Updated Contour plot, needs

Today I spent time rounding off the different special cases for quads and triples. Special cases being: cosmic scatter=0, cosmic scatter=10 000kpc. I did these for pairs, here is an update version of the contour plot:

The underlying problem here being the ones that match the model best are at moderate to high coherence lengths. These are at roughly ellc=10 to 30 kpc or so. This is against the findings of the likelihood calculations, which found the smallest coherence lengths (ell_c=0.1 kpc) to be the most likely data set. This needs to be reconciled in some way.
NEEDED FOR PAIRS: must compare the values of matching to A and simulating B, and the values for matching to B and simulating A …from the SAME absorption system.

Testing Cloud-to-Cloud Cosmic Scatter

Insofar, i’ve been testing the TC08 model as if there is cosmic scatter of 0.25dex at EVERY LOS that’s simualted. This was a result we found in a previous test of the TC08 model. While we took measures to stop ridiculous scatter at very small separations, it’s important to test whether LOS-to-LOS scatter is actually true. TC08 does not tell us where the scatter is occurring, just that there is 0.25dex scatter of the data round their best-fit parameters to the model.

to that end, I want to test what happens if we have cloud-to-cloud scatter. I’m approximating this by using a coherence length=10 000 kpc. Any separation in the sample size will be dwarfed by this number, and force both LOS in any pair/triple/quad to be scatter the same amount. Note that there is still different scatter values for every new halo mass randomly chosen, but within each individually chosen halo, the scatter is one value.
Note also that I’ve previously tried using a cosmic scatter of CS=0.0, which I did as a first test. All this does is test the underlying TC08 form. which has been shown to not fit the data in Tinker & Chen 2008. Trying ell_c=10 000 will allow cosmic scatter to stay, but only on a cloud-to-cloud basis.
cov_frac:0.0100000 ell_c: 10000.0 Significance:1.7986632e-09 D:0.67555539
cov_frac:0.100000 ell_c: 10000.0 Significance:1.2078819e-08 D:0.64777819
cov_frac:0.200000 ell_c: 10000.0 Significance:7.1495750e-07 D:0.58333309
cov_frac:0.300000 ell_c: 10000.0 Significance:0.00014028578 D:0.48555589
cov_frac:0.400000 ell_c: 10000.0 Significance:0.0020535367 D:0.42555521
cov_frac:0.500000 ell_c: 10000.0 Significance:0.0078758335 D:0.39111161
cov_frac:0.600000 ell_c: 10000.0 Significance:0.0072536699 D:0.39333289
cov_frac:0.700000 ell_c: 10000.0 Significance:0.0072536699 D:0.39333289
cov_frac:0.800000 ell_c: 10000.0 Significance:0.011321198 D:0.38111159
cov_frac:0.900000 ell_c: 10000.0 Significance:0.014883888 D:0.37333379
cov_frac:1.00000 ell_c: 10000.0 Significance:0.012251771 D:0.37888801
Triples/Quads and Contour plots
As mentioned, a triple will have 6 KS tests associated with one configuration of coherence length and covering fraction (ell_c,f_c). The question is, how do you make a contour plot with these values?
First, i believe there will be a result of 3 contour plots here. One contour plot per matched sightline. i.e. for all the LOSA matches, a contour plot depicting the values found in testing BOTH the LOSB and LOSC simulated distributions. As the significance value is the ‘probability of getting a value equal to D or more,’ we could multiply these 2 probabilities together…because we want to know when there are good values that include BOTH distributions at the same time.
Then there would be 2 other contour plots, one for matches made LOSB, and one for matched made to LOSC. Per (ell_c,f_c) there are 3 contour plots.
Scratch the above……i think its better to have 6 individual contour plots of the triples…
The above figure shows a contour plot for triples for all matches to a LOS A. so the line of sight that was given the designation ‘A’ from the authors, typically because it has the strongest absorption line in MgII. And this contourplot is ONLY comparing the distribution of all the subsequent EWBs that were simulated given a match the objects LOSA.
the contourplot, and KS-plots, both show much lower significance in matching a y=x curve. This is an interesting result, because if a match is made to LOSA, the way in which LOSB is found is exactly the same as pairs. The only difference is the location of the ‘midpoint’ position X. but this only slightly different. quite simply, the triples don’t match as well as the pairs.
contour plots for LOSA,LOSC ……LOSB,LOSA……..LOSB,LOSC……..LOSC,LOSA…..LOSC,LOSB to follow

Checking Quads: were 900 matches made in each LOS?

I needed to check, just like i did for triples, whether each LOS in the quad had 900 matches or 0. 900 meaning that it was a LOS that could be matched to, and 0 meaning it was simply an upper limit. After doing the same test, it seems that there is one LOS that has not been matched up to 900 times. i.e.

OBJ: 2 z=0.676 LOSA:696 LOSB:0 LOSC:0 LOSD:2703 TOTAL=3399.0000
so there were a total of 3399 matches to this absorption system, but only 696 of them were a match to LOSA, the rest were to LOSD. I need to go back and add more matches to this LOS, at least 300 for every run.
————————^——-Problem fixed—————-^—————-
Need to create the same KS tests for each of the quads now…replicate Triples

What happens when cosmic scatter is zero?

If the cosmic scatter in my model is zero, then I am essentially following the TC08 model exactly. There is no upper or lower envelope of EW values for a given mass profile of the halo. Just one curve.

cov_frac:0.0100000 ell_c: 1.00000 Significance:1.4538320e-19 D:0.94777800
cov_frac:0.100000 ell_c: 1.00000 Significance:1.1752003e-15 D:0.85333300
cov_frac:0.200000 ell_c: 1.00000 Significance:4.6867554e-11 D:0.72555600
cov_frac:0.300000 ell_c: 1.00000 Significance:8.3111776e-09 D:0.65333300
cov_frac:0.400000 ell_c: 1.00000 Significance:2.0814730e-05 D:0.52333300
cov_frac:0.500000 ell_c: 1.00000 Significance:0.0010673220 D:0.44111100
cov_frac:0.600000 ell_c: 1.00000 Significance:0.011778121 D:0.38000001
cov_frac:0.700000 ell_c: 1.00000 Significance:0.038453044 D:0.34444401
cov_frac:0.800000 ell_c: 1.00000 Significance:0.15768489 D:0.29333300
cov_frac:0.900000 ell_c: 1.00000 Significance:0.016071932 D:0.37111101
cov_frac:1.00000 ell_c: 1.00000 Significance:0.00072479580 D:0.45000001

The output from the KS test. It shows that even for cosmic scatter of zero, the worst fitting distributions are those at very low covering fraction, and the best ones are around fc=0.8 roughly.