrees 89.7 ±0.1 89.7 ±0.1 89.7 ±0.1
the anisotropy parameter g and the albedo ω have been 4. Results
taken from Bruzual et al. (1988). Our task has been to
findthosevalues ofthe parametersinEqs.(1)-(6)which
In Tables 2 through 6, we give the parameters of the best
createimages ofthe modelgalaxiesas close aspossible to
fit models to the observeddataalongwith their 95%con-
the images of the observedgalaxies.For the model fitting
fidenceintervalsforNGC4013,IC2531,UGC1082,NGC
techniques that we use, the reader is referred to Papers I
5529 and NGC 5907 respectively (for Table 7 describing
and II.
NGC 891 see Sect. 5). Using the values of the parame-
ters that describe the stellar anddust distributions of the
galaxies,givenintheabovetables,wehavecreatedmodel
imagesandhavecomparedthemwiththeobservedimages
E. M. Xilouris et al.: Arespiral galaxies optically thin or thick? 5
Table 5. Global model fit parameters for NGC 5529.
Parameter Units I band V band
Is mag/arcsec2 17.13 ±0.05 18.42 ±0.04
zs kpc 0.42 ±0.01 0.43 ±0.01
hs kpc 4.30 ±0.1 4.59 ±0.1
I mag/arcsec2 10.98 ±0.06 12.25 ±0.07
b
Re kpc 1.95 ±0.01 1.95 ±0.01
b/a – 0.59 ±0.01 0.58 ±0.01
τf – 0.42 ±0.01 0.65 ±0.01
λ
z kpc 0.37 ±0.01 0.32 ±0.01
d
h kpc 7.70 ±0.2 7.10 ±0.1
d
θ degrees 87.2 ±0.1 87.4 ±0.1
Table 6. Global model fit parameters for NGC 5907.
Parameter Units I band V band B band
Is mag/arcsec2 17.49 ±0.02 18.99 ±0.02 19.86 ±0.03
zs kpc 0.32 ±0.01 0.34 ±0.01 0.34 ±0.01
hs kpc 3.86 ±0.1 4.91 ±0.1 5.02 ±0.1
I mag/arcsec2 9.38 ±0.04 10.80 ±0.04 11.88 ±0.05
b
Re kpc 1.02 ±0.01 1.01 ±0.01 0.93 ±0.01
b/a – 0.34 ±0.01 0.34 ±0.01 0.45 ±0.01
τf – 0.30 ±0.01 0.49 ±0.01 0.55 ±0.01
λ
z kpc 0.10 ±0.01 0.11 ±0.01 0.13 ±0.01
d
h kpc 5.30 ±0.3 5.29 ±0.2 5.30 ±0.2
d
θ degrees 87.2 ±0.1 87.2 ±0.2 87.0 ±0.2
Table 7. Global model fit parameters for NGC 891.
Parameter Units K band J band I band V band B band
Is mag/arcsec2 15.41 ±0.13 16.01 ±0.11 17.43 ±0.03 18.89 ±0.05 19.81 ±0.06
zs kpc 0.34 ±0.01 0.43 ±0.01 0.38 ±0.01 0.42 ±0.01 0.43 ±0.01
hs kpc 3.87 ±0.1 3.86 ±0.1 4.93 ±0.1 5.48 ±0.2 5.67 ±0.2
I mag/arcsec2 8.32 ±0.54 9.35 ±0.16 10.38 ±0.11 10.97 ±0.22 11.42 ±0.32
b
Re kpc 0.86 ±0.05 0.87 ±0.05 1.97 ±0.06 1.51 ±0.09 1.12 ±0.09
b/a – 0.76 ±0.04 0.71 ±0.08 0.54 ±0.01 0.54 ±0.01 0.60 ±0.02
τf – 0.09 ±0.01 0.21 ±0.01 0.52 ±0.01 0.85 ±0.01 1.00 ±0.01
λ
z kpc 0.25 ±0.03 0.25 ±0.02 0.24 ±0.01 0.29 ±0.01 0.31 ±0.02
d
h kpc 8.33 ±0.4 8.32 ±0.4 7.54 ±0.1 7.68 ±0.2 8.01 ±0.3
d
θ degrees 89.6 ±0.1 89.6 ±0.1 89.7 ±0.1 89.8 ±0.2 89.8 ±0.2
(see Figs. 1 and 2). In Fig. 1 the I-band observations of axis)andphotometricallyaveragedimagesofthegalaxies,
all five galaxies are presented (NGC 4013, IC 2531, UGC whicharealsothe imagesthatwereusedforthe modelfit
1082, NGC 5529 and NGC 5907 from top to bottom). In (see Paper I). In each plot, the horizontal axis represents
Fig. 2 we show the model images of these galaxies in the the offset (in kpc) along the vertical direction, with zero
I-band with the same scale and sequence as in Fig. 1 so lyingonthemajoraxisofthe disk.Theverticalaxisgives
that a direct comparison can be made between the two the surface brightness (in mag/arcsec2). Realdata arein-
figures. In Figs. 3-7 we give a more detailed comparison dicated by stars, while the model is shown as a solid line
between model and observation for each galaxy and each for each profile. The six profiles in each plot are vertical
filter by showing vertical cuts along the minor axis. For cuts at six different distances along the major axis. The
this demonstration we use the ‘folded’ (around the minor cutsareatdistances0,0.5hI,1hI,1.5hI,2hI and2.5hI and
s s s s s
6 E. M. Xilouris et al.: Arespiral galaxies optically thin or thick?
Fig.1.I-bandobservationsofthegalaxiesNGC4013,IC2531, Fig. 2. I-band models of the galaxies NGC 4013, IC 2531,
UGC 1082, NGC5529 and NGC 5907 (top to bottom). UGC 1082, NGC 5529 and NGC 5907 (top to bottom).
are plotted from bottom to top, with hI being the scale-
s
Table 8. Percentage coverage of the galaxy’s image when the
length of the stars as derived from the I-band modelling.
absolute value of the residuals is below a certain value.
The magnitude scale corresponds to the lower profile of
eachset,the otherprofiles areshifted upwards(in bright- Galaxy <10% <20% <30% <40% <50%
ness)by2,4,6,8and10magnitudesrespectively.Profiles NGC 4013 46.6% 73.2% 87.0% 94.3% 97.8%
between 0 and 1.5hI correspond to brightness averaged IC 2531 35.8% 66.0% 83.4% 94.4% 99.5%
s
over 4′′ (7.5′′ for NGC 5907) parallel to the major axis, UGC 1082 38.0% 65.0% 82.2% 91.1% 95.0%
while profiles at 2hI and 2.5hI are averaged over 8′′ (15′′ NGC 5529 41.7% 73.9% 87.6% 94.1% 97.5%
s s NGC 5907 38.5% 66.2% 83.0% 92.7% 97.4%
forNGC5907)alongthesamedirection.Thiswasdoneto
reduce as much as possible the localclumpiness that may
existin particularareasofthe galaxy.Inthese plots,only
the data above the limiting sigma level (∼3 sigma of the
Approximatelythesamepictureholdsfortheotherbands
local sky) that were used for the fit are plotted, while the
(see Papers I & II). These numbers indicate the ability of
foreground stars have been removed.
our model to describe quite accurately the observed sur-
One can clearly see a good agreement between model
face brightnessofthe galaxiesthatwemodelledusingrel-
and observation despite the small deviations in some
ativelysimpleandsmooththreedimensionaldistributions
places. It is worth remembering here that a global fit was
of stars and dust compared to the real ones with all the
done to the observed galaxy’s image and the derived set
smallscaleclumpiness andspiralstructurethat they may
of parameters (Tables 2 - 6) gives the best galaxy image
have.
as a whole.
Subtracting the model image from the observationwe
obtain residual maps that give the distribution of the ab- 4.1. Dust mass calculations
solute value of the residuals throughout the galaxy’s im-
age (see Papers I & II). From these maps we can de- Having found the parameters that best describe the dust
rive the percentage coverage of the galaxy’s image with distributionineachgalaxy,weareable tohaveagoodes-
residuals below a certain value. We do so in Table 8, timateofthetotaldustmassofeachgalaxy(seePaperI).
where the percentage coverage of the residuals below Inwhatfollowswedothesecalculationsandalsocompare
10%,20%,30%,40%and50%isgivenfortheI-banddata. with the total gas mass reported in the literature as well
E. M. Xilouris et al.: Arespiral galaxies optically thin or thick? 7
11.5 11.0 9.5
12.5 12.0 10.5
13.5 13.0 11.5
14.5 14.0 12.5
15.5 15.0 13.5
2mag/arcsec 11116789....5555 2mag/arcsec 11116789....0000 2mag/arcsec 11114567....5555
− − 20.0 − 18.5
B 20.5 V I 19.5
21.0
21.5 20.5
22.0
22.5 21.5
23.0
23.5 22.5
24.0
24.5 23.5
−3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0
z offset (kpc) z offset (kpc) z offset (kpc)
Fig. 3. Vertical surface brightness profiles for NGC 4013 in the B (left), V (middle), I (right) bands. The six profiles in each
plot are vertical cuts of the galactic plane at distances of 0,0.5hI,1hI,1.5hI,2hI and 2.5hI along the major axis as plotted
s s s s s
from bottom totop respectively.Starsrepresent averagedprofilesofthe‘folded’ imageoftheobservation,while solid linesgive
the model. From bottom to top, the magnitude scale is shifted upwards (in brightness) by 0, 2, 4, 6, 8 and 10 magnitudes
respectively. Seethe text for a more detailed description.
as with the dust mass calculated using the IRAS fluxes Eq. (4) of Devereux & Young (1990), the dust mass is
(wherever measurements are available). foundtobe1.9×106M⊙.Thisimpliesagas-to-dustmass
For NGC 4013 the mass of the atomic hydrogen is ratioof1900.However,usingtheparametersderivedfrom
reported to be 1.3×109M⊙ (Bottema 1995), while the ourmodel,wecalculateadustmassofMd =9.9×106M⊙
mass of the molecular hydrogen is 8.9×108M⊙ (Gomez and the gas-to-dust mass ratio then becomes 360.
&Garcia1997),givingatotalofMg =2.2×109M⊙forthe Adopting a 21 cm line flux of 40.8 Jy km s−1 (Hucht-
gas mass. Using the parameters derived from our model, meier&Richter1989)forNGC5529,wederiveanatomic
the dust mass was calculated (see Sect. 5.3 of Paper I) to hydrogenmass of M(HI)=8.4×109M⊙. Doubling it, in
be Md = 4.5×106M⊙. This implies a gas-to-dust mass the absence of molecular hydrogen mass information, we
ratio of 490. Using the IRAS 60µm and 100µm fluxes for get a total gas mass of Mg = 1.7×1010M⊙. The 60µm
this galaxy (Moshir et al. 1990) and Eq. (4) of Devereux and 100µm IRAS fluxes (Moshir et al. 1990) give a dust
& Young (1990), the dust mass is calculated to be 1.9× mass of 5.7× 106M⊙ which implies a gas-to-dust mass
106M⊙, giving a gas-to-dust mass ratio of 1200. ratio of 3000.With our model calculations we find a dust
InthecaseofIC2531the21cmlinefluxwasmeasured mass of 3.6×107M⊙, giving a gas-to-dust mass ratio of
to be S =40.3Jy kms−1 (Huchtmeier &Richter 1989) 470.
HI
and thus the atomic hydrogen mass was calculated using For NGC 5907 exact gas mass calculations are pre-
Eq. (2) of Devereux & Young (1990) and is found to be sented in Dumke et al. (1997). The total gas mass is re-
M(HI)=4.6×109M⊙. We have not been able to locate ported to be Mg = 7.8×109M⊙. The IRAS 60µm and
a measurement for the 2.6 mm CO line for this galaxy in 100µm fluxes (Moshir et al. 1990) give a dust mass of
order to calculate the molecular hydrogen mass M(H2), 3.6×106M⊙, while with our model parameters we derive
but a crude approximation is to assume the same mass a dust mass of 1.5×107M⊙. The gas-to-dust mass ratio
as that of the atomic hydrogen (see Sect. 5.3 of Paper I). thenbecomes2200usingtheIRASmeasurementsand520
Thus, the total gas mass is approximately M = 9.2× using our model’s parameters.
g
109M⊙. The dust mass for this galaxyas calculatedfrom
our model parameters is Md = 2.2×107M⊙, setting the 4.2. Relative extinction values
gas-to-dust mass ratio to 420.
ForUGC1082the21cmlinefluxhasbeenreportedto Adopting a mean scaleheight for the dust from all bands
beS =5.47Jykms−1(Giovanelli&Haynes1993).This (see Sect. 5) and using the values derived for the face-on
HI
givesanatomichydrogenmassofM(HI)=1.8×109M⊙. central optical depth (τλf = 2κλzd) in each filter, we can
In absence of a 2.6 mm CO line measurement in order to derivethe extinctioncoefficientκ ineachband.We have
λ
calculate the molecular hydrogenmass we approximate it found that κ /κ = 1.33 and κ /κ = 0.72 for NGC
B V I V
to be the same as that of the atomic hydrogen. The total 4013, κ /κ = 1.33, κ /κ = 0.74, κ /κ = 0.20 anad
B V I V J V
gasmassisthenMg =3.6×109M⊙.UsingtheIRAS60µm κK/κV = 0.06 for IC 2531, κB/κV = 1.26 and κI/κV =
and100µmfluxes forthis galaxy(Moshiretal.1990)and 0.62 for UGC 1082, κ /κ = 0.65 for NGC 5529 and
I V
8 E. M. Xilouris et al.: Arespiral galaxies optically thin or thick?
11.5 11.0 10.0
12.5 12.0 11.0
13.5 13.0 12.0
14.5 14.0 13.0
15.5 15.0 14.0
2mag/arcsec 11116789....5555 2mag/arcsec 11116789....0000 2mag/arcsec 11115678....0000
− 20.5 − 20.0 − 19.0
B 21.5 V I
21.0 20.0
22.5
22.0 21.0
23.5
23.0 22.0
24.5
24.0 23.0
25.5
−3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0
z offset (kpc) z offset (kpc) z offset (kpc)
9.0 8.0
10.0 9.0
11.0 10.0
12.0
11.0
13.0
2ec 14.0 2ec 12.0
s s 13.0
arc 15.0 arc 14.0
g/ 16.0 g/
ma 17.0 ma 15.0
J− 18.0 K− 16.0
19.0 17.0
20.0 18.0
21.0 19.0
22.0 20.0
−3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0
z offset (kpc) z offset (kpc)
Fig. 4. Same as in Fig. 3, butfor IC 2531. In addition, J and K band cuts are shown.
12.5 12.0 11.0
13.5 13.0 12.0
14.5 14.0 13.0
15.5 15.0 14.0
2mag/arcsec 1111267890.....55555 2mag/arcsec 11116789....0000 2mag/arcsec 11115678....0000
− − 20.0 − 19.0
B 21.5 V 21.0 I 20.0
22.5
22.0 21.0
23.5
23.0 22.0
24.5
24.0 23.0
25.5
−3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0
z offset (kpc) z offset (kpc) z offset (kpc)
Fig. 5. Same as in Fig. 3, butfor UGC 1082.
E. M. Xilouris et al.: Arespiral galaxies optically thin or thick? 9
11.0 10.0
12.0 11.0
13.0 12.0
14.0 13.0
15.0 14.0
2g/arcsec 111678...000 2g/arcsec 111567...000
ma 19.0 ma 18.0
− 20.0 − 19.0
V I
21.0 20.0
22.0 21.0
23.0 22.0
24.0 23.0
−4.0 −2.0 0.0 2.0 4.0 −4.0 −2.0 0.0 2.0 4.0
z offset (kpc) z offset (kpc)
Fig. 6. Same as in Fig. 3, butfor NGC 5529.
11.5 11.0 10.0
12.5 12.0 11.0
13.5 13.0 12.0
14.5 14.0 13.0
15.5 15.0 14.0
2mag/arcsec 11116789....5555 2mag/arcsec 11116789....0000 2mag/arcsec 11115678....0000
B− 2201..55 V− 20.0 I− 19.0
21.0 20.0
22.5
22.0 21.0
23.5
23.0 22.0
24.5
24.0 23.0
25.5
−3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0 −3.0 −1.0 1.0 3.0
z offset (kpc) z offset (kpc) z offset (kpc)
Fig. 7. Same as in Fig. 3, butfor NGC 5907.
κ /κ = 1.12 and κ /κ = 0.61 for NGC 5907. These face-on, despite their obvious dust lane in their almost
B V I V
ratios are identical to the ratios of the extinction values edge-on orientation seen in the observations. The values
A /A . of the optical depth in all bands are plotted in Fig. 8 for
λ V
eachgalaxy.Differentsymbolsindicatedifferentbands.In
particular, open circles correspond to the B-band, open
5. Discussion
squaresto the V-band, opentriangles to the I-band, solid
squares to the J-band and solid triangles to the K-band.
Havinganalyzedatotalofsevengalaxies,wearenowable
todrawsomegeneralconclusionsconcerningthedustand Itisofinteresttoseehowthescaleheightofthestarsis
stellardistributioncharacteristicsofspiralgalaxies.Inor- related to that of the dust. We show this in Fig. 9, where
dertohaveaconsistentsetofparametersforallthegalax- the parameters z and z (in kpc) as well as their ratio
s d
ies,wereanalyzedthegalaxyNGC891(alreadypresented are plotted for each galaxy. The symbols have the same
in Paper II), but now using the R1/4 law for the bulge meaningasinFig.8.Forthe caseofUGC 2048(analyzed
stellar distribution instead of the modified Hubble profile in Paper I), we give half of the derived scaleheight values
that was used in Paper II. The values derived from the since, as mentioned in Paper I, it’s distance has probably
modelling are presented in Table 7 of the present paper. beenoverestimatedbyafactorof2.Doingthestatisticsin
Wehavequantifiedtheopacityofthegalaxiesinterms theV-banddatawederiveameanratioofz /z =1.8±0.6
s d
oftheircentralface-onopticaldepthτf.For all thegalax- implying that the dust is more concentrated to the plane
ieswehavefoundcentralface-onopticaldepthswithvalues of the disk with respect to the stars. This was of course,
less than one in all the bands that we analyzed, indicat- evident from the prominent dust lanes. This mean value
ing that they would appear to be transparent when seen of z /z is plotted as a horizontal dashed line. One can
s d
10 E. M. Xilouris et al.: Arespiral galaxies optically thin or thick?
1.1
1.0
1.0
fτ) 0.9
h ( 0.8
pt 0.8 c) 0.6
e p
d k
cal 0.7 z (s0.4
pti 0.6 0.2
o
al 0.5 0.0
ntr 0.5
e 0.4
c 0.4
n c)
−o 0.3 kp 0.3
ace 0.2 z (d0.2
f 0.1
0.1
0.0
0.0 4.0
NGC891 NGC5529 NGC4013
UGC2048 IC2531 NGC5907 UGC1082 3.0
z/zsd2.0
Fig. 8. Values of the face-on central optical depth in all the 1.0
bands that were modelled for each galaxy. Different symbols 0.0
NGC891 NGC5529 NGC4013
arefordifferentbands.OpencirclescorrespondtotheB-band, UGC2048 IC2531 NGC5907 UGC1082
opensquarestotheV-band,opentrianglestotheI-band,solid
squares to the J-band and solid triangles to the K-band. For
UGC 2048 the valuesare taken from Paper I. Fig. 9. The values of zs (top graph), zd (middle graph) and
zs/zd (bottom graph) for each galaxy. All lengths are given
in kpc. For the explanation of the symbols see Fig. 8. The
also notice that there is not a significant trend of zs with dashed linein thelast graph gives themean valueof theratio
wavelength.This means thatthe mainbody ofthe disk is calculated by using theV-banddata.
dominatedbytheoldstellarpopulation,atleastathighz
distances,givingroughlythesamescaleheightinallbands.
Of particularinterest is the distribution of dust in the
radial direction relative to the stars, as can be seen from
the values that were derivedfor the scalelengths.Inorder 10.0
to have a better view of how the scalelengths of the stars 8.0
and the dust are related we give a plot (Fig. 10) similar c) 6.0
p
k
to that of the scaleheights described above. The symbols h (s 4.0
here, have exactly the same meaning as that in Fig. 8. 2.0
As with the scaleheights of UGC 2048, we adopt half the 0.0
10.0
values of the scalelengths derived from the model. The
8.0
statisticsthatweredoneinthe V-band,giveameanratio pc) 6.0
ohforhizdo/nhtsal=lin1e..4I±n0a.l2l.sTevheins vgaalluaxeieiss wsheowhanveasfoaunddasthheadt h (kd 4.0
the dust is radially more extended than the stars. This 2.0
result has recently been confirmed for our Galaxy using 0.0
3.0
COBE/DIRBEdata(Daviesetal.1997a).AnalysisofISO
data for severalgalaxies(Davies et al. 1997b,Alton et al. hs2.0
1998a), as well as SCUBA observations of NGC 891 in h/d
1.0
450µm and 850µm (Alton et al. 1998b) also indicate a
more extended radial distribution for the dust than for 0.0
NGC891 NGC5529 NGC4013
the stars.Another workthat alsosupports this, is that of UGC2048 IC2531 NGC5907 UGC1082
Lequeux & Guelin (1996) where a systematic reddening
of background galaxies is found in the outer regions of
thegalaxyofAndromeda,suggestingtheexistenceofdust Fig. 10.Thevaluesof hs (top graph),hd (middlegraph)and
even beyond the optical disk. hs/hd (bottom graph) for each galaxy. All lengths are given
in kpc. For the explanation of the symbols see Fig. 8. The
It is important to notice at this point the deviations
dashed linein thelast graph gives themean valueof theratio
with wavelength shown in Figs. 9 and 10 for the dust pa- calculated by using theV-banddata.
rameters. These deviations, which are mainly due to the
different appearance of the clumpy nature of the galaxies