An automated photometric pipeline for measuring the corotation radius of spiral galaxies

Kimia Yazdani; Sahel Mesforoush; Wayne B. Hayes

astro-ph.GANov 3, 2026

An automated photometric pipeline for measuring the corotation radius of spiral galaxies

Authors: Kimia Yazdani, Sahel Mesforoush, Wayne B. Hayes

Abstract

The corotation radius R_CR of a spiral galaxy marks the radius where the angular speed of the spiral pattern matches the orbital speed of the disk material. Despite its importance for understanding spiral structure and galaxy evolution, very few galaxies have corotation measurements, often derived using heterogeneous techniques. We present an automated photometric pipeline that identifies corotation radii by tracking the azimuthal phase offset between young and old stellar populations. Building on the color-gradient framework of \citet{Puerari1997}, we extract azimuthal brightness profiles from deprojected dual-band images, fit periodic models to the profiles, and identify corotation candidates at radii where the phase difference between the two stellar tracers changes sign. Each candidate is assigned an adaptive uncertainty interval and reported with a goodness-of-fit metric. We benchmark the method against a cross-method literature compilation, scoring every technique -- including our own -- against a reference built from the published measurements alone and evaluated leave-one-out. Over the $90$ galaxies for which such a reference exists, the pipeline places a correct corotation radius in $80.0\%$ of them, recovers $63.6\%$ of their known corotation radii, and reaches a harmonic mean of recall and purity of $0.58$ , the highest values of any method in the comparison. Unlike the published methods, each of which was applied to a small, curated set of galaxies, our pipeline is run on the entire reference sample without any pre-selection, a sample two to six times larger than existing methods. The pipeline is scalable to large surveys, flexible with respect to spiral mode, and naturally recovers multiple corotation radii in galaxies with complex spiral structure, providing a uniform framework for studying disk resonances across diverse galaxy populations.

Figures & tables

Figure 1: Construction of the azimuthal brightness profiles. (a) Two-band composite of a deprojected synthetic spiral galaxy with three sampled annuli highlighted in color. (b) Schematic of a single annulus, showing its radial width, set to $0.04\,R_{25}$ in the analysis and drawn here schematically, and the partition into $120$ equal-azimuth bins of $3^{\circ}$ each, one of which is highlighted. (c) Mean-subtracted azimuthal brightness profiles $I_{R}^{\prime}(\theta)$ in the $g$ - and $i$ -bands at the three sample radii. The thin lines show the raw mean-subtracted profiles, while the thick lines show Gaussian-smoothed versions for display. Note that the blue curve shifts leftward from the top panel to the bottom (i.e., with increasing radius).

Figure 2: Anatomy of the cosine fit at a single annulus. The light curve shows the raw mean-subtracted brightness profile

I_{R}^{\prime}(\theta)

, the bold curve the smoothed version, and the dashed black curve the best-fit cosine model Eq. 2 with

m=2

. The peak-to-peak amplitude

2A

, the constant offset

D

, and the phase shift

c/m

that defines the angular position of the arms are indicated.

Figure 3: Schematic evolution of the cosine fits across radii in both bands. Each panel shows the raw azimuthal profiles (thin lines) and the corresponding cosine fits (thick lines) for the $g$ -band (blue) and $i$ -band (red) at increasing galactocentric radius. The dotted vertical lines mark the angular position of the fitted peak in each band; their relative shift with radius reflects the radial dependence of the phase difference between the two stellar populations.

Figure 4: Per-band phase as a function of radius and the resulting phase difference. (a) Fitted phase shifts

c_{\mathrm{blue}}(R)

and

c_{\mathrm{red}}(R)

obtained from the

g

- and

i

-band fits. (b) Phase difference

\Delta\phi(R)=c_{\mathrm{blue}}(R)-c_{\mathrm{red}}(R)

. Zero-crossings of

\Delta\phi(R)

, marked by green points, define the candidate corotation radii of the galaxy.

Figure 5: Candidate corotation radii for NGC 6300. The curve is the measured phase difference

\Delta\phi(R)

, which is scanned for sign changes. Dark circles mark the two candidates, at

0.40

and

0.53\,R_{25}

, with their uncertainty intervals shaded. The vertical green line is the gold-standard value,

0.41\,R_{25}

, and the green band the tolerance used for scoring; the candidate at

0.40\,R_{25}

coincides with it. Grey bands mark the radial range excluded from candidate selection.

Method	Type	$N$	$N_{\rm c}$	Compl.	Recall	Purity	$F_{1}$
This work	phase offset	90	72	80.0 %	63.6 %	52.5%	0.58
Buta and Zhang (2009)	potential–density	40	29	72.5%	57.7%	35.9%	0.44
Abdeen et al. (2020)	multi-band offset	16	11	68.8%	52.5%	56.2 %	0.54
Ruiz-García et al. (2024)	bar torque	21	11	52.4%	38.5%	52.4%	0.44
Elmegreen and Elmegreen (1995)	morphological	44	22	50.0%	29.4%	51.1%	0.37
Williams et al. (2021)	Tremaine–Weinberg	19	9	47.4%	40.5%	47.5%	0.44

Table 1: Agreement of each method with the literature gold standard (criterion: predicted

R_{\mathrm{CR}}

within

0.10\,R_{25}

of a gold-standard value).

N

is the number of galaxies scored,

N_{\rm c}

the number with a correctly located

R_{\mathrm{CR}}

, and

F_{1}

the harmonic mean of recall and purity. Recall and purity are counted per corotation radius, completeness per galaxy; all three are conditional on the galaxies each method reports on, and

N

therefore differs between rows.

Figure 6: Fraction of galaxies in which at least one predicted

R_{\mathrm{CR}}

lies within

0.10\,R_{25}

of the gold standard. Numbers in brackets give the number of galaxies scored. Each published method is scored against a gold standard built without its own measurements.

Figure 7: Fraction of gold-standard corotation radii recovered by at least one predicted

R_{\mathrm{CR}}

within

0.10\,R_{25}

(recall). Numbers in brackets give the number of galaxies scored.

Figure 8: Harmonic mean of recall and purity (the

F_{1}

score), for the same methods and criterion as Fig. 6 .

Figure 9: Accuracy per galaxy, the mean fraction of a galaxy’s predicted radii within

0.10\,R_{25}

of the gold standard, against the number of galaxies scored. Error bars are one standard error over galaxies.

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Topic pending

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Abstract

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