tokens: the redshift of the clusters. 4.1. Ridge fitting Since we are trying to create a general method to use for many different sets of galaxies at different redshifts, we have decided to use a single set of parameters across all the bins. By doing so we retain a generally low dispersion in the fits as it makes sure that there are no systematic errors due to using different parameters. As can be seen in Fig. 4 , we mostly obtain good fits for both the ridges with a few outliers and even fewer ridges that we do not find at all. The main exceptions to this are at around redshift z 0.05 where the bins do not contain many galaxies and we end up with sparse ridges. For the redshift bins very close to us we cannot fit anything below redshift z = 0.021 as the ridges are too irregular and the method can no longer fit them to satisfying precision. For the star-forming ridge we see a large increase in dispersion at higher redshift. This is mainly due to how sparse the ridge becomes at this point, making it harder to detect. Fig. 4. Standard deviation of the fit of the ridges in each of the redshift bins. At redshifts of z 0.021, the method does not detect any ridges due to the number of galaxies in the bins. We also see increasing irregularity in the ridges below about redshift z 0.05. Besides this we the star-forming ridge having very high dispersion at redshifts above z 0.15 due to being very sparse at these redshifts. 4.2. Evolution of ridges in redshift By plotting each of our measured ridge SFRs, we can then see a relationship between the SFR and redshift (Fig. 5 ). It is obvious that the relationship is linear for the whole range of redshifts for the star-forming ridge and linear in about half the redshift range for the quenched ridge. It could be argued that a logarithmic fit would make a better fit for the quenched ridge but it seems more likely that there is another answer for the high redshift part of the quenched ridge, since the SFR values for the ridge stay almost constant in that part. This is likely due to a few different factors such as difficulty in observing the quenched ridge at this redshift or due to us using a shallower incline in the SFR– M ⋆ plane than appropriate or that the ridges are not linear in the SFR– M ⋆ plane but actually curve downwards at higher mass ranges as suggested by Schreiber et al. (2014) and Ciesla et al. (2017) . This would lead to higher estimates as we go to higher z since we only detect the high mass end of the ridge in that region. This fit does not seem to be widely accepted as people are still using linear ridges in some papers ( Renzini Peng 2015 and Davies et al. 2016 ). Fig. 5. Evolution of star-forming ridge and the quenched ridge SFR with redshift. For the star-forming ridge the best fit seems to be a linear one whereas for the quenched ridge it seems that above about redshift log( z + 1)=0.055 the measurements diverges from the linear fit. This could be due to a systematic error in the measurement of
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