When did round disk galaxies form?

3 MB·English

by  Tomoe M. Takeuchi

When did round disk galaxies form?
T. M. Takeuchi, and K. Ohta
Department of Astronomy, Kyoto University, Kyoto 606-8502, Japan
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1 [email protected]
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2
S. Yuma
n
a Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa 277-8582, Japan
J
and
2

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A K. Yabe
National Astronomical Observatory of Japan, Mitaka 181- 8588, Japan
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.
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p
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o
ABSTRACT
r
t
s When and how galaxy morphology such as disk and bulge seen in the present-day universe
a
emergedisstillnotclear. Intheuniverseatz &2,galaxieswithvariousmorphologyareseen,and
[
star-forminggalaxiesatz ∼2showanintrinsicshapeofbar-likestructure. Then,whendidround

1 disk structure form? Here we take a simple and straightforwardapproachto see the epochwhen
v
a round disk galaxy population emerged by constraining the intrinsic shape statistically based
0
on apparent axial ratio distribution of galaxies. We derived the distributions of the apparent
0
5 axial ratios in the rest-frame optical light (∼5000 ˚A) of star-forming main sequence galaxies at
0 2.5 > z > 1.4, 1.4 > z > 0.85, and 0.85 > z > 0.5, and found that the apparent axial ratios of
0 them show peaky distributions at z &0.85, while a rather flat distribution at the lower redshift.
.
1 Byusingatri-axialmodel(A>B >C)forthe intrinsicshape,wefoundthebest-fitmodelsgive
0 the peaks of the B/A distribution of 0.81±0.04, 0.84±0.04, and 0.92±0.05 at 2.5 > z > 1.4,
5
1.4>z >0.85,and0.85>z >0.5,respectively. The lastvalueis closeto the localvalue of0.95.
1
Thickness (C/A) is ∼ 0.25 at all the redshifts and is close to the local value (0.21). The results
:
v indicate the shape of the star-forming galaxies in the main sequence changes gradually, and the
i
X round disk is established at around z ∼ 0.9. Establishment of the round disk may be due to a
cease of violent interaction of galaxies or a growth of a bulge and/or a super-massive black hole
r
a resides at the center of a galaxy which dissolves the bar structure.
Subject headings: galaxies: evolution — galaxies: formation — galaxies: structure
1. Introduction metry. Meanwhile,intheuniverseatz &3,galax-
ies with various morphology are seen, and many
When and how did disk galaxies form? At
of them show the presence of clumps and/or ir-
z . 1, disk galaxies that can be classified with
regularity, though the morphology is traced in
the Hubble’s tuning fork exist (e.g., Schade et al.
the rest-frame UV (e.g., Giavalisco et al. 1996;
1995;Abraham et al.1996;Lilly et al.1998;Scarlata et al.
Steidel et al.1996). Hence,theemergenceofmor-
2007;Sargent et al.2007);theyareidentifiedwith
phologyclassifiedwiththe Hubble’stuning forkis
their apparent morphology, and/or their surface
considered to be around at z ∼1−3, and forma-
brightness distribution, and/or empirical indices
tion of disk structure would also be expected at
describingsuchascentralcondensationandasym-
the epoch.
1
TheWideFieldCamera3(WFC3)ontheHub- jor merges, particularly those with large stellar
ble Space Telescope (HST) enables us to study mass. Another piece of the suggestion for the
morphology of galaxies in the rest-frame optical disk progenitor scenario stems from the cluster-
light well up to at z ∼ 3. Conselice et al. (2011) ingpropertyofsBzKgalaxies;sBzKgalaxieswith
studiedmorphologyevolutionbasedoneyeinspec- K < 23 mag are considered to be a progenitor
tion. Theyfoundthediskpopulationisincreasing of present-day disk galaxies with regard to their
withredshift graduallyandthe populationis very weak clustering strength (Hayashi et al. 2007). It
rareatz >2. Byusingapparentmorphology,sim- would be reasonableto suppose most of the sBzK
ilartrendisreportedbyCameron et al.(2011)for galaxies in this magnitude range will evolve into
galaxies with a stellar mass range of 1010−12M⊙ the present-daydisk galaxies,though the brighter
and by Talia et al. (2014). Mortlock et al. (2013) sBzK galaxies may be a progenitor of elliptical
alsostudiedthemorphologyevolutionwitheyein- galaxies.
spection and a clearer emergence of the disk pop- Motivated by the finding of the presence of
ulation at z ∼ 2 is seen after correcting for the manyrotatingdiskamongsBzKgalaxiesandclus-
statistical morphology misclassification. tering nature of them, we took a simple and
However, from the optical surface brightness straightforward approach to see whether the in-
distribution, the fraction of the disk galaxies is trinsic shape of faint sBzK galaxies at z ∼ 2 is
higheratz >2(Mortlock et al.2013;Bruce et al. disk-like or not statistically based on apparent
2012; Buitrago et al. 2013). If the S´ersic index axial ratio distribution. We studied the surface
(n) less than 2.5 is regarded to be an indicator of brightness distribution and the apparent axial ra-
disk galaxies, the fraction of the disk population tio in both rest-frame UV and optical light for
is larger at z > 2 and is decreasing with redshift, sBzK galaxies with KS < 24 mag (Yuma et al.
though the details of the evolutional trend is not 2011, 2012). Yuma et al. (2011) and Yuma et al.
so simple; e.g., if irregular galaxies are included (2012)revealedthesurfacebrightnessdistribution
in the sample, the disk fraction is more constant of them is characterized by S´ersic index of n∼1,
againstredshift(Buitrago et al.2013),orthefrac- and the half-light radius and surface stellar mass
tion is rather constant for less massive galaxies density is similar to those in the present-day disk
(<1010.5M⊙) (Mortlock et al. 2013). Bruce et al. galaxies (Barden et al. 2005). However, it was
(2012) triedto model the two-dimensionalsurface turned out that the intrinsic shape of the sBzK
brightness distribution with two components of galaxies is not a round disk (round means intrin-
S´ersic index of n = 1 and n = 4, and found a sic axialratioof∼0.9−1.0); their intrinsic shape
fractionofthe disk(n=1component)dominated isbar-likeoroval(intrinsicaxialratio∼0.6−0.8)
galaxiesdecreasesatz ∼2rathersharplyforstel- with the thickness similar to that of the present-
lar mass larger than 1010.5M⊙. day disk galaxies. The intrinsic bar-like structure
Thus the opposite views are obtained in terms of star-forming galaxies at z ∼ 2 is also pointed
of the disk evolution. Other parameters charac- out by Law et al. (2012). It should be noted here
terizingthemorphologicalfeaturessuchascentral thatthisbar-likestructuredoesnotimplyadirect
condensation, asymmetry, Gini, M20, etc seem progenitor of the local barred galaxies as discuss
not to be suitable to trace the morphology of later.
galaxies in distant universe (Wang et al. 2012; Then, when did round disk galaxies appear af-
Mortlock et al. 2013; Talia et al. 2014). ter z ∼ 2? Emergence of the round disk popula-
On the other hand, studies of internal kine- tionshouldreflecttheevolutionprocessofthedisk
matics in star-forming galaxies such as BM/BX structure. Hence,revealingevolutionoftheintrin-
and star-forming BzK (sBzK) galaxies at z ∼ 2 sic shape of the galaxies is expected to give us an
revealed about one third of them show a clear ro- insighttophysicalprocessofthegalaxyevolution.
tation kinematics (F¨orster Schreiber et al. 2009). Inthispaper,westudytheintrinsicshapeofmain
This suggests we witness disk galaxies and they sequence galaxies with KS < 24 mag in the red-
may be progenitor of present-day disk galax- shift rangefrom2.5to 0.5using the same method
ies, though a fraction of them may evolve into as Yuma et al. (2011) and Yuma et al. (2012) to
the present-day elliptical galaxies through ma- see the redshift that the round disk galaxy pop-
2
ulation emerged. In the subsequent section, data obtained from CANDELS data release v1.0. Op-
sources and sample galaxies are summarized. In tical images were taken from SXDS project (B,
§3, we derive the surface brightness distributions V, RC, i′, and z′) (Furusawa et al. 2008). We
and axial ratios of the galaxies. Then, in §4, we used HST/ACS images taken with F814W filter
examinethedistributionsoftheapparentaxialra- (i814). MIR 3.6µm and 4.5µm images were taken
tiosandconstraintheintrinsicshapeofthegalax- from Spitzer Public Legacy Survey of UKIDSS
ies. Conclusionanddiscussionaregivenin§5. We UDS (SpUDS; PI: J. Dunlop). We also use the
adopt a cosmology with H0 = 70 km s−1 Mpc−1, far-UV and near-UV data taken from Galaxy
Ωm = 0.3, and ΩΛ = 0.7. All magnitudes in this EvolutionExplorer(GALEX;Martin et al.2005)
paper are given in the AB magnitude system. archivedimage (GR6) andthe u-banddata of the
Canada-France-Hawaii Telescope Legacy Survey
2. Data sources and sample galaxies (CFHTLS) wide field as supplemental informa-
tion, though the limiting magnitudes are shallow.
Samplegalaxiesinthisstudyarecollectedfrom
Object detection was made based on KS-band
the Great Observatories Origins Deep Survey-
South (GOODS-S)1 (Dickinson et al. 2003) and image by using SEXTRACTOR (Bertin & Arnouts
1996). We made photometry using these data
the Subaru XMM-Newton Deep Survey (SXDS)
for each source detected in KS images at the
(Furusawa et al. 2008), which almost overlapsUl-
same position and derived total magnitudes us-
tra Deep Survey (UDS) in UK Infrared Telescope
ingSEXTRACTOR. FortheimagestakenwithACS
InfraredDeepSkySurvey(UKIDSS)(Lawrence et al.
and IRAC, we applied a correction for the aper-
2007). The data sources are the same as those
ture photometry to obtain a total magnitude fol-
used by Yuma et al. (2012) and the details are
lowing the manner by Yuma et al. (2012). Spec-
described in the paper. Here we briefly summa-
tralenergydistribution(SED)wasconstructedfor
rize them. In GOODS-S region, near infrared
eachobjectfromthe photometry in allthe bands.
(NIR) images (J-, H-, and KS-band images) Then photometric redshifts were derived by us-
were taken from GOODS/ISAAC (Infrared Spec-
ing HYPERZ (Bolzonella et al. 2000). Compar-
trometer And Array Camera) data release final
isonswithspectroscopicredshiftsavailableshowed
version (Retzlaff et al. 2010). Five sigma limit-
∆z/(1+z)of∼0.05and∼0.03inGOODS-Sand
ing KS-band magnitude is 24.4 mag. NIR im- SXDS, respectively. With the photometric red-
ages taken with WFC3 on HST with F125W
shifts,stellarmass,star-formationrate(SFR),and
and F160W filters were obtained from CAN-
colorexcess (E(B−V)) were derivedfor eachob-
DELS (Cosmic Assembly Near-infrared Deep Ex-
jectthroughSEDfitting byusingSEDfitprogram
tragalactic Legacy Survey; Grogin et al. 2011;
(Sawicki 2012). The SEDfit employs population
Koekemoer et al. 2011)2 data release v0.5. Opti-
synthesis code of BC03(Bruzual& Charlot 2003).
calimagesweretakenfromver. 2.0dataproducts
Salpeter initial mass function with a mass range
ofGOODSHST/ACS(AdvancedCameraforSur-
of0.1−100M⊙ and the solarmetallicity wereas-
veys)treasureprogram(B435,V660,i775,andz850) sumed. Extinction law used was that by Calzetti
(Giavalisco et al. 2004) and from ESO/GOODS
etal. (2000). MoredetailsaredescribedbyYuma
program (U and R) (Nonino et al. 2009). Mid-
et al. (2011, 2012) and Yabe et al. (2012, 2014).
infrared (MIR) images at 3.6 µm and 4.5 µm
Using these data, we selected galaxies brighter
takenwith InfraredArrayCamera(IRAC) onthe
Spitzer Space Telescope (SST) were from data than KS = 24.0 mag. We divided the galaxies in
three epochs of 2.5>z >1.4, 1.4>z >0.85,and
release 1 and 2 obtained in Spitzer Legacy Sci-
0.85>z >0.5basedonthephotometricredshifts;
ence program. In SXDS/UDS region, NIR im-
these epochs are chosen to take a comparable du-
ages (J, H, and KS) were taken from data re-
ration (∼ 2 Gyr) of the epochs in the cosmic age
lease ver. 8 of UKIDSS UDS. Five sigma limiting
and to keep a reasonable sample size.
magnitude is KS = 24.6 mag. NIR images with
HST/WFC3withF125WandF160Wfilterswere Figure 1 shows distribution of the SFR against
stellar mass in each epoch. As like in other works
1 http://www.sci.edu/science/goods (e.g., Noeske et al. 2007; Daddi et al. 2007), the
2 http://candels.ucolick.org/index.html SFRsarelargerinmoremassivegalaxiesandthey
3
make a sequence referred as main sequence. The and F850LP(z850) in GOODS-S and F814W(i814)
main sequence shows a gradual cosmological evo- inSXDSfor0.85>z >0.5. Magnituderangesfor
lution down to z ∼ 0, where we see disk galaxies the sample galaxiesin three epochs were virtually
in the sequence. Most of our sample galaxies at H160< 24 mag and J125< 24 mag, and z850< 25
2.5 > z > 1.4 are also sBzK galaxies. Galaxies mag in GOODS-S and i814< 24 mag in SXDS.
in the most massive part of the main sequence Pixel scales after drizzle were 0.′′06, 0.′′06, and
at the higher redshifts may soon stop star for- 0.′′03 in H160, J125, and z850/i814, respectively.
mation and evolve into passive elliptical galax- TheradialdistributionisfittedwithS´ersicpro-
ies according to a simple theoretical expectation file: I(r) = I exp[−κ {(r/r )1/n−1}], where r
e n e e
(e.g., Bouch´e et al. 2010). But most of the sam- is the half light radius, I is the surface bright-
e
ple galaxies occupy less massive part of the main ness at r , and n characterizes the shape of the
e
sequence and they are expected to reside in the profile (S´ersic index). Two dimensional surface
main sequence at the present epoch. A branch brightnessfittingwasmadebyusingGALFITver-
seen above the main sequence shows very high sion 3 (Peng et al. 2010). Initial guess parame-
SFR at a fixed stellar mass, and they are con- ters on the central position, axial ratio, position
sidered to be violently forming stars often under angle, and r are taken from the output parame-
e
stronggalaxyinteraction(e.g.,Daddi et al.2007). ters of SEXTRACTOR. Initial S´ersic index was set
Thusweselectedstar-forminggalaxiesinthemain to be 1.5, which does not affect the final results
sequence bracketed by thresholds shown in Fig- significantly. Point spread function in each image
ure 1. The stellar mass limit at 5 × 109M⊙ is was constructed from 5∼20 isolated unsaturated
to avoid the inclusion of Magellanic-type galaxies stars.
that would tend to show bar-like structure even
Figure 2 shows example of the profile fitting.
in the local universe. A star-forming galaxy with
As seen in the figure, the surface brightness pro-
a stellar mass of ∼ 5 × 109M⊙ at z = 2.5 is a files extend to ∼ 1 arcsec in radius correspond-
progenitor of the Milky Way class galaxy (stel-
ing to ∼ 8 kpc at z = 1 ∼ 2 and ∼ 6 kpc at
lar mass of 5×1010M⊙), if we adopt the abun- z = 0.5. The surface brightness we use to fit the
dance matching in terms of the number density modelreaches23.5∼25magarcsec−2 inthe rest-
(van Dokkum et al. 2013). Ranges of the specific
frame V band after correcting for the cosmolog-
SFR (sSFR) we use are 3 × 10−11 − 2 × 10−8
ical dimming. This level of the surface bright-
yr−1 (z = 1.4−2.5), 3×10−11 −1×10−8 yr−1
ness can be regarded as the outskirt of galaxies,
(z = 0.85−1.4), and 2×10−11−3×10−9 yr−1
and is deep enough to confront with the shape
(z = 0.5−0.85). SFR limit is just an additional
of local disk galaxies. Considering the fading of
threshold; SFR > 2.0M⊙ yr−1 (z = 1.4− 2.5), galaxy luminosity to the present epoch, the value
>0.6M⊙yr−1(z =0.85−1.4),and>0.2M⊙yr−1 would be ∼ 1 mag arcsec−2 fainter at z ∼ 0
(z = 0.5−0.85). A fraction (typically 10−15%)
(e.g., Brinchmann et al. 1998; Miller et al. 2011).
of them show multiple-structure in the rest-frame
We obtained r , n, and apparent axial ratio (b/a,
e
optical HST images; if an object detected by
where a is a major axis and b is a minor axis) for
SEXTRACTOR locates within a radius of median each galaxy. About 60-70% of the sample galax-
size (FWHM) of the galaxies in each epoch, we
ies show n = 0.5−2.5. We then examined the
regard them as multiple. Such galaxies are not
distribution of r and stellar mass of the sample
e
adequate to examine the shape and we discarded
galaxies with n = 0.5−2.5. In each epoch, the
them in this study.
distributionof r againststellar massis similarto
e
that for local disk galaxies (Barden et al. 2005).
3. Two-dimensional surface brightness fit-
Accuracy for the S´ersic index as well as for
ting
the axial ratio was examined by putting artifi-
We made two-dimensional surface brightness cial objects into the images used for the analy-
distribution fitting to the galaxies selected above. sis. The artificial objects were created by using
The images were taken with HST in the rest- ARTDATA/MKOBJECTSin IRAF. Mock galax-
frameopticalwavelength(∼0.5µm): F160W(H160) ies with S´ersic index of 1 or 4 were generated in
for2.5>z >1.4,F125W(J125)for1.4>z >0.85, both GOODS-S and SXDS with half-light radius
4
Fig. 1.— Star formationrate versus stellar mass of the sample galaxies at three epochs: From right to left,
2.5>z >1.4, 1.4>z >0.85, and 0.85>z >0.5. Large red points are sample in this study and solid lines
in each panel show the selection criteria
(see text).
of 0.′′1 − 1.′′0 in a magnitude range of 20 − 25 ined and the rate is almost constant in the range
mag. The ranges of input parameters are cho- of b/a=0.2 and 1.0 (Yuma et al. 2011).
sen to mimic those of the sample galaxies. Ax-
ial ratio and position angle are randomly chosen
andthe galaxiesareputintoH160, J125, z850,and
i814 images randomly. As we did for the real ob-
jects, we first used SEXTRACTOR to derive posi-
tion, position angle, axial ratio, and FWHM. We
then performed GALFIT with these parameters
as well as n = 1.5 as the initial guess. Results
for H160(GOODS-S, SXDS/UDS) were presented
by Yuma et al. (2012). Accuracy for the S´ersic
index in H160 image is good enough (< 10 %)
in this magnitude range in case of n = 1. Even
if the intrinsic n is 4, the misclassification into
n = 1 disk is negligible, though the accuracy is
slightly worse in z850 image (Yuma et al. 2011, Fig. 2.— Example of the surface brightness dis-
2012). Weshowtheaccuracyoftheaxialratiode- tribution fitting at 0.85 > z > 0.5(upper), 1.4 >
rived for J125(SXDS/UDS), z850(GOODS-S), and z > 0.85(middle), and 2.5>z >1.4 (lower). The
i814(SXDS/UDS) in case of n=1 in Figure 3. In images are taken with HST i814(upper), WFC3
allthe panels,the obtainedaxialratiosagreevery J125(middle), and WFC3 H160(lower). In each
wellwiththoseofinputvalueinthebrightmagni- row, from left to right, original image, best-fit
tude range, and the accuracy is getting worse for model image, residual, and radial surface bright-
the fainter objects. However, at the faintest mag- ness profiles along the major axis are shown. In
the rightmost panel, the observed surface bright-
nitude level of the sample galaxies in each band,
ness and the best-fitted profile smoothed with
the accuracy of the obtained axial ratio is less
point spread function is shown with circles with
than5%onaverage,whichissmallerthanthe bin
size of the histograms of the axial ratio distribu- error and solid curve, respectively. Point spread
tion described below. The accuracy of axial ratio function is shown with thin solid curve.
in H160(GOODS-S, SXDS/UDS) is presented by
Yuma et al. (2012), and it is comparable to those
in other bands. Detection rate in KS-band image
against the apparent axial ratio was also exam-
5
4. Axial ratio distribution the edge-on thickness (C/A) is assumed to be de-
scribed with Gaussian distribution with mean of
4.1. Distribution of apparent axial ratios
µ anddispersionof σ . With this parameterset,
γ γ
theexpectedapparentaxialratiodistributionseen
In order to see whether they have round disk
fromrandomviewinganglescanbecalculatedand
structure, we take a simple and straightforward
canbecomparedwiththeobservedapparentaxial
approach; i.e., we constrain the intrinsic shape of
ratio distribution.
these galaxies statistically based on distribution
of apparent axial ratios of the sample galaxies at The model axial ratio distributions were cal-
three epochs. Figure 4 (upper row) shows the culated in a range of µ = −3.95 ∼ −0.05, σ =
apparent axial ratio distributions of the sample 0.2∼2.0, µγ =0.1∼0.98, and σγ =0.01∼0.35,
galaxieswithn=0.5−2.5amonggalaxiesselected with a step of ∆µ=0.15,∆σ=0.15,∆µγ =0.02,
in §2. If the intrinsic shape of disk galaxies is an and ∆σγ = 0.02. With these parameter sets, we
infinitesimally thin circulardisk,the apparentax- searched for the best-fit parameter set using χ2
ial ratio distribution is exactly flat. In fact, the method with 1σ statistics by Gehrels (1986). To
distribution for ∼ 300,000 local disk galaxies is estimate the uncertainty of the best-fit parame-
almost flat except for around at b/a∼ 0 and ∼ 1 ters, we made Monte Carlo realization of the ob-
(Padilla and Strauss 2008), since real disks have servedhistogramofthe axialratio1000timesand
a finite thickness and are not perfectly round. As derivedthe best-fitparametersetforeachrealiza-
seenintherightpanel(2.5>z >1.4)oftheupper tion. We took 68% confidence level as the uncer-
row of Figure 4, the axial ratio distribution peaks tainty of the model parameter. The peak value
at ∼0.45 and sharply decreases to both sides. In of the distribution of intrinsic B/A is given by
themiddlepanel(1.4>z >0.85),thedistribution 1−exp(µ−σ2). The uncertaintyonthe peakB/A
isslightlyflatter,butstillshowsaslightpeakydis- was calculated based on the propagationof errors
tribution. The histograms suggest these galaxies with the uncertainty ofµ andσ mentionedabove.
do not have a round disk structure. Meanwhile in Thebest-fitmodelsareshownwithsolidcurves
the left panel (0.85>z >0.5), the distribution is in Figure 4 (upper row), and the best-fitted pa-
rather flat and is close to that for the local disk rameters as well as the uncertainties are shown
galaxies, suggesting they have the intrinsic shape in Table 1. Resulting distributions of intrinsic
of round disk. axial ratios at the epochs are shown in Figure
4 (bottom row). The best-fit model B/A peaks
at 0.81 ± 0.04,0.84 ± 0.04, and 0.92 ± 0.05 at
2.5>z >1.4,1.4>z >0.85, and 0.85>z >0.5,
respectively, and the last value of B/A is very
close to that for the local disk galaxies (0.94)
(Padilla and Strauss 2008). The mean C/A is
∼ 0.25 at all the epochs and is close to that of
Fig. 3.— Accuracy of the obtained axial ra- the local disk galaxies (0.21) (Padilla and Strauss
tio against magnitude of input artificial object 2008). The intrinsic shape of the star-forming
in J125(left), z850(middle), and i814(right). Error main sequence galaxies at 2.5 > z > 0.85 is bar-
bars represent 1σ dispersion of the distribution. like or oval, while they have round disk structure
at z < 0.85, i.e., the emergence of the round disk
population is z ∼ 0.9, though the precise redshift
4.2. Intrinsic axial ratio distribution determination is difficult due to the the gradual
cosmologicalevolution and small sample size.
To constrain the intrinsic shape quantitatively,
we employ a tri-axial model with axial lengths 4.3. Robustness of the results
of A > B > C following the method by Ryden
(2004). Theface-onellipticity(ǫ=1−B/A)isas- In order to examine the robustness of the re-
sults, we constructed samples by changing selec-
sumed to be described by log-normal distribution
with mean of µ(= ln ǫ) and dispersion of σ, while tioncriteriaslightlywithrespecttoKS-bandmag-
nitude, stellar mass, sSFR, i814/z850/J125/H160
6
Fig. 4.— Normalizedhistogramsoftheobservedaxialratiosateachepoch(upperpanels):Fromrighttoleft,
2.5 > z > 1.4, 1.4 > z > 0.85, and 0.85 > z > 0.5. Numbers in vertical axis are multiplied by 10. Number
in the parenthesis at the top of each panel refers to the sample size. Best-fit model distributions are shown
with solid curves. Axial distribution of local disk galaxies from the Sloan Digital Sky Survey Data Release
6 by Padilla & Strauss (2008) is also shown with dotted curve (left panel). Distribution of best-fit intrinsic
axial ratios of B/A and C/A (bottom panels). Red solid, green dot dashed, and blue dashed curves refer
to the intrinsic model axial distribution at 2.5 > z > 1.4, 1.4 > z > 0.85, and 0.85 > z > 0.5, respectively.
Black dotted curves show the distribution for local disk galaxies (Padilla and Strauss 2008). Y-axis is an
arbitraryunit. Peaksfor the B/A distribution are shownby tick marks with uncertainty abovethe curves.
Table 1: Best-fit parameter sets for the tri-axial model.
Local∗ z =0.5−0.85 z =0.85−1.4 z =1.4−2.5
µ −2.33+0.13 −1.85+0.35 −1.70+0.12 −1.40+0.08
−0.13 −0.18 −2.30 −0.08
σ 0.79+0.16 0.80+0.19 0.35+0.19 0.50+0.17
−0.16 −0.60 −0.13 −0.18
µ 0.21+0.02 0.24+0.02 0.24+0.01 0.26+0.02
γ −0.02 −0.02 −0.01 −0.16
σ 0.050+0.015 0.07+0.16 0.05+0.01 0.09+0.01
γ −0.015 −0.06 −0.01 −0.08
∗Padilla&Strauss(2008)
magnitude, and S´ersic index, and made the same agree with the best-fit value within 1 σ error. If
fitting to these samples. wetakeamassivesample(stellarmasslargerthan
If we take samples in each epoch with 0.5 mag 1.0×1010M⊙), the results mostly agree within 1
brighter or fainter in KS band, virtually all the σ error. Ifweincludelessmassivegalaxies(stellar
best-fit parameters are within 1σ error. The peak mass largerthan 3×109M⊙), peak values of B/A
values of the intrinsic axial distribution (B/A) agree within the error, but the resulting parame-
7
ters for the highest-redshiftbin change more than ing trend of B/A with decreasing z is still seen,
1 σ. It should be noted that even in local uni- except for the B/A for the larger color excess at
verse such less massive galaxies often show bar- 2.5>z >1.4.
like structure as like Magellanic irregular galax-
ies. We also test the dependence on sSFR by tak- 5. Conclusion and discussion
ing 3×10−11 yr−1 < sSFR < 2×10−8 yr−1 at
z =2.5−1.4, 3×10−11 yr−1 < sSFR <5×10−9 We constrain the intrinsic shape of the star-
yr−1 atz =1.4−0.85,and3×10−11yr−1 <sSFR forming main sequence galaxies at z = 2.5 to
<7×10−9 yr−1 at z =0.85−0.5. Almost all the 0.5 based on the distributions of the apparent
axial ratios by employing the tri-axial model of
obtained best-fit parameters as well as the peak
A > B > C. At z & 0.9, the intrinsic shape of
values of B/A agree within 1σ error. If we take
them is bar-like or oval with B/A ∼ 0.8, while at
the threshold SFR 2-3 times larger, the resulting
z . 0.9, B/A is 0.92 that is close to the value for
parameters are almost within 1 σ. The axial ra-
the local galaxies (0.95). Hence, the emergence
tiosarederivedbyusingi814, z850, J125,andH160
of the round disk can be regarded to be z ∼ 0.9,
images. More accurate axial ratios are expected
though the precise redshift determination is diffi-
to be obtained with the brighter sample. Hence
cult due to the gradual evolution and the small
we take about 0.5 mag brighter samples (i814<
sample size. The thickness (C/A) is about 0.25
23.5 mag, z850< 24.5 mag, J125< 23.5 mag, and
and does not show significant cosmological evo-
H160< 23.5 mag) from the KS < 24.0 mag sam-
lution down to z ∼ 0. Similar result has been
ple. The resulting peak axial ratios are within or
obtained very recently by adopting a slightly dif-
marginallywithin1σuncertainty,andtheconclu-
ferentmodelfortheintrinsicshape;thetriaxiality
sion in this study does not change. We also make
of star-forming galaxies with stellar mass larger
sampleswithS´ersicindexof0.5−1.5and0.5−3.5,
and find again the conclusion does not change. than109.5M⊙ islargeatz &1,butsmallatz .1
(van der Wel et al. 2014). It is worth noting the
Dustobscurationmayaffecttheaxialratiodis-
bar-like structure we see at the high redshifts is
tribution; the redder disk galaxies tend to show
unlikely to be a direct progenitor of bar struc-
thesmalleraxialratiosinthelocaluniverseaswell
ture in the present-day barred galaxies, because
asatz =0.6−0.9(e.g.,Padilla and Strauss2008;
theapparentaxialratiosareobtainedmainlyfrom
Patel et al. 2012). This trend is considered to be
outside beyond the bar region in the present-day
duetothelargerdustobscurationinmoreinclined
barred galaxies; the bar region in a present-day
galaxies. In orderto see the effect, we divided the
barred galaxy is brighter than ∼22 mag arcsec−2
sampleintotwosubsampleswithsmallerorlarger
in V band (Ohta et al. 1990, 2007). Further-
color excess (E(B−V)) at each epoch. The color
more, large barred galaxies are disappearing as
excesswasderivedfromtheSEDfittingmentioned
redshift increases (van den Bergh et al. 1996): Its
in §2, and we divided the sample at around the
fraction among disk galaxies is only 10-20% at
median E(B −V) of 0.2 or 0.25 mag. Resulting
z = 0.8 ∼ 1.0 (Sheth et al. 2008; Melvin et al.
histograms of the axial ratios show that a slight
2014).
excess at smaller axial ratio (b/a ∼ 0.2−0.4) is
At z & 3, most of star-forming galaxies
seen at z = 0.5 ∼ 0.85, but such a clear trend
show S´ersic index of ∼ 1 in the rest-frame UV
is not seen at the higher redshifts. We made the
(Ravindranath et al. 2006) and in the rest-frame
modelfittingtothesubsamples. Abouthalfofthe
optical (Akiyama et al. 2008). However, the
bestfitµandσvaluesagreewiththoseofthetotal
distribution of the apparent axial ratios is not
samplewithintheuncertaintyforthetotalsample.
flat, suggesting the elongated intrinsic structure
However, it should be noted that the uncertainty
(Ravindranath et al. 2006). The results obtained
forthesubsamplesislargeduetothesmallersam-
here reveal that although the disk-like structure
ple size. We also derived the peak B/A with the
is seen among star-forming galaxies at z & 1,
subsamples. The peak B/A values in the smaller
its intrinsic shape is bar-like or oval. Physi-
colorexcess(largercolorexcess)are0.81(0.93)at
cal mechanism to make such structure is not
2.5 > z > 1.4, 0.91 (0.78) at 1.4 > z > 0.85, and
clear, but they may be bar-like due to galaxy
0.99 (0.97) at 0.85 > z > 0.5. Thus the increas-
8
interaction and/or minor merge (Noguchi 1987; inGOODS-ShavebeencarriedoutusingtheVery
Berentzen et al. 2004). Or the baryonic matter Large Telescope at the ESO ParanalObservatory
might have been already highly concentrated in a underProgramID168.A-0485. Basedonobserva-
darkmatterhalo,resultingintothebarinstability tionsobtainedwithMegaPrime/MegaCam,ajoint
(Ostriker & Peebles 1973). projectofCFHTandCEA/IRFU,attheCanada-
Then how did they become round? Numer- France-Hawaii Telescope (CFHT) which is oper-
ical simulations show a central mass condensa- ated by the National Research Council (NRC)
tion (either of a bulge and/or a super-massive of Canada, the Institut National des Science de
black hole (SMBH)) with a mass fraction of 1- l’Univers of the Centre National de la Recherche
10% of a disk dissolves the bar-like structure Scientifique (CNRS) of France, and the Univer-
(Athanassoula et al. 2005; Hozumi 2012). Thus sity of Hawaii. This work is based in part on
the emergence of round disk population may dataproductsproducedatTerapixavailableatthe
be related to the growth of a central bulge Canadian Astronomy Data Centre as part of the
and/or a SMBH. According to the simulations Canada-France-Hawaii Telescope Legacy Survey,
by Athanassoula et al. (2005), the bar-like struc- a collaborative project of NRC and CNRS.
ture gradually evolves into a round disk with a
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