Astronomy C

[Ashernoel]

So I already talked about this with East and Lumosityfan on IRC earlier and got a good answer, but I'll ask it again because I think it's really interesting:

In a typical CO white dwarf, a type Ia supernova will occur after carbon burning begins due to the runoff nuclear reaction that follows it. But from what I found (Carrol and Ostlie's Introduction to Modern Astrophysics) carbon burning begins at 1.3 solar masses. The "vanilla" explanation (as someone on stackexchange put it) for the type Ia supernova is that it occurs after the Chandrasekhar limit is reached; the value of which is 1.4 solar masses. Comparing these, I suspected that this was a misconception- the type Ia supernova is (at least somewhat) unrelated to the Chandrasekhar limit, and does not need to reach it to explode, although white dwarfs cannot surpass that limit (except in special cases). East and Lumosityfan seemed to confirm this, and the white dwarf does not need to hit the limit; anyone else have input on this?

I've also heard that the values were different and unrelated (though I tend to stick with 1.4 for most tests since that's what usually gets the points).

I wonder if the rotation of the object has anything to do with it? When a star is rotating rapidly, its centrifugal pseudo-force would have an effect on the pressure on the core, increasing the total mass that the white dwarf can accommodate. The conventional mass of 1.4 I believe is for non-rotating objects.

As for the 1.3, can you explain how fusion makes the white dwarf unstable? In my head, I imagine that fusion would have the effect of decreasing the "load" on the degenerate matter and help prevent collapse.

Rotation does. White dwarfs can exist with mass greater than the Chandrasekhar if they are spun up.

Most of the times they explode before the Chandrasekhar limit so it is the accepted value but yes detonation is as it approaches the limit, not when it hits it

[ReBobville]

I've also heard that the values were different and unrelated (though I tend to stick with 1.4 for most tests since that's what usually gets the points).

I wonder if the rotation of the object has anything to do with it? When a star is rotating rapidly, its centrifugal pseudo-force would have an effect on the pressure on the core, increasing the total mass that the white dwarf can accommodate. The conventional mass of 1.4 I believe is for non-rotating objects.

As for the 1.3, can you explain how fusion makes the white dwarf unstable? In my head, I imagine that fusion would have the effect of decreasing the "load" on the degenerate matter and help prevent collapse.

Rotation does. White dwarfs can exist with mass greater than the Chandrasekhar if they are spun up.

Most of the times they explode before the Chandrasekhar limit so it is the accepted value but yes detonation is as it approaches the limit, not when it hits it

The Chandrasekhar limit (~1.44M) is simply a limit of electron degeneracy pressure. However the limit is subject to some assumptions, such as slow rotational velocity and being subjected to newtonian physics. In reality, the type 1a event occurs due to carbon (and oxygen) fusion, which produces sufficient energy to unbind the star. This fusion can begin below the limit.

Hope this helps!

[Unome]

So why is it that sun-like stars form a degenerate helium and core but significantly higher-mass stars don't? (or is the helium flash unrelated to this?)

[ReBobville]

So why is it that sun-like stars form a degenerate helium and core but significantly higher-mass stars don't? (or is the helium flash unrelated to this?)

It all has to do with mass. Smaller stars are not large enough to generate the pressure required to initiate helium fusion once the hydrogen is exhausted (for the most part). As a result, the helium rich core of the star begins to collapse, until degeneracy pressure arrests this process. However, the core continues to collapse and increase in temperature, which eventually triggers helium fusion inside a star composed of alot of degenerate matter. This is what leads to the helium flash you alluded to.

[clapjack]

Hi,

Does anyone know how to solve this question? The answer key says it's 6\pi

If the closest distance from a planet to its host star is 1.50 AU and its farthest distance from its host star is 4.50 AU, what is the area that this planet sweeps out over the course of a full orbit (in AU2)?

To me, this seems like just finding the area of the ellipse. From the given information, I get d_aphelion = 4.5, d_perihelion = 1.5, a = 3, e = 0.5, and f = 1.5. However, doing this I get an answer of frac{9sqrt{3}}{2}\pi \approx 7.794

Thanks,
clapjack

[Unome]

Hi,

Does anyone know how to solve this question? The answer key says it's 6\pi

If the closest distance from a planet to its host star is 1.50 AU and its farthest distance from its host star is 4.50 AU, what is the area that this planet sweeps out over the course of a full orbit (in AU2)?

To me, this seems like just finding the area of the ellipse. From the given information, I get d_aphelion = 4.5, d_perihelion = 1.5, a = 3, e = 0.5, and f = 1.5. However, doing this I get an answer of frac{9sqrt{3}}{2}\pi \approx 7.794

Thanks,
clapjack

From Google: Apparently the major axis is perihelion+aphelion which equals 6, so I guess that's what they wanted you to do? No idea why that works though.

[JCicc]

The Astronomy exam from the PA state tournament should be up on the test exchange some time soon. It has been submitted and they're pretty good about getting them up quickly. Message me with questions if you have any. Regional exam to follow.

The top scores went as follows, out of 100: 62, 58, 54, 51, 42, 40.

While we are on the subject, a number of people question the difficulty level of my exams. Allow me to reiterate. As a supervisor I need to clearly differentiate 36 teams quickly and efficiently, and easy exams cause the top teams to "pile up" at the top, making it necessary to break numerous ties. I would rather break a tie for 14th place than 1st. When I construct an exam, I have the rules in front of me. I tend to go "deeper" than the rules (for example, "neutron stars" includes a lot of subcategories, does it not?) specifically to differentiate the best from the second best and the third best, and so on.

I am also a member of the national committee for Astronomy, so there's that.

[Unome]

The Astronomy exam from the PA state tournament should be up on the test exchange some time soon. It has been submitted and they're pretty good about getting them up quickly. Message me with questions if you have any. Regional exam to follow.

The top scores went as follows, out of 100: 62, 58, 54, 51, 42, 40.

While we are on the subject, a number of people question the difficulty level of my exams. Allow me to reiterate. As a supervisor I need to clearly differentiate 36 teams quickly and efficiently, and easy exams cause the top teams to "pile up" at the top, making it necessary to break numerous ties. I would rather break a tie for 14th place than 1st. When I construct an exam, I have the rules in front of me. I tend to go "deeper" than the rules (for example, "neutron stars" includes a lot of subcategories, does it not?) specifically to differentiate the best from the second best and the third best, and so on.

I am also a member of the national committee for Astronomy, so there's that.

This should be fun; looking forward to taking your test when I get home today I was pleasantly surprised to see your name on the SOSI schedule last summer, and was hoping you'd starting posting tests again. Also: 62 was your highest this time? Seems a bit lower than in past years, weren't they usually in the 70s and 80s?

Edit: I've added the files onto the test exchange.

Edit 2: Super happy to have scored 63-65 on the state test solo + binder (or possibly in the mid-50s if math has to be super exact, several of mine were within a few percent) since Harriton has done so well in the event at invitationals. Hopefully this one is actually a reflection of my true skills, rather than all of my (relative) fails from previous tests...

Edit 3: Also 65/75 on the regionals test, though I have no idea how good that is. After taking both of the tests it was really interesting to see how they line up, with the regionals test serving as a good overview of the entire event and the state test focusing more on difficult stuff.

[EastStroudsburg13]

While we are on the subject, a number of people question the difficulty level of my exams. Allow me to reiterate. As a supervisor I need to clearly differentiate 36 teams quickly and efficiently, and easy exams cause the top teams to "pile up" at the top, making it necessary to break numerous ties. I would rather break a tie for 14th place than 1st. When I construct an exam, I have the rules in front of me. I tend to go "deeper" than the rules (for example, "neutron stars" includes a lot of subcategories, does it not?) specifically to differentiate the best from the second best and the third best, and so on.

To the contrary, I've always found this sort of strategy to be ideal, and theoretically a standard to which other supervisors should hold themselves to. I've definitely encountered tests that could be defined as "too hard", and yours were never on them; the difficulty is always such that the teams that deserve to do well end up doing well. Plus, I think the challenge of a difficult, but doable, test is something that a lot of teams welcome; I know I did when I first got to take one in an actual competitive setting.

[Ashernoel]

66 on the state test . Would have been better if I didn't get literally 8 wrong in a row a math page ((( but I'm dso theory guy this year so whatev...but I did take like an hour and a half around I think so idk if that's allowed

edit: looool 69 on the regional. What are the peibert classes? I can't find them :///

Edit: I think I miscounted and got 34 on state test not 66...edit: wait no -34 is 66 not 34 mb