LB3

lab5.mp4_(HD_720_-_WEB_(H264_2500))-20211025_023315

0:12 Hello again, welcome to Lab 5.

0:15 Just letting you know right off

0:16 the bat this is going to be way

0:18 easier than the previous lab.

0:19 Barely any math.

0:20 There's an Excel plotting, but it's

0:21 not nearly going to be as complicated,

0:23 which means that the editing is going

0:25 to be way less stressful on my end.

0:27 There was almost 50 minutes of footage

0:28 in the last video that I made and it took

0:31 me three or four hours to edit that.

0:33 And then it took another six hours

0:35 with dealing with icollege ********

0:37 in order to get it to upload,

0:38 so hopefully that won't happen this week.

0:41 The gist of this lab is that you will be

0:43 measuring a distance using one of the

0:45 rungs of the cosmic distance ladder,

0:47 which we'll get to in a couple of labs.

0:49 This one is just really well known.

0:50 It deals with the topic of stellar

0:52 evolution that you've hopefully

0:53 gotten to in your lecture.

0:54 But besides parallax,

0:55 the way that we measure distance

0:57 in astronomy has to do with

0:59 two fundamental concepts.

1:00 The first is the magnitude system,

1:02 where a little M is the apparent

1:03 magnitude of an object.

1:05 It is the apparent brightness of

1:06 something how we measure it on Earth.

1:07 And then there's capital M.

1:10 No one likes this notation.

1:11 The only thing different is that

1:13 one is capital and one is not.

1:14 So the difference is capital M

1:16 is the absolute magnitude or the

1:18 intrinsic brightness of something.

1:19 If you were to go right up to it,

1:20 how bright would it be?

1:21 And you compare apples to apples to

1:23 always measure things to the same scale.

1:25 The absolute magnitude is the

1:27 brightness of something that's

1:28 measured at a distance of 10 parsecs.

1:29 Remember what a parsec is?

1:31 1 parsec is 3.26 light years.

1:34 The reason why we get this number is

1:36 that one parsec is the distance that

1:38 some celestial object would have to be

1:41 to have a parallax angle of 1 arcsecond.

1:43 So parallax arcsecond?

1:45 Parsec that distance is 3.26 light years.

1:47 Using these two things tells us

1:49 what the distance must be and I'll

1:50 write the equation in just a second.

1:52 But conceptually it makes sense

1:53 if we measure the brightness of

1:55 something as it appears on Earth and

1:56 we know how bright it actually is,

1:58 then the farther apart those two numbers are,

2:01 the greater the distance must be.

2:02 If they were the same number,

2:03 that means that we're right next

2:05 to the object.

2:05 The further apart they are in value,

2:08 the further away the object must be.

2:09 So the difference between those two m - M.

2:12 So this quantity here is referred

2:14 to as the distance.

2:15 Modulus and the distance modulus

2:17 equation is m - m = 5 log d - 5.

2:23 So the difference between these two

2:25 objects on a log scale gives us what?

2:28 The distance must be and this distance

2:30 is always measured in parsecs.

2:31 The thing with this so if we want

2:33 to measure

2:33 distance to objects that are

2:34 farther away from something that we

2:36 can measure easily with parallax,

2:37 we can always measure what the

2:38 apparent magnitude is. On earth.

2:39 It's much much harder to measure

2:41 the absolute magnitude of something,

2:42 because we're not next to it.

2:44 We can't make a measurement of something

2:45 at 10 parsecs if we're not at 10 parsecs.

2:47 So what we have to do,

2:48 what the whole distance ladder concept

2:50 means is find something that gives

2:52 us absolute magnitude so that we can

2:54 compare to the brightness on earth so

2:56 that we can constrain the distance.

2:58 That's the that's the basic concept.

3:00 One of the best,

3:00 easiest ways to do that for things

3:02 in the local universe,

3:03 including other galaxies,

3:04 is using what are known as C feed

3:07 variable stars.

3:08 Hopefully you've touched on this in lecture.

3:10 If not, I'll go over really quickly.

3:12 What is a variable star?

3:13 Well, the first question we want to

3:15 ask is how do stars normally work?

3:16 You have a core that's producing

3:19 fusion that's emitting a bunch

3:21 of radiation pressure.

3:22 All the while the entire mass of

3:24 this thing is made of is always.

3:26 Pushing inwards so this is the force

3:28 of gravity and the reason why stars

3:31 keep their shape is because the force

3:33 of gravity is equal to the force.

3:36 The force of gravity is equal to

3:37 the force of radiation pressure.

3:38 The amount of radiative force

3:40 that the core is pushing out from

3:42 nuclear fusion is matched exactly

3:44 by the force of gravity.

3:45 Wanting to crush everything

3:46 in this is how our son works.

3:48 This is how most stars work.

3:50 The thing with variable stars

3:51 is that this isn't the case.

3:53 You have a mismatch between the

3:54 amount of force the gravity has

3:55 in the amount of force that the

3:57 radiation pressure has.

3:58 So let's say at step one by variable

4:00 star is producing more radiation pressure

4:02 than it is gravitational pressure,

4:04 so.

4:04 This here is way more powerful than

4:07 the force of gravity pushing it inward.

4:09 So here my radiation pressure is

4:11 more than my my force of gravity.

4:13 That means that things pushing outward

4:14 are stronger than things pushing inward,

4:16 and so this thing it will push

4:18 everything out and so this thing

4:19 will expand it as it expands.

4:21 What happens to a gas when you let it expand?

4:23 It cools off that gets less dense,

4:25 and the radiation the photons have an

4:27 easier time getting out of the atmosphere.

4:30 So this thing starts to cool off.

4:31 The radiation pressure goes down,

4:32 which means that it starts to collapse again,

4:34 this time gravity.

4:35 Starts to win,

4:36 and so the star shrinks back down.

4:38 And what happens when you compress a gas?

4:40 The pressure goes up,

4:41 the temperature goes up,

4:42 which means that the radiation pressure

4:43 that the core is causing from nuclear fusion.

4:46 If you're upping the pressure and

4:47 you're upping the temperature,

4:48 you're increasing the amount

4:49 of nuclear fusion in the core,

4:51 and so this thing starts to heat

4:53 up and the

4:54 force of radiation.

4:55 Get stronger than gravity again and

4:57 the star starts to expand out and

4:59 then this whole cycle begins again.

5:00 The way that we observe this.

5:02 Like usually we can't see how big stars are.

5:04 We can just see how bright they are.

5:06 So if we were observing

5:08 variable stars overtime,

5:09 if we go from here to here,

5:11 the star has gotten bigger and the

5:13 photons have an easier time getting out

5:15 so the luminosity goes up in this step

5:18 and then as it starts to cool off in,

5:20 the temperature goes down and

5:21 the star compresses again,

5:22 the luminosity goes down.

5:23 You can press the gas it gets,

5:25 it goes up in temperature.

5:26 The radiation pressure starts to increase,

5:28 which means that the star

5:29 starts to expand again,

5:30 which means luminosity goes up.

5:32 It compresses the luminosity goes down,

5:33 and so over time,

5:34 not only is the star changing

5:36 its temperature and its size,

5:37 the luminosity of the star

5:39 is changing over time,

5:40 and so we were to observe a variable

5:42 star over a long period of time and plot

5:44 what's happening to its luminosity.

5:45 It'll start to look something like this.

5:48 Overtime, luminosity goes up,

5:49 the star cools off,

5:51 and it shrinks down,

5:52 so the luminosity goes down,

5:54 increase the radiation pressure it goes up,

5:56 and then it starts to cool down and compress.

5:58 And Luminosity goes back down again.

6:01 But the reason why this applies to distances?

6:04 Because this behavior is related to

6:05 how bright the stars intrinsically are,

6:07 the absolute magnitude depends on this.

6:09 If we measure the period,

6:11 remember for the last couple of labs,

6:13 the period is how long something

6:14 takes to repeat itself,

6:15 and so if it hits maximum brightness here,

6:17 the period is from here until it

6:19 goes back to where it was before,

6:21 and so this would be one period

6:22 for CP at variable stars,

6:24 which is just a specific kind of

6:25 variable star there period of pulsation.

6:27 So how fast they're shrinking and growing

6:29 is related to how bright they intrinsically.

6:32 Promote we've observed

6:33 perceive variable stars.

6:34 If you have a longer period of pulsation,

6:37 you have a brighter star,

6:38 and so we can't ever

6:40 measure absolute magnitude.

6:40 But we can measure the period, right?

6:42 We just have to observe a star for

6:44 a long period of time and then just

6:45 measure how long it takes to get

6:47 back to the beginning of the cycle.

6:48 And so this is telling us if

6:50 you observe the period,

6:51 then you can just use this relationship to

6:53 get what the absolute magnitude that star is,

6:56 because every different period is related

6:58 to a uniquely different absolute magnitude.

7:01 Which means if we measure

7:02 one specific period.

7:03 This relationship tells us what

7:05 the absolute magnitude is,

7:06 and that's all we were looking

7:07 for in the first place.

7:08 We want absolute magnitude

7:09 to measure the distance.

7:10 We can't measure it directly,

7:12 but this thing tells us if

7:13 we measure the period,

7:14 we can get the absolute magnitude

7:15 from this relation,

7:16 plug it into the distance modulus

7:17 and get the distance that way.

7:19 OK,

7:19 so part one table when you're given

7:21 the apparent magnitude of four

7:22 different stars in the same star

7:24 cluster and using their distance,

7:25 you're going to calculate their

7:27 absolute magnitudes.

7:27 So for each one of these stars,

7:28 the distance is 2600 parsecs.

7:30 So for all four of those stars,

7:32 you're going to use this same distance.

7:34 Using this equation and equals

7:36 m + 5 - 5 log D if you're using

7:40 a scientific calculator.

7:41 This is log base 10.

7:42 If you're not using a scientific

7:44 calculator and you have no idea

7:45 what the **** I just said,

7:46 don't worry about it.

7:47 If you to do the do the log something

7:48 to the logarithm of something,

7:50 just type it into your phone and

7:51 then hit the log button.

7:52 If you tip your phone sideways

7:53 and whatever that number is,

7:55 that's the log of whatever

7:56 you're plugging in the table.

7:57 One will have four stars where you

7:59 have the absolute magnitudes and then

8:01 table two table two will give you

8:02 seven additional stars where it's

8:04 already calculated the absolute magnitude.

8:05 For you,

8:06 but in table one and table to you

8:08 also have their periods the log P,

8:10 which is just the logarithm of the period.

8:11 Again type it in your phone,

8:13 take the log and that will give

8:14 you the log

8:15 of the period and So what you're going

8:16 to do is you're going to take all the

8:17 values from table one and table two,

8:19 so 11 total stars and you're going to

8:22 plot log P versus absolute magnitude.

8:24 So the period versus absolute magnitude

8:27 in Excel or pages or whatever

8:29 spreadsheet software that you're using,

8:31 and then construct your own

8:33 period luminosity relationship.

8:34 And I'll show you how to do that right now.

8:36 OK, so here I've copied.

8:37 Over all of the data from table two,

8:39 and then I'm going to use that as

8:40 the example because I don't want to

8:42 give you the answers from table one

8:43 just to let you know you will also

8:45 have the data from table one here

8:47 and so you will have 11 total data

8:49 points in your graph for Part 2.

8:51 So what you're going to do is you're

8:54 going to select the log P&M columns,

8:56 so click this, hold shift click, see.

8:58 So you have both of these highlighted.

9:01 Click on insert,

9:02 go to recommended charts and

9:05 then click on scatter.

9:07 OK, so here is our rough graph here.

9:10 You can make it a little bigger if

9:12 you want to just make it clearer

9:13 we should click on your graph,

9:14 make sure chart design is selected,

9:16 click on add chart elements axis

9:19 titles and then primary horizontal.

9:22 And probably very vertical.

9:23 So that both of these now pop up here,

9:25 the X axis is log P.

9:29 And the Y axis is absolute magnitude.

9:32 Now the last step,

9:32 once our data is here and remember,

9:34 you're going to have four other

9:35 data points from the absolute

9:36 magnitudes that you calculate.

9:38 In part one,

9:38 we're going to draw a trendline that kind

9:40 of best represents what the data is doing.

9:42 So again,

9:43 we're going to go to add chart elements,

9:45 and we're going to go to trendline linear.

9:48 Boom,

9:49 that just happened,

9:51 so hopefully you have something

9:52 that looks like this or I don't

9:54 think I I couldn't find a way in

9:55 pages to flip the axis.

9:56 I know that Excel can do it,

9:58 but I couldn't find a way

9:58 that numbers could do it,

9:59 so I just said yours on your

10:01 spreadsheet will probably look flipped,

10:02 so this is this is fine.

10:04 These values are just mirrored.

10:06 Keep that on your spreadsheet.

10:08 That's something that you're

10:08 going to turn in with your lab so

10:10 that I can see that you did it so

10:11 I can give you credit for it,

10:12 but keep this in mind while

10:13 we move to part three.

10:14 In part three,

10:15 you're going to plot the light curve,

10:17 meaning how much the.

10:18 Brightness of ACV variable

10:20 star is changing over time.

10:22 For one CP had variable in one

10:24 of the satellite dwarf galaxies

10:25 of the Milky Way table.

10:27 Three gives you data points,

10:28 so it gives you time in days and

10:30 it gives you apparent magnitude.

10:32 There are 25 data points there.

10:33 Throw them all into Excel or

10:35 numbers or whatever and

10:36 plot it using the same exact

10:38 way that you plotted the period

10:39 luminosity relation in Part 2.

10:41 Same exact way, same exact directions

10:42 and then once you do that your

10:44 light curve should look something

10:45 like this and I flipped this too,

10:47 so this should actually look like what?

10:49 You guys got in on a mirrored version of it,

10:51 so you should have something

10:52 that looks like this.

10:53 The first thing that you're

10:53 going to want to do,

10:54 the reason why we use CP variables

10:56 in the first place is that we want to

10:58 measure their period of pulsation,

10:59 and so the easiest way I think you can do

11:01 it is go from one peak to the other peak.

11:04 Remember,

11:04 the magnitude scale is always reversed,

11:07 and so if you have 20 up

11:09 here and 10 right here,

11:11 a smaller number of magnitude means brighter,

11:13 and so the peaks of the brightness.

11:14 Or actually the troughs.

11:16 Here I know it's weird anyway,

11:18 so you have a time here.

11:20 So this is time one.

11:21 Of one peak and then the period will

11:23 be how long does it take to get

11:24 back to that same peak brightness

11:26 and that will be over here.

11:27 So just find out what the time is over here.

11:30 T2 the period is just T 2 - T one.

11:34 As your period,

11:35 it's the amount of time between the two

11:37 peaks and then log P is just take this value,

11:39 type it into your calculator,

11:40 hit the log button and that gives you

11:42 your log of the period of pulsation.

11:44 OK,

11:44 the next step is getting the

11:46 absolute magnitude.

11:46 The way to do that is to go back

11:48 to Part 2 where you graphed

11:50 your period luminosity relation.

11:52 When you graph this thing when you have.

11:55 Log P here at M here.

11:57 I think it looks like this for you

11:58 guys anyway, so you calculated log P is.

12:03 You calculated the log P as some number.

12:05 Find that same number down here with

12:06 the graph that you made in Part 2,

12:08 just eyeball go up to the line that

12:10 you drew through all the data points

12:12 and then find what absolute magnitude

12:14 that that log P corresponds to,

12:16 and that's your end. User log P.

12:18 Go up to the line,

12:19 find what absolute magnitude

12:20 that corresponds to for number 5,

12:22 the apparent magnitude the answer is

12:23 going to be the average of all of

12:25 the apparent magnitudes from table three,

12:27 and they're already in Excel,

12:28 so all you have to do is take that

12:30 column and say what is the average of it,

12:32 and that will give you what it is.

12:33 Remember,

12:33 all of them are around 15 something,

12:35 and so the average should also

12:36 be around 15 something and for

12:38 number 6 you're going to take

12:39 that average apparent magnitude,

12:40 and you're going to subtract it

12:42 from the absolute magnitude that

12:44 you got from your graph over here

12:45 and then finally #7 the distance

12:47 just rearranging equation one is 10

12:49 to the power of M minus capital M + 5 / 5.

12:55 This is all in the exponent.

12:57 10 is not multiplied by this 10 is right

12:59 here, and this is all in the exponent,

13:00 so Please remember your PEMDAS do

13:03 everything in the parentheses first,

13:05 then take 10 to the power

13:07 of whatever this thing is.

13:08 It should be between 50,002.

13:13 50,000 to maybe like 80,000

13:15 parsecs or something like that.

13:16 It doesn't have to be exact as long as I can

13:18 see your data and where you got your values.

13:20 As long as you get something near here,

13:23 it's completely fine with me.

13:24 OK, that's about it.

13:25 If you have any questions,

13:27 my office hours are going

13:28 to be the same bat time,

13:29 same bat place Wednesdays and Thursdays.

13:31 One or two PM.

13:32 I tried to make the directions

13:33 as straightforward as possible,

13:35 so hopefully the Excel stuff

13:36 isn't too hard for you guys.

13:38 But anyway happy early October and

13:40 to celebrate the start of the fall.

13:43 Finally, and and the coming of Halloween,

13:46 I figured that for this month,

13:48 besides having bloopers

13:49 at the end of my video,

13:50 I'm just going to show quick clips from

13:52 some of my favorite Halloween movies.

13:54 So enjoy it and I'll see you guys next time.

14:00 Whatever.

14:02 I put on you.

14:10 You