THE DISTRIBUTION OF BAR STRENGTHS IN SPIRAL GALAXIES BASED ON A GRAVITATIONAL TORQUE INDICATOR

1. THE DISTRIBUTION OF BAR STRENGTHS IN SPIRAL GALAXIES BASED ON A GRAVITATIONAL TORQUE INDICATOR S.O. VASYLYEV, R.J. BUTA (UNIVERSITY OF ALABAMA), H. SALO, E. LAURIKAINEN (UNIVERSITY OF OULU) LOGO ABSTRACT SAMPLE OF GALAXIES RESULTS CONCLUSIONS The distribution of bar strengths in disk galaxies is a fundamental property of the galaxy population that has only begun to be explored. We have applied the bar-spiral separation method of Buta, Block, and Knapen (2003, AJ, 126, 1148) to derive the distribution of maximum relative gravitational bar torques, Qb, for 147 spiral galaxies in the statistically well-defined Ohio State University Bright Galaxy Survey sample. Our goal is to examine the properties of bars as independently as possible of their associated spirals. We find that the relative frequency of bars declines approximately exponentially with increasing Qb, with more than 40% of the sample having Qb < 0.1. In the context of recurrent bar formation, this suggests that strongly-barred states are relatively short-lived compared to weakly-barred or non-barred states, while in the context of natural (spontaneous) bar formation, this suggests that the bar instability preferentially forms weak bars. The distribution of bar strengths undoubtedly includes a variety of bar formation and evolution processes that could possibly be deciphered with numerical modeling. We do not find compelling evidence for a bimodal distribution of bar strengths. Instead, the distribution is fairly smooth in the range 0.0 < Qb < 0.8. Our analysis also provides a first look at spiral strengths Qs in the OSU sample, based on the same torque indicator. We are able to verify a possible weak correlation between Qs and Qb, in the sense that galaxies with the strongest bars tend also to have strong spirals. The OSUBGS sample (Eskridge et al. 2002) consists of 205 nearby spiral galaxies having the following criteria: type index in the Third Reference Catalog of Bright Galaxies (de Vaucouleurs et al. 1991, RC3) 0< T < 9 (S0/a to Sm), total magnitudes BT< 12.0, standard isophotal galaxy diameters D25 < 6.5’, and declinations in the range -80º < Dec < +50˚. Only OSUBGS galaxies with inclinations less than 65˚ were included, which limited the sample to 158 galaxies. Galaxies with inclinations higher then 65˚ cannot be deprojected reliably. There are in addition 22 2MASS galaxies in our sample which satisfy the same criteria as the galaxies in the OSUBGS, except that they have D25> 6.5’ . The final sample consisting of 180 galaxies is representative of typical luminous spiral galaxies in the nearby universe. • Using a simple Fourier technique, the bars and spirals in 147 OSUBGS galaxies were separated, and for the first time the distribution of actual bar strengths in disk galaxies was derived. • Bars were separated from spirals by assuming that the radial profiles of relative Fourier intensity amplitude, Im/I0, obey a symmetry assumption. • The results show that when spiral torques are removed, the distribution of bar strengths is a declining function from a maximum in the bins < 0.1. • For higher bar strengths, some correlation between Qb and Qs may be present that can only be confirmed with a larger sample of strongly barred spirals including SB0 galaxies. GRAVITATIONAL TORQUE METHOD Bar strength – the ratio of the maximal tangential force to the mean axisymmetric radial force FT – maximal mean tangential force over azimuth for the 4 different image quadrants FR – azimuthally averaged axisymmetric force at each radius There is an assumption used that the surface density  is proportional to the surface brightness obtained from the near-IR image. The lighttraces the mass; i.e.,the mass-to-light ratio isconstant across much ofthe disk. The bar-induced gravitational potential is calculated from a deprojected H-band image using generally 10 even Fourier components (Laurikainen, Salo, Buta, and Vasylyev 2004). The images are first “smoothed” by calculating the Fourier decompositions of the surface densities in different radial zones. PURPOSE AND HYPOTHESIS Our goal is to examine the properties of bars as independently as possible of their associated spirals. The idea of the gravitational torque method (GTM) is to transform a deprojected near-infrared image of a spiral galaxy into a gravitational potential. The next step is to compute the ratio of the tangential force to the mean radial force as a function of position in the plane of the galaxy. The potential is derived from Poisson’s law after assuming an exponential vertical density law and a constant mass-to-light ratio (Quillen. Frogel, and Gonzalez 1994). The mean radial force represents the axisymmetric background due to the bulge, disk, and bar. A fully quantitative measure of bar strength can be defined from the maximum of the tangential-to-radial force ratio. THE DISTRIBUTION OF BAR STRENGTHS NGC 6951 BAR/SPIRAL SEPARATION ACKNOWLEDGMENTS H-band Image of NGC 1300 (OSUBGS Sample of Spiral Galaxies). This is an example of a strongly barred galaxy with a bar strength Qb=0.52 and spiral strength Qs=0.18 This work was supported by NSF Grants AST 0205143 and AST 0507140 to the University of Alabama, and by the Academy of Finland and the Magnus Ehrnrooth Foundation. Funding for the OSU Bright Galaxy Survey was provided by NSF grants AST-9217716 and AST-9617006, with additional funding from the Ohio State University. • We measure the maximum in the radial QT profile for the combination of bar plus spiral • New Method: To separate bar from spiral and measure “pure” bar strength – Qb and spiral– Qs. • A Fourier-based method of separating bars from spirals in NIR images is introduced (R.Buta,D.L. Block, and J.H. Knapen, 2003) • QT radial profile for NGC 6951 is a good example REFERENCES Block, D.L., Bournaud, F., Combes, F., Puerari, I., and Buta R.J. 2002. Gravitational torques in spiral galaxies: Gas accretion as a driving mechanism of galactic evolution 394:L35.  Block, D. L., Buta, R., Knapen, J. H., Elmegreen, D. M., Elmegreen, B. G., & Puerari, I. 2004. Gravitational bar and spiral arm torques from Ks-band observations and implications for the pattern speeds. Astronomical Journal 128:183.  Bournaud, F. & Combes, F. 2002. Gas accretion on spiral galaxies: Bar formation and renewal. Astronomy & Astrophysics 392:83. Buta, R. and Block, D. L. 2001. A dust-penetrated classification scheme for bars as inferred from their gravitational force fields. The Astrophysical Journal 550:243.  Buta, R., Block, D. L., and Knapen, J. H. 2003. A technique for separating the gravitational torques of bars and spirals in disk galaxies.Astronomical Journal 126:1148. Buta, R., Vasylyev, S., Laurikainen, E., Salo, H. 2005. The distribution of bar and spiral arm strengths in disk galaxies. The Astronomical Journal 130:506-524.