銀河進化研究会、６月７−９日、大阪大学

遠方銀河におけるガスの運動学
但木謙一（国立天文台）

銀河進化研究会2017の講演内容（遠方銀河観測）
望遠鏡

空間分解能
21%

27%
55%
18%

79%

SubaruALMA
other

Point source
Spatially-resolved

近年の運動学的研究におけるマイルストーン

pellari et al.

ATLAS3D

No. 2, 2009SINS

SINS SURVEY OF HIGH-REDSHIFT GALAXIESCappellari+11

140

Foerster Schreiber+09

近傍早期型銀河slow rotator
fast rotator

Figure 17. Velocity fields for 30 of the 62 galaxies of the SINS Hα sample. The velocity fields correspond to that derived from the Hα line emission as described
Section 5.1 (the exception is K20–ID5 for which it was obtained from the [O iii] λ 5007 line instead). The color coding is such that blue to red colors correspond to th
blueshifted to redshifted line emission with respect to the systemic velocity. The minimum and maximum relative velocities are labeled for each galaxy (in km s−1
All sources are shown on the same angular scale; the white bars correspond to 1"" , or about 8 kpc at z = 2. The galaxies are approximately sorted from left to righaccording to whether their kinematics are rotation-dominated or dispersion-dominated, and from top to bottom according to whether they are disk-like or merger-lik
as quantified by our kinemetry (Shapiro et al. 2008). Galaxies observed with the aid of adaptive optics (both at the 50 and 125 mas pixel−1 scales) are indicated by thyellow rounded rectangles.
(A color version of this figure is available in the online journal.)

遠方星形成銀河

technique developed by the SAURON team for analysis of local
galaxies (Krajnović et al. 2006) to applications for high-redshift
studies. It provides a measure of the degree of asymmetry
in the observed velocity and velocity dispersion maps, where
the lower (higher) the asymmetry, the more disk-like (mergerlike) the object. Of the first 11 SINS galaxies classified bykinemetry, eight are disks and three are mergers (see Shapiro
et al. 2008). This initial set has now been expanded to include theanalysis of four additional sources, two of which are classified as
disk-like and two as merger-like. The kinemetric classification isreported in Table 9. The resulting fractions of disk- and mergerlike systems is thus 2/3 and 1/3, respectively. The uncertainties
of our method are discussed by Shapiro et al. (2008), to which
we refer for details. Based on these, we expect to correctly

asymmetry in the velocity field and dispersion map (essentiallythe same criteria as for our quantitative kinemetry). We find i
this way similar fractions of ∼2/3 of the objects that appea
to have Hα kinematics consistent with rotation in a singl
disk, and ∼1/3 with asymmetric or irregular Hα kinematicsuggestive of a merger. We note that for the 15 objects classifie
quantitatively, our kinemetry confirmed in all cases our prio
qualitative assessment (see Förster Schreiber et al. 2006a
Genzel et al. 2006, 2008; Shapiro et al. 2008). As noted i
Section 2, the SINS Hα sample includes three pairs of galaxies aapproximately the same redshift and with projected separationof ≈ 15–30 kpc. The individual components can in principle b
counted and inspected separately (see Section 9.4) or taken athree merging systems, but this has little consequences on ou

merger -> 回転円盤銀河

0

運動学のトレーサー

NGC 3522
NGC 3796
NGC 4168
NGC 4191
NGC 4261
NGC 4476
NGC 4636
NGC 4690
NGC 5322
NGC 5481
NGC 5631
PGC028887

192.0
67.5
102.5
178.0
103.0
219.0
32.5
191.5
102.0
233.5
305.0
216.5

5.5
12.2
1.2
5.7
0.5
7.5
1.0
1.5
1.0
3.8
2.0
8.0

78.5
58.0
142.5
4.5
52.0
12.5
125.5
139.5
171.0
7.5
174.0
4.5

89.9
18.8
89.8
7.5
3.3
13.7
89.8
25.8
7.3
19.4
9.0
12.4

ATLAS3D銀河の例
CO（分子ガス）On the origin of gas in early-type galaxies
連続光吸収（星）Hβ（電離ガス）

Notes. Columns defined as in Table 2. Kinematic misalignments for the slow-rotating SAURON ETGs are tabulated
in Sarzi et al. (2006).

電離ガスと星の運動

Davis+11

Figure 4. Histogram showing the kinematic misalignment angle between
the ionized gas and the stars for all the slow-rotating galaxies with measurable kinematic misalignments. These systems are listed in Table 3.
Figure 2. Histogram showing the kinematic misalignment angle between

fast rotator

T. A. Davis et al.

tribution however, we suggest that this is due to observational
tter. We therefore conclude that the ionized and molecular maal are always kinematically aligned with each other, even wheny are kinematically misaligned with respect to the stars, strongly
ggesting they share a common origin (as previously discussed
a subsample of these galaxies by Crocker et al. 2011). This iscussed further in Section 4.1.
Assuming 30◦ rather than 40◦ for the cut-off between aligned andsaligned gas can at most bias our results by ≈4 per cent (this isarea under the error distribution at misalignments greater than
, normalized by the total area under this error distribution curve.)
r the typical number of galaxies included in our analysis this canult in the misclassification of one to two galaxies.

deviation of 15◦ , as shown in Fig. 3.
The galaxies which have a misalignment between 15◦ and 40◦
are IC 0676, NGC 1222, NGC 3032, NGC 4150 and PGC 029321.
These small misalignments can always be understood as arising from small-scale kinematic substructures within the galaxies
affecting the ionized component, that are usually unresolved at
the resolution of our CO interferometry. IC 0676 has its ionizedgas kinematic PA affected by a bar. NGC 1222 is a highly disturbed starbursting system that may be in the process of undergoing a three-way merger (Beck, Turner & Kloosterman 2007). As
discussed above, NGC 3032 and 4150 have KDCs that may beaffecting the gas properties (McDermid et al. 2006; Sarzi et al.
2006). The ionized and molecular material in PGC 029321 has asmall angular extent, and as we showed above this can increase theerror in the kinematic PA determination.
The uncertainty on ionized gas PA measurements is larger than
the average 10◦ we have estimated for the molecular gas PAs. As
discussed above, this is because the ionized gas is often patchy,
has a smaller angular extent than the molecular gas and can beless relaxed. Despite this increased uncertainty, and greater intrinsic
variance due to small substructures in the galaxies, our conservative
threshold for misalignment (# > 30◦ ) ensures that we still set astrong lower limit on the importance of externally accreted material.
Despite the increased uncertainty, we only show plots of the ionizedgas misalignment from here on, taking advantage of the increased
number of galaxies available to improve our statistics. When one
examines the molecular gas kinematic misalignments all results
remain unchanged.
One galaxy (NGC 3032) has a molecular to ionized gas kinematic misalignment greater than the 30◦ cut-off we have taken to
denote the boundary between aligned and misaligned gas. As the
distribution of misalignments closely follows the Gaussian error

slow rotator

the molecular gas and the stars for all of the galaxies listed in Table 1. The
dashed line overplotted is a normalized Gaussian distribution with its centre
at zero and a standard deviation of 7◦ , showing the expected scatter.

88

電離ガスと分子ガスの運動
不一致
一致

Several individual galaxies have a KDC coincident with themolecular gas. NGC 4476 is a pathological example, as it has alarge stellar KDC, kinematically aligned with (and likely formedfrom) the molecular gas, while the stars have little sense of rotation
outside this region within the SAURON IFS field of view. PMAS
Fibre Pack (PPAK) IFS stellar kinematics suggest that the stellar
velocity field may become inverted outside the SAURON field ofview (Crocker et al., in preparation), hence the molecular gas could
be considered to be counter-rotating with respect to the stellar bodyat large radii. For consistency, however, we use only the SAURON
stellar kinematics in this work (probing roughly one effective radius),withand hencelabel constrained
NGC 4476’s molecular
gas as gas
co-rotating.
gure 1. Examples of the data for one of the galaxies
the best
molecular
PA (NGC 0524, top), and the galaxy with the worst constrain
It is worth bearing in mind, however, that the stellar kinematics
Ionized gas
andPAstars(NGC2768, bottom). Left: CO velocity field (colours). Middle: stellar velocity fields from the SAURON IFU (data from Emsellem etoleculargas
Figure 5. Histogram showing the kinematic misalignment angle between
inFigure
the outerparts of allof thesegalaxies misalignment
could be different
fromFigure 3. Histogram showing the kinematic misalignment angle between
4. Histogram
showing
the kinematic
angle between
theionized
gas
and
the
stars
for
all
the
fast-rotating
galaxies
listed
in
Table
2.
004).
Right:
Hβemissionline
kinematics
fromthe
SAURON
IFU
(data
from
Sarzi
et
al.
2006).
Thesetheare
overlaid
thegasCO
integrated
intensity
the molecular and ionized gas are always aligned and are likely
theDiscountinggalaxies
the fewwith
galaxies
molecular
gas and with
the ionized
for allthe galaxies listed
in Table 1.(blathekinematics
ionized gas inandthethecentral
stars forregions.
all the slow-rotating
measurdashedorigin,line overplotted
is a normalized
Gaussiandistribution with suchitsableas
The dashed line overplotted is a normalized Gaussian distribution with its
share
aThe
commoninvestigating
themolecular
kinematic
misalignment
this, wheretheoriginofassociatedthesystems
gas is hardto judge,
kinematic
misalignments.
are listed
in Table
3. notntours)andthebest-fitting
kinematicPA,
and
itsTheseerroraswould
calculatedinthis paper (solid black line and dashed black lin◦ , showinggas/stellar
centre
at
zero
and
a
standard
deviationof15
theexpectedscatter.
centre at zero and a standard deviation of 15◦ , showing the expected scatter.
ween the ionized gas and the stars can therefore also shed lightsignificantly alter our conclusions.

横軸：kinematic misalignment angle

最近の大規模探査（電離ガス・星）
MaNGA (~10k galaxies)

he Astrophysical Journal, 798:7 (24pp), 2015 January 1

Bundy et al.

vH [km s-1]

H

200

10

100

0

0
-100

-10

[km s-1]

The SAMI Galaxy Survey: Early Data Release

1571

250

10
[arcsec][arcsec]

P9-127A

SAMI (~3k galaxies)

200
150

0

100
-10

PSF

PSF

50

-200
-10

0
10
[arcsec]-10[SII] 6731/ 6717

log (H flux)
1.50

-10
PSF

0.50

0

0.00

-10

0.8

2.00

10

1.00

0

E(B-V)

2.50

1.50
1.00

0.4
0.2

-10

0.50
PSF

0
10
[arcsec]

-10

0

PSF

0.0
-10

10

log ([NII]/H )

-0.00
-0.20

-10
PSF

-0.40

1.5

0.0

10

0.5

-0.5
-1.0
-1.5
-1.5

0
10
[arcsec]Sy

1.0[arcsec]

05007 / H )[arcsec]

0.20

2.0

log ([OIII]

0.40

10

SF

-1.0 -0.5 0.0 0.5
log ([NII] 6583 / H )

PSF

1.0

-10

-10

-0.50
PSF

0
10
[arcsec]

Sy

1.0
0.5
0.0

LINER
-0.5 KMOS Redshift
TheOne Spectroscopic Survey
-10
-1.0

-1.5
-1.5

SF

Bryant+15

Figure 3. Example SAMI data for the galaxy 511867, with z = 0.05523 and M∗ = 1010.68 M" . Upper panel: flux for a central spaxel (blue) and one 3.75
arcsec to the North (red). Lower panels, from left to right: SDSS gri image; continuum flux map (10−16 erg s−1 cm−2 Å−1 ); stellar velocity field (km s−1 );10
Hα flux map (10−16 erg s−1 cm−2 ); Hα velocity field (km s−1 ). The two velocity fields are each scaled individually. For the stellar velocity map, only spaxels
with per-pixel S/N >5 in the continuum are included. Each panel is 18 arcsec square, with North up and East to the left. The grey circle in the second panel
0shows
the FWHM of the PSF.
The Astrophysical Journal, 799:209 (27pp), 2015 February 1
Wisnioski et al.

KMOS (~1k galaxies at z>0.5)[arcsec]

00.005007 / H )0.50

log ([OIII][arcsec]10

010[arcsec]

Resolved BPT [SII]

2.0
1.5

0
-10

Comp

Bundy+15

log ([OIII]/H )

-10

0
10
[arcsec]

Resolved BPT [NII]
0.60

-10

Wisniosk

0.6
0

0.00
-10

The Astrophysical Journal, 799:209 (27pp), 2015 February 1

10[arcsec][arcsec]10

010[arcsec]

1895

PSF

-1.0 -0.5 0.0 0.5
log ([SII] 6583 / H )

1.0

-10

0
10
[arcsec]

gure 14. Panoramic view of resolved, ionization diagnostic information available for MaNGA targets, taken from Belfiore et al. (2014). Results for the P-MaNGA
get, P9-127A (NGC 2916), are shown. The black diamonds in the BPT diagrams represent the value obtained in the central fiber. Flux measurements are given in
its of 10−17 erg s−1 cm−2 Å−1 . Central white spaces are regions where one or more emission lines are too weak to provide reliable ratios or diagnostic measurements.
foreground star in the upper portion of the IFU data has been masked. See the text (Section 7.2) for details.

rived for each individual fiber spectrum that incorporate information about the IFU bundle metrology (i.e., fiber location
within an IFU), dithering, and atmospheric chromatic differential refraction, among other effects. Fiber spectra from all
exposures for a given galaxy were then combined into a single datacube (and corresponding inverse variance array) using
these astrometric solutions and a nearest-neighbor sampling algorithm similar to that used by the CALIFA survey. For the
P-MaNGA datacubes, a spaxel size of 0.## 5 was chosen. The typical effective spatial resolution in the reconstructed datacubes
can be described by a Gaussian with FWHM ≈ 2.## 5. Whenbinning the datacubes, the resulting error vectors are scaled toapproximately account for wavelength and spatial covariancein the P-MaNGA error cubes. A more accurate estimation of

andard stars covered with single fibers at each of the threether positions. The flux calibration vectors derived from thesengle-fiber spectra were found to vary by ∼10% from exposure
exposure, depending on the amount of light lost from the fiber
ue to atmospheric seeing and astrometric misalignments. Whileis uncertainty is acceptable for the present science purposes,
e flux calibration uncertainty of the single fibers ultimately
ove the design decision of the MaNGA survey to use sevenber IFU “mini-bundles” for each calibration standard star,hich results in a 2%–3% photometric uncertainty (see R. Yanal., in preparation).
Flux-calibrated spectra from the blue and red cameras wereombined across the dichroic break using an inverse-varianceeighted basis spline function. Astrometric solutions were de-Stott+15

20

Wisnioski+15

最近の大規模探査（分子ガス）
CARMA EDGE-CALIFA (125 galaxies at z=0.006-0.03)
Bolatto+17

KMOS3D survey

The Astrophysical Journal, 799:209 (27pp), 2015 February 1

VLT/KMOS

Wi

Wisnioski+15

credit: Iztok Boncina/ ESO

Figure 1. Properties of the observed KMOS3D sample at 0.7 < z < 1.1 (top) and 1.9 < z < 2.7 (bottom) in the SFR−M∗ plane (left) and (U−V)rest − M
Small gray points show the 3D-HST sample without the magnitude and OH contamination selection criterion imposed (Section 2.1). Large symbols argalaxies that have been observed thus far. Large red symbols are galaxies with Hα detections from KMOS and large gray symbols are not detected w
KMOS data. SFRs are derived from a Herschel calibrated ladder of SFR indicators (Wuyts et al. 2011a) and M∗ are derived from SED fits. The bro
parameterization, valid between log M∗ [M# ] = 9.2–11.2, is shown by the solid lines, as defined using 3D-HST data in all CANDELS fields fromusing UV+IR SFRs (Whitaker et al. 2014). Power-law coefficients for redshifts between the bins given in Whitaker et al. (2014) are obtained through ithe coefficients as a function of stellar mass. Dashed lines and dotted lines show 4× and 10× above and below the canonical MS, respectively.

Hα IFU survey in an unbiased sample of >600 galaxies at 0.7<z<2.7
The reduction steps include flat fielding, illumination correc-of the PSF for KMOS3D observations will be p

IFUデータの解析
Vcir, σ0, Mdyn,

生データ(Mhalo, λ)ディスクモデリング

パイプライン

3D CUBEThe Astrophysical Journal, 831:149 (22pp), 2016 November 10
λhe Astrophysical Journal, 831:149 (22pp), 2016 November 10

ガウシアン

フィッティング

velocity map
Wuyts et al.

h Hα surface brightwill argue in Section 3.2 that the asymmetry of broad Hα/[N ii]
cubes. Likewise, weline emission is direct evidence for such differential extinction.
egrated line emission
It is unclear, however, what the general impact of the differential
extinction would be on clump The
scales.
One might naively expect
ernel. We multiplied
Astrophysical Journal, 799:209 (27pp), 2015 February 1
Astrophysical Journal, 799:209 (27pp), 2015 February
1
Wisni
z=0-4にある星形成銀河
that the effect increases
gas column densities/masses relative tom all pixels with Hαaverages on larger scales. However, there
areToomre
almost certainly
nstructed pixel–pixel
criticalparameter. For instance, the sSFR is dalso evolutionary effects, such that inona stellar
given mass
aperture
there
ispersion (δσ = σ(e.g.,
Damen et al. 2009; Bouché et
may be very high dust column densities
in both etneutralcloudsace brightness, andWhitakeral. 2014)
and the samples included in theand H ii regions with relatively low haveextinction.
spatialhtness. Before invesaverageSuch
stellarmasses ranging from log M∗ =separations of 300 pc to >1 kpc are seen
spirals,
suchsame stellar mass, we adjust thons, we culled pixels
Forinanearby
comparison
at theas M51 (Rand & Kulkarni 1990), as well
as atdispersionz ∼ 1 (Tacconi
n addition, in the casevelocity
for each sample to a reference ste
et al. 2010). As a result, the Kennicutt–Schmidt
ral bulge, AGN and aof log M∗scaling= 10.5relation
using the ratio of Equation (3) solv
in Equation (2) may break down or bereference
significantly
nuclear region.
massalteredand theon
average mass of the sample. Th
small scales (e.g., Schruba et al. 2010 inabsolute
M33 onadjustment!80 pc scales).
is 5 km s−1 with the largest adjustmtes and Gas Masses
to the PHIBSS sample (25 km s−1 ), which has an avera
2.4. Spatial Distribution of the Toomre Q-parameter
mass of log M∗ = 11.0.
gas surface densities
expected
range ofA rotating, symmetric and thin gasThedisk
is unstableto velocity dispersions at a giveof Kennicutt (1998b)
canQ-parameterbe widened (Toomre
by increasing the range of rotational
gravitational fragmentation if the Toomre= L (Hα)0 /2.1 × 1041
consideredin Equation1964) is !1. For a gas-dominated disk ina background
potential (8). The boundary values ofluxes for spatially−1(vobs [kms ])are used in Figure 10 to encomp(of dark matter and an old stellar component)Q<
is 250related01) extinction curveof the z ∼isotropy),
1 and z ∼ 2 histograms of rotational
to the local gas velocity dispersion σpeaks
the extra “nebular”
0 (assuming
2KMOS3D galaxies
ofthecircularvelocityv,
epicyclic
frequencyκ(κ= 4 (v c /Rdisk )2 + in Figure 7 and are consistend by Calzetti (2001).
cother surveys
Rdisk d(v c /Rdisk )2 /dRdisk ), gas surface density
Σgas , andconsidered
radius of with the exception of the stegrated UV/optical
−1
Law
et
al.,
which
has
average
v
=
50
km
s
.
the
disk
R
via
the
relation(Binney&
Tremaine
2008;
Escalarot2).10.
Försterure
Same Schreiber
as Figure 8 but showing the disk
medians (horizontal lines)
Figure11. Medians(horizontal
the disk stability
diagnostic,/σ ,Weal.havemadelines)
theofassumption
that
all diskvrotgalaxieLarson2008; Elmegreen
2009;
Dekel
et
2009a)
ameansnebularcorrection(circles)of samples that&have
high-resolution
IFS
data,
their
for IFS samples
with(Genzel+11)
boxes representing the central 50% of the sample and thea gas-rich, marginally unstable
disk
ered
for
thistheanalysisare quasi-stable
disks
with
Qc
rdistributions
formation(boxes)
rates andof 90% distribution (vertical lines). The points&#
verticallines
representing
90%
distribution.
Thevaluesareadjustedtoan$%! " the2value derived for a pure thin gas disk. However, thesenting each sample are sized to the average relative half-lightaverage
10.5.
a v∗c)R=disk/GThe upper and lower boundaries of the curve are theσ0 κ size of theσ0 log(Mxies and adjusted using Equations (3)–(6) to Q
angas
averagepredictions Toomre
following Equation(8) where
Qcrit =for0.67,
for a thickdiskand= log(M∗ ) == 10.5.
parameteris 0.67
a 2.0
thick
gas gas
disk
2
ies
(and
masses,invc composite
πRΣcritgray band is described by σ0 = vrot Qcrit fgas (z)/a whereπfGΣ
and
disk.
= 1, the value adopted in this analysis, is shown by
gasis the gasgas (z)gas1–2diskQ
byfactors
for a stellar-plus-gas disk (e.g., Kim &omEquation(8)ofdata are "from the same surveys as described in Figure 8 and" !Qcrit =the1"solid line.
! The"!
ion as√a function of redshift as determined by Equations!(3)–(7),There
are indications from our data and the
σ0
aMtot
σ0
a
Figure 10. 2007).
used
aChabrier= 2 for IMF
rotational
velocity.
a log(M∗ ) = 10.5 disk with constant== that disk galaxies. at z (3)∼ 1–2 are both thick (e.g., Elm
upper and lower boundaries of the curves are defined by v
vobs
=
250
and
M
v
f
c
gas
c
gas
km s−1 , respectively.
Elmegreen 2006; Genzel et al. 2011) and composite (eσ、v/σの赤方偏移進化

Disk modeling in KMOS3D
in Wuyts+16 paper,
we derive Mdyn and σ0 by contrasting the data with convolved disk models

data

LINEFIT code
(Davies+09, Forster Schreiber+09)
1. extracting spectra in each spatial pixel
or aperture
2. Gaussian fitting to derive rotation
velocity and velocity dispersionl, 831:149 (22pp), 2016 November 10

disk model
DYSMAL code
(Davies+11, Cresci+09)

contrastcharacterizing morphology
re: effective radiusn: Sersic index
from HST 0.2″resolution map
h: scale height
i: inclination
PA: position angle
characterizing kinematics
v : rotation velocity (Mdyn)
σ: velocity dispersion
Wuyts et al.

best-fit
model

vrot
rotational velocity vrot in the midplane,
applying1thedphydrostatic
Σ(r) = Σ
=
f
,
(1)
(r)
+
g
# $ ρ drEquation
2. ROTATIONCURVES OF 2PRESSURIZED,TURBULENT
equation
r
σ
r
2
dp
v
1
GALACTIC
DISKS
rot
.
(8)Equation
h=
exp
=
f
,
(1)
(r)
+
For(9)example,
for a
g
leads
to
where r is therdistancethegalactic
center,
f
is
the
value
g
πGΣ0 fromrρ dr dLet us ofconsidera turbulentforce,galactic
gasthedisk.
We analyze
the gravitationalp ispressure
which its
consists ofsupport(asymmetric
where r is thepressure
distance from thegalactic center,fg is the value2
2 drift)2
rotational
velocityv
inthe
midplane,
applyingthehydrostaticaturbulent(kinetic),andthermal
part,
p
=
ρ(σ
+
c
)
with
ρ
rot
InsertingρfromEquation(7)
into
Equation(3),
therotationv
0s Burkert+10
rot = vof the gravitational force, p is the pressure which consists ofhydrostatic
equation
equation
2one-dimensional
2disk isdensity,σthermalthevelocity
curve
in thethe gasequatorial
planeof characteristic
apart,
pressurizedgas
Note thata turbulent(kinetic),
and
p
=
ρ(σ
+
c
)
with
ρ
s
2
dpassume to be
vrot
dispersion
thegas which1one-dimensional
weisotropic andcsthatits v rot is thethe gasdensity, σ ofthecharacteristic
velocitygas, wNote
the actuall
=
f
,
(1)
(r)
+
g assume(9)theleads
dispersionof thegas rwhich
wetobe isotropic andcs its curve
sound
speed.
We
definetheρ2 dlnΣzero-pressure
velocityv0Equation(r)
the gas,while v0 negligible
is
rotat
2
2
dr
v
=
v
+
2σ
.
(9)
rot the0 force ofsoundasspeed.
definezero-pressure
vpressureは無視できる)
gravitationalpressure
gradient(thermal
0 (r) gradients
the Werotational
velocity
thevelocity
gas ifcurvepressureare (σ = significannegligible0). For vro
dlnr
where
r isnegligible,
the distancegalacticfg r.
is Equationthe
2 center,as therotational
velocityof thethe =gas
if vpressure
gradients
arevalue significantly
by turi.e.,from
dp/dr
0:
≡
f
×
(1) then reduced
g
A
very
sim
0
2
negligible,
i.e.,
dp/dr
=
0:
v
≡
f
×
r.
Equation
(1)
then
of
the
gravitational
force,
pisthepressurewhich
consistsof(zero-pressure)g profile with scale length r A very similar equation hold0 diskFor example,
forto
an exponential
reducesdof theJea22
reduces toa turbulent(kinetic), and thermal part, p = ρ(σ + cs ) with ρ of the Jeans equation(Binne$ 1 d !
#
was
deriv
"
dp
r
was
derived
for
an
expon
the gas density,2 σ thecharacteristic
one-dimensional
velocity!
"22
d vr2 + 2
1 =Note thatandv rota isconth
2 2 r=dp
2
ρσ
.
(2)
v
v
+
ρσ
.
(2)
v
=
v
+
+
=
v
rot = Σwe
0 ×assume0 isotropic
and a constant velocity disp
.
(10)
exp
−
Σ(r)
rot gas0which0ρ0dispersion of the
to
be
and
c
its
dr
ρ
dlnr
s
ρ dr
ρ dlnrrd
the gas,aswhile
vcom
i
0 th
more
more complex
parts ofhigh-z disks are highly turbulent

sound speed. We define the zero-pressure
negligible(σ =0
exponential disk velocity curve v0 (r) densities,
while
other
parts
densities,
Here,
we
have
neglected
thethermalpressure
term
as
the
sound
Here, wevelocity
have neglected
the thermalpressure
term
the sound(see Burkert+10
and Binney&Tremaine08) asastherotational
of
the
gas
if
pressure
gradientsaresignificantly
reduc
Equationtoaddition,thevelocity
disp
speed speedis(9)in leads
generalmuchsmallerthantheturbulentvelocity.
addition,2
isin
generalmuchsmallerthantheturbulentvelocity.
negligible,
i.e.,
dp/dr
= 0:generalv0 ≡ form,fg × withoutr. Equation(1) then In thisAcase,wouldhaveryonesimilarequ
Equation
(2)
is
the
most
specifying
In
this
ca
circularvelocity#$
Equation
(2)
is
the
most
generalform,
without
specifying
reduces
to dependence2 of σ andThe best-resolved
high-redrof the Jeansequatithe radial
ρ. It demonstrates
that a negative
2
2
The
best
the
radialdependence
of
σ
and
ρ.
It
demonstrates
thatanegative
.
(11)
v
=
v
−
2σ
constant
velocity
dispersion
rot reduces0radial pressure gradient
the rotational
velocityofthewasderivedfor!
"rconstantdpdr
1dgradienttherotational
velocityofthe2of pressure
2
2 reduces
2 pressure
exponentiallydecreasing Hαgas asradial
part
thegravitationalforce
isbalancedbytheobserved(2)
vrot = v0 += pressure
v0 + support ρσ .
andaconstantvel
exponent
star-forming gas with scaof velocity
thegravitational
force is balanced by the thepressurerotation
ρ dr
ρ dlnrforce.gas as partcomplexas p
Note To
thatforce.
v rot is thethepossible
actuallyobservablerotational
velocity
ofwithin morethe
1–3 diskscalestar-fo
lengt
illustrate
importanceof pressure
effects,
letdensities,
while 1–othe usgas,
v0 thatis theexpected
if pressure
effectsare
et al. 2010,
in preparation)
Here,
we
have
the
thermalpressuretermofaspressure
the
sound
withinnowwhile
assumeσ isrotation
independentofr. Then
To neglectedillustratethepossible
importanceeffects,let
σが大きいほど見かけの回転速度が遅くなる
curves are
flat
velo
negligible
=
0).
For
vsmaller3, thevelocity
speed
is us
in (σ
generalmuch
thantherotational
turbulentvelocity.isrotationaddition,
etthe
al. and201a
rotσ/σis !
now assume thatindependent
of
r.
Then
vmaxcase,
will beuse
2 turbulent
2
2 dlnρ
In3).thisonesignificantlybypressureeffects specifying
for r " r (Figure.
rotationcEquation(2) reducedis the mostgeneralform, withoutPosition-velocity diagram
Velocity [km s-1 ]

+500
+250
0
-250
-500

Velocity [km s-1 ]

+500
+250
0
-250
-500

+500

Velocity [km s-1 ]dynamical mass

The Astrophysical Journal, 831:149 (22pp), 2016 November 10

+250
0
-250
-500
-0.6

-0.3

0

+0.3 +0.6

Positional offset [arcsec]

-0.6

-0.3

0

+0.3 +0.6

Positional offset [arcsec]

local velocity dispersion

-0.6

-0.3

0

+0.3 +0.6

Positional offset [arcsec]

Dynamical mass
Wuyts+16

240 star-forming galaxies at 0.6<z<2.6
stellar mass 3DfractionWuyts et al.

Figure 6. Inclination distribution of our KMOS sample (black) and thecomplete underlying 3D-HST population matched in mass, redshift, size, andstar formation activity (green), contrasted to the expectation for random
viewing angles (dashed red line). Top panel: inclinations as inferred from theaxial ratio b/a measured with GALFIT (Equation (1)). Middle panel:
distribution of inclinations that yield the best ﬁt of the DYSMAL stellar massmodels to the observed kinematics. Bottom panel: distribution of inclinations
that yield the best ﬁt of the DYSMAL stellar + gas mass models to theobserved kinematics. Our KMOS sample shows a similarly ﬂat distribution of
inclinations as the underlying matched population, with only a slight paucity ofvery edge- or face-on systems compared to the expectation for random viewing
angles. In contrast, an implausibly large number of edge-on inclinations would
be required to optimally reproduce the observed kinematics when ﬁxing thetotal mass to our best estimates of the stellar or baryonic mass present.

28% 31% 42%

baryonic mass fraction

45% 54% 89%

a thicker column of obscuring material when seen edge-on.
This could reduce the Hα S/N and potentially cause them todrop out of our sample more easily. On the other hand, asreported in Section 2.3, some galaxies, while Hα detected, did
not pass our sample selection because their face-on view
prevented meaningful constraints on the enclosed dynamical
mass. The top panel of Figure 6 illustrates that nevertheless theinclination distribution of our sample as inferred from axial
Figure 7. Stellar mass fraction (top row) and baryonic mass fraction (bottom
ratio measurements on the HST imaging is relatively ﬂat,row) as a function of redshift. Large circles mark the median for each redshiftbin. Filled circles represent results assuming the default Chabrier (2003) IMF,
mimicking that of the underlying matched 3D-HST population
while large open circles indicate the shift if a Salpeter (1955) IMF were
遠方銀河の内側（R<Re）では、(normalized distribution
shown in green). Modulo
a minoradopted instead. Galaxies in our highest-redshift bin (z _ 2.3) are entirely
dearth of very edge-on and face-on systems, the distributions
baryon-dominated within Re.
ほとんどの質量はバリオン（星＋ガス）が担っている
are in line with the expectation for random viewing angles.
The middle and bottom panels of Figure 6 convincingly
4.3. Trends with Other Galaxy Properties
demonstrate that this is no longer the case when considering theEquations(5)–(7)offer
an interesting
futureM§observadisk,
embeddedina Navarro–Frenk–White(NFW;
Navarroet a∼0.037
and its
dispersio
for theirdark matter
halos,
in
terms
of
mean
spin
parameter
to values that are consistent
with
2
3 1/2
large.
tionaltesttheofdisk
ourassumptions
aswith
for
an
H
=
Hdark
+and
(1
−
ΩΛtheir−exponentialΩ+distributionz)disk+density,ΩM (1 but+ z)do] not. d
1997)
halo
with
density0 [ΩΛmatter
M )(1surface
ituation is different for
rotation- correlate
parameters
withradialscale
stellar(10)) with constant velocity dispersion the scale
sure effects play a minor
As stellar(Equation
halorole.
mass,
mass,
or
redshift.
Ourexponentiallydata thusDISK
supportthe long-standing assumption that on
3.
GALACTIC
MODEL
heighthshouldincreasewithradius4ρc
We adopt aofstandard
ΛCDM
cosmology
withHkm
studies at low redshifts(e.g., Mo
0 = 73
redshifts,
the speciﬁc angular momentum
disk
galaxies
reﬂects
that
of
their
dark
matter
halos
(
ρ
(r)
=
,
(1
Given
DM
−1
2 Burkert+16$(1998)# al.
07), we argue that theobserved,Ω=
0.238,
andΩ=
0.762.
(r/r
)(1
+
r/r
)
2
s
s
M
Λ
Weλ×(
adopt
the
model
by
Mo
et
of
an
exponential
)
and
the
nuclearstellardensityΣ(1
kpc)
favors a be
scenarcorrelation
betweenjd/jMpc
Exponential
Disk
withinan
NFW
Dark
MatterHalo(Mo+98)
DM
σ
r
*
cal
better accord with cosmological.
(8)anetexponential
h Navarro–Frenk–White
=
exp
The
galactic
disk is assumed
to follow
suro
angular momentum
redistribution
leads
toπ GΣ
“compaction”
insidemassivehigh-redshiftdisks.inFor
disk,
embeddedina(NFW;
Navarroal.
anrtheir dark matter halos did not
0 halo scaledwhere profilers is theradiusandρcsurfaceis the dark
matteratdensi
density(Equation(10)).
Its
densityr In=
average forstellar to1997)
dark dark
mattermattermass halo
ratio withis ∼2%,
consistent
with abundance matching results.
density
distribution
curve,
we propose an explanation
at rsDark. The scaleradiusis related
to the virial
12 radius r200 v
NFW
MatterHalo(Navarro+97)
Mm
corr
gas,
the
total
baryonic
disk
to
dark
matter
mass
ratio
is
∼5%
for
halos
near
10
Σ
is
determined
by
the
total
disk
mass
M
×M
InsertingρfromEquation(7)
into
Equation(3),
therotation0e,dwhich
0 r = r /c, where c is the halo concentrationd =200
e more common
many parameterhigh-zavalu
DMinhaloparameter.
Th
s
200
4ρ
curve
in
the
equatorial
plane
of
a
pressurized
gas
disk
is
c
cosmologicallyavailable
baryons,
implyingthat
high-redshift
disks
are
strongly
baryondominaThe
AstrophysicalJournal,826:214(21pp),
2016
August1
mddarkthe
disk
mass fractionof theurce of turbulencerotationcurve correspondingρ halo(r) =, galaxyto Equation(12) (12)a isfirst(Min these, R disks,Vλ)DM halo massDM

virialvirial,

DM

2
(r/r
)(1
+
r/r
)
s
s
Key
words:
cosmology:
observations–
galaxies:
evolution– galaxies:
high-redshift
–and
infra
a
on factor (cpsf,v) between the observed maximum rotation velocity
and2the intrinsic
maximumrotation velocityof an exponentia
dlnΣ "
2
2!
M
観測不可Disk within
3Dr/rs )B.2. Exponential
NFW
Dark
MatterHalo
vrotfor=v0 + 22σ. ln(1 + r/r
r200observations,−as(9)(r/rs )200s )/(1 +(1.68 Rd) for a single-GaussianPSF (open symbols,
appropriate
seeinglimited
such
in
KMOS
), asthiswell pr
a
2an
Σ
=
m
.
dlnr
(r)
=
V
v
.
(1
0
d
PRESSURIZED, TURBULENT
where
r
is
the
halo
scale
radius
and
ρ
is
the
dark
matterdensity
2 masses as labeled in th
DM show the
200 correctionsc
ate for AO observations (ﬁlled symbols). Circles,s stars, and squares
for different
disk
2π
r
r
ln(1
+
c)
− c/(1 + c)
followd
TIC DISKS
FollowingMo
etrsexample,(1998),
wetheisnow
onvirial
a second
atFor
. al.
The
scale
relatedto theradiusviaratio of the rad
200 thesizeRanda sets can be well describedby a ﬁtting
functionthatdependsonratio
of focus
Rprofile
for anradius
exponential
disk
with
scale
lengthrrdthe1.
INTRODUCTION
1/2 to beam
1/2,beam
HereG
isgravitationalcorotatio
Exponential
thin
disk
(Freeman+70)
rs we= rthatwherec is= thehaloparameter.
The
to analyze
Rparameter
the graph
show
the
case
Rvel
R1/2
). Right
panel:
correction
factorfromtheobserved
ve
mined,
200 /c,High-resolution
numerical
cold
dark
matter(CDM)
simulation
1/2 (inassuming
galacticRvel,gas relative
disk.
We
its
approach,anexponential
baryonic
disk
with
disk
$ −1
#concentrationThe
circularvelocity
curve
of
an
exponential
disk
is
(Free
Hubbleconstants
at
z
and
z=
(SectiIn thecold dark
matterparadigm,
baryonicr kmtos show
the intrinsic
velocity
dispersion(assumedin (CDM)
this
speciﬁcsimulation
to be
σ0al.
=disk
55
, appropriate
forz ~ 2–2.6,
Wisniosko
darkhalo
rotation
curve
corresponding
Equation(12)
is
idplane,applyingthehydrostatic(e.g.,
Zhao
et
2009)
that
c
depends
strongly(M, Rdisk,vdisk,masses
σcenters(R)=Σexp(−R/R) densities
is inoftheΛplot),surface
distribution
Σhalos
1970)
.
(10)
× exp
−&
Σ(r)
Σ0(e.g.,disk
0)energyandmometotal
d=0colors,dasgalaxies
form
atdensity
theofdark matter
Fallfordifferent
stellarandinclinations(symbolshapesandrespectively,
labeledandaga
R1/2/R1/2,beamrcosmologicalredshift.
d While c decreases with halo virial ma" for! 2010sectioclosuredensity.
theoembedded
in
an
NFW
dark
matterhalo.
Itsfactor
velocityand AOobservations(ﬁlledsymbols).
The
outervelocity
dispersion
correction
bedescribed
by aTidal
singletorqueparameter
Efstathiou
1980;
Fall
1983;
see
Mo
et
al.
a +review).
ln(1
r/r
r
)the
− cannot
(r/r
1 dp
観測可 2
s circulars )roughly
2 200
2 s )/(1 + r/r
atlow
redshifts,
concentrationisconstantwi
2 M200
v
(r)
=
4π
GΣ
r
y
[I
(y)K
(y)
−
I
(y)K
(y)],
,Deﬁning
(1)
+
(r)
=
V
v
.
(13)
(z))
have
to
be
used
to
createalook-uptable
toestimatetheintrinsic
velocity
dispersion
for
each
gal
h(r)graphs(fordifferent
σ
0
d
0
0
1
1
0
White 1984)
suggests that w
Equation(9) region
leads
the
halotheradiusasofthewithinwhich
theDM
200 tois given
by
sum
the
disk
and
contribution
ρ drc ≈disk
independent
r4 andhaloln(1+ c) of− haloc/(1 mass+ c) at z ≈ 2. The halo viri
4. Athvirialized dark matter particles have on parameters
average 200r times
thecentrifugal
supportofbaryon
#
$
and
M
are
related
to
each
other
through200I and K denoting the modified Be
he galactic center, fg is the value
rthe
with
y2 = r/(2r) and2
2 halo’s
2 2 200
観測された回転速度において、dvelocity,n “DM”n from here on) is small an
2mean mass density of theuniverse,thevirialv
v
v,(simulations
10) also the earlier
High-resolution
numerical
cold
dark
matter
(CDM)
.
(11)
v
=
v
−
2σ
virialvelocity
V
(Mo
et
al.
1998):
rot DM0pressure whichof determine
200 Mo et al. (1998;
circ
diskvirial
r thesimulateddata consists
sets toits
parameters.
seefunctions(Binney&
Tremaine2008).
rd diskで説明できない分は
, its
MDM
, and(e.g.,
its virial
radiusRvirialare giveninthatthev=virial
2 mass
2
Zhao
et
al.
2009)
show
c1980
depends
strongly
on derivedFig
mal
part,
p
ρ(σ
+
c
)
with
ρ
een the measured
velocity
dispersion
by
Fall
&
Efstathiou
and
Fall
1983)
sio
s
3
We
will
neglectabulge
becauseweareinterested
inthespherical
collapse
model
(for
a
ﬂat
ΛCDM
universe)by
the
V200 (z) redshi(z)
V200DMからの寄与と考える
eristic
one-dimensional
Xavirial
JDM M
withthevelocity
“thin
disk
limit”(Freeman
1970;
et
al.
1997)
cosmologicalredshift.
Whilec Navarrodecreaseswith
halovirialmass
IFU観測データ
HST観測データ
Note
that
v
is
the
actuallyobservablerotational
velocity
of
rot
),
where
the
,
adopting
non-self-gravita
isk parts
(R
∼
2–2.5
R
expressions
for
λ
and
M
1/2
DM
M


F
r
,
M
.
(1
(z)
=
(z)
=
disk
parts
where
the
bulge
contribution
totherotation
curv
200
200
relations(Peebles
1969;
Gunn
&
Gott
assume to following
be isotropicwelland cknown
s its
M
at
low
redshifts,
theconcentrationisroughly
constantwiththewhile vexponential
expectedif(z)pressurein
effectsare200gas,10H
10GH (z)halo
0 is the rotation
X
RThe
q
d
virial,cs
eared
rotationisminimal
(with
the
disk,
embeddedanisothermal
virialw
2
Bertschinger
1985;
Mo
et
al.
1998)
2
ro-pressure1972;
velocity
curve
v
(r)
0
negligible
(σ
=
0).
For
v
/σ
!
3,
the
rotational
velocityisc 2≈4d )andindependent
ofradius
halo mass
at z. ≈
2. The halo of
virial
rot
v
y

R
R

Q
G
4
R
y
(
4
0
d
disk
FörsteCombination
Equations(1)solutionalready
removed).
The
righttruncation
atR
原理的には観測データからhalo
massとhalospinparameterが得られる
virialhe gas if pressure gradients are
significantly
reducedbyturbulentpressureeffects
for
r
"
r
.
H
is
the
Hubbleparameterthatdependsoncosmologicalredshidparameters
r
and
M
are
related
to
each
other
throughthevvirial
200
200
where
ω=v
et al.
rot/R is the angula(3)yields
s02 these
correction
factors.
In≡ fg dispersion
× r. Equation
(1)
then
q
I
y
K
y

I
y
K
y
[
(
)
(
)
(
)
(
)]
,
Rvirial 
A and
very
similar equation
holds
for
stellardisks
asa
specialform
0 virial
0velocity
11z:
V200 (Mo et al. halo1998):spin parameterand“vi20
velocity) at R, and
(
)
10
H
z
halo
mass
factors depend on inclination, ofstellarthe Jeans equation (Binney & Tremaine 2008).tangential
Equation (11)and 2
2 ⎞1 and “centrifugal
3 1/2
3
nentiathevirialradius”⎛
wasderivedforanexponential
surfacedensity
distribution
⎛
⎞
H
=
H
[Ω
+
(1
−
Ω
−
Ω
)(1
+
z)
+
Ω
(1
+
z)
]
. (1
persion,
such
that
we
createdlook-up
3
!
"
j
d
1
0
Λ
Λ
M
M
v
R
v
R
virialdvirialvirial
2
2
(z)
V
(z)
V
d
200
200
ρσ M
. DM2 intrinsic= thev0 + beam corrected,where (2) 2velocity⎛⎞
anda constantvelocity
dispersion.
In
general,thesituation
isò is(14)
M

q
q
2
about
⎟
⎜
R
⎜
⎟
virialThe
constant
∼
,
J
and
j are
2
r
,
M
.
(z)
=
(z)
=
200
200
ρ dlnr⎜10GH (z⎟)⎝⎠
v DM  GvvirialqRj⎠with H0 = 73the⎝ surface
more complex asWe
partsof (z)
thedisk mightΛCDM
haveconstant
10H
10GH
(z)
2−
virial
DM
di
adopt
a
standard
cosmologykmsangular momenta, and E∼GM
e purpose of this analysis we assumed⎝ R ⎠ 3 −1
1 2

densities, while other parts might show a steep gradient. In

Monte-Carlo search of halo parameter
Astrophysical Journal, 826:214 (21pp), 2016 August 1

Burkert et al.

Burkert+16

md<0.25
red: observed properties and uncertainties
cyan: mean of converged disk-halo models
md<0.25(cosmic baryonic fraction, 0.17)

ure 11. NFW MC modeling of BX 455. The large red triangles with error bars show the galaxy’s observed physical properties and uncertainties. Small blue points

for their dark matter halos, in terms of mean spin parameter M§∼0.037 and its dispersio
parameters correlate with the disk radial scale and with their stellar surface density, but do not d
The Astrophysical
826:214the(21pp),
2016 August assumption
1
halo mass, stellar mass, or redshift.
Our dataJournal,
thus support
long-standingthat onence of the inferred λ×( j /j )redshifts,
parameters fromthe
the NFW
MC modelingfor the “best”(ﬁlled blue circles)“full”galaxies(ﬁlled plus open
blue circles)
speciﬁcangularmomentumof anddisk
reﬂects
that of their dark matter halos (. The nomenclature is the same as intion Burkert+16
of (from left to right) rotation velocity at R∼R , stellar surface density within R and R /(1 + z)
)
and
the
nuclearstellarcorrelation
betweenamong
λ×(jd/jexploredee plots in this ﬁgure show the strongest
parameter correlations
the trends
inSection
3.2(withslopes differingfrom density
zero at the Σ*(1 kpc) favors a scenarDM
angular momentum redistribution leads to “compaction” inside massive high-redshift disks. For oaverage stellar to dark matter mass ratio is ∼2%, consistent with abundance matching results. Ingas, the total baryonic disk to dark matter mass ratio is ∼5% for halos near 1012Me, which corr
cosmologically available baryons, implying that high-redshift disks are strongly baryon domina

Monte-Carlo search of halo parameter
d

DM

1/2

1/2

d

−0.75

Keythewords:
cosmology:
observations
galaxies:
evolution– galaxies:
high-redshift– infraon factor (cpsf,v) between
observedmaximum rotation
velocity–and
the intrinsic
maximumrotation velocityof an exponentia(1.68 Rd) for a single-Gaussian PSF (open symbols, appropriate for seeing limited observations, such as in KMOS3D), as well a
ate for AO observations (ﬁlled symbols). Circles, stars, and squares show the corrections for different disk masses as labeled in th
size R1/2,beam
and theratio of the rada sets can be well described by a ﬁtting
function that depends on the ratio of R1/2 to beam Here
1. INTRODUCTION
G is thegravitationalcofactorfrom theobserved
ve
mined, Rvel, relative to R1/2 (in the graph we show the case Rvel = R1/2). Right panel: correction
Hubbleconstants
at
z
and
z=
−1
In thedispersion
cold dark
matterin (CDM)
paradigm,
the intrinsic velocity(assumed
this speciﬁc
simulationbaryonic
to be σ0 =disk
55 km s , appropriate for z ~ 2–2.6, Wisniosk
energyasdensities
andandtotalgalaxies
formstellar
at themasses
centers
dark matter
halos(e.g.,& respectively,
for different
and ofinclinations(symbolshapesandFallcolors,labeled inof
theΛplot),aga
R1/2/R1/2,beamclosuredensity.
theoand AO observations
symbols).
The outervelocity
dispersion
correction
factor cannot
be describedby aTidal
singletorqueparameter
Efstathiou(ﬁlled
1980;
Fall 1983;
see Moet al.
2010 fora review).
have tobe usedcreatea look-up
table whichto estimate
velocity
dispersion
for eachh graphs (fordifferent σthe0(z))halo
White
1984)
suggests
thatgalw
Deﬁningradiusastotheregionwithinthethe intrinsic

virialized dark matter particles have on average 200 times thecentrifugal support of baryon
mean mass density of the universe, the halo’s virial velocity,“DM”
fromsee
hereon)theis smallr simulated data sets to determine
its virial parameters. Mo et al.
(1998;
also
earlieranvvirial, its mass MDM, and its virial radius Rvirial are given in theeen the measured
velocitymodel
dispersion
by Falluniverse)& Efstathiou
derived si
spherical collapse(for a ﬂat ΛCDM
by the 1980 and Fall X1983)
JDM M
virial
),
where
the
,
adoptinganon-self-gravita
isk parts following(R ∼ 2–2.5
R
expressions
for
λ
and
M
1/2
DM
M


F
well known relations (Peebles 1969; Gunn & GottR virialwq
virial,cs
eared rotation
is minimal 1985;(withMotheet al. 1998)
exponential disk, embedded in an X
isothermal
halo
1972; Bertschinger

solution already removed). The righttruncation radius at Rvirial. Combination of Equations (1)o total halo mass ratios as a function of M for v
ourdisks of the “full” (open and ﬁlled blue circles) and “best” (ﬁlled blue circles) samples fromourvirialwhereω=vLeft:is the forangularot/R(3)yieldssng.
thesedispersionrightcorrection
factors.
In
Figure4.
Distributionofinferred
λ×(
j
/j
)
parameters.
distribution
all 31andd
DMThe blue cross in the upperR
denotesthetypical1σuncertainties.
The
continuous
cyan
line
denotestheaverage
trend
of
the
“full”
sampleinvirialred ﬁlled square
marks
the10
medianofour measurements.
TheMC
red arrowdenotes under
the average
fromparameterstellarinfactorslog(M ). The
NFW
modeling,
the correction
assumptionofno toadiabaticvelocity)
contraction atof thetangential
R, dark
andmatte“vi
H (valuez) mass
halo
spin
halo
dependon
inclination,
stellarM*) § _ 0.58). Thesquares,
right verticalaxis
denotes theratioof the circles
stellar disk
mass tothe
the same NFW MC modeling, but this ti
sses, including the molecular gas contribution (M (Mredthetriangles,
and
green
denote1 and “centrifugal
2
3,
adoptingacosmicbaryontodark
halo
fraction
of
0.17.
The
thick
gray
and
black
curvesgive
ﬁttingfunctionobtainedby
Mosteretal.
(2013)
thevirialradius”⎞⎛⎛⎞
persion,
such
that
we
createdlook-upv and dark
Rvirialvvirialcontraction,asz=2.6,
well asrespectively.
without adiabatic
contraction
the corrections for va
d curves but jincludingdd abundance matching of stellar mass functionsvirial
matter halo simulations
for z=0.8 andThe black R
dashed
,
where
M


M

q
q
2
⎟
⎜
⎜ z=1three⎟z=2DM
uncertaintyof the combinedz=0.8
and intrinsicz =2.6 Moster velocity
et al. (2013) models. theMagentaand greeninthicklines markandTheconstant
ò is ∼ of
J and
j are
2 ,thehistogramthedashedleft panel
we theshow
other,
simpler estimates
λ distribu
the beamcorrected
10GH
(
)
G
z
⎝
⎠
R
j
ing results of Behroozi et al. (2010, 2013b).
⎝ DMthe⎠ simple assumption MDM2
virialdisk sample if instead of the NFW
MCmodeling
angularmomenta, and E∼GM
e purpose of this analysis we assumed “best”
2
the full sample is used, the centroid is similar, but the scatter is larg
m = 0.05.3If1instead
DM

DM

gas

gas

redshift.
Whilec decreases
density in the midplane(z =0) at radiusr and with halo virial mass
with ρ0 (r) the cosmologicalredshift g
actic disk
M200 at low redshifts,
the concentration is roughly constant with
he derived
The dataσh =independent, of halo mass at(5)z ≈ 2. The halo virial√c ≈ 4 andral energyFörster-S
2π Gρ0pplication
parameters r200 and M200 are related to each other through the
et al. (20Hα RCs of 2155 low-z disk galaxies
hey found CATINELLA,&HAYNES
virialet al.Σ(r)1998):
the scaleGIOVANELLI,
height.
Thevelocity
total
massVsurface
densityof such aVol. 640
200 (Moand 20–3
ibly high.
disk is (Binney & Tremaine 2008) (Catinella+06)
nential de which isabove, each template
mentioned
3
V200 (z)V200 (z)veraging
at least four samples
situation
about the
Σ
=
2ρ
h,
(6)
r
,
M
.
(14)
(z)
=
(z)
=
0
200
200
the averagelence
can of 3 or less points
10H (z)10GH brighter(z)
the disk’mplateRC
pointswereobtained
he impact
so thatpatial bins (i.e., bins
resultingies segre2
inI-bandmagnitude
dynamical
πGΣ
parameterthat depends on
cosmological redshift
individual RC points) in order H is the Hubble
=
.
(7)
ρ
of vmax /0pressure,and error bars of the2
Positions
2σz:dominate
ispersionaverage of the corresponding
Equations (5)–(7) offer an interesting future observastent with
objects w
2
3 1/2
tionaltestof
our
assumptions
as
for
an
exponential
disk
H
=
H
[Ω
+
(1
−
Ω
−
Ω
)(1
+
z)
+
Ω
(1
+
z)
]
.
(15)
0
Λ
Λ
M
M
rotationlasses
was initially done with agradients(Equation
(10))
with
constant
velocity
dispersion
the
scale
ornsrole.
at theAs
faint end of the intervaltion curv
heighth should
increaseradiusWe
adoptexponentiallya standard with
ΛCDM
cosmology with H0 = 73 km s−1
void
theMo
overlap of
the corre(e.g.,
triangles;observed
in particular, two classes, M i Mpc−1 , Ω = 0.238,
$
#
and
Ω
=
0.762.
2MΛ#1
σr
Mi i # hv! r; Mj ij ! 10 km s .
Note thamological.
(8)an exponential surfaceh=exp
The galactic disk is assumed
to follow
span the I-band absolute magπ GΣ0rds(18didobjects
not with luminosities
not to thedensity
profile(Equation(10)).
Its
surfacedensityatr=0,
nationford).
Figure1Σisdetermined
by
the
total
disk
mass
M
=
m
×
M
with
InsertingρfromEquation(7)
into
Equation(3),
therotation
0
0
d
d
200
ny
RCshigh-z
was identical for the rd andhave radin the equatorial
planemassof a pressurized
gasthediskgalaxyis
md the disk
fraction ofr the disks
values of the curve
grid spacing
hese

Outer rotation curves(as in list points 2 and 3 above).
spacing and !r were chosen to22
2 dlnΣ
M200 (9)vrot = v0 + 2σ.
s,takingintoaccount
thattheturnover radius~2.16 rd dlnr Σ0 = md.
(16)
BULENT2o is 3:31 $ 0:01 for the sample
Fig. 1.—Template RCs parameterized as functions 2πof exponential
disk scalerdEach curve is disklabeledprofileon the rightby scaleits meanlengthI-band absolutemags.
For example, forlengths.
anexponential
with
r
d
#1
#1
Mpc ).disk
The final (Freeman+70)
sample includes 2155 RCs extending
nitude ( H0 ¼ 70 km s thinlope of observed H!/½N ii& RCs Exponential(
nalyze its
inclination
tocurvethe$line of ofsightani < 80. The vertical dottedbeyond
2rd and with#The
circularvelocity
exponential
disk is (Freeman
internal extinction in the inner
lines
show
the
interval
over
which
the
velocity
normalization
was
performedrydrostatic
dust attenuation is more severe 1970). on the mean. Polyex
(10)
×
exp
−
Σ(r)
=
Σ
(see x 2). The error
fits to the data
0 bars are Poissonian errorsrpoints are indicated by solid lines; thecally brighter systems. For thisd fit coefficients are presented in Fig. 3 and(Table 1.
nation i ' 80 were excluded
2
2
v
(r)
=
4π
GΣ
r
y
[I0 (y)K0 (y) − I1 (y)K1 (y)],
(17)
(1)
0
d
Equation(9) leads todisk
entioned. Seeing may
also sysof observed RCs, especially for
expanded to include at #least$10 elements; hence, their spacing

nated galthe dispeorder 100
250 km s
The s
specified
2001; Buz

–120

RESEARCH LETTER
Major-axis offset (kpc)

+210

–100
–200
–2

200

–10

0
0

10

0

+40

–100

–120
2.5″ (21 kpc)

–200

300

+215

–1

0

–10

200

22 h

100
0

–215
1.1″ (9 kpc)
+190

–100
–200
–300

200

–1

0

1

–10

0

10

28 h

100

100

–100

–190
2.6″ (22 kpc)

2.6″ (22 kpc)

–2

+170

–1

–10

9h

0

0

22 h

0
–2

200

–200
–300

200

–1

0

1

–10

0

10

0

1

28 h

100
0

–1
–10

0

–200
–2

2

1

0

10

+170

200
100

–1
–10

2

0

10

0

1

9h

0
100 –170

–100

+140

1.2″ (10 kpc)

–200

200

+40

–1

0

–10

0

1
10

–220

300
200

–1
–20

–10

0

10

0

1

20

12 h

100

+134

3.5″ (27 kpc)

0
100

–100

+220

–200
–300

0

–1

0

1

–10

0

10

–3 –2 –1

2

3

Major-axis offset (″)

200
Figure 1 | Hα gas dynamics fromKMOS and SINFONI in six massive
star-forming galaxies. The galaxies
150 have redshifts between z = 0.9+30
and z = 2.4. KMOS
provides seeing-limited data (full-width at half100
maximum, FWHM ≈ 0.6″); SINFONI
allows both seeing-limited and+140
adaptive-optics-assisted observations (FWHM ≈ 0.2″). a, For each50
galaxy, the distribution of the integrated Hα line surface brightness isshown (colour scale; with a linear 0scaling), superposed on the stellar
1
2
–2
–1
0
1
2
surface density (Σ*; top three panels) or the H-band continuum surface
0
10
–10
10
brightness (ΣH; bottom three panels)(white contours;
square-root
200+58
scaling). The horizontal white bar denotes the physical size scale.

are they representative of high-z SF galaxies?
–200

10

–100

- outer rotation curves drop beyond the turnover radius
0

0

1

–100

–190

0
10

10

+190

+60

1

0

0

200

2

1

10 h

100

+120

–1

D3a 6397, z = 1.5

2.6″ (21 kpc)

Major-axis offset (kpc)
–10

0

+170

1.1″ (9 kpc)

Rotation velocity dispersion (km s–1)

100

–10

200

–215

10

33 h

0

0

e

GS4 43501, z = 1.6

0

–1

100

d

COS4 01351, z = 0.9

–170

200

1.5

–10

200

Rotation velocity (km s–1)

D3a 15504, z = 2.4
zC 406690, z = 2.2
zC 400569, z = 2.2
GS4 43501, z = 1.6

c

b

a

+215

Rotation velocity (km s–1)

Genzel+17

–200

300

zC 400569, z = 2.2

Outer rotation curves

2.5″ (21 kpc)

at 0.2″ (filledcontinuous la combinatio
NFW halo w
at z ≈ 2 and calso take into
velocity disppanel indicat(d; colour sc
dispersion dOuter rotation curves

LETTER RESEARCH

nal, 840:92 (24pp), 2017 May 10

tation curves
idual velocity
such that thel data point is
all data points
d together, theurve becomes

Lang et al.

stacking of 101 high-z SFGsa
Normalized rotation velocity

Lang+17

Genzel+17b
sive disksam0=
Average z

1.0

Milky Way
M31

Infinitely thin
Freeman disk

Stack (ref. 18)
0.5
on curves are
GS4 43501
zC 400569
eaming along
D3a 15504
nematic axis,
zC 406690
rium motions
COS4 01351
Thick, turbulent
disk
D3a 6397
aryonic accre0
es in three of
1
2
3
4
0
1
2
3 0
n one, but the
R/RmaxR/R1/2
ed rotation curve (black circles), shown together with a baryonic-only exponential disk model (black lines), and models with added dark
edifferent
satellite.
We(colored lines). Eachmodel is convolved
with aexplained
PSF of the representative
average
FWHM
baryonic massfractionin the disk, mrotation
falling
curves
can
be
by
two
affects
Figure| Normalized
rotationcurves.
Thetovarious
decrease with symbols denoteization. Also shown are versions ofeach models2with
implemented pressure support(dashed lines),
with V /σa,adopted
5,region
ranging fromin
6.3 oneto 4.8.
1. highbaryonic
fraction
the folded
and binned
rotation curve data for the six galaxies in Fig. 1,
ccretion of gas2. pressure
combinedwiththemstacked
rotation curve of 97 z = 0.6–2.6 star-forming
RC together with a normalized
pure support
settingd=0.17, representing the cosmic baryon fraction
18
stableat highbaryonic
Althoughthisdeland additional
plus darkrelative to thatof allthe dark
matter (Ωb/ΩDM). we(Methods).
Forrotationcurves,averageddata points
galaxiesdrot0al circular velocity at the half-light radius (rest-frame optical) R1/2, including bulge, exponential disk (n = 1) and dark matter, and corrected for asymmetric drift:) 2 = ν rot(R ) 2 + 3.36σ 20 (R /R1 / 2) n= 1.
lge is the baryonic mass confined to the central 1 kpc of the galaxy, less the contribution from the exponential disk.
; numbers in parentheses are the ±2 r.m.s. or upper limits (goodness of fit δχ2 = 4, abouto of dark-matter mass to total mass at the best-fit half-light radius of the optical light, fDM(R = R1 / 2) = (v DM/vc ) 2

Comparisons with low-redshift results
R = R1 / 2

probability) uncertainties. We use an NFW halo with concentration parameter c and no adiabatic contraction.
220
BERSHADY ET AL.

Vol. 716
DiskMass survey (Martinsson+13, Bershady+10)

Genzel+17

galaxies. Large gas columns can easily dissipate angular momentum
and drive gas inward. The strong redshift dependence of the gas
fractions could explain the decrease in fDM between z = 2.3 and z = 1
z=0(Fig. 3). Second, massive galaxies at high redshift are thought to growlate-type disks
by rapid gas accretion, gas-rich mergers and star formation triggered
0.8
The IMF of massive
bulges3185
by this accretion27,28. In this dissipation-dominated
peak
phase
of
SWELLS survey (Dutton+13)
galaxy growth, the centres of dark-matter haloes can become baryondominated in ‘compaction events’ that are triggered by mergers, disk
instabilities or colliding streams in the intergalactic web29, or by gas
0.6‘pile-up’ at early times when the gas accretion rates were larger than thestar formation consumption rates. However, results from abundance
Milky Way
matching indicate that the average stellar-to-dark-matter ratio at
z = 0 massive,
Figure1. Postage
imagesofthe galaxiesof
analysed
this paper.
The images
are depend
obtained from multicolour
HST images
described in epoch
SWELLS-I
thestampvirial
radiustheinhalonotstrongly
on ascosmic
ATLAS3D(Cappellari+11)
Figure 9.does(Continued)
z=0
and III.
bulgeddisks
0.4
and is well below the cosmic baryon
fraction fb ≈0.17, suggestive ofearly-type disks(Pohlen & Trujillo 2006). In
these cases, we redid the fitting
Section 5.1 failed to provide an adequate description of the
302 the redshift
Tableand1. Basic
propertiesscales.
of galaxies
analysed inthiswaspaper.because
All errors correspond
1σ . Column 1thelists radial
the lens region
ID; Column
the deflector;
after toby
identifying
outsidebreak
disk radialluminosity
Typically
thisvery
efficient
removalof
baryonsgalactic
outflows. of anofinnerColumn 3 gives the velocity dispersion of the singular isothermal ellipsoid (SIE) lens model from paper III; Columns 4 and 5 give half-light sizes for the bulge
corresponding
totheextentoftheSparsePak
footprint.
Thea light profile
showedevidencefor
inner
breaks(type
Iand(circularized) and disc (major axis) from papers I and III; Columns 6, 7 and 8 give the stellar masses for the bulge, disc and total, assuming a Chabrier (2003)
Third,
itis
alsopossiblethatthebaryondominanceiscaused
by
a
lack
disk
centralsurfacebrightness
andscale-length
valuesin
II luminosity
profiles;Freeman1970)
and/orouter
breaks
IMF; Columns 9 and 10 give the model (dust-reddened) rest-frame V-band luminosities for the bulge and disc; Columns 11 and 12 give the model (B −theV)colours for the bulge
and
disc.
of dark matter in the inner disk. These dark-matter haloes could deviate
ID
z
σ
R
R
log(M
)profile,log(M) withlog(M low)log(L )
log(L )(B − V)(B − V)
0.2
from
the
standard
NFW
concentration
parameter
Figure 9. (Continued)(km s )(kpc) (kpc)
(M" )
(M" )
(M" )
(L" )
(L" )
(c(2)< 5),(3)if they
still
rapidlyand (9)not yet(10)in equilibrium,(1)(4) were(5)(6) growing
(7)
(8)
(11)
(12)
(Pohlen & Trujillo 2006). In these cases, we redid the fitting
ection 5.1 failed to provide an adequate description of the
0.116± 4.4were2.42 perturbed
23.43 11.05 ± 0.09
± 0.09 11.45± 0.07 and10.54 ±
0.04 10.84± 0.040.79
0.70
if 251.2
theyby11.23strongstellaractivegalactic-nucleus
after identifying the radial regionJ0841+3824
outside of or
an
inner
break
sk radial and luminosity scales. Typically this was because
J0915+4211 0.078 195.7 ± 2.2 1.56
4.15 10.60 ± 0.09 10.17 ± 0.09 10.74 ± 0.08 10.03 ± 0.05
9.73 ± 0.05
0.81
0.72
corresponding to the extent of the SparsePak feedback.
footprint. The
light profile showed evidence for inner breaks (type I andsomeof these
alternatives,
as0.04low0.87concenJ0955+0101 0.111 238.4 ± 7.3 We
1.62 discuss
3.72 10.63± 0.09 10.17± 0.09 10.76± 0.07 10.00 ± 0.04such
9.73 ±
0.73
disk central surface brightness andJ1251−0208
scale-length0.224
valuesin theluminosity profiles; Freeman 1970) and/or outer breaks
203.0 ± 2.6 1.68 12.01 10.68 ± 0.07 10.96 ± 0.07 11.14 ± 0.06 10.16 ± 0.04 10.68 ± 0.03
0.82
0.65
and
providea quantitative
comparison
between
J1331+3638 tration
0.113 248.1 ±parameters,
4.4 2.86 12.46 10.89± 0.1010.46 ± 0.10
11.03 ± 0.07 10.38 ± 0.04
10.34 ± 0.04
0.78
0.47
0
100
200
300
400
observations and simulations in Methods.
Adiabatic
contractionfDM(R = R1/2)

1.0dvc (km s–1)

SIE
−1

bulge

disc

Chab
SPS,b

Chab
SPS,d

Chab
SPS,t

V ,b

V ,d

,V

,V

b

d

paper III concluded that a global Salpeter IMF is on average ruled
2.3 Gas kinematics
out by the data. Basic properties of the subsample analysed in thisobtained major
axis long-slitData
spectradisplay
for all fiveitems
galaxies andwith
OnlineContent Methods, along with anyWeadditional
Extended
paper are given
in Table 1.
the
Low
Resolution
Imaging
Spectrograph
(Oke
et
al.
1995)
on
Source Data, are available in the online version of the paper; references unique thetoKeck I 10-m telescope between 2008 November and 2011 April.
these sections appear only in the onlineTypical
paper.
exposure times were 60 min, with seeing conditions of full
2.2 Strong lensing
width at half-maximum (FWHM) ∼ 1.0 arcsec. On the red side weStrong lensing models for our sample galaxies are presented inused the600/7500
line grating
which gives a pixel scale of 1.26 Å
Received 13 November 2016; accepted
31
January
2017.
SWELLS-III. The parameter that is most directly constrained by
pixel−1 . With a 1 arcsec wide slit the resulting spectral resolution
strong lensing is the circularized Einstein radius b (Treu 2010, andis & 4.2 Å, corresponding to a velocity dispersion resolution ofreferences
therein).
This
isdefinedtobetheradiusinsidewhich∼70 km s−1 at the wavelength of Hα. We adopt spatial samplings
Figure 9. (Continued)
1.
White,
S.
D.
M.
&
Rees,
M.
J.
Core
condensationin heavy
halos: a two-stage
the average surface density is equal to the critical density for strongof & 1.1–1.5 arcsec (5–7
pixels) correspondingto ∼1 data point perlensing:theory for galaxy formation
andclustering.
Mon.
Not.
R.
Astron.
Soc.
183,
seeing
FWHM.
Figure 6 – Continued
Wemeasuredrotationcurvesbyfitting
Gaussians
to one(1978).
Dsc2341–358
Mproj (b)dimensional spectra extracted along the slit. To improve centroiding
=" ≡
.
(1)

ure 3 | Dark-matter fractions. Dark-matter fractions fDM from- passive galaxies are probably the descendants of massive star-forming
erent methods are listed as a function of the circular velocity of thegalaxiesthe half-light radius of the disk R1/2, for galaxies
k vc, at approximately
he current Universe and about 10 Gyr ago. The large blue circles with
Figure9. (Continued)
outlines-indicate
dark-matter
fractions derived
fromthe outer-disk
the thelow
dark-matter
fractions
may be preserved in the properties of theation curves for the six high-redshift disks presented here (Table 1),
local passive population
ng with the ±2 r.m.s. uncertainties of the inferred dark-matter fractions

10

Tully-Fisher relation (TFR)
Uebler+17
Reyes+2011 (z~0) Reyes+2011 (z~0)(a=3.60, b=2.36) (a=3.60, b=2.36)

Lelli+2016 (z~0) Lelli+2016 (z~0)(a=3.75, b=2.18) (a=3.75, b=2.18)z~0.9∆b=−0.44 dex

z~0.9∆b=−0.44 dex

z~0.9∆b=−0.44 dex

z~0.9∆b=−0.44 dex

z~2.3∆b=−0.42 dex

z~2.3∆b=−0.42 dex

z~2.3∆b=−0.27 dex

z~2.3∆b=−0.27 dex

z=0-1

z=1-2

z=0-1

z∼0.9 (N= 65) z∼0.9 (N= 65)z∼0.9 (N= 65) z∼0.9 (N= 65)z∼2.3 (N= 46) z∼2.3 (N= 46)z∼2.3 (N= 46) z∼2.3 (N= 46)

3D subsamples at z ⇠ 0.9 (blue) and3Dtosubsamples
Figurefits
5.-Fixed-slope
for andthe sTFR(left)and thebTFR(right)using
localto(black)slopesourstellar
KMOSatxed-slopefor
sTFRfits(left)
the bTFR(right)using
local(black)slopesour KMOSz mass⇠ 0.9 (blue)
atthefixedvelocity,
higherbaryonicmass
andsimilaratandz ⇠ the2.3local(red).relations,
For the we
local
relations,give a and b tocorresponding
to our adopted
form
TFR give
Equation (2), withd). Forgivea and bwecorresponding
our adopted functional
formfunctionalof the TFR
giveofinthe
Equation(2),inwith
z~2.3
ascomparedtoz~0.9
log(vFor
Forfindthe nosTFR,
we findno (or evolution
only marginal)of the sTFR
in the studied
range. Comparingm/s])=0.
the sTFR, we(or only
marginal)of theevolution
sTFR zero-pointin thezero-point
studied redshift
range. redshift
Comparingref [km/s])=0.
to thebylocal
relationby Reyesal. (2011)= 0.44anddex zat⇠z 2.3,
⇠ 0.9
and z ⇠ 2.3,
respectively.
Forfindthe abTFR, we findrelation
Reyes
et al. (2011)
weetfindb = we0.44findand b 0.42
dex atz ⇠ 0.42
0.9 andrespectively.
Forthe bTFR, we-zero-point
zeroofpoint
monotonic
positivethe zero-point
z2.3.
⇠ 0.9
and z ⇠ 2.3.
Comparingto theby Lellial. (2016)
we findlutionof the evolution
betweenzoffset⇠ 0.9between
and isz ⇠notComparingto thelocal relation
bylocalLellirelation
et al. (2016)
we et
find
b = 0.44
and b = 0.44 and
0.27anddexz at⇠ z2.3,⇠ 0.9
and z ⇠ 2.3, respectively.
t z ⇠ 0.9
respectively.

ein the legend.5 The grey lines show our final toy model following Equations (4)gasand (5) andf
DM including
eakinAppendix
D.
(⇢
=
0.37,
=
1.1
⇥
10
).
galaxy
(see
e.g.
the
discussionson
halocontractionvs.
equationspredict
a
TFR
evolu
he
radius 7.
Rh wherethe(a)
mean
densitysmooth TFR evolution scenario in the theore
in Figureq 200 times
in insetin Figure
7. equals
gain
We constrain
our
toy
m
expansion
byv Duffy
et al.
Duttonal.
2016;
Vel-et al. evolving
2 2010;2 (r). etzero-point
with
cosm
critical density of the
Universe.
The
correspondingbySomerville(2008).
Also
the
recent
obs
(r)
=
v
(r)
+
v
(D4)
circ
bar
DM

Toy modelofbaryonic
TFR
liscig et al. 2014). However, through recent studies andand butzet⇠al.
2.3(2012)
asonfollows:thH (z),
alsochangesina
a finite thickness.
This does
not affectthe radius,
scalings presented
shift-dependent
relations
betweenhalo
mass
compilationbySwinbank
showedete.g.
al.
(1998),
accounting
forcanadiabatic
contraction).
Itconhas(e.g.
NFW
Einasto,98),
foradiabatic
contraction).
ItTremaine
(e.g.
NFW
or Einasto,
Navarroetoral.
1996;
EN
the accountingThebaryonic
contribution
behas
computed,for instance,
tainedthroughtheempirica
modelling
of
high
z
SFGs
we
now
have
a
numberofhere(see
Courteau
&
Rix
1999;
Binney&cosmictime.
, andvelocity
Vh beenare shown that the ratio betweenevolution(althoughqualified
as consistentwitht
1. circularDM
Halo(Mo+98)
howeverR
andR
is
Equations
(3)
can
be
c
been
shown
that
the
ratio
betweenR
andR
is
Equations
(3)
can
be
combined
to
using
the
expression
foraninfinitely
thin
exponential
disk
h
don
2008, and references
therein).
To associate
baryonic
scalingby Sainton
d diskstraints
handywhichhthe
implicitly
contain information
We
noterelations
that deviations
froevolution
scenario).
3halo, one canto the dark
assumeainsimple
model
where
approximately
constantformassive
SFGs in the redshift(Freeman1970),
At fixed
circular deve
Vformately constantmassiveSFGs
theredshift
the
DM
halo
profileongalactic
scales.
Vcan(2017).
be andrelatedto fixed
additionalhhEvaluating
Equations
(4)
(5)
at
v
(R
3
2
2 M
1 =e
circ
massesare related throughaMthe; zandRcorresponding= (Burkert(3)2016).
h =corresponding
hradii
h
M
=
R
H
(z)
10
G
.2eg
with
redshift,
where
z
⇠
range
0.8
<
<
2.6
et
al.
This
does
also
RelationstoEquations
(3)
for
the
centralh22surfacedensity⌃(Courteau
8 < z < proportionality
2.6 10G(Burkertetal.
2016).
This
does
also
· H (z)10H(z)hvfactor:I1 (y)Kthe(D5) (i) if f DM (Re ) decreases with incr
following:
1 (y)],bar (r) = 4⇡G ⌃0 Rd y [I0 (y)K0 (y)are about a factor of eight hbaryonicgalaxycan thenbederived
via assuming
hold
for
our
TFR
sampleandtheaveragevalues ataz direct
⇠ 0.9
our
TFR
sampleandtheaveragevaluesatz⇠
0.9
shift, the baryonic and stellar
mass will
increaseo et al. 1998), whereM
H (z)theh Hubble
parameter,andVia
inserting
Equations= myis; Rdbar=andr f ·halo
Ri (y)(D3)
bar
f ·=Mr/(2R
h . andThe
redshift
evolution
of (D
fD
where
),
I
and
K
(y)
are
the
modifiedVia
inserting
Equations(D3)
into
Equation
mapping
betweenthegalaxymass
andradius.
iandtherez ⇠ 2.3,
even though
there foris substantial
scatter
for
toy
D.2.
Observational
constrain
2.3,
even
thoughissubstantial
scatterquently the TFR zero-point
will increase;(ii)byifa Mms the gravitationalBessel
constant.
Theon
first
equationshows
stitutingRthroughreconstantobservational
resultsdfunctions
of
first
and
second
kind.
At
r
=
R
,
this
Information
the
inner
halo
profileiscontainedinpam f is conventionallyknow
as the disk mass fraction m dlastitutinge Rd through a re-arranged Equation(D
individual
objects.
f
,
m
gas
d
with
increasing
redshift,thebaryonic
andstellaralobjects.
tlar
the relation
between
M
and
V
is
a
smoothfunctionhhatEquation
(4)
given
in
local
Universe,andbyW1
2 such elsewhere
we duselatterexpression
in thetext. fraction
Rbar
becomes
rameters
as the disk
mass
m
=DM
Mbarto/MthedEquationh , given in Section 5. After intr
Mand
=Cthis×R
bar/m
1equation
d3H(z)
at(4)
To
quantify
thecontributionsofbaryonsanddecrease
andForconsequently
the
TFR
zero-point
wio
edshift.
Inthefollowing
paragraphs
2 (r).
ntify
thecancontributions
baryonsandDM tobe expressed
the disk
scale
lengthRf DM
orthe= v 2 (r)/vted
d ,thetune
theredshift
evolution
orthroughtheofcentralDM
fraction(r)fraction
f
=
M
/M
gas
gasEquabcirc f
DM fraction
Mbar
=
M
/M
,
one
arrivesatcircularvelocityatacertainradius
we
write
2
00
gas
gas
bar
(iii)
if
f
increaseswithincreasing
redshift,theseffective
radius
R
,
which
for
rotation-dominatedsystemshas
theadoptedredshift
evolutionn theory,
thearelation
betweenthese
haloproperties
ande galaxies,
gas
vknow
) = stellar· C mass,(D6)
velocityatcertainour
radiuswe write
lowedby these
observation
2. Exponential
disk(Freeman+70)
weM⇤ and effectivebar (Re theirequationspredicta
TFR
q in Rare related
throughRe ⇡ Rdcan· 1.68.
As
noted
Sectiond to 5,nic
equationspredict
athe
TFR
evolution
withaFigurcon
willdecreaseand consequently
the context.
sTFR
zero-potoy
model
responding
galactic
properties
becomplexdue
q radius Re , their baryonic2 mass
the
toy
model
and
the
obse
M
and
gas
mass
frac2bar (r).
evolving zero-point with
we take r f to 2be independentofredshift.
In
standard
00
v
(r)
=
v
(r)
+
v
(D4)
circ
2
evolving
zero-point
withcosmictime,dependwhereC
isaconstant.
The
DM
component
can
be
deual
and
combined
effectsof inacrease.
These
effects
areillustrated
individuallybar central
DM scaling relations,
response
of
the
halo
to
the
formationof thethispaper.
f(R)
evolve
tion
f
=
M
/M
from
empirical
vcirc
(r)
=
v
(r)
+
v
(r).
(D4)
DM
e
gas
gas
bar
models of diskbar
galaxy evolution,
H (z), ofbutf alsoonchan
DM r f combines information
D2)
rived
simplythroughaDMfractionattheradiusofinterest,
evolutions
,
m
,
and
in
AppendixD.
axy (see one.g.
discussions
halocontraction
H (z),
but DM
also on changes
in fractions
mgasd , fdDMwhich(Ref D)z ⇠ 2 DM
andtheir oncircularvcirc(r)vs.
and related
centralthethehalo
spinparameter,on
thevelocity
halo canconcentration
Thebaryonic
contribution
becomputed,for
instance,
cosmictime.
2 (r)/v 2 (r), or via adopting a full mass profile
f DM
(r)
=
v
evolution.
onic
contribution
canbecomputed,for
instance,We
constrain
our
toy
model
at0.redshiftsz=ansionbyDuffyusing
etand
al.
2010;
Duttonetal.
2016;
Velthanatz=
m d is constra
circ
nic
parameter,ontheratiosoftheangularmomenta
fractionf DM (r) fromdynamical
modelling,
as detailedincosmictime.
DMthe expression
for aninfinitely
thin exponential
disk
Weredshift
note
that
deviatio
massesandthin
DM and(cf.
Equation(28)of Mo givenand
ure
z
⇠
2.3
as
follows:
theevolutionofig
et al. and2014).
However,throughrecentstudies
andexpression
for(Freeman
anof baryons
infinitely
exponential
disk
results
by
Mosteretal. (201
§§
2.2
and
2.3
in
the
references
there.
We
furWe
note
that
deviations
fromtheproposed
2=(1-fDM)vcir2 1970),v
canberelatedtomolecula
additiobartaineddisk
throughthe empiricalatomic
and
at
0.8
<
z
<
2.6
we
adop
delling
nowanhavea numberof averagecon- baryonictherwehave
estimateof theirmass1970),of high z SFGs
canberelatedtoadditional
dependencieson2
2
surfacedensity⌃(Courscaling
relations
et al. (2011)
andet al. (2016).
DetailsonTat
aints handy whichvimplicitly
information
onWeIcanfraction
mcontainet0al.
2016).
combinethis(D5)
in- by Saintonge
(r)
=
4⇡G
⌃
R
y
[I
(y)K
(y)
(y)K
(y)],
d (Burkert
0
d
0
1
1
bar
2
surface density ⌃ (Courteauet areal. 2007).
=
4⇡G
⌃
R
y
[I
(y)K
(y)
I
(y)K
(y)],
(D5)
parameters
given
in App(2017).
At fixed circular velocity, f gas
evolvess
0 d
0 scales.
1construct
1 a toy model of the TFR
formation
to/R
zero-point
DM halo profile
on0 galactic∝Mbardwhereevolution,
yto=Equations
r/(2R
and
(y)central
and Ki dependencies(y) aretheredshift,modifiedd ),weIn
Figure7have
we gas
show
ho
where
take
the
redshiftof thesewithwhere z ⇠ D.2.
2 galaxies
fract
Relations corresponding(3)
forIitheObservationalcon= r/(2Rd ), andBessel
Ii (y)and parameters
Ki (y)
are first
themodifiedfunctionsofthesecondAtr =D.1
Raefor,factorthisredshift-dependentDMfravariousintoandaccount(seekind.
Appendixa of eight
are
about
higher than
in
the
loca
D.2.
Observational
constraints
on
the
redsh
yonic galaxy can thenbederivedvia
assumingadirect
fg
2
M
/R
=C
×(1-f
)v
nctions
of
the
first
and
second
kind.
At
r
=
R
,
this
bar d equation
DM
cir
e
gas
in ourbecomesdetailed
derivation):
The redshift evolution off fractions(Rde,)andisinterplay
constrained
pping between
the2 haloandgalaxy mass and radius.
DM
f gas
,m
f DM (Re )tIn thefollowingparag
becomes on the inner halo profile is 3contained in paimately
explainoural.observe
observational
resultsbyMartinssonet(2013
ormation
3/2
Mbarf DM (Rv2circ (Re ) [100 e , z)] In the following paragraphs,
wediscussthetheadoptedredshiftevo
zero-point
offsetsatfi(Rde =) =·Mbar /M·h 1/2
C
,
(D6)
M
·C
(4) and byTFR
local
Universe,
W16
at
z
⇠
0.9
and
z
⇠
bar =vbarm
meters such as the diskMmass
fraction
,
bar
R
H
(z)
2
00
d
m d (z) the adopted redshift tion
evolutionoff)gas, mInd the
,paa
theof
model
context.
oftoy
cosmictime.
2 (r)/v 2 (r).
(R
)
=
·
C
,
(D6)
e
tune
the
redshift
evolutionf(R
withinhe centralvDM
fraction
f
(r)
=
v
For
DM
e
bar
DM
circ
DM
R00d is a constant.
z ual= 0.9,z = summariz
2.3,
while
where
C
The
DM component
canbede-observations
andcombinedthetoycontext.
FigureD7
lowedbymodelthese
toand
optimizetheeffect
matc
galaxies, we know their stellar mass M⇤ and effective

and z ⇠ 2.3 as follows: the redshift evolution ofliscig et al. 2014). However, through recent studies andtained through the empiricalatomic and moleculamodelling of high z SFGs we now have a number of con23
scaling relations by Saintonge et al. (2011) and Ta
straints handy which implicitly contain information on
The redshift
evolutionof f gas on galactic scales.The recent
by Burkert
etofal.
finds circulara typ- velocity,(2017).
At fixed
evolvessi
D.2.1. study
The redshift
evolution
f gas(2016)
The recentf gas
study
by Burthe DM
halo
profileUebler+17 md is a dominant factor fDM is a dominant factor
ical valueofthe
m dcentral= 0.05 for SFGs
at 0.8 <wherez < 2.6 ical value of m d gas= 0.05
with theredshift,fract
Relationscorresponding
to Equations
l approach,we consider
the gas fraction
For our (3)toy formodel
approach, we consider
gas fraction z ⇠ 2 galaxies havebasedassumingon R11a Monte-Carlo
NFW modellingofdata fromthe based on athanMonte-Carlo
NF
/ L16
are
a factor
in
the
loca
baryonicgalaxybeby
deriveda directand
molecular
and atomic
gas canmassthendividedf gas tovia
be the 3D
sum of molecularatomicgasabout
mass divided
byof eight higher
3D and SINS/zC-SINF
KMOS
andSINS/zC-SINF(FörsterSchreiber
et
al.
2009;
KMOSfgas
total baryonicmass,radius.
f gas = (Mgas,molThe+ Mgas,at)/(Mgas,mol+
ass, f gas= (Mgas,mol+ Mgas,atthe)/(Mhalo+ theredshift
evolutionof f DM (Re ) is constrained t
mapping
betweengalaxymass andgas,molandfDM(Rete) al. 2011) survey
MancinietTheal. evolution2011) surveys.
These galaxies
have masses Mancini
R11 / L16
M
+
M
).
of
the
moleculargasmass-toevolutionofthemoleculargasmass-togas,at is contained⇤
observational results by similar
Martinsson
et al. (2013
Information on the inner halo profile
in pathe galaxies
in ou
mdto×10similartothegalaxies
in
our
TFR
sample.
We
adopt
their
stellar mass ratio is given through thelocal
scaling
relationbys giventhroughthescaling
relationbyby W16at mzd ⇠= 0.05
0.9 andz <⇠rameters such as the disk mass fraction, < z < 2.6. Universe,mand
d d== Mbar /Mvalue offor 0.8
value
ofmm
0.05
for h0.8
d=0.05
Tacconietal.
(2017):):
2
2 (r). For
thea redshift
evolutionof f DM (Rz =e )0 within
and z = the0.8or the central DM fraction f DM (r) = vBetween= 0 and z = 0.8 we tune
assumelinear increaseof Between! zcirc
DM (r)/v⇥⇤ 2 AsClearly,
this is
simp
⇥
lowed
by
these
observations
optimizethea matc
our galaxies,
we know ⇤theirstellarmass
M⇤ andeffectivem dM. gas,mol
Clearly,
thisis 3.62a simplifying
conjecture.
for the m d . to2(a) log
⇡
0.12
·
log(1
+
z)
0.66
0.12 3.62 · log(1 + z) 0.66
Matomicofgas
masses,we empF⇤R(D8)
D.2.1.
The
redshift
evolutionf gas
we⇥ emphasize
assumption
thethattoythismodel
andthehasobserved
TFR
evolutionpbT gasradius Re , their baryonic(D8)mass Mbaratomic
andgas masses,
mass frac⇤⇥⇤primarily cosmetic effects, w
0.33effects,· log(M])
10.7.
primarily
cosmeticwhile
thecrucialquantity
is
the
⇤ [M
this
paper.
f(R)
evolvessignificantlywith redf gas ⇤ =[MM])gas /M
fromempirical
scaling
relations,
0.33tion· log(M10.7.
For our toy model
approach,
we consider
the gas fraction
DM
e
bar
(a)
relativedifferenceinm d betw
relativedifferenceinmbetween
z
=
0,
z
⇠
0.9,
and
z
⇠
2.3.
f
to
be
the
sum
of
molecularandatomicgas
mass
divided
by of
d
gas
z
⇠
2
DM
fractions
which
are
about
a
factormd=0.012
and their circular velocity vcirc (r)andwerelated
centralDM the additionalHere,
do not take
into accountdependencies
into account the additional dependencies
D.2.3.
The redshif
thetotal baryonicmass,
f gasis=constrained(Mgas,mol + Mgas,at
)/(M
+ TF
gas,mol
D.2.3.
The
redshift
evolution
of
f
(R
)
given
in
the
full
parametrizationby
Tacconi
et
al.
on
MS
than
at
z
=
0.
m
by
the
abundanceDMfractionf(r)
fromdynamical
modelling,as
detailed
in
d
DM
bof
rametrization by sTFR
Tacconiet al. on MS
Mgas,at + M⇤ ). The evolution of the For
molecular
gas mass-toKMOS
theDM
fraction
offset,andoffsetfromthe
M-R
relation,but
assumethattheresults
by
Mosteral. (2013)
in the relation
local Univers
2.2relation,
andbTFR
2.3butandin thegiven
there.
fur-of local
For TFthe
DM We
fractiondisk
we etfollow
m the§§
M-R
assumethatreferencesthestellarmassgalaxies,
ratio
is giventhroughthe scaling
by& DuKMOSRsFigure1byCourteaumodel galaxies lie on these relations. at 0.8 < z < 2.6 we adopt the value deduced
Figure1 by Courteau& Duttonoththerhave anestimate of their averagebaryonic
disk mass
1. (2015)
gas etfraction(Mgas/M) shows galaxies from the
Tacconial.which,(2017):amongstar
n theserelations.
toy model including
ers,
Locally, the galactic gas mass is dominated by atomicgas.
f (z), f (R ,z), m (z)! (Martinsson
ers,galaxies from
DiskMasssurveyet al.
(2016).
Details on
parametrization
shown in inset
tic gasfraction
mass is dominatedby(a)atomicm das (Burkert
et al. gas.
2016).ToWe
canshows
combinein- theMgas,mol⇥ et the⇤ 2At vcirc =of
al. 2013b,a).
account
for atomic thisgas mass
at z =log0, we
use thefitting⇡
0.12
3.62· Appendix
log(1 + z) D.2.
0.66
et theal. 2013b,a).
At vcirc = 242 parameters
km/s, MDM fractions
of inlomic gasformation
mass at z =we use thea fitting
are
given
to0,construct
toy modelofTFR
zero-pointcal
disk
galaxieslie(D8)roughly⇤ use a local
functions presented by Saintonge et al. (2011). We⇤ with largecaldisk galaxiesof
lietheseroughly between
0.55⇥ and f how
DM (r 2.2 )7=we
by Saintonge
et al.where(2011).we
Wetakeuse thea local)=
0.75,
In fFigure
empirically
evolution,
redshiftdependencies
referencestellar mass of log(Mi.e. the stellar
0.33 · showlog(M⇤DM[M(r 2.2])these10.7.
⇤ [M ]) = 10.94,
f
(r
)
=
0.75,
with
large
scatter
anduncertainties.
DM 2.2s of log(M]) = 10.94, i.e.
the stellar
At higher disk
redshift,
W16⇤ [M parameters
to ourfor
referencevelocity
vref = 242Tacconi+17
km/s DM fractions,redshift-dependent
mass
fracd
variousintoaccountmass(seecorresponding
Appendix D.1
a
Here,
we
do
not
take
into
account
theadditional
dependencies
3D
At time.
higherredshift,
W16
derivedTFRzero-point
offsets of thestellar and baryonicas a function of cosmic
The KMOS
data is shownas yellow
stars DM fractions from the difference between dynamic
to ourreferencevelocity
vref =mass
242TFRs
km/s
inthe
context
of
the
sTFR
fit
by
Reyes
et
al.fractions(2011). interplay in our toy model framework
TF
relationgas
nd blueBaryonicsquares(bTFR),
inrelationtothecorresponding
local
normalizations
by
Reyes
et
al.
(2011;
R11)
and
Lelli
et
al.
(2016b;L16).
detailed derivation):zero-point
offset
term
given
in
the
full parametrization
2.
disk
mass
fraction(Mby/MDM)et al. on MS
barTacconi
3D subsample
difference
betweendynamical
andbaryonic
masses
of
the
3D
sTFR
Reyes
etdataal.points(2011).
KMOS
of 240 S
ontal
errorfit
barsbyof theKMOS3D
indicate the spanned range inTo
redshift,while
thevertical
error
bars
show
fit
uncertainties.
account forsTFR
atomic KMOS
gas massesoffset,
at imatelyz >and0, offset
weexplainfollow
the
from
the
M-R
relation,but
assumethattheourobserved
TFR
evolution,
spec
3D
R data points are corrected for neglected3atomic gas at z ⇠ 0.9 and z ⇠ 2.3, as detailed
in
the
main
text.
The
green
dashedand
3/2
KMOS
subsample
of
240
SFGs,
which
represents
our
parm
at
z=0:
Moster+13
d=0.012ent
sample.
Correspondingomic
gas masses
at z and> sTFR0,
wethetheoreticalprediction
that,
at
fixed
M
,
the
ratio
of
atomicgas
vcirc(Rfollow)s show predictions
for the bTFR
evolution
from
our
toy
model
(Equations
(4)
and
(5)).
This
model
takes
into
account
the
[1
f
(R
,
z)]
⇤
e
DM
e
galaxies
lie on these
relations.
3DmodelTFRzero-point
offsets
at
fixed circularvelocity
ly motivated redshift dependencies
of
f
,
f
(R
),
and
m
,
in
particular
as
they
are
shown
in
inset
(a).
Regionsinredshift
space
gas
e
m
=0.05
at
z=0.8<z<2.6
Burkert+16
M
=
·
·
C
(4)
DM
d
d
ent
sample.
Corresponding
values,also
corrected
for
mass
bar
completeness,
are
given
in T
th
ne modelthat,isatnotfixed
M
,
the
ratio
of
atomicgas
mass
tostellar
mass
does
not
changesignificantlywithredshift
bTFR
KMOS
⇤
1/2
well constrained due to aH
lack
of observational constraints in particular on m d are indicated as dashed lines.
Locally,thegalactic
gas
mass
is
dominatedbyatomicgas.
s(z)
m d for(z)
onal constraints come from Saintonge et al. (2011) and Tacconi et al. (2017)
f gas (z), from Martinsson
etgivenal. (2013b,a)and W16
for
tion
offor
cosmictime.
this weis valid
completeness,
their
Table
1.
param
does
not
changesignificantlywithredshift(e.g.
Fu
et al. 2012).areWe
useinagain
thefittingfunctionsby massInat particular,To
account
atomic gas
z For= 0,convenience,
we use the fittingz), andStellar
from MosterTF
et al. (2013)
and Burkert et al. (2016) for m d (z), as detailed in Appendix D.2. Our proposed parametrizationsarerelation
3. zdark
matterfraction(MDM
atReas) follo
barredshift
y up We
to z ⇡ use
2.6, asagain
indicated theby thefitting
grey shadingin the main figure
andinset (a). For
As cyanshadedareas wetoindicate
way of example
fractionwith=the0.9,
and
zmass
= the
2.3,DM
while
we/M
have
partially
convenience,
we byparametrize
evolutionofSaintongeetal.
(2011)
now
determinetheatomicgas).
functionsbyfunctionspresented
bySaintongeetal.
(2011).
Weuse
alocal intoy
model
includingmodel TFR evolution would change if DM fractions would be higher/lower by 0.1 at z = 0, z = 0.9, and z = 2.3 (horizontal ranges are
2.5 ]. This3Dz)gives
anzero-po
evolutifractionwithredshiftasfollows:
f
(R
)
=
0.7
·
exp[
(0.5
·
The
evolutionis reasonably
matchedgas
by a model
whereforthe3/2disk
scale lengthis proportional
tothe(Rhalo=radius,and3galaxies
with
log(M
[M
])
10.50,
which
corresponds
referencestellar
mass
of
log(M
[M
])
= 10.94, i.e.
the stellarinbetween.
Our
observed
KMOS
TFR
DM
e
f
(z),
f
,z),
m
(z)
1)observed
to nowTFRdetermine
theatomic
mass
⇤
⇤
[1
f
(R
,
z)]
[1
f
(z)]
v
(R
)
gas
DM
e
d
DM
e
gas
e
redshift, while f DM (Re ) decreases with redshift.
0
as and m d increase with circ2.5 ]. This gives
than
what
by jusmass
correspondingreferencevelocityvis= 242 km/s
M⇤])== 10.50,· corresponds 1/2
·C
, (5)
an
evolutionwhichis(bluesomewhatstrongerto thez)averagestellarmass
ofinour
TFRgalaxies
at squares)vto=
as shown
inset(a)
ref suggested
refourg(M⇤ [M
which
bTFR
and
the
sTFR
(yellowstars)
z=0:
Courteau&Dutton
2015
Hcorrection(z) for atomic gas at msumes
vided
by (2011).
Courteau & Dutto
the context
of the sTFR
fit proby Reyes
et al.
km/s
inbothisofredshiftbins.
than evolutionwhatsuggestedtakingtheaveragevaluesplot,mass
we alsoof
performa redshift
f gas , f DM (Rand just
m d asinshowne ),byar
our a TFR
galaxies at vref = d242(z)z=0.9,2.3:
Wuyts+16
and
z
⇠
2.3
are
shown
in
relationto the local TFR
shift:7 we follow the theoretical prediction that, atby the blue, purple, and black lines, respectively, in inset
To account for atomic gas masses at z > 0, we follow theInterpretation of TFR zero-point offset

fgas

fDM(Re)md ×10

3D

3D

gas

DM

e

d

dshiftbins.
0 mass does not, the ratioof atomic gas mass to stellar

Between0 and z = 0.9,
we assumea smooth
TFR evovided zby= Courteau& Dutton(2015)and W16,
but easily within the uncertainties pres(a) in Figure 7 (details are given in Appendix D.2). In thisCO observations with ALMA
credit: ESO/NAOJ/NRAO

CO(3-2) observations in the most massive galaxies at z=2.5 (Tadaki+17)
0.4

U4-16795

0.3

CO (blue)PAmorv/σ=7.0

Flux density [mJy/beam]

0.2
PAkin

0.1

PSF
CO (red)0.0−1000 00.4

1000

Velocity [km s-1 ]J125H160870µm

WFC3/H160

ALMA/870µm

CO velocity

U4-16504

0.3v/σ=4.1

0.2
0.1
0.0
−1000 01000

Velocity [km s-1 ]J125H160870µm

WFC3/H160

ALMA/870µm

CO velocity

z=2にある重い銀河はslow rotatorになる？
8

Veale et al.

Observations (Veale+16)

Nslow /Ntotal

and flattens to ⇡ 0.2 at R ⇡ 160 00 and beyon
1.0
12/13
and the rest of the paper, we therefore adopt
MASSIVE
ized) Re = 177 00 from the 2D profile fits of Ko
ATLAS3D
0.8
21/28(2009) and e = 0.2 for NGC 4472. This valu
logMstar>11.2
result in classification as a fast rotator by the
0.6
terion, but we note that our value may be
9/21
high due to the unusual pointing scheme: we
0.4
pointings along the major axis to cover the lthis galaxy, resulting in more coverage along
5/24
0.2 6/36
5/39
than minor axis (see Figure D8). The value of
3/44 3/49 4/46
by averaging over all spatial bins, including t
0.0
minor axis where V and are small. The “m
22
23
24
25
26
axis coverage for NGC 4472 at the outer bi
Mk [mag]fore result in an inflated at 50 00 and beyond
Fast and slowcoredrotators
Illustris elliptical
3891 galaxies separat
andinnon-cored
Simulations (Penoyer+17)
below and above e ⇡ 0.25 independent of "Figure 4. Fraction of slow rotators as a function of absoluteK-band magnitude MK for the 41 MASSIVE galaxies and the
Krajnović et al. 2013), and NGC 4472 falls am
ATLAS3D sample.
slow rotators according to that classification
reasons, we classify NGC 4472 as an interm
this paper.
and NGC 7426. They are color-coded individually in Figure 3 and subsequent figures. The 33 slow rotators are shown
4.2 Radial profiles ofas filled red circles/ellipses. (We leave NGC 4472 unclassislow rotator
fied as discussed below.) We find a much higher fraction
Figure 5 shows the (cumulative) angular momof slow rotators (33/41 ⇠ 80%), compared to 36 out of 260(top panel), local (R) (middle), and velocit
ATLAS3D galaxies (⇠ 14%). Figure 4 shows the fraction oftom) for the 41 MASSIVE galaxies. The colorslow rotators in bins of MK for the MASSIVE subsample
tical to that in Figure 3, with slow rotato
studied here and the ATLAS3D galaxies. The slow fraction
fast rotators labeled individually. All three何が銀河の回転を止めたのか？
a strongly-lensed quiescent galaxy at z=2.6
the most massive
star-forming galaxies at high-z
V/σ>>1quenching
The Astrophysical Journal Letters, 813:L7 (7pp), 2015 November 1

Figure 4. Left: resolved Balmer absorption lines extracted in several spatial bins. Corresponding spectra on opposite sides of the galaxy center have been shifted to thesystemic redshift and coadded. The FIRE and MOSFIRE spectra are combined in the lower spectrum and demonstrate no signiﬁcant gradients in Balmer line strength
over 0.6Re –1.6Re . Right: the top panel illustrates the position of the spectrograph slit as seen in the WFC3/F140W image. The middle panel compares the ﬂux
distributions in the spectra to the PSFs (dotted), demonstrating that we spatially resolve Image 1. Five extraction bins are indicated. The lower panel indicates thepresence of rotation measured using the stellar absorption lines.

quiescent galaxies at high-z
V/σ~1

only SFR  2 o 1 M: yr1 (accounting for magniﬁcation),
indicating that star formation was recently and quickly
truncated in this galaxy. The speciﬁc star formation rate issizeevolutionlog SSFR yr1  11.1 (68% CL) independent of magniﬁcation. Dust attenuation is moderate with AV  0.52 o 0.08
assuming the Calzetti et al. (2000) reddening curve. (These4

slow rotators at z=0
V/σ<<1
Newman+2015

まとめ

AA51CH04-Walter

ARI

24 July 2013

10:18

AA51CH04-Walter

ARI

24 July 2013

10:18

a

CO(J=1-0)

ters, 841:L25 (6pp), 2017 June 1

Tadaki et al.
CO(high-J)

a

ULAS J1319+0950, z = 6.132

ﬁne structure lines
ULAS J1319+0950, z = 6.132

Carilli+2013
1''

Bolatto+2017

ys.
2013.51:105-161.
Downloaded
from www.annualreviews.org:105-161.
Downloaded
from www.annualreviews.org-Observatory
National Observatory
of
Japan
on
08/21/13.
For
personalof Japan on 08/21/13. For
personal
use
only. use only.

[CII] mapz=2.5 detected in the CO J  3  2 line. From left to right: spatially averaged CO spectra; three-color images with HST/
μm-band (2 5×2 5), monochromatic images at F160W- and 870 μm-band with blue and red contours displaying blueshifted andlocity width of 150 km s−1; CO velocity ﬁeld with white contours indicating the velocity-integrated CO ﬂuxes. The contours aredashed lines indicate the morphological major axis of 870 μm continuum emission and the kinematic major axis of CO,

observations at a high-frequency

In the PV diagrams, we use the pixels with a ﬂux above 3σ to[CII] velocity field
1''

c
c

[CII] map
[CII] velocity field
SDSS J2310+1855, z = 5.99

SDSS J2310+1855, z = 5.99

1''[CII] map

[CII] velocity field1''

redshift

Figure 10[CII] observations
mapvelocity
field from z
Results fromof [CII][CII]158-µmemission

the total intensity plus the intensity-weighted mean gas vel
isFigure± 30010km s−1 (red to blue), whereas that in panel c is ± 1
scales of ∼7 kpc (∼1 arcsec at z ∼ 6). (b) The Very Large A
Results from observations of [CII] 158-µm emission fromboth frames. The contours on the left show the 250-GHz c