https://www.legacysurvey.org//viewer/?ra=90.9853&dec=-35.9682&layer=ls-dr9&zoom=15
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Whenever someone includes it in a successful proposal, which doesnāt seem to have happaned yet.
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Maybe we should write a proposal 
You could always write one for cycle 5. Youād need a good science case though.
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I think the fact that this is one of the best gravitational lenses found so far is a pretty good reason. I am pretty sure that it will happen soon. If not, we can certainly write a proposal for it. I tried searching the proposals but I am new to the system and it thinks I am a robot because I tried searching by target location.
https://www.stsci.edu/jwst/science-execution
https://www.stsci.edu/jwst/science-execution/approved-programs
Here are the cycle - 4 - go ones
https://www.stsci.edu/jwst/science-execution/approved-programs/general-observers/cycle-4-go
These are some of the proposals that could include such an image already in cycle 4
https://www.stsci.edu/jwst/science-execution/program-information?id=7049
https://www.stsci.edu/jwst/science-execution/program-information?id=7184
https://www.stsci.edu/jwst/science-execution/program-information?id=7511
https://www.stsci.edu/jwst/science-execution/program-information?id=7677
Iām not sure what ābestā is supposed to mean in this scenario. JWST time is extremely difficult to get, even when you have a good science case & program design.
I guess the first question is why do you want to observe it with JWST? Is it to do some sort of investigation into this kind of lensing, or do you just want a pretty picture? If its the former, I guess its feasible if you can show you need JWST (and HST for example isnāt sufficient for you science goals). If its the latter, thereās no shot.
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Well you could argue that you want both HST and JWST to image this lens. I would have thought that Proposal 7184 using timing might be a good reason since it requires angular precision of the lenses as well as data over time to get H0. I think the angular precision might be the correct application for JWST. Also, proposal 7677 which is looking for population iii stars could be benefited by a mid inferred image of this lens too.
Actually, now that I think of it I might have been thinking about the wrong category since this cluster is z ~ 0.5
https://www.stsci.edu/jwst/science-execution/approved-programs/general-observers/cycle-4-go
But I donāt think any of the current proposals overlap 
Why though? What are you trying to investigate that requires both optical and mid-infrared observations?
Iām curious what your top pick for JWST to look at is? Iāve wondered it myself if I could only choose one. It is such a target rich environment. I have galaxy interactions iād like a closer look at. several distant grand design spirals please.
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I suppose I would be glad enough to see a HST image of this object if we couldnāt get time on JWST, but maybe someone could work it into an existing proposal since there are probably some that are looking at large galaxy clusters. And at least from the lens perspective it presents a target for another dark matter in cluster distribution study as well as a nice independent measurment to H0 from timing. And I am sure that any study that is working on large clusters between no and cosmic noon would want to know things that can only be obtained by both HST and JWST. But anyway. It is on my wishlist 
Actually, I think, in terms of galaxy clusters, I would be more interested in seeing a better image of CL J1001+0220: https://en.wikipedia.org/wiki/CL_J1001%2B0220
You can barely see the smudges if you turn the contrast up in the dr10 survey
https://www.legacysurvey.org//viewer/?ra=150.2373&dec=2.3358&layer=ls-dr9&zoom=16
https://www.legacysurvey.org//viewer/?ra=150.2373&dec=2.3358&layer=ls-dr10&zoom=16
The reason for this one is to see how clusters have evolved since (CL J1001+0220) is the most distant cluster known.
Actually, if I could only pick one, I would like a new JWST Ultra Deep Field to check for z = 28.5 galaxies 
Yeah 100 Million years after the big bang!
Looking in these coordinates: https://www.legacysurvey.org//viewer/?ra=188.7522&dec=52.3694&layer=ls-dr10&zoom=15&desi-spec-dr1
Use filters F227W, F356W, F410M, and F444W for the first 120 hours of exposure and then pick a few of the highest z objects and use a mask to get their spectra. 
Oh, and I would let F227W be blue, F356W and F410M for the green, and F444W for red.
Oopsā¦ I just realized that F444W is still not the longest wavelength filter for JWST.
I think we need to go all the way up to 280000 Ang. Thinking F2100W, F2300C, and F2550W should be used. Probably F1500 and F1800W as Blue.
So filters
I made this filter graph on matlab. You can get the filter profiles from
These are the only ones for NIRcam, MIRI has the longer filters extending out to 28.5 microns.
You may have seen this already, but there is an HST image of your original object.
https://arxiv.org/html/2408.10320v1
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Those coordinates are in the COSMOS field ā perhaps the most-imaged bit of sky. Iām certain JWST will have observed there already.
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True, but as far as I know they havenāt pulled out all the stops. If there was a z=28 object it could take hundreds of hours to expose to say nothing of the amount of background noise that would need to be removed, could be potentially the main reason why no-one has proposed such a project. Actually in cycle-3 there is such a proposal but in a different part of the sky here is the abstract for it:
ABSTRACT
We propose to perform a slitless spectroscopic survey with NIRCam/WFSS targeting the COSMOS-Web field together with deep parallel MIRI
imaging, to establish a treasury dataset covering the largest ever field (0.33 deg2, including 500 arcmin^2 with MIRI) in the infrared, and secure
redshifts of ~20000 galaxies and 5000 AGN over a survey volume of 3x10^7 Mpc^3, including >4000 galaxies and up to 500 AGN at z>5, into the
epoch of reionization (EoR), providing a true 3-D panoramic view of the early Universe and addressing the following key scientific questions:
(1) How did the early massive galaxies emerge? Do they pose a challenge to modern cosmology? We will measure unbiased 3-d galaxy correlation
function at EoR to map the growth of early dark matter halos and unveil the earliest galaxy protoclusters.
(2) How did the early supermassive black holes (SMBHs) emerge? What is the nature of the puzzling āLittle Red Dotsā unveiled by JWST? The survey will provide a complete AGN census in the early universe to probe the modes of early SMBH accretion and growth.
(3) How did āCosmic Webā of the Universe emerge? Whatās the sources of reionization? How did galaxies and SMBHs evolve in that context? The
survey will produce the first IGM tomographic map at EoR and trace IGM/galaxy connections from cosmic noon to reionization.
This treasury dataset will enable a wide-range of extragalactic science, including the measurements of high-z galaxy luminosity function, census of
dusty galaxies across cosmic time, supernovae and AGN detections through variability. The team will provide fully reduced spectra and valued added
spectroscopic and photometric catalogs to the community.
https://www.stsci.edu/jwst/science-execution/program-information?id=5893
Iām not sure where youāre getting this redshift z=28 number from, but that is WAY beyond the current limits.
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Well, letās keep it under wraps until I can publish my next paper with the full correct prediction. Then if we find it as predicted that is a good sign. And if it is correct we should get detectable galaxies up to about z = 28.5 which is just barely within the capabilities of JWST. I mean, think about it, if you already get galaxies 100 million years later at z = 14.32 and that are such tightly compacted and with an absolute magnetude of about -20.81 (a galaxy about 10 billion times as luminus as the sun), then there should be a normal distribution of peak ignition times for those stars to begin shining (they donāt all start shining at once) such that a substantial amount of stars from 100 million years earlier should have already ignited. The question is what is the spread for the birth rate. These arenāt even population iii stars. So population iii take some time even if you squeeze it into 30 million years there must still be a spread. All I am saying is that I donāt think that the 13.8 billion years is the correct age of the universe. I know I am in the minority when it comes to cosmology. But things like the Hubble tension and the cosmological constant problem (related to the UV and IR mixing in QFT) and the BAO starting to deviate from LCDM, as well as Sigma-8 tension, the final parsec problem, and many more. I think I have an answer that will solve all of these problems including give a reason for the Higgs hierarchy.
Oh by the way, I potentially solved the cosmological constant problem and the value predicts specific sizes of cosmologies were maybe even the Hubble constant may only be allowed to have certain descrete values. And they are quite large jumps between them. The model favors the SH0ES result with a prediction of H0 = 73.62694+/-0.00083 km/s/Mpc this ends up being the 80th Hubble level. The 79th value is about 429 km/s/Mpc and the 81st is 12.6 km/s/Mpc. So it is rather remarkable that there are these quantized jumps between hubble constants. So it could potentially be like Lambda-CDM but quantized.
Here is the peer reviewed paper, granted the site score for the journal is only 3.2, but it is kinda currious, here is the link if you are interested see section 2:
https://doi.org/10.1016/j.physo.2024.100235
Also here are some figures that are not in the paper but they help clearify the idea.
Cosmology sizes
