Reproduction of Iye et al. (2021)

This page provides code and data for the reproduction of the analysis and results of Masanori Iye , Masafumi Yagi, Hideya Fukumoto, 2021, AJ, Spin Parity of Spiral Galaxies. III. Dipole Analysis of the Distribution of SDSS Spirals with 3D Random Walk Simulations.
The code implements Equation 2, where hi is the spin direction of the galaxy and theta is the angular distance between the galaxy and the dipole, as specified in the paper.

The code that implements the method is iye_et_al_method.cpp. Since the simulation requires substantial computing time, it is written in C.

To compile the code: g++ -o iye_et_al_method iye_et_al_method.cpp

The data used in (Iye et al 2021) is galaxies.csv. That is the exact same 'clean' dataset used in (Iye et al 2021).

To run the code on the data: ./iye_et_al_method galaxies.csv
The program will print the results in the standard output. The program takes several hours to run, and could be more than a day, depends on the processor. To make it run faster you can increase the value of the variable increment, or reduce the number of simulations (line 162) from 2000 to a smaller number.

The output of applying the code to the data is in the file iye_et_al_results.csv
The axis has statistical significance of 2.14 sigma. That is much higher than the 1.29 sigma reported by Iye et al (2021) for the exact same analysis and exact same data.

A visualization of the results (iye_et_al_results.csv) using Mollweide projection.

A simpler and much faster analysis is to separate the data into two hemispheres by the RA of the galaxies. One hemisphere at (70 < RA < 250) and the opposite hemisphere is (70>RA or RA>250). All values are in degrees. Simple binomial distribution will show that the distribution is not random.

The results are summarized in the following table.

Hemisphere (RA) # Z-wise   # S-wise   #Z/#S      P (one-tailed) P (two-tailed)
70-250 23,037 22,442 1.0265 0.0026 0.0052
>250 U <70 13,660 13,749 0.9935 0.29 0.58

That shows that the sky can be separated into two asymmetric hemispheres. The asymmetry in one of them is statistically significant, even after applying a Bonferonni correction (P=~0.01).

The following code executes a Monte Carlo simulation of the distribution to test the frequency of such distribution or stronger to occur in any possible two opposite hemispheres (separated by RA) when the spin directions of the galaxies are random.
Compile: g++ -o distribution_simulation distribution_simulation.cpp
Run: ./distribution_simulation galaxies.csv
In 100,000 runs it will happen about 70 times (P=~0.007).

Important note: The dataset used in (Iye et al., 2021) was taken from (Shamir, 2017, PASA). That paper does not make any attempt to show any kind of axis in that dataset. No claim for an axis in that dataset was made in any of my other papers. All of my papers cited in (Iye et al., 2021) as papers that showed a dipole axis used other datasets, and not the one used in (Iye et al., 2021).

The dataset used in (Shamir, 2017, PASA) is a dataset of bright objects (i<18) and therefore, on average, lower redshift. Previous work showed lower asymmetry in lower redshift ranges. The dataset also uses a minimum of 10 peaks in the radial intensity plot to make an annotation, rather than 30 peaks in the papers showing a dipole axis. Still, the distribution in the dataset is not random, as shown here.

New: The NAOJ explains why the paper is not reproducible

The NAOJ, where the research was done, provided an expalantion to the different results when reproducing the paper, compared to the results stated in the paper. The explanation is here.

In summary, the NAOJ explains, "Because it is hard to verify the detail of simulations, we here calculate the analytic solution by Chandrasekhar (1943) which assumes uniform samples in the hemisphere."
That is, to reproduce the results, one needs to assume that the distribution of the galaxies is uniform in the hemisphere. That assumption is not mentioned in the paper. More importantly, the distribution of galaxies in SDSS is not even close to uniform distribution. Also, there is no reason to make that assumption, as all galaxies have their exact coordinates. That false (and unnecessary) assumption, that is not mentioned in the paper, explains why the paper as published is not reproducible.