# FRESCO: An extended, massive, rapidly rotating galaxy at $z=5.3$

Erica Nelson Department for Astrophysical and Planetary Science, University of
Colorado, Boulder, CO 80309, USA  Gabriel Brammer Cosmic Dawn Center (DAWN),
Denmark  Niels Bohr Institute, University of Copenhagen, Jagtvej 128, DK-2200
Copenhagen N, Denmark  Clara Giménez-Arteaga Cosmic Dawn Center (DAWN),
Denmark  Niels Bohr Institute, University of Copenhagen, Jagtvej 128, DK-2200
Copenhagen N, Denmark  Pascal A. Oesch Department of Astronomy, University of
Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Cosmic Dawn Center
(DAWN), Niels Bohr Institute, University of Copenhagen, Jagtvej 128, København
N, DK-2200, Denmark  Hannah Übler Kavli Institute for Cosmology, University of
Cambridge, Madingley Road, Cambridge, CB3 0HA, UK  Cavendish Laboratory,
University of Cambridge, 19 JJ Thomson Avenue, Cambridge, CB3 0HE, UK  Anna de
Graaff Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg,
Germany  Jasleen Matharu Cosmic Dawn Center (DAWN), Denmark  Niels Bohr
Institute, University of Copenhagen, Jagtvej 128, DK-2200 Copenhagen N,
Denmark  Rohan P. Naidu NASA Hubble Fellow  MIT Kavli Institute for
Astrophysics and Space Research, 77 Massachusetts Ave., Cambridge, MA 02139,
USA  Alice E. Shapley Department of Physics & Astronomy, University of
California, Los Angeles, 430 Portola Plaza, Los Angeles, CA 90095, USA
Katherine E. Whitaker Department of Astronomy, University of Massachusetts,
Amherst, MA 01003, USA  Cosmic Dawn Center (DAWN), Denmark  Emily Wisnioski
Research School of Astronomy and Astrophysics, Australian National University,
Canberra, ACT 2611, Australia  ARC Centre of Excellence for All Sky
Astrophysics in 3 Dimensions (ASTRO 3D)  Natascha M. Förster Schreiber  Max-
Planck-Institut für extraterrestrische Physik, Giessenbachstrasse 1, D-85748
Garching, Germany  Renske Smit Astrophysics Research Institute, Liverpool John
Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK  Pieter van Dokkum
Astronomy Department, Yale University, 52 Hillhouse Ave, New Haven, CT 06511,
USA  John Chisholm Department of Astronomy, The University of Texas at Austin,
2515 Speedway, Stop C1400, Austin, TX 78712-1205, USA  Ryan Endsley Department
of Astronomy, The University of Texas at Austin, 2515 Speedway, Stop C1400,
Austin, TX 78712-1205, USA  Abigail I. Hartley Department for Astrophysical
and Planetary Science, University of Colorado, Boulder, CO 80309, USA  Justus
Gibson  Department for Astrophysical and Planetary Science, University of
Colorado, Boulder, CO 80309, USA  Emma Giovinazzo Department of Astronomy,
University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Garth
Illingworth Department of Astronomy and Astrophysics, University of
California, Santa Cruz, CA 95064, USA  Ivo Labbe Centre for Astrophysics and
Supercomputing, Swinburne University of Technology, Melbourne, VIC 3122,
Australia  Michael V. Maseda Department of Astronomy, University of Wisconsin-
Madison, 475 N. Charter St., Madison, WI 53706, USA  Jorryt Matthee Department
of Physics, ETH Zürich, Wolfgang-Pauli-Strasse 27, Zürich, 8093, Switzerland
Institute of Science and Technology Austria (IST Austria), Am Campus 1,
Klosterneuburg, Austria  Alba Covelo Paz Department of Astronomy, University
of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Sedona H. Price
Department of Physics and Astronomy and PITT PACC, University of Pittsburgh,
Pittsburgh, PA 15260, USA  Naveen A. Reddy Department of Physics and
Astronomy, University of California, Riverside, 900 University Avenue,
Riverside, CA 92521, USA  Irene Shivaei Centro de Astrobiología (CAB), CSIC-
INTA, Ctra. de Ajalvir km 4, Torrejón de Ardoz, E-28850, Madrid, Spain  Andrea
Weibel Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290
Versoix, Switzerland  Stijn Wuyts Department of Physics, University of Bath,
Claverton Down, Bath, BA2 7AY, UK  Mengyuan Xiao Department of Astronomy,
University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Stacey
Alberts Steward Observatory, University of Arizona, 933 N. Cherry Avenue,
Tucson AZ 85721 USA  William M. Baker Kavli Institute for Cosmology,
University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK  Cavendish
Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge, CB3 0HE,
UK  Andrew J. Bunker Department of Physics, University of Oxford, Denys
Wilkinson Building, Keble Road, Oxford OX1 3RH, UK  Alex J. Cameron Department
of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford
OX1 3RH, UK  Stephane Charlot Sorbonne Université, CNRS, UMR 7095, Institut
d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France  Daniel J.
Eisenstein Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Zhiyuan Ji Steward Observatory, University
of Arizona, 933 N. Cherry Avenue, Tucson AZ 85721 USA  Benjamin D. Johnson
Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA  Gareth C. Jones Department of Physics, University of
Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK  Roberto
Maiolino Kavli Institute for Cosmology, University of Cambridge, Madingley
Road, Cambridge, CB3 0HA, UK  Cavendish Laboratory, University of Cambridge,
19 JJ Thomson Avenue, Cambridge, CB3 0HE, UK  Department of Physics and
Astronomy, University College London, Gower Street, London WC1E 6BT, UK  Brant
Robertson Department of Astronomy and Astrophysics University of California,
Santa Cruz, 1156 High Street, Santa Cruz CA 96054 USA  Lester Sandles Kavli
Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge,
CB3 0HA, UK  Cavendish Laboratory, University of Cambridge, 19 JJ Thomson
Avenue, Cambridge, CB3 0HE, UK  Katherine A. Suess Department of Astronomy and
Astrophysics, University of California, Santa Cruz, 1156 High Street, Santa
Cruz, CA 95064 USA  Kavli Institute for Particle Astrophysics and Cosmology
and Department of Physics, Stanford University, Stanford, CA 94305, USA
Sandro Tacchella Kavli Institute for Cosmology, University of Cambridge,
Madingley Road, Cambridge, CB3 0HA, UK  Cavendish Laboratory, University of
Cambridge, 19 JJ Thomson Avenue, Cambridge, CB3 0HE, UK  Christina C. Williams
NSF’s National Optical-Infrared Astronomy Research Laboratory, 950 North
Cherry Avenue, Tucson, AZ 85719 USA  Joris Witstok Kavli Institute for
Cosmology, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue,
Cambridge, CB3 0HE, UK

###### Abstract

With the remarkable sensitivity and resolution of JWST in the infrared,
measuring rest-optical kinematics of galaxies at $z>5$ has become possible for
the first time. This study pilots a new method for measuring galaxy dynamics
for highly multiplexed, unbiased samples by combining FRESCO NIRCam grism
spectroscopy and JADES medium-band imaging. Here we present one of the first
JWST kinematic measurements for a galaxy at $z>5$. We find a significant
velocity gradient, which, if interpreted as rotation yields $V_{rot}=240\pm
50$ km/s and we hence refer to this galaxy as Twister-z5. With a rest-frame
optical effective radius of $r_{e}=2.25$kpc, the high rotation velocity in
this galaxy is not due to a compact size as may be expected in the early
universe but rather a high total mass, ${\rm log(M}_{dyn}/{\rm
M}_{\odot})=11.0\pm 0.2$. This is a factor of roughly 4$\times$ higher than
the stellar mass within $r_{e}$. We also observe that the radial H$\alpha$
equivalent width profile and the specific star formation rate map from
resolved stellar population modeling is centrally depressed by a factor of
$\sim 1.5$ from the center to $r_{e}$. Combined with the morphology of the
line-emitting gas in comparison to the continuum, this centrally suppressed
star formation is consistent with a star-forming disk surrounding a bulge
growing inside-out. While large, rapidly rotating disks are common to $z\sim
2$, the existence of one after only 1Gyr of cosmic time, shown for the first
time in ionized gas, adds to the growing evidence that some galaxies matured
earlier than expected in the history of the universe.

galaxies: formation – galaxies: evolution – galaxies: high-redshift –
galaxies: kinematics – galaxies: structure

††facilities: JWST, HST††software: Grizli

##  1 Introduction

Recently with the James Webb Space Telescope (JWST), very massive galaxy
candidates have been discovered in the first billion years of cosmic history
(Labbé et al., 2023; Casey et al., 2023; Akins et al., 2023). This is
surprising as $\Lambda$CDM cosmology predicts that galaxies form
hierarchically from the merging of smaller galactic units. If confirmed
spectroscopically, the existence of very massive galaxies so early is hard to
reconcile with current models. In some cases, the stellar mass of these
galaxies pushes up against the total number of baryons available in the most
massive halos (e.g. Boylan-Kolchin, 2023). Further buttressing this idea is
the prodigious number of bright galaxies with photometric redshifts $z>10$ (or
$<500$ Myr after the Big Bang), pointing again to a very early onset for
galaxy evolution (e.g. Oesch et al., 2016; Mason et al., 2023a; Naidu et al.,
2022; Finkelstein et al., 2022; Castellano et al., 2022; Bunker et al., 2023;
Tacchella et al., 2023a).

In addition to the surprising discovery at early times of massive and/or
luminous galaxies is the discovery with JWST of apparently disk-dominated
early galaxies (e.g. Ferreira et al., 2022; Nelson et al., 2023; Robertson et
al., 2023; Baker et al., 2023; Kartaltepe et al., 2023). An abundance of disk-
dominated galaxies at early cosmic time is unexpected in the context of
studies based on projected axis ratios in $<1.6$µm imaging with HST which show
that the fraction of galaxies with inferred disk-dominated morphologies drops
dramatically at $z>2$ (e.g. van der Wel et al., 2014; Zhang et al., 2019). It
is also unexpected in the context of kinematic measurements showing that the
majority of star-forming galaxies are less rotation-dominated at higher
redshifts (e.g. Förster Schreiber et al., 2006, 2009, 2018; Wisnioski et al.,
2011, 2015, 2019; Gnerucci et al., 2011; Kassin et al., 2012; Miller et al.,
2012; Tacconi et al., 2013; Simons et al., 2017; Turner et al., 2017; Johnson
et al., 2018; Übler et al., 2019; Price et al., 2020). These results are also
surprising theoretically. First, in an expanding $\Lambda$CDM cosmology, the
universe is expected to be much denser at early times than at later times.
With more galaxies per unit volume, the rate at which galaxies interact with
one another should theoretically be much higher. In such a state of frequent
bombardment, large disks would be unexpected. Second, owing to higher star
formation efficiency or stellar feedback efficiency in high star formation
surface density galaxies driving turbulence, early galaxies are expected to be
more dispersion supported (e.g. Übler et al., 2019; Pillepich et al., 2019;
Girard et al., 2021). If more massive, more luminous, and larger disk galaxies
really exist at early cosmic times, the universe may be able to form mature
galaxies earlier than we thought.

However, the implications of this early JWST work on our understanding of the
early universe remain hazy owing to observational uncertainties. First, very
massive galaxies at very early times may be neither massive nor particularly
early because both their redshifts and stellar population properties are
uncertain. Their photometry could be affected by active galactic nuclei (AGN),
bursty star formation histories, and potentially yet unconsidered other
oddities of the early universe (e.g. Endsley et al., 2023; Whitler et al.,
2023; Kocevski et al., 2023; Mason et al., 2023b; Papovich et al., 2023).
Second, the disky nature of these galaxies has also been inferred only from
imaging. As this is just a two-dimensional projection of a three-dimensional
object, there are degeneracies in the implied intrinsic shape. For instance,
low axis ratios could reflect edge-on disks or prolate shapes (e.g. van der
Wel et al., 2014).

Determining how common massive disk galaxies are at early times requires
spectroscopy, which allows us to measure redshifts, masses, and kinematics.
However, owing to the wavelength coverage of previous facilities, measurements
of ionized gas kinematics using rest-frame optical emission lines like
H$\alpha$ and [O III] have thus far only been possible to $z<3.5$ (e.g.
Förster Schreiber et al., 2006; Genzel et al., 2008; Law et al., 2009; Cresci
et al., 2009; Epinat et al., 2009; Jones et al., 2010; Wisnioski et al., 2011,
2012, 2015; Mancini et al., 2011; Swinbank et al., 2012; Stott et al., 2014;
Leethochawalit et al., 2016; Turner et al., 2017; Price et al., 2020). Studies
using millimeter and radio telescopes have begun to trace kinematics at
$z>3.5$ using e.g. the CII 158µm or CO line which traces cooler gas with some
finding significant rotation (e.g. Hodge et al., 2012; Smit et al., 2018;
Tadaki et al., 2019; Neeleman et al., 2020; Tsukui & Iguchi, 2021; Jones et
al., 2021; Pope et al., 2023; Parlanti et al., 2023) and even surprisingly low
velocity dispersions (e.g. Rizzo et al., 2020, 2021, 2023; Lelli et al., 2021;
Fraternali et al., 2021; Xiao et al., 2022).

With the launch of JWST, optical emission line kinematic measurements for
galaxies at $z>4$ have become possible for the first time. Here we present
H$\alpha$ kinematics of a massive, rapidly rotating galaxy at $z=5.3$ using
the NIRCam F444W grism. This galaxy is edge-on, extended, and is fortuitously
aligned with the grism dispersion direction and hence provides a simpler test
of this methodology than the typically smaller, fainter, less well-aligned
galaxies which will require more sophisticated modeling (as in e.g. de Graaff
et al., 2023). In §2 we describe the observations and data reduction, in §3
the methodology we use to measure kinematics and our kinematic results, and in
§4 the spatial distribution of the line emission relative to the continuum.
Finally, in §5 we discuss the implications of these results in the context of
other recent work as well as the potential for using NIRCam grism spectroscopy
to measure kinematics with JWST. In this paper, we assume the WMAP9
$\mathrm{\Lambda CDM}$ cosmology with $\Omega_{M}=0.2865$,
$\Omega_{\Lambda}=0.7135$ and
$H_{0}=69.32\,\mathrm{km}~{}\mathrm{s}^{-1}~{}\mathrm{Mpc}^{-1}$ (Bennett et
al., 2013). All magnitudes in this paper are expressed in the AB system (Oke,
1974).

Figure 1: Star-forming main sequence for galaxies with grism spectroscopic
redshifts $4.5<z<6$ in FRESCO with detected H$\alpha$. Star formation rates
are computed from the measured H$\alpha$ fluxes corrected for dust attenuation
using empirical relations based on the UV slope (Shivaei et al., 2020). A fit
to the SFMS from Speagle et al. (2014) is indicated by the red line for
context. The typical measurement error is indicated by the cross in the lower
right corner. Twister-z5, the galaxy featured in the present study, is at the
very massive end of this distribution on the upper end of a continuation of
the locus of points. Figure 2: We infer the spatial distribution of H$\alpha$
(right) from the difference between the F444W broadband filter (center) and
F410M medium band filter (left) which covers the H$\alpha$ emission line at
this redshift. The circle in the middle panel shows the size (FWHM) of the
PSF.

##  2 Data

The data in this paper come from the FRESCO and JADES programs in GOODS-S
(Oesch et al., 2023; Rieke et al., 2023; Eisenstein et al., 2023). The object
that forms the focus of our analysis which we refer to as Twister-z5 has
coordinates [53.10169662, -27.83616465] and lies in the GOODS-S field. FRESCO
is a 53.8 hour grism spectroscopic survey covering 124 arcmin2 in the GOODS-N
and GOODS-S fields (Oesch et al., 2023). It uses the NIRCam F444W grism, which
has a maximal wavelength coverage of 3.8-4.9µm and spectral resolution of
R$\sim 1600$ to measure H$\alpha$ [6563$\mathrm{\AA}$] at the end of the epoch
of reionization. Observations in GOODS-S were taken between November 13 and
18, 2022, with an exposure time of 7ks for the grism spectroscopy and 0.9ks
for the imaging. Data reduction was conducted using the grizli software
(Brammer, 2023). A full description of the methods will be presented in
Brammer et al. in prep, but we summarize here for completeness. The rate files
from MAST are aligned to a Gaia-matched reference frame; the direct images are
then used to align their associated grism exposures. Bad pixels are masked,
then individual exposures are combined.

We use a running median filter to subtract all continuum emission, leaving a
frame with just emission lines. This method subtracts both the continuum from
nearby sources that contaminates the spectrum as well as the continuum
emission from the source of interest (Kashino et al., 2023; Matthee et al.,
2023a). This empirical method has the significant advantage of simplicity.
However, it cannot be used if the continuum is of scientific interest, may
over-subtract nearby emission lines (e.g. [NII]), and does not model
underlying Balmer absorption. The continuum-filtering is a two step procedure.
For the first pass, the continuum is subtracted from each row of the image
using a running median filter with a 12-pixel central gap to avoid self-
subtraction of emission lines. On the second pass, pixels with significant
line flux are identified and masked then the median filtering is run again.
The position of the spectrum on the detector is computed based on the F444W
image and spectral trace in the v4 grism configuration files.

In addition, imaging in 8 filters (F090W, F115W, F150W, F200W, F277W, F356W,
F410M, F444W) was conducted as part of the JWST Advanced Deep Extragalactic
Survey (JADES; Eisenstein et al. 2023). Data are reduced as described in
Tacchella et al. (2023b) and Rieke et al. (2023). Specifically, the standard
jwst pipeline was used with the CRDS context map jwst_1039.pmap. We used
customized procedures to correct for “wisps” and 1/f noise, and a background
subtraction has been performed both on the individual exposure level and the
full mosaics. The mosaic images have been aligned to Gaia-EDR3 catalog.

Photometry is performed on HST and JWST images Point Spread Function
(PSF)-matched to the NIRCam F444W filter. Multi-wavelength catalogs are
generated using SExtractor (Bertin & Arnouts, 1996). Sources are detected in
dual-image mode using F444W as the detection image. Fluxes are measured in
0.16” aperture radius and corrected to total using the AUTO flux measurement
and a small additional correction for the remaining flux outside this aperture
based on the encircled energy for the PSF. All fluxes are corrected for Milky
Way foreground extinction using Fitzpatrick & Massa (2007). Uncertainties on
the fluxes are measured from the rms map and multiplied by a scale factor to
account for noise not accounted for in the reduction pipeline. In order to
determine this scale factor, we place circular apertures in empty regions of
the image and computing the scatter among the flux measurements (see e.g.
Whitaker et al., 2011; Skelton et al., 2014).

Stellar population properties are derived using prospector (Leja et al., 2017,
2019; Johnson et al., 2021) with redshifts set to those inferred from the
location of the H$\alpha$ emission line in the grism spectrum of each galaxy.
We adopt a 19 parameter physical model that includes redshift, stellar mass,
stellar and gas-phase metallicities, star formation history, a two component
dust model (Charlot & Fall, 2000), and emission from active galactic nuclei
(Naidu et al., 2022). We use FSPS (Conroy et al., 2009) with MIST stellar
models (Choi et al., 2016). Star formation rates are computed from the
measured H$\alpha$ fluxes assuming a Chabrier (2003) initial mass function
with Kennicutt (1998). The fluxes are corrected for dust attenuation using
empirical relations based on the UV slope (Shivaei et al., 2020).

Fig.1 shows the distribution of all galaxies with clearly detected H$\alpha$
in the SFR-M∗ plane. A locus of points is clearly detected implying the
existence of the star-forming main sequence at $z\sim 5$ as shown in Shapley
et al. (2023). The galaxy which is the focus of the present study has
log(M∗/M⊙)=10.4 and SFR=185M⊙/yr placing it at the high mass end of this
distribution and on the star-forming main sequence at this epoch.

We use the GALFIT software package (Peng et al., 2002, 2010) to fit the size
and shape of this galaxy accounting for the PSF following the procedure
described in Suess et al. (2022) and Nelson et al. (2023). This fitting is
performed on the direct images and the H$\alpha$ map (see §3). An empirical
PSF is constructed by stacking images of isolated point sources using
EPSFBuilder in Photutils (see Ji et al., 2023, for more details). We create a
segmentation map to identify all sources to be modeled or masked. Galaxies
that have centers within 3″of the target galaxy center and are less than 2.5
mag fainter are modeled simultaneously. Fainter and more distant galaxies are
masked. With all sufficiently bright galaxies identified, we estimate and
subtract the background in each stamp using the SExtractor background
algorithm as implemented in photutils. For F444W, we find effective radius
$r_{e}=2.2$kpc, sersic index $n=1.75$, and axis ratio $q=0.5$. For the medium-
band-derived H$\alpha$ map, we find $r_{e}=2.3$kpc, $n=0.2$, and $q=0.25$.

Figure 3: Velocity gradient. As described in §3, we fit the light weighted
center along the x-axis in the grism image, which corresponds to the
dispersion direction (left), F444W direct image (center), and a stack of the
rest-frame UV emission (right). The grism has a spectral resolution of $R\sim
1600$, meaning that the grism spectrum contains both spatial and spectral
information across in the dispersion direction. The difference between the
grism and direct image centroids is the velocity in that spatial pixel. The
error bars on the velocity curve are given by the difference between using the
rest-UV emission and F444W direct image.

Figure 4: Velocity dispersion profile. As described in §3, the width of the
H$\alpha$ line in the spectral direction is broadened by three things: the
line-of-sight velocity dispersion of the H$\alpha$ gas (including beam
smearing), the spectrograph line spread function, and the intrinsic spatial
extent. To measure the line-of-sight velocity dispersion, we subtract the
latter two terms off in quadrature. Twister-z5has a centrally peaked velocity
dispersion co-spatial with centrally concentrated light, perhaps indicative of
a bulge. We measure a disk velocity dispersion of 50-150 km/s, which is likely
an upper limit because dynamical forward-modeling has not been performed. The
fact that the velocity dispersion peaks in the center and is lower in the disk
suggests that the observed velocity gradient is likely due to rotation as
opposed to a merger (for which one would expect peaks in the velocity
dispersion on either side.

##  3 Kinematics

A benefit and drawback to slitless grism spectroscopy, depending on the
science goal, is that the dispersion axis contains not only spectral
information, which is typical, but also spatial information. For HST/WFC3 or
JWST/NIRISS the spectral resolution of $R\sim 100$ corresponds to
$\sim$1000km/s. In the low resolution regime, both axes of the emission line
distribution are effectively spatial and the continuum subtracted line
emission is essentially just an emission line map (e.g. van Dokkum et al.,
2011; Nelson et al., 2012, 2013, 2016a; Brammer et al., 2012; Matharu et al.,
2021, 2022, 2023). The exception is broad-line active galactic nuclei (AGN)
with line widths of $>1000$km/s which can be identified by their compact
distribution in the spatial direction and extended distribution in the
spectral direction (Nelson et al., 2012). However, the spectral resolution of
the NIRCam F444W grism is much higher – $R\sim 1600$ at $4\mu$m –
corresponding to a velocity dispersion of $\sigma\sim 80$ km/s. This
resolution means that for galaxies with velocity gradients of $>80$km/s, we
can place constraints on their kinematic properties in addition to the spatial
distribution of their line emission.

Because the morphology of the emission line along the grism spectral axis is
due to both the spatial and kinematic properties, additional data are needed
to break the degeneracy. Here we use the F410M medium band which covers the
short wavelength portion of the F444W filter in which the H$\alpha$ line of
this object falls. As shown in Fig.2, the difference between the F410M and
F444W image essentially provides a map of the H$\alpha$ line emission (e.g.
Williams et al., 2023; Withers et al., 2023). To model the kinematics, we fit
the light-weighted center of the H$\alpha$ emission in each row of both the
medium band-derived map and the 2D grism spectrum. These datasets share a
spatial centroid so the measured difference in light-weighted center is due to
velocity. Hence our velocity gradient is inferred by subtracting the medium
band H$\alpha$ map light-weighted center from the grism image light-weighted
center in each row. This method is shown pictorially in Fig. 3 alongside our
results. The uncertainty on the velocity in each spatial pixel is calculated
by bootstrap resampling the grism and medium band images within the noise.

We measure an observed velocity difference $v_{obs}$ from the maximum and
minimum velocities by

$v_{obs}=\frac{1}{2}(v_{max}-v_{min})=235\pm 50\textrm{ km/s}$

as in (e.g. Wisnioski et al., 2015). If this velocity gradient represents
rotation (more on this below), the observed velocity difference must be
corrected for inclination in order to reflect the intrinsic rotation velocity:

$v_{rot}=v_{obs}/\textrm{sin}i$

We use the axis ratio measured from the medium band H$\alpha$ image (see §2)
to infer the inclination of the galaxy using

$\textrm{cos}^{2}i=(q^{2}-q_{0}^{2})/(1-q_{0}^{2})$

where $q=0.25$ is the measured axis ratio and $q_{0}$ is the intrinsic axis
ratio. As we do not in fact know the intrinsic axis ratio, we include the full
range of possible intrinsic axis ratios in our error budget $0.05<q_{0}<q$.
Because the measured axis ratio is 0.25, this correction is very small in
practice regardless of the assumed $q_{0}$ ($<$5%). We find $v_{rot}=242\pm
50$ km/s.

With the combination of a medium band H$\alpha$ map and grism spectrum, it is
also possible to measure the line-of-sight velocity dispersion. The width of
the line in the spectral direction is broadened by three things: the
spectrograph line spread function, the line-of-sight velocity dispersion of
the H$\alpha$ gas (including beam smearing), and the intrinsic spatial extent.
The contribution of the line spread function is well-known and the degeneracy
between the velocity dispersion and spatial extent can be broken using the
combination of the medium-band and grism data.

We fit a Gaussian to the emission line in each row of the H$\alpha$ in both
the medium-band map and grism image. These widths are shown in Fig. 4. To
infer the line-of-sight velocity dispersion, we subtract off the instrumental
line spread function and spatial width in quadrature. As shown in Fig. 4, the
galaxy has an average velocity dispersion of $\sim 100$km/s in the disk and
$\sim 225$km/s in the center. The most obvious physical explanation for the
higher central velocity dispersion is a dynamically hot bulge. Beam-smeared
rotation could also play some role, but we note that the measured rotation
curve is close to linear. The ratio of rotation to velocity dispersion in the
disk, an oft-used metric for the dynamical state of a system is $V/\sigma\sim
2$.

As discussed in Simons et al. (2017), an observed velocity gradient can be an
indication of either a rotating disk or a merger. If the object is a disk, one
expects centrally peaked velocity dispersions while in a merger the velocity
dispersion is expected to be higher on either side and dip in the center.
Because we see a centrally peaked velocity dispersion profile and no strong
morphological indications for a merger, we interpret the observed velocity
gradient as rotation but note that Twister-z5 may have experienced a merger in
the past and whether it is virialized is uncertain.

We infer total dynamical mass of the system using our measured kinematics
following Price et al. (2022). We compute the circular velocity $V_{circ}$
accounting for turbulent pressure support with

$V_{circ}=(V_{rot}^{2}+\alpha\sigma_{0}^{2})^{0.5}$

(e.g. Burkert et al., 2010; Wuyts et al., 2016; Wisnioski et al., 2018;
Förster Schreiber et al., 2018) where $\alpha=3.36R/R_{e}$. The dynamical mass
within the effective radius of this galaxy, if it can be described by a
rotating disk, is

$M_{dyn}=k(R)\frac{V_{circ}^{2}(R)R}{G}$

The virial constant $k(R)$ is dependent on the distribution of mass within the
galaxy; we adopt $k(R=R_{e})=2.128$ which is the virial coefficient evaluated
for $q=0.4$ and $n=1$ which invokes an elevated $q$ to account for the
spherical halo (as in e.g. Miller et al., 2011; Price et al., 2020). We
include the range of velocity dispersions measured in the disk in our
dynamical mass uncertainty budget.

Figure 5: Radial surface brightness profiles of F444W (left), H$\alpha$
(center), and the radial H$\alpha$ equivalent width profile (right). The
H$\alpha$ distribution is much less centrally concentrated than the 4.4µm
continuum emission resulting in an H$\alpha$ equivalent width profile that
rises from the center to 2kpc consistent with this $z=5.3$ galaxy growing
inside-out in a bulge-disk system.

We find a dynamical mass of ${\rm log(M}_{dyn})=11.0\pm 0.2$. With a stellar
mass of log(M∗)=$10.4\pm 0.4$, Twister-z5 has a significantly larger dynamical
mass than stellar mass within the effective radius. This stands to reason as
the dynamical mass includes the dark matter and gas masses in addition to the
stellar mass. We infer a gas mass of ${\rm log(M}_{gas})=10.4$ by scaling the
SFR with the Kennicutt-Schmidt relation using the effective radius of the
H$\alpha$ emission (Kennicutt, 1998). Gas fractions are expected to rise
dramatically to high redshift (Tacconi et al., 2020), so a gas fraction of 50%
is not surprising. Using these estimates of the mass components we infer a
baryonic mass that is $\sim 50$% of the total dynamical mass. At $1<z<3$ many
studies of ionized gas or stellar kinematics find that massive galaxies
($\log(M_{\star}/M_{\odot})\gtrsim 10$) are baryon-dominated within the galaxy
scale, sometimes with stellar masses alone that match or even exceed their
dynamical masses (e.g. Förster Schreiber et al., 2009; Bezanson et al., 2013;
van Dokkum et al., 2015; Alcorn et al., 2016; Burkert et al., 2016; Stott et
al., 2016; Wuyts et al., 2016; Lang et al., 2017; Genzel et al., 2017; Barro
et al., 2017; Förster Schreiber et al., 2018; Price et al., 2020). On the
other hand, the first study of the ionized gas kinematics of $z>5$ galaxies
with JWST finds dynamical masses an order of magnitude larger than stellar
masses, for low mass galaxies ($\log(M_{\star}/M_{\odot})\sim 7-9$; de Graaff
et al., 2023). Larger samples of $z>3$ galaxies covering a range of stellar
masses and sizes will be needed to systematically study the baryon-to-dark
matter ratios of early disks.

Figure 6: Resolved stellar populations based on SED fitting of the JWST
imaging. The top row shows maps of the stellar mass (left), star formation
rate (middle), and specific star formation rate (right) from spatially
resolved SED modelling of the JWST images. The bottom row shows the radial
surface density profiles of the stellar mass, star formation rate, and
specific star formation rate, respectively. A clear central depression can be
seen in the specific star formation rate, a feature that is typically seen in
bulge-disk systems growing inside-out.

##  4 The spatial distribution of H$\alpha$: Inside-out growth

At $z\sim 5-6$, the F444W grism captures H$\alpha$ emission, a tracer of star
formation, and the F444W direct image captures the rest-frame R-band
continuum, a reasonable proxy for stellar mass. As such, their quotient, the
H$\alpha$ equivalent width (EW(H$\alpha$)) can serve as a proxy for the
specific star formation rate (SFR/M∗) which shows how the galaxy is growing
(e.g. Nelson et al., 2013).

Owing to the impact of velocity on the observed morphology of H$\alpha$, we
cannot measure a radial surface brightness profile in elliptical apertures.
Instead, we effectively collapse the light distribution in both the direct and
grism images along the detector axis corresponding to the dispersion axis in
the grism image. In practice, to optimize the signal-to-noise ratio of our
profiles, we instead shift each row to the light weighted centroid and sum
along each row encompassing the effective semi-minor axis. The resulting
profiles are shown in Fig.5.

The F444W light is much more centrally concentrated than the H$\alpha$
emission and hence the H$\alpha$ equivalent width profile rises sharply from
the center to the effective radius at 2.25 kpc. Taking the EW(H$\alpha$) as a
proxy for the specific star formation rate, the rising equivalent width we
observe suggests that this galaxy is building mass more rapidly at $r\sim
r_{e}$ than in the center. Further, the F444W profile is significantly steeper
than the H$\alpha$ profile; PSF effects would only accentuate this difference
as the PSF is slightly broader in F444W than F410M. Because the H$\alpha$ and
continuum have the same wavelength, the attenuation they experience from
diffuse dust is expected to be the same. While extra attenuation is expected
toward HII regions (e.g. Price et al., 2014; Reddy et al., 2015), a variation
in the quantity of extra attenuation toward HII regions would need to change
as a functon of radius to create the rising EW(H$\alpha$) observed. Given that
this extra attenuation is surrounding birth clouds, this kind of geometric
effect seems unlikely but resolved measurements of H$\beta$ would be needed to
be sure (e.g. Nelson et al., 2016b; Lorenz et al., 2023; Shapley et al.,
2023). Further, even in the presence of significant dust attenuation, the
H$\alpha$ equivalent width is a reasonably good proxy for the sSFR (e.g.
Nelson et al., 2019). The most obvious interpretation of these features is
that this galaxy is growing inside-out with a star-forming disk surrounding a
bulge with relatively suppressed star formation. The surprise of course is
that this is not $z\sim 1$ where this structured inside-out growth is typical
(e.g. Nelson et al., 2016a) but $z>5$.

We also perform spatially resolved SED fitting of the JWST imaging to
determine if the conclusions hold with more sophisticated modeling following
Giménez-Arteaga et al. (2023). Briefly, images in all JWST filters are PSF-
matched to the F444W resolution and the SED of each pixel is fit. Fits are
performed with BAGPIPES (Carnall et al., 2018) with SPS models by Bruzual &
Charlot (2003), nebular emission with CLOUDY (Ferland et al., 2017), a Kroupa
(2001) initial mass function (IMF), a Calzetti et al. (2000) attenuation
curve, and constant star formation history following Carnall et al. (2023) and
Giménez-Arteaga et al. (2023). The redshift is fixed to the grism
spectroscopic redshift. Visual extinction is allowed to vary $A_{V}=0-3$, the
maximum age 1Myr - 5Gyr, and metallicity $Z=0-Z_{\odot}$ all with uniform
priors. The resulting maps of stellar mass, star formation rate, and specific
star formation rate are shown in Fig. 6. As in the case of H$\alpha$
equivalent width, the inferred specific star formation rate is lower in the
center than at larger radii, suggesting that this galaxy is building from the
inside-out.

##  5 Discussion

We measure kinematics and spatially resolved H$\alpha$ emission for a ${\rm
log(M}_{*}/M_{\odot})=10.4$ galaxy using FRESCO JWST/NIRCam spectroscopy
combined with JADES medium band imaging. We measure the effective radius of
the rest-frame optical (0.55$\micron$) emission in the F356W filter, which is
not expected to be dominated by line emission. This galaxy has a rest-optical
effective radius of $r_{e}=2.25$ kpc, comparable to the half-light radii of
similar-mass galaxies at $z=0.5-1$ (e.g. van der Wel et al., 2023), much
larger than we anticipate for an early galaxy if galaxy sizes scale with the
scale factor of the universe. It is also significantly larger than one would
expect based on existing measurements of the effective radius of galaxies as a
function of redshift ($r_{e}(z)$), which finds $r_{e}\sim 1$kpc at $z=5.3$
(Holwerda et al., 2020). It has a rising EW(H$\alpha$) profile, a proxy for
specific star formation rate, and appears to be a bulge-disk system growing
inside-out. We measure a rotation velocity of $240\pm 50$km/s, similar to or
greater than local massive spiral galaxies. In many ways this appears to be a
typical $z\sim 2$ disk galaxy. Oddly, it is not at $z\sim 2$, but $z=5.38$.
That massive, extended, rotating disk galaxies could exist at such early times
is surprising. In particular because this does not appear to be a one-off
situation but rather adds to the growing body of evidence for massive,
extended, rotating disks seen in some studies of [CII] with ALMA (e.g. Hodge
et al., 2012; Neeleman et al., 2020; Tsukui & Iguchi, 2021; Parlanti et al.,
2023).

Considering the dynamical mass with respect to the stellar mass, Twister-z5
has a stellar mass fraction of $\sim 25$%, and a baryonic mass fraction of
$\sim 50$% within the effective radius. With a dynamical mass of
log(Mdyn/M⊙)=11.1, these mass fractions are similar to galaxies with similar
dynamical masses at $z=1-3$ (e.g Förster Schreiber et al., 2018; Price et al.,
2020). If this is confirmed by larger samples, it may mean that the central
baryon fraction of massive galaxies is more-or-less set by $z\sim 5$. A number
of studies find that galaxies become more baryon-dominated in their centers
going from $z\sim 0$ to $z\sim 3$ (e.g. Übler et al., 2018; Price et al.,
2020). However, at dynamical masses of $10^{11}$M⊙, the ratios of stellar-to-
dynamical mass and baryonic-to-dynamical mass remain fairly constant (see e.g.
Fig 4. Price et al., 2020). On the other hand, low mass, high redshift
galaxies are possibly strongly dark matter dominated (de Graaff et al., 2023).
More massive galaxies at $z\sim 7$ have been suggested to show a range in
their baryonic to dynamical mass ratio depending on the luminosity-weighted
age (Topping et al., 2022), although these measurements are based on spatially
unresolved measurements of the [CII] emission line widths and therefore may be
affected by mergers and non-virial motions. One interpretation of this result
is that the total mass may be more important than the cosmic epoch for
determining how baryon dominated the centers of galaxies are. Some theoretical
models find that galaxies transition from prolate to oblate when their centers
become baryon dominated (e.g. Ceverino et al., 2015), consistent with the
rotation-dominated kinematics we find.

We find $V/\sigma\sim 2$ for Twister-z5, meaning that although it is rotation
dominated, the velocity dispersion in the disk is much higher than that of
local galaxies. This is likely to be an upper limit on the velocity
dispersion, however, as we do not forward-model the velocity field (as in e.g.
de Graaff et al., 2023) which can result in velocity dispersions which are
biased high (e.g. Rizzo et al., 2022). That caveat noted, a mix of rotational
and dispersion support is qualitatively consistent with many recent studies of
H$\alpha$ kinematics at the peak of the cosmic star formation history at
$z=1-3$ which have found higher high velocity dispersions in the disks of
higher redshift galaxies (e.g. Wisnioski et al., 2015; Swinbank et al., 2017;
Turner et al., 2017; Übler et al., 2019). A number of these studies find that
$V/\sigma$ declines with redshift to $\sim 1$ at $z\sim 3$. Based on
analytical modeling, Übler et al. (2019) suggest that the significant levels
of turbulence in disks at $z>1$ is driven by a combination of gravitational
instabilities and stellar feedback (e.g. Krumholz et al., 2018; Varidel et
al., 2020). Quantitatively, the rotation dominance we observe is higher than
one would expect based on the extension of lower redshift H$\alpha$ studies.
Stott et al. (2016) and Turner et al. (2017) find that the rotation dominated
fraction, which they define as $V/\sigma>1$, declines with redshift as
$RDF\propto z^{-0.2}$. If extrapolated, this relation implies the likelihood
of finding a rotation dominated galaxy at $z\sim 5.3$ is less than 10%.
$V/\sigma\sim 2$ is, however, consistent with an extrapolation of the
$V/\sigma$ values predicted in the TNG50 cosmological hydrodynamical
simulation (Pillepich et al., 2019). On the other hand, it is significantly
lower than the values found by some studies of $z\sim 4-5$ galaxies in [CII]
emission with ALMA which find $V/\sigma\sim 10$ in some massive galaxies at
this epoch (e.g. Rizzo et al., 2020, 2021; Fraternali et al., 2021; Lelli et
al., 2021). It is possible that the discrepancy between ionized and molecular
gas kinematics is due to actually different kinematics in different gas phases
(see e.g. Übler et al., 2019). However, in a detailed study of H$\alpha$ vs.
CO kinematics in a $z=1.4$ galaxy, Übler et al. (2018) find the two tracers
yield comparable velocity dispersions. With the objects having kinematic
measurements in any tracer at $z>5$ numbering less than 50, resolving this
discrepancy will require kinematics for much larger samples in multiple
tracers.

Although the kinematics of Twister-z5 appear typical for an extrapolation of
cosmological simulations, the structure does not. The axis ratio distribution
in the TNG50 simulation skews toward higher values than observed galaxies
suggesting it has fewer prominent disks than the real universe (Kartaltepe et
al., 2023). Interestingly, there are almost no objects at $5<z<6$ in TNG50
with $n>2$ suggesting that bulge-disk systems such as this are not expected in
large numbers. Similar mass galaxies in the TNG50 cosmological hydrodynamical
simulation have a median observable effective radius of $\leq 1$ kpc
(Costantin et al., 2023), making an observed effective radius of
$r_{e}=2.25$kpc much larger than expected. There are very few (if any)
galaxies with $r_{e}>2$, $n=2$, and $b/a=0.4$ – i.e., a spatially extended
bulge-disk system such as this. A number of studies find or predict that
galaxies form bulges at early cosmic times then build an extended stellar
structure around it later (e.g. Bezanson et al., 2009; Nelson et al., 2014;
Zolotov et al., 2015; van Dokkum et al., 2015; Wellons et al., 2015), which is
qualitatively consistent with what we see in the the structure, kinematics,
and particularly the sSFR gradient of Twister-z5. However, a number of studies
suggest that building an extended disk is hard at such early times. Disks at
early cosmic epochs are expected to grow slowly, with formation times of $\sim
1.5$Gyr, due to instabilities which drive gas and stars to the center (e.g.
Ceverino et al., 2015; Park et al., 2019; Costantin et al., 2022). Given the
mass of this galaxy, it will likely be massive and quiescent by $z\sim 2$,
placing it in a population of galaxies remarkable for their compactness
($M_{*}\sim 10^{11}M_{\odot}$ with $r_{e}\sim 1kpc$), suggesting that the disk
of this galaxy will likely need to be destroyed.

This study and many others are pointing to the existence of mature galaxies at
surprisingly early cosmic epochs. Remarkably luminous galaxy candidates have
been found to $z\sim 13$ (e.g. Oesch et al., 2016; Naidu et al., 2022;
Castellano et al., 2022; Finkelstein et al., 2022; Bunker et al., 2023;
Tacchella et al., 2023a; Harikane et al., 2023; Donnan et al., 2023; Casey et
al., 2023) and candidate massive galaxies with $M_{*}>10^{10}M_{\odot}$ have
been found at $z=5-9$ (e.g. Labbé et al., 2023; Xiao et al., 2023; Akins et
al., 2023). All of these unexpected sources require spectroscopic confirmation
of their nature. Spectra obtained thus far reveal a mixed bag with some
redshifts holding (e.g. Curtis-Lake et al., 2023; Roberts-Borsani et al.,
2023), some falling (e.g. Arrabal Haro et al., 2023), and some have remarkable
mass or luminosity due to active galactic nuclei instead of stars (e.g
Kocevski et al., 2023; Maiolino et al., 2023; Matthee et al., 2023b). If a
number of these results hold, the combination of JWST and ALMA might show us
that mature galaxies form earlier than we previously thought possible. This
study provides both redshift and dynamical confirmation of a massive galaxy at
early cosmic time.

This paper presents a new method for kinematic measurements with JWST which
has the potential to enable dramatic multiplexing for unbiased samples:
slitless spectroscopy with medium band imaging. With the fairly high spectral
resolution of the NIRCam grism ($R\sim 1600$), this mode of spectroscopy could
provide an efficient way to derive kinematic constraints on large samples of
massive galaxies. Even stronger kinematic constraints could be placed using
multiple grism dispersion directions. While validation tests need to be done
against IFU data, this methodology could provide an exciting way to make
kinematic measurements for large, unbiased samples of galaxies at early times,
allowing us to understand their seemingly rapid early assembly.

Support for this work was provided by NASA through grant JWST-GO-01895 awarded
by the Space Telescope Science Institute, which is operated by the Association
of Universities for Research in Astronomy, Inc., under NASA contract NAS
5-26555. HÜ gratefully acknowledges support by the Isaac Newton Trust and by
the Kavli Foundation through a Newton-Kavli Junior Fellowship. This work has
received funding from the Swiss State Secretariat for Education, Research and
Innovation (SERI) under contract number MB22.00072, as well as from the Swiss
National Science Foundation (SNSF) through project grant 200020_207349. The
Cosmic Dawn Center (DAWN) is funded by the Danish National Research Foundation
under grant No. 140. RS acknowledges an STFC Ernest Rutherford Fellowship
(ST/S004831/1). RPN acknowledges support for this work provided by NASA
through the NASA Hubble Fellowship grant HST-HF2-51515.001-A awarded by the
Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Incorporated, under NASA contract
NAS5-26555. MVM acknowledges support from the National Science Foundation via
AAG grant 2205519 and the Wisconsin Alumni Research Foundation via grant
MSN251397. RM also acknowledges funding from a research professorship from the
Royal Society. AJB, AJC, & GCJ acknowledge funding from the ”FirstGalaxies”
Advanced Grant from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (Grant agreement No.
789056). IL acknowledges support by the Australian Research Council through
Future Fellowship FT220100798. DJE is supported as a Simons Investigator and
by JWST/NIRCam contract to the University of Arizona, NAS5-02015. RM, JW, LS,
and WB acknowledge support by the Science and Technology Facilities Council
(STFC), by the ERC through Advanced Grant 695671 “QUENCH”, and by the UKRI
Frontier Research grant RISEandFALL. BER acknowledges support from the NIRCam
Science Team contract to the University of Arizona, NAS5-02015. The research
of CCW is supported by NOIRLab, which is managed by the Association of
Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation.

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