# Telescope sensitivity vs size for planet characterising...

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I've been doing some reading about detecting exoplanets by the transit method and was trying to find something that explains the physics of it - does anyone know how it works / have a reference to some good explanation?

For example Kepler was designed to detect exoplanets by measuring the dip in light as a planet passed between us and the parent star. It was supposed to monitor 115 square degrees (I guess 10x10 degrees of the sky) with a sensitivity of 20 parts per million for a magnitude 12 star over a 6.5 hour period with a 1.4 m diameter telescope. It's a survey instrument designed to monitor a large field to find planets. It seems to me that if you wanted to monitor a particular individual star at the same precision for light intensity you should be able to use a smaller telescope, if you are monitoring one hundredth the sky it seems like you shouldn't' need as much light gathering, I'm not interested in resolution only in light intensity and precision of the measure - and only relative precision over time anyway.

I haven't found anything that lays out the math relating size, focal length, light gathering and precision - does anyone have any info/good references?

If you wanted to see 20 ppm variation for a single star how big/small a mirror would you need? if you wanted to see 0.1 ppm? if you wanted to do spectroscopy with 100 wavelength 'bins' then is that like another factor of 1/100 in ppm sensitivity needed? How much mirror would it take to do reasonable spectroscopic sample of an Earth like planet transiting in front of a sun like star? A lot of the things I've read seem to be shooting for the harder goal of imaging secondary transits and even non transiting planets.

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When used for imaging, a telescope is basically the same as a camera. So a photography resource might help. Photographers typically use focal length and focal ratio (which they sometimes call "aperture") while astronomers more usually use focal length and aperture (the diameter of the main mirror/lens). In telescope terms, focal length / aperture = focal ratio.

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Ever here the roman saying 'divide and conquer' . So the apply this strategy to star hunting.

1. If you know absolutely nothing about exoplanets, which is basically were we are when kepler was designed, literally. We could only see binaries and super huge gas giants (those on the verge of becoming stars themselves) and not very many of them. Then your science strategy is basically to see if you can find planets around any stars. In this case you want a pretty broad field and you are going to generate tons of data, which you can't process and so you crowd source it. Also this scope will not last very long, so you want to be able to pan large sections of the sky in fairly short time.

2. Now you have a short list of targets you are interested in. You have seen alot of stars with gas giants vacuum cleaning the habitable zone of the star, lots of binaries that would never support life, and all kinds of weird configurations. The problem with transits is this they only work if the planetary disk is roughly planer to the telescope. That severely limits the stars you can observe transits of. Theres another problem, light scattering is the inverse forth power of the wavelength, that widely fantastic halo you see around stars is about 1000 times bigger than the star itself. You need to shave that way down. Telescope also produces optics that need to be gotten rid of.

So the bottom line here its not just about mirror size and camera pixels, its about telescope design, wavelength, cooling systems, starfinders, etc. Ultimately you do want a bigger telescope, because ultimately you want to point it and generate 5 pixels or so and use the spectrophotometer and get an idea of what the atmosphere/surface is.  Right now we are not there. There are some who have proposed building a scaffold a km across and having three mirrors, I think we need to invest in a manned space telescope, 100 times bigger than hubble, built basically in space. We can see stuff on close stars, on distant stars you are limited to transects.

Edited by PB666
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2 hours ago, DBowman said:

It seems to me that if you wanted to monitor a particular individual star at the same precision for light intensity you should be able to use a smaller telescope, if you are monitoring one hundredth the sky it seems like you shouldn't' need as much light gathering, I'm not interested in resolution only in light intensity and precision of the measure - and only relative precision over time anyway.

No, it doesn't really work like that. If you maintain (or reduce) diameter while maintaining or narrowing down the field of view your signal from a given point source (star) gets weaker, making it more difficult to resolve transits. In telescopes, bigger really is always better. I don't know if it would be actually possible to detect those 'dips' through our atmosphere with any reliability regardless of 'scope size (I'm guessing no).

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3 hours ago, DBowman said:

I haven't found anything that lays out the math relating size, focal length, light gathering and precision - does anyone have any info/good references?

If you wanted to see 20 ppm variation for a single star how big/small a mirror would you need? if you wanted to see 0.1 ppm? if you wanted to do spectroscopy with 100 wavelength 'bins' then is that like another factor of 1/100 in ppm sensitivity needed? How much mirror would it take to do reasonable spectroscopic sample of an Earth like planet transiting in front of a sun like star? A lot of the things I've read seem to be shooting for the harder goal of imaging secondary transits and even non transiting planets.

I think the keyword here is photometer, here's something that can give you a jump start.

Also, here look for photometer. http://www.jpl.nasa.gov/news/press_kits/Kepler-presskit-2-19-smfile.pdf

For the formulas, the best thing you can do is look for a book on photometry and telescopes, so you have concise ideas.

Edited by Beduino
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7 hours ago, PB666 said:

Ever here the roman saying 'divide and conquer' . So the apply this strategy to star hunting.

1. If you know absolutely nothing about exoplanets, which is basically were we are when kepler was designed, literally. We could only see binaries and super huge gas giants (those on the verge of becoming stars themselves) and not very many of them. Then your science strategy is basically to see if you can find planets around any stars. In this case you want a pretty broad field and you are going to generate tons of data, which you can't process and so you crowd source it. Also this scope will not last very long, so you want to be able to pan large sections of the sky in fairly short time.

2. Now you have a short list of targets you are interested in. You have seen alot of stars with gas giants vacuum cleaning the habitable zone of the star, lots of binaries that would never support life, and all kinds of weird configurations. The problem with transits is this they only work if the planetary disk is roughly planer to the telescope. That severely limits the stars you can observe transits of. Theres another problem, light scattering is the inverse forth power of the wavelength, that widely fantastic halo you see around stars is about 1000 times bigger than the star itself. You need to shave that way down. Telescope also produces optics that need to be gotten rid of.

So the bottom line here its not just about mirror size and camera pixels, its about telescope design, wavelength, cooling systems, starfinders, etc. Ultimately you do want a bigger telescope, because ultimately you want to point it and generate 5 pixels or so and use the spectrophotometer and get an idea of what the atmosphere/surface is.  Right now we are not there. There are some who have proposed building a scaffold a km across and having three mirrors, I think we need to invest in a manned space telescope, 100 times bigger than hubble, built basically in space. We can see stuff on close stars, on distant stars you are limited to transects.

A Manned space telescope would almost certainly be in LEO, which is also worse for telescopes.

You know, let's first concentrate on building ATLAST. http://www.stsci.edu/atlast and Lunar Radio telescopes.

Then we might be able to build a L-point manned space telescope (assuming the funding can ever pull through)

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I did some reading and it sounds like:

The error/uncertainty in photon count (how bright is what I'm looking at) is inversely proportional to the square of the number of photons. If you half the collection area then you can compensate by doubling the 'exposure time'. If you went from a 1m diameter telescope to a 0.1m diameter scope you could get the same certainty of brightness by looking for 100 times as long.

That doesn't help you much for time limited events, like a planetary transit which takes like one day every few hundred days (for some Earth like planet). You could use the smaller scope if you were happy to wait 100 years for the data...

The diameter of the mirror controls the maximum angular resolution, how big a dot on the detector a point source makes. It is proportional to wavelength/diameter. So the small mirror above would be 10x as blurry as the big one.

You can use interferometry to combine the light of two telescopes separated by Dist so they deliver the same resolution as a mirror with diameter Dist. So two 0.1m telescopes with a 1m spacing could deliver a picture as sharp as the 1.0m one, but 1/50th as faint / you'd need 50x the exposure time to get the same error in brightness.

'Somehow' they can arrange that the light of a star destructively interferes with itself leaving the light of any planets untouched. This lets them do emission spectroscopy of the planets, which is good because you can look at them throughout their orbit - more time for light gathering so less error / smaller scope needed. On the other hand maybe reflected light is less bright than the light transmitted though a primary transiting planets atmosphere...

I still have not read directly what controls the 'spectral resolution'. I am thinking that the prism or grating just deflects the different wavelength differently so if you start with low res incoming light then the spectral signature will be more 'blurred' than if you started with high res incoming light. Depending on the signature you are looking for you might not need high resolution. The wavelengths get shifted by doppler effects also...

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If you want a finer difference in intensity what you want is either larger aperture (small intensity becomes large, as well as small difference becomes large) or a more sensitive (and less noisy) detector. Yes it's true that S/N (signal to noise ratio) grows with time, but after some time it's not worth it (the growth in S/N is simply too slow). More time means more photons, so a large LGP can also do the same trick too. The caveat is how not to trip your detector to it's limits, because it's easier to happen in a large LGP 'scope. Look up CCD textbooks, even for amateurs, they'll contain this.

For spectrograph / spectrometer, you'll want a slow telescope (something with f ratio larger than 10), as this limits which star will be processed by the grating (although today's grating are more advanced, so any telescope will do). The fineness of the resulting spectrum only depends on the grating. In some case, two gratings are placed perpendicular to each other, making the spectrum even more refined. That is called Michelson Spectrometer, and the resulting spectrum will not be a line. (my profile picture is an example, taken from NOAO website)

Edited by YNM
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43 minutes ago, YNM said:

Michelson Spectrometer

ok so this spreads a point source in in the x direction (say) and a second grating at 90 degrees then spreads that in the y direction. If you have a high res scope the specta are much more spread out and you can discern finer detail. The exact same setup with a low res telescope would do the same spreading but would be spreading blurred info - the spectrum resolution you can extract is limited by the resolution of the scope? It kind of seems like one mental model is that each frequency has it's own Airy disk - but that would mean if you could spread them far enough apart then you could resolve even frequencies close together? I guess I'm wondering if the diameter also effects the frequency resolution as well as the spacial resolution? does anything effect the frequency resolution? since frequency is space and time then does that mean the diameter does limit frequency resolution?

On a separate track - if I do multiple disjoint samples of some target at different times, then I can just add the data together maybe years later and reduce the error by root two? (assuming the target wasn't changing or that I was interested in 'average behaviour') I guess I could do the same thing with spectra samples also?

There are some great images in here from the CHARA interferometer at Mount Wilson - six 1 m telescopes working together - first measurement of the diameter of an exoplanet, 'images' of stars (not point sources), etc

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@ DBowman : actually no. In most (very close to all) cases (bar old telescopes like 1920 Carl-Zeiss that we have here and michelson interferometer), the spectrograph will only take a line, a part of the projected light available from the aperture. This line will pass the grating. The resulting image will be a line, with each line corresponds to the spectrum of an object (to know which object will be processed, you can "turn off" the grating, making view of the background available and the object(s) observed obstructed by a black line). This is how you can take spectra of multiple objects at once, or how to take separate spectra of disk, bulge and halo of a spiral galaxy at once. It really have no problem with what telescope you use - except smaller diameter telescopes will need more time to gather enough light, given that you'll split them, and will be less resolved (each linear length corresponds to larger angular length).

At least that's how it worked on simulations, an SBIG soectrograph which I forget the type and even some modern observatories. Even I heard a project where each object's light will be passed through fiber optic cables, all to its own signal processor, to obtain an all-sky survey.

Edited by YNM
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@YNM it sounds like you are 'in the business'? Are you really in Java - there cannot be too many 1920s Carl-Zeiss scopes around...

I read you as saying that, all else being equal, a 1 hour 'exposure' on a 1m telescope and a 100 hour exposure on a 0.1m telescope would deliver the same spectral information with the same error/uncertainty and the same resolution between frequencies in the spectra - is that right? I wasn't expecting that, but I guess light-wave-quantum physics-expect the unexpected.

Maybe you can clear me up on this also: if I have 2 1m telescopes pointed at the same star and one has half the field of view as the other do they each catch the same number of photons from the star? is there a difference - maybe noise to signal or the narrow field has a lower error from having less background photons? or does the smaller field of view get more 'on the detector' from that star?

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Yes, I do reside in Java. I just happen to closely know the people in bussiness at a point tbh. Today, I'm not (or rather, no longer, although I myself consider to be never in the professional part because it was just for a few months) in it, apart from amateur things. I base this off what those people have showed me and explained to me. There are real data pictures but I'm no longer in appropriate contact for asking such things. And no, I don't have such expensive equipment like CCDs, spectrograph etc.

For your first question : Yes. Apart that the same "laws" of photometry measurement applies (ie. too long exposure means mediocre S/N, too short means low S/N), as long as the grating are equally good it'll be the same.

For the second, guess the difference is in the focal length then ? Well the telescope with longer focus will generate a bigger star "spots". The light will spread over larger portion of the detector while the radiant intensity stays the same, so you'll end up with a bigger (more resolved) but overall fainter image. The other one with shorter focal length will produce small star "dots", with each dots as bright as the spots from other telescope. But because each dots corresponds to smaller amount of pixel, the maximum count (representative to the amount of photons) will be higher - careful not to trip the maximum count limit ! Over time, it'll damage the detector, producing hot pixels.

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