Variation of Galactic Bar Length with Amplitude and Density as Evidence for Bar Growth over a Hubble Time
Bruce G. Elmegreen, Debra Meloy Elmegreen, Johan H. Knapen, Ronald J. Buta, David L. Block, Ivanio Puerari
aa r X i v : . [ a s t r o - ph ] N ov Variation of Galactic Bar Length with Amplitude and Density asEvidence for Bar Growth over a Hubble Time
Bruce G. Elmegreen
IBM Research Division, T.J. Watson Research Center, 1101 Kitchawan Road, YorktownHeights, NY 10598, USA; [email protected]
Debra Meloy Elmegreen
Vassar College, Dept. of Physics & Astronomy, Box 745, Poughkeepsie, NY 12604, USA;[email protected]
Johan H. Knapen
Instituto de Astrof´ısica de Canarias, E-38200 La Laguna, Spain; [email protected]
Ronald J. Buta
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487,USA; [email protected]
David L. Block
School of Computational & Applied Mathematics University of the Witwatersrand P.O Box60 Wits, 2050, South Africa; [email protected]
Ivˆanio Puerari
Instituto Nacional de Astrof´ısica, Optica y Electr´onica, Tonantzintla, PUE 72840, Mexico;[email protected]
ABSTRACT K s -band images of 20 barred galaxies show an increase in the peak amplitudeof the normalized m = 2 Fourier component with the R -normalized radius atthis peak. This implies that longer bars have higher m = 2 amplitudes. The longbars also correlate with an increased density in the central parts of the disks,as measured by the luminosity inside 0 . R divided by the cube of this radiusin kpc. Because denser galaxies evolve faster, these correlations suggest thatbars grow in length and amplitude over a Hubble time with the fastest evolutionoccurring in the densest galaxies. All but three of the sample have early-typeflat bars; there is no clear correlation between the correlated quantities and theHubble type. 2 – Subject headings: galaxies: structure — galaxies: spiral
1. Introduction
Bars should slow down and grow over time as bar angular momentum is transferred tothe disk (Tremaine & Weinberg 1984) and halo (Kormendy 1979; Sellwood 1980; Little &Carlberg 1991; Hernquist & Weinberg 1992; Debattista & Sellwood 1998, 2000; Valenzuela &Klypin 2003; Athanassoula 2002, 2003). With this growth, the bars should become stronger,longer and thinner (Athanassoula 2003).Pattern speeds are difficult to measure (Knapen 1999) but bar lengths are not (Erwin2005). To investigate the model predictions, we examined relative bar lengths and intensitiesin 20 galaxies with conspicuous bars and a range of Hubble types. We consider how theseparameters correlate with each other and with the central density of the galaxy. Centralluminosity density is used as an indirect measure of the inner angular rotation rate becausefew galaxies in our sample have observed rotation curves. Galaxies with high central densitiesshould have high central rotation rates and evolve more quickly than galaxies with low centraldensities. If there is a secular change in bar length or amplitude with angular momentumtransfer, then denser galaxies should show the later evolutionary stages.
2. Observations and Analysis K s -band images of barred galaxies were obtained with the Anglo-Australian Telescope(AAT) from 2004 June 28 to July 5. We used the Infrared Imager and Spectrograph (IRIS2)with a 1024 × f / − and a field of view of 7.7 arcminsquared. Exposure times were around one hour in almost all cases and the angular resolutionwas typically 1.5 arcsec. Full details of the observations will be presented in Buta et al.(2007).Images were pre-processed using standard IRAF routines, and each image was cleanedof foreground stars and background galaxies. Deprojections were derived as follows. For eachgalaxy, estimates of the orientation parameters were obtained using an ellipse fitting routine, IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Associa-tion of Universities for Research in Astronomy, Inc., under cooperative agreement with the National ScienceFoundation. sprite , originally written by W. D. Pence. These fits were either based on the K s -band imageitself, or on an optical image if available. Because the bulges may not be as flat as the disks,we used a two-dimensional multi-component decomposition code (Laurikainen, Salo, & Buta2005) to derive the parameters of the bulges and disks. Images were deprojected, assumingthe bulges are spherical, using the IRAF routine IMLINTRAN. This assumption has littleimpact on our Fourier analyses. The results of the decompositions, as well as the orientationparameters used, will be presented in Buta et al. (2007).
3. Results
Bar and spiral arm amplitudes were measured from the m = 2 Fourier components ofazimuthal intensity profiles taken at various radii from polar plots using the deprojected,star-cleaned, background-subtracted images (as in Regan & Elmegreen 1997 and Block et al.2004). The m =2 Fourier intensity amplitude, I , was normalized to the average intensity, I , at each radius; I is defined to be the amplitude of the sinusoidal fit to the azimuthalprofile. Figure 1 shows this normalized amplitude, A = I /I , versus the radius normalizedto the standard isophotal radius R for each galaxy ( R is half the diameter D of the µ B = 25 mag arcsec − isophote given by de Vaucouleurs et al. 1991). The 20 profiles havebeen divided into four panels for clarity. Figure 1 shows that A increases with radius andthen decreases. The maximum, A max , occurs at a radius which we denote by R . Thisradius is approximately equal to the bar length determined by eye in all cases. Theorysuggests the two lengths should scale together, with R slightly less than the visible barlength (Athanassoula & Misiriotis 2002). A correlation may be seen in Figure 1 in the sensethat galaxies with higher A max also have larger radii at this peak (the peaks are indicatedby the circles; empty circles are flat bars and circles with plus-signs are exponential bars).This correlation is shown in Figure 2 (top left), which plots A max versus the normalizedradius R /R . The dashed line is a bi-variate least squares fit, repeated in the other panels.Longer bars are higher amplitude in relative intensity. This is sensible considering thegeneral exponential decline of disk intensity: longer bars extend further out in the disk,placing their ends where the average background is fainter. For example, each radial intervalof ∼ . R/R corresponds to about one exponential scale length in most galaxies, whichis a factor of 2.7 in disk brightness. This factor is only slightly larger than the increasein Figure 2. Thus, growing bars can stay somewhat flat in their intensity profile and stillincrease their relative amplitude along with their length because the surrounding disk isdecreasing with radius. Bars apparently grow relative to the disk size even if the disk growstoo because of angular momentum transfer from the bar (Valenzuela & Klypin 2003). 4 –Figure 2 (top right) includes three previous surveys in which this correlation was presentbut not noticed. The crosses are from K -band images of 8 different barred galaxies studiedby Regan & Elmegreen (1997), the circles are from K s -band images of 24 different earlytype (S0-Sa) barred galaxies in Buta et al. (2006), and the triangles are from 10 I -bandimages of different galaxies in Elmegreen & Elmegreen (1985). Among these three samples,there are only 3 overlapping galaxies and they are only between the 1985 and 1997 surveys.The Regan & Elmegreen A max values were multiplied by 2 because they used the standarddefinition of a Fourier component, which, for example, gives a relative value of 0.5 for anazimuthal profile of 1 + sin(2 θ ). We and the other references in Figure 2 use twice the Fouriercomponent to reflect the amplitude of the sinusoidal part of the profile.The lower panels of Figure 2 show correlations present in data from two other studiesof bar Fourier amplitudes. The lower left panel shows data from Laurikainen et al. (2006),who determined the Fourier amplitudes and bar radii for 28 early type galaxies (S0,Sa, Sab)in K s band. The lower right panel shows data from Laurikainen et al. (2004), who usedthe Ohio State Bright Galaxy Survey and 2MASS to measure the H-band properties of 113galaxies of various Hubble types. Their tabulations give the bar lengths, not the radii atthe peak of the Fourier amplitude. Bar length is slightly larger than R , so the points areshifted to the right of the dashed lines in the figures. Also, A is lower for S0 galaxies thanother early types, which lowers some of the points in the lower left panel (Laurikainen, Salo,& Buta 2004). The present correlation was not noticed in either study but it is present inthe data.Our previous study of K s -band images for 17 barred galaxies (Block et al. 2004) founda length-amplitude correlation related to the present one. There we plotted the bar/interbarintensity contrast at 0.7 bar length versus the deprojected length of the bar (determined byeye). There was no overlap in galaxies with the present or the Buta et al. (2006) samples,and only one overlap each with the Regan & Elmegreen (1997) and Elmegreen & Elmegreen(1985) samples. The bar/interbar intensity contrast was shown by Block et al. to correlatewith the relative amplitude of the m = 2 Fourier component, and with the bar torqueparameter, Q b . This previous study discussed the length-amplitude correlation in a differentcontext, however, noting that the long and high-amplitude bars tended to be early Hubbletype and flat-profile, while the short and low-amplitude bars tended to be late Hubble typeand exponential. This is true in general, but the present result is in addition to that. In thepresent work, the length-amplitude correlation is present even for the flat bars, and there isno strong correlation with Hubble type because most of our galaxies are flat-barred.The R /R length is plotted versus Hubble type for our sample in Figure 3. The circledplus-signs are exponential bars, and the rest are flat bars. Most of the galaxies in our current 5 –sample are Hubble types Sbc or earlier. The three exponential bars in our sample haveslightly weaker Fourier components than the average for the flat bars (Fig. 2). Evidently,there are two length-amplitude correlations: one discussed by Block et al. differentiatingearly and late type bars (which is presumably related to different bar resonances; Combes& Elmegreen 1993), and another found here that remains even for early-type, flat bars. Thelower right panel of Figure 2 illustrates these two correlations in another way by plotting thevarious Hubble types with different symbols. The late types tend to be confined to the lowerleft in the figure, while the early types display the full range of bar lengths and amplitudes.Laurikainen, Salo, & Buta (2004) found no correlation between the peak relative torque, Q g , normalized to the radial force, and the relative radius at the peak of this torque. Therelative torque is a combination of the azimuthal bar amplitude, which determines the torque,and the radial force from the bulge, which is used to normalize this torque. Stronger-bulgegalaxies have weaker bar torques for the same relative m = 2 component. Bulges do notaffect the peak A much because the bulge intensity at the end of the bar is small. On theother hand, bulges do affect Q g because the radial force from the bulge is still large at thebar end.The central luminosity densities of the galaxies were measured from the K s -band lumi-nosities inside 0 . R , 0 . R , and 0 . R . The K s -band is dominated by old stars andtraces the mass fairly well if dark matter is not significant there. Most of the galaxies areearly type and centrally condensed so the 3 luminosities measured in this way were all aboutequal. Because the R /R lengths vary from ∼ . R to ∼ . R , and we want a represen-tative density in the bar region, we use the luminosity inside 0 . R . The central density isthen taken to be this luminosity divided by the cube of the radius at 0 . R , measured inkpc using the distances in Table 1 (from the galactocentric GSR in the NASA/IPAC Extra-galactic Database). Figure 4 shows the central K s -band density versus the normalized radiusat the peak m = 2 amplitude (plus signs denote exponential bars). There is a correlation inthe sense that longer bars occur in denser galaxies.These two correlations provide new information to supplement properties found in otherbar correlations. Athanassoula & Martinet (1980) and Martin (1995) found a correlation be-tween the lengths of bars and bulges, and Elmegreen & Elmegreen (1985) found a correlationbetween bar length, amplitude, and early versus late Hubble types, as mentioned above (seereview in Ohta 1996). 6 –
4. Discussion
We find that among fairly early type galaxies, relative bar length and relative m = 2intensity correlate with each other but not obviously with the Hubble subtype. The lengthsand amplitudes also correlate with the central luminosity density of the galaxy. Thesecorrelations are in the sense expected by numerical simulations which suggest that angularmomentum gradually transfers from a bar to the surrounding disk, bulge, and halo (seeAthanassoula 2003 and references therein). With a loss of angular momentum, bars shouldslow down, and this means their corotation radii move outward. The stellar orbits in the barshould also get more elongated as angular momentum is proportional to the orbital area, andthis translates to ellipticity for a constant orbital energy. As the orbital ellipticity increases,the stars become more concentrated in the bar and the bar gets stronger. If the orbitsalso scatter in energy, then their semi-major axes should grow too, following the movingcorotation resonance. In this case, bars would grow in length as they get higher relativeamplitudes during angular momentum loss. This is apparently what we observe here.The correlation with central density is consistent with angular momentum loss becausegalaxies with higher central densities evolve faster. In a given galaxy lifetime, the barswhich evolve faster will have transferred more of their angular momentum outward and atthe present time will have longer and higher-amplitude bars. The correlation with centraldensity could also result from a larger reservoir for bar angular momentum in the largerbulges. An inverse process might be responsible too, where a strong bar forms first and thiscauses the bulge to grow through accretion (e.g., Athanassoula 1992, 2003).The lack of a correlation between relative bar length and peak relative bar torque Q g may be understood from our correlations with central density. For a given bulge, angularmomentum transfer should increase both the peak amplitude and the peak torque of thebar over time. Galaxies with denser bulges do this faster, so at any given time, the peakamplitude correlates with bulge density. However, denser bulges weaken Q g because thisquantity is normalized to the radial force (Laurikainen, Salo, & Buta 2004). This normaliza-tion offsets the increasing bar amplitude that comes from angular momentum transfer. Asa result, Q g does not show the same correlations as the m = 2 Fourier amplitude.Galaxies with dense bulges should not have bars if bulges prevent bar formation orgrowth (e.g., Sellwood 1980). However, our data show that high central densities correlatewith high-amplitude bars. The observed correlation suggests that bars and bulges growtogether, in agreement with Sheth et al. (2007). 7 –
5. Conclusions
Bars in intermediate and early type spirals have a correlation between their relativelengths and their relative m = 2 Fourier components, and both increase with the centraldensity. These correlations are consistent with models in which bars lose angular momentumto the surrounding disk, bulge, and halo over long periods of secular evolution. The barscontain very old stars and must have been present for a high fraction of the Hubble time,like the bulges.We thank Emma Allard for help during the observations and with the data reduc-tion, and Stuart Ryder for excellent support at the AAT. We thank Heikki Salo and EijaLaurikainen for useful comments on the manuscript. Helpful comments by the referee areappreciated. DME thanks Vassar College for publication support through a Research Grant.RB acknowledges the support of NSF grant AST 05-07140. I.P. acknowledges support fromthe Mexican foundation CONACyT under project 35947.E. This research has made use ofthe NASA/IPAC Extragalactic Database (NED) which is operated by the Jet PropulsionLaboratory, California Institute of Technology, under contract with the National Aeronauticsand Space Administration. REFERENCES
Athanassoula, E. 1992, MNRAS, 259, 345Athanassoula, E. 2002, ApJ, 569, L83Athanassoula, E. 2003, MNRAS, 341, 1179Athanassoula E., & Martinet L., 1980, A&A, 87, L10Athanassoula, E., & Misiriotis, A. 2002, MNRAS, 330, 35Buta, R., Corwin, H. G., & Odewahn, S. C. 2007, The de Vaucouleurs Atlas of Galaxies,Cambridge, Cambridge University PressButa, R., Laurikainen, E., Salo, H., Block, D.L., & Knapen, J.H. 2006, AJ, 132, 1859Buta, R. et al. 2007, in preparationBlock, D.L., Buta, R., Knapen, J.H., Elmegreen, D.M., Elmegreen, B.G., & Puerari, I. 2004,AJ, 128, 183 8 –Combes, F., & Elmegreen, B. G. 1993, A&A, 271, 391Debattista V. P., & Sellwood J. A., 1998, ApJ, 493, L5Debattista V. P., & Sellwood J. A., 2000, ApJ, 543, 704de Vaucouleurs, G. et al. 1999, Third Reference Catalogue of Bright Galaxies, Springer(RC3)Elmegreen B. G., & Elmegreen D. M., 1985, ApJ, 288, 438Erwin, P. 2005, MNRAS, 364, 283Hernquist L., & Weinberg M. D., 1992, ApJ, 400, 80Knapen , J.H. 1999, ASPC, 187, 72Kormendy J., 1979, ApJ, 227, 714Laurikainen, E., Salo, H., Buta, R., & Vasylyev, S. 2004, MNRAS, 355, 1251Laurikainen, E., Salo, H., & Buta, R. 2004, ApJ, 607, 103Laurikainen, E., Salo, H., & Buta, R. 2005, MNRAS, 362, 1319Laurikainen, E., Salo, H., Buta, R., Knapen, J., Speltincx, T., & Block, D. 2006, ApJ, 132,2634Little B., & Carlberg R. G., 1991, MNRAS, 250, 161Martin P., 1995, AJ, 109, 2428Ohta K., 1996, in Buta R., Crocker D., & Elmegreen B., eds, ASP Conf. Ser. Vol. 91, BarredGalaxies. (San Francisco: Astron. Soc. Pac.), p. 37Regan, M.W., & Elmegreen, D.M. 1997, AJ, 114, 965Sellwood, J.A. 1980, A&A, 89, 296Sheth, S., et al. 2007, ApJ, in pressTremaine S., & Weinberg M. D., 1984, MNRAS, 209, 729Valenzuela, O., & Klypin, A. 2003, MNRAS, 345, 406
This preprint was prepared with the AAS L A TEX macros v5.2.
Galaxy typetablenotemarka D (Mpc) R (arcsec) R /R I /I NGC175 SB(r¯s)ab 53.9 64.1 0.2 0.33NGC521 SB(r¯s)bc 69.6 94.9 0.15 0.18NGC613 SB(rs)bc 19.8 164.9 0.5 0.4NGC986 (R ′ )SB(rs)b 25.7 116.7 0.6 0.62NGC4593 (R ′ )SB(rs)ab 35.6 116.7 0.5 0.48NGC5101 (R R ′ )SB(r¯s)a 23.7 161.1 0.3 0.36NGC5335 SB(r)b 63.2 64.1 0.2 0.5NGC5365 (R)SB0 − R ′ )SB(r)a 52.6 65.6 0.4 0.37NGC6907 SAB(s)bc 44.5 99.3 0.3 0.42NGC7155 SB(r)0 o ′ )SB(s)ab 21.7 101.7 0.55 0.6NGC7582 (R ′ )SB(s)ab 21.3 150.4 0.45 0.45IC1438 (R R ′ )SAB(r)a 20 72 0.3 0.385IC4290 (R ′ )SB(r)a 64.3 47.6 0.4 0.42IC5092 (R)SB(s)c 43.3 86.5 0.2 0.33UGC10862 SB(rs)c 24.8 82.6 0.2 0.31 a Classifications are either from the de Vaucouleurs Atlas of Galaxies (Buta, Corwin,& Odewahn 2007) or estimated by RB in the same system based on available imagematerial. b Relative radius of peak relative m = 2 Fourier amplitude. c Peak relative m = 2 Fourier amplitude.
10 – m = R e l a t i v e F ou r i e r A m p li t ude NGC 521IC 5092NGC 5335 NGC 6907IC 4290 NGC 7582NGC 986NGC 7513NGC 175 IC 1438 m = R e l a t i v e F ou r i e r A m p li t ude NGC 4593UGC 10862 NGC 5365NGC 7155 NGC 6782 NGC 613NGC 7329NGC 5101NGC 6221 NGC 7552
Fig. 1.— Relative amplitude of the m = 2 Fourier component of the bar and spiral patternversus radius for 20 galaxies. Circles show the peaks. Circles with plus signs are bars withexponential intensity profiles, the others have relatively flat profiles. 11 – /R P ea k R e l a t i v e m = A m p li t ude , I /I This study, K s band /R I band (EE85)K band (RE97)K s band (BLSBK06) Laurikainen et al. 2004, H bandS0/a, Sa, Sab, Sb, SbcSc, Scd, Sd, Sdm, Sm P ea k R e l a t i v e m = A m p li t ude , I /I Laurikainen et al. 2006, K s bandEarly type (S0,Sa,Sab) Fig. 2.— Peak relative amplitude of the m = 2 Fourier component versus the normalizedradius at the peak. Left: galaxies in Fig. 1 all imaged in K s band (plus signs are exponentialbars). Slight displacements among a triplet at R /R = 0 . K s band in a combinedsouthern and northern survey by Laurikainen et al. (2006). Bottom right: 104 galaxiesimaged in H-band with the Ohio State Bright Galaxy Survey and 9 galaxies imaged in H-band with 2MASS, all of various Hubble types, using measurements in Laurikainen et al.(2004). All surveys indicate that bars that are longer compared to their galaxy size havehigher peak relative m = 2 Fourier amplitudes. This correlation is present even for early typegalaxies. A second, well-known correlation between bar length and Hubble type is evidentfrom the lower right panel where the late Hubble types (solid symbols, plus and cross) tendto have shorter and weaker bars than the early types (open symbols). 12 – S0SaSabSb
SbcSc R /R H ubb l e T y pe Fig. 3.— Hubble type versus the normalized radius at the peak relative m = 2 Fouriercomponent (i.e., the relative bar size) showing little correlation in our sample. The circleswith plus signs are galaxies with exponential bars; the rest have flat-profile bars. Slightdisplacements are for clarity. 13 – R /R K –band F l u x / k p c a t R / Fig. 4.— Luminosity density at R / m = 2 component. Luminosities are in units of the count rate per unit solid angle integratedinside R //