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Young2002AJ124.788

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Astronomical The Journal, 124:788810, 2002 August # 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A. MOLECULAR GAS IN ELLIPTICAL GALAXIES: DISTRIBUTION AND KINEMATICS L. M. Young Physics Department, New Mexico Institute of Mining and Technology, Socorro, NM 87801; lyoung@physics.nmt.edu Received 2002 March 10; accepted 2002 May 8 ABSTRACT I present interferometric images ($700...

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Astronomical The Journal, 124:788810, 2002 August # 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A. MOLECULAR GAS IN ELLIPTICAL GALAXIES: DISTRIBUTION AND KINEMATICS L. M. Young Physics Department, New Mexico Institute of Mining and Technology, Socorro, NM 87801; lyoung@physics.nmt.edu Received 2002 March 10; accepted 2002 May 8 ABSTRACT I present interferometric images ($700 resolution) of CO emission in five elliptical galaxies and nondetections in two others. These data double the number of elliptical galaxies whose CO emission has been fully mapped. The sample galaxies have 108 to 5 109 M of molecular gas distributed in mostly symmetric rotating disks with diameters of 212 kpc. Four out of the five molecular disks show remarkable alignment with the optical major axes of their host galaxies. The molecular masses are a few percent of the total dynamical masses that are implied if the gas is on circular orbits. If the molecular gas forms stars, it will make rotationally supported stellar disks that will be very similar in character to the stellar disks now known to be present in many ellipticals. Comparison of stellar kinematics to gas kinematics in NGC 4476 implies that the molecular gas did not come from internal stellar mass loss because the specific angular momentum of the gas is about 3 times larger than that of the stars. Key words: galaxies: elliptical and lenticular, cD -- galaxies: evolution -- galaxies: individual (UGC 1503, NGC 807, NGC 3656, NGC 4476, NGC 5666, NGC 4649, NGC 7468) -- galaxies: ISM -- galaxies: kinematics and dynamics -- ISM: molecules 1. INTRODUCTION It is now well known that elliptical galaxies often do have interstellar media with some cold neutral gas and dust. Huchtmeier, Sage, & Henkel (1995) have found that about two-thirds of ellipticals in the Revised Shapley-Ames (RSA) catalog contain H i at levels MH i=LB ! 103 in solar units; Wardle & Knapp (1986) reach similar conclusions. Colbert, Mulchaey, & Zabludoff (2001) find that dust is apparent in optical images of about 75% of all ellipticals regardless of their environment (field vs. X-raydetected poor groups). The molecular gas content of ellipticals is more difficult to quantify because, with few exceptions, only the ones that are bright in the far-infrared (FIR) have been searched. However, Knapp & Rupen (1996) quote CO detection rates of 20%80% for ellipticals that are brighter than 1 Jy at 100 lm. Since it was believed for many years that elliptical galaxies have little or no cold molecular gas, detailed studies of that molecular gas can offer fundamental insight into the evolution of ellipticals. For example, one would obviously like to know the origin of the molecular gas. Did it come from internal sources (stellar mass loss) or from an external source (another galaxy)? Has it been there for a Hubble time or significantly less? The distribution and kinematics of the molecular gas, and particularly comparisons of the specific angular momentum of the gas and the stars, can help clarify the origin of the molecular gas. Molecular gas is also the raw material for star formation. Therefore, the properties of the molecular gas determine where and how much star formation can happen; this determines the future morphology of the galaxy. Finally, molecular gas distribution and kinematics are valuable because the dissipational nature of gas means that the shapes of the gas orbits are much better known than are the stellar orbits (e.g., de Zeeuw & Franx 1989; Cretton, Rix, & de Zeeuw 2000). Gas kinematics can be used to infer the galaxy potential in a way that is more robust than, or at least complementary to, what one can do with stellar kinematics. This paper uses high-resolution CO 788 observations to investigate these ideas about elliptical galaxy structure and evolution. Several authors have used single-dish telescopes to search for CO emission from ellipticals. The largest of these works are Lees et al. (1991), Wiklind, Combes, & Henkel (1995, hereafter WCH95), and Knapp & Rupen (1996). A very small number of elliptical galaxies have been mapped in CO with millimeter interferometers or with multiple pointings on single-dish telescopes. These include NGC 759 (Wiklind et al. 1997), NGC 1275 (Reuter et al. 1993; Braine et al. 1995; Inoue et al. 1996), NGC 7252 (Wang, Schweizer, & Scoville 1992), NGC 1316 (Horellou et al. 2001), and NGC 5128 = Cen A (Quillen et al. 1992; Rydbeck et al. 1993; Charmandaris, Combes, & van der Hulst 2000). In all of these galaxies except NGC 7252, molecular gas is found in a rotating disk on the order of a kpc or a few kpc in radius and containing about 109 M of H2. In Cen A, a nearby galaxy which permits detailed observations, the large scale CO disk closely follows the prominent optical dust lane and is strongly warped (Quillen et al. 1992). About 10% of the CO in Cen A is associated with stellar and H i shells at galactocentric radii of 15 kpc (Charmandaris et al. 2000). The CO in NGC 7252, a merger remnant, has compact but irregular structure and kinematics. The present paper doubles the number of elliptical galaxies with CO maps; I show images of CO emission in five elliptical galaxies and nondetections in two others. In addition, the present sample is valuable because it employs a clearly defined set of selection criteria (in contrast to the semirandom collection of interesting galaxies mentioned above). 2. SAMPLE SELECTION The observed galaxies were chosen from a survey of CO emission in ellipticals that was made with the IRAM 30 m telescope by WCH95. WCH95, Lees et al. (1991), Gordon (1991), Sage & Wrobel (1989), Knapp & Rupen (1996), and several other sets of authors selected galaxies for single-dish MOLECULAR GAS IN ELLIPTICAL GALAXIES CO surveys based on a combination of IRAS 60 lm and 100 lm fluxes and galaxy type. The most common FIR flux criterion (used by WCH95 and all of the surveys mentioned here except Sage & Wrobel 1989) is S100 lm > 1:0 Jy, where the 100 lm fluxes were taken from the compilation of Knapp et al. (1989). WCH95 attempted to pick out `` genuine '' ellipticals by restricting their sample to galaxies known to have an r1=4 profile or, in their words, `` a consistent classification as E in several catalogs.'' Those criteria defined a sample of 29 ellipticals, of which 16 were detected in CO. The present sample contains all but one of the galaxies that were detected by WCH95 with 12CO 10 integrated intensities greater than 5.0 K km s1 (23 Jy km s1 ) and that lie within the declination range accessible to the BerkeleyIllinois-Maryland Association (BIMA) telescopes and the Owens Valley Radio Observatory (OVRO). NGC 759, which also meets these criteria, was excluded because a high-resolution CO map of this galaxy has already been published (Wiklind et al. 1997). To this list I also added NGC 4649, for which a CO detection is reported by Sage & Wrobel (1989). The resulting sample is given in Table 1. There is significant overlap between the sample selected here from the survey of WCH95 and other single-dish CO surveys. NGC 5666 and NGC 4476 have the second- and third-highest CO 21 intensities in the sample of 24 galaxies studied by Lees et al. (1991). NGC 5666 has the highest CO 21 intensity in the sample of seven ellipticals studied by Gordon (1991). The galaxies observed by WCH95 are found almost evenly divided among the field, groups, and clusters. Of the galaxies observed here, three are classified by WCH95 as being field ellipticals, one is a member of a small group, two are in the Virgo cluster, and one is most likely a merger remnant. If molecular gas is associated with dust, then this distribution of environments is consistent with the study of Colbert et al. (2001), who found that optical signatures of dust are found in field ellipticals at the same rate as in ellipticals in X-raybright groups. Additional discussion of selection effects in the present sample can be found in x 5.5. 3. OBSERVATIONS AND DATA REDUCTION 789 ten-element Berkeley-Illinois-Maryland Association (BIMA) millimeter interferometer at Hat Creek, CA (Welch et al. 1996). The BIMA observations were carried out in the C configuration (projected baselines 334 k) between 1998 November and 2001 June. One additional track in the D configuration was obtained for NGC 5666 in 1999 March, giving projected baselines down to 2.3 k for that galaxy. Each galaxy was observed with a single pointing centered on the optical center of the galaxy; the primary beam FWHM is about 10000 . Each observation covered a velocity range of about 1000 km s1 centered on the velocity of the CO detected by WCH95. The optical velocities of the galaxies are uncertain by up to 100 km s1, but are always well within the velocity range covered. Table 1 gives some basic data for the sample galaxies, and Table 2 summarizes important parameters of the observations and the final images. Reduction of the BIMA data was carried out using standard tasks in the MIRIAD package (Sault, Teuben, & Wright 1995). Electrical line length calibration was applied to most of the tracks, with a few exceptions in cases where the measurement was too noisy to be useful or where the line length was a very smooth function of time. Data from an atmospheric phase monitor (Lay 1999) were used to estimate the magnitude of amplitude decorrelation, as described by Regan et al. (2001) and Wong (2001). A small interferometer with a fixed 100 m baseline measures the rms path length difference in the signal from a commercial broadcast satellite; those data are scaled to the observing frequency and are scaled by projected baseline length raised to the 5/6 power to estimate the amount of amplitude decorrelation in the data (Akeson 1998).1 An rms path length difference of 300 lm on a 100 m baseline produces an amplitude decorrelation of 0.82 for observations at 3 mm wavelength (Akeson 1998), but the longest baseline in the present data is 88 m. Twelve tracks with rms path lengths less than 300 lm were not explicitly corrected for decorrelation because normal amplitude calibration can take out most of the decorrelation effect (Wong 2001). Fourteen tracks with rms path lengths in the range 300700 lm were corrected using the MIRIAD task uvdecor, which multiplies up the data ampli- 3.1. BIMA Data Six galaxies (UGC 1503, NGC 807, NGC 3656, NGC 4476, NGC 4649, and NGC 5666) were observed with the 1 BIMA Memo Series (Lay 1999; Akeson 1998) is available at: http:// bima.astro.umd.edu/memo/memo.html. TABLE 1 Sample Galaxies R.A. (J2000.0) 02 01 19.8 02 04 55.7 11 23 38.4 12 29 59.2 12 43 39.6 14 13 09.1 23 02 59.3 Decl. (J2000.0) +33 19 46 +28 59 15 +53 50 31 +12 20 55 +11 33 09 +10 30 37 +16 36 19 Velocity (km s1) 5086 (6) 4764 (12) 2869 (13) 1978 (12) 1117 (6) 2221 (6) 2081 (6) Distance (Mpc) 69 64 45 18 18 35 28 LB (1010 L) 1.7 3.2 1.6 0.35 6.7 0.63 0.39 Galaxy UGC 1503........ NGC 807 ......... NGC 3656........ NGC 4476........ NGC 4649........ NGC 5666........ NGC 7468........ Environment field field merger remnant Virgo cluster Virgo cluster field group Note.--Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. Velocities are taken from the NASA Extragalactic Database (NED); they refer to H i where available or to stellar velocities. The distance estimates are taken from WCH95, who used H0 75 km s1 Mpc1 and a Virgocentric infall model that is described in their paper. The members of the Virgo cluster were assumed to be at 18 Mpc. Blue luminosities are taken from integrated magnitudes in RC3; environmental descriptors are taken from WCH95. 790 YOUNG TABLE 2 Observation and Image Parameters Linear Resolution (kpc) 2.4 2.1 2.2 2.0 2.9 2.6 1.7 1.3 0.73 0.49 0.72 0.53 1.7 1.3 1.4 1.0 0.89 0.74 Vol. 124 Galaxy UGC 1503........ NGC 807 ......... NGC 3656........ NGC 4476........ NGC 4649........ NGC 5666........ NGC 7468........ Observation Dates 2000 Nov2001 Jun 2000 Dec2001 May 2000 Mar, Apr 2000 Mar, Apr 2000 May 1998 Nov1999 Apr 2001 Apr, May Flux Calibrator Uranus Uranus 3C 273 3C 273/Saturn 3C 273 Mars/3C 279 Uranus/3C 454.3 Velocity Range (km s1) 45305580 42305280 23753335 14802440 4501800 18652555 16282772 Beam (arcsec) 7.10 6.26 7.00 6.34 9.43 8.46 7.76 6.16 8.29 5.66 8.22 6.07 10.32 7.63 8.27 5.99 6.54 5.45 Channel (km s1) 30 30 50 30 20 30 20 30 30 30 20.8 Noise mJy beam 1 8.5 8.0 6.8 16 19 11 13 24 15 17 13 tudes to correct for decorrelation losses and decreases the weights of data with large decorrelation losses. Data with rms path lengths larger than 700 lm were generally not used. The worst track that was used had a median amplitude correction factor of 1.15. Amplitude corrections were applied to all observed sources and calibrators before the absolute flux calibration was made. Absolute flux calibration was based on observations of Uranus or Mars. When suitable planets were not available, I used the secondary calibrator, 3C 273, which is usually monitored several times per month (see Table 2). Phase drifts as a function of time were corrected by means of a nearby calibrator observed every 3040 minutes. Gain variations as a function of frequency were corrected by the online passband calibration system; inspection of the data for 3C 273 indicate that residual passband variations are on the order of 10% or less in amplitude and 2 in phase across the entire band. The calibrated visibility data were weighted by the inverse square of the system temperature and the inverse square of the amplitude decorrelation correction factor, then Fourier transformed. No continuum emission was evident in the line-free channels of any galaxy (Table 3). The dirty images were lightly deconvolved with the Clark clean algorithm, as appropriate for these compact, rather low signal-to-noise ratio detections. Integrated intensity and velocity field maps were produced by the masking method: the deconvolved image cube was smoothed along both spatial and velocity axes, and the smoothed cube was clipped at about 2.5 in absolute value. The clipped version of the cube was used as a mask to define a three-dimensional volume in which the emission is integrated over velocity. This masking method is described in greater detail by Wong (2001) and Regan et al. (2001). 3.2. OVRO Data One galaxy, NGC 7468, was observed with the six-element OVRO millimeter interferometer (Padin et al. 1991). Those data were obtained in the C, L, and E configurations (projected baselines 444 k) during 2001 April and May. A single pointing was made on the optical center of the galaxy; the primary beam FWHM was about 6500 . The correlator was set up with four modules of 32 channels, each channel 4 MHz wide; the modules were overlapped to cover a total bandwidth of 464 MHz. The data were calibrated using the MMA package (Scoville et al. 1993). Absolute flux calibration was based on observations of Uranus; the passband and time-dependent phase calibration used the nearby source 3C 454.3. The calibrated data were mapped in AIPS using `` natural '' weighting. Subsequent image analysis was identical to that for the BIMA data. TABLE 3 3 mm Continuum Flux Density Limits 3 mm Continuum (mJy) <5.0 <5.4 <13 <7.0 <12 <13 <5.3 4. RESULTS 4.1. Nondetections No CO emission was detected in the data cubes for NGC 4649 or NGC 7468. Upper limits to the CO fluxes from these galaxies were determined by first summing the data cube over a square region 22>5 on a side, centered on the optical center of the galaxy, to produce a spectrum. The 22>5 region was chosen to be similar in size and area to the beam of the IRAM 30 m telescope. A spectrum was also produced for a 5500 square region (similar to the area of the NRAO 12 m telescope) for NGC 4649. Nothing but noise is apparent in the spectra (Figs. 1 and 2). The spectra were then summed over the velocity ranges described below. The uncertainty in the sum is calculated from the rms in the spectrum and the number of channels summed, as described by Young (2000) and Lees et al. (1991); 3 limits are given in Table 4. This estimate assumes the channels are uncorrelated, which is an Galaxy UGC 1503......................... NGC 807 .......................... NGC 3656......................... NGC 4476......................... NGC 4649......................... NGC 5666......................... NGC 7468......................... Note.--Continuum images were made by averaging all of the line-free channels in the final image cubes. The values quoted here are 3 times the rms noise in the continuum images, so they should be interpreted as flux density limits for point sources at the centers of their host galaxies. No. 2, 2002 MOLECULAR GAS IN ELLIPTICAL GALAXIES 791 Fig. 1.--CO spectrum of a square region, 22>5 on a side, centered on the optical center of NGC 7468. Fig. 2.--CO spectrum of a square region, 22>5 on a side, centered on the optical center of NGC 4649. excellent assumption for these data, since no baseline or continuum emission needs to be subtracted. WCH95 reported a detection, which they characterize as tentative, of 6.7 K km s1 $ 31 Jy km s1 in the 12CO 10 line from NGC 7468. Their line is centered at 2300 km s1 (220 km s1 distant from the optical velocity) and 665 km s1 wide. The present OVRO observations give a sum of 4:7 2:9 Jy km s1 over the 22>5 square region and over the same velocity range as the CO line of WCH95. The OVRO data also give a sum of 3:6 2:0 Jy km s1 over the same spatial region but over a 300 km s1 velocity range centered on the H i velocity. (The H i line in NGC 7468 is about 200 km s1 wide at 20% of peak intensity; see van Driel et al. 2000.) Emission as strong as that reported by WCH95 should have been easily detected. I also consider it unlikely that CO in NGC 7468 is invisible to the interferometer by virtue of being smoothly distributed; the 2300 beam of the 30 m telescope is only 3 times larger than the 700 beam of the OVRO data, so the relevant spatial scales are well sampled in the interferometer data. Thus, the OVRO data for NGC 7468 confirm the nondetection of the 21 line of CO by Lees et al. (1991). Those authors quote an upper limit H2 mass of 8 107 M (after scaling to the conversion factor and distance assumed here), which is consistent with the present 6 107 M limit. Details of the H2 mass estimates are described in x 4.2. Sage & Wrobel (1989) report the detection of 18:7 2:3 Jy km s1 of emission in 12CO 10 from NGC 4649. Those observations were made with the NRAO 12 m telescope, which has a beam of 5500 ; the reported line is 225 km s1 wide. The detection is not considered tentative, but again there is a rather large offset (200 km s1) between the CO velocity and the optical velocity. A sum over a 5500 box and over the same velocity range noted by Sage & Wrobel (1989) gives an integrated flux of 33 18 Jy km s1 in the present images. A sum of the BIMA data over a 22>5 box and over a 300 km s1 range centered on the optical velocity of the galaxy gives an integrated flux of 5:6 6:0 Jy km s1. If the CO detected by Sage & Wrobel (1989) was smoothly distributed over the 225 km s1 velocity range and over the 5500 beam of the 12 m telescope, it would be too faint to be detectable in the current interferometer images. Furthermore, it would be invisible to the interferometer, which does not sample those 5500 spatial scales. If, however, the CO detected by Sage & Wrobel (1989) was concentrated within one 800 600 beam for each individual channel, it would have TABLE 4 H2 Mass and Morphology CO Diameter CO Flux (Jy km s1) 32.(6) 29.(6) 200.(20) 30.(3) <18. 39.(4) <6.2 M(H2) (108 M) 18 14 47 1.1 <0.68 5.7 <0.57 CO Shape P.A. (deg) 111.(1) 143.(1) 174.8 (0.1) 151.(1) ... 166.(5) ... Kinematic Major Axis P.A. (deg) 123 (2) 149 (3) 191 (3) 152 (1) ... 165 (2) ... Galaxy UGC 1503........ NGC 807 ......... NGC 3656........ NGC 4476........ NGC 4649........ NGC 5666........ NGC 7468........ (arcsec) 30 40 34 27 ... 28 ... (kpc) 11.(1) 12.(1) 7.4 (0.7) 2.4 (0.2) ... 4.7 (0.5) ... 0.37 (0.05) 0.58 (0.09) 0.73 (0.02) 0.57 (0.04) ... 0.11 (0.06) ... Note.--Upper limits are 3 for a 22>5 22>5 region and 300 km s1 velocity range. See text for further information. Ellipticities and position angles (both morphological and kinematic) for the CO distributions are the median values from fits to three or four images made at different resolutions or with different clip levels. The values in parentheses for these last three columns are estimates of the uncertainty based on the spread among the different fits, because those spreads are always larger than the formal uncertainties of the fits. Position angles are measured north through east to the receding major axis. 792 YOUNG Vol. 124 been detectable at the 48 level. Additional mosaic observations of NGC 4649 in BIMA's D configuration have better sensitivity to large-scale structures; those observations will be reported in a future paper, and they also fail to detect CO in NGC 4649. 4.2. CO Fluxes and H2 Masses For the galaxies with CO detections, Figures 37 show images of the integrated CO intensity, individual channel maps, velocity fields, spectra, and position-velocity diagrams along the major axis. Total fluxes were measured from the integrated intensity images in Figures 3a, 4a, 5a, 6a, and 7a. The uncertainties in the CO fluxes are probably 10% for the stronger detections (NGC 3656, NGC 4476, and NGC 5666), dominated mostly by the absolute calibra- tion. For NGC 807 and UGC 1503 the uncertainty is probably a bit larger, perhaps 15%20%, because of uncertainties in the absolute calibration and in choosing the spatial region to be summed. The CO fluxes measured in the present images of UGC 1503, NGC 807, and NGC 4476 are consistent within 20% of the 12CO 10 fluxes measured by WCH95 using the IRAM 30 m telescope. WCH95 detected a larger CO flux from NGC 5666, 60 Jy km s1, than I find in the BIMA image (40 Jy km s1). The difference is nominally larger than the combined uncertainties, which are about 10% for the BIMA image and probably 10%15% for the data of WCH95 (C. Henkel 2002, private communication). However, there is no compelling evidence that the interferometer has missed a significant component of the molec- Fig. 3a Fig. 3.--UGC 1503. (a) Molecular gas. Gray scale and black contours are an optical image from the red portion of the second-generation Digitized Sky Survey. Heavy white contours show the CO integrated intensity in units of 20%, 10%, 10%, 20%, 30%, 50%, 70%, and 90% of the peak, which is 6.3 Jy beam1 km s1 3:9 1021 cm2 using the H2/CO conversion factor described in x 4.2. The small ellipse at the top indicates the size of the beam. (b) Individual channel maps showing CO emission. Contour levels are 3, 2, 2, 3, 5, 8.3, 13.9, and 23.1 times 8.0 mJy beam1 $1 . The velocity of each channel (in km s1) is indicated in the upper left corner and the beam size in the upper right corner. The cross marks the kinematic center of the gas, which coincides with the morphological center of the gas and the optical center to within 100 200 . (c) Velocity field. The CO intensity-weighted mean velocity (moment 1) is shown in gray scale and in contours from 4860 to 5120 km s1 in steps of 20 km s1. The ellipse shows the beam size. (d ) CO spectrum. The spectrum was constructed by first using the integrated intensity image (a) to define an irregular mask region within which the emission is located. The intensity was integrated over the same spatial region for every channel, so the noise in the line-free regions of the spectrum should be indicative of the noise on the line as well. (e) position-velocity diagram. This slice is centered on the kinematic center of the molecular gas (R.A. 02h01m1998, decl. +33 190 4700 , J2000) and follows the kinematic major axis at 123 . Contour levels are 20%, 20%, 30%, 50%, 70%, and 90% of 61.1 mJy beam1. No. 2, 2002 MOLECULAR GAS IN ELLIPTICAL GALAXIES 793 Fig. 3b ular gas in this galaxy. Conversely, the images shown here reveal that the molecular gas distributions for UGC 1503, NGC 4476, and NGC 5666 are not very much larger than the 2300 (FWHM) beam of the 30 m telescope, so there is no compelling evidence that the single-dish spectra missed significant components of the molecular gas in these galaxies. The exception to this latter statement is NGC 3656, which has a factor of 2 larger flux in the BIMA images than in the spectrum of WCH95; most likely this is because the gas dis- tribution is larger than the 30 m beam. The CO line widths agree well in all cases. H2 masses (Table 4) are calculated using the distances in Table 1 and a `` standard '' H2/CO conversion factor of 3:0 1020 cm2 (K km s1)1, as in WCH95. With this conversion factor, H2 masses are related to CO fluxes SCO by MH2 1:18 104 M D2 SCO , where D is the distance in Mpc and SCO is the CO flux in Jy km s1. No correction has been made for the presence of helium. 794 YOUNG Vol. 124 Fig. 3c Fig. 3d Fig. 3e 4.3. CO Morphology Figures 3a, 3b, 4a, 4b, 5a, 5b, 6a, 6b, 7a, and 7b show integrated CO intensity maps and channel maps for the five galaxies with detected CO emission. The molecular gas in these five elliptical galaxies is found in very regular, symmetric rotating disks with diameters of a few up to 12 kpc. The disks appear flat at the current resolution and sensitivity; the only feature that can be reliably identified outside of the flat disks is in NGC 3656 (Fig. 5a). In this galaxy, the majority of the molecular gas is found in a disk oriented northsouth, following the optical dust lane (Balcells et al. 2001). Roughly 6% of the galaxy's total CO flux comes from a feature at 11h23m40s, 53 500 2000 (J2000), about 1000 west of the southern end of the main CO disk. The feature is also visible in the individual channel images (Fig. 5b) near 2975 km s1. The features above and below the disk of NGC 807 (Fig. 4a) may simply be noise. With the current rather low resolution it is difficult to be sure whether the elongated molecular gas distributions come from disks or bars. I assume in the majority of this paper that they are disks because of the characteristic `` butterfly '' pattern, which is apparent in the channel maps for UGC 1503, NGC 807, and NGC 4476 (Figs. 3b, 4b, and 6b). No. 2, 2002 MOLECULAR GAS IN ELLIPTICAL GALAXIES 795 Fig. 4a Fig. 4.--NGC 807. (a) Molecular gas. Heavy white contours show the CO integrated intensity in units of 20%, 10%, 10%, 20%, 30%, 50%, 70%, and 90% of the peak (7.6 Jy beam1 km s1 2:6 1021 cm2). Other features as in Fig. 3a. (b) Individual channel maps showing CO emission. The contour intervals are the same as for Fig. 3b, but the multiplicative unit is 1 6:8 mJy beam1. The cross marks the kinematic center of the molecular gas; that location is coincident with the optical center of the galaxy, given the uncertainties (about 200 ) in each position. (c) Velocity field. The CO intensity-weighted mean velocity (moment 1) is shown in gray scale and in contours from 4450 to 4900 km s1 in steps of 50 km s1. The ellipse shows the beam size. (d ) CO spectrum, constructed in the same manner as for Fig. 3d. (e) Position-velocity diagram. This slice is centered on the kinematic center of the molecular gas (R.A. 02h04m5596, decl. +28 590 1700 , J2000) and follows the kinematic major axis at 149 . Contour levels are 20%, 20%, 30%, 50%, 70%, and 90% of 56.8 mJy beam1. In this pattern, the channels near to the systemic velocity show gas distributions that are elongated in the direction of the kinematic minor axis, but the edge channels show much more compact gas distributions. This pattern is characteristic of roughly circular gas disks inclined to the line of sight. NGC 807 and UGC 1503 also show rotation curves that rise and then flatten in the manner common to spiral galaxy gas disks (x 4.4). The butterfly pattern is not obvious in the channel maps for NGC 3656 (Fig. 5b); I continue to assume that the gas is in a disk rather than a bar, but higher resolution observations would be beneficial. Two of the galaxies show evidence for asymmetries in their gas distributions (the CO emission is stronger on one side than the other). This effect is dramatic for NGC 807 (Fig. 4a), where approximately 30% of the CO emission comes from the northwest half of the galaxy and 70% from the southeast half. The asymmetry is also apparent in the channel maps of Figure 4b, where the peak intensity in the channel at 4880 km s1 is 10 but the peak intensity in the matching channels on the other side of the systemic velocity (4430 and 4480 km s1) is only 5 . Such a large intensity difference is unlikely to be due to noise. WCH95's spectrum of NGC 807 does not show the high-velocity side to be stronger than the low-velocity side, but this is probably because the peak intensity in the 4880 km s1 channel occurs 1000 away from the galaxy center (see also Fig. 4c). This means that the strongest emission in the galaxy comes from regions at the half-power point of the IRAM 30 m telescope beam, and the 30 m telescope has much less sensitivity to this feature than the interferometer. A lopsided CO distribution is 796 YOUNG Fig. 4b also evident in NGC 4476 (Fig. 6a), although to a lesser extent. None of the galaxies show definitive evidence for CO at large radii as in Cen A (Charmandaris et al. 2000). In that galaxy, at least 10% of the CO emission of the galaxy is not associated with the optical dust lane but is found in stellar shells at 15 kpc radius. The rms noise levels in the images (Table 2) are such that an unresolved source appearing in one channel at the 5 level would have a CO flux of 12 Jy km s1, which is less than 10% of the CO fluxes of all of the galaxies detected here (Table 4). Thus, if 10% of the CO emission were in features like those of Cen A it would most likely have been detected. The numbers are particularly compelling for NGC 3656 (the galaxy that, optically, looks most disturbed). Molecular gas associated with the optical shell and containing as little as 1% of the total CO flux of that galaxy would probably have been detected. Thus, the present images suggest that Cen A is unique or at least unusual in having such large quantities of molecular gas associated with its shells. Fig. 4c Fig. 4d Fig. 4e 798 YOUNG Vol. 124 Fig. 5a Fig. 5.--NGC 3656. (a) Molecular gas. Heavy white contours show the CO integrated intensity in units of 5%, 2%, 2%, 5%, 10%, 20%, 30%, 50%, 70%, and 90% of the peak (81.1 Jy beam1 km s1 4:7 1022 cm2). Other features as in Fig. 3a. (b) Individual channel maps showing CO emission. As for Fig. 3b, but the contour levels are multiplied by 1 16 mJy beam1. The cross marks the morphological center of the molecular gas, which is coincident with the optical center to 100 . (c) Velocity field. The CO intensity-weighted mean velocity (moment 1) is shown in gray scale and in contours from 2650 to 3000 km s1 in steps of 50 km s1. The ellipse shows the beam size. (d ) CO spectrum, constructed in the same manner as for Fig. 3d. (e) Position-velocity diagram. This slice is centered on the morphological center of the molecular gas (R.A. 11h23m38957, decl. +53 500 32>3, J2000) and follows the kinematic major axis at 191 . Contour levels are 20%, 10%, 10%, 20%, 30%, 50%, 70%, and 90% of 292.7 mJy beam1. In order to quantify the axis ratios and position angles of the CO distributions, the integrated intensity maps were fitted with elliptical Gaussians. The ellipticity and position angle of the fitted Gaussians are given in Table 4 along with estimates of the maximum detected extent of the CO. 4.4. CO Kinematics Initial kinematic analysis of the molecular gas was performed by fitting simple solid body rotation profiles to the velocity fields in Figures 3c, 4c, 5c, 6c, and 7c. NGC 807 and UGC 1503 were also fitted with profiles that rise in their inner parts and then flatten. None of these fits constrain the disk inclination angles i or maximum rotation velocity particularly well; the product V sin i is better constrained. But this procedure does give good estimates of the position angle of the kinematic major axis (Table 4), which were used for the position-velocity plots in Figures 3e, 4e, 5e, 6e, and 7e. Since the fits are weighted by the integrated intensity, the fitted angle is really the kinematic major axis at small radii. The only case in which the major axis clearly varies with radius is NGC 3656, which is described in more detail below. Table 4 compares the morphological major axis described in x 4.3 to the kinematic major axis for each galaxy. In two cases (NGC 5666 and NGC 4476) the two axes are aligned to within a degree or so, well within the combined errors. In these galaxies all of the evidence is consistent with the molecular gas being in an intrinsically circular disk. In one case (NGC 3656) there is a dramatic misalignment of nearly 17 between the two angles in Table 4, much larger than the combined errors of the fits. This misalignment is clearly visible in Figure 5c from the fact that the kinematic minor axis (the isovelocity curve at the systemic velocity) is not perpendicular to the kinematic major axis at large radii or to the morphological major axis. However, the kinematic major axis at large radii does appear to be closely aligned with the morphological major axis. Thus, the molecular gas No. 2, 2002 MOLECULAR GAS IN ELLIPTICAL GALAXIES 799 Fig. 5b in NGC 3656 is either in a warped disk or is on elliptical orbits in a nonaxisymmetric potential (Binney & Merrifield 1998, pp. 513, 713715).Optical images of this galaxy clearly show an S-shaped dust lane (e.g., Balcells et al. 2001), in which the twist of the dust lane is in exactly the sense needed to explain the twist in the CO kinematic major axis, so the CO probably follows the warped dust lane. The remaining two cases (NGC 807 and UGC 1503) show moderate misalignments of 6 and 12 between the CO morphological and kinematic major axes. These misalignments are nominally greater than the uncertainties in the fits, but they are probably not reliable. These are the two galaxies for which the morphological position angles are the most questionable because the integrated intensity contours are the least elliptical. The position-velocity diagrams show steeply rising, approximately solid body rotation regions in the center of each galaxy. In NGC 4476 and NGC 5666 the CO does not extend past the region of solid body rotation, which is at least 34 beams across. In NGC 3656 there are some signs that the CO rotation flattens curve near the edges of the CO distribution; note in particular the low-velocity side of the position-velocity diagram (Fig. 5e) and the velocity field (Fig. 5c). In NGC 807 and UGC 1503 (the most luminous 800 YOUNG Vol. 124 Fig. 5c Fig. 5e Fig. 5d galaxies of the sample, with the largest CO disk linear sizes) the rotation curve clearly turns over and becomes flat at radii of approximately 2.0 kpc (NGC 807) and 1.4 kpc (UGC 1503). For these latter two galaxies whose rotation curves turn over, the kinematic centers of the gas are coincident with the optical centers of the galaxies (Cotton, Condon, & Arbizzani 1999) within an arcsecond or so (10% of the beam). For NGC 4476, NGC 3656, and NGC 5666 the kinematic centers are not well constrained, but the morphological centers of the molecular gas disks are closely coincident with the optical centers. No. 2, 2002 MOLECULAR GAS IN ELLIPTICAL GALAXIES 801 Fig. 6a Fig. 6.--NGC 4476. (a) Molecular gas. Heavy white contours show the CO integrated intensity in units of 20%, 10%, 10%, 20%, 30%, 50%, 70%, and 90% of the peak (12.4 Jy beam1 km s1 7:3 1021 cm2). Other features as in Fig. 3a. (b) Individual channel maps showing CO emission. As for Fig. 3b, but the contour levels are multiplied by 1 11:5 mJy beam1. The cross marks the morphological center of the gas, which is coincident with the optical center of the galaxy to about 200 . (c) Velocity field. The CO intensity-weighted mean velocity (moment 1) is shown in gray scale and in contours from 1860 to 2040 km s1 in steps of 20 km s1. The ellipse shows the beam size. (d ) CO spectrum, constructed in the same manner as for Fig. 3d. (e) Position-velocity diagram. This slice is centered on the morphological center of the molecular gas (R.A. 12h29m59906, decl. +12 200 54>2, J2000) and follows the kinematic major axis at 152 . Contour levels are 15%, 15%, 30%, 50%, 70%, and 90% of 125.1 mJy beam1. The crosses indicate stellar velocities measured along the major axis by Simien & Prugniel (1997); they have been uniformly shifted in velocity by 12 km s1 to make the systemic velocity of the stars agree with that of the molecular gas. The difference between heliocentric velocities (in the stellar data) and local standard of rest (in the CO) is 4 km s1 at this position. 4.5. Dynamical Masses These interferometric observations provide two important pieces of information that are missing from single-dish CO surveys of ellipticals: the linear sizes and axial ratios of the molecular disks. If the disks are assumed to be intrinsically circular, with gas on circular orbits, the inclination angle of the disk is given by i ! cos1 b=a where b=a is the minor/major axis length ratio and the equality is achieved only in the limit that the disk is very thin. The observed gas velocities can then be used to calculate the dynamical mass interior to the disk's outer edge: Mdyn 2:33 105 M V 2 R ; where R is the radius of the outer edge in kpc and V is the observed velocity in km s1, corrected for inclination. The implied dynamical masses (Table 5) range from a few 109 M to nearly 1011 M interior to the edge of the CO disk, and the observed masses of molecular gas are a few percent of these dynamical masses. Table 5 also gives the orbital time for gas at the edges of the CO disks. 802 YOUNG Vol. 124 Fig. 6b 4.6. CO versus Stellar Morphology Optical images from the red plates of the second-generation Digitized Sky Survey (DSS) were used in a comparison of CO and stellar morphologies. After sky subtraction, elliptical isophotes were fitted to the optical images. The ellipticity, position angle, and center of each isophote were allowed to vary freely. The isophote fits are generally not good within a semimajor axis of 500 , where the Sky Survey images are overexposed, or beyond 3000 , where the images are underexposed. The region from 1000 to roughly 3000 is comparable to the size of the CO disks, and that is the region I focus on here. A second round of fitting, in which the ellipse centers were held fixed, did not significantly change the results over this radius range. For comparison purposes, elliptical isophote fits were also performed on the J, H, and K images of NGC 4476 from the Two Micron All Sky Survey (2MASS) data. Isophote fits to NGC 3656 are more complicated because of the fine structure and the prominent dust lane, so the results of Balcells (1997) are used for that galaxy. Table 6 gives the radius range over which the isophote fits are considered reliable, the mean ellipticity and position angle for each galaxy, and the dispersion about the mean for roughly 12 independently fitted annuli in that radius range. NGC 807, NGC 4476, and NGC 3656 are better described by r1=4 surface brightness profiles than by exponential profiles over the radius range in question. UGC 1503 and NGC 5666 are about equally well fitted by either, although the reliable radius range for NGC 5666 is rather small. There is no evidence of position angle twist in any of the galaxies except for NGC 5666, which shows a 10 change in position angle at semimajor axes around 1500 . UGC 1503 shows no significant trend in ellipticity with radius, but the others do, and the dispersions about the mean ellipticities are determined mostly by the magnitude of those trends. The Sky Survey data for NGC 4476 give results that are consistent with those from the 2MASS data and the work of Prugniel, Nieto, & Simien (1987); my fits for UGC 1503 are consistent with those of Fasano & Bonoli (1989). The stellar isophotes are significantly rounder than CO isophotes, as one would expect in the case where the stars are dynamically hot and gas is dynamically cold. The only exception to this statement is NGC 5666, where the stars and the gas have equal ellipticities within the errors. Table 6 also gives the misalignment angle between the optical major axis and the CO kinematic axis; except for NGC 3656, No. 2, 2002 MOLECULAR GAS IN ELLIPTICAL GALAXIES 803 Fig. 6c Fig. 6e Fig. 6d which is close to a minor axis gas/dust disk, they are close to zero. In other words, four of the five galaxies have remarkably well aligned (within 13 ) major axis gas disks. 5. DISCUSSION 5.1. The Origin of the Molecular Gas Two ideas about the origin of molecular gas in ellipticals are (1) that the gas came from mass loss from the galaxy's own evolved stars or (2) that the gas was acquired in an interaction or a merger with another gas-rich galaxy. In the second category I also include the idea that the molecular gas in ellipticals may simply be left over from the formation of the elliptical, if ellipticals are formed by the merger of two roughly equal mass spiral galaxies (Toomre & Toomre 1972). In the first model, internal stellar mass loss, Faber & Gallagher (1976) estimate that mass-loss rates would be 1.5 M yr1 per 1011 L of optical luminosity. Over 1010 yr, this gas would be comparable to the observed gas masses, at 804 YOUNG Vol. 124 Fig. 7a Fig. 7.--NGC 5666. (a) Molecular gas. Heavy white contours show the CO integrated intensity in units of 10%, 5%, 5%, 10%, 20%, 30%, 50%, 70%, and 90% of the peak (21.3 Jy beam1 km s1 7:5 1021 cm2). Other features as in Fig. 3a. (b) Individual channel maps showing CO emission. As for Fig. 3b, but the contour levels are multiplied by 1 15 mJy beam1. The cross marks the morphological center of the molecular gas, which coincides with the optical center given in NED to better than 100 . (c) Velocity field. The CO intensity-weighted mean velocity (moment 1) is shown in gray scale and in contours from 2120 2340 km s1 in steps of 20 km s1. The ellipse shows the beam size. (d ) CO spectrum, constructed in the same manner as Fig. 3d. (e) Position-velocity diagram. This slice is centered on the morphological center of the molecular gas (R.A. 14h33m09925, decl. +10 300 38>7, J2000) and follows the kinematic major axis at 165 . Contour levels are 20%, 10%, 10%, 20%, 30%, 50%, 70%, and 90% of 149.7 mJy beam1. least within a factors of a few (the uncertainties in the H2/ CO conversion factor are at least factors of a few). The difficulty with this model is that the cold gas contents of elliptical galaxies are uncorrelated with their optical luminosities (Knapp, Turner, & Cuniffe 1985; Lees et al. 1991). Furthermore, the stellar mass loss is thought to be shock-heated by the stellar velocity dispersions to X-ray temperatures, and the hot plasma is thought to destroy dust grains on relatively short timescales (Wiklind & Henkel 2001). The second idea, that the molecular gas in ellipticals has been acquired in a major or minor merger, may plausibly agree with the data presented here. Barnes (2002) has shown, via numerical simulations, that the merger of two gas-rich spiral galaxies produces systems that are qualitatively similar to the present sample of ellipticals and their gas disks. Some of the gas loses its angular momentum in shocks and falls to the nucleus of the galaxy, but up to 60% of the original gas contained in the spirals can form a rota- tionally supported gas disk with a radius of up to 20 kpc. Thus, the gas disks formed in these simulations are large enough to explain the observed gas disks (keeping in mind that the mass and size of the simulated disks are highly dependent on the geometry of the interaction). More careful analysis of the distribution and kinematics of the molecular gas in these ellipticals offers some important insight into these competing models and the origin of the molecular gas. 5.1.1. Gas and Stellar Kinematics Figure 6e shows CO and stellar kinematics along the major axis of NGC 4476. The stellar kinematics are taken from Simien & Prugniel (1997), who also give a value of 14>8 for the effective radius (re ) of this galaxy. The CO velocity rises linearly with radius to a maximum velocity of 100 km s1 at 700 radius. The stellar velocities also rise linearly with radius to a maximum rotation velocity of 35 km No. 2, 2002 MOLECULAR GAS IN ELLIPTICAL GALAXIES 805 Fig. 7b s1 (3 times smaller than the CO velocity) at 700 radius. Beyond 700 , the stellar velocities appear to decline again, so that there is little sign of rotation at re . The stellar velocity dispersion is 65 13 km s1 in the center of the galaxy, much larger than the stellar rotation velocities; the stars are primarily pressure-supported rather than rotationally supported. This means that the stellar rotation velocities in Figure 6e significantly underestimate the circular rotation speed of the galaxy (the asymmetric drift effect). The cold molecular gas probably gives a good indication of the circular speed. But the stellar rotation velocities do indicate the specific angular momentum of the stars. Within re , the specific angular momentum of the gas is about 3 times larger than that of the stars. Furthermore, if the observed trend in stellar rotation continues beyond re , then the stars in the outer parts of the galaxy also have very small specific angular momentum. If internal stellar mass loss had produced this molecular gas, one would expect the gas to have the same specific angular momentum as the stars, or perhaps smaller, and this is clearly not the case. The only way to reconcile the specific angular momenta of the gas and the stars is to suppose that they have very different inclinations to the line of sight, but that would again be unlikely if the gas originated in the stars. An external origin for the gas in NGC 4476 is strongly favored. A similar situation seems to be true for NGC 3656. Balcells & Stanford (1990) obtained stellar kinematics along two position angles, both of which are 50 away 806 YOUNG Vol. 124 Fig. 7c Fig. 7d Fig. 7e from the CO major axis. They infer that the maximum stellar rotation velocity in the inner 1000 is on the order of 50 km s1 and that the stellar rotation axis is very close to what is now known to be the CO rotation axis. The CO rotation velocity is 270 km s1, five times larger than that of the stars, but firm statements about the specific angular momenta of the stars and the gas are not possible in this case because the stellar rotation curve may still be rising at large radii. Similar comparisons of gas and stellar kinematics for the other galaxies in the sample will be vital for a broader understanding of the origin of the molecular gas in ellipticals. No. 2, 2002 MOLECULAR GAS IN ELLIPTICAL GALAXIES TABLE 5 Dynamical Masses i (deg) 51 65 74 65 27 V sin i (km s1) 130 (10) 230 (10) 270 (10) 100 (10) 100 (20) V (km s1) 167 (13) 254 (11) 280 (10) 110 (11) 217 (43) R (kpc) 5.5 (0.6) 6.2 (0.6) 3.7 (0.4) 1.2 (0.1) 2.4 (0.2) Mmin (1010 M) 2.2 7.6 6.3 0.27 0.55 Mmax (1010 M) 3.6 9.3 6.8 0.34 2.6 torb (108 yr) 2.0 1.5 0.82 0.66 0.75 807 Galaxy UGC 1503........ NGC 807 ......... NGC 3656........ NGC 4476........ NGC 5666........ M(H2)/Mdyn 0.0500.082 0.0150.018 0.0700.075 0.0340.042 0.0220.10 Note.--The inclination angle i of the gas disk is given by cos i 1 , with given in Table 4. If the gas disk is not thin, i is a lower limit, and the true circular velocity will be somewhere between V sin i and V; the enclosed dynamical mass will be between Mmin and Mmax. The range in M(H2)/Mdyn comes from the range in the enclosed dynamical mass, ignoring the uncertainty in the H2/CO conversion factor, which is probably at least 50%100%. 5.1.2. Orientation of Molecular Gas and Dust There are two cases in the present sample for which published optical images clearly show that there is a very close correspondence between the dust and molecular gas distributions. These cases include NGC 3656, mentioned in x 4.4, and NGC 4476. Tomita et al. (2000) show that the dust in NGC 4476 is settled into a very regular, highly inclined disk of diameter 2000 ; the CO disk is also very regular, highly inclined, and has diameter of 2700 . The other galaxies of the present sample do not have good dust images in the literature, and dust features are not visible in the Digitized Sky Survey images, so detailed comparisons of their dust versus CO morphologies will require higher quality optical images. As mentioned in x 5.1, the cold gas contents of ellipticals are unrelated to their optical luminosities, and this fact is usually interpreted as evidence of the gas's external origin (Wardle & Knapp 1986; Lees et al. 1991). But the cold gas and dust distribution within an individual galaxy are clearly not independent of the stars. van Dokkum & Franx (1995) studied the orientations of dust features in Hubble Space Telescope (HST) images of ellipticals; they found that dust features with semimajor axes smaller than 250 pc are well aligned with the optical major axes of their host galaxies. More recent workers (Verdoes Kleijn et al. 1999; Martel et al. 2000; Tran et al. 2001) classify dust features into two classes: (1) smooth, regular disks and (2) irregular lanes or filaments. They find that the disks are closely aligned with their host galaxies' major axes, whereas the lanes are randomly oriented. The interpretation common to all of these studies is that the dust has been acquired from an external source; the initial orientation of the dust features is random and their structure is irregular, but the dust gradually settles into the preferred plane of the galaxy and becomes a regular disk. The close alignments between the CO disks and the optical major axes of the present sample are consistent with what is seen in the dust studies mentioned above, if the present sample of CO disks correspond to the older and more relaxed dust systems. Note, however, the curious fact (probably a selection effect) that the CO disks studied here are larger than the dust features seen by van Dokkum & Franx (1995), Verdoes Kleijn et al. (1999), and Tomita et al. (2000). Most of the dust features have diameters smaller than 2 kpc, whereas only one of the CO disks (NGC 4476) is that small. 5.2. The Shape of These Galaxies Many attempts have been made to infer the intrinsic shape distribution of elliptical galaxies from their optical photometry and kinematics, but the true shape distribution is still poorly known because it is model-dependent. Some ellipticals may be oblate, but it seems highly unlikely that all of them are (Khairul Alam & Ryden 2002; Bak & Statler 2000 and references therein). However, the preponderance of major-axis disks in the present sample suggests that the majority of the sample galaxies are oblate. The principal plane of an oblate spheroid is perpendicular to the short axis, and this short axis always projects onto the apparent minor axis if the galaxy is axisymmetric (de Zeeuw & Franx 1989). Thus, a relaxed gas disk in an oblate galaxy should be aligned with the optical major axis. At present it is not clear whether there is a discrepancy between the number of oblate ellipticals in the present sample and in the optical studies mentioned above. The number of elliptical galaxies with CO maps is still too small to confirm or reject the hypothesis that the CO sample has been drawn from the same parent population as the optical studies. But when the number of ellipticals with CO maps is significantly greater, it should prove interesting to investigate whether the amount of molecular gas in these galaxies correlates with their intrinsic shape. TABLE 6 Alignment with Optical Major Axis Optical Morphology Radii (arcsec) 1027 1030 ... 1030 1020 P.A. (deg) 124 (2) 140 (1) 110 (5) 155 (1) 151 (4) Misalignment jDP:A:j (deg) 1 (3) 9 (3) 81 (6) 3 (2) 13 (5) Galaxy UGC 1503...... NGC 807 ....... NGC 3656...... NGC 4476...... NGC 5666...... 0.21 (0.02) 0.35 (0.05) 0.20 (0.04) 0.35 (0.02) 0.14 (0.02) Note.--Optical ellipticities and position angles are mean values over the semimajor axis range indicated under `` Radii.'' Optical morphology information for NGC 3656 is taken from Balcells 1997, so is not restricted by the overexposed/underexposed regions of the DSS. The parenthetical values in the and P.A. columns are the dispersion about the mean and P.A. over that radius range. Because these dispersions are normally larger than the formal fit uncertainties, they indicate something about the magnitude of possible radial variations in and P.A.. The misalignment angle DP.A. is the difference between the molecular gas's kinematic P.A. (Table 4) and the optical major axis P.A. 808 5.3. Star Formation and the Future of the Molecular Gas YOUNG Vol. 124 5.4. Stability of the Asymmetries in NGC 807 Molecular gas is understood to be the raw material for star formation; the transformation of gas into stars will create rotationally supported stellar disks within these ellipticals. An estimate of the masses of the stellar disks can be obtained from Table 5, which shows that the molecular gas masses in the sample galaxies are a few percent of the dynamical masses within the edge of the CO disks. Comparing the masses of the stellar disks to the masses of the spheroidal stellar components depends on an assumption that the dynamical mass within the CO disk arises mostly from stars. This assumption is reasonable for the galaxy interiors.2 It is also likely that not quite all of the gas will be transformed into stars. These assumptions imply that the stellar disks will have masses on the order of 1% of the total stellar mass in the galaxies--perhaps somewhat more, if some of the molecular gas has already been transformed into stars. The stellar disks that are likely to form out of these molecular disks will be very similar to the stellar disks that are now known to be common at least in disky ellipticals. Scorza et al. (1998), Scorza & Bender (1995), Cinzano & van der Marel (1994), and others who have done detailed photometric and kinematic studies of ellipticals find that many ellipticals contain both the usual spheroidal component (a bulge) and a stellar disk. In this respect, the ellipticals have structure that is qualitatively similar to spirals, but with much larger bulge/disk ratios (Kormendy & Bender 1996). Scorza et al. (1998) and Scorza & Bender (1995) found that the stellar disks inside ellipticals are rotationally supported; their sizes vary widely but are commonly on the order of re , and their disk/bulge (luminosity) ratios are commonly a few percent, up to 0.3. Presumably, smaller stellar disks may exist as well but are more difficult to detect. In short, after star formation ceases and the molecular gas is gone, the current sample of ellipticals will look much like known disky ellipticals. The formation of a rotationally supported stellar disk may already have happened in NGC 4476, where the stellar rotation appears to die out at the edge of the CO disk. I propose that careful kinematic analysis of that galaxy will show a small stellar disk of radius 1...

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1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.289.766H1997MNRAS.
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THE ASTROPHYSICAL JOURNAL, 478 : 144161, 1997 March 20( 1997. The American Astronomical Society. All rights reserved. Printed in U.S.A.THE MOLECULAR INTERSTELLAR MEDIUM IN ULTRALUMINOUS INFRARED GALAXIES P. M. SOLOMONAstronomy Program, State Univ
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1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B1978ApJ.224.132B
UVA - AE - 554
1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y199
UVA - AST - 554
1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y1991ARA&amp;A.29.581Y199
UVA - AST - 554
1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.1825B1981AJ.86.18
UVA - PHYS - 356
Phys 356Instructions:Final ExamMay 2, 2007This is an in-class, three hour exam. You may refer to your textbook, class notes, and homework solutions, and you may use a calculator. No other reference materials are permitted. Turn in your solutio
UVA - PHYS - 831
Assignment 33.1 A spherical liquid drop floats in equilibrium with its saturated vapor. The drop has radius r and surface tension , assumed constant. (a) Find the pressure difference between the liquid inside the drop and the saturated vapor. Assume
UVA - PHYS - 831
Assignment 11.1 A gasoline engine uses an approximation to the Otto cycle, in which an ideal gas with initial pressure, volume, and temperature (P1 , V1 , T1 ) is first adiabatically compressed to volume V2 , then heated at constant volume to temper
UVA - PHYS - 831
Thermodynamic VariablesGeneralized forcesPressure Surface tension Tension Magnetic field Electric field Chemical potential Temperature PGeneralized displacementsJ H E Volume Area Length Magnetization Polarization Number Entropy V A L M P N S
UVA - PHYS - 831
Physics 831 Statistical Mechanics ISpring 2009Phys 831 Statistical Mechanics I is a graduate level course in the theories of thermodynamics and statistical mechanics. We will discuss the foundations and relationships of both theories, and survey
UVA - PHYS - 831
Assignment 22.1 Prove that for xed N , (a) E X (b) E Y (c) T dS = CX T Y dY + CYX=Y TTY TX=TTX T+YYX Y T XTdXY2.2 Take N xed throughout this problem. (a) By equating two dierent expressions for dE, show that T dS = CV dT + T
UVA - PHYS - 521
Assignment 85.2 Foucault gyrocompass A gyroscope in the form of a symmetric top is mounted with no gravitaional torque, and its symmetry axis is constrained to move only in the horizontal plane parallel to the earth's surface. The gyroscope is set s
UVA - PHYS - 521
Assignment 95.3 A tilted coin (a sharp-edged uniform disk) of radius a and mass M rolls without slipping on a horizontal plane in a circle of radius b. A set of orthogonal coordinate axes has its origin at the center of ^ ^ mass, with e3 perpendicul
UVA - PHYS - 521
Assignment 62.1 Larmor's Theorem (a) The Lorentz force implies the equation of motion m = e(E + c-1 v B). Prove that the effect of a r weak uniform magnetic field B on the motion of a charged particle in a central electric field E = E(|r|)^ can r b
UVA - PHYS - 521
Assignment 126.8 I went through 6.7 in class on 11/29, so you shouldnt have too much trouble here. For the rotation part, set up the initial coordinates q as spherical (or cylindrical) coordinates with axis along n. Then determine how n L is rel
UVA - PHYS - 356
Phys 356Instructions:Final ExamMay 9, 2008This is an in-class, three hour exam. You may refer to your textbook, class notes, and homework solutions, and you may use a calculator. No other reference materials are permitted. Turn in your solutio
UVA - PHYS - 831
Manipulating DifferentialsA differential relation dF = Adx + Bdy contains a great deal of information, and can be manipulated much like an algebraic relation. For instance, the following derivations are valid: (a) Set dy = 0 and divide by dx: F = A.
UVA - PHYS - 521
Assignment 21.12 The orbit of the planet mercury has an eccentricity of 0.206 and a period of 0.241 year; moreover, the perihelion advances slowly at a rate of 43 seconds of arc per century. One possible explanation of this effect is that the potent
UVA - PHYS - 521
Assignment 106.4 The relativistic motion of a particle in a static potential V (r) can be obtained from the lagrangian L = -mc2 (1 - v 2 /c2 )1/2 - V (r). (a) Write out Lagrange's equations and verify the above assertion. (b) Find the canonical mome
UVA - PHYS - 521
Assignment 11.2 A uniform spool of mass M and diameter d rests on end on a frictionless table. A massless string wrapped around the spool is attached to a weight m which hangs over the edge of the table. If the spool is released from rest when its c
UVA - PHYS - 831
UVA - PHYS - 521
Physics 521 Theoretical MechanicsFall 2008Phys 521 Theoretical Mechanics is a capstone course in the theory of classical mechanics. We will cover in detail the motion of particles and rigid bodies, with an emphasis on problem-solving techniques.
UVA - PHYS - 831
UVA - PHYS - 831
UVA - PHYS - 831
UVA - PHYS - 521
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UVA - PHYS - 521
Phys 521 Final Exam10 December 2008This is a closed book, closed notes exam, to be taken in a single three-hour period. The problems should be worked on separate pages and attached to this sheet when completed. There are six problems, which will
UVA - PHYS - 521
Assignment 33.5 A massless inextensible string passes over a pulley which is a xed distance above the oor. A bunch of bananas of mass m is attached to one end A of the string. A monkey of mass M is initially at the other end B. The monkey climbs the
UVA - PHYS - 521
Assignment 10 Hints6.4 The relativistic generalization of Newton's Law is d (mv) = -V (r) dt where = (1 - v 2 /c2 )-1/2 . In part (c), the radial coordinats r and are defined in the usual way.^ 6.5 In part (c), you have some flexibility in cho
UVA - PHYS - 831
Maryville MO - MKT - 4000
MKT 4000 MARKETING MANAGEMENT Section 3 Spring 2009 Instructor: Office: Office Hours: Classroom: Course website: Dr. Shaoming Zou E-mail: zou@missouri.edu 335 Cornell Hall Office Phone: 884-0920 11:00am-11:45am M. &amp; W. and by appointment 219 Cornell
Maryville MO - MKT - 8720
MKT 8720 INTERNATIONAL MARKETING Winter 2008 Instructor: Office: Office Hours: Classroom:Course website:Dr. Shaoming Zou E-mail: Zou@missouri.edu 335 Cornell Hall Office Phone: 884-0920 1:00-1:45pm Tu. &amp; Th. and by appointment Room 42 Cornell Hall
UVA - ECON - 836
Econ 836: Empirical MacroeconomicsUniversity of Virginia Econ 836 Fall 2008 Chris Otrok Email: otrok@virginia.edu Phone: 924-3692 Office: Dynamics Building, room 407 Class Meets: Tue-Thurs, 2:00-3:15, Cabell 139 Office Hours: Wednesday 10:00-12:00am
UVA - ASTR - 211
Practice Problems: ASTR 211 Final Exam1. An object in the sky is located at celestial coordinates RA: 19h 23m 14s , Dec: -30 22 3. (a) What is the latitude, north of which the object will not be on the horizon? (b) At what times of the year will the
UVA - ASTR - 211
Practice Problems: ASTR 211 Final Exam1. An object in the sky is located at celestial coordinates RA: 19h 23m 14s , Dec: -30ffi 22' 3&quot;. (a) What is the latitude, north of which the object will not be on the horizon? Since the object is located at -3
UVA - ECE - 458
Class CS/ECE 457 Fall 2005 Quiz 7: TCP and UDP 1. Which of these statements is correct? X a. The window size at the receiving end of a TCP connection is communicated in one of the mandatory fields of the TCP header. b. The maximum segment size used o
UVA - ECE - 715
CS/ECE 715 Spring 2004 Homework 9 (Due date: April 27)Problem 1. Consider the network in Figure 1. There are four sessions: ACE, ADE, BCEF, and BDEF sending Poisson traffic at rates 100, 200, 500, and 600 packets/min, respectively. Packet lengths ar
UVA - ECE - 715
CS/ECE 715 Spring 2004 Homework 7 SolutionProblem 1. Consider the Markov chain in Fig. 1 of [Reference 1]. Assume m = 2 , q r = 0.5 and = 0.3 . Solve for steady state probability p 0 , p 1 , and p 2 .[Solution]P02 P12 0 P10 P00 P11 P22 1 P21 2
UVA - ECE - 715
Homework 1a: (Due date: Feb. 12, 2004)Question 1. Prove properties III and IV of a Poisson process (merging and splitting) listed in the class notes posted on the web site for the lecture on Stochastic processes. For the splitting case, just prove t
UVA - ECE - 457
Course prerequisiteComputer Networks CS/ECE 457 Fall 2008Malathi Veeraraghavan Professor Charles L. Brown Department of Electrical &amp; Computer Engineering THN E213CS 333: Computer architecture or equivalentCourse web site: https:/collab.itc.virg
UVA - ECE - 715
Networks of QueuesTing Yan and Malathi Veeraraghavan, April 19, 20041. IntroductionNetworks of Queues are used to model potential contention and queuing when a set of resources is shared. Such a network can be modeled by a set of service centers.
UVA - ECE - 715
M/M/1 and M/M/m Queueing SystemsM. Veeraraghavan; March 20, 2004 1. Preliminaries 1.1 Kendalls notation: G/G/n/k queue G: General - can be any distribution. First letter: Arrival process; M: memoryless - exponential interarrival times - Poisson arri
UVA - ECE - 715
CS/ECE 715 Spring 2004 Homework 4 (Due date: March 4, 2004)Problem 1. Derive an expression for the frequency of entering state 0 (server idle) in an M/M/1 queue. This quantity is useful in estimating the overhead of scheduling. Plot this frequency a