Astronomy C

[Adi1008]

Answers (possibly) (Click to Show Hidden Text)

(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

[PM2017]

c0c05w311y, can you post a question and revive the thread?

[themightyweeaboo]

Time to revive this thread

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

[PM2017]

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.

[Unome]

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.

[cacodemon]

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.

[MAAAAC]

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

[PM2017]

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:

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 (Click to Show Hidden Text)

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 (Click to Show Hidden Text)

Using the temperature of 4455 K from the last problem, and a spectral class chart, you get a spectral class of G5.

C (Click to Show Hidden Text)

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...

[Unome]

Attempts (Click to Show Hidden Text)

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

[PM2017]

Attempts (Click to Show Hidden Text)

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.