Spirality: A Novel Way to Measure Spiral Arm Pitch Angle

Abstract

We present the MATLAB code Spirality, a novel method for measuring spiral arm pitch angles by fitting galaxy images to spiral templates of known pitch. Computation time is typically on the order of 2 min per galaxy, assuming 8 GB of working memory. We tested the code using 117 synthetic spiral images with known pitches, varying both the spiral properties and the input parameters. The code yielded correct results for all synthetic spirals with galaxy-like properties. We also compared the code’s results to two-dimensional Fast Fourier Transform (2DFFT) measurements for the sample of nearby galaxies defined by DMS PPak. Spirality’s error bars overlapped 2DFFT’s error bars for 26 of the 30 galaxies. The two methods’ agreement correlates strongly with galaxy radius in pixels and also with i-band magnitude, but not with redshift, a result that is consistent with at least some galaxies’ spiral structure being fully formed by z=1.2, beyond which there are few galaxies in our sample. The Spirality code package also includes GenSpiral, which produces FITS images of synthetic spirals, and SpiralArmCount, which uses a one-dimensional Fast Fourier Transform to count the spiral arms of a galaxy after its pitch is determined. All code is freely available.

Probing the Low-mass End of the Black Hole Mass Function via a Study of Faint Local Spiral Galaxies

“…These small outer annuli with unstable pitch angles are excluded. As a result, the measurements with small inner radii or N B, we utilized the SPIRALARMCOUNT software [30,66] to overlay the best-fit pitch model output from 2DFFT. Thus, the overlaid spiral is a representation of, and equivalent to, the inverse Fourier transform from 2DFFT.…”

“…There is not a way to classify a galaxy as, for example, "three arms, plus or minus one arm." However, other software such as SPIRALARMCOUNT [30,66] is capable of measuring the relative contributions from each choice of the number of arms. Moreover, the 2DFFT software [60,61] used in our current manuscript is capable of computing the pitch angle for the superposition of any number of arms.…”

“…Combining Equation 3 from Shields et al [30] and Equation 3 from Davis et al [29], even a modest φ = 20 • spiral that remains intact for 2π radians and begins at an inner galactic radius of 1 kpc would extend out to an outer radius of ≈10 kpc and cover a total arc length of ≈26 kpc as it wraps around the galaxy.…”

“…2 As a result, the M • -φ relation is a useful method both for measuring the SMBH mass of spiral galaxies locally and at higher redshift, with the caveat that spiral structure be sufficiently resolved in imaging. For example, Shields et al [30] find that pitch angles are reliably measured out to z = 1.2 for spiral galaxies in he Great Observatories Origins Deep Survey [31]. In recent years, pitch angles have been measured for spiral galaxies spotted at incredible redshifts: z = 2.54 [32] and z = 4.41 [33].…”

“…thanks David Nelson for the use of his secluded office space during the COVID-19 pandemic. This research made use of 2DFFT [60,61], 2DFFT UTILITIES (https://github.com/AGES-UAR 2DFFTUTILS MODULE (https://github.com/ebmonson/2DFFTUtils-Module), DAOPHOT [73], FITDISTR-PLUS [79], Fox and Weisberg [82], GALFIT [67], GGPLOT2 [138], IRAF [62,63], ELLIPSE [65], KEDD [80], the NASA/IPAC Extragalactic Database (NED), the NASA Astrophysics Data System (ADS), PEAR-SON_DS [74], PEARSPDF (https://www.mathworks.com/matlabcentral/fileexchange/26516-pearspdf), R [139], SAOIMAGEDS9 [140], and SPIRALARMCOUNT [30,66].…”