Astronomy C

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Magikarpmaster629
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Re: Astronomy C

Postby Magikarpmaster629 » February 22nd, 2017, 6:01 pm

Alright. Sorry for more math whoops.

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Above is the light curve of an eclipsing binary system of Star A and Star B that is perfectly edge on. Star A, the primary and larger star, has a temperature of 3000 Kelvin and 2 times the radius of Star B. The absolute magnitude of the system is 1.24.

a. What is the temperature of Star B in Kelvin?
b. What is the luminosity of Star A in solar luminosities?
c. What is the luminosity of Star B in solar luminosities?
d. What are the radii of Stars A and B respectively in km?
Assuming both stars eclipse fully (since as far as I know that can't really be derived from the problem without being stated)
a. 36,000 K b. 6.72 L[sub]sun[/sub] c. 20.15 L[sub]sun[/sub] d. I have lost myself among the various luminosity/flux conversions
So I solved this using what I remember from exoplanet transits. How do you start with solving for temperature, which is what I assume you're supposed to do since its problem a? I solved for A's radius first, which was 1.31*10^7 km.
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Re: Astronomy C

Postby Unome » February 22nd, 2017, 6:16 pm

Alright. Sorry for more math whoops.

Image

Above is the light curve of an eclipsing binary system of Star A and Star B that is perfectly edge on. Star A, the primary and larger star, has a temperature of 3000 Kelvin and 2 times the radius of Star B. The absolute magnitude of the system is 1.24.

a. What is the temperature of Star B in Kelvin?
b. What is the luminosity of Star A in solar luminosities?
c. What is the luminosity of Star B in solar luminosities?
d. What are the radii of Stars A and B respectively in km?
Assuming both stars eclipse fully (since as far as I know that can't really be derived from the problem without being stated)
a. 36,000 K b. 6.72 L[sub]sun[/sub] c. 20.15 L[sub]sun[/sub] d. I have lost myself among the various luminosity/flux conversions
So I solved this using what I remember from exoplanet transits. How do you start with solving for temperature, which is what I assume you're supposed to do since its problem a? I solved for A's radius first, which was 1.31*10^7 km.
I converted the magnitude difference of 1.2 to luminosity, giving me almost exactly 3 times. Assuming both stars fully eclipse each other, I solved for each temperature using (T1/T2)^4*(R1/R2)=(L1/L2)
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Re: Astronomy C

Postby Ashernoel » February 22nd, 2017, 6:46 pm

Assuming both stars eclipse fully (since as far as I know that can't really be derived from the problem without being stated)
a. 36,000 K b. 6.72 L[sub]sun[/sub] c. 20.15 L[sub]sun[/sub] d. I have lost myself among the various luminosity/flux conversions
So I solved this using what I remember from exoplanet transits. How do you start with solving for temperature, which is what I assume you're supposed to do since its problem a? I solved for A's radius first, which was 1.31*10^7 km.
I converted the magnitude difference of 1.2 to luminosity, giving me almost exactly 3 times. Assuming both stars fully eclipse each other, I solved for each temperature using (T1/T2)^4*(R1/R2)=(L1/L2)
If you use the magnitude difference, doesn't that say that when there combined they are 3x brighter? Instead of just the second star?
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Re: Astronomy C

Postby Magikarpmaster629 » February 27th, 2017, 10:50 am

While we wait for slowpoke to return with an explanation, can you write a question Unome?
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Re: Astronomy C

Postby Tom_MS » February 27th, 2017, 1:21 pm

So I solved this using what I remember from exoplanet transits. How do you start with solving for temperature, which is what I assume you're supposed to do since its problem a? I solved for A's radius first, which was 1.31*10^7 km.
I converted the magnitude difference of 1.2 to luminosity, giving me almost exactly 3 times. Assuming both stars fully eclipse each other, I solved for each temperature using (T1/T2)^4*(R1/R2)=(L1/L2)
If you use the magnitude difference, doesn't that say that when there combined they are 3x brighter? Instead of just the second star?
I got something different
I started by solving for distance using the apparent magnitude of the system and the given absolute magnitude. Using that, I solved for the luminosity of the larger star, and through subtraction, that of the smaller star. Once the luminosity of the larger star was found, its absolute radius could be found. Then, once that was found, the radius of the smaller star B could be found. Then, the temperature of the first star could be found, and in the process, the other 3 parts. I got 8.47 and 17.1 solar luminosities for the star, 5057K for B, and 5.4 and 10.8 solar radii for the stars.

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Re: Astronomy C

Postby Unome » February 27th, 2017, 1:22 pm

I converted the magnitude difference of 1.2 to luminosity, giving me almost exactly 3 times. Assuming both stars fully eclipse each other, I solved for each temperature using (T1/T2)^4*(R1/R2)=(L1/L2)
If you use the magnitude difference, doesn't that say that when there combined they are 3x brighter? Instead of just the second star?
I got something different
I started by solving for distance using the apparent magnitude of the system and the given absolute magnitude. Using that, I solved for the luminosity of the larger star, and through subtraction, that of the smaller star. Once the luminosity of the larger star was found, its absolute radius could be found. Then, once that was found, the radius of the smaller star B could be found. Then, the temperature of the first star could be found, and in the process, the other 3 parts. I got 8.47 and 17.1 solar luminosities for the star, 5057K for B, and 5.4 and 10.8 solar radii for the stars.
You got the expected ratio of radii (which I didn't get), so if you want to take the question instead of me go ahead.
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Re: Astronomy C

Postby Tom_MS » February 27th, 2017, 6:31 pm

A certain star A known to be on the main sequence is observed through spectral analysis as rotating around a companion B. Star A is known to be to have a parallactic angle of 4.848*10^-8 radians has an apparent magnitude of 13. The system is eclipsing.
a. Determine the approximate surface temperature of star A in Kelvin.
b. What distinctive spectral features can we expect to see from star A?
c. Given that the observable H-beta line (486.10 nm) of the Balmer series is observed to have a maximum shift in wavelength to 486.13 nm for star A, determine its radial velocity in the system.
d. Through spectral analysis, star B is determined to be a cool red dwarf. If the combined luminosity of the system is 5.1 solar luminosities, what is the angular diameter of the system in radians? Make sure to show your work.

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Re: Astronomy C

Postby Unome » March 1st, 2017, 7:47 am

trying
a. Absolute magnitude of 3, so I assume I'm supposed to look at an H-R diagram since it says main sequence? I get ~9000K. b. I think Hydrogen lines peak at around this temperature, not entirely sure though. c. ~18.5 km/sec d. No idea. Does this have something to do with the size of star necessary to eclipse at a certain orbital distance?
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Re: Astronomy C

Postby Magikarpmaster629 » March 1st, 2017, 1:59 pm

trying
a. Absolute magnitude of 3, so I assume I'm supposed to look at an H-R diagram since it says main sequence? I get ~9000K. b. I think Hydrogen lines peak at around this temperature, not entirely sure though. c. ~18.5 km/sec d. No idea. Does this have something to do with the size of star necessary to eclipse at a certain orbital distance?
Yeah, I'd say D is unsolvable. To Tom_MS: No offence, but these are pretty badly written questions. While there are charts and relations between luminosity and temperature and mass, typically I see tests avoid having these relations match up because the purpose of the math in this event isn't for the student to look up the answer in a table, but to use real math and solve for variables using Kepler's law, Wien's law, Stefan-Boltzmann law, etc. I'd suggest you look at some of the tests in the test exchange (https://scioly.org/wiki/index.php/2017_ ... #Astronomy) for past questions.

Unome, you should go next.
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Re: Astronomy C

Postby Unome » March 1st, 2017, 2:19 pm

trying
a. Absolute magnitude of 3, so I assume I'm supposed to look at an H-R diagram since it says main sequence? I get ~9000K. b. I think Hydrogen lines peak at around this temperature, not entirely sure though. c. ~18.5 km/sec d. No idea. Does this have something to do with the size of star necessary to eclipse at a certain orbital distance?
Yeah, I'd say D is unsolvable. To Tom_MS: No offence, but these are pretty badly written questions. While there are charts and relations between luminosity and temperature and mass, typically I see tests avoid having these relations match up because the purpose of the math in this event isn't for the student to look up the answer in a table, but to use real math and solve for variables using Kepler's law, Wien's law, Stefan-Boltzmann law, etc. I'd suggest you look at some of the tests in the test exchange (https://scioly.org/wiki/index.php/2017_ ... #Astronomy) for past questions.

Unome, you should go next.
I don't know about D, but the rest seem pretty typical to me; I've seen plenty of questions like that (which I why I thought of doing it with an H-R diagram).
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Re: Astronomy C

Postby Tom_MS » March 1st, 2017, 5:48 pm

trying
a. Absolute magnitude of 3, so I assume I'm supposed to look at an H-R diagram since it says main sequence? I get ~9000K. b. I think Hydrogen lines peak at around this temperature, not entirely sure though. c. ~18.5 km/sec d. No idea. Does this have something to do with the size of star necessary to eclipse at a certain orbital distance?
Yeah, I'd say D is unsolvable. To Tom_MS: No offence, but these are pretty badly written questions. While there are charts and relations between luminosity and temperature and mass, typically I see tests avoid having these relations match up because the purpose of the math in this event isn't for the student to look up the answer in a table, but to use real math and solve for variables using Kepler's law, Wien's law, Stefan-Boltzmann law, etc. I'd suggest you look at some of the tests in the test exchange (https://scioly.org/wiki/index.php/2017_ ... #Astronomy) for past questions.

Unome, you should go next.
Alright. I intended for you to notice that it is about an A type star, so there are those spectral features characteristic of those stars. The idea with D was that there is the main-sequence mass-luminosity relation. I realized that this relation wasn't consistent across all sources, but I figured that if work was shown, it would be a creative way to solve for the separation of the system and therefore the angular diameter.

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Re: Astronomy C

Postby Magikarpmaster629 » March 14th, 2017, 3:50 pm

Starting this up again:

Star C and Supernova A have the same apparent magnitude. Supernova A is a type Ia and is located in a galaxy 15 Mpcs distant. Assume all type Ia supernovae are all the same brightness, with an absolute magnitude of -19.3.

a) What is the recessional velocity of the galaxy in which Supernova A is located? Answer in m/s.
b) Type Ia supernovae have strong silicon lines. One Si II line from Supernova A has an apparent wavelength of 126.94 nm. What was its emitted wavelength in nm?
c) What is the apparent magnitude of Star C?
d) What is the distance to Star C in parsecs?
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Re: Astronomy C

Postby jonboyage » March 14th, 2017, 6:00 pm

Starting this up again:

Star C and Supernova A have the same apparent magnitude. Supernova A is a type Ia and is located in a galaxy 15 Mpcs distant. Assume all type Ia supernovae are all the same brightness, with an absolute magnitude of -19.3.

a) What is the recessional velocity of the galaxy in which Supernova A is located? Answer in m/s.
b) Type Ia supernovae have strong silicon lines. One Si II line from Supernova A has an apparent wavelength of 126.94 nm. What was its emitted wavelength in nm?
c) What is the apparent magnitude of Star C?
d) What is the distance to Star C in parsecs?
Answer
a) 1,050,000 m/s b) ~126.50nm c) ~11.58 d) missing information :(
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Re: Astronomy C

Postby Magikarpmaster629 » March 14th, 2017, 6:20 pm

Starting this up again:

Star C and Supernova A have the same apparent magnitude. Supernova A is a type Ia and is located in a galaxy 15 Mpcs distant. Assume all type Ia supernovae are all the same brightness, with an absolute magnitude of -19.3.

a) What is the recessional velocity of the galaxy in which Supernova A is located? Answer in m/s.
b) Type Ia supernovae have strong silicon lines. One Si II line from Supernova A has an apparent wavelength of 126.94 nm. What was its emitted wavelength in nm?
c) What is the apparent magnitude of Star C?
d) What is the distance to Star C in parsecs?
Answer
a) 1,050,000 m/s b) ~126.50nm c) ~11.58 d) missing information :(
Oh whoops, I wrote these questions for my event partner and I took out some info. (d) should read:
The observed flux from Star C is measured to be 6.04*10^-13 W/m^2. If the luminosity of Star C is 0.286 solar luminosities, What is the distance to Star C in parsecs? Calculate using the Stefan Boltzmann Law. (You could just use distance mod, it's the same thing, but my partner needed some SB practice)
Answer is~123 parsecs Your turn!
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Re: Astronomy C

Postby jonboyage » March 15th, 2017, 7:52 am

Let's assume we are on a hypothetical planet which has a perfectly circular orbit around a hypothetical main sequence star. The value of the time it takes the planet to orbit the star in years is exactly half of the value of the mass of the star in solar masses, which is between 2 and 20 solar masses (hint hint). The peak wavelength emitted by the star is 115.9nm and the radius is 3.6789 solar radii. While on the planet, we observe a different star, for which we find the parallax is 35mas. Would we have been able to use geometric parallax to observe this star accurately from Earth, assuming the same relative distance to the star (Using Hipparcos)? What would be the equivalent parallax of this star if observed from Earth?

Information for easy reference:
-Between 2 and 20 solar masses
-115.9nm
-3.6789 solar radii
-35mas
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