Question about energy at one wavelength:

Doing some research on my own about gravitational lensing, I need to know the energy level at a specific wavelength coming from Sirius that reaches us here.

I know the total is 9.8 nanowatts per square meter is what reaches our neck of the woods but I want to narrow that down to the energy at exactly 1 micron (IR band).

Like you have a filter that could filter out all but the wavelength of 1 micron, from Sirius, how much energy would that represent, in watts per square meter?

Not sure how to do that, I posed that question on one of the 'ask an astronomer sites' but it will take a while to get a response if any.

Originally posted by sonhouse
Doing some research on my own about gravitational lensing, I need to know the energy level at a specific wavelength coming from Sirius that reaches us here.

I know the total is 9.8 nanowatts per square meter is what reaches our neck of the woods but I want to narrow that down to the energy at exactly 1 micron (IR band).

Like you have a filter that cou ...[text shortened]... stion on one of the 'ask an astronomer sites' but it will take a while to get a response if any.

The energy of a photon is Planck's constant times its frequency. I'm guessing you mean something else. If you want the fraction of energy at some frequency then that depends on the distribution - if you know the distribution then you can work out the fraction.

Originally posted by DeepThought
The energy of a photon is Planck's constant times its frequency. I'm guessing you mean something else. If you want the fraction of energy at some frequency then that depends on the distribution - if you know the distribution then you can work out the fraction.

What I mean is if you have a power meter with a perfect filter at one micron and aimed at Sirius, what would you read powerwise out of that 10 nanowatts per square meter?

I realized after I said that I probably don't need to worry about it for my purposes since the volume involved with a 1 micron wavelength includes the volume of the shorter wavelengths so I probably don't need to know the specifics of one frequency.

Originally posted by sonhouse
What I mean is if you have a power meter with a perfect filter at one micron and aimed at Sirius, what would you read powerwise out of that 10 nanowatts per square meter?

I realized after I said that I probably don't need to worry about it for my purposes since the volume involved with a 1 micron wavelength includes the volume of the shorter wavelengths so I probably don't need to know the specifics of one frequency.

The light coming from a star is not uniform over the whole spectrum. It has different energy levels at different wavelengths. But even if it was uniform, you could not really ask what the energy level at a specific wavelength was but rather over a small range of wavelengths, and the size of that range is everything. Think of it like 'area under a curve'. You cannot find the area under a single point on a curve.

Even if you chanced on a specific wavelength emitted by a specific atoms emissions which does result in laser-like light of a single wavelength, you will find that the relative velocity of the star causes red-shift/blue-shift of of the overall spectrum, and the rotation of the star results in red-shift on one side and blue-shift on the other. Overall even a bunch of lasers on the star would be received as a range of frequencies by us.
The above is significant enough that we can measure the stars relative velocity accurately enough to detect its wobble due planets orbiting it.

Originally posted by sonhouse
What I mean is if you have a power meter with a perfect filter at one micron and aimed at Sirius, what would you read powerwise out of that 10 nanowatts per square meter?

I realized after I said that I probably don't need to worry about it for my purposes since the volume involved with a 1 micron wavelength includes the volume of the shorter wavelengths so I probably don't need to know the specifics of one frequency.

Any "perfect filter" of one fixed frequency will let through nothing out of any input signal, so the power will be 0.

Originally posted by KazetNagorra
Any "perfect filter" of one fixed frequency will let through nothing out of any input signal, so the power will be 0.

Ok, a reasonable bandwidth then, say 10 nanometers on either side of 1 micron.

Originally posted by sonhouse
Ok, a reasonable bandwidth then, say 10 nanometers on either side of 1 micron.

It is the exact bandwidth that counts. So you are saying a total bandwidth of 20 nanometres.
Assuming uniform spread of energy across the the spectrum, merely divide the total spectral range by 20 nanometres and multiply by the total power. But immediately we see that an infinite spectral range is not possible, so it cant possibly be uniform. In addition shorter wavelength photons have higher energy so it is likely the energy is strongly biased towards shorter wavelengths overall.
In short, we can't really do much without an approximate spectrum. You can probably assume a black body spectrum if you know the stars temperature. It will take a bit of research though.
And you would want to make sure your special filter doesn't coincide with any prominent absorption lines.

Originally posted by twhitehead
It is the exact bandwidth that counts. So you are saying a total bandwidth of 20 nanometres.
Assuming uniform spread of energy across the the spectrum, merely divide the total spectral range by 20 nanometres and multiply by the total power. But immediately we see that an infinite spectral range is not possible, so it cant possibly be uniform. In addition ...[text shortened]... ould want to make sure your special filter doesn't coincide with any prominent absorption lines.

Yes, absorption lines would interfere with that but I am talking theoretical anyway, just a ballpark but it doesn't really matter since for my purposes a 1 micron cubed area will contain the higher frequencies anyway so I can make a judgement that should not be off by more than a factor of 2 or so. I can pretty much use the full 10 nanowatt /meter^2 figure given in the books.

A black body spectrum will be a reasonable approximation. You can find the analytical formula as a function of wavelength somewhere on Wikipedia. I don't know the surface temperature of Sirius but I guess it will not be too far off from that of the Sun (6000K). So with these approximations you have what you need and you just need to choose your desired wavelength window for the integration. The black body radiation of a star is peaked around the visible spectrum so it should still have a reasonable intensity around 1µm.

Originally posted by KazetNagorra
A black body spectrum will be a reasonable approximation. You can find the analytical formula as a function of wavelength somewhere on Wikipedia. I don't know the surface temperature of Sirius but I guess it will not be too far off from that of the Sun (6000K). So with these approximations you have what you need and you just need to choose your desired ...[text shortened]... is peaked around the visible spectrum so it should still have a reasonable intensity around 1µm.

For what it is worth, the surface temp of Sirius is about 10,000K. That would put the peak closer to the blue end of the spectrum. Sirius IS a blue star.

Here you go:
http://www.rkblog.rk.edu.pl/w/p/sirius-spectrum/

If I am not mistaken about those units, one micrometer would not be the ideal wavelength.

For added interest, Sirius is actually a binary star but Sirius B is a lot fainter so won't affect total energy much. However, if your plan was anything other than theoretical, you might need to take into account the wobble caused by it being a binary system.
That might make it an ideal candidate for gravitational lensing studies, or a terrible candidate depending on what exactly you are studying.

https://en.wikipedia.org/wiki/Sirius

Originally posted by twhitehead
Here you go:
http://www.rkblog.rk.edu.pl/w/p/sirius-spectrum/

If I am not mistaken about those units, one micrometer would not be the ideal wavelength.

For added interest, Sirius is actually a binary star but Sirius B is a lot fainter so won't affect total energy much. However, if your plan was anything other than theoretical, you might need to tak ...[text shortened]... le candidate depending on what exactly you are studying.

https://en.wikipedia.org/wiki/Sirius

I have been fascinated by the energy reaching our solar system, which measures 9.8E-9 w/meter^2. Although totally overwhelmed by the energy of the sun, still, it means the surface of the sun gets about 15 gigawatts of energy hitting it directly from Sirius and even Jupiter gets something like 15 kilowatts on it's 'surface'.

What interests me about Sirius also is following the path of its energy away from the sun, it starts to get focused at around 80 billion Km out and stays focused in a line reaching out about the same distance as the distance to Sirius, or about 8 light years long.

Which is why I was interested in the energy there. I am trying to make a rough approximation of the amount of energy focused in that line and so I used what I call the bubble method. That is to say, a volume of space around the sun, which I arbitrarily called 1 meter cubed, would contain almost all the energy coming from Sirius per volume. So if you stretch out the circle around the sun close to the 'surface' you have a line about 4.4 million km. So if you line up those 1 meter bubbles, you get what seems like about 40 watts (where each meter^2 has its 10 nanowatts of energy) and the energy of those bubbles will come together at around 80 billion km away from the sun following the path of the light from Sirius. The path of light doesn't change after the deflection of light around the sun, that is my main MO and that means all those 1 meter sized bubbles will converge. The thing is, that is just the line closest to the 'surface' of the sun. If you look at a volume at 2 r, where the first was at a distance of 1 r, the radius of the sun, you get a total of 86 watts worth of the same bubbles but because the angle of deflection is now half and the radius is doubled, the gist of that is the place of that particular set of bubbles is now 4 times greater at about 320 billion km away from the sun.

Each radius number, say out to radius #100, means at that distance if focused, the energy will now be 4300 watts so the energy in the line goes up till it peters out at about 8 light years out. At that distance, the energy from Sirius far exceeds the energy from the sun at that distance so there would seem to be uses for that energy, for instance, it might cause an Oort cloud object to be illuminated where it shouldn't be due to interception with that focused light. Of course the chances are low but a diligent search could reveal a new way of looking for Oort cloud objects.

So you can see a continuum of those bubbles all lining up in a line stretching in this example from 80 billion km out to 320 billion km out.

Of course that is not the end of the story since the amount of deflection, although it continues to diminish going away from the sun, it never reaches zero so you can calculate the angle at any arbitrary distance just using the formula defined by Einstein, 4GM/C^2r where G is the gravitational constant times 4 and mass in kg, in this case about 2 E30 Kg divided by C squared times the radius in meters gives the angle in radians which is about 8.4 E-6 radians which is the famous 1.75 arc second number given in the press. Radians are much more useful in figuring out the distance of focus because you just invert the radian number and you get the multiplier that you multiply the radius of and you get the focus distance directly.

So now you have two competing effects, one is the variable angle of deflection vs radius number and the increasing angle of the radiation from a given star as it goes away from the line drawn center to center of the stars in question.

At some point the lowered deflection angle will be unable to deflect the increasing angle of light from the star, in this case Sirius and the focusing ends. It turns out that end point is about the same distance on the other side of the sun as the distance to Sirius so there is a line of focus staring for every distance source at about 80 billion km away from the sun and ending at whatever the distance is between the two stars, so Sirius gives a line about 8 ly long, Alpha Centauri would give a focus line extending about 4 light years long and so forth.

There are interesting implications of that line of focus which is the main area of my research.

Sorry for the lengthy reply, but it helps my writing of it to spell it out in one place, which for now has just been on tablets.....

Using the sun as a sort of telescope has been proposed:
https://en.wikipedia.org/wiki/Gravitational_lens#Solar_gravitational_lens

Using gravitational lensing to find free floating planets is also a thing:
https://en.wikipedia.org/wiki/Gravitational_microlensing#Detection_of_extrasolar_planets

Lensing due to a free floating planet is quite significant. I forget the exact figures and couldn't find a source, but I believe the star momentarily gets several times brighter than normal.

Originally posted by twhitehead
Using the sun as a sort of telescope has been proposed:
https://en.wikipedia.org/wiki/Gravitational_lens#Solar_gravitational_lens

Using gravitational lensing to find free floating planets is also a thing:
https://en.wikipedia.org/wiki/Gravitational_microlensing#Detection_of_extrasolar_planets

Lensing due to a free floating planet is quite signific ...[text shortened]... ldn't find a source, but I believe the star momentarily gets several times brighter than normal.

I found more interesting things about that lensing effect in my research. For instance, picture 2 advance spacecraft at some distance from a star. Say 1 light year away to pick some arbitrary number.
Closer would mean the whole experiment would be over sooner.

Anyway, ship #1 sends out a stream of RF, starting at say 1/100th of a hertz and increasing the frequency up to some reasonable number, say 1 gigahertz or so.

The energy from that stream approaches the target star.

Ship # 2 is on the opposite side in the focus line at some arbitrary number of Km away.

What ship # 2 WON"T see is the first frequencies emitted, looking for an energy density higher than what it would receive if the sun is not there. The lowest frequencies will not be able to be focused because the wavelength is simply too large to be effected by that deflection we see in Thz radiation of visible light.

But at some point going up the frequency spectrum, ship # 2 WILL see an amplified version of the signal sent by ship # 1.

That information, exactly what frequency you do see amplification, will tell them the mass and density of the star independent of any orbital mechanics.