Molecular Gas Filaments and Fallback in the Ram Pressure Stripped Coma Spiral NGC 4921

The Coma cluster is the nearest very massive cluster, and thus a great environment in which to study the effects of ram pressure at high resolution. There is clear evidence for the effects of strong ram pressure in Coma, most strikingly illustrated by the long tails of stripped gas found and studied in such works as Yagi et al. (2007, 2010), Cramer et al. (2019), and Chen et al. (2020). An excellent galaxy in the Coma cluster in which to study the effects of ram pressure stripping (RPS) on the dense ISM in the disk is NGC 4921, a massive (M_B = −22), nearly face-on (i ∼ 13°) spiral. We show a summary of basic properties of NGC 4921 in Table 1. We show in Figure 1 the location of NGC 4921 in the cluster, as well as its projected velocity relative to the cluster center (∼−1500 km s⁻¹) and projected distance to the cluster center (700 kpc). We estimate a significant component of the orbital motion of NGC 4921 in the cluster is azimuthal not radial, based on compressed dust and H i on the NW side, and slight H i elongation to the SE, although we note that the orientation of these features does not necessarily track the instantaneous direction of ram pressure, but may retain some signature of prior wind angles. The galaxy is also blueshifted by 1500 km s⁻¹ with respect to the cluster center, so there is a component of the ram pressure wind acting perpendicular to the disk, and thus pushing gas in the redshifted direction to the observer. The outer galaxy H i asymmetry angle in NGC 4921 is PA = 345° (J. Kenney et al. 2021, in preparation). Analysis of ram pressure stripping simulations shows that these angles are generally good indicators of the projected wind direction, to within 5–10° in cases of strong increasing ram pressure (E. Mas et al. 2021, in preparation), like NGC 4921. The orientation of NGC 4921, nearly face on, and its relative closeness make it possible to study the effects of ram pressure on the ISM in the disk at extremely high resolution. Most studies of the ISM in ram pressure stripped disks have been of highly inclined galaxies, as this orientation is more common to the observer.

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NGC 4921 has a truncated H i disk with a head-tail morphology characteristic of galaxies undergoing ram pressure, with the largest degree of truncation on the NW side of the galaxy, presumably the leading side (Kenney et al. 2015). The galaxy has been previously observed with the Hubble Space Telescope (HST) in F350LP, F606W, and F814W, and the images are quite deep (proposal ID: 10842 and 12476, PI: Cook).

Studies show that the ISM on the leading side of NGC 4921 has a very different morphology, as well as different star-forming properties, than other regions of the disk. Lee & Jang (2016) found that on the leading side of the galaxy, the star clusters formed were more massive and more luminous, possibly due to the formation of giant molecular clouds with unique properties due to ram pressure compression of gas. The dust structures on the leading side of the galaxy have also been studied in depth with HST by Kenney et al. (2015). They found thin, kiloparsec-long filaments of dust, extending out into the otherwise dust-stripped zone of the galaxy. Some of these filaments have luminous young star complexes at the heads. Kenney et al. (2015) suggested the structure of these filaments was consistent with magnetic binding inhibiting the decoupling of the ISM under ram pressure. The filaments appear similar to "elephant trunk" features in H ii regions observed in the Milky Way (although the filaments in NGC 4921 are many times larger in scale), which have been suggested to be the result of the influence of magnetic fields (Carlqvist et al. 2003). Carlqvist (2013) examined the filaments in NGC 4921, but did not include any discussion of the influence of ram pressure in NGC 4921, instead proposing the filaments may be magnetically supported spiral arm outgrowths. Other regions of the main ring of dust on the leading side appear to have been pushed in radially, creating "c-shaped" concavities (Kenney et al. 2015). The clarity of these unique structures in dust suggested that they may also be visible with sufficiently deep ALMA observations. Such deep, high-resolution observations of molecular gas allow us to track the impact of RPS on the dense ISM in the disk.

We observed the NW quadrant (the leading side) of the galaxy NGC 4921 with ALMA in 2016–17 during Cycle 4 (project code 2016.1.00931.S, PI: Kenney). We observed in Band 6, centered around the CO(2−1) line at 230.36 GHz, in a 50'' × 20'' rectangular area.

For the CO(2−1) data, the full mosaic is composed of 7 pointings with the 12 m array, each with a half-power beamwidth (HPBW) of 25'', and 25 pointings with the 7 m Atacama Compact Array (ACA), each with a HPBW of 44''. The velocity resolution of the data is 1.2 km s⁻¹ and the total time on source with the 12 m array is 156 minutes, and with the ACA, 31 minutes.

Flux calibration is based on observations of Ganymede (ACA), and J1229+0203 (12 m), the bandpass calibration uses J1229+0203 (12 m and ACA), and the phase calibrator is J1303+2433 (12 m) and J1331+3030 (ACA).

The data have been calibrated using the CASA pipeline, and combined using the CASA software package (version 5.4.0, McMullin et al. 2007) with the tclean command after checking for proper weighting. No significant continuum emission is found in the spectral windows around the CO(2−1) line. We chose to weight the data with a Briggs robustness of 2.0 (closest to natural weighting). The resulting beam size is 045 × 035 (220 pc × 170 pc).

The data were cleaned using the CASA tclean procedure; due to extended diffuse structure in the data cube, we utilized the multiscale clean option. Emission was found in 37 binned 5 km s⁻¹ channels, ranging from 5340 km s⁻¹ to 5525 km s⁻¹. The data were cleaned down to an rms level of ∼6 mJy beam⁻¹. The final maps have some slight negative bowl (no greater than ∼2.5σ) features due to the lack of total power observations of the galaxy. We found that the default CASA immoment routine made decent moment maps, but did not capture some of the low-level emission seen in the channel maps. We thus used a dilated masking approach implemented in Python ¹⁰ to exclude noise before calculating the moment images. The mask is defined from an initial 4σ contour and expanded to the enclosing 2σ contour. From totaling the moment 0 map, we measured a total CO(2−1) flux (of all flux above 1.5σ significance) of 46 ± 15 Jy km s⁻¹ in the leading quadrant of the galaxy.

As part of a survey of Coma cluster spirals (project c1025; PI T. Wong), observations of CO(1–0) emission from NGC 4921 were conducted in 2012 August and October using the Combined Array for Research in Millimeter-Wave Astronomy (CARMA) in the most compact "E" configuration (baselines approximately 2.4–24 kλ) and the slightly less compact "D" configuration (baselines approximately 4–40 kλ). Total on-source integration time was approximately 6.8 hr in E configuration and 5.5 hr in D configuration. The galaxy was observed in a 7 point hexagonal mosaic with pointings separated by 30'' (approximately half the primary beamwidth of the 10 m telescopes), yielding a half-power field of view (FOV) with radius ≈50''. Two spectral windows of 191 channels each were allocated to the CO line, covering radial velocities from 5140 km s⁻¹ to 5800 km s⁻¹ with a channel spacing of 3.4 km s⁻¹.

The data were calibrated with the MIRIAD software package (Sault et al. 1995). Frequency-dependent (passband) gains were determined using observations of one of the bright quasars J1927+739, 3C273, or OJ 287 (J0854+201). The planet Mars was used as the primary flux calibrator; for the D-array track a planet was not available and a flux of 4.5 Jy was adopted for OJ 287 based on calibrated measurements within a few days of the observation. Antenna gain calibration was performed using observations every half hour of the quasar J1310+323.

The calibrated visibilities were imaged in MIRIAD and deconvolved using an implementation of SDI CLEAN designed for mosaics (task MOSSDI2). CLEAN components were searched for down to the 2σ level over the entire region where the sensitivity was within a factor of 3 of the FOV center. Cubes were generated with 1'' pixels and 10 km s⁻¹ wide channels across a velocity range of 5240–5590 km s⁻¹ (radio definition, LSR frame, which we use throughout this paper). The synthesized beam of the data cube was 65 × 48, with an rms noise of 27 mK per channel.

To create the moment maps of the CARMA data we again used a dilated masking approach ¹¹ to exclude noise before calculating the moment images. The mask is defined from an initial 4σ contour and expanded to the enclosing 1.5σ contour. From totaling the moment 0 map, we measured a total CO(1−0) surface brightness (of all emission above 2.5σ significance) of 53 ± 12 Jy km s⁻¹.

Similar to the dust distribution seen with HST (Figure 2), the CO(1−0), as observed with CARMA (see Figure 3), is concentrated in a central ring, with a significant gap to the SE (the trailing side). The inner bound of the CO(1−0) detection (r ∼ 20'' = 12 kpc) is just outside the stellar bar region of the galaxy, and the outer truncation radius of the CO(1−0) broken ring (r ∼ 30'' = 18 kpc) is similar to the maximum detected radius of the H i. This broken ring feature has a total measured CO(1−0) flux of ∼45 Jy km s⁻¹, which accounts for 86% of the total CO(1−0) flux detected in the galaxy with CARMA. The strongest peak in the CO(1−0) integrated flux (∼85 mJy km s⁻¹) is on the leading side of the galaxy at an azimuthal angle of 30° west from north on the sky. This is near where we estimate that the galaxy is experiencing the strongest ram pressure based on the morphology of the H i (Figure 2) and the HST dust morphology (Kenney et al. 2015).

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The molecular gas extent on the leading side is similar to the H i truncation radius as seen in Figure 3 bottom left. This suggests the atomic and the molecular gas may have both been pushed back, and compressed along the north side of the apparent molecular gas and dust ring (some atomic gas may have also been stripped and gravitationally unbound from the galaxy) and the remaining molecular gas is "effectively stripped" by disassociating into strippable density gas on a short timescale, as has been postulated by others, e.g., Kenney et al. (2004), Vollmer et al. (2012), and Boselli et al. (2014).

The distribution of the molecular gas as a function of azimuthal angle shows that a majority of the molecular gas is in the leading NW quadrant and the SW quadrant of the galaxy, which is rotationally downstream from the NW quadrant. The concentration of the molecular gas in the leading quadrant is coincident with the enhanced star formation in this same region observed by Lee & Jang (2016). About 180° opposite the estimated angle of incidence of ram pressure, the most shielded part of the galaxy, is a gap in the molecular gas ring. Outside the central broken ring, CO is also detected in the dust arm seen with HST on the NE side of the galaxy just past the dust ring at r = 32'' (see Outer Arm in Figure 3 top right). Other "emission" blobs outside the main ring are likely to be residual noise peaks from the cleaning, because they are only detected in a single channel of the data cube. However, the blob to the north near the leading side, seen in black in the moment 1 map (at ∼5300 km s⁻¹) is detected in three channels of the cube at ∼3σ, and its peak surface brightness is approximately three times higher than that of any of the other blobs outside the main ring. Its very offset velocity (up to ∼200 km s⁻¹) from the nearest ring CO is intriguing, but unfortunately this feature is not seen in any other wavelength we have access to, and is outside the field of view of our ALMA observations. If it is indeed a real feature it would be a likely candidate fallback feature; it will require further follow-up with deeper observations to confirm.

Our ALMA observations of the leading side of NGC 4921, upon which ram pressure is most strongly incident, show the detailed morphology of the molecular gas, as traced by CO(2−1) in this region. We display our ALMA observations as moment maps where we have down-weighted pixels with low primary beam sensitivity so as to limit the noise and make robust detections more apparent (Figure 4). We also show a larger version of this impressive, high-resolution overlay in Figure 5. We see a prominent outer ridge of CO(2−1) at about r ∼ 25–28'' from the nucleus, coincident with the region of dust and young star clusters seen in the HST image (Figure 5). This is also part of the broken ring feature seen with CARMA discussed in Section 3.1. The outermost front of the ridge of molecular gas contains the peak CO(2−1) line luminosity in the moment 0 map (Figure 4) of ∼2.5 × 10⁴ K km s⁻¹ pc². We also detect part of an inner ring feature at r ∼ 22'' in CO(2−1) that is seen in dust (Figure 5), although this feature is not detected as strongly in CO(2−1) as the main ring. Finally, we also detect four clouds past the radius of the main ring at r = 30'' (marked as "c1," "c2," "c3," and "c4," in Figure 5) that appear to be decoupled from any surrounding molecular gas; the properties of these clouds are discussed later in this paper.

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Table 1. NGC 4921 Properties

R.A. (J2000)	13h01m2612
Decl. (J2000)	$+27^\circ 53^{\prime} 09\buildrel{\prime\prime}\over{.} 56$
Type	SBab
z	0.01829
Length scale	005 = 25 pc
Projected distance from cluster center	700 kpc
vLSR	5400 km s−1
vgal − vComa	−1500 km s−1
MB mag	−22''
PA, inclination	177°, 13° a

Note.

^a See Section 3.3 for details.

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Along the outer ring of molecular gas, we see similar structure when comparing the CO(2−1) and the dust (as seen via the HST dust extinction). C-shaped pockets along the ring, also identified in Kenney et al. (2015), are seen in the molecular gas. We also detect in CO(2−1) what appear to be three separate filaments of dust protruding from the main gas ring, indicated in Figure 5 as "f1," "f2," and "f3" (although we note we detect CO only at the base of "f2," unlike for "f1" and "f3," which are detected along their full length). This type of filament is not seen in dust in any other quadrant of the galaxy, suggesting that either they formed as a result of a recent, significant change in the strength of ram pressure, or that they do not persist as they rotate out of the leading quadrant. Filaments 1 and 2 are the smallest, about 15 (750 pc) in length, and both have bright blue star concentrations at the head. They have total masses of molecular gas along their length of 8.8 × 10⁶ and 2.7 × 10⁶ M_⊙, respectively. Filament 3 is the largest filament we detect, with a total length of 45 (2.1 kpc) and a total mass of molecular gas of 4.3 × 10⁷ M_⊙, and again, a clump of blue stars near the head, with a visible cap of dust at the top end. We show a list of the filament properties in Table 2, and find their average molecular gas surface density ranges from ∼25 to 45 M_⊙ pc⁻². A similar filament of dust sticking out into the otherwise stripped zone, with a clump of young stars at the head, was also observed in the Virgo cluster galaxy NGC 4402, and was found to have an average surface density of only 7 M_⊙ pc² (Cramer et al. 2020). We analyze and discuss these filaments further in Section 5.1.2.

Table 2. Properties of Select CO Features in NGC 4921

Feature	Integrated Flux (Jy km s−1)	Mass ${M}_{{{\rm{H}}}_{2}+\mathrm{He}}$ (M⊙)	Surface Area (pc2)	Surface Density (M⊙ pc−2)
Filament 1	0.28	8.8 × 106	3.4 × 105	26
Filament 2	0.09	2.7 × 106	1.0 × 105	27
Filament 3	1.36	4.3 × 107	9.6 × 105	44

Note. From left to right: (1) the feature name (abbreviated in some figures as "f1," "f2," and "f3"); (2) the integrated CO(2−1) flux based on the moment 0 map; (3) total mass of H₂ and He assuming $\alpha =4.3\,{M}_{\odot }\,{\mathrm{pc}}^{-2}\,{({\rm{K}}\,\mathrm{km}\,{{\rm{s}}}^{-1})}^{-1}$ and R₂₁ ≈ 0.8, and the mass fraction of He/H₂ to be 1.34; (4) surface area of features based on the spatial extent of the CO feature in dust; (5) estimated average surface density of these features by dividing column (3) by column (4).

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Beyond the galactocentric radius of the main ridge of CO, there is no molecular gas other than that associated with the filaments and the previously mentioned decoupled clouds.

Our high-resolution ALMA observations allow us to study in detail the kinematics of the molecular gas on the leading side of NGC 4921 and assess how they may be influenced by ram pressure. However, to identify kinematics that deviate from normal motion associated with rotation, we must measure the average rotation curve of the galaxy and generate a model of the galaxy velocity field based on it.

To generate a model of the average circular velocity in NGC 4921, we fit the moment 1 CARMA map (shown in Figure 3) with DiskFit. DiskFit is a program that uses a tilted ring model to fit the kinematics of disk galaxies and is able to account for the beam size of the observations (see Sellwood & Spekkens 2015 for documentation). Along with the moment 1 map, we also input a central x and y position of the galaxy from the peak of the surface brightness in the HST F606W image as well as an estimated central velocity V_sys based on that estimated from the H i velocity field. We also input a position angle (PA = −3°) and a disk ellipticity (0.1), based on the value determined from an isophotal analysis of the galaxy halo from a deep r-band image taken with the Dragonfly telescope (provided by Allison Merritt). We measured the isophotal properties of NGC 4921 in the range r = 20–64'', and found that beyond a radius of r = 42'' we reached a consistent measurement of the position angle and ellipticity. Within r = 42'', irregular structure due to spiral arms, the bar, and bright star-forming regions make values of the position angle and inclination more inconsistent. To further constrain our estimates we used the DiskFit bootstrapping procedure, whereby these parameters were varied until a minimized chi-squared value for the model fit was achieved. We find the best-fitting values to be PA = 2° ± 3°, e = 0.06 ± 0.04 (corresponding to an inclination of ${20}_{-9}^{+5}\circ$), and V_sys = 5400 ± 5 km s⁻¹.

3.3.1. Measuring the Systemic Velocity

3.3.2. Estimating the Inclination

3.3.3. Comparing the Model and Data

The input image, resulting model, and residual map are shown in Figure 7. The model does not agree in all regions of the galaxy equally well. To the north and south there are still significant velocity residuals of up to ±50 km s⁻¹ (Figure 7). These residuals are especially large when considering that the projected maximum circular velocity is comparable in magnitude at 42 ± 8 km s⁻¹. Due to the fact that the rest of the CO ring has velocity residuals near 0 ± 10 km s⁻¹, and that we are confident in the best-fitting inclination and position angle from DiskFit, we suspect these large residuals are probably due to a real kinematic disturbance in these regions. One possible source of noncircular motions may be the prominent bar feature in the galaxy having disturbed some gas within r < 20'' (the approximate extent of the stellar bar) as the bar previously passed through. However, the regions with large residuals north and south along the major axis extend out to as far as r = 32''. It is not obvious what the source of these residuals could be. We note that the region to the south contains a large concentration of optically blue stars that are likely recently formed; the dust in this region also appears more irregular and disturbed. This region may have been previously compressed and kinematically disturbed by ram pressure. We would also expect the north side to be experiencing stronger ram pressure than the south side, as is also evidenced by the H i morphology. Along the quadrant of the galaxy in which we also have ALMA observations, the residuals from the CARMA data are between 0 ± 10 km s⁻¹, which given the CARMA channel width of 10 km s⁻¹, indicates a good match.

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We interpolate the model image to the resolution of our ALMA data and measure the kinematic residuals, where V_residual = V_obs − V_model, as shown in Figure 8. We find the main CO ring does not appear to show any widespread detectable offset from the predicted circular velocity in the direction of ram pressure. This is somewhat surprising, as we might expect that the leading side, being exposed to strongest ram pressure, would have higher noncircular motions consistent with ram pressure pushing when compared to gas that had just begun to rotate into the leading side pressure. In the Virgo spiral NGC 4402 a similar region of strong, active star formation on the leading side of the galaxy had a velocity offset in the direction of ram pressure of ∼20 km s⁻¹ (Cramer et al. 2020). We still do not have an explanation for the lack of a similar detectable kinematic offset in NGC 4921, although there are a number of factors that could cause the two regions to have different kinematics, including systematic factors such as the uncertainty in the kinematic modeling and physical factors such as gas density, the relative ram pressure and restoring force, and the disk−wind angle. We go into further detail on this in Section 5.2, where we estimate the strength of ram pressure NGC 4921 is experiencing.

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Examining the kinematic residuals from the ALMA data we find, as in the CARMA data, the main ring of CO has only small deviations from the circular velocity predicted from our model. However, with the increased resolution of ALMA, we find significant velocity deviations from circularity in some of the already morphologically identified features of interest: decoupled clouds, filaments, and c-shapes. To interpret the meaning of these residuals, we must consider that the velocity residual along the line of sight V_residual is composed of some combination of three velocity components in the frame of reference of the galaxy: V_z the vertical motion, V_t the azimuthal motion, and V_r the radial motion, as described in Equation (1)

$$\begin{eqnarray}&&{V}_{\mathrm{residual}}={V}_{{\rm{z}}}\cos i+\sin i\left[{V}_{t}\cos \theta +{V}_{r}\sin \theta \right]\end{eqnarray} \tag{ 1 }$$

where i is the inclination (which we estimate to be ${{13}_{-2}^{+3}}^{\circ }$°), and θ is the azimuthal angle with respect to the position angle of the major axis.

The largest, and brightest in total flux, clouds to the north outside the main CO ring are indicated with arrows in Figure 8 and labeled clouds 2 and 3. They are blueshifted by ∼20–50 km s⁻¹. Cloud 1 is further beyond the CO main ring, but does not show any velocity residual, and is in a region of the observations with low sensitivity. The more downstream large bright cloud, Cloud 4, is also blueshifted by 20 km s⁻¹, and we show a PVD of the cloud and nearby ring region indicating they are kinematically separate in Figure 9. Clouds 2 and 3 are close to the major axis, where θ ≈ 0, such that radial motions in the disk plane produce no component along the line of sight. However, from these observations alone we cannot determine the relative contributions to the observed blueshift due to vertical motion toward the galaxy disk, or azimuthal motion from these clouds rotating slower than the predicted circular velocity. If the motion of the clouds were entirely vertical, the correction for projection effects is very small as the disk is nearly face on, so the observed residual of −20 to −50 km s⁻¹ would correspond to a vertical streaming motion toward the observer of −20 to −51 km s⁻¹. If instead the motion were entirely azimuthal, the correction for inclination effects is large due to the inclination of the disk. Correcting for the inclination yields residuals due to azimuthal streaming of −95 to −240 km s⁻¹. Determining the likely components of the motion of these clouds requires additional evidence to consider outside of just our ALMA observations, which we explore further in Section 5.1.1.

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The large filament (filament 3) is redshifted by ∼20 km s⁻¹, which may indicate the filament gas is moving away from the observer. However, as the filament is located in between the minor and major axis, it may also be an azimuthal, or a radial motion, of up to 95 km s⁻¹. We discuss this further in Section 5.1.2. The smaller filaments more toward the north, filaments 1 and 2, do not show a measurable deviation from normal rotation within our velocity resolution. Moment maps and PVDs of these features, as well as a c-shaped gap in the dust and gas ring discussed further in Section 5.1.3, can be seen in Figure 9.

5.1.1. Evidence for Fallback Features

Even without any image processing, it is apparent that Clouds 1, 2, and 3, to the north of the main gas ring, have almost no visible dust overlapping the CO detection, especially when compared to the nearby filaments (see Figure 11 (top)).

Clouds 2 and 3 are also blueshifted relative to the gas disk, as seen in Figure 8, and appear to be the only features in the whole ALMA-HST comparison map with a clear CO detection but no dust extinction detection, as shown in Figure 11 bottom (regions near bright star clumps are excluded, as we cannot estimate extinction in them). At the azimuthal angle of these clouds, the radial velocity component becomes negligible, so the possible velocity components of the observed residual could be either V_z or V_t . The correlation between blueshifted clouds and CO detection but no visible dust extinction suggests that these are clouds behind the midplane of the stellar disk, and are either falling back toward the galaxy at a velocity range of ∼20–60 km s⁻¹, or rotating with significantly slower than predicted azimuthal velocity (we predict corresponding azimuthal velocity residuals of −95 to −240 km s⁻¹). If the clouds are behind the disk, the observer would not see any sign of dust extinction since the disk stars would be in front of the dust. Cloud 1 is likely behind the disk as it is not seen in dust, but is not falling back at this time as its velocity residual is near 0.

To constrain the likelihood of the observed velocity residual being dominated by either V_z or V_t , we consider information from a hydrodynamical simulation that uses the adaptive mesh refinement (AMR) code ENZO and does not include magnetic fields presented in Tonnesen (2019; run RCCW). The simulation involves a galaxy under a constant wind at a disk−wind angle of 53°, and a projected wind angle at 30° east from north, and shows gas falling back at all stages of the simulation in the same quadrant as we observed in NGC 4921. We show gas 0.1–3 kpc behind the disk from this simulation in Figure 12. We find a dense concentration of gas falling back toward the disk from behind the galaxy, similar to the decoupled clouds from our observations. In the simulation, these clouds are rotating faster, not slower, than the predicted circular velocity. This is due to the fact that, while the azimuthal component of the wind is slowing the rotation of the gas, the radial component of the wind pushes gas to a smaller radius, and thus, due to conservation of angular momentum, the gas swings out to higher velocities. Because the larger component of the wind at this angle in the simulation is radial, the net effect is a higher rotational velocity. The correlation between fallback and increased velocity in this quadrant persists for hundreds of megayears. This supports the notion that the blueshifted residual velocity of the observed decoupled clouds is not in fact from an azimuthal motion, but rather from a vertical motion from re-accretion. These results are also seen in simulations by co-author Smith, as presented in Bellhouse et al. (2020).

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Re-accretion of previously stripped gas that does not reach escape velocity is predicted in simulations (e.g., Vollmer et al. 2001; Kapferer et al. 2009; Tonnesen & Bryan 2010; Quilis et al. 2017), but has not been robustly observed before. Some possible signs of fallback of stars on the disk have been postulated (Hester et al. 2010; Kenney et al. 2014; Cramer et al. 2019), but the kinematic evidence, in combination with the evidence from dust extinction, that we present supporting fallback of gas is new.

5.1.2. Properties and Evolution of Filament 3

Through analysis of the properties of filament 3, including the mass and velocity profile, and comparison with a similar looking filament formed in simulation, we can investigate the possible formation of these types of structures.

The observed filament 3 is the largest filament we detect, with a total length of 45 (2.1 kpc), and a width of ∼1'' (0.5 kpc). Like filaments 1 and 2 shown previously in Figure 5, it features a complex of blue stars near the head; it also has a visible cap of dust at the top end. The fact that filament 3 is well resolved along its length (although not along its width) by our ALMA observations means that it is possible to study the mass and kinematic profile along the length of the filament. We show a zoom-in of our observations of this filament in Figure 13 (top), including the HST image, our ALMA observations, and a PVD along the length of the filament. Overall, we detect CO along the entire length of the filament as seen in dust, including in the region of blue stars at the head where dust extinction is difficult to detect. The filament appears to be connected to the main CO ring, with a region of strong extinction in an inverted Y-shape at the base where the filament starts (see Figure 13 top left). The filament also appears to be connected kinematically at its base to the main ring of CO. The PVD shown in Figure 13 (top right) supports that the filament is not entirely decoupled from the surrounding ring, instead remaining connected in position–velocity space. Although the connection appears faint in position–velocity space, it is apparent in dust extinction and in the CO moment 0 map. Both the dust and CO are fainter at the connection, suggesting that this filament may be in the process of detaching from the main gas ring.

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To further investigate the spatial and kinematic profile of filament 3, we plot the total mass, average mass, and velocity profile in a series of rectangular regions along the filament, shown at the top of Figure 14. We find for the observed filament that, just as is seen in dust, the region just past the base of the filament has a lower total mass of gas than either in the base or further along the filament. The region further along the filament from its base is fairly uniform in mass per length, and has relatively constant velocity. However, there remains a significant velocity offset (∼20 km s⁻¹ in the redshifted direction compared to the predicted circular velocity from our model) between the gas along the body and head of the filament and the attached ring. The head of the filament may have been more dense in the past before the onset of star formation as some gas originally in the head has been converted to stars. Furthermore the effects of feedback after star formation may have already blown away some of the molecular gas.

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The formation of this type of filament, and the influences that affect its shape and evolution, are still not entirely clear. One possible formation scenario we considered is that the head of the filament is a dense region of gas that resisted ram pressure as the surrounding gas was pushed away, and that the body of the filament is ablated gas that was stripped away from the dense cloud at the head. This is seen to happen in hydrodynamical simulations, such as those by Tonnesen & Bryan (2012), which use the AMR code ENZO and do not include magnetic fields. We show an example of this type of filament feature in Figure 13 (bottom). In the simulation snapshot shown, there is a high projected density gas cloud beyond the stripping radius, with a tail of material streaming off it that overlaps in projection with the downstream disk. However, the PVD of the simulated filament (Figure 13), as well as the mass and velocity profile along the simulated filament (Figure 14), are quite different from those of the observed Filament 3. While the body of the simulation filament is also offset in the ram pressure direction (blueshifted), in contrast to filament 3, the further from the head of the simulated filament, the more ram pressure appears to have accelerated the gas. In the region of projected overlap with the disk, the simulated filament does not appear kinematically connected to the disk gas, but is instead offset from the disk gas by ∼150–200 km s⁻¹.

The PVD and velocity profile of the filament in the simulation are consistent with this filamentary feature being formed from ablated gas originating from the cloud at the head, which is highly accelerated by ram pressure, such that we see a clear positive velocity gradient along the filament from head to base in the direction of ram pressure. By contrast, in the observed filament, we do not see this sort of profile, instead the gas along the filament beyond the base region has a relatively constant velocity. Moreover, at the base of the filament, it appears connected both spatially and kinematically to the surrounding disk gas.

Furthermore, the mass of the ablated cloud in the simulation is concentrated at the head and is lower along its length. It is also much lower than in the region where it overlaps with the disk when compared to filament 3 (Figure 14). The observed mass and velocity profile support that the filaments we observe in NGC 4921 are held together by magnetic binding that inhibits decoupling of low- and high-density gas in the filament, as the region undergoes stripping. This scenario was first suggested by Kenney et al. (2015) based on the dust morphology. Most detailed simulations of ram pressure stripping do not include star formation and/or magnetic fields in both the galaxy and the ICM. Our observations support that a more complete understanding of these factors, especially on the leading side of ram pressure affected galaxies, are necessary to fully understand the formation of structures like filament 3.

Finally, we consider the implication of the observed redshift when compared to the circular velocity model along the observed filament. First we consider whether the observed redshift could be consistent with the filament being formed via radial pushing of the surrounding gas. As these filaments are only observed in the leading quadrant between the area of the main CO ring of PA ∼ 25° and 55° from the major axis, we assume they formed within the time it took the galaxy to rotate between 25° and 55°. The circular velocity at the radius of the filament (∼30'' or 14.8 kpc) as determined from DiskFit and the Tully–Fisher relation is ∼300 km s⁻¹; thus we estimate the rotation period of the disk here is ∼300 Myr. The fractional time the galaxy would take to rotate from 25° and 55° is thus ∼30 Myr. If we consider a scenario in which the head of the filament was originally part of the main ring, and that the main ring was then pushed down to where it lies now, i.e., moved the distance of the length of the filament, that would be a total distance traveled of ∼2 kpc. The gas pushed by ram pressure would need to travel at an average velocity in the radial direction of ∼65 km s⁻¹ to match this distance traveled over 30 Myr (assuming for the estimation that ram pressure is constant over this time period). We previously calculated that, when compared to the kinematic model of the circular velocity, filament 3 has a velocity residual of ∼20 km s⁻¹, which could be due to a radially inward velocity of up to 95 km s⁻¹, although any of the three components of motion could contribute (as described in Equation (1)). A radially inward motion for the filament is difficult to explain given that the filament appears to be the only gas remaining in the otherwise stripped zone; we would expect the downstream gas to have a strong radial motion residual, but not the filament. We still do not fully understand the kinematics of these filaments. Uncertainty inherent in our approach to generating the circular velocity model is also a source of systematic error that makes interpreting these residuals more difficult. We explore these uncertainties further in Section 5.3.

5.1.3. C-shaped Pockets

We have estimated the surface density of a number of ISM features that appear to be affected by ram pressure. To analyze the role of ram pressure in the formation and evolution of these features, we would like to estimate the strength of ram pressure and the opposing restoring force from the disk around the affected region in NGC 4921. By estimating the ICM gas density ρ_ICM, the relative velocity of the galaxy with respect to the cluster v, and the restoring force per unit mass dΦ_g /dz, we can use the Gunn & Gott (1972) stripping criteria ${\rho }_{\mathrm{ICM}}{v}^{2}\,\geqslant {{\rm{\Sigma }}}_{\mathrm{ISM}}\tfrac{d{\rm{\Phi }}}{{dz}}$ to estimate the surface density of gas Σ_ISM that would be stripped. We estimate ρ_ICM to be ∼7 × 10⁻²⁸ g cm⁻³, based on a β-profile for an isothermal spherical distribution with coefficients given by Mohr et al. (1999) and Fossati et al. (2012), and the 3D distance of NGC 4921 to cluster center being equal to its projected distance of ∼675 kpc. The line-of-sight velocity of NGC 4921 with respect to the cluster center, estimated as the average of the line-of-sight velocity of the two brightest central elliptical galaxies in Coma, NGC 4889 and NGC 4874, is v_gal − v_Coma = 1500 km s⁻¹. The leading side of NGC 4921 has a significantly different dust morphology than the trailing side, being much more compressed due to the influence of a component of ram pressure acting in the plane of the sky. Thus, the true 3D velocity of NGC 4921 is likely to be larger than the line-of-sight velocity. We estimate the maximum 3D velocity according to simulations for galaxies in a Coma-like cluster from Jáchym et al. (2017), who found that an infalling galaxy with an open orbit would have a 3D velocity of at least ∼3000 km s⁻¹. Thus the maximum ram pressure we estimate for NGC 4921 is approximately P_ram =ρ v² ∼ 6 × 10⁻¹¹ dyne cm⁻².

We estimate the gravitational restoring force per unit mass $\tfrac{d{\rm{\Phi }}}{{dz}}$ as approximately equal to ${V}_{\mathrm{rot}}^{2}{R}^{-1}$, as done in Cramer et al. (2020). At the radial distance of the outer edge of the main dust ridge, r ∼ 30'' = 18 kpc, the circular velocity predicted from Tully–Fisher is ∼300 km s⁻¹, so ${V}_{\mathrm{rot}}^{2}{R}^{-1}=2\times {10}^{-13}$ km s⁻². Using the Gunn & Gott formula, we estimate the surface density of gas that would be stripped under these conditions as Σ_ISM ≈ 18 M_⊙ pc⁻² for the upper limit velocity estimate.

Both the estimated surface density of gas that could be stripped by ram pressure, and the surface density of features in the ISM we have estimated in this paper, have significant sources of uncertainty, like the true 3D velocity of the galaxy, and the X factor for converting CO to H₂ mass α_CO. Despite these uncertainties, our estimates of the surface density of gas that could be susceptible to stripping are consistent with the observed properties of the stripped zone. The decoupled clouds of gas detailed in Table 3 have estimated surface densities between ∼25 and 55 M_⊙ pc⁻² (measured at a resolution of 220 pc × 170 pc); for them to be falling back onto the galaxy we would indeed expect them to be denser than the maximum surface density of gas that could be stripped by our estimate of the ram pressure. Furthermore, the filaments are the only other ISM surviving in the otherwise stripped zone beyond r ∼ 30'', and they also have estimated surface densities higher than that which we expect to be stripped (shown in Table 2) of ∼26–44 M_⊙ pc⁻². Interestingly, a very similar filament feature with star formation at the head seen in NGC 4402, a ram pressure stripped galaxy in the Virgo cluster, was found to have an estimated surface density of only 7 M_⊙ pc⁻² (Cramer et al. 2020). The Virgo cluster has a much lower total mass than the Coma cluster, and generally has much weaker ram pressure. It would be interesting if the surface density of these unique filamentary features seen in ram pressure affected galaxies were related to the conditions of the ram pressure the respective galaxies were experiencing. However, a larger sample of these types of features would be needed to establish this sort of connection.

Table 3. Properties of Select CO Features in NGC 4921

Feature	Integrated Flux† (Jy km s−1)	Mass ${M}_{{{\rm{H}}}_{2}+\mathrm{He}}$ (M⊙)	Area† (pc2)	Surface Density (M⊙ pc−2)
Cloud 1	0.58	1.8 × 107	3.4 × 105	53
Cloud 2	0.93	2.9 × 107	7.2 × 105	40
Cloud 3	0.38	1.2 × 107	4.8 × 105	25
Cloud 4	0.68	2.1 × 107	3.9 × 105	29

Note. From left to right: (1) the feature name (abbreviated in some figures as "c1," "c2," and "c3"); (2) the integrated CO(2−1) flux based on the moment 0 map; (3) total mass of H₂ and He assuming $\alpha =4.3\,{M}_{\odot }\,{\mathrm{pc}}^{-2}\,{({\rm{K}}\,\mathrm{km}\,{{\rm{s}}}^{-1})}^{-1}$ and R₂₁ ≈ 0.8, and the mass fraction of He/H₂ to be 1.34; (4) surface area of features based on the spatial extent of the CO feature in dust. (5) estimated average surface density of these features by dividing column (3) by column (4).

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Overall, the measured surface density of NGC 4921 ISM features remaining in the otherwise stripped zone is consistent with all lower surface density gas having been stripped, leaving behind only these dense clouds. This stripping of gas could result from the pushing of the low-density gas, or evaporation of the low-density gas. It is interesting that overall we detect no large-scale significant velocity residual on the leading side; on the surface this seems to support the evaporation scenario. However, there is more evidence supporting that gas has been radially pushed by ram pressure. First, in a similar kinematic analysis of molecular gas in the ram pressure stripped galaxy NGC 4402 in the Virgo cluster, Cramer et al. (2020) found that the leading side of the disk of that galaxy had velocity residuals of up to 60 km s⁻¹, consistent with gas being pushed by ram pressure. Our CARMA observations of NGC 4921, as well as previously taken H i observations, also appear to be consistent with gas having been radially pushed by ram pressure. As noted previously, the leading quadrant has the highest peak surface brightness in the CARMA CO map. The H i contours in this region are also more compressed than in anywhere else in the galaxy. It was also noted that in the leading quadrant, there was a much higher number of young star concentrations than anywhere else in the galaxy (Lee & Jang 2016). This is consistent with the triggering of star formation from gas compression on the leading side. Furthermore, it can be seen in Figure 5 that, on the leading side, young stars and molecular gas are spatially offset, with molecular gas downstream from the young stars. This supports the scenario in which star formation has been triggered earlier in the ram pressure stripping process, and gas has since been pushed inward radially from where this star formation took place. Finally, the c-shaped features have higher velocity residuals in the cup than at the edges, consistent with lower density gas in the cup being pushed further radially inward than denser gas at the edges.

There are a number of factors that could explain why, despite evidence for the radial pushing of gas by ram pressure in NGC 4921, we do not observe a large-scale velocity residual like we do in NGC 4402. We may not be able to detect any velocity residual in NGC 4921, even if the gas is being significantly kinematically affected, due to projection and the ram pressure disk−wind angle. If the disk−wind angle is close to edge-on, most of the velocity residual will not be along the line of sight.

Furthermore, we note that our approach to estimating the rotation curve via a kinematic model of the molecular gas that assumes only normal circular motion is limited by the molecular gas in the galaxy likely being disturbed by ram pressure (as well as bar and spiral arm motions). We believe this is mitigated due to the fact that the kinematics of the gas on the leading side are likely to be more strongly influenced by ram pressure (as was seen in Cramer et al. 2020), and thus by excluding this region from the fit, the residuals in this region based on a fit to the rest of the galaxy should still reveal some elevated level of residuals on the leading side. However, significant uncertainty still remains; for example, a different rotation curve that is fit to reduce the N−S residuals would result in different residuals in the area of the leading side we study. Ultimately, observations of stellar kinematics are likely necessary to make more accurate measurements of the noncircular motions of the gas, as the stellar kinematics should not be strongly affected by ram pressure.

Keeping this significant uncertainty in mind, if the model is indeed close to accurate, there are a number of explanations for the velocity residual patterns we observe. First, we note that we will only observe a velocity difference between the different gas densities if they are actively in the process of being pushed back, whereas if all of the gas that could be pushed already had been, we would not observe a residual. It is possible that the disk−wind angle in NGC 4921 contributes to gas being pushed radially into already dense gas in the main ring of NGC 4921. This ring of gas is seen in dust along nearly the entire galaxy. Gas pushed into this ring could slow down as it was compacted against this dense, more strongly gravitationally bound gas front, leading to an overall lower velocity residual than for gas on the leading side of NGC 4402 that is being pushed in the direction out of the disk, instead of into it.