Astronomy C

[Magikarpmaster629]

Alright. Sorry for more math whoops.



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) (Click to Show Hidden Text)

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.

[Unome]

Alright. Sorry for more math whoops.



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) (Click to Show Hidden Text)

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)

[Ashernoel]

Assuming both stars eclipse fully (since as far as I know that can't really be derived from the problem without being stated) (Click to Show Hidden Text)

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?

[Magikarpmaster629]

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

[Tom_MS]

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 (Click to Show Hidden Text)

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.

[Unome]

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 (Click to Show Hidden Text)

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.

[Tom_MS]

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.

[Unome]

trying (Click to Show Hidden Text)

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?

[Magikarpmaster629]

trying (Click to Show Hidden Text)

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.

[Unome]

trying (Click to Show Hidden Text)

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).