# Getting XYZ coordinates of Luminous Red Galaxies catalogue

So I want to get the XYZ (rectangular/Cartesian) coordinates of the LRG (luminous red galaxies) catalog. The catalog is available for download from here: https://data.sdss.org/sas/dr16/eboss/lss/catalogs/DR16/ You just have to search the "LRG" ones. Since I'm not very interested in clustering at first I figured I'd download the eBOSS_LRG_full_ALLdata-vDR16.fits. In this fits file, I see RA and DEC coordinates but I don't see any measure of distance. Thus I'm not sure how to covert this RA and DEC to XYZ coordinates. I've read some papers where they say they have done this so in principle it should be possible just I am not sure how. Am I supposed to use the magnitude to somehow estimate the distance (something like this: https://ned.ipac.caltech.edu/level5/Willick/Willick1_2.html)? For some reason, I expected this would be precomputed in the catalog measurements but maybe I'm misunderstanding something.

I understand that BAO (Baryon Acoustic Oscillation) is used for determining distance. According to https://www.sdss.org/dr16/spectro/lss/ the SDSS fits files link I posted above also contains information about BAO (it is the files that contain "rec" I am using the eBOSS_LRGpCMASS_clustering_data_rec-NGC-vDR16.fits file for example). However, I can't find what the fields mean and more importantly how to get distance from them.

Any and all help appreciated if I'm missing some documentation please let me know.

• The format of those catalogs is described in the SchemaBrowser which shows there is a Z column which gives you the redshift (distance). Assuming a cosmological model for the Universe can let you convert redshifts to distance e.g. with AstroPy – astrosnapper Feb 19 at 22:42
• What @astrosnapper posted I think is a good way to go about it. I just found a good cosmology calculator code in python2 from Ned Wright (see here: astro.ucla.edu/~wright/CC.python) that also seems to work. This website looks like an online implementation of it. However, I think it's probably easier to just call the WMAP9 astropy code. Thanks for pointing me to this. I'm still not entirely sure how to use the BAO measurements but I think for now should be fine :) – kauii8 Feb 19 at 22:54