Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge
AAstronomy & Astrophysics manuscript no. taffy˙pdb˙v8a © ESO 2021January 25, 2021
Low star formation efficiency due to turbulent adiabaticcompression in the Taffy bridge (cid:63)
B. Vollmer , J. Braine , B. Mazzilli-Ciraulo , , B. Schneider , Universit´e de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, all´e Geoffroy Saint-Hilaire, 33615 Pessac,France LERMA, Observatoire de Paris, PSL Research University, CNRS, Universit´e de Sorbonne, UPMC, Paris, 75014,France AIM, CEA, CNRS, Universit´e Paris-Saclay, Universit´e Paris Diderot, Sorbonne Paris Cit´e, F-91191, Gif-sur-Yvette,FranceReceived ; accepted
ABSTRACT
The Taffy system (UGC 12914/15) consists of two massive spiral galaxies which had a head-on collision about 20 Myrago. It represents an ideal laboratory to study the reaction of the interstellar medium to a high-speed ( ∼ − )gas-gas collision. New sensitive, high-resolution (2 . (cid:48)(cid:48) or ∼
800 pc) CO(1-0) observations of the Taffy system with theIRAM Plateau de Bure Interferometer are presented. The total CO luminosity of the Taffy system detected with thePdBI is L CO , tot = 4 . × K km s − pc , 60 % of the CO luminosity found with the IRAM 30m telescope. About 25 % ofthe total interferometric CO luminosity stems from the bridge region. Assuming a Galactic N (H ) /I CO conversion factorfor the galactic disks and a third of this value for the bridge gas, about 10 % of the molecular gas mass is located in thebridge region. The giant H ii region close to UGC 12915 is located at the northern edge of the high-surface brightnessgiant molecular cloud association (GMA), which has the highest velocity dispersion among the bridge GMAs. Thebridge GMAs are clearly not virialized because of their high velocity dispersion. Three dynamical models are presentedand while no single model reproduces all of the observed features, they are all present in at least one of the models. Mostof the bridge gas detected in CO does not form stars. We suggest that turbulent adiabatic compression is responsible forthe exceptionally high velocity dispersion of the molecular ISM and the suppression of star formation in the Taffy bridge.In this scenario the turbulent velocity dispersion of the largest eddies and turbulent substructures/clouds increase suchthat giant molecular clouds are no longer in global virial equilibrium. The increase of the virial parameter leads to adecrease of the star formation efficiency. The suppression of star formation caused by turbulent adiabatic compressionwas implemented in the dynamical simulations and decreased the star formation rate in the bridge region by ∼
90 %.Most of the low-surface density, CO-emitting gas will disperse without forming stars but some of the high-density gaswill probably collapse and form dense star clusters, such as the luminous H ii region close to UGC 12915. We suggestthat globular clusters and super star clusters formed and still form through the gravitational collapse of gas previouslycompressed by turbulent adiabatic compression during galaxy interactions. Key words.
Galaxies: interactions – Galaxies: ISM – Galaxies: kinematics and dynamics
1. Introduction
Head-on collisions between spiral galaxies represent an ideallaboratory to study the behavior of the interstellar medium(ISM) under extreme conditions. During the collision theinterstellar media of both galactic disks collide, heat up,and exchange momentum. In merging galaxy pairs, an ISM-ISM collision occurs towards the end of the interactionprocess (see, e.g., Renaud et al. 2015 or di Matteo et al.2008). The Taffy system (UGC 12914/15; Fig. 1) is a spe-cial case because both spiral galaxies are particularly mas-sive, were gas-rich before the collision, and collided at highspeed ( ∼ − ; Condon et al. 1993, Vollmer et al.2012). We observe the galaxy pair about 20 Myr after theimpact that occurred in the plane of the sky. The transversevelocity difference at the present time is 650 km s − . (cid:63) Based on observations carried out with the IRAM Plateaude Bure Interferometer. IRAM is supported by INSU/CNRS(France), MPG (Germany) and IGN (Spain).
The Taffy system attracted attention through its strongradio synchrotron bridge (Condon et al. 1993), a very un-usual feature. The bridge is H i -rich and was subsequentlyfound to be rich in molecular gas as well through CO ob-servations (Gao et al. 2003, Braine et al. 2003). Dust ap-pears to be underabundant with respect to gas in the bridge(Zink et al. 2000, Zhu et al. 2007), presumably due to grainablation during the collision. The system contains about1 . × M (cid:12) of H i and a similar quantity of moleculargas, dependent on the N (H ) /I CO conversion factor fromCO emission to H column density. Some 10 – 20 % of thegas is in the bridge, making it at least as rich in moleculargas as the entire Milky Way. The ionized gas is highly dis-turbed kinematically, with gas spread in two main filamentsbetween the two galaxies. Hot, X-ray emitting gas that haspresumably been shock heated during the collision, is alsopresent in the bridge region (Appleton et al. 2015). Thishot and tenuous gas is spatially more correlated with the a r X i v : . [ a s t r o - ph . GA ] J a n Vollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge
Fig. 1.
The Taffy system UGC 12914/15. Upper panel:SDSS color image. Lower panel: color: stellar content(Spitzer 3.6 µ m emission), light grey contours: H i emission(Condon et al. 1993), black contours: CO emission (Gao etal. 2003).low density atomic gas and seems to avoid the high densitymolecular gas.The head-on collision of the Taffy system was simulatedby Vollmer et al. (2012) with a model which includes a col-lisionless (halo and stellar particles) and a collisional (gas)component. A wealth of observational characteristics areavailable for the comparison with simulations: a distortedstellar distribution, a prominent H i and CO gas bridge withlarge linewidths and H i double-line profiles, and a large-scale magnetic field with projected field vectors parallelto the bridge. Since these authors could not find a sin-gle simulation which reproduces all observed characteris-tics, they presented two “best-fit” simulations. The firstsimulation better reproduced the H i and CO line profiles of the bridge region (Braine et al. 2003), whereas the sec-ond simulation better reproduced the stellar distribution ofUGC 12915, the symmetric gas velocity fields of the galac-tic disks, the projected magnetic field vectors in the bridgeregion, and the distribution of the 6 cm polarized radiocontinuum emission (Condon et al. 1993). The stellar dis-tribution of the model secondary galaxy is more distortedthan that of UGC 12915. These models were successful inproducing (1) the prominent H i and CO gas bridge, (2)the offset of the CO emission to the south with respect tothe H i emission in the bridge region, (3) the gas symmet-ric velocity fields in the galactic disks, (4) the isovelocitycontours of the CO velocity field which are parallel to thebridge, (5) the H i double-line profiles in the disk region,(6) the large gas linewidths (100-200 km s −
1) in the bridgeregion, (7) the velocity separation between the double lines( ∼
330 km s − ), (8) the high field strength of the regularmagnetic field in the bridge region, (9) the projected mag-netic field vectors, which are parallel to the bridge, (10)the offset of the maximum of the 6 cm polarized radio con-tinuum emission to the south of the bridge, (11) and thestrong total power emission from the disk. The structureof the model gas bridge was found to be bimodal: a dense( ∼ .
01 M (cid:12) pc − ) component with a high velocity disper-sion >
100 km s − and a less dense ( ∼ − M (cid:12) pc − )component with a smaller, but still high velocity disper-sion ∼
50 km s − . The synchrotron lifetime of relativisticelectrons is only long enough to be consistent with the ex-istence of the radio continuum bridge (Condon et al. 1993)for the less dense component. On the other hand, only thehigh-density gas undergoes a high enough mechanical en-ergy input to produce the observed strong emission of warmH (Peterson et al. 2012).The star formation efficiency of the molecular gas inthe bridge region is at least two to three times smaller thanthat of the molecular gas located within the galactic disks(Vollmer et al. 2012). There is one exception: a compact re-gion of high star formation is located about 15 (cid:48)(cid:48) or 4 . southwest of the center of UGC 12915. Despite low star for-mation rates in the bridge, the [C II] emission appears tobe enhanced (Peterson et al. 2018) consistent with shockand turbulent gas heating (Joshi et al. 2019).In this article we present new high-resolution CO(1–0)observations of the Taffy system to better understand thedistribution and kinematics of the dense molecular gas. Inaddition, we investigate why the star formation efficiencywith respect to the molecular gas ( SF R/M H ) is so low inthe gas bridge. To do so, the dynamical model of Vollmer etal. (2012) was modified to include the effects of turbulentadiabatic compression and expansion. Both effects are ableto temporarily suppress star formation in the dense gas.
2. Observations
Observations of the CO(1—0) emission were carried outwith the IRAM Plateau de Bure Interferometer (PdBI) insummer 2014 using all six antennas in C and D configu-ration. The system was covered by a mosaic of 11 PdBIprimary beams. Each position was observed during 55 min.The bandpasses calibration was on 3C454.3 on May 30thand Nov 21st and on 1749+096 on May 29th. Phase and We use a distance of 60 Mpc for the Taffy galaxy system.ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 3 amplitude calibrations were performed on 2319+272 (ev-ery day), 0007+171 (21 nov), and 0006+243 (May 29thand 30th). The absolute flux scale was checked on MWC349 every day. A total bandwidth of 640 MHz with a spec-tral resolution of 2 . ∼ . − wide velocity channels. Applyingrobust weighting in the mapping process, a beam size of2 . (cid:48)(cid:48) ( ∼
800 pc) was derived.
3. Results
The CPROPS (CloudPROPertieS) software (Rosolowsky &Leroy 2006) was used to identify and measure the properties(size, flux, velocity dispersion) of molecular cloud associa-tions (GMAs) in the 2 . (cid:48)(cid:48) datacube. The CPROPS programfirst assigns contiguous regions of the datacube to individ-ual clouds and then computes the cloud properties (flux, ra-dius, and velocity width) from the identified emission. Thealgorithm ignores clouds smaller than a resolution elementand does not decompose clouds smaller than two resolutionelements. We used the modified CLUMPFIND algorithm(ECLUMP) and required a peak of at least 1 . σ in everydistinct cloud and at least two channels. The CPROPS de-composition was used to produce the moment maps whichare presented in Fig. 2. As a consistency check, we cleanedthe datacube with a velocity channel width of 6 . − byiteratively (i) boxcar averaging of each spectrum (width=4channels), (ii) fitting Gaussians to the boxcar-averagedspectrum ( v is the central velocity), (iii) all correspondingvoxels in a 3D mask that are located between v − FWHMand v +FWHM are set to one, (iv) the Gaussian is sub-tracted from the boxcar-averaged spectrum, (v) the nextGaussian is fitted to the spectrum until its amplitude issmaller than 5 σ of the boxcar-averaged spectrum, (vi) the3D mask is applied to the initial datacube. Moment mapswere produced without clipping the datacube (Figs. A.1).The moment maps based on CPROPS and the “cleaned”moment maps are consistent, the former being deeper asexpected from the lower CLUMPFIND limit of 1 . σ . Thecloud or GMA properties derived by CPROPS are shownin Table 1. The optical image of UGC 12915 (upper panel of Fig. 1)shows an asymmetric dust ridge or tilted ring visible inabsorption and two symmetric stellar arms, the northernarm being brighter than the southern arm. The moment 0map (Fig. 2) shows a bright, asymmetric, and twisted thinmolecular disk rather than a tilted ring in UGC 12915which corresponds to the asymmetric dust ridge. The sur-face brightness distribution along the major axis is asym-metric. The second brightest maximum in this disk cor-responds to the galaxy center. The brightest maximum islocated in the southeastern half of the disk. The northwest-ern half has a much lower surface brightness and is approx-imately twice as extended as the southeastern half of thedisk. Moreover, the most northwestern part of UGC 12915’smolecular disk is bent to the north, away from UGC 12914and the bridge region.The optical image of UGC 12914 (upper panel of Fig. 1)shows an inner lens structure with dust lanes and a much For the CLUMPFIND algorithm see Williams et al. (1994).
Fig. 2.
CO(1-0) moment maps based on detections identi-fied by CPROPS. Disk, bridge, and northern emission re-gions are labelled.
Vollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge
Table 1.
Molecular entities from CPROPS. number total number RA DEC radius velocity dispersion flux regionof pixels (degrees) (degrees) (pc) (km s − ) (K km s − pc )1 545 0 . . .
47 14 .
18 4 . E + 07 UGC 129152 1011 0 . . .
03 16 .
88 1 . E + 08 UGC 129153 1425 0 . . .
25 15 .
93 1 . E + 08 UGC 129154 2297 0 . . .
43 31 .
56 1 . E + 08 UGC 129155 2558 0 . . .
34 44 .
94 2 . E + 08 UGC 129156 1271 0 . . .
04 21 .
25 8 . E + 07 bridge7 238 0 . . <
300 12 .
99 1 . E + 07 bridge8 1117 0 . . .
71 29 .
10 8 . E + 07 UGC 129159 2228 0 . . .
19 50 .
21 1 . E + 08 bridge10 1361 0 . . .
85 30 .
11 1 . E + 08 bridge11 465 0 . . .
04 14 .
64 2 . E + 07 bridge12 108 0 . . <
300 18 .
04 6 . E + 06 bridge13 1994 0 . . .
07 30 .
94 1 . E + 08 bridge14 251 0 . . .
32 15 .
90 1 . E + 07 bridge15 1789 0 . . .
35 23 .
51 1 . E + 08 bridge16 4934 0 . . .
62 65 .
40 6 . E + 08 UGC 1291517 266 0 . . .
70 11 .
04 1 . E + 07 bridge18 1710 0 . . .
03 38 .
68 8 . E + 07 bridge19 241 0 . . .
82 19 .
70 1 . E + 07 bridge20 703 0 . . .
97 19 .
81 3 . E + 07 bridge21 2203 0 . . .
63 44 .
71 1 . E + 08 UGC 1291522 91 0 . . <
300 24 .
26 6 . E + 06 bridge23 4616 0 . . .
16 50 .
50 7 . E + 08 UGC 1291524 216 0 . . <
300 10 .
53 1 . E + 07 bridge25 173 0 . . .
85 7 .
18 1 . E + 07 bridge26 61 0 . . .
03 7 .
20 2 . E + 06 bridge27 100 0 . . .
03 7 .
08 7 . E + 06 bridge28 290 0 . . <
300 26 .
86 1 . E + 07 bridge29 2111 0 . . .
00 32 .
61 2 . E + 08 UGC 1291430 266 0 . . .
93 18 .
41 1 . E + 07 bridge31 187 0 . . <
300 16 .
24 1 . E + 07 bridge32 1744 0 . . .
61 33 .
99 2 . E + 08 UGC 1291433 329 0 . . .
83 16 .
89 2 . E + 07 UGC 1291434 80 0 . . <
300 9 .
99 5 . E + 06 UGC 1291435 95 0 . . <
300 11 .
19 6 . E + 06 UGC 1291536 330 0 . . .
34 13 .
51 1 . E + 07 bridge37 196 0 . . .
89 10 .
65 1 . E + 07 bridge38 158 0 . . <
300 10 .
93 8 . E + 06 bridge39 178 0 . . <
300 16 .
71 1 . E + 07 bridge40 354 0 . . .
41 16 .
46 1 . E + 07 bridge41 90 0 . . <
300 14 .
51 5 . E + 06 bridge42 134 0 . . <
300 14 .
96 8 . E + 06 bridge43 115 0 . . <
300 10 .
12 7 . E + 06 bridge44 387 0 . . .
19 13 .
80 2 . E + 07 bridge45 177 0 . . .
13 14 .
99 1 . E + 07 bridge46 522 0 . . .
92 23 .
21 3 . E + 07 bridge47 167 0 . . .
88 7 .
06 8 . E + 06 bridge48 558 0 . . .
95 17 .
79 3 . E + 07 bridge49 241 0 . . <
300 14 .
52 2 . E + 07 UGC 1291550 208 0 . . .
54 27 .
73 1 . E + 07 bridge51 276 0 . . .
13 17 .
27 2 . E + 07 UGC 1291452 1519 0 . . .
39 27 .
38 1 . E + 08 UGC 1291453 159 0 . . <
300 14 .
64 1 . E + 07 UGC 1291454 621 0 . . .
50 13 .
26 4 . E + 07 UGC 1291455 46 0 . . <
300 10 .
67 4 . E + 06 UGC 1291456 270 0 . . .
58 10 .
49 1 . E + 07 UGC 1291457 57 0 . . <
300 17 .
80 4 . E + 06 UGC 1291458 202 0 . . <
300 14 .
72 1 . E + 07 UGC 1291459 118 0 . . .
53 26 .
59 8 . E + 06 UGC 1291460 144 0 . . .
83 12 .
13 9 . E + 06 UGC 12914 (a) When CPROPS was unable to deconvolve the cloud size, we put <
300 pc.ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 5
Table 2. continued. number total number RA DEC radius velocity dispersion flux regionof pixels (degrees) (degrees) (pc) (km s − ) (K km s − pc )61 90 0 . . .
47 11 .
36 6 . E + 06 UGC 1291462 146 0 . . <
300 18 .
75 7 . E + 06 UGC 1291463 58 0 . . <
300 6 .
85 3 . E + 06 UGC 1291464 1585 0 . . .
63 42 .
77 1 . E + 08 UGC 1291465 72 0 . . <
300 9 .
30 5 . E + 06 UGC 1291466 506 0 . . .
13 19 .
15 2 . E + 07 UGC 1291467 341 0 . . .
13 11 .
67 2 . E + 07 UGC 1291468 550 0 . . .
39 13 .
50 3 . E + 07 UGC 1291469 1118 0 . . .
53 16 .
26 1 . E + 08 UGC 1291470 465 0 . . .
87 19 .
69 2 . E + 07 bridge71 597 0 . . .
07 14 .
06 5 . E + 07 UGC 1291472 1130 0 . . .
35 18 .
64 9 . E + 07 UGC 1291473 85 0 . . .
77 12 .
53 8 . E + 06 UGC 1291474 72 0 . . <
300 20 .
01 4 . E + 06 UGC 1291475 82 0 . . <
300 11 .
65 7 . E + 06 UGC 1291576 79 0 . . <
300 6 .
95 4 . E + 06 UGC 1291477 82 0 . . <
300 11 .
28 5 . E + 06 UGC 1291478 477 0 . . <
300 29 .
15 2 . E + 07 bridge79 120 0 . . .
35 11 .
56 9 . E + 06 bridge80 65 0 . . <
300 7 .
42 4 . E + 06 bridge fainter outer double-ring structure. In addition, a stellararm starts from the northern tip of the stellar lens structurejoining the eastern faint outer stellar ring. The CO emis-sion distribution of UGC 12914 has three maxima along themajor axis: the galaxy center (D1) and the two elongatedstructures at a distance of ∼ (cid:48)(cid:48) or 5 . ∼ (cid:48)(cid:48) –30 (cid:48)(cid:48) or ∼ ii region closeto UGC 12915 (upper panel of Fig. 3). It roughly connectsthe center of UGC 12915 and the southern CO maximumof UGC 12914. Four distinct CO clouds (B1–B4) are lo-cated parallel to the bridge to the west (upper panel ofFig. 2). Finally, three CO clouds (N1–N3) seem to connectthe northern part of UGC 12914 and the northern part ofthe disk of UGC 12915.The total CO luminosity of the Taffy system identifiedby CPROPS is L CO , tot = 4 . × K km s − pc . This rep-resents 60 % of the CO luminosity found by Braine et al.(2003) with the IRAM 30m telescope. We divided the mo-ment 0 into disk and bridge regions (Fig. A.2). The CO lu-minosity of the bridge is L CO , bridge = 1 . × K km s − pc .Thus, 25 % of the total CO luminosity stems from thebridge region. Assuming a Galactic N (H ) /I CO conver-sion factor for the galactic disks and a third of this valuefor the bridge gas, we obtain the following H masses: M H , tot = 1 . × M (cid:12) and M H , bridge = 1 . × M (cid:12) . Thus, about 10 % of the molecular gas mass is located inthe bridge region.An overlay with the Spitzer 8 µ m PAH emission mapis shown in Fig. 3. Within the galactic disks, the CO(1-0)emission closely follows the high surface brightness 8 µ memission. In the bridge region there is dense gas traced byCO emission which is not forming stars, as shown by a lackof PAH emission, which is usually a tracer of star formation.This implies that the bulk of the bridge high-density gasdoes not form stars (see also Braine et al. 2003 and Gaoet al. 2003). The luminous compact extraplanar H ii regionsouth of UGC 12915 represents the exception to that rule.A close-up of the region (lower panel of Fig. 3) shows thatthe H ii region does not coincide with, but is located at thenorthern edge of a high-surface brightness GMA (GMA 9in Table 1). This GMA has the highest velocity dispersionof the bridge GMAs.The velocity fields of UGC 12914 and UGC 12915 aredominated by rotation. The bridge shows a mixture of pos-itive and negative radial velocities with respect to the sys-temic velocities of the galaxies (4350 km s − ). The region ofhigh surface brightness close to UGC 12915 has an overallpositive velocity with respect to the systemic velocity. TheCO clouds aligned parallel to the bridge share this velocityrange.The internal velocity dispersions of the CO clouds de-rived by CPROPS are shown in Fig. 4. The velocity disper-sion of the inner parts of the molecular disk in UGC 12914is about 30 km s − , roughly normal for an edge-on spiralgalaxy at 800 pc resolution. The highest velocity disper-sions are found in the southeastern disk of UGC 12915 andits center. A cloud with a velocity dispersion of ∼
50 km s − (GMA 9 in Table 1 and Fig. 4) is found in the high sur-face brightness part of the bridge, close to the extraplanarH ii region. Overall, the northern half of the gas bridge hassignificantly higher velocity dispersions than the southernhalf. Vollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge
Fig. 3.
CO(1-0) contours on the Spitzer 8 µ m PAHemission map. Upper panel: the whole Taffy system.The stripe starting from the southern end of thedisk of UGC 12915 is an image artifact. Contourlevels are (2 , , , , , , , − . Lowerpanel: zoom on the compact extraplanar star form-ing region south of UGC 12915. Contour levels are(10 , , , , , , ,
80) K km s − . We separated the CO clouds identified by CPROPS intodisk and bridge clouds according to Fig. A.2. The resultingassignments are given in Table 1. The cloud properties arecompared to those of extragalactic GMAs from Bolatto etal. (2008) and those of M 33 derived by Gratier et al. (2012)in Fig. 5. With a resolution of 2 . (cid:48)(cid:48) or 800 pc we can only Fig. 4.
Internal velocity dispersion of the CPROPS molec-ular clouds (color) on the moment 0 map (greyscale). Disk,bridge, and northern emission regions are labelled as inFig. 2.detect associations of giant molecular clouds (GMAs). It isremarkable that the GMAs in the disk and bridge regionsfollow, as the molecular clouds in M 33, the size–linewidthrelation established by Bolatto et al. (2008) which is validfor extragalactic and Galactic molecular clouds. The scatteraround the relation is also comparable to that of Bolatto etal. (2008) and Gratier et al. (2012). It is especially surpris-ing that the disk GMAs follow the relation, because a signif-icant fraction of their linewidth is expected to be caused bylarge-scale motions, i.e. rotation and non-circular motions.The offset between the velocity dispersion determined byCPROPS and that predicted by the size–linewidth relationis presented in Fig. 6. For clarity we only colored GMAswhose linewidths are outside 1 σ of the size–linewidth rela-tion. Two regions with exceptionally high linewidths standout from this figure: the southeastern half of UGC12915’sdisk and the region around the extraplanar H ii region closeto UGC12915.The size–luminosity relation of the GMAs in the bridgeand disk regions is different. Whereas the clouds in thegalactic disks follow the relation established by Bolatto etal. (2008), the majority of the bridge clouds show aboutthree times lower CO luminosity than expected from therelation. The molecular clouds in M 33 are also CO-underluminous by about a factor of two. Gratier et al.(2012) argued that this is due to a two times higher N (H ) /I CO conversion factor. For the Taffy bridge regionBraine et al. (2003) excluded a higher N (H ) /I CO conver-sion factor based on their CO measurements. On the con-trary, Braine et al. (2003) and Zhu et al. (2007) argued thatthe N (H ) /I CO conversion factor is several times lower inthe bridge than in the galactic disk.
4. Comparison to dynamical models
Vollmer et al. (2012) calculated 17 models of head-on col-lisions of two gas-rich spiral galaxies. To the two “best-fit” ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 7
Fig. 5.
Properties of CPROPS molecular entities (bridge:red triangles; galaxies: blue boxes) compared to data fromBolatto et al. (2008; green crosses) and Gratier et al. (2012;black pluses). Upper panel: velocity dispersion as a functionradius. Lower panel: CO line flux as a function of radius.The lines correspond to the relations determined by Bolattoet al. (2008).models presented by these authors we added a third modelwith a higher velocity between the two galaxies. The maxi-mum impact velocity is 1200 km s − and the transverse ve-locity difference at the present time is ∼
900 km s − versus ∼
700 km s − for the previous simulations. We call this newsimulation “sim19fast”. Because of the high time resolutionof our simulations the cloud collisions are well resolved evenfor this enormous impact velocity. The system is observedat the same lapse of time (20 Myr) after impact as the twosimulations in Vollmer et al. (2012). Fig. 6.
Velocity dispersion offset of CPROPS molecularclouds with respect to the relation for extragalactic GMCsfound by Bolatto et al. (2008). Only GMAs with linewidthoutside 1 σ of the size–linewidth relation shown in Fig. 5 arecolored. The disk GMAs are marked with a black contour. The comparison between the observed surface brightnessdistribution and the model moment 0 maps is shown inFig. 7. All three simulations develop a gas-rich bridge andshow the observed sharp western border of gas distribu-tion of UGC 12914 which is mainly a tidal feature. As al-ready stated in Vollmer et al. (2012), none of the modelsreproduce the detailed morphology of the system. Whereasthe model bridge starts close to the center of the northerngalaxy, as is observed, it joins the southern galaxy also closeto its center. In the observations the bridge joins the diskof UGC 12914 further to the south. The edge-on projec-tion of UGC 12915 is better reproduced by sim20. On theother hand, the east–west asymmetry of its surface bright-ness is better reproduced by sim19 and sim19fast. Contraryto observations, all models show a second bridge filamentto the west of the main bridge. This filament is brightest insim19fast. The northern part of the disk of UGC 12914 withits filaments pointing toward UGC 12915 is reproduced bysim19fast and to a much lesser degree by sim19. It is notreproduced by sim20, because the northern galaxy passedthrough the southern galaxy at this location, removing allgas there. Only in model sim19fast, the gas near the north-ern galaxy is much denser than that close to the southerngalaxy, as is observed.The comparison between the observed velocity field andthe model moment 1 maps is shown in Fig. B.1. The velocityfield of UGC 12914 is reasonably reproduced by sim19fastand to a lesser degree by sim19, whereas that of UGC 12915is best reproduced by sim20. The velocity field of the bridgewith its positive and negative velocities with respect to thesystemic velocity is best reproduced by sim20 and to a muchlesser degree by sim19fast. The model secondary bridge fil-aments to the north with their high velocities with respectto the systemic velocity are not observed. We concludethat a single model among our limited set of simulations
Vollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge observations sim 19sim 19 fast sim 20
Fig. 7.
CO(1-0) moment 0 maps together with the model H moment 0 maps. Upper left panel:PdBI observations (contour) together with the Spitzer 3 . µ m map. The contour levels are(0 . , . , . , . , . , . , . , . , . , . , .
0) K km s − . Other panels: contour: stellar distribution; color:molecular gas distribution. The color stretch is the same as the contours of the upper left panel.(see Vollmer et al. 2012) is not able to reproduce the ob-served characteristics of the Taffy system. However, almostall characteristics can be found in one of the three models.In many ways, this is to be expected as the initial gas dis-tribution is not known. The advantages and disadvantagesof the models are summarized in Table 3.The comparison between the observed velocity disper-sion and the model moment 2 maps is shown in Fig. B.2.None of the models reproduce the extremely high velocitydispersion in the disk of UGC 12915. In sim19 and sim20the regions of highest velocity dispersion are located closeto the southern galaxy. In sim20 another region of high ve-locity dispersion is located in the middle of the bridge where the two bridge filaments cross. Only sim19fast shows a ve-locity dispersion in the bridge region close to the northerngalaxy which is comparable to the observed velocity dis-persion. We conclude that sim19fast is in rough agreementwith the observed distribution of the velocity dispersion inthe bridge. To appreciate the full wealth of information provided bythe datacubes, we decided to compare the observed andthe model datacubes by means of a 3D visualization. Here,we provide four different views of the datacubes rendered ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 9 at the same given intensity (Fig. 8 and Figs. B.3 to B.5).The total linewidth of UGC 12914 is significantly smallerthan that of the southern model galaxy. This can be dueto an overestimated model inclination angle or an overesti-mated rotation velocity of the southern model galaxy. Thebridge region of high surface brightness and intensity nearUGC 12915 has an inverted V-shape in the projection ofFig. 8. Moreover, it is confined to a relatively narrow ve-locity range around the systemic radial velocity. A filamentof low surface brightness and intensity emanating from thisregion smoothly joins the high radial velocity part of thedisk of UGC 12914. The only model which reproduces thesefeatures is sim20. However, the region of high intensities isfurther away from the northern galaxy than is observed forUGC 12915. All models show emission emanating from thesides of highest and lowest radial velocities in the northerngalaxy. These features are not observed in UGC 12915. Thevelocity structure of the southern galaxy is rather well re-produced. As already mentioned, only the northern part ofthe gas disk of the southern galaxy is missing in the modelsim20, because the impact entirely removed the gas there.Inspection of Fig. B.3 to B.5 corroborates these conclusions.
5. Star formation suppression caused by turbulentadiabatic compression
What do the Circumnuclear Disk in the Galactic Center, athick obscuring AGN torus, the ram-pressure stripped andtidally distorted Virgo spiral galaxy NGC 4438, Stephan’sQuintet, and the Taffy galaxies all have in common? Atthe first glance, all these systems are very different. First ofall, the spatial scales and timescales differ enormously. TheCND and AGN tori have spatial extents of about 10 pc androtation timescales of 10 yr, whereas the relevant scalesand timescales in NGC 4438, Stephan’s Quintet, and theTaffy galaxies are of the order of tens of kpc and 100 Myr.The common property of all these systems is that theyare undergoing gas-gas collisions with high energy injec-tion rates. In these collisions, one gaseous body is the tur-bulent clumpy multi-phase ISM, while the other can be ofdifferent mean density and temperature (e.g. ISM, intra-group or intracluster gas): NGC 4438 is affected by ongo-ing ram pressure caused by its rapid motion through theVirgo intracluster medium (Vollmer et al. 2005, 2009), andthe intragroup gas of the Stephan’s Quintet is compressedby a high-velocity intruder galaxy (Appleton et al. 2017).We suggest that the common theme of all these gas-gas in-teractions is adiabatic large-scale compression of the ISMleading to an increase of the turbulent velocity dispersion ofthe gas (Robertson & Goldreich 2012; Mandal et al. 2020).It is generally assumed that within the disks of iso-lated galaxies turbulence is driven by energy injectionthrough stellar feedback (SN explosions). In an equilib-rium state a balance between turbulent pressure and grav-ity is reached leading to a global virial equilibrium stateof the GMCs (Heyer et al. 2009). If the energy injectionthrough large-scale gas compression exceeds that of stellarfeedback deduced via the star formation rate, the veloc-ity dispersion of the largest eddies is expected to increase.In this case, we presume that the velocity dispersion ofthe turbulent substructures/clouds also increases (Fig. 2of Mandal et al. 2020). Such clouds were observed in theGalactic Center region by Oka et al. (1998, 2001). As a result, these GMCs will no longer be in global virial equi-librium. Oka et al. (2001) argued that the high virial pa-rameters ( α vir = 5 σ R cl / ( G M cl ), where σ cl , R cl , and M cl are the cloud 1D velocity dispersion, radius, and mass) ofthe Galactic Center GMCs may explain the paucity of starformation activity in this region. Indeed, analytical and nu-merical models of turbulent star-forming gas clouds predicta decreasing star formation efficiency per free fall timescalewith the virial parameter of a GMC (Fedderath & Klessen2012; Padoan et al. 2012, 2017).Following Robertson & Goldreich (2012) and Mandal etal. (2020), we expect turbulent adiabatic heating, i.e., anincrease of the turbulent velocity dispersion due to the p dVwork, to occur if the timescale of large-scale gas compres-sion t comp = ρ/ ( dρ/dt ) (1)is smaller than the dissipation timescale of turbulence t diss . From the dynamical simulations of Vollmer et al.(2012) we derived a compression timescale within thebridge of t comp < ∼
10 Myr (Fig. C.4). The driving lengthin the bridge is somewhere between the average cloudsize ( l cl ∼ ∼ t cross ∼ /
50 km s − ∼
40 Myr and this can be taken as t diss . A detailed comparison between the compression anddissipation timescales of the model is given in Appendix C.The t comp is signicantly smaller than t diss in the bridge butnot in the galaxies. Thus, we expect high virial parame-ters and weak star formation in the bridge gas. Adiabaticcompression and its effect on star formation are includedin the dynamical model and the results are compared toobservations in Appendix C.
6. Discussion
The shorter the timescale, the more important the pro-cess is. In this work, we compare the dissipation timescale,a few Myr as given in Eq. C.8 which assumes energy in-jection via star formation, to the compression timescale(Eq. 1). In a disk environment, there is little compression,i.e. dρ/dt is small, and hence the compression time is long,such that dissipation is the dominant process (Fig. C.3).During the Taffy collision, and afterwards in the bridgeregion, extremely strong shocks are present (as witnessedby the H emission observed by Peterson et al. 2018) and dρ/dt becomes enormous, and thus t comp short (Fig. C.4).Furthermore, the dissipation timescale ( l driv /v turb ) in thebridge is higher due to the much longer driving scale(Sect. C.4). These two factors result in t comp < t diss . Theinjected energy cannot be evacuated and this largely sup-presses the star formation in the bridge.A single model among our limited set of simulationscannot reproduce all observed characteristics of the Taffysystem. However, all characteristics are present in one ofthe models (Table 3). The models sim19 and sim19fast failto reproduce the gas morphology of UGC 12915, becausethe model inclination is significantly lower than the ob-served edge-on projection. Since the parameter space forthe head-on collision of both galaxies is vast, we did nottry to search for better initial conditions than those foundin Vollmer et al. (2012) and thus a better reproduction ofthe Taffy system. We could show that the observed detailed observations sim 19 v r (km s − )RA offset (arcsec) DEC offset (arcsec) sim 19 fast sim 20 Fig. 8.
First 3D view of the observed CO(1-0) datacube and the model H data cubes. These views correspond to aposition-velocity diagram. The axis labels are only shown for the observations. For a better understanding of these views,three 3D animations of the rotating datacube are attached to this figure ( taffy cube3D z.gif , taffy cube3D z1.gif ,and taffy cube3D x.gif ).velocity structure of the gas bridge can be well reproducedby one of our models (sim20; Fig. B.1). The observed north–south surface brightness gradient of the gas bridge and theincreased velocity dispersion of its high surface brightnesspart can be reproduced by model sim19fast (Fig. 7). Weare thus confident that such a model is in principle possibleto account for all observed characteristics (Table 3).Based on our models, we could show that a high-velocityhead-on encounter can lead to a significant fraction ofthe bridge gas undergoing turbulent adiabatic compression ∼
20 Myr after impact. We claim that the absence of starformation in bridge regions is due to turbulent adiabaticcompression where the turbulent velocity dispersion of thelargest eddies increases. It is expected that the velocitydispersions of the turbulent substructures/clouds increasesuch that GMCs are no longer in global virial equilibrium.The increase of the virial parameter leads to a decrease ofthe star formation efficiency per free fall timescale in the turbulent ISM (Fedderath & Klessen 2012; Padoan et al.2012, 2017) and thus to the suppression of star formation.Relating the Virial mass of a gas cloud to its CO-derivedmass yields σ = (cid:112) π/ G R Σ , (2)where R and Σ are the radius and surface density ofthe cloud. For the disk clouds we applied the Galactic N (H ) /I CO conversion factor, for the bridge clouds a threetimes lower N (H ) /I CO conversion factor. The resulting re-lation is shown in Fig. 9. Whereas the Virial mass of themolecular clouds from Bolatto et al. (2008) and Gratieret al. (2012) are higher than the gas masses derived fromthe CO luminosities, the Virial masses of the Taffy diskGMAs are consistent with the gas masses derived from theCO luminosities. Again, this is surprising because a signifi-cant fraction of their linewidth is expected to be caused bylarge-scale motions, i.e. rotation and non-circular motions.Therefore, one should not expect a correlation and the onewe found is most probably coincidental. ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 11 Table 3.
Comparison between our CO(1-0) and GALEX FUV observations and the models. feature sim19 sim19fast sim20gas morphology of UGC 12915 - - +gas morphology of UGC 12914 + + ∼ morphology of the gas bridge ∼ ∼ ∼ velocity field of UGC 12915 ∼ ∼ +velocity field of UGC 12914 + + +velocity field of the gas bridge ∼ ∼ +velocity dispersion of the gas bridge - + -global FUV morphology ∼ + ∼ large-scale magnetic field (a) + + (a) based on the results of Vollmer et al. (2012). Based on the comparison between simulations and ob-servations, Vollmer et al. (2012) concluded that the bridgeextent along the line-of-sight is small compared to its ex-tent in the plane of the sky and the dominant componentof the gas velocities follows the bridge geometry with smallline-of-sight gradients. Applying a Virial analysis and as-suming a N (H ) /I CO conversion factor of a third of theGalactic Value, these GMAs have masses well below theVirial mass. They are thus far from being self-gravitating.The same behavior is observed in the Σ R – σ relation (Eq. 2)and is expected in a scenario where the turbulent ISM iscompressed adiabatically.The gas in the bridge region has different phases: themolecular gas is mainly arranged in a filament with a widthof ∼ i maximum stems fromgas which belongs to UGC 12914 than to the bridge (seesim19 in Fig. 7). The ionized gas is prominent at nega-tive velocities with respect to the systemic velocity. It thusbelongs kinematically more to UGC 12914. The morphol-ogy of the hot X-ray emitting gas is reminiscent of the gasdistribution of the northern bridge filament in sim19 andsim19fast. In our simulations this gas has mostly positivevelocities with respect to the systemic velocity. It is thusunlikely that the observed ionized gas coincides with thenorthern bridge filament. The observed H i in the bridge re-gion (Condon et al. 1993) has a double line structure, asthe ionized gas. At low velocities (4060 to 4320 km s − )the H i channel maps show a northwest–southeast velocitygradient. At high velocities (4440 to 4570 km s − ) thereseems to be a southwest–northeast gradient present. Thelow-velocity part of the H i emission belongs to UGC 12914,whereas the high-velocity part belongs to UGC 12915.What is the fate of the bridge gas? Will the high surfacedensity bridge region close to UGC 12915 collapse and formstars or will it expand and disperse? We think that most ofthe low-surface density, CO-emitting gas will disperse with-out forming stars. On the other hand, the high-density gas will probably have a different fate. It is remarkable thatthe luminous extraplanar H ii region close to UGC 12915does not coincide with a bridge GMA (but there is a GMAclose to it; lower panel of Fig. 3). This implies that the gascloud(s) from which the H ii region has formed has alreadybeen disrupted by stellar feedback (stellar wind and su-pernova explosions). For this process we offer the followingexplanation: the compression timescale is proportional tothe gas density (Eq. C.11), where the dissipation timescaleis proportional to the square root of the density (Eq. C.8).At the beginning of the phase of adiabatic compression thegas density is not too high permitting t comp < t diss . Duringthe phase of adiabatic compression the gas density increasesuntil t comp > t diss and the region collapses and forms stars.On the Spitzer 3 . µ m 1 . (cid:48)(cid:48) -resolution image the H ii regionis round and has FWHM of 5 (cid:48)(cid:48) or ∼ . ∼ × M (cid:12) assuming a N (H ) /I CO conversion factorwhich is one third of the Galactic value), but a comparablevelocity dispersion. The size of the Antennae cloud is only24 pc. This implies that GMA 9 will certainly be resolvedinto several distinct clouds. We can only speculate that sin-gle massive high-velocity dispersion molecular clouds col-lapsed due to their high density and formed the H ii regioncomposed of several dense star clusters. High-resolutionALMA CO observations (Appleton et al., in prep.) will givefurther insight into the formation scenario of this atypicalH ii region.We suggest that star clusters with extreme stellar densi-ties ( > ∼ stars pc − ), such as globular clusters and superstar clusters (O’Connell et al. 1994), formed and still formthrough the gravitational collapse of gas previously com-pressed by turbulent adiabatic compression during galaxyinteractions. During the compression phase the cloud accu-mulates mass and increases its velocity dispersion. The highvelocity dispersion prevents collapse but once the criticaldensity reached the turbulent energy is dissipated rapidlyand the cloud collapses and forms an extremely dense andmassive star cluster.This scenario probably applies to the extragalactic H ii region close to UGC 12915 (lower panel of Fig 3): the Pa- α emission of the H ii region detected in the HST NICMOS F190N filter (upper panel of Fig. 10) has a complex struc- Retrieved from the MAST HLA database.2 Vollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge
Fig. 9.
CO cloud properties. Upper panel: cloud Virial massas a function of the gas mass derived from the CO lumi-nosity. We applied a N (H ) /I CO conversion factor whichis one third of the Galactic value to the bridge clouds (redtriangles). The orange triangles correspond to a Galactic N (H ) /I CO conversion factor. Lower panel: cloud velocitydispersion as a function of the product of size and mass sur-face density. CPROPS clouds (bridge: red triangles; galax-ies: blue boxes) compared to data from Bolatto et al. (2008;green crosses) and Gratier et al. (2012; black pluses). Theorange triangles correspond to a Galactic N (H ) /I CO con-version factor. The solid line corresponds to Eq. 2.ture within a circular region of ∼
600 pc diameter: a centralprominent compact source with a FWHM of 0 . (cid:48)(cid:48) = 120 pcwith a northern extension and three fainter compact sourcesof about the same size. In the F187N off-band filter (lowerpanel of Fig. 10) only the prominent compact source anda second compact source in the northern ionized extensionare visible. The size of the compact source is in excess butcomparable to the size of the largest super star cluster in the Antennae galaxies (SSC˙B: FWHM of 1 (cid:48)(cid:48) = 95 pc andmass of 5 × M (cid:12) ; Gilbert & Graham 2007). The F187Nemission is either dominated by massive O stars if the su-per star clusters are younger than ∼ ∼
20 Myr. Based onthese findings we suggest that super star clusters were andmaybe still are formed within the bridge H ii region close toUGC 12915.
7. Conclusions
The Taffy system is composed of two massive spiral galaxieswhich had a head-on collision about 20 Myr ago. We presentnew high-resolution ( ∼ . (cid:48)(cid:48) ) CO(1-0) observations with thePlateau de Bure Interferometer. An rms of ∼ . − channel was reached by our observations. TheCPROPS software (Rosolowsky & Leroy 2006) was usedto identify and measure the properties of giant molecularcloud associations (GMAs). The detected CO luminosity ofthe Taffy system is L CO , tot = 4 . × K km s − pc . Wedivided the CO intensity map into disk and bridge regions(Fig. A.2). The CO luminosity of the bridge is L CO , bridge =1 . × K km s − pc , 25 % of the total CO luminosity.Assuming a Galactic N (H ) /I CO conversion factor for thegalactic disks and a third of this value for the bridge gas, weobtain H masses of M H , tot = 1 . × M (cid:12) and M H , tot =1 . × M (cid:12) . Thus, about 10 % of the molecular gas massis located in the bridge region.The bulk of the bridge high-density gas does not formstars (Braine et al. 2003, Gao et al. 2003). The lumi-nous extraplanar H ii region south of UGC 12915 repre-sents the exception to that rule. A close-up of the region(lower panel of Fig. 3) shows that the H ii region does notcoincide with, but is located at the northern edge of ahigh-surface brightness GMA (GMA 9 in Table 1) with aflux of 1 . × K km s − pc and a velocity dispersion of50 km s − ). This GMA has the highest velocity dispersionof the bridge GMAs.We separated the CO clouds identified by CPROPS intodisk and bridge clouds. It is remarkable that the GMAs inthe disk and bridge regions approximately follow the size–linewidth relation established by Bolatto et al. (2008) forextragalactic and Galactic molecular clouds. The scatteraround the relation is also comparable to that of Bolattoet al. (2008) and Gratier et al. (2012). On the other hand,the size–luminosity relations of the GMAs in the bridgeand disk regions are different: the bridge GMAs have lowerluminosities for their sizes than the disk GMAs and thebridge GMAs are clearly not virialized.The CO(1–0) observations were compared to the dy-namical models of Vollmer et al. (2012) together with a newsimulation. None of the simulations reproduce all observedfeatures of the Taffy system. However, all characteristicscan be found in one of the three models. Table 3 lists thefeatures reproduced (or not) by each of the models.Rapid turbulent adiabatic compression induced by the ∼ − collision could explain the high velocity dis-persions and the subsequent suppression of star formation(Fedderath & Klessen 2012; Padoan et al. 2012, 2017) in theTaffy bridge. In this scenario the turbulent velocity disper-sions of the largest eddies and their substructures/cloudsincrease such that GMCs are no longer in global virial equi-librium. ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 13 Fig. 10.
Close-up of the giant bridge HII region, CO(1-0)contours on the HST NICMOS F190N (Pa- α ; upper panel)and F187N (off-band; lower panel) image (PropID 11080,PI: D. Calzetti). The HST astrometry was approximatelyaligned with the Spitzer astrometry. Contour levels are(10 , , , , , , ,
80) K km s − .The suppression of star formation caused by turbulentadiabatic compression was implemented in the dynamical simulations: once the gas compression timescale is shorterthan the turbulent dissipation timescale, star formation issuppressed. This mechanism decreased the model star for-mation in the bridge region by a factor of about three tofive, consistent with observations.The bulk of the bridge molecular gas is not gravita-tionally bound and will disperse. The densest regions willprobably become self-gravitating and form stars as in thegiant bridge H ii region. Because of their enhanced velocitydispersion these regions are much denser and more massivethan common galactic GMCs. This mechanism could ex-plain the extreme stellar densities in globular clusters andsuper star clusters (O’Connell et al. 1994), as observed inthe Antennae. Acknowledgements.
We would like to thank the IRAM staff for thehelp observing the Taffy system with the PdBI. Based on obser-vations made with the NASA/ESA Hubble Space Telescope, andobtained from the Hubble Legacy Archive, which is a collabora-tion between the Space Telescope Science Institute (STScI/NASA),the Space Telescope European Coordinating Facility (ST-ECF/ESA)and the Canadian Astronomy Data Centre (CADC/NRC/CSA). Wethank Dominique Aubert for the creation of the 3D views.
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Appendix A: Moment maps and bridge separationAppendix B: Additional moment maps and 3Dviews of the datacubesAppendix C: Comparison with models
Our modeling effort is based on the combination of a large-scale dynamical model (Sect. C.1) together with a small-scale analytical model (Sect. C.3) to handle the propertiesof a turbulent ISM in a simplified way. All cloud–cloud colli-sions conserve mass and momentum. Our method is akin toa sticky-particle scheme (e.g. Combes & Gerin 1985) wherethe cloud-cloud collisions are resolved due to the high timeresolution. The dynamical simulations follow Boltzmann’sequation with a collisional term involving binary partiallyinelastic collisions.The simulations do not include stellar feedback and donot follow the thermal evolution of the gas. For the thermalevolution of the gas in a galaxy-galaxy head-on collision werely on the results of Yeager & Struck (2019). Our star for-mation recipe is based on cloud-cloud collisions (Sect. C.2).We verified that our SFR recipe based on cloud-cloud col-lisions leads to Schmidt-like star formation law ˙ ρ ∗ ∝ ρ . .Following Robertson & Goldreich (2012) and Mandal etal. (2020), we expect turbulent adiabatic heating to occurwhen the gas compression is faster than dissipation of tur-bulence t diss (Sect. C.4). Since t diss is not available fromthe dynamical model, we compare t comp to the t diss thegas would have if it formed stars as in a galactic disk (i.e.following a Kennicutt-Schmidt law). When compression en-ergy exceeds that of stellar feedback, the velocity dispersionis expected to increase. In this case, we assume that the ve-locity dispersion of the clouds also increases such that starformation will be signicantly reduced (Sect. C.5). C.1. Large-scale dynamics - the dynamical model
We used the dynamical simulations of Vollmer et al. (2012).The ISM is simulated as a collisional component, i.e. as dis-crete particles that possess a mass and a radius and canhave partially inelastic collisions. In contrast to smoothedparticle hydrodynamics (SPH), which is a quasi-continuousapproach where the particles cannot penetrate each other,our approach allows a finite penetration length, which isgiven by the mass-radius relation of the particles. Duringthe disk evolution, the cloud particles can have partially in-elastic collisions, the outcome of which (coalescence, massexchange, or fragmentation) is simplified following the ge-ometrical prescriptions of Wiegel (1994).
Fig. A.1.
Classical CO(1-0) moment maps. ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 15
Fig. A.2.
Separation between the disk and bridge regions.The particle trajectories are integrated using an adap-tive timestep for each particle. This method is describedin Springel et al. (2001). The criterion for an individualtimestep is ∆ t i = 5 km s − /a i , where a i is the accelerationof the particle i . The minimum value of ∆ t i defines theglobal timestep used for the Burlisch-Stoer integrator thatintegrates the collisional component. The global timestep is typically around 10 yr. For a velocity of 1000 km s − this corresponds to ∼
10 pc.During each cloud-cloud collision the overlapping partsof the clouds are calculated. Let b be impact parameterand r and r the radii of the larger and smaller clouds. If r + r > b > r − r the collision can result into fragmenta-tion (high-speed encounter) or mass exchange. If b < r − r mass exchange or coalescence (low speed encounter) can oc-cur. If the maximum number of gas particles/cloud (40000)is reached, only coalescent or mass exchanging collisions areallowed. In this way a cloud mass distribution is naturallyproduced. The cloud masses and velocities resulting from acloud-cloud collision are calculated by assuming mass andmomentum conservation. In Vollmer et al. (2012) we nor-malized the mass-size relation of the model clouds such thatthe gas mass of the bridge agrees with that derived from COobservations of the Taffy system. The cloud particle massesand radii range between 10 and 10 M (cid:12) and 35 and 145 pc,respectively. The gas particles/clouds cannot be taken asthe real clouds in the ISM of galactic disks, because the life-time of giant molecular clouds (GMCs) of several 10 Myr(e.g., Zamora-Aviles & Vazquez-Semadeni 2014) does notpermit frequent GMC-GMC collisions. On the other hand,during an ISM-ISM collision as in the Taffy system, there In addition, the integrator divided this timestep at least intothree sub-timesteps of about 3000 yr. will be a significant number of GMC-GMC collisions sincethe collision time is small t ∼ / (1000 km s − )=1 Myr.Following the direct cloud-cloud collision scenario of Harwitet al. (1987), the gas is heated to temperatures correspond-ing to a sizable fraction of the kinetic energy of the colli-sion (millions of K). The shock-heated gas will then cooldown with a rate that depends on its density. For a den-sity of 10 cm − the cooling rate is about 10 yr (Harwitet al. 1987). Note that there will also be collisions betweenthe clouds and more diffuse gas as simulated by Yeager &Struck (2020). Since we are only interested in the densemolecular gas, our cloud particles can be identified withcool gas a few Myr after impact. C.2. Star formation
In numerical simulations, the star formation recipe usu-ally involves the gas density ρ and the free-fall time t ff = (cid:112) π/ (32 Gρ ): ˙ ρ ∗ ∝ ρ t − ∝ ρ . . In our dynamical modelthe star formation rate (SFR) is proportional to the cloud-cloud collision rate and stars are formed in cloud-cloud col-lisions.The newly created star particles have zero mass (theyare test particles) and the positions and velocities of the col-liding clouds after the collision. These particles then movepassively with the whole system. The information about thetime of creation is attached to each newly created star par-ticle. The UV emission of a star particle in the two GALEXbands is modeled by the UV flux from single stellar popu-lation models from STARBURST99 (Leitherer et al. 1999).The age of the stellar population equals the time since thecreation of the star particle. The total UV distribution isthen the extinction-free distribution of the UV emission ofthe newly created star particles.We verified that our SFR recipe based on cloud-cloudcollisions leads to the same exponent (1.4-1.6; Fig. C.1) ofthe gas density in a simulation of an isolated spiral galaxyand for the Taffy system at impact and ∼
20 Myr after im-pact. As a consequence, our code reproduces the observedSFR-total gas surface density, SFR-molecular gas surfacedensity, and SFR-stellar surface density relations (Vollmeret al. 2012a). To go a step further we show the comparisonof our model results with observed scaling relations for themolecular gas surface density, star formation rate, and starformation efficiency in Fig. C.2. The model relations agreequite well with the observed relations.
C.3. Small-scale ISM properties - the analytical model:
The model of Vollmer & Beckert (2003) and Vollmer &Leroy (2011) considers the warm, cold, and molecularphases of the ISM as a single turbulent gas. The gas is takento be clumpy, so that the local density can be enhancedrelative to the average density of the disk. From the localdensity, the free-fall time of an individual self-gravitatinggas clump is used as the timescale governing star formation.The star formation rate is used to calculate the rate of en-ergy injection by supernovae. Turbulence is driven by thisenergy injection into turbulent eddies that have a charac-teristic length scale l driv and a characteristic velocity v turb ; l driv and v turb are linked to the volume filling factor of self-gravitating GMCs Φ V . All model parameters are describedin Table C.1. The Vollmer & Beckert (2003) model does not observations sim 19sim 19 fast sim 20 Fig. B.1.
CO(1-0) moment 1 maps together with the model H moment 0 maps. Upper left panel: PdBI observations,other panels: simulations.address the spatial inhomogeneity of the turbulent drivingnor the mechanics of turbulent driving and dissipation. Itis assumed that the energy input rate into the ISM due tosupernovae is cascaded to smaller scales without loss. Theenergy of self-gravitating clouds is dissipated via cloud con-traction and star formation. The smallest scale investigatedby the analytical model is the scale where the gas cloudsbecome self-gravitating. The size, density, and turbulentcrossing time of these clouds are l cl = l driv /δ , ρ cl = (cid:104) ρ (cid:105) / Φ V ,and t turb , cl = l cl /v turb , cl = δ − . l driv /v turb , where (cid:104) ρ (cid:105) is thelarge-scale gas density.Following Vollmer & Leroy (2011) the star formationrate per unit volume is given by˙ ρ ∗ = Φ V ρ t − , cl = (cid:112) Φ V ρ t − = (cid:15) ff ρ t − , (C.1)where Φ − = ρ cl /ρ is the overdensity of self-gravitatingclouds, ρ the gas density, t ff , cl the free-fall time of a self-gravitating gas cloud, t ff = (cid:112) π/ (32 G ρ ), and (cid:15) ff = √ Φ V ∝ t turb /t ff the star formation efficiency per free-falltime. Vollmer et al. (2017) found that for star formationrates comparable to those of nearby spiral galaxies and gasvelocity dispersions around 10 km s − , Φ V is about con-stant and has values of a few times 0 . (cid:15) ff = √ Φ V ∝ v turb , which is consistentwith the predictions of feedback-regulated star formationin turbulent, self-gravitating, strongly star-forming galac-tic gas disks (Ostriker & Shetty 2011, Faucher-Gigu`ere etal. 2013; however, see Krumholz et al. 2018 for a differentpoint of view).For self-gravitating clouds with a Virial parameter ofunity the turbulent crossing time equals twice the free-falltime: 2 t ff , cl = 2 (cid:115) π Φ V G (cid:104) ρ (cid:105) = √ l cl v turb , cl , (C.2)where l cl and v turb , cl are the size and turbulent 3D velocitydispersion of the cloud. Using Larson’s law ( l cl /v turb , cl = l driv /v turb / √ δ ), the star formation rate per unit volume is˙ ρ ∗ = 4 √ δ √ V (cid:104) ρ (cid:105) v turb /l driv . (C.3)We can connect the energy input into the ISM by SNe di-rectly to the star formation rate. With the assumption of aconstant initial mass function independent of environmentone can write 12 (cid:104) ρ (cid:105) v l driv = ξ ˙ ρ ∗ . (C.4) ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 17 observations sim 19sim 19 fast sim 20 Fig. B.2.
CO(1-0) moment 2 maps together with the model H moment 0 maps. Upper left panel: PdBI observations,other panels: simulations.This leads to the following expression for the volume fillingfactor: Φ V = √ v √ δξ , (C.5)and the star formation law becomes˙ ρ ∗ = (cid:115) √ √ δξ v turb ρ t − . (C.6)We thus find (cid:15) ff ∝ v turb , which is equivalent to Eq. 22 ofOstriker & Shetty (2011), Eq. 37 of Faucher-Gigu`ere et al.(2013), and Eq. 54 of Krumholz et al. (2018).Using Eq. C.1 and Eq. C.4, the large-scale turbu-lent crossing time, which equals the turbulent dissipationtimescale, is t turb = t diss = l driv v turb = v ξ √ Φ V (cid:115) π G (cid:104) ρ (cid:105) . (C.7)Inserting Eq. C.5 into Eq. C.7 leads to the final expressionfor the turbulent dissipation timescale: t diss = v turb (cid:115) π √ δ √ G (cid:104) ρ (cid:105) ξ . (C.8) Alternatively, we can assume a constant (cid:15) ff (Krumholz& McKee 2005, Krumholz et al. 2012). In this case theequation for the energy injection and dissipation becomes12 (cid:104) ρ (cid:105) v l driv = ξ(cid:15) ff (cid:104) ρ (cid:105) t − (C.9)and the dissipation timescale is t diss ,(cid:15) = v ξ (cid:15) ff (cid:115) π G (cid:104) ρ (cid:105) . (C.10)This timescale equals t diss (Eq. C.7) for v turb = (cid:15) ff (cid:113) ξ √ δ √ =6 . − . For higher velocity dispersions t diss ,(cid:15) > t diss .Within the framework of Vollmer et al. (2017) thedependence of (cid:15) ff on the turbulent velocity dispersion is (cid:15) ff ∝ √ v turb leading to t diss ∝ v . . For v turb >
10 km s − ,Eq. C.8 represents the lower limit for the dissipationtimescale. Since we require t comp < t diss for turbulent adia-batic compression, this lower limit of t diss is an appropriate,conservative choice.The dissipation timescale t diss is compared to the com-pression timescale t comp for the quiet disks before the in-teraction in Fig. C.3 and for the system ∼
20 Myr after im-pact in Fig. C.4. The dissipation timescale of the quiet disks observations sim 19 v r (km s − ) RA offset (arcsec) sim 19 fast sim 20 Fig. B.3.
Second 3D view of the observed CO(1-0) datacube and the model H data cubes. The axis labels are onlyshown for the observations. For a better understanding of these views, three 3D animations of the rotating datacube areattached to this figure ( taffy cube3D z.gif , taffy cube3D z1.gif , and taffy cube3D x.gif ).(right panel of Fig. C.3) shows the 1 / (cid:112) (cid:104) ρ (cid:105) -dependence ofEq. C.8. Roughly half of the particles have a 1D velocitydispersion of about 10 km s − (green contours), and about25 % have twice that velocity dispersion. Three quarters ofall particles have t comp > t diss (left panel of Fig. C.3).The picture changes for the system at the time of in-terest where we geometrically divided the system into abridge and disk+tidal tail regions. The majority of the gasparticles of the system show significantly higher velocitydispersions and thus higher t diss (right panels of Fig. C.4).At the same time the compression timescale of the majorityof particles is significantly shorter than those of the quietdisks (left panels of Fig. C.4). About half of the particleshave t comp < t diss . The gas densities in the bridge do notexceed (cid:104) ρ (cid:105) ∼
10 cm − (lower panels of Fig. C.4) which isdue to the coarse spatial resolution of our simulations. Thegas particles located within the bridge region almost ex-clusively have high velocity dispersions (lower right panel of Fig. C.4) and show t comp < t diss (lower left panel ofFig. C.4). C.4. Turbulent adiabatic compression
In our simulation of an isolated spiral galaxy the 1D ve-locity dispersion of the model clouds is constant, v disp ∼
10 km s − , during 1 Gyr. Since there is no stellar feedback,the cloud velocity dispersion is increased when the gas iscompressed. In kinetic theory, particles move with randommotions around the sound speed and over a length scalegiven by the collision mean free path. In the eddy-viscositymodel (Boussinesq approximation), eddies also move withrandom motions, at a typical speed given by the turbulentvelocity dispersion and over a typical length scale calledthe mixing length. Since these time scales are well-resolvedin our simulations, we can identify the particle/cloud ve-locity dispersion with the velocity dispersion of the largestturbulent eddies. ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 19 observations sim 19 v r (km s − ) DEC offset (arcsec)RA offset (arcsec) sim 19 fast sim 20 Fig. B.4.
Third 3D view of the observed CO(1-0) datacube and the model H data cubes. The axis labels are onlyshown for the observations. For a better understanding of these views, three 3D animations of the rotating datacube areattached to this figure ( taffy cube3D z.gif , taffy cube3D z1.gif , and taffy cube3D x.gif ).Since the dissipation timescale is not part of the dy-namical model, we compare the gas compression timescaleto the turbulent dissipation timescale t diss = l driv /v turb fol-lowing Eq. C.8, i.e. in the absence of adiabatic compression (Eq. C.4). The large-scale velocity dispersion and densityare taken from the dynamical model. Eq. C.8 implies thatthese quantities approximately correspond to their values atthe turbulent driving lengthscale. Within an unperturbed observations sim 19 v r (km s − ) DEC offset (arcsec) sim 19 fast sim 20 Fig. B.5.
Fourth 3D view of the observed CO(1-0) datacube and the model H data cubes. The axis labels are onlyshown for the observations. For a better understanding of these views, three 3D animations of the rotating datacube areattached to this figure ( taffy cube3D z.gif , taffy cube3D z1.gif , and taffy cube3D x.gif ).galactic disk the driving lengthscale is l driv = v turb t turb ∼
100 pc and 30 pc at densities of n ∼ − and 10 cm − ,respectively. These values are broadly consistent with (i)the length scale at which Elmegreen et al. (2003) observeda break in the Fourier transform power spectrum of az-imuthal optical and H i intensity scans and (ii) the verticalthickness of the Galactic cold neutral medium (Wolfire etal. 2003). The driving length in the bridge is estimated inSect. 5. Using Eq. C.7 instead of Eq. C.8 leads to equivalentnumbers of bridge clouds affected by adiabatic compressionat the time of interest (today).The timescales t diss (Eq. C.8) and t comp (Eq. 1) are im-portant to identify the primary source of energy loss. If t diss is shorter than t comp , then the dominant energy injectionmechanism is star formation and cloud-scale dissipation is more important than adiabatic compression. This is truefor galactic disks (Vollmer & Beckert 2003).The compression timescale was calculated using the con-tinuity equation d ρ d t + ∇ · ( ρ(cid:126)v ) = 0 . (C.11)All quantities which are needed to derive t comp and t diss are calculated from the dynamical model via a Smoothed-Particle Hydrodynamics (SPH)-type algorithm involvingthe 50 nearest neighbouring particles. ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 21 Table C.1.
Model Parameters.
Parameter Unit Explanation G = 5 × − pc yr − M − (cid:12) gravitation constant l driv pc turbulent driving length scale v turb pc yr − gas turbulent 3D velocity dispersion at l driv l cl pc cloud size v turb , cl pc yr − cloud 3D velocity dispersion σ cl pc yr − cloud 1D velocity dispersion δ = l driv /l cl scaling between driving length scale and cloud sizeΦ V volume filling factor of self-gravitating clouds (cid:104) ρ (cid:105) M (cid:12) pc − mean gas density t ff = (cid:112) π/ (32 G (cid:104) ρ (cid:105) ) yr ρ cl = (cid:104) ρ (cid:105) / Φ V M (cid:12) pc − cloud density t ff , cl yr cloud free fall timescale at size l cl t turb , cl yr cloud turbulent timescale at size l cl t life , cl yr cloud lifetime t dep yr gas depletion timescale˙ ρ ∗ M (cid:12) pc − yr − star formation rate per unit volume ξ = 4 . × − pc yr − constant relating SN energy input to SF (cid:15) ff star formation efficiency per free fall time f SF fraction of the star-forming molecular gas mass (cid:15) ∗ cloud mass fraction converted into stars (cid:15) life = t ff , cl /t life , cl cloud free-fall time divided by the lifetime t diss = l driv /v turb yr turbulent dissipation timescale t comp = ρ/ ( dρ/dt ) yr gas compression timescale C.5. Star formation suppression caused by turbulentadiabatic compression
It is generally assumed that within the disks of isolatedgalaxies turbulence is driven by energy injection throughstellar feedback (SN explosions). In an equilibrium state abalance between turbulent pressure and gravity is reachedleading to a global virial equilibrium state of the GMCs(Heyer et al. 2009). If the energy injection through large-scale gas compression exceeds that of stellar feedback de-duced via the star formation rate, the velocity dispersionof the largest eddies is expected to increase. In this case,we presume that the velocity dispersion of the turbulentsubstructures/clouds also increases (Fig. 2 of Mandal et al.2020). In our toy model, we decided to suppress star forma-tion during a cloud-cloud collision if the energy injection bylarge-scale gas compression exceeds that from stellar feed-back expected from an ISM that forms stars according to aKennicutt-Schmidt law. For the latter case, the turbulentenergy dissipation timescale t diss can be calculated via ouranalytical model.We included the effect of star formation suppression byturbulent adiabatic compression in the following way: if fora cloud-cloud collision t comp > t comp < t diss , no stel-lar particle is created. In addition, rapid expansion alsosuppresses star formation ( | t comp | < t diss / / C.6. Suppressed star formation in the Taffy bridge
We calculated the star formation rate within our simula-tions using the cloud-cloud collisions as described in Sect. 5.In the following, we separate the bridge region from thedisk regions based on geometry and the gas density. Theseconditions appear appropriate based on examining the sep-aration in three dimensions. Fig. C.5 shows the gas massin the model bridges. The total gas masses range between10 M (cid:12) for sim19fast to almost 3 × M (cid:12) for sim19.The total (disk and bridge) star formation rate is shownin Fig. C.6 for all three models. It is constant during about2 / Fig. C.1.
The local star formation rate ˙ ρ ∗ (in arbitraryunits) as a function of the volume density ρ . Upper panel:unperturbed simulation after 0 . ρ ∗ ∝ ρ n for the unperturbed galaxy simulationis n = 1 .
4, whereas it is n = 1 . µ m emission (Fig. 3). The corresponding maps from the models without turbulent adi-abatic compression are shown in Fig. C.11. The GALEXFUV image does not show structures whose morphology re-sembles that of the CO emission with the exception of thecompact star formation region close to UGC 12915. TheFUV images of sim19 and sim20 still show some trace ofthe dense bridge gas. Overall, sim19fast most resembles theGALEX UV image: the emission UGC 12914 and the bridgeregion are well-reproduced. However, as for the gas distri-bution, the model northern bridge filament is not presentin the observations. ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 23 Fig. C.2.
Model of an unperturbed spiral galaxy. Upperpanel: star formation rate as a function of the moleculargas surface density. Middle panel: star formation rate asa function of the stellar surface density. Lower panel: starformation efficiency with respect to the molecular gas as afunction of the stellar surface density. The solid lines markthe observed relations found by Leroy et al. (2008).
Fig. C.3.
Compression (Eq. C.8, left panel) and dissipa-tion (Eq. C.8, right panel) timescales as a function of themean gas density (cid:104) ρ (cid:105) for the quite disks before the interac-tion. Negative compression timescales, i.e. gas expansion,are marked as red points in the left panel. The green con-tours mark the regions of highest particle density in the (cid:104) ρ (cid:105) - t diss relation. Fig. C.4.
Compression (Eq. C.8, left panel) and dissipation(Eq. C.8, right panel) timescales as a function of the meangas density (cid:104) ρ (cid:105) for the timestep of interest of sim19. Themeaning of the colors is the same as in Fig. C.3. Upperpanels: all gas particles within the geometrically defineddisk and tidal tail regions. Lower panels: all gas particleswithin the geometrically defined bridge region. Fig. C.5.
Evolution of the total gas mass in the bridge. Thedotted vertical lines mark the impact time and the time ofinterest (today).
Fig. C.6.
Evolution of the normalized total star forma-tion rate. Solid line: with turbulent adiabatic compression.Dashed line: without turbulent adiabatic compression. Thedotted vertical lines mark the impact time and the time ofinterest (today). ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 25
Fig. C.7.
Evolution of the normalized total star formationrate in the bridge. Solid line: with turbulent adiabatic com-pression. Dashed line: without turbulent adiabatic compres-sion. The dotted vertical lines mark the impact time andthe time of interest (today). sim 19sim 19 fastsim 20
Fig. C.8.
Model maps of non-starforming and starforming gas. ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 27 sim 19sim 19 fastsim 20
Fig. C.9.
Model maps of gas affected by turbulent adiabatic compression and rapid expansion. observations sim 19sim 19 fast sim 20
Fig. C.10.
Observed star formation map based on Spitzer 24 µ m and GALEX FUV maps together with the model starformation maps. ollmer et al.: Low star formation efficiency due to turbulent adiabatic compression in the Taffy bridge 29 observations sim 19sim 19 fast sim 20 Fig. C.11.
Observed star formation map based on Spitzer 24 µ m and GALEX FUV maps together with the model starformation maps without the suppression of star formation by turbulent adiabatic compression. The relations between the model star formation rateand the molecular gas surface density of the three mod-els including adiabatic gas compression are presented inFig. C.12. Fig. C.13 shows the star formation efficiency(SFE=SFR/M H ) of models 19 and 20 without adiabaticgas compression. The SFE is approximately constant andthe gas located in the bridge has only a marginally lower(0 . ∼ sim 19sim 19 fastsim 20 Fig. C.12.