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Register a new userMeasurement of Galactic Logarithmic Spiral Arm Pitch Angle Using Two-Dimensional Fast Fourier Transform Decomposition
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Benjamin L. Davis
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A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.
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Context: In spiral galaxies, star formation tends to trace features of the spiral pattern, including arms, spurs, feathers, and branches. However, in our own Milky Way, it has been challenging to connect individual star-forming regions to their larger Galactic environment owing to our perspective from within the disk. One feature in nearly all modern models of the Milky Way is the Sagittarius Arm, located inward of the Sun with a pitch angle of ~12 deg. Aims: We map the 3D locations and velocities of star-forming regions in a segment of the Sagittarius Arm using young stellar objects (YSOs) from the Spitzer/IRAC Candidate YSO (SPICY) catalog to compare their distribution to models of the arm. Methods: Distances and velocities for these objects are derived from Gaia EDR3 astrometry and molecular line surveys. We infer parallaxes and proper motions for spatially clustered groups of YSOs and estimate their radial velocities from the velocities of spatially associated molecular clouds. Results: We identify 25 star-forming regions in the Galactic longitude range l~4.0-18.5 deg arranged in a narrow, ~1 kpc long linear structure with a high pitch angle of $psi = 56$ deg and a high aspect ratio of ~7:1. This structure includes massive star-forming regions such as M8, M16, M17, and M20. The motions in the structure are remarkably coherent, with velocities in the direction of Galactic rotation of $240pm3$ km/s (slightly higher than average) and slight drifts toward the Galactic center (-4.3 km/s) and in the negative Z direction (-2.9 km/s). The rotational shear experienced by the structure is 4.6 km/s/kpc. Conclusions: The observed 56 deg pitch angle is remarkably high for a segment of the Sagittarius Arm. We discuss possible interpretations of this feature as a substructure within the lower pitch angle Sagittarius Arm, as a spur, or as an isolated structure.
In this paper we study the morphological properties of spiral galaxies, including measurements of spiral arm number and pitch angle. Using Galaxy Zoo 2, a stellar mass-complete sample of 6,222 SDSS spiral galaxies is selected. We use the machine vision algorithm SpArcFiRe to identify spiral arm features and measure their associated geometries. A support vector machine classifier is employed to identify reliable spiral features, with which we are able to estimate pitch angles for half of our sample. We use these machine measurements to calibrate visual estimates of arm tightness, and hence estimate pitch angles for our entire sample. The properties of spiral arms are compared with respect to various galaxy properties. The star formation properties of galaxies vary significantly with arm number, but not pitch angle. We find that galaxies hosting strong bars have spiral arms substantially ($4-6^mathrm{o}$) looser than unbarred galaxies. Accounting for this, spiral arms associated with many-arm structures are looser (by 2$^mathrm{o}$) than those in two-arm galaxies. In contrast to this average trend, galaxies with greater bulge-to-total stellar mass ratios display both fewer and looser spiral arms. This effect is primarily driven by the galaxy disc, such that galaxies with more massive discs contain more spiral arms with tighter pitch angles. This implies that galaxy central mass concentration is not the dominant cause of pitch angle and arm number variations between galaxies, which in turn suggests that not all spiral arms are governed by classical density waves or modal theories.
Spiral structure is ubiquitous in the Universe, and the pitch angle of arms in spiral galaxies provide an important observable in efforts to discriminate between different mechanisms of spiral arm formation and evolution. In this paper, we present a hierarchical Bayesian approach to galaxy pitch angle determination, using spiral arm data obtained through the Galaxy Builder citizen science project. We present a new approach to deal with the large variations in pitch angle between different arms in a single galaxy, which obtains full posterior distributions on parameters. We make use of our pitch angles to examine previously reported links between bulge and bar strength and pitch angle, finding no correlation in our data (with a caveat that we use observational proxies for both bulge size and bar strength which differ from other work). We test a recent model for spiral arm winding, which predicts uniformity of the cotangent of pitch angle between some unknown upper and lower limits, finding our observations are consistent with this model of transient and recurrent spiral pitch angle as long as the pitch angle at which most winding spirals dissipate or disappear is larger than 10 degrees.
Fragmentation of a spiral arm is thought to drive the formation of giant clumps in galaxies. Using linear perturbation analysis for self-gravitating spiral arms, we derive an instability parameter and define the conditions for clump formation. We extend our analysis to multi-component systems that consist of gas and stars in an external potential. We then perform numerical simulations of isolated disc galaxies with isothermal gas, and compare the results with the prediction of our analytic model. Our model describes accurately the evolution of the spiral arms in our simulations, even when spiral arms dynamically interact with one another. We show that most of the giant clumps formed in the simulated disc galaxies satisfy the instability condition. The clump masses predicted by our model are in agreement with the simulation results, but the growth time-scale of unstable perturbations is overestimated by a factor of a few. We also apply our instability analysis to derive scaling relations of clump properties. The expected scaling relation between the clump size, velocity dispersion, and circular velocity is slightly different from that given by the Toomre instability analysis, but neither is inconsistent with currently available observations. We argue that the spiral-arm instability is a viable formation mechanism of giant clumps in gas-rich disc galaxies.
Aims: To gain insight into the expected gas dynamics at the interface of the Galactic bar and spiral arms in our own Milky Way galaxy, we examine as an extragalactic counterpart the evidence for multiple distinct velocity components in the cold, dense molecular gas populating a comparable region at the end of the bar in the nearby galaxy NGC3627. Methods: We assemble a high resolution view of molecular gas kinematics traced by CO(2-1) emission and extract line-of-sight velocity profiles from regions of high and low gas velocity dispersion. Results: The high velocity dispersions arise with often double-peaked or multiple line-profiles. We compare the centroids of the different velocity components to expectations based on orbital dynamics in the presence of bar and spiral potential perturbations. A model of the region as the interface of two gas-populated orbits families supporting the bar and the independently rotating spiral arms provides an overall good match to the data. An extent of the bar to the corotation radius of the galaxy is favored. Conclusions: Using NGC3627 as an extragalactic example, we expect situations like this to favor strong star formation events such as observed in our own Milky Way since gas can pile up at the crossings between the orbit families. The relative motions of the material following these orbits is likely even more important for the build up of high density in the region. The surface densities in NGC3627 are also so high that shear at the bar end is unlikely to significantly weaken the star formation activity. We speculate that scenarios in which the bar and spiral rotate at two different pattern speeds may be the most favorable for intense star formation at such interfaces.
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