Astronomers usually express a star’s color using apparent magnitudes. The star’s apparent magnitude as viewed through a B filter is called mB, and its apparent magnitude as viewed through a V filter is mV. The difference mB - mV is called the B–V color index (“B minus V”). (a) Is the B–V color index positive or negative for very hot stars? (b) What about very cool stars? Explain your answers.

Last edited by Adi1008 on November 13th, 2015, 4:11 pm, edited 1 time in total.

University of Texas at Austin '22
Seven Lakes High School '18
Beckendorff Junior High '14

The B-V color index is inversely proportional to temperature; hot high-mass stars have lower, negative values, and cooler low-mass stars have higher values. This works well for the HR diagram because the values can increase when moving the right on the graph.

Ladue Science Olympiad (2014ish-2017)

A wild goose flies over a pond, leaving behind a voice in the wind.
A man passes through this world, leaving behind a name.

The B-V color index is inversely proportional to temperature; hot high-mass stars have lower, negative values, and cooler low-mass stars have higher values. This works well for the HR diagram because the values can increase when moving the right on the graph.

Correct, your turn.

The reason why B-V color index is inversely proportional to temperature is because hotter stars will have a lower peak wavelength per Wien's Displacement Law. As a result, they'll emit light with shorter wavelength than longer wavelength. The B and V mean blue and violet, so since a hotter star will emit more violet light while emitting less blue (since violet has a shorter wavelength). As a result, mV/mB increases.

Last edited by Adi1008 on November 13th, 2015, 6:24 pm, edited 1 time in total.

University of Texas at Austin '22
Seven Lakes High School '18
Beckendorff Junior High '14

1. What kind of object is this?
2. Which DSOs on this year's list are this object?
3. This object has roughly the same radius as Jupiter, yet is much more massive. How is this possible, and how does this effect the properties of this object?

Ladue Science Olympiad (2014ish-2017)

A wild goose flies over a pond, leaving behind a voice in the wind.
A man passes through this world, leaving behind a name.

1. Brown dwarf
2. WISE 0855-0714, 2MASSJ22282889-431026, GD 165B
3. Not sure if this is what you're looking for, but it has a higher density due to star-like formation while planets solely accumulate mass through accretion in the outskirts of the protoplanetary disk, this causes them to be relatively cooler than other stars and thus emit mostly in the infrared region

1. Brown dwarf
2. WISE 0855-0714, 2MASSJ22282889-431026, GD 165B
3. Not sure if this is what you're looking for, but it has a higher density due to star-like formation while planets solely accumulate mass through accretion in the outskirts of the protoplanetary disk, this causes them to be relatively cooler than other stars and thus emit mostly in the infrared region

Yep, your turn

Ladue Science Olympiad (2014ish-2017)

A wild goose flies over a pond, leaving behind a voice in the wind.
A man passes through this world, leaving behind a name.

Star C has a transiting exoplanet orbiting it with an inclination of 66 degrees at an average distance of 2 AU. C has a mass of 30 Jupiter masses and radius 0.5 solar radii while the exoplanet has a mass of 4 Jupiter masses. If C has a density that is equal to that of the exoplanet...

1. What is the radius of the exoplanet in solar radii?
2. What is the period of the exoplanet's orbit in years?
3. What is the total duration of the exoplanet's transit across the star in years?

Star C has a transiting exoplanet orbiting it with an inclination of 66 degrees at an average distance of 2 AU. C has a mass of 30 Jupiter masses and radius 0.5 solar radii while the exoplanet has a mass of 4 Jupiter masses. If C has a density that is equal to that of the exoplanet...

1. What is the radius of the exoplanet in solar radii?
2. What is the period of the exoplanet's orbit in years?
3. What is the total duration of the exoplanet's transit across the star in years?

1. Due to the Kelvin-Helmholtz mechanism it should be roughly the same as Jupiter's 0.1 solar radii (not entirely sure about that)
2. Using Kepler's third law, p^2=(2 AU)^3 p^2=8 p=2.83 years
3. Using sketchy math, I got 0.0005 years
EDIT: just realized a bad mistake in problem 1...
If the densities are the same then the radius of C beta would be 4/60 or 0.0666... solar radii

Ladue Science Olympiad (2014ish-2017)

A wild goose flies over a pond, leaving behind a voice in the wind.
A man passes through this world, leaving behind a name.

Star C has a transiting exoplanet orbiting it with an inclination of 66 degrees at an average distance of 2 AU. C has a mass of 30 Jupiter masses and radius 0.5 solar radii while the exoplanet has a mass of 4 Jupiter masses. If C has a density that is equal to that of the exoplanet...

1. What is the radius of the exoplanet in solar radii?
2. What is the period of the exoplanet's orbit in years?
3. What is the total duration of the exoplanet's transit across the star in years?

1. Due to the Kelvin-Helmholtz mechanism it should be roughly the same as Jupiter's 0.1 solar radii (not entirely sure about that)
2. Using Kepler's third law, p^2=(2 AU)^3 p^2=8 p=2.83 years
3. Using sketchy math, I got 0.0005 years
EDIT: just realized a bad mistake in problem 1...
If the densities are the same then the radius of C beta would be 4/60 or 0.0666... solar radii

That is incorrect. For #1, remember, density is not simply mass over length which is what I think you did in your edited answer. As for #2, Kepler's Third Law in that form is a generalized form for our solar system (where the mass of the central body is 1 solar mass) of the equation . I'm not sure what you did for #3 but your answers for #1 and #2 are both needed to calculate it (so the method you used might be correct).

Also, yes, I guess it would make more sense that C is much denser than the planet but eh.

EDIT: oops I think with the numbers I gave, the planet does not actually transit the star, so I guess disregard #3....

Star C has a transiting exoplanet orbiting it with an inclination of 66 degrees at an average distance of 2 AU. C has a mass of 30 Jupiter masses and radius 0.5 solar radii while the exoplanet has a mass of 4 Jupiter masses. If C has a density that is equal to that of the exoplanet...

1. What is the radius of the exoplanet in solar radii?
2. What is the period of the exoplanet's orbit in years?
3. What is the total duration of the exoplanet's transit across the star in years?

1. Due to the Kelvin-Helmholtz mechanism it should be roughly the same as Jupiter's 0.1 solar radii (not entirely sure about that)
2. Using Kepler's third law, p^2=(2 AU)^3 p^2=8 p=2.83 years
3. Using sketchy math, I got 0.0005 years
EDIT: just realized a bad mistake in problem 1...
If the densities are the same then the radius of C beta would be 4/60 or 0.0666... solar radii

That is incorrect. For #1, remember, density is not simply mass over length which is what I think you did in your edited answer. As for #2, Kepler's Third Law in that form is a generalized form for our solar system (where the mass of the central body is 1 solar mass) of the equation . I'm not sure what you did for #3 but your answers for #1 and #2 are both needed to calculate it (so the method you used might be correct).

Also, yes, I guess it would make more sense that C is much denser than the planet but eh.

EDIT: oops I think with the numbers I gave, the planet does not actually transit the star, so I guess disregard #3....

Yeah, for number 3 I got that it didn't transit the star which confused me so I drew it out and got that answer. I totally could have gotten the right answers in 1 and 2, I just completely derped. I'll get correct answers when I get back from what I'm currently doing or someone better can do it instead.

Ladue Science Olympiad (2014ish-2017)

A wild goose flies over a pond, leaving behind a voice in the wind.
A man passes through this world, leaving behind a name.