# Transforming gas-rich low-mass disky galaxies into ultra-diffuse galaxies by
ram pressure

Kirill A. Grishin1,2,8 Igor V. Chilingarian3,1,8 Anton V. Afanasiev4,5,1,8
Daniel Fabricant3 Ivan Yu. Katkov6,1 Sean Moran3 Masafumi Yagi7

###### Abstract

Faint extended elliptically-shaped ultra-diffuse galaxies and slightly
brighter and more compact dwarf elliptical and lenticular stellar systems are
common in galaxy clusters. Their poorly constrained evolutionary paths can be
studied by identifying young ultra-diffuse galaxy and dwarf elliptical analogs
populated with bright, massive stars. Using data mining we identified 11 such
low-mass ($2\times 10^{8}<M_{*}<2\times 10^{9}M_{\odot}$) galaxies with large
half-light radii ($2.0<r_{e}<5$ kpc) and recently quenched star formation in
the Coma and Abell 2147 galaxy clusters. All galaxies happen to have ram-
pressure-stripped tails with signs of current or recent star formation. Deep
spectroscopic observations revealed rotating stellar discs containing 70–95%
dark matter by mass. A large fraction of the disc stars (10–60%) formed in
intense star bursts 180–970 Myr ago, probably triggered by ram pressure.
Observed global gradients of stellar age corroborate this scenario. Passive
evolution in the next 10 Gyr will transform 9 of the 11 galaxies into ultra-
diffuse galaxies. If we assume a constant rate of galaxy infall, 44$\pm$16 %
of the most luminous present-day ultra-diffuse galaxies in Coma must have
formed via ram pressure stripping of disky progenitors.

Sternberg Astronomical Institute, M.V. Lomonosov Moscow State University, 13
Universitetsky prospect, Moscow, 119992, Russia Department of Physics, M.V.
Lomonosov Moscow State University, 1 Vorobyovy Gory, Moscow, 119991, Russia
Center for Astrophysics – Harvard and Smithsonian, 60 Garden St. MS09,
Cambridge MA 02138, USA Université de Paris, CNRS, Astroparticule et
Cosmologie, F-75013 Paris, France LERMA, Observatoire de Paris, PSL Research
University, CNRS, F-75014 Paris, France New York University Abu Dhabi, 129188,
Saadiyat Island, Abu Dhabi, United Arab Emirates Subaru Telescope, National
Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
These authors contributed equally to this work

T he first systematic studies of the two nearest galaxy clusters (Virgo and
Fornax) three decades ago[1, 2] revealed large populations of low-luminosity
($L_{B}\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}3\times 10^{9}L_{\odot}$) early-type
galaxies, including some very extended examples ($r_{e}>5~{}kpc$). Recently,
dozens[3] and then hundreds[4] of similar extended “ultra-diffuse” galaxies
(UDGs) were found in the more distant ($d=99$ Mpc)[5] and populous Coma
cluster and also in galaxy groups[6]. These UDGs include several extreme
examples with the size but $<$1% of the stellar mass of the Milky Way.
Initially some UDGs were thought to be “failed galaxies”[7]: massive dark
matter halos that formed few stars following rapid gas loss at an early
evolutionary stage. This gas loss could arise from the cluster environment,
including ram pressure stripping by hot intracluster gas[8] and tidal
interactions[9] or from internal processes such as supernovae (SN) driven
winds[10]. Gas loss from a low-mass star-forming galaxy will quench star
formation, allowing the galaxy to evolve into a quiescent early-type system.
Recent observations[11] and simulations[12, 13] suggest that a dwarf galaxy
can be puffed up by SN feedback or tidal interactions and transformed into a
UDG. It is unclear whether UDGs and dEs belong to the same family[14, 15] and
share similar evolutionary paths or if they represent different galaxy types
with different formation scenarios. In-depth observational studies of UDGs are
challenging because their surface brightnesses are significantly below that of
the night sky. This fundamental limitation can be overcome by identifying
recently quenched low-mass galaxies, still containing young stars, that will
passively evolve into dEs or UDGs.

Data mining the multi-wavelength Reference Catalog of Spectral Energy
Distribution of galaxies (RCSED[16]) revealed 12 blue but non-starforming
galaxies (mean stellar age $<1.5$ billion years) with half-light radii $r_{e}$
between 2.0 kpc and 5.2 kpc. The RCSED galaxies are part of the main galaxy
sample from the 7th Data Release of the Sloan Digital Sky Survey[17], and form
a nearly complete magnitude-limited sample within the SDSS footprint. Nine
galaxies reside in the Coma cluster (Figure 1), two are Abell 2147 cluster
($d=156$ Mpc) members (Figure 2), and one is a group member. Four of the nine
Coma cluster members were previously classified as “blue k+a” post-starburst
galaxies (PSGs)[18] based on their integrated-light spectra. However, a recent
starburst is needed to properly reproduce the spectra and colours of the
remaining galaxies, so they are also PSGs. Two Coma galaxies (GMP 4060 and GMP
2923) are known[19] to exhibit spectacular tails of material stripped by the
ram pressure of the hot intracluster medium[8] with H$\alpha$ emission
suggesting current star formation. Their discs, unlike most other galaxies in
the the Subaru SuprimeCam H$\alpha$ survey of the Coma cluster, are not
starforming. Young stars are UV-bright and expose a 250 kpc long tail in the
most massive galaxy in our sample, GMP 2640[20]. Visual inspection of Subaru
HyperSupremeCam images revealed filamentary tails in both Abell 2147 members
(Figure 2). Deep broad-band and H$\alpha$ images of the remaining Coma
galaxies also expose faint low-contrast structures near them (Extended Data
Figure References) that are likely the leftovers of ram-pressure-stripped
tails significantly dimmed because of stellar evolution.

Figure 1: Positions of Coma cluster members selected from RCSED and one
additional galaxy, GMP 3016. The insets showing zoomed-in galaxy images were
constructed from Subaru and Canada-France-Hawaii Telescope (CFHT) optical data
in the $u*$, $B$, $V$ and $R$ bands. A scale bar corresponding to 10 kpc is
shown inside each inset. In GMP 2640 the image reveals a blue clump of
recently formed stars south-east of the centre which was masked for dynamical
modelling purposes.

None of the tails point away from the cluster centre suggesting that these
galaxies have orbits with significantly tangential shapes. The galaxies with
the brightest tails have the youngest mean stellar ages of the 11 PSGs. The
lack of star formation in their discs suggests that they could be classified
as “post-jellyfish” galaxies. Similar, but typically more massive “jellyfish”
systems[21] have active star formation in their discs and tails[22]. Two
similar low-mass quenched PSGs with impressive tails, IC 3418[23] and VCC
1249[24] in the nearby Virgo cluster are believed[23] to have been recently
transformed by ram pressure stripping from star forming galaxies into
quiescent dwarfs. However, at the Coma cluster distance both galaxies would
have fallen below the SDSS magnitude limit. Prior to stripping, ram pressure
can compress gas and induce a burst of star formation[25, 26], consistent with
the PSG classification of our galaxies.

Figure 2: Positions of the two Abell 2147 cluster members selected from RCSED
and an additional photometrically selected PSG, J160231.45+155749.9. The
insets showing zoomed-in images for individual galaxies (marked by red arrows)
are constructed from $g$, $r$, and $i$ broadband HSC images. The two galaxies
from the main sample exhibit tails of stripped material. We mark the positions
of clumps in the tails with white arrows.

## Results

We observed the 11 low-mass PSGs in the Coma and Abell 2147 clusters using the
high-throughput multi-object Binospec spectrograph[27] operated at the 6.5-m
MMT. GMP 3640 was also observed with the 8 m Gemini-North telescope using the
GMOS-N spectrograph. We added five additional galaxies to the sample. These
include GMP 3016, the remaining known Coma cluster member with H$\alpha$
detected in the tail but not in the main disc[19]. GMP 3016 is 0.03 mag below
the SDSS magnitude limit and would have been excluded by the original
selection criteria. We also included four additional galaxies without SDSS
spectra, three fainter UDGs in the Coma cluster with mean stellar ages $<2$
Gyr[15] and one photometrically selected faint PSG in Abell 2147.

To assess the current properties of PSGs and predict their evolution, we
adopted a simple physically motivated scenario for their star formation
histories (SFHs). This scenario includes a period of constant star formation
rate (SFR) that started 12 Gyr ago and a more recent ram pressure-induced
starburst followed by the shutoff of star formation[28].

Figure 3:  Top panel for each galaxy: an optical colour image with an over-
plotted slit position; middle panel: stellar radial velocity $v$; bottom
panel: stellar velocity dispersion $\sigma$. Black lines show the best-fitting
Jeans models for stellar kinematics. The estimated dark matter contribution
within $1r_{e}$ (indicated by vertical dashed lines) and the anisotropy
parameter $\beta_{z}$ are shown in the upper and lower corners of each $v$
panel. For 8 out of 9 galaxies $\sigma$ and $v$ profiles are shown in the same
scale. For the most massive galaxy, GMP 2640 the scale of these profiles is
decreased. This galaxy also has a clump of young stars whose dynamics cannot
be explained in the framework of axisymmetric modelling – the data points
corresponding to this clump are greyed out.

We simultaneously fit Binospec spectra and broadband fluxes from the far-
ultraviolet ($\lambda=0.17$ $\mu$m) to the near-infrared ($\lambda$=4.5
$\mu$m) extracted from the same region against a grid of PSG stellar
population models using the NBursts+phot technique[29] (see Extended Data
Figures References–Transforming gas-rich low-mass disky galaxies into ultra-
diffuse galaxies by ram pressure). The best-fitting solution yields four
parameters: (i) the truncation age (i.e. end of ram pressure stripping); (ii)
the fraction of gas consumed from a primordial reservoir before truncation,
which is linked to the final stellar metallicity; (iii) the mass fraction of
stars born in the final starburst; and (iv) a coefficient for galactic winds.
In addition, we obtain radial velocity ($V_{R}$) and velocity dispersion of
stars ($\sigma$). In the primary sample of 11 PSGs, the truncation ages range
from 180 Myr to 970 Myr. In 9 of the 11 galaxies the mass fraction of stars
born in the ram pressure-induced starburst lies between 10% and 40%. The
fraction of consumed gas for all 11 galaxies is higher than 60%, reaching
90–96% in six cases, corresponding to mass-weighted stellar metallicities of
$-1.04\dots-0.62$ dex. The estimated truncation ages for the seven galaxies
with bright tails (including GMP 3016) are younger ($180\dots 500$ Myr) than
for the remaining five, whose tails faded close to the limit of detectability.
Deriving mass-to-light ratios from our best-fitting parameters, we estimate
the total stellar masses of our PSGs to be in the range 5.1$\times
10^{8}M_{\odot}$ (GMP 3176) to 2.36$\times 10^{9}M_{\odot}$ (GMP 2640).
Therefore, despite their large sizes these are all dwarf galaxies. Truncation
age profiles (see Extended Data Figure References) for most galaxies show weak
global gradients across the disc superimposed on radially increasing
gradients. The radial gradients are more pronounced for denser and more
massive galaxies, e.g. GMP 4348, GMP 2640, GMP 3640. The radially increasing
gradients correspond to the outside-in star formation quenching expected from
the ram pressure stripping. SN feedback would cause inside-out quenching and
produce radially decreasing truncation age profiles. Ram pressure strips the
disc gradually from one side to the other (excepting in face-on cases),
consistent with the observed truncation age gradients across the disc. The
gradients across the disc are preserved for hundreds of Myr because the inner
regions of all the galaxies in our sample rotate like a solid body.

Young stars boost the surface brightness and allow us to measure stellar
kinematics ($V_{R}$ and $\sigma$) to radii as large as 2.5 $r_{e}$ (Figure 3),
substantially further than for other low-mass galaxies beyond the Local Group.
All 11 galaxies from the primary sample have $V_{R}/\sigma>1$ in their outer
parts suggesting that they are rotationally supported systems; GMP 3016 has a
nearly face-on orientation. The absence of observed UDGs with such a
pronounced degree of rotational support can be explained by the lack of
observations to a comparably large radius and also because the stellar
rotation in the inner part of a disc slows down over time due to disc
expansion. If we restrict our view of the low-mass PSGs to the $0.5\dots
1.0~{}r_{e}$ typically reached for faint dEs[30] and UDGs[15], only 6 have
rotational velocities exceeding 10 km/s.

We fit axisymmetric Jeans anisotropic models[31] to the stellar kinematics and
structural properties assuming that each galaxy resides in a spherical dark
matter halo. In all cases, the modelling yielded significant dark matter
fractions, from 70% to 95% of the total mass within $1~{}r_{e}$, and
moderately anisotropic orbits, similar to those of UDGs[15]. However, the data
are of far higher quality for the diffuse PSGs. The gravitational potential in
these objects is rapidly changed by the removal of a substantial fraction of
the gas by ram pressure on a timescale of $30\dots 70$ Myr, significantly
shorter than typical dynamical times in galaxies ($200\dots 350$ Myr). The
rapid gravitational potential change transforms quasi-circular stellar orbits
to rosette-like[32] orbits even in a massive dark matter halo. The stellar
density decreases and its radial profile becomes shallower, the orbital radial
anisotropy increases, manifested by a rotational velocity drop in the galaxy
central regions. The disc expansion due to slow stellar mass loss during slow
passive evolution ($5\dots 10$ Gyr) can be neglected when a galaxy has a
massive dark matter halo. However, numerical simulations[33] suggest that a
dark matter halo will be gradually stripped by tidal interactions with other
galaxy cluster members during flybys, which would cause the overall stellar
disc expansion by about 25% over 10 Gyr.

Assuming passive evolution, based on best-fitting stellar population
parameters and a slow disc expansion, we can predict internal properties
(luminosity, surface brightness, luminosity- and mass-weighted stellar
metallicities) of our galaxies up-to 10 Gyr from now (Figure 4). The
Faber–Jackson[34] relation connecting stellar velocity dispersion to total
luminosity and the luminosity–metallicity relation, predict that our low-mass
PSGs will settle in the locus of known UDGs (7 Coma galaxies and 2 Abell 2147
galaxies) and dEs/dS0s (2 Coma galaxies) in 3–10 Gyr. The luminosity-weighted
stellar metallicity will decrease over time because the contrast of the final
ram pressure-induced starburst over an underlying metal-poor population will
diminish. Stellar velocity dispersion will also decrease following the
expansion of a galaxy. The same 9 “future UDGs” will also settle in the UDG
locus in the $\langle\mu_{Rc}\rangle$ \- $r_{e}$ diagram presenting their
global structural properties[35].

Figure 4: Predicted passive evolution of low-mass PSGs from their SFHs during
the next 10 Gyr on the Faber–Jackson $\sigma-M_{B}$ (a),
metallicity–luminosity $[\rm{Fe/H}]-M_{B}$ (b) and mean surface brightness –
effective radius $\langle\mu_{Rc}\rangle$ \- $r_{e}$ (c) relations. We show
our primary targets from the Coma and Abell 2147 clusters and additional PSGs
galaxies not included in the statistical calculations by green, cyan and grey
arrows respectively. Each arrow starts at the currently observed position of a
galaxy and points to its expected location in 10 Gyr. On the Faber–Jackson
relation we show the $L\sim\sigma^{4}$ and the $L\sim\sigma^{2.5}$ best-
fitting linear correlations[36] for giant and dwarf galaxies. A cyan solid
line in the right panel at $\langle\mu_{Rc}\rangle=24.0\
\rm{mag}/\rm{arcsec}^{2}$ denotes the UDG surface brightness cut. All PSGs but
two will move into the UDG locus in the next 10 Gyr. The two remaining
galaxies, GMP 2640 and GMP 2923 will settle in dE region. The literature
sample includes dEs[37, 30, 38], photometric[39, 40, 41] and spectroscopic[42,
11, 15, 43, 44] samples of UDGs, Local Group dwarf spheroidal galaxies[45],
Local Volume dwarf late-type galaxies from _Little Things_[46], a sample of
giant early-type galaxies[47] complemented by a selection of Coma cluster
early-type galaxies (grey dots) and elliptical galaxies at $z<0.2$ (grey
shaded region) from RCSED. In panel (c), the red tracks display evolutionary
models of the two _Little Things_ objects, NGC 4214 and DDO 168 if they were
ram pressure stripped: (i) a ram pressure induced starburst and disc expansion
(curved tracks) followed by (ii) slow passive evolution (straight tracks).
Table 1: Internal dynamics, and dark matter contents of diffuse post-starburst
galaxies.

No. Name RA Dec $v_{r}$ $\sigma_{*}$ DM$(<r_{e})$ $\beta_{z}$ $\log\rho_{0}$
$r_{s}$ $M_{200}$ $R_{200}$ deg deg km/s km/s % $M_{\odot}$kpc-3 kpc
$10^{8}M_{\odot}$ kpc 1 GMP 4348 194.57587 27.84848 7524$\pm$1 51$\pm$2
85$\pm$8 0.3 -0.5 1.2 213 57.8 2 GMP 3176 194.94282 27.74625 9690$\pm$2
46$\pm$4 88$\pm$5 0.4 -0.5 1.0 123 48.2 3 GMP 2639 195.12170 27.33322
8449$\pm$1 43$\pm$2 84$\pm$3 0.4 -0.8 1.0 56 37.2 4 GMP 4118 194.65901
27.82258 5350$\pm$3 33$\pm$7 80$\pm$10 0.5 -1.2 1.5 66 39.6 5 GMP 4060
194.67746 27.76050 8683$\pm$1 26$\pm$2 87$\pm$15 0.0 -1.2 2.0 141 60.4 6 GMP
2923 195.03358 27.77332 8665$\pm$1 40$\pm$1 69$\pm$9 0.6 -1.0 1.5 112 47.1 7
GMP 2640 195.12180 27.51484 7304$\pm$1 78$\pm$2 90$\pm$4 0.7 -0.4 2.2 1445
181.4 8 GMP 3640 194.81245 28.25101 7446$\pm$1 37$\pm$2 87$\pm$10 0.5 -0.8 1.5
186 56.1 9 GMP 4188 194.63453 28.37797 5863$\pm$1 41$\pm$2 80$\pm$9 0.4 -1.5
2.1 195 54.3 10 J160154.20+160016.8 240.47583 16.00467 11506$\pm$1 52$\pm$2
96$\pm$2 0.6 -0.8 2.0 407 85.3 11 J160215.29+160904.3 240.56369 16.15119
12478$\pm$2 44$\pm$5 95$\pm$19 0.5 -1.0 1.2 58 37.6 Additional sample 12 GMP
3016 195.00431 28.08188 7702$\pm$2 31$\pm$5 83$\pm$7 0.6 n/a n/a n/a n/a 13
GMP 2673 195.10945 27.45978 6915$\pm$4 41$\pm$8 82$\pm$6 0.8 n/a n/a n/a n/a
14 GMP 2552 195.16098 27.47647 7885$\pm$3 52$\pm$5 96$\pm$1 0.0 n/a n/a n/a
n/a 15 J160231.45+155749.9 240.63104 15.96387 11270$\pm$5 39$\pm$12 87$\pm$15
0.0 n/a n/a n/a n/a 16 GMP 2662 195.11375 27.43855 7360$\pm$6 54$\pm$12
94$\pm$2 0.6 n/a n/a n/a n/a GMP[48] designations for Coma cluster galaxies
and IAU-style names for Abell 2147 members (Name). Positions on the sky (RA,
Dec), radial velocities ($v_{r}$) and stellar velocity dispersions
($\sigma_{*}$) obtained from the full spectrum fitting. Dynamical parameters:
dark matter contribution to total mass within $r_{e}$ (DM),the orbital
anisotropy parameter ($\beta_{z}$), logarithm of the central density
($\log\rho_{0}$) and radial scale ($r_{s}$) of the dark matter halo (for the
main galaxy sample), dark matter halo mass ($M_{200}$) inside $R_{200}$,
radius ($R_{200}$), where the dark matter density reaches the value 200 times
greater than the critical density.

## Implications for evolution of ultra-diffuse galaxies

Because our PSG sample in the Coma cluster is complete and because all
galaxies were likely formed via ram pressure stripping, we can estimate the
observed UDG fraction formed through this evolutionary channel. We compare the
surface brightness evolution of low-mass PSGs to a complete photometric sample
of Coma UDGs[41]. The reconstructed SFHs followed by passive evolution and
slow stellar disc expansion, allow us to estimate how long each PSG will
remain above the SDSS magnitude limit ($m_{r}<17.77$ mag) after star formation
quenching, and if (or when) its surface brightness drops below the adopted UDG
threshold ($\langle\mu_{e,R}\rangle>24.0$ mag arcsec-2). The ratio of the
duration of the UDG phase to the duration of the SDSS spectroscopic phase
gives us a statistical estimate of the number of UDGs corresponding to each
PSG in our sample. We estimate that in the next 10 Gyr, 7 of the 9 low-mass
Coma PSGs (not counting GMP 3016) combined correspond to 19.3$\pm$7.0 “future”
UDGs with $\langle\mu_{e,R}\rangle>24.0$ mag. The remaining 2 galaxies will
evolve into dEs/dS0s with higher surface brightnesses. To estimate the number
of present-day Coma cluster UDGs which could have met the SDSS spectroscopic
surface brightness and magnitude selection criteria any time in the past, we
need to make an assumption about their SFHs. We bound the possibilities with
the extreme assumption of an instantaneous starburst 12 Gyr ago represented by
a simple stellar population. This produces 90 UDGs, with 21$\pm$7% formed via
ram pressure stripping. If we assume a scenario suggested by our PSGs but that
occurred 10 Gyr ago, constant star formation and a final starburst that formed
30% of the stellar mass, we end up with 44 UDGs and a fraction of 44$\pm$16 %
formed by ram pressure stripping (see Extended Data Figure References).

Table 2: Structural properties, Stellar population parameters and stellar
masses derived from the Binospec spectra and SED modelling of diffuse post-
starburst galaxies.

No. $M_{Rc}$ $\langle\mu_{Rc}\rangle$ $r_{e}$ $t_{\mathrm{trunc}}$ Starburst
Gas $\lambda$ $[Z/H]_{L}$ $[\alpha/Fe]_{L}$ $[Z/H]_{M}$ $[\alpha/Fe]_{M}$
$(M/L)_{Rc}$ $M^{*}$ fraction fraction mag mag/arcsec2 kpc Myr % % dex dex dex
dex $10^{8}M_{\odot}$ 1 -18.21 22.45 2.73 825.6$\pm$3.0 40$\pm$2 98$\pm$1 3.7
-0.55$\pm$0.01 0.09$\pm$0.02 -0.74$\pm$0.01 0.09$\pm$0.01 0.45$\pm$0.02 6.0 2
-17.75 22.51 2.21 233.5$\pm$1.2 10$\pm$1 99$\pm$2 1.5 -0.07$\pm$0.04
0.06$\pm$0.06 -0.43$\pm$0.02 0.07$\pm$0.03 0.59$\pm$0.01 5.1 3 -18.69 23.34
4.99 779.3$\pm$5.5 60$\pm$1 83$\pm$1 1.5 -0.45$\pm$0.01 0.10$\pm$0.02
-0.58$\pm$0.01 0.09$\pm$0.01 0.39$\pm$0.01 7.9 4 -17.88 22.79 2.98
563.8$\pm$5.8 10$\pm$1 99$\pm$1 5.1 -0.58$\pm$0.05 0.07$\pm$0.07
-0.83$\pm$0.03 0.09$\pm$0.04 0.59$\pm$0.01 5.8 5 -18.43 22.32 3.09
413.4$\pm$2.7 40$\pm$2 47$\pm$1 1.5 -0.64$\pm$0.01 0.05$\pm$0.01
-0.83$\pm$0.01 0.06$\pm$0.01 0.35$\pm$0.01 5.8 6 -18.33 21.78 2.14
182.8$\pm$1.1 10$\pm$1 96$\pm$8 1.5 -0.04$\pm$0.06 0.05$\pm$0.09
-0.43$\pm$0.03 0.07$\pm$0.04 0.54$\pm$0.02 8.0 7 -19.59 21.31 3.06
351.3$\pm$0.5 20$\pm$1 98$\pm$2 2.5 -0.28$\pm$0.03 0.06$\pm$0.04
-0.58$\pm$0.02 0.07$\pm$0.02 0.50$\pm$0.02 23.6 8 -18.68 22.47 3.74
517.8$\pm$3.7 30$\pm$4 98$\pm$1 3.7 -0.57$\pm$0.02 0.07$\pm$0.02
-0.80$\pm$0.01 0.08$\pm$0.02 0.45$\pm$0.03 9.2 9 -18.06 22.68 2.69
400.1$\pm$4.9 10$\pm$1 55$\pm$1 2.5 -0.72$\pm$0.02 0.06$\pm$0.02
-0.93$\pm$0.01 0.09$\pm$0.02 0.53$\pm$0.01 6.1 10 -18.81 22.33 2.85
498.9$\pm$9.9 30$\pm$2 98$\pm$1 5.1 -0.64$\pm$0.01 0.06$\pm$0.01
-0.87$\pm$0.01 0.07$\pm$0.01 0.41$\pm$0.01 9.4 11 -18.54 23.23 3.77
969.9$\pm$10.9 60$\pm$38 78$\pm$3 1.5 -0.43$\pm$0.12 0.11$\pm$0.18
-0.56$\pm$0.04 0.10$\pm$0.07 0.41$\pm$0.21 7.4 Additional sample 12 -17.34
22.86 2.17 264.7$\pm$3.8 10$\pm$1 96$\pm$2 5.1 -0.53$\pm$0.02 0.06$\pm$0.03
-0.84$\pm$0.01 0.08$\pm$0.02 0.51$\pm$0.01 3.1 13 -17.04 24.33 3.70
327.2$\pm$3.1 5$\pm$2 91$\pm$1 1.5 -0.25$\pm$0.02 0.06$\pm$0.03 -0.51$\pm$0.01
0.08$\pm$0.02 0.69$\pm$0.01 3.1 14 -16.13 23.80 1.90 786.7$\pm$4.5 20$\pm$4
99$\pm$1 1.5 -0.22$\pm$0.03 0.08$\pm$0.04 -0.44$\pm$0.01 0.08$\pm$0.01
0.64$\pm$0.05 1.3 15 -17.25 23.29 2.20 245.8$\pm$3.7 5$\pm$1 99$\pm$1 5.1
-0.51$\pm$0.02 0.06$\pm$0.03 -0.82$\pm$0.01 0.09$\pm$0.01 0.59$\pm$0.02 3.2 16
-15.74 23.63 1.66 230.0$\pm$5.1 10$\pm$3 96$\pm$8 5.1 -0.51$\pm$0.01
0.06$\pm$0.01 -0.83$\pm$0.01 0.08$\pm$0.01 0.50$\pm$0.02 0.7 Galaxy number
corresponding to the Table 1. Structural parameters: absolute magnitude, mean
surface brightness in the $Rc$ band within the effective radius and effective
radii ($\langle\mu_{Rc}\rangle,r_{e}$). Stellar population parameters from the
full spectrum fitting: age of truncation ($t_{\mathrm{trunc}}$), fraction of
stellar mass formed in the final ram-pressure-induced starburst (SB fraction),
fraction of gas consumed into stars prior to ram-pressure stripping (Gas
fraction), linear coefficient for galactic winds ($\lambda$). Parameters
computed from the stellar population models: luminosity-weighted metallicities
($[Z/H]_{L}$), $\alpha$-enhancements ($[\alpha/Fe]_{L}$) and their mass
weighted equivalents ($[Z/H]_{M}$, $[\alpha/Fe]_{M}$)

All nine low-mass Coma PSGs have high peculiar radial velocities ($500\dots
2000$ km/s) and move on non-radial orbits like many jellyfish galaxies[49].
Their positions in the $\Delta v_{r}-d_{\mathrm{proj}}$ caustic diagram of the
Coma cluster are consistent with the hypothesis that they have entered the
inner part of the cluster for the first time. They have never crossed the
dense cluster centre and are unlikely to ever do so, allowing them to survive
for an extended period in a dense cluster environment. Observations[50] and
simulations[13, 51] confirm that ram pressure efficiently strips galaxies on
tangential orbits, but the longer stripping timescales increase the efficiency
of star formation triggered by ram pressure-induced gas compression[52].
During such a starburst a galaxy may reach its maximum lifetime surface
brightness. GMP 4188, GMP 4118, and J160215.29+160904.3 are examples of
systems on non-radial orbits with lower stellar mass and therefore low surface
brightness, which barely made it into the SDSS.

For a galaxy infalling on a radial orbit, the ram pressure-induced starburst
produces fewer stars due to rapid gas removal, and the stripped tail will be
longer, fainter and harder to detect. Qualitatively, we can assume that for a
galaxy infalling towards the cluster centre, the ram pressure becomes
sufficient to ignite a starburst when it reaches some critical pressure value
($P_{SB}$); and then when it reaches $P_{S}=P_{SB}+\Delta P;\Delta P\ll
P_{SB}$, the galaxy is stripped completely. The mass of stars formed should
depend on the time needed to gain $\Delta P$. $\Delta P$ will be gained much
faster if a galaxy approaches the cluster core on a purely radial orbit with a
pericentral distance close to zero than if it approaches on an orbit with a
similar eccentricity ($e\sim 1$) but with a larger pericentral distance just
sufficient to strip the galaxy completely. In the former case, the radial
density gradient and the radial component of the orbital velocity
$v_{r,\mathrm{orb}}$ work together because $P\propto\rho v_{\mathrm{orb}}^{2}$
and $v_{\mathrm{orb}}\approx v_{r,\mathrm{orb}}$. The large fraction of
rapidly removed gas would also strongly increase the orbital anisotropy and
decrease the observed stellar rotational velocity. The galaxies on radial
orbits will fade and evolve into the UDG regime more quickly, but their low
surface brightnesses will reduce their chances of inclusion in the SDSS
spectroscopic sample anytime during their lifetime. Fainter and smaller GMP
3016, GMP 2673, GMP 2662[15], and J160231.45+155749.9 illustrate such a
fainter continuation of the UDG evolutionary sequence. Such galaxies will also
be harder to distinguish from those formed via different proposed UDG
formation channels, which often produce non-rotating spheroidal stellar
systems[7].

Were the late-type UDG progenitors normal-sized dwarf galaxies prior to
falling onto the cluster that expanded due to ram pressure stripping? Or were
they pre-processed by tidal interactions and supernovae feedback that had
puffed them up first, followed by ram pressure stripping that quenched them
without increasing their size? Simulations[32] suggest that a stellar disc of
a low-mass gas-rich (gas fraction 70%) galaxy sitting in a
$M_{200}=10^{11}M_{\odot}$ dark matter halo (slightly more massive than our
PSGs) would expand by a factor of $\sim$1.5 due to ram pressure stripping
alone while the stellar mass loss would remain negligible. On the other hand,
the “Little Things” survey[46] of local dwarf late-type galaxies includes 9 of
37 objects with regular kinematics having $r_{e}>1$ kpc, high gas fractions,
and dark halo masses in the range of $10^{10.2}\dots 10^{10.7}M_{\odot}$[53].
If they fell onto a cluster, they would first become brighter because of the
ram pressure induced starburst, but later, when stripped, would expand to
$r_{e}=1.5\dots 5$ kpc and fade as a result of passive evolution, finally
ending up in the UDG locus of the $\langle\mu_{e}\rangle-r_{e}$ diagram as
shown by red tracks for the two examples in Fig. 4. Their largely undisturbed
morphology and kinematics along with sparse environment suggest that they are
“normal” low-mass discs, which did not undergo significant pre-processing,
hence, corroborating the scenario that ram pressure stripping alone can
transform many dwarf spiral and irregular galaxies into UDGs by causing both
quenching and disc expansion. Because the radial distribution of neutral gas
in gas-rich dwarfs is usually much shallower than stellar density
profiles[46], the ram pressure induced star formation could further grow
$r_{e}$ by stronger stellar surface density increase in the outer parts of the
disc compared to the inner regions. A search in RCSED for low-mass
($M_{*}<3\times 10^{9}M_{\odot}$) extended ($r_{e}>2$ kpc) star-forming
galaxies within 5 Mpc from the Coma cluster centre reveals about 50 objects
with the morphologies resembling those of “Little Things” dwarfs, which might
become the progenitors of a new generation of PSGs and then UDGs, should they
fall onto the Coma cluster core in the future.

Our observations of recently ram-pressure stripped low-mass disc galaxies
suggest: (i) that ram pressure stripping is a viable channel of UDG formation
and that UDGs formed via this channel _de facto_ extend the corresponding
dE/dS0 sub-class to lower surface brightnesses and larger sizes; (ii) that ram
pressure stripping is responsible for a substantial fraction of large rotating
UDGs in galaxy clusters including extreme objects like DF 44[54] and also
higher surface brightness, spatially extended, dwarf early-type galaxies;
(iii) that ram pressure stripping affects not only morphological appearance
but also stellar dynamics by increasing the stellar disc orbital anisotropy;
and (iv) that the tangential orbits of UDG progenitors at large pericentral
distances lead to higher ram pressure-induced star formation efficiencies, and
higher stellar masses and surface densities.

###  0.1 PSG selection criteria.

We select blue extended PSGs from the RCSED[16] database by applying two sets
of selection criteria. One of them has a stricter stellar age limit, and
another one limits the integrated $g-r$ colour with slightly more relaxed
stellar age restriction. This allows us to minimize the loss of possible
objects of interest because of the age-metallicity degeneracy that affects the
results of the full spectrum fitting of a large galaxy sample using simple
stellar population models: the reported overestimated intermediate stellar age
(2–3 Gyr) is compensated by the underestimated stellar metallicity, and this
degeneracy can be resolved by using broad-band colours. The first set of
selection criteria includes:

  * •

$F_{H\alpha}/\Delta F_{H\alpha}<5$ AND $F_{[O\mathrm{III}]}<2\times
10^{-16}erg/cm^{2}/s$ to select galaxies without prominent emission lines.

  * •

Mean stellar populations younger than 1 Gyr. If a spectrum of a galaxy has low
signal-to-noise ratio (SNR), its age may shift to the higher values with lower
values of metallicity due to age-metallicity degeneracy. To take into account
this fact we supplemented our criteria by joining with boolean OR a
metallicity condition: $\mathrm{[Z/H]}<-1.3$ dex.

  * •

Galaxies with spectral SNR $>$ 4 reported by SDSS, which is typically
underestimated by 30–35%. This criterion rejects spectra with unreliable
signal.

  * •

There is no template mismatch, $\rm\chi^{2}_{ssp}<1$

  * •

We select extended objects by setting the difference between 3-arcsec fiber
magnitude and integral magnitude greater than 0.5 mag in the $r$ band. This
criterion selects galaxies with $r_{e}>1.5kpc$ at the Coma cluster distance.

  * •

Blue integrated colour $g-r<0.55$ mag

  * •

Low redshift $0.015<z<0.06$

This set of criteria returned 7 objects. After visual inspection we rejected
one with unreliable $H\alpha$ flux measurements and another one with
unreliable integrated photometry in SDSS DR7 bringing its $g-r$ colour below
0.55 mag, when in Dark Energy Camera Legacy Survey (DECaLS[55]) it has
$g-r=0.61$ mag. Finally this filter yielded 5 galaxies.

The second filter includes the following conditions:

  * •

$F_{H\alpha}/\Delta F_{H\alpha}<10$ AND $F_{H\alpha}<2.5\times
10^{-16}erg/cm^{2}/s$ AND $F_{[O\mathrm{III}]}<2.0\times 10^{-16}erg/cm^{2}/s$

  * •

Mean stellar populations younger than 2 Gyr.

  * •

$\chi^{2}_{ssp}<1$

  * •

Difference between 3-arcsec fiber magnitude and integral magnitude greater
than 0.5 mag in the $r$ band.

  * •

Blue integrated colour $g-r<0.4$ mag

  * •

Low redshift $0.015<z<0.06$

These criteria select 10 galaxies. We rejected one object that is apparently
interacting with a companion and has incorrect photometric measurements in the
SDSS/RCSED, leaving 9 galaxies.

We joined the lists of galaxies selected using both sets of criteria. The two
lists have two objects in common, leaving 12 galaxies. All belong to the SDSS
main galaxy sample so that these 12 galaxies form a nearly complete magnitude
limited sample within the SDSS DR7 footprint. Ten galaxies are Coma cluster
members, 2 galaxies are Abell 2147 cluster members, and the remaining galaxy
is a group member[5]. In this study we consider only 11 cluster galaxies,
because the remaining object does not possess deep high-quality optical
imaging data that can be used to assess its structural properties.

We selected additional candidate PSGs without SDSS spectroscopic confirmation
as blue 5$\sigma$ outliers towards fainter near-UV magnitudes from the
universal three-dimensional ultraviolet–optical colour–colour–magnitude
relation for non-active galaxies[56] with sizes corresponding to $r_{e}>1.5$
kpc at the distance of their host cluster (Coma or Abell 2147). This selection
returned 5 objects in Coma and 2 in Abell 2147. We placed three Coma and one
Abell 2147 candidates in the Binospec slitmasks and all were spectroscopically
confirmed as PSGs without current star formation and members of their host
clusters.

###  0.2 Spectroscopic observations and data reduction.

We obtained spectroscopic observations of 11 PSGs using the 6.5-m MMT. We
obtained long-slit spectroscopy for each galaxy with the Binospec[27] multi-
object spectrograph and reduced the data using the Binospec data reduction
pipeline[57] optimized for extended low-surface brightness objects. Small
angular distances between galaxies allow us to observe 2–3 galaxies
simultaneously with the same slit mask. For nine galaxies in Coma cluster we
designed 4 masks: “Coma 1” (GMP 2640, GMP 2639), “Coma 3” (GMP 4348, GMP 4118,
GMP 4060), “Coma A” (GMP 2923, GMP 3176) and “Coma B” (GMP 4188, GMP 3640).
“Coma 1” was observed in two runs: (i) December 14, 2017, during the
instrument commissioning and (ii) April 10, 2018. To increase S/N both
datasets were combined into one. “Coma 3” was observed on April 7, 2018. “Coma
A” was observed in two consecutive nights: 4th and 5th of June 2018 with mean
seeing of 1 arcsec. “Coma B” was observed on 8th of June 2018 with 1 arcsec
seeing. Both galaxies in Abell 2147 were placed on one “A2147” mask which was
observed on the 14th of June 2018. GMP 3016 was observed on 29th of January
2020 as a filler target for another Binospec program. In all runs we used the
1000 line mm-1 grating with a 1 arcsec-wide slitlets with the central
wavelength of 4400–4500 Å that yielded the overall wavelength coverage of 3760
Å to 5300 Å. This configuration provides an instrumental resolution of
$\sigma_{\mbox{inst}}$ $\sim$ 26$\dots$34 km/s. The total exposure time was 2h
20min for the “Coma 1” mask and 2h for all remaining masks.

We also added optically selected galaxies and UDGs as filler targets to each
mask. Spectra of UDGs obtained with these masks were used for dynamical
modelling and dark matter contribution estimate[15]. After the analysis of all
dwarf galaxy spectra, we created an additional sample that comprised of five
galaxies: 3 filler galaxies in Coma cluster and one in A2147 that met our
post-starburst selection criteria. The fifth galaxy, GMP 3016, is the only
galaxy from study[19] without detected emission inside its 27 mag isophote in
the deep $R$-band Subaru imaging. There is no SDSS spectrum for this galaxy,
because its total magnitude is 0.03 mag below the magnitude limit of the SDSS
spectroscopic selection. These galaxies have low stellar masses and surface
brightnesses and are not included in SDSS spectroscopic sample.

After the reduction of all spectroscopic data using the Binospec data
reduction pipeline[57] we obtained sky subtracted, flux calibrated, wavelength
calibrated two-dimensional images with error frames for each slitlet. For the
sky subtraction we used a global sky model implemented in the pipeline.

Additionally, we observed GMP 3640 using the GMOS-N spectrograph operated at
the 8 m Gemini-North telescope on the 24th and 25th of June of 2017 (fast
turnaround program N2017-FT-22) with the median image quality of 0.7 and 0.9
arcsec for these two nights respectively. We used the B 1200 grating and a
0.75 arcsec slit with the wavelength setup centered at 4500 Å that yields the
spectral resolution $\sigma_{\mbox{inst}}$ $\sim$ 45 km/s. The total exposure
time was 3h 25min. We reduced the data using our own data reduction pipeline
for GMOS data.

###  0.3 Stellar population properties.

For all PSGs we simultaneously fit optical spectra and broadband magnitudes.
We take ultraviolet fluxes from the catalogs based on deep (23 ksec in near-UV
and 18 ksec in far-UV) GALEX imaging data. Mid-infrared magnitudes were
obtained by applying Sextractor[58] to Spitzer IRAC frames available from the
Spitzer Heritage Archive combined into super mosaics. Optical broadband fluxes
were generally taken from SDSS[17] and DECaLS surveys. We use deep CFHT
observations in the $u^{*}$ band instead of shallow data in SDSS $u$. We take
near-IR magnitudes from UKIDSS LAS DR10 data and CFHT $K$ and $J$ where
available. We apply foreground extinction correction and K-correction[59] to
all magnitudes.

We use a 4-dimensional miles-based (for spectra) and pegase.2-based (for
broad-band SEDs) grid of stellar population models[28] computed for the Kroupa
IMF[60] to perform stellar population analysis. We treat the chemical
evolution of the stellar population self-consistently using an analytic
formulation[61] of the “leaky box” model[62, 63, 64]. This model allows a
fraction of heavy elements produced in stars to escape via galactic winds with
the rate proportional to the current SFR[65, 66]. We model the evolution of
iron and $\alpha$-elements separately, accounting for the delayed contribution
from SN Ia explosions[67]. We use spatially co-added spectra in one $r_{e}$ to
maximize S/N of optical spectra . As galaxy rotation may smooth spectral
details, we correct spectra for the radial velocity profile. We minimize a
linear combination of $\chi^{2}$ values for spectrum and SED with the weight
of $\chi^{2}_{SED}$ varying between 0.4 and 0.6 for different galaxies against
the two parameters: truncation age and fraction of consumed gas. During this
procedure we model observed spectra as a template convolved with the Gaussian
LOSVD and multiplied by a polynomial continuum with degree from 9 to 15.
Because the spectral resolution of miles-based models is lower than that of
Binospec spectra, we convolve the data with a Gaussian to match the resolution
of stellar population models. Then we scan the grid of two remaining
parameters: fraction of stellar mass born in the final starburst and galactic
winds coefficient $\lambda$. We obtain uncertainties for the first two
parameters from the covariance matrix resulting from the minimization
procedure. For the two remaining parameters we estimate the uncertainties by
approximating the $\chi^{2}$ profile near the minimum by a quadratic function.
We provide formal statistical uncertainties in Tables 1–2, but for our
galaxies with high SNRs, the systematic errors that originate from the choice
of input spectral and SED templates are much higher than statistical ones
(10–15% on truncation age and $\sim$0.1 dex on metallicity and
$\alpha$-enhancement). We compare luminosity weighted metallicities computed
for the SFHs with the parameters derived from our modelling with the values
obtained in other studies in the 3-rd panel of Fig. 4. For this comparison we
only use spectroscopic measurements of stellar populations from the literature
done using different forms of the full spectrum fitting of intermediate- and
high-resolution spectra and exclude those based on SED fitting[68] or line-
strength indices[69] and also obtained through excessively wide slits hence
reducing the spectral resolution[70]. We also excluded spectroscopic
measurements of NGC1052-DF2[71] from our analysis despite on good quality of
data and reliable measurements, because distance to this galaxy remains a
matter of debate[72, 73].

###  0.4 Stellar kinematics.

We use the NBursts[74] full spectrum fitting technique to measure radial
velocity and velocity dispersion profiles. We use adaptive binning along the
slit to reach sufficient signal-to-noise ratio to reliably measure internal
kinematics (7–10 per pixel depending on the object). We use pegase.hr-based
models[28] that implement PSG SFHs with self-consistent evolution of stellar
metallicity. These models are similar to those used for the stellar population
analysis but do not include $\alpha$-element enhancements. The spectral
resolution (R$\sim$10000) of the model exceeds Binospec’s (R$\sim$4000) making
it possible to measure velocity dispersion down to 10 km/s[75]. All galaxies
from the main sample exhibit some sort of regular rotation within $r_{e}$. GMP
4060, GMP 2640 and GMP 4188 have noticeable kinematical disturbances localised
in the area of significant morphological irregularities. Detailed analysis of
high-resolution HST images for the brightest galaxy in our sample, GMP 2640,
revealed a large number of luminous star clusters in its central part whose
asymmetric distributions on the sides of the slit causes the non-uniform slit
illumination and, hence, affects the radial velocity measurements.
Disturbances of kinematics profiles of GMP 4060 and GMP 4188 are also of the
same origin. We notice that some simulations suggest that the ram pressure
stripping by itself can lead to the displacement of the dark matter cusp in a
low-mass galaxy[76], which will cause a slight lopsidedness a galaxy with a
stellar mass close to the lower end of what we sample in our study.

###  0.5 Structural parameters and deep Subaru images.

For Coma cluster galaxies we use deep $Rc$-band Subaru Suprime-Cam[77] images
(1470 – 7980 s exposure time) to determine structural parameters. For Abell
2147 only raw archival Subaru Hyper Supreme-Cam[78] images are available, so
we reduced and co-added them. Using GALFIT[79] we model each galaxy with a
double Sérsic profile convolved with the point-spread-function (PSF) obtained
from Gaussian fits to non-saturated stars. We use uncertainty frames obtained
from reduced, sky subtracted Subaru images for the fitting procedure, adding
sky background as a constant value obtained from the sky variation analysis.
We derive the deprojected effective radius for each galaxy as follows. We
construct the deprojected image of the galaxy using the Sérsic components from
the fit results, changing the axis ratio to 1. We then measure the radius
enclosing exactly half the total flux of the deprojected image.

We also inspected Subaru Suprime-Cam $B$-band, $V$-band, $Rc$-band, and
H$\alpha$ images downloaded from the Japanese Virtual Observatory. $Rc$-band
images of GMP 3176 revealed a filamentary structure 70 kpc to the west from
the galaxy main body. Another galaxy, GMP 3640 has three bright filaments,
emerging from its main body. Several galaxies show clumps or other
irregularities in their central parts. GMP 4060 and GMP 3640 exhibit the most
noticeable disturbances. However, they are substantially less significant in
the $Rc$ band compared to the bluer bands ($V$ and $B$) and, therefore, they
are likely caused by different stellar population properties (i.e. younger
stellar age) rather than variations in the stellar mass density which would
significantly affect the gravitational potential. For Abell 2147 we retrieved
raw Hyper Supreme-Cam data in the $g$, $r$, and $i$ bands with the total
exposure times of 3720, 240, and 2160 sec correspondingly from the Subaru
archive and reduced them using the Hyper Suprime-Cam pipeline. In $g$-band
images both Abell 2147 galaxies reveal faint tails with a complex filametary
structure reaching 70 kpc in length. Both these tails point roughly towards
the cluster centre. The brightest filaments of these tails are also detected
in the $r$ and $i$ bands.

###  0.6 Dynamical modelling.

We base our dynamical modelling algorithm on the JAM routine[31] which has
been used extensively to model galactic kinematics in nearby and intermediate-
redshift galaxies. It solves the Jeans[80] equations assuming axial symmetry.
For each galaxy we construct a suite of dynamical models that correspond to
different parameter values. We use a customised version of this code, which
allows us to handle a dark matter halo separately from the stars. The main
steps are as follows: (i) We use GALFIT to fit the $R$-band Subaru image of
each galaxy using a two-component Sérsic model. (ii) The model image of a
galaxy is converted into multiple two-dimensional Gaussians (6–10 per galaxy).
The same procedure is applied to a spherical Burkert[81] dark matter density
profile, and then the two Gaussian sets are co-added to construct a model of
the gravitational potential. The dark matter density profile is truncated at
$R_{200}$ to prevent the divergence of the multiple Gaussian expansion
procedure. (iii) A set of Gaussians is then supplied to the modelling routine
that computes the radial velocity and velocity dispersion profiles convolved
with the PSF from observations for a grid of parameter values. We then scan
$\chi^{2}$ values evaluated for each model to find the best values of
following parameters: the dark matter central density $\rho_{0}$, halo scale
radius $r_{s}$ and stellar vertical anisotropy $\beta_{z}$. We also allow the
inclination $i$ to vary between $\arccos(b/a)$ and $90\deg$. The stellar mass-
to-light ratio $M/L_{*}$ is fixed to the best-fitting value from the stellar
population analysis. We compute grids of dynamical models with the following
steps: 0.1 for $\beta_{z}$, 0.25 for $\log\rho_{0}$, 0.2 kpc for $r_{s}$, and
$6^{\circ}$ for inclination. This spacing allows us to confidently locate the
position of the $\chi^{2}$ minimum, but does not yield statistical
uncertainties for these parameters.

We apply this method to all the galaxies in our main sample because it is more
physically motivated than the traditionally used “mass follows light”
approach. It also better reproduces the observed kinematics of our galaxies.
The “mass follows light” approach implies that the mass and luminosity
profiles of a galaxy have the same shape and differ only by a constant factor
$M/L_{\mathrm{dyn}}$, which becomes an extra free parameter of the fitting
procedure. We use this approach for the additional galaxy sample, because the
lower quality of spectra prevents us from reliably determining the dark matter
halo parameters. As we mentioned above, the kinematic disturbances in three
galaxies, GMP 4060, GMP 2640 and GMP 4188 are unlikely to be of a dynamical
origin.

###  0.7 Disc expansion due to ram pressure stripping.

By selection, the galaxies in our sample already have sizes comparable to
rather large UDGs being at the same time substantially more extended than
typical gas-rich dwarfs in sparse environments. To estimate the importance of
ram pressure stripping as a disc expansion mechanism for “normal” dwarf late-
type galaxies infalling on-to a massive galaxy cluster like Coma, we took two
galaxies from Little Things[46] sample: NGC 4214 having stellar mass
comparable to GMP 2640, the most massive galaxy in our sample, and DDO 168
comparable to the smallest galaxy in the additional sample. Because the ram
pressure timescale is shorter than the rotation period at $r_{e}$ by a factor
of a few, we estimate the average disc expansion using a formula for the
change of the orbital radius in case of the rapid mass loss[82]
$r_{f}/r_{i}=\frac{\varepsilon}{2\varepsilon-1}$. In this formula,
$\varepsilon=M_{f}/M_{i}$, $M_{i}$ is initial total mass inside $r_{e}$ that
includes dark matter[83], stars and gas; $M_{f}$ is the same without gas. This
approach suggests that there is no change in the outer surface brightness
profile slope, but in the inner parts the dark matter contribution decreases
causing the orbital expansion to a higher degree than in the galaxy’s
outskirts. This creates a large flat core in the surface brightness profile
and also increases $r_{e}$.

Our modelling shows that ram pressure stripping is capable in expanding a
stellar disc by a factor of 2 and even more and might be solely responsible
for transforming compact gas-rich galaxies to quiescent stellar systems with
UDG sizes and densities. We model the ram pressure induced starburst with a
constant SFH for 60 Myr so that the stellar mass formed in it is 20% of the
total final stellar mass, the rest of the gas is stripped. We expect that the
disc expansion initiated by ram pressure stripping will continue for 300 Myr,
which roughly corresponds to the rotation periods of the galactic discs in our
PSGs as well as in NGC 4214 and DDO 168. Both, the starburst and the disc
expansion start simultaneously but the expansion lasts longer – these stages
correspond to the curved parts of the red tracks with an arrow at the end in
Fig. 4. Then the galaxies are left to evolve passively for 10 Gyr with a slow
disc expansion due to stellar evolution (straight portions of the tracks in
Fig. 4.) At the end of the first stage of the disc expansion, 300 Myr after
they entered the cluster DDO 168 and NGC 2414 would resemble GMP 3016 and GMP
2640 respectively.

###  0.8 Slow disc expansion modelling.

After a stripping event, the stars evolve, and the most massive of them will
die. We assume that the galaxy will stay in the cluster after stripping and
the final starburst, and that the gas released as a result of stellar
evolution will be gradually stripped and will not form new stars. Therefore,
the stellar mass decrease with time, leading to disc expansion.

We estimate the expansion of the disc assuming angular momentum conservation,
which gives us the following expression:

$v(M_{tot}(t_{0}),r(t_{0}))\cdot r(t_{0})=v(M_{tot}(t_{0}+\delta
t),r(t_{0}+\delta t))\cdot r(t_{0}+\delta t).$ (1)

For $\delta t\xrightarrow{}0$ we get the exact expression for $\dot{r}$:

$\dot{r}/r=\frac{\partial{M_{tot}}}{\partial{t}}\frac{\partial{v}}{\partial{M_{tot}}}/\left(\frac{\partial{v}}{\partial{r}}r+v\right)$
(2)

This formula can be expressed in terms of logarithmic derivatives:

$\dot{r}/r=\alpha(r)\cdot\dot{M}/M;\;\alpha(r)=M_{tot}\frac{\partial{v}}{\partial{M_{tot}}}/\left(\frac{\partial{v}}{\partial{r}}r+v\right)$
(3)

Applying it to an exponential disc, we find that $\alpha(r)$ is a smooth
function with values between 1.3 and 3.0, reaching the maximum (3.0) at $r=0$
and $r\xrightarrow{}\infty$, with the minimum at $2r_{e}$. The central disc
expansion is therefore larger than in the outskirts. Therefore, the slope of
light profile will decrease with time and the Sersic index will drop to values
seen in ordinary ultra-diffuse galaxies.

The presence of significant amounts of dark matter keeps the relative change
of $M_{tot}$ and its derivative ${\partial{M_{tot}}}/{\partial{t}}$ quite
small, driving the full expression for $\dot{r}/r$ to near-zero values. This
leads to a decrease of overall disc expansion from 20% with no dark matter
case to 3–5% for PSGs with dark matter fractions of 70–90%. This small value
cannot affect mean surface brightness by more than 0.1 mag arcsec-2. However,
numerical simulations suggest that dark matter haloes of low-mass galaxies can
be efficiently stripped by tidal forces during close passages near other
cluster members, therefore one would still expect a slow disc expansion over
time reaching the same 20–25% over 10 Gyr. Strong tidal interactions, which
substantially disturb the galaxy morphology are rare so they generally have
little effect on the UDG shapes or leave visible tidal features[84]. The disc
expansion will lead to the decrease of the average stellar surface density in
the disc by 40–50% without substantial disc thickening. In addition, the
stellar volume density also decreases because of the slow stellar mass loss
reaching 20% over 10 Gyr. These two factors combined will lower the stellar
velocity dispersion by $\sim$35% because $\sigma$ is proportional to the
square root of the local stellar density.

Simulations[33] also show that disc expansion causes the dark matter density
decrease by some 40% in the central parts of galaxies what leads to the drop
of the circular velocity by 20%, because it is proportional to the square root
of combined density of stars and dark matter, which dominates the mass.
Combined with the stellar density decrease, this effect reaches $\sim$25%.
However, observed stellar rotational velocity is smaller than the circular
velocity at a given position in a galaxy due to asymmetric drift ($v_{a}$) and
to estimate the change of its value we applied the formula 4.228 from Binney &
Tremaine[85] under the assumption that during the process of slow expansion
the ratios of the different velocity dispersion components do not change. In
this case, the change of the asymmetric drift velocity is proportional to
$\sigma_{R}^{2}/v_{c}$. For 85% of dark matter inside $1~{}r_{e}$ the decrease
of stellar rotational velocity will be 25%.

###  0.9 UDG number statistics.

We assess the importance of the ram pressure stripping scenario to other UDG
formation channels. We statistically estimate how many present-day UDGs
correspond to each PSG in our primary sample of 9 Coma cluster galaxies and
compare the result to the observed number of UDGs in the Coma cluster. We
model the surface brightness evolution from the reconstructed SFH and
calculate the two epochs: (i) $t_{\mathrm{SDSS}}$ when a galaxy becomes too
faint to be included in the SDSS spectroscopic sample
($r_{\mathrm{tot}}>17.77$ mag) and (ii) $t_{\mathrm{UDG}}$ when it dims enough
to be classified as a UDG. UDG classification has a surface brightness cutoff
of $\langle\mu_{R}\rangle_{\mathrm{eff}}>24$ mag/arcsec2. Statistically
speaking, a given PSG will correspond to the number of UDG estimated as
$N_{\mathrm{UDG}}=(t_{\mathrm{SDSS}}-100\mathrm{Myr})/(10\mathrm{Gyr}-t_{\mathrm{UDG}})$
if $t_{\mathrm{UDG}}<10$ Gyr. At 100 Myr emission lines disappear from a PSG
spectrum, and 10 Gyr is the reference passive evolution time. At the end we
co-add $N_{\mathrm{UDG}}$ for all 9 galaxies in the primary sample. We find
that only 7 galaxies reach the UDG regime within 10 Gyr. The total number of
expected UDGs from these 7 progenitors is 19.34$\pm$7.00. This estimate is
made assuming a constant rate of infall of galaxies on a cluster.
Simulations[86] show that during the first 2–3 Gyr of the cluster formation
epoch, the infall rate might be up-to twice as high as now. This may only
increase our estimate of UDGs formed via the ram pressure stripping channel.
The uncertainty is estimated by assuming the Poisson process of the galaxy
infall and propagating stellar population parameter statistical errors and the
estimated 10% systematic errors for the effective radii[39] and truncation
ages[61].

We now need to estimate the total number of present-day UDGs in a complete
magnitude limited sample[4, 41] with sufficient stellar mass so that 100 Myr
after star formation quenching they would be bright enough to meet the SDSS
spectroscopic selection. Our initial PSG selection criteria includes a minimum
0.5 mag difference between the 3-arcsec fiber magnitude and the total
magnitude. This corresponds to a lower $r_{e}$ limit of $\approx$1.5 kpc for
galaxies at the distance of the Coma cluster. During passive evolution, these
galaxies will expand by $\approx$25%, so we only count the present-day UDGs
having $r_{e}>1.875$ kpc. To estimate the stellar mass we need to assume an
SFH in a present-day UDG, which we cannot infer directly from the available
data. The most extreme case would be an instantaneous starburst modelled by a
simple stellar population. Such a SFH leads to the minimal possible stellar
mass cutoff and, hence, the largest number of UDGs passing the selection. For
a 10 Gyr age, there are 90 galaxies in UDG sample[41] which could satisfy the
selection criteria for our PSGs in the past at some moment during their
lifetime. Our lower limit of of UDGs is therefore 21$\pm$7 %, which could be
explained by the ram pressure stripping formation scenario.

For a more realistic estimate we consider a typical observed SFH for our PSGs:
a truncated constant SFR started 13.0 Gyr with 30% of the total stellar mass
formed in the final starburst 10 Gyr ago. This corresponds to the median mass
fraction we found in the PSG analysis. The number of UDGs that could possibly
satisfy our selection criteria decreases to 44, increasing the importance of
the ram-pressure-stripping UDG formation channel to 44$\pm$17 %. This fraction
would increase even more if we take UDG SFHs with a lower final starburst
fraction. In Extended Data Figure References we show how the adopted SFH
affects the total number of UDGs from the study[41] that satisfy the SDSS
spectroscopic selection criteria and our selection criteria anytime during
their lifetime. We consider three SFHs, all starting 13 billion years ago with
truncation ages of 10, 8 and 5 billion years. In all cases we estimate the
number of UDGs as described above. In the case of earlier truncation time, M/L
ratio and stellar mass change significantly. Given the SDSS magnitude limit we
have a individual magnitude limit of UDG for each scenario of star formation.
If a galaxy was bright enough 10 billion years ago to pass the selection
criteria, this galaxy can now be very faint, and many galaxies from the sample
of present-day UDGs are brighter than this limit. In case of more extended
scenario of star formation, the M/L ratio and stellar mass change less, we
infer a significant fraction of long-lived old stars. The magnitude limit for
UDGs is correspondingly brighter, decreasing the number of UDGs. The most
extreme case is a SFH with truncation age of 5 Gyr without a final starburst,
i.e. constant SFR from 13 Gyr to 5 Gyr. In this case none of known UDGs pass
the SDSS selection criteria.

Reduced flux calibrated Binospec spectra co-added within 1$r_{e}$ and thier
best-fitting NBursts+phot spectrophotometric models (see Extended Data Figures
References–Transforming gas-rich low-mass disky galaxies into ultra-diffuse
galaxies by ram pressure), the spatially resolved profiles of internal
kinematics and stellar populations and corresponding axisymmetric Jeans models
for every galaxy as are available through Zenodo data repository with the
following permanent identifier: https://doi.org/10.5281/zenodo.5031351. That
package also contains a compilation of data points used in Fig. 4 and a python
procedure to reproduce the figure. Fully reduced Subaru and CFHT images used
for the dynamical modelling procedure are available in the corresponding open
access data archives (http://jvo.nao.ac.jp/index-e.html; http://www.cadc-
ccda.hia-iha.nrc-cnrc.gc.ca/en/).

Received: 24 October 2020; Accepted: 27 July 2021;
Published online: 01 November 2021

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KG, IC, AA, IK acknowledge the Russian Science Foundation (RScF) grants No.
19-12-00281 for supporting the search of UDG progenitors and data analysis of
a multi-wavelength spectrophotometric dataset, and No. 17-72-20119 for
supporting the development of stellar population models used in the data
analysis; and the Interdisciplinary Scientific and Educational School of
Moscow University “Fundamental and Applied Space Research”. KG acknowledges
the support from the Foundation of development of theoretical physics and
mathematics “Basis”. IC’s research is supported by the Telescope Data Center
at Smithsonian Astrophysical Observatory. We thank D. Eisenstein, F. Combes,
G. Mamon, and O. Sil’chenko for fruitful discussions related to this project.
We are grateful to the staff of the MMT Observatory jointly operated by
Smithsonian Astrophysical Observatory and the University of Arizona for their
support of Binospec operations and service mode observations. This study is
based in part on data collected at Subaru Telescope and retrieved from the
SuprimeCam and Hyper-SuprimeCam data archive system, which is operated by
Subaru Telescope and Astronomy Data Center at National Astronomical
Observatory of Japan and on observations obtained at the international Gemini
Observatory (proposal GN-2017A-FT-22), a program of NSF’s NOIRLab, which is
managed by the Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foundation on behalf
of the Gemini Observatory partnership: the National Science Foundation (United
States), National Research Council (Canada), Agencia Nacional de Investigación
y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación
(Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações
(Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).

K.G. computed stellar population models, prepared Binospec observations,
analyzed Binospec data and wrote the manuscript; I.C. formulated PSG search
criteria and discovered the galaxies in the RCSED catalog, reduced Binospec
data, modified the full spectrum fitting code to analyze them and wrote the
manuscript; A.A. performed surface photometry, performed dynamical modelling
and wrote the manuscript; D.F. led the development of the Binospec
spectrograph and proposed the observational strategy; I.K. jointly with I.C.
developed the spectrophotometric fitting code NBursts+phot and validated the
spectroscopic data analysis; S.M. supported preparation and execution of
observations; M.Y. provided cutouts of deep Subaru images and did the
reduction of archival Subaru data for Abell 2147; I.C., D.F., and S.M.
performed Binospec observations during the commissioning and science
verification of the instrument; all authors discussed the manuscript.

The authors declare no competing interests.

Extended data is available for this paper at
https://doi.org/10.1038/s41550-021-01470-5.
Correspondence and requests for materials should be addressed to Igor
Chilingarian (email<EMAIL_ADDRESS><EMAIL_ADDRESS>and
Kirill Grishin (email: grishin@voxastro.org).
Peer review information Nature Astronomy thanks Jeffrey Kenney and the other,
anonymous, reviewer(s) for their contribution to the peer review of this work.
Reprints and permissions information is available at www.nature.com/reprints.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.

Low-contrast filaments suspected to be ram-pressure-stripped tails for five
Coma galaxies. For GMP 2639 we show an inverted $Rc$-band image binned with a
4$\times$4 pix window. For GMP 4118 and GMP 4348 we show $H_{\alpha}$ images
without continuum subtraction convolved with a 2-D Gaussian kernel having FWHM
in range $5\dots 7$ pix depending on S/N of input images. For GMP 3176 we show
a difference between $B$ and $Rc$ Subaru frames. A spot at the end of the
short filament in GMP 4188 pointed by an arrow is a bright H$\alpha$ source.

Observed data (black) degraded down to correspond template resolution and
best-fitting templates (red) for Binospec spectra (left panels) and broad-band
SEDs (right panels) for PSGs from the main sample. For the spectra we also
show $1\sigma$ uncertainty profiles (magenta) and fitting residuals (grey).
SED panels show observations and best-fitting models as black and red dots
correspondingly. The residuals are shown with black stars around a cyan line
representing zero level in the same scale as SEDs. The upper right corner of
each spectrum contains a median signal-to-noise ratio for a degraded spectrum
per pixel. Main spectral features and broad-band filter bandpasses are marked
in the upper row of panels.

The same as Extended Data Figure References for the additional galaxy sample.

Resolved stellar population profiles for the PSGs from the main sample and GMP
3016 obtained from full spectral fitting of long-slit spectra using pegase.hr-
based templates[28]. We perform the $\chi^{2}$ minimization varying the
truncation age and final metallicity which describes the metallicity of final
starburst while other parameters (wind coefficients and SB fraction) are fixed
to values derived from the modelling of the co-added 1D spectra with broadband
photometry. For galaxies with non-radial age gradients likely caused by the
ram pressure stripping, solid blue lines show the gradient trend sometimes
over-imposed on the radial gradient illustrating the outside-in quenching.
Dotted and dashed lines mark $\pm r_{e}/2$ and $\pm r_{e}$ respectively.

[h!]  A number of UDGs from the Subaru Coma cluster survey[41] that could pass
the SDSS spectroscopic selection criteria and satisfy our PSG selection
criteria at some moment during their lifetime as a function of a mass fraction
of stars born in the final star burst for three different truncation ages: 5,
8, and 10 Gyr.