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In an answer to my previous question about the first stars it was stated they probably formed at Z=20 to Z=60 and may have had a mass between tens to 100s to 1000s of times the mass of the Sun.

Given that, what would the dominant wavelength of the light emitted by these supernova and approximately how bright would they be in the reference frame of the supernova?

What would the wavelength and brightness of those supernova be if we observed them today?

Is there any chance that a current telescope, a planned telescope or a reasonably potentially possible future telescope could detect these supernova?

For this telescope, would the field of view be so narrow that we would be unlikely to ever see one of those supernova in a reasonable time?

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The short answer is probably "yes we can", and possibly "we've already seen supernovae from the first galaxies", in the form of long-duration gamma-ray bursts. GRB 090429B has been given a redshift z=9.4, beating the previous record-holder GRB 090423 at z=8.2. As we continue to watch the skies, we're seeing more and more of these objects, and we'll gradually push back the boundary. I don't know what sets the upper limit on how far away we can see GRBs but I don't think it's a coverage problem: Swift covers something like a tenth of the sky.

Note that despite the high redshifts, they're probably not quite high enough to be the first stars. If someone reported a long GRB at z=15, then I'd think it more likely.

I'm not an observer, so I'm not sure about what colours and magnitudes are usually associated with supernova, but I can try. With a bit of Googling, Daniel Kasen's page suggests that they're relatively bright in most bands. Off the top of my head, I think we see them most in optical, but that might just be a selection effect. I think, until now, we've been finding Type Ia supernova up to about z=1.5. That boundary is being pushed, but I'm not sure how. (Possibly improved IR spectroscopy from a Hubble servicing?) The overall brightness of supernovae is of the order of 10$^{51}$ ergs. Type Ia's have typical absolute visual magnitude -19.3, according to Wiki.

As for other types of supernova, I suspect that as you move further out, isolating a single supernova in a low-resolution galaxy image is a major obstacle, but that's pure speculation on my part. That is, the supernova needs to be significantly brighter than the surrounding galaxy. Fortunately, I think this is the case for GRBs, but I'm doubt it for other supernova.

I'm much less knowledgable on this than my previous answer, so I welcome corrections.

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A recent paper by Dan Whalen titled, Finding the First Cosmic Explosions. I. Pair-instability Supernovae discusses this very problem.

The pair-instability supernova (PISNe) is a special case of massive stars, around 100 $M_\odot$, in which the thermal pressure inside the star is reduced via the production of electron-positron pairs. Runaway thermonuclear burning results, much like the Type Ia SNe, producing on the order $10^{53}$ ergs of energy. The difference here is now the exploding star leaves no degenerate remnant because the energy released completely unbinds the star.

The bolometric luminosity of the PISNe peaks at about $10^{46}$ erg/s, about 3 orders of magnitude larger than the typical Type Ia. With redshifting the photons from $z\simeq7$ to now, we expect the signal to be in the NIR wavebands with a magnitude around 28. Currently, there is no observatory capable of detecting these.

However, there is one observatory coming soon that might be able to detect these: James Webb Space Telescope (JWST), with a threshold of 32 magnitude. This telescope should be able to detect the remnants of PISNe. It also looks like the Wide-Field Infrared Survey Telescope (WFIRST) is making its way into being built and launched, but this telescope has a slim chance of observing PISNe at a detection limit of 27 magnitude.

It also appears that SN 2007bi is a PISNe (see this paper). The data was taken at the Palomar Observatory with a 1.2 m telescope in the R-band.

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