First Draft, Jan 30, 2020 Preprint typeset using LATEX style emulateapj v. 12/16/11 DETERMINING THE CO-ROTATION RADII OF SPIRAL GALAXIES USING SPIRAL ARM PITCH ANGLE MEASUREMENTS AT MULTIPLE WAVELENGTHS Shameer Abdeen 1,2, Daniel Kennefick1,2, Julia Kennefick1,2, Ryan Miller3, Douglas W. Shields1,2, Erik B. Monson1,2 and Benjamin L. Davis4 First Draft, Jan 30, 2020 ABSTRACT The spiral arms spanning disk galaxies are believed to be created by density waves that propagate through galactic disks. We present a novel method of finding the co-rotation radius where the spiral arm pattern speed matches the velocities of the stars within the disk. Our method uses an image- overlay technique, which involves tracing the arms of spiral galaxies on images observed in different wavelengths. Density wave theory predicts that spiral arms observed from different wavelengths show a phase crossing at the co-rotation radius. For the purpose of this study, 20 nearby galaxies were analyzed in four different wavelengths with pitch angle measurements performed by two independent methods. We used optical wavelength images (B-band 440nm), two infrared wavelength images pro- vided by Spitzer (3.6µm and 8µm) and ultraviolet images from GALEX (1350A,˚ 1750A).˚ The results were compared and verified with other records found in the literature. We then found rotation curve data for six of our galaxies and used our co-rotation radii estimates to measure the time that would elapse between star formation and moving to their observed positions in the B-band spirals. The average time lapse for this motion was found to be ∼ 50 Myr. The success of this new method of finding the co-rotation radius confirms density wave theory in a very direct way. Keywords: galaxies: corotation | galaxies: spiral galaxies| galaxies: density waves 1. INTRODUCTION gue that the spiral arms must be long-lived. Evidence The density wave theory, introduced by C.C. Lin & for these color gradients is presented in Pour-Imani et al. Frank Shu (Lin & Shu 1964; Bertin & Lin 1996; Shu (2016); Miller et al. (2019) using a different approach, 2016) proposed a theoretical explanation for the exis- which demonstrates that the spiral arm pitch angle in tence of spiral structures in galaxies due to long lived wavebands associated with star-formation is consistently quasi-stationary density waves. Subsequent development larger than those associated with the stellar population. of the theory has focused on the highly dissipative na- This suggests that new-born stars are found downstream ture of the galactic disk, which casts doubt on the semi- of the star-formation region in a manner consistent with permanence of the spiral patterns envisaged by the orig- the density-wave theory. A study by Yu & Ho (2018) inal theory (Toomre 1969). Numerical simulations of with a large number of galaxies strongly confirms this density waves in disks have especially fostered the view picture and agrees with the work of Mart´ınez-Garc´ıa& that spiral patterns created by density waves may be Gonz´alez-L´opezlira (2015). Pour-Imani et al. (2016) also transient in nature (Sellwood & Carlberg 1984), possi- agrees with theirs in broad outline (but see Section 4.2 bly lasting only as long as one or two rotations of the below for one significant detail where they differ). galactic disk (recall that the Milky Way has a rotation In this paper, we seek to take advantage of this discov- period of 250 Myr). Nevertheless some simulations con- ery to further explore the nature of the spiral structure. tinue to suggest that spiral patterns could be quite long- We show how overlaying the different spiral arms, from lived, lasting many rotational periods (Sellwood 2012; the star-forming region and from the stellar arm enables Sellwood & Carlberg 2014) . us to find the co-rotation radius (RCR) of a galaxy. Then, It is not only theorists who disagree on this topic. for those galaxies for which rotation curves are available, we calculate the time that elapses between stars being arXiv:2002.02307v1 [astro-ph.GA] 6 Feb 2020 Observational studies have also contradicted each other upon this point. Foyle et al. (2011) point out that the born in the star-forming region and then being observed absence of color gradients in the spiral arms of galaxies downstream in the B-band. This time is found to be a would suggest that the density waves are too transient significant fraction of the rotational period of a galaxy, to permit time for such gradients to develop. But the thus suggesting, in agreement with Mart´ınez-Garc´ıa& work of Mart´ınez-Garc´ıa & Gonz´alez-L´opezlira (2015) Gonz´alez-L´opezlira (2015), that the spiral arms cannot does find evidence for such color gradients and they ar- be extremely transient. Due to the differential rotation of the disk, stellar pop- 1 Department of Physics, University of Arkansas, 226 Physics ulations move faster than the spiral arm density wave in- Building, 825 West Dickson Street, Fayetteville, AR 72701, USA side the co-rotation radius, while they lag behind the spi- 2 Arkansas Center for Space and Planetary Sciences, Univer- ral arm density wave outside the co-rotation radius. The sity of Arkansas, 346 1/2 North Arkansas Avenue, Fayetteville, AR 72701, USA; [email protected] general motion of stellar populations about the galactic 3 Department of Physics, Utica College, 1600 Burrstone Rd, center can be considered as a motion along an axially Utica, NY 13502, USA; symmetric gravitational field, and with a proper selec- 4 Centre for Astrophysics and Supercomputing, Swinburne tion of an appropriate reference frame, one can express University of Technology, Hawthorn, VIC 3122, Australia 2 Abdeen et al. this as an epicyclical motion. The inner Lindblad (ILR) In agreement with the PD method, we were able to and the outer Lindblad (OLR) resonances are defined in introduce a novel way of determining the co-rotation ra- terms of this epicyclic frequency. The pattern speed (Ωp) dius, based on an image overlaying technique, which in- and the angular velocity of the disk Ω(R) are related to volves tracing the arms of spiral galaxies on images ob- the epicyclic frequency κ by the equation, Ωp= Ω(R) ± served from different wavelengths. In a previous study κ/2, where the plus and minus signs give the ILR and (Pour-Imani et al. 2016), convincing evidence was given the OLR, respectively. in favor of an implication of density wave theory, which Identifying the location of the co-rotation radius is of states that the pitch angle varies with wavelength for central importance to understanding the evolution of the a given galaxy. Thus we have different apparent spiral spiral structure. The existence of a co-rotation radius it- arms at different wavelengths. Since these spiral arms self serves as evidence of the validity of the density wave have different pitch angles, it is possible for them to cross theory. Furthermore, since the co-rotation radius acts over each other when they are overlaid on the same image as a region of resonance or a stable region within the of the galactic disk. The crossing-point should be the co- galaxy structure, it has a dynamical influence on the rotation radius. Below we measure the co-rotation radius matter and the chemical composition distribution pro- by this method and compare it to other methods which cess of the galaxy (Scarano & L´epine2013). The region have been used for our sample and find it is successful at of stability around the co-rotation radius creates an ideal correctly measuring the position of this radius. environment for a Galactic habitable zone (GHZ) e.g. 2. THE DATA SAMPLE Marochnik (1983); Sundin (2006).There are multiple pa- pers (Creze & Mennessier 1973; Mishurov & Zenina 1999) The accuracy of our method relies on three cardinal cri- among others, that claim to find the location of the Sun teria. (a) The inclination of the galaxy. If the galaxy has close to the galactic co-rotation radius of the Milky Way. a very high inclination angle, most of the crucial details There are many methods of identifying the co-rotation will be lost in the de-projection process. We selected our radius. The Tremaine-Weinberg method (Tremaine & galaxies such that the inclination angles are ≤ 60◦. (b) Weinberg 1984) hereafter TW, requires certain specific Well defined spiral structure. The overlaying technique morphological features along with the assumptions (a) requires the galaxy sample to have a well-defined, clear the disc of the galaxy is flat, (b) the disc has a well- spiral structure in order to accurately overlay the syn- defined pattern speed, and (c) the surface brightness thetic spirals. (c) The variation of the spiral arm pitch of the tracer obeys the continuity equation. The TW angle with the galactic radius remains constant for a sig- method directly measures the bar pattern speeds. Using nificant proportion of the galactic radius. This amounts the TW method some authors (Merrifield et al. 2006; to a criterion that the spiral arms are logarithmic spirals. Grand et al. 2012) have claimed to observe multiple spi- Although we assign a mean value for the pitch angle, the ral arm pattern speeds that vary with the radius from the extent to which the spiral arms are intrinsically logarith- galactic center, which may result in observing multiple mic plays a vital role in this criterion. co-rotation radii. Our galaxy sample (see Table 1) was selected based Finding the co-rotation radius from morphological on the availability of co-rotation radii measurements in features is also a common technique. Elmegreen & the literature, along with considering the above men- Elmegreen (1990) claimed to observe sharp end points to tioned criteria.