Astronomy C

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Adi1008
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Re: Astronomy C

Postby Adi1008 » March 1st, 2018, 6:46 pm

Answers (possibly)
(a - c) Are definitely going to be lines of equal mass/etc., though I'm not certain what any of them actually are. If this were an actual test, I'd probably put mass for all of them. I think dark blue is most likely to be mass though, (d) I'm not sure, but I would assume a larger braking index implies an increasing decrease in period - therefore: top, middle, bottom. (e) logarithmic
there's no way I would know this if I hadn't read the paper that this graph came from a few months ago, but the blue lines are constant magnetic field strength since its basically proportional to sqrt(P*Pdot), the green lines are constant characteristic age since thats P/(2*Pdot), and the light blue lines are constant Edot since thats basically proportional to Pdot / P^3 (drawing the lines does use some assumptions)
c0c05w311y is correct about everything he said and Unome is correct about the x-axis being logarithmic. You can use the general mathematical relationships c0c05w311y mentioned to tell which line is which. A higher braking index results in a lower slope on the P-Pdot diagram
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Re: Astronomy C

Postby PM2017 » March 11th, 2018, 9:38 pm

c0c05w311y, can you post a question and revive the thread?
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Re: Astronomy C

Postby themightyweeaboo » March 22nd, 2018, 2:20 pm

Time to revive this thread :)

Name and describe 4 different ways a star's core can collapse

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Re: Astronomy C

Postby PM2017 » March 29th, 2018, 8:29 pm

Time to revive this thread :)

Name and describe 4 different ways a star's core can collapse
I don't think I fully understand your question. I thought that there was one way a star's core can collapse (something like this:http://cse.ssl.berkeley.edu/bmendez/ay1 ... /snII.html) Either that or I am seriously missing something.
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Re: Astronomy C

Postby Unome » March 30th, 2018, 4:42 am

Time to revive this thread :)

Name and describe 4 different ways a star's core can collapse
I don't think I fully understand your question. I thought that there was one way a star's core can collapse (something like this:http://cse.ssl.berkeley.edu/bmendez/ay1 ... /snII.html) Either that or I am seriously missing something.
The question is a little vague with respect to what counts as a different type of collapse. Types In, Ic, and II all have essentially the same collapse mechanism but with different outer layer compositions. Different ways of core collapse could include things like the pair-instability effect.
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Re: Astronomy C

Postby cacodemon » April 11th, 2018, 7:09 pm

Since nobody has posted on this for a while I thought I would add a few questions.
Keep in mind these are unrelated.

1) Derive the distance modulus relationship (prove that m-M = 5 log (D) - 5,, or if you want m-M = 5 log (D/10)).
2) Star 1 has the same absolute luminosity has Star 2. The apparent magnitude of Star 1 is 3, the apparent magnitude of Star 2 is 5, and the distance to star 1 is 13.6 pc. Calculate the distance to Star 2.
3) The radius of a giant molecular cloud is 100 pc. Calculate its mass in Msun.

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Re: Astronomy C

Postby MAAAAC » April 17th, 2018, 5:27 pm

Since nobody has posted on this for a while I thought I would add a few questions.
Keep in mind these are unrelated.

1) Derive the distance modulus relationship (prove that m-M = 5 log (D) - 5,, or if you want m-M = 5 log (D/10)).
2) Star 1 has the same absolute luminosity has Star 2. The apparent magnitude of Star 1 is 3, the apparent magnitude of Star 2 is 5, and the distance to star 1 is 13.6 pc. Calculate the distance to Star 2.
3) The radius of a giant molecular cloud is 100 pc. Calculate its mass in Msun.
I guess I will give it a shot to start this back up... well not the first one, but the others seem simple enough.
2) I got ~34.4 pc
3) I probably got a different answer than you, but here's my thought process:
Assuming the GMC is roughly spherical, the volume in pc^3 would be 4/3piR^3 which gets you 4188790.20479 pc^3
4188790.20479 pc^3 * (3.2407557442396⋅10^19)^3 cm^3 / 1 pc^3) = 1.425697893×10^65 cm^3
According to http://homepage.physics.uiowa.edu/~rlm/ ... on%201.htm GMCs have densities of about 10^3 atoms per cm^3
Assuming this is all hydrogen gas... This means a density of about 10^3(1.67 x 10^-24) grams per cm^3 or 1.67*10^-21 grams per cm^3
Factoring in the volume of the GMC, you get a total of (1.67*10^-21)*(1.425697893×10^65) or 2.3809154813×10^44 grams
This is equal to 2.3809154813×10^41 kg
1 Msun is 1.989 × 10^30 kg, so 2.3809154813×10^41 kg * (1 Msun / 1.989 × 10^30 kg ) = 1.1970414687×10^11 Msun
This either means my math is wrong, my methods/information is wrong, or this is just a very unrealistic GMC considering the usual cap for the mass of a GMC is around 10^7 Msun...

I guess I should ask a question too...
If the period of a Type I Cepheid is 10 days, and the energy of one photon from the peak emission of a star with the same absolute magnitude as this variable star is 3.056E-19 Joules, then
A) What is the radius of this star in Rsun?
B) What is the spectral class of this star?
C) Assuming this star is on the main sequence, what is its density in kg/m^3?

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Re: Astronomy C

Postby PM2017 » April 17th, 2018, 10:40 pm

Since nobody has posted on this for a while I thought I would add a few questions.
Keep in mind these are unrelated.

1) Derive the distance modulus relationship (prove that m-M = 5 log (D) - 5,, or if you want m-M = 5 log (D/10)).
2) Star 1 has the same absolute luminosity has Star 2. The apparent magnitude of Star 1 is 3, the apparent magnitude of Star 2 is 5, and the distance to star 1 is 13.6 pc. Calculate the distance to Star 2.
3) The radius of a giant molecular cloud is 100 pc. Calculate its mass in Msun.
I guess I will give it a shot to start this back up... well not the first one, but the others seem simple enough.
2) I got ~34.4 pc
3) I probably got a different answer than you, but here's my thought process:
Assuming the GMC is roughly spherical, the volume in pc^3 would be 4/3piR^3 which gets you 4188790.20479 pc^3
4188790.20479 pc^3 * (3.2407557442396⋅10^19)^3 cm^3 / 1 pc^3) = 1.425697893×10^65 cm^3
According to http://homepage.physics.uiowa.edu/~rlm/ ... on%201.htm GMCs have densities of about 10^3 atoms per cm^3
Assuming this is all hydrogen gas... This means a density of about 10^3(1.67 x 10^-24) grams per cm^3 or 1.67*10^-21 grams per cm^3
Factoring in the volume of the GMC, you get a total of (1.67*10^-21)*(1.425697893×10^65) or 2.3809154813×10^44 grams
This is equal to 2.3809154813×10^41 kg
1 Msun is 1.989 × 10^30 kg, so 2.3809154813×10^41 kg * (1 Msun / 1.989 × 10^30 kg ) = 1.1970414687×10^11 Msun
This either means my math is wrong, my methods/information is wrong, or this is just a very unrealistic GMC considering the usual cap for the mass of a GMC is around 10^7 Msun...

I guess I should ask a question too...
If the period of a Type I Cepheid is 10 days, and the energy of one photon from the peak emission of a star with the same absolute magnitude as this variable star is 3.056E-19 Joules, then
A) What is the radius of this star in Rsun?
B) What is the spectral class of this star?
C) Assuming this star is on the main sequence, what is its density in kg/m^3?

Mac Hays, Durham Academy Science Olympiad
Number 1 is also fairly simple, but longwinded, so ill just post an image of my handwritten work (lol this is my third version, the first being me just wokring things out, second being a rough draft, and this being me painstakingly writing neatly lol)

anyways:
Image
Wait... I messed up with a sign somewhere. I'll fix it sometime...
EDIT: Fixed!

EDIT: Guess I'll take a stab at your questions as well, since I took the post after you.
A
A) So to find radius, i'll need luminosity and temperature, both of which I can easily find. lots of typing though... e = hc/lamda 3.056e-19 J = 6.626e-34 Js*3e17nm/s/(lamda) lamda = 650.5 nm T = 2.898e6 nmK/(lamda max) T = 2.898e6 nmK/(650.5 nm) T = 4455 K (will be reused in part B) T = 4455K/5778K T-sol T = 0.771 T-sol M = -2.81log(p)-1.43 M = -2.81log10)-1.43 M = -2.81-1.43 M = -4.24 L = 10^(-0.4(-4.24-4.85)) L = 10^3.636 L-sol L = 4325 L-sol L = R^2*t^4 R = sqrt(L) /T^2 R = sqrt (4325)/ (0.771)^2 [b]R = 110.6 R-sol[/b]
B
Using the temperature of 4455 K from the last problem, and a spectral class chart, you get a spectral class of G5.
C
Since this is a fairly massive star I will assume a Mass-Luminosity relationship of L = 1.4*M^3.5. M = L^(1/3.5) L = 4325 L-sol M = 1.4*[4325 ^(1/3.5)] M = 15.3 M-sol M = 15.3 M-sol (2e30 kg/1M-sol) M = 3.06e31 kg R = 110.6 R-sol R = 110.6 R-sol (6.95e8m/1R-sol) R = 7.69e10 m V = 4/3*pi*r^3 V = 4.189*(7.69e10)^3 V = 1.90e33 m^3 D = M/V D = 3.06e31kg/1.90e33 m^3 D = 1.61e-2 kg/m^3
My turn to ask I guess...
Make the following (incorrect) assumptions about an imaginary neutron star: 1) all loss of rotational energy is emitted in the plane of the Earth (that is, the luminosity we observe is the total energy output of the neutron star, and the neutron star only emits energy by losing kinetic energy). 2) The core of the progenitor star was 10% of the total mass, and the entire core collapsed to make the neutron star. 3) The radius of the progenitor star was 1.5 R-sol 4) The radius of the neutron star is 9 km. 5)The mass of the neutron star is 2 M-sol. 6) The rotational period of the neutron star is 25 ms.

These assumptions make no sense whatsoever realistically, but bear with me.

A: The neutron star has an observed slow-down rate of 7.6e-13 s/s. Calculate the luminosity of the neutron star in watts. (2.489e32 W)
B: What was the rotational period of the progenitor star (in days)?
C: If this progenitor star was a Type I Cepheid, and had an apparent magnitude of 6, how far in kPc is the neutron star?


Never again am I making questions like these again...
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Re: Astronomy C

Postby Unome » April 18th, 2018, 5:44 am

Attempts
1. I ended up with 1.7E29 W, no idea if it works though. I used P = 0.5(pdot)(mass)(initial velocity squared), where I computed the initial velocity from v = 2(pi)(r). 2. Calculating via L = (m)(r^2)(1/p) since angular velocity = 1/p, I got p_initial = 28935 days. 3. Rotational period =/= pulsation period so... idk
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Re: Astronomy C

Postby PM2017 » April 18th, 2018, 6:41 am

Attempts
1. I ended up with 1.7E29 W, no idea if it works though. I used P = 0.5(pdot)(mass)(initial velocity squared), where I computed the initial velocity from v = 2(pi)(r). 2. Calculating via L = (m)(r^2)(1/p) since angular velocity = 1/p, I got p_initial = 28935 days. 3. Rotational period =/= pulsation period so... idk
Yeah, I'm sorry, those were some really bad questions... I don't know what exactly I was thinking.
Just ignore myvquestions and just continue the thread (although for number 1. and therefore 2. I got vastly different answers, which I will post when I get home.)

Again, apologizing for those terrible questions.
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Re: Astronomy C

Postby Unome » April 18th, 2018, 6:53 am

Image

1. What DSO does this data come from?
2. What spectral regions are each of these graphs showing?
3. This graph shows two phases. Based on the graph, over how many phases was data actually collected?
4. The bottom graph is phase-shifted from the other two. Considering the properties of the system that produced this data, why is this so?
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Re: Astronomy C

Postby jonboyage » April 18th, 2018, 6:55 am

Attempts
1. I ended up with 1.7E29 W, no idea if it works though. I used P = 0.5(pdot)(mass)(initial velocity squared), where I computed the initial velocity from v = 2(pi)(r). 2. Calculating via L = (m)(r^2)(1/p) since angular velocity = 1/p, I got p_initial = 28935 days. 3. Rotational period =/= pulsation period so... idk
Yeah, I'm sorry, those were some really bad questions... I don't know what exactly I was thinking.
Just ignore myvquestions and just continue the thread (although for number 1. and therefore 2. I got vastly different answers, which I will post when I get home.)

Again, apologizing for those terrible questions.
How I did #1
[math]E = \frac{1}{2}I\omega^2[/math] [math]E = \frac{1}{5}mr^2 * \frac{1}{p^2}[/math] [math]\frac{dE}{dt} = \frac{1}{5} mr^2 (\frac{-2}{p^3} \frac{dp}{dt})[/math] [math]dE = \frac{-2mr^2}{5p^3}dp[/math] [math]dE = \frac{-2mr^2}{5p^3} \dot{P}[/math] Then plug in values and I got 6.2676E30 Watts
Edit: forgot to plug in 2/5 for moment of inertia of sphere instead of just mr^2
Last edited by jonboyage on April 18th, 2018, 8:20 am, edited 2 times in total.
I was in a bin

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Re: Astronomy C

Postby PM2017 » April 18th, 2018, 7:09 am

Attempts
1. I ended up with 1.7E29 W, no idea if it works though. I used P = 0.5(pdot)(mass)(initial velocity squared), where I computed the initial velocity from v = 2(pi)(r). 2. Calculating via L = (m)(r^2)(1/p) since angular velocity = 1/p, I got p_initial = 28935 days. 3. Rotational period =/= pulsation period so... idk
Yeah, I'm sorry, those were some really bad questions... I don't know what exactly I was thinking.
Just ignore myvquestions and just continue the thread (although for number 1. and therefore 2. I got vastly different answers, which I will post when I get home.)

Again, apologizing for those terrible questions.
How I did #1
[math]E = \frac{1}{2}Iw^2[/math] [math]E = \frac{1}{2}mr^2 * \frac{1}{p^2}[/math] [math]\frac{dE}{dt} = \frac{1}{2} mr^2 (\frac{-2}{p^3} \frac{dp}{dt})[/math] [math]dE = \frac{-mr^2}{p^3}dp[/math] [math]dE = \frac{-mr^2}{p^3} \dot{P}[/math] Then plug in values and I got 1.5669E31 Watts
That's how I did it.
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Re: Astronomy C

Postby cacodemon » April 19th, 2018, 7:46 pm

[hide]
1) PM2017: looks good
2) yep: d2 = d1 * sqrt(2.512^m2-m1) => d2 = 34.16 pc.
3) This question was kind of obscure and probably won't come up this year (maybe not ever on a scio astro test)
I should have mentioned that the GMC was in virial equilibrium.
The way I did it was: using linewidth-size correlation you can get dispersion velocity:
(dispersion velocity) = (0.72pm0.03)(R/pc)^(0.5pm0.05) (km/s)
= 9.44 km/s
Then use virial theorem:
GM/R = (dispersion velocity)^2
M = (R * (dispersion velocity)^2) / G
= ((9.46e17 m)*(9440 m s^-1)^2) / (6.67e-11 m^3 kg^-1 s^-2)
= ((9.46e17)*(8.9e7) m^3 s^-2) / (6.67e-11 m^3 kg^-1 s^-2)
= ((9.46e17)*(8.9e7) kg) / (6.67e-11)
= 1.26e36 kg
= 1.26e36 / 1.9891 * 10^30 Msun
= 6.346e5 Msun

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Re: Astronomy C

Postby c0c05w311y » April 26th, 2018, 10:00 pm

I'll try to answer Unome's question:
1. DEM L241 2. From top to bottom, radio, xray, gamma 3. 2? I'm basing this on how many dots appear to be on top of each other. However I'm really not sure if this is how the question was supposed to be answered. 4. The bottom graph is gamma, and the system is an xray/gamma binary. So the gamma emissions come from the acceleration of particles around the neutron star, and the periodicity is due to its orbit (more particles in the area when its closer to the companion in its elliptical orbit). However I'm blanking on how there would be a phase shifted emission in radio and xray. Can someone explain?


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