The Secret of Sight? : )

[Solfe]

I have always been bothered by this question and cannot figure it out and cannot phrase a google search to get an answer.

This is going to be rough, I will try not to use any numbers.

Photons have infinite range, of course limited by how much time you have on your hands. So every second we can see that much farther into the universe. That makes a goodly amount of sense to me.

What I don't understand is how we can see stars at all. I really enjoy looking at them, but do not understand how they can be seen over vast distances.

If a star throws out a finite number of photons, distributed in a finite volume, then there must be a threshold that you cannot resolve a star. (I do hear that people can see a single photon, but I firmly believe stars appear to be bigger than a single photon. Even dust would mask everything that small anyway.)

It seems like the volume of space involved with interstellar distances should reach this threshold of visibility very quickly. Star emit vast quanities of photons a second, but really, is the number of photons emitted so large that even interstellar volumes of space do not "swallow" them up?

Speaking in terms of photons, it strikes me (no pun intended) that a star doesn't have the output to cover all of the space/angles to allow for resolving them. It is easy to picture a child's drawing of the sun with a person standing between the rays. That person would not see the sun becuase they are "between the photon's paths." Or maybe that should read "between the crayon's paths." : )

Even when I "quit" the idea of photons, and switch to waves, it is boggling to think our sun has enough power to allow it to be as clearly visible as it is. Shouldn't it appear grainy or "wavey?"

What am I missing?

Solfe.

[Tobin Dax]

The sun releases a huge amount of photons, though it is still finite. The sun puts out about 4x10^26 Joules of energy per second. For the sake of argument, let's say that the average photon from the sun has a 500 nm wavelength. The energy of each photon is about 4x10^-19 Joules. That means that the sun as a whole is emitting 10^45 photons per second. There are 41,253 square degrees in a circle, so the sun emits 2.5x10^40 photons per square degree. One lightyear is about 10^13 km, and the Earth is about 6400 km in radius, so half the angle that Earth makes in the sky of, say, Alpha Centauri is 6400/4x10^13 = 1.5x10^-13 arcseconds = 4x10^-17 degrees. The angular area is therefore about 2x10^-32 square degrees. That gives 5x10^7 photons per second hitting the Earth. That's a whole lot. That's why we can see stars over such vast distances.

[sonofanape]

actually, you got it. there is a threshold, but so happens that the threshold is a lot further away than the stars around us. stars, normal stars just like the sun, are very very bright. extreamly. there is enough photon for everyone and their dog. so many infact that some people have asked, if in taking that photons can travel infinite distances, why the sky isn't a whole lot brighter than it is. but i don't know who those people are, so be content that there are mant more stars in existance than you can see, and all are fountains of photons visable at ginormous scales.

[trinitree88]

The sun releases a huge amount of photons, though it is still finite. The sun puts out about 4x10^26 Joules of energy per second. For the sake of argument, let's say that the average photon from the sun has a 500 nm wavelength. The energy of each photon is about 4x10^-19 Joules. That means that the sun as a whole is emitting 10^45 photons per second. There are 41,253 square degrees in a circle, so the sun emits 2.5x10^40 photons per square degree. One lightyear is about 10^13 km, and the Earth is about 6400 km in radius, so half the angle that Earth makes in the sky of, say, Alpha Centauri is 6400/4x10^13 = 1.5x10^-13 arcseconds = 4x10^-17 degrees. The angular area is therefore about 2x10^-32 square degrees. That gives 5x10^7 photons per second hitting the Earth. That's a whole lot. That's why we can see stars over such vast distances.

Tobin Dax. Nit pik...that's 41,253 square degrees per sphere, not circle...

[Tobin Dax]

Tobin Dax. Nit pik...that's 41,253 square degrees per sphere, not circle...

Details.

[Joe87]

The sun releases a huge amount of photons, though it is still finite. The sun puts out about 4x10^26 Joules of energy per second. For the sake of argument, let's say that the average photon from the sun has a 500 nm wavelength. The energy of each photon is about 4x10^-19 Joules. That means that the sun as a whole is emitting 10^45 photons per second. There are 41,253 square degrees in a circle, so the sun emits 2.5x10^40 photons per square degree. One lightyear is about 10^13 km, and the Earth is about 6400 km in radius, so half the angle that Earth makes in the sky of, say, Alpha Centauri is 6400/4x10^13 = 1.5x10^-13 arcseconds = 4x10^-17 degrees. The angular area is therefore about 2x10^-32 square degrees. That gives 5x10^7 photons per second hitting the Earth. That's a whole lot. That's why we can see stars over such vast distances.

If 5x10^7 Alpha Centauri photons hit the earth per second, how many hit my eyeball when I'm looking at Alpha Centauri? If my pupil at night opens to an area of, say, 1 sq cm, and the cross sectional area of the earth that is hit by Alpha Centauri photons is 1.3x10^18 sq cm, then the number of photons hitting my eye per second is 4x10^-11, or one photon per 12,700 years.

So how is it that I can see Alpha Centauri?

[Tobin Dax]

If 5x10^7 Alpha Centauri photons hit the earth per second, how many hit my eyeball when I'm looking at Alpha Centauri? If my pupil at night opens to an area of, say, 1 sq cm, and the cross sectional area of the earth that is hit by Alpha Centauri photons is 1.3x10^18 sq cm, then the number of photons hitting my eye per second is 4x10^-11, or one photon per 12,700 years.

So how is it that I can see Alpha Centauri?

For those of you paying as much attention at I was, 6e4/4e13 is not ~1e13. Oops. The actual number cross-section of Earth is 6e-27, not 2e-32, so 300,000 more photons reach us than what I said initially. That's a better number, but still about one photon every 12 days. Do you want to double-check my math, Joe?

[Grey]

If 5x10^7 Alpha Centauri photons hit the earth per second, how many hit my eyeball when I'm looking at Alpha Centauri? If my pupil at night opens to an area of, say, 1 sq cm, and the cross sectional area of the earth that is hit by Alpha Centauri photons is 1.3x10^18 sq cm, then the number of photons hitting my eye per second is 4x10^-11, or one photon per 12,700 years.

So how is it that I can see Alpha Centauri?

I think the math above is wrong. The original estimate of 10⁴⁵ photons per second is reasonable. The surface area of a sphere is 4 pi r², and a light year is about 10¹⁸ cm, so by the time the photons reach us, they've spread over a sphere of about 2 x 10³⁸ cm². So that gives us about 5 million photons per second per square cm. Your pupil is probably a little smaller than a square centimeter, even when fully dilated at night, but that's still plenty of photons to see.

[Joe87]

OK, that's why we can see a star 4 light years away. Now let's look at a galaxy 13x10^9 light years away with a 300 cm diameter telescope. The area of a sphere at that distance is 2.8x10^67 and 10^11 stars will put out 10^56 photons/sec, and our telescope has a cross sectional area of 2.8x10^5 cm. So there should be 10^-6 photons per second hitting the telescope, or one every 11 days. Does that mean the telescope can't see that galaxy? How does Hubble do it, it doesn't have a 3 meter diameter telescope?

[George]

The eye has the ability to "see" stars which only provide us a few photons per second, if no other light conflicts with it. The eye's operating range is over a trillion times this level.

[Grey]

OK, that's why we can see a star 4 light years away. Now let's look at a galaxy 13x10^9 light years away with a 300 cm diameter telescope. The area of a sphere at that distance is 2.8x10^67 and 10^11 stars will put out 10^56 photons/sec, and our telescope has a cross sectional area of 2.8x10^5 cm. So there should be 10^-6 photons per second hitting the telescope, or one every 11 days. Does that mean the telescope can't see that galaxy? How does Hubble do it, it doesn't have a 3 meter diameter telescope?

Check your math. I get 2 x 10⁵⁷ cm² as the area of that sphere, so there would still be many photons hitting that telescope. Still, I think that's at the edge of visibility. Looking in the news, I see here that although we've seen a galaxy that far away, it got a boost in brightness from an intervening gravitational lens. That same article talks about using 8 m to 10 m scopes to view "galaxies and quasars" out to about 12 billion light years, but it may only be the quasars (which put out significantly more energy) that are visible at that distance.

[zenbudda]

heh, until i read this thread, i never realized that the photons i'm seeing outside right now (in the form of light) cannot be seen by anyone else. i'm talking the actual photons that are hitting my eyeballs. people can see other photons that produce the same kind of light, but they cannot see the photons i see becuase the photons have already been used up by my eye.

[Relmuis]

Might this effect occasionally cause us to overestimate the redshift?

If the redshift is measured by identifying a spectral line and measuring how far into the red it has shifted, there is of course no problem. But if the redshift of a very weak source is measured by (essentially) counting red and blue photons, there might be trouble, because a situation might occur where enough red photons reach the detector to be detected, while blue photons arrive too sparsely to be noticed.

[George]

I get about 5 billion photons per second per sq. cm. reaching us (but I rushed the math).

[Grey]

heh, until i read this thread, i never realized that the photons i'm seeing outside right now (in the form of light) cannot be seen by anyone else. i'm talking the actual photons that are hitting my eyeballs. people can see other photons that produce the same kind of light, but they cannot see the photons i see becuase the photons have already been used up by my eye.

It's fascinating, isn't it? It's also impressive to realize that stars are emitting enough photons that, even though they are far enough away that it's hard to really comprehend it, they're still producing enough light that millions of photons from them are hitting every square centimeter every second.

Might this effect occasionally cause us to overestimate the redshift?

If the redshift is measured by identifying a spectral line and measuring how far into the red it has shifted, there is of course no problem. But if the redshift of a very weak source is measured by (essentially) counting red and blue photons, there might be trouble, because a situation might occur where enough red photons reach the detector to be detected, while blue photons arrive too sparsely to be noticed.

Probably not. As you can see, even for a galaxy at the limit of how far we can observe (because the universe is only so old) is producing enough photons that a typical telescope is receiving tens of thousands of photons every second. Even when we're using photometric rather than spectroscopic methods for determining the redshift, this is going to be a tiny source of error.