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Jan/O5/2001 The Milky Way Galaxy Page MW- 1

In this activity we explore the structure of our own local universe, the Milky Way. We might alsobe able to look outside our galaxy, at the globular clusters which orbit around our galaxy I Vlrhichwere used by Shapely to determine the distance to the galactic core. It may even be possible tolook far away and see other galaxies that are close to ours (e.g. Andromeda).

A. OBJECTIVESThe main purpose of this lab is to recreate some of the historical measurements made to

determine the size and shape of the galaxy in which we live. The objectives are:

1. Observe features of the Milky Way (orientation, poles, core, dust lanes etc.)

2. Recreate Herschel's "star gauging" measurement of the variation of the density of stars withgalactic latitude, and estimate the thickness of the galaxy.

3. Observe a globular cluster, and its relation to the galactic core.

4. Possibly view one of the closer galaxies (M31, M104, M51).

B. STUDENT PREPARATION.It would be helpful if you give the discussion a quick reading before coming to lab..A ruler might be useful, as well as protractor. Bring your starmaps and lab manual!.A red flashlight and clipboard will be useful (its hard to read in the dark!)..Bring a computer disk to copy the "Galactic Coordinate Calculator" program..Dress for cold weather!

C. INSTRUCTOR PREPARA TION (Students can ignore this)This activity has some seasonal restrictions. At least one of the galactic poles should be visible,

along with some portion of the Milky Way. Hence in Fall, it should be done in late November sothat the south pole is up (although it will be low in the southern sky). The Andromeda galaxy will benear zenith, and there are a few good globs nearby! In Winter it will need to be done near the endof the quarter, later at night so that the north pole will be up in the east (Andromeda will probably betoo low, as will most of the good globulars) In Spring it must be done early, because later (May)the Milky Way is nearly on the horizon. Ideally the moon should dark, or at most crescent.

Encoders should perhaps be put on the scopes to aid in determining exact locations that thesamples are taken. Extra copies of data sheets are needed for the students, along with some starcharts. Specific parameters of the lab telescopes will need to be provided in advance for studentsto calculate telescope properties.

For bad weather there is a good "computer" alternative, which closely mimics the observationalactivity.

The instructor will need to provide some sort of introductory lecture about galactic coordinates.There is a computer program for converting RAlDec into galactic coordinates.

~';l'Lo~ @Jan2001, W. Pezzaglia Winter 2001SCU Astrolab

MILKY WAY & GALAXIESPractice1 Astronomy@ 11/24/89 W. Pezzag1iaDisK: 1 7/MW

11- DISCUSSION.

Only 70 years ego, it wes thought that the stars around us was the whole universe. Hubble(around 1925) proved that the "spiral nebulae" catalogued by Messier were independent "islanduniverses" very far away outside of our own. Now we know that our own galaxy, the Milky Way isbut one of billions in the universe. So in less than'a century, we have realized that the universe isfar bigger then ever anticipeted, with our own gelexy being only one of billions eoch conteiningbillions or even trillions of stars. We have taken a step into a larger universe from which wecennot ever retreat.

The study of the types and shape of galaxies tells us about how the evolved, and the groupings ofgalaxies tells us about the evolution of the whole universe. Even though the closest galaxies aremore than 1000 times further away than the objects we have been looking at up to now (and manygalaxies are more than a million or billion times further) alot of them are so very big, so brightthat you can see them in a small telescope.

A. 6-o.."iac.tic.. Co(!)r"'d\n~te;sThe Milky Way on a dark clear night can be so.brilliant you wonder how you've missed it before.The Greeks interpreted this faint cloud of light to be milk from the breast of Hera (consort ofZeus). In foct, the word galaxy comes from the greek word "gala" for milK. With his telescope,Galileo was the first to realize that the "milk" was a rich field of faint stars. Later observers(n.b. Herschel) mapped star densities to deduce that the universe was a giant disk of stars skewedby about 60 degrees to our equator.

I. The M.iltv.Wo~ .$G:~.Jacb~,r:!~~_~~~1~:Our own galaxy is a disk I which appears to us a glant surrounding ring of dense faint stars

called the Milky Way. It crosses the equator at two places, called the golactic nodes; theascending one in Aquila the eagle, the descending one in Monoceros (the unicorn). The galacticequator is a circle drawn right throught the middle of the Milky Way (ie. the galactic plene),inclined by 62 degrees to the celestial equator.

For talking about positions of objects in the galaxy it is convenient to use galactic coordinates.6alact1c long1tude (symbol a script "L ,,) is measured in degrees around the galactic equator(figure 1). The origin is chosen to line up with the approximate center of the galaxy I in theconstellation of Sagittarius ( 17h 42.4m, -28°55', 1950 coordinates). Oloor books used adifferent system, with the origin at the ascending nc:xr;, now called "system I". aAd the current

"system II".

To view the Milky Way the limiting magnitude of the sky must be around m=+4 or better. Thepresence of the moon will usually wipe out any possible observations. You generally want a VERYshort focal ratio telescope to view the Milky Way, usually you just see more stars (but alot morethan you would anywhere else). Due to the high inclination of the Milky Way, the galoctic planewill be nearly parallel to the horizon when the sidereal time is around 13 hours. At this time, theMilky Way gres almost around the horizon and can't be observed. This happens in the earlyevening in May. At all other times of the year some part of it is visible.

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2. Galactic Latitude

Table MW-l Approximate GaJactjc Coordjnates of Some Sta,rs

Slar Lon~. Lat.« Ophiuchi 350+220« Corona: nor. 400 + 540« Aquila: (Altair) 470 -80C Hcrculis 530 + 400y Lyra: 630 + 130« Lyra: (Vega) 670 + 190Y Cygni 780 + 20«Cygni(Deneb) 840+ 20

"1 Draconis 920+410"1 Ursa: Maj. 1000 +660fJ Ursa: Min. -1500 + 550{ Ursa: Maj. (Mizar) 1120 +'620~ Ursa: Maj. 1220 +610fJ Ccti 1100 -800a Ursa: Min. (Polaris) 1230 + 260Y Cassiopeia: J 230 -200 Ursa: Maj. J 330 + 590

« Ursa: Maj. (Dubhe) 1430 +500

Star Long. LAt.y Vclorum 2630 -80

.8 Virginis 2700+61'"« Volanlis 2820 -130« Eridani (Achernar) 2900 -590« Crucis 3QOo+ I".8 CcIllauri 3120+ 10« Ccnlauri 3160 0"« Virginis (Spica) 3170 + 51"« Trianguli Aus. 3210 -150{ Ara: 3230 -8c.8 Gruis 3460 -58?-« 'Gruis 3500 -520« Scorpii (Antares) 3520 -I. 15"

.8 Scorpii 3540 +230~ Sagillarii 3590 -100« B06lis (Arcturus) 140 + 690« Pisco A. (Fomalhaut) 200 -650'1 Scrpcnlis 270 + 50

SIAr Long. LAI.V Ursa: Maj. 1540+460« Aurig~ (Capella) 1620 + 40'" Ursa: Maj. 1650+630.8 Aurig~ 1670 + 100« Tauri (Aldebaran) 1820 -200« Gcminorum (Castor) 1870 +220.8 Gcminorum (Pollux) 1920 + 230)' Orionis (Bellatrix) 1970 -160« Orionis (lJeuigeuse) 2000 -90

.8 Orionis (Rigel) 2090 -250« Canis Min. (Procyon) 2140+ 130« Leonis (Regulus) 2270 + 490« Canis Ma.i. (Sirius) 2270 -80

0 Lconis 2370 +640« Hydra: (ALphard) 2410 +290'7 Canis Maj. 2420 -60

.8 Lconis (Denebola) 2510+710« Carin~ (Canopus) 2610 -250

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Jan/O5/2001 Milky Way Galaxy Lab Page M'N- 8

3. Pro ram to Convert Celestial Coordinates to Galactic CoordinatesThis program will enable you to quickly convert Right Ascension and Declination into GalacticLatitude, and Galactic Longitude (System 2).

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Run Program: GalCoord. exeEnter RA in Hours and MinutesEnter Declination in Degrees and Arc-minutes. Be sure to put a minus sign in front of the"degrees" if its below (south) of the equator. Note if the declination was 30' below the equator,you would enter a minus zero for the degrees: -0 30.Press the "Calculate Galactic Coordinates" button.

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For example below, we see that entering the coordinates lSh40m, 0 degrees, describing theapproximate position of the Ascending Galactic Node, returns ALMOST 0 degrees galactic latitude(oops its 2), and a longitude of 32 degrees from the Galactic core. Entering the RA & Dec ofBetelgeuse returns the correct galactic latitude (-9 degrees) and longitude (200 degrees) as seen earlierin Table MW-I. .

~~'~Mathematical Details: How was this done?

The formal relationship between galactic and equatorial coordinates is a rotation around the line of thegalactic nodes by the inclination of the galactic plane. Galactic latitude lIb II and longitude ,~ II is related tothe Right Ascension (RA = a) and Declination (Dec =0),

sin b = CDS () sin <5 -sin () CDS <5 sinf a-A)

CDS <5 CDS( a-A)

tan(L+ 1) = sin (} sin 6 + cos (} cos 6 sin( a-A)

cos 6 cos( a-A)

where A =18" 43m is the right ascension of the ascending galactic node. The inclination of the galactic planeis 0=62.6 degrees, and ),,=327 degrees is the adjustment in galactic longitude to put zero degrees at the coreof the galaxy (equivalently, the ascending galactic node is at 33 degrees galactic longitude).

Winter 20011 2'1@Jan2001 , W. PezzagliaSCU Astrolab

B. The Milkv Way as a GalaxyGalileo was the first to resolve the Milky Way into stars. Kant (1775) suggested that the band of the Milky Waysuggested that the universe was a gigantic disk of stars, tilted 60 degrees to the eclipitc.

1. Search for the Center of the UniverseIn 1914, Shapley studied the orbits of Globular clusters, which he assumed orbited around the center of the universe (theGalaxy). Simple statistical studies will show you that there are virtually no glob clusters found near Orion, but that theconcentration is at the opposite side of the Milky way, around Sagittarius. This just happens to correspond to the placein the Milky Way that is the thickest (now called the "central bulge"). In later studies, he was able to estimate thedistance to the center of the galaxy (he was offby a factor of nearly 4 too big, we now know its about 8.5 kpc away.

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2. The Golactic Ofsk .

From star density counts along the Mi1ky way, and away from it, the Mi1ky Way is measured tobe approximate1y a disK 500 parsecs thIck, compared to a diameter of 30 to 50 kpc. TowardSSagittarius, there is a thickened contra1 bu1go, which is the center of the galaxy, about 10 kpcaway. EmIssIon nebulae and open clusters are found all along the M11ky Way. Second generation(Population I) stars dam inate the disk, containing bright new type 0& B stars (with nebu1ae) ,along with new c1usters.

..iThere are numerous dust 1ones or absorptfon nebu1oe in the Milky W'd'f (fIgure A.1. The

largest runs some 50 degrees near1y tight down the midd1e of the ga1actic disk from Deneb toserpens cauda, makIng It look lIke two parallel pIeces. On the other sloo of the galaxy aroundPerseus there are more, but sma11er. These come from thick gas & dust in the spiral arms of thegalaxy. The extinction (absorptIon of light) In the galactic disk due to this dust aver~ about 1magnitude for every 1000 parsecs. Looking oyt away from the center of the ga1axy (Auriga),there is st111 about 10 kpc (kpc= 1 000 pc) of d1sk, an extlnct1on of over 10 maJnltudes! You can'tsee much irr any direction in the Milky Way, its 1ike fCKJ.

.' 5'" -Look ing down on the ga 1 act ic disk (figure ~ ), we see that the sun is just insioo what is ca 11ed

the Or1on Arm of the galaxy. Hence when we 100K at the nebulae near Orlan (M42, Rosette) we areseeing fairly close objects. Across a 1000 parsec void in the other direction is the SagittariusArm, with all of its nebulae (Lagoon, Trifid, Eagle). The sun orbits the galaxy I moving in thedirection of Cygnus.

3. The Core & Ho10GalaCtic latitude is measured up from the galactic plane, with 0 degrees being the Milky Way,

and 90 be1ng the North Pole of the galaxy. On figure 1. the "center" of the c1rcle of the milKY wayrepresents the "pole" of the galaxy. The galactic north pole is in Coma Bcrcnjces ( 12h43',..28°), with the south one in Sculptor. From a side view of the galaxy (figure 3) you can seethat when you are looking up at Coma Berenices, you are looking straight out of our galaxy,through the least amount of gas & dust. Hence you can see deepest into the surrounding universe(i.e. see the furthest other galaxies) along the galactic poles (e.g. the Coma Berecices group of

galaxies).

Globular clusters are generally found above or below the geloctic plane, with more towards thegalactic core. This is because they orbit the galaxy like little "moons". Study of their orbitsdetermined the center of the galaxy to be 8 kpc away. They usually have very elliptical orbits,f}Jing way out of the disk into the oalactic halo. Some will be see near the Milky Way where theirorbits are crossing the galoctic equator. They are oom inated by first generation stars (Populationtype II). i.e. no new ste Ilar format ion. so types GKM main sequence or giants.

The core is found to be about 3 kpc in diameter, made of mostly first generation stars(population II). i.e. no new stellar formation, similar to globular clusters. In the micX1le is asmall nucleus of about 4 parsecs in size, a radio source called Saoittarius A. Deep inside this is avery small oonse core, an IR about 1 pc in size. Inside that is an erratic X-ray 5tJurce smallerthan 10 AU thouoht to be a B lock Hole.

Sep/17/2001 Milky Way Galaxy Lab Page M'W- 11

c. Herschel's Star Gau!!:in!!:In 1784 (much before Shapley), W. Herschel attempted to detennine the size of the galaxy fromstudies of the densities of stars. In this lab activity, we will re-create his experiment.

1. Star CountsHerschel) using a large 20 foot focal length telescope (was it his 72" aperture scope?» sampled thedensity of stars in 683 regions of the sky) some along the Milky Way) and others far away from theMilky Way (i.e. near the Galactic Poles). His field of view was only 15') which in some regions of thesky (probably near the poles) had only 1 or 2 stars. However) in the Milky Way he often had over athousand stars in the field) and in one area close to 116)000! Ideally we'd like to do similarmeasurements) several along the Milky Way) some near the Pole(s» and several halfway between atvarious galactic latitudes.

Just using a star map) you can easily verify that there are more stars along the Milky way. From amap that goes down to m=+8) using a field of 10 degrees in diameter) I got approximately 30 stars inthe field near Cygnus (in the Milky W~y), but only 10 near the Galactic north pole.

Apparent Mag Depth in parsecs

2. Soace Penetratinf! PowerAt a distance D (in parsecs), a star of absolute magnitude M will have an apparent magnitude of:m=M + 5 Log{D/10). Stars very far away will be so faint that we cannot see them with our telescope.The furthest distance we can see a star was called by Herschel the "space penetrating power". Thiswill depend upon the limiting magnitude of our telescope, and the absolute magnitude of the star.Like Herschel, we make a simplifying assumption that all stars are approximately the same absolutebrightness. We'll assume that the "average" star has an absolute magnitude ofM=O (seebelow**).

With this assumption, the naked eye, on a darknight with limiting magnitude of m=+6 couldpenetrate the galaxy to 158 parsecs. However, inSanta Clara on an average night we can perhaps onlysee down to 4th magnitude, so its more like 53 parsecs.

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The Mak-Newt finderscopes have a limit ofm=+10.6The Mak-Newt scopes have a limit of m=+ 12.9Each of these should be decreased probably by 2magnitudes due to local Santa Clara bright sky.

Note 1000 parsecs is the distance to Sagittarius Arm.

m = M + 5 Log(D/lO)

(m-M) /5]D = 10 * 10"

* *If instead we assume the average star has absolute magnitude close to that of the sun (M=+5), it

would decrease the space penetration by a factor of 10. This would change all of our numbers, ourestimation of stellar densities wou'd be 1000 times bigger, estimation of distances between stars 10times smaller, and estimation of the thickness of the galaxy smaller by a factor of 10. After we havedone this lab several times, we'll have adjust this assumption to make the numbers come out right. Itmay be that a better number is 2.5 or 3.

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Sep/17/200 1 Milky Way Galaxy Lab Page MW- 12

3. Stellar DensitiesThe assumption is that the number of stars we see isproportional to the volume of space contained in a conedescribed by our field, out to the distance of our spacepenetration. The volume of a cone is given by,

V=(7t/3)D3 [tan(8/2)r (3)

where D is the space penetration in parsecs, and 8 is -,the field. Hence the density of stars in units of stars per C- Icubic parsec is simply the count of stars seen (along the ( 'J 'PMilky Way) divided by this volume.

For my star-map calculation, with field of 10 degrees, (tangent of 5 degrees is 0.0875) and a spacepenetration of D=400 parsecs, the volume would be around V=490,000 cubic parsecs (0.00049 cubic kpc).Dividing the count of 30 stars by this gives density of 0.00006 stars per cubic parsec (this is probably toosmall). Taking the inverse we get 16,000 cubic parsecs per star. Take the cube root of this we get anestimation of 25 parsecs between stars (...ye'd expect something more like 1 to 5 parsecs average between stars,so perhaps our original assumption of M=O for an average star needs to be changed).

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4. Thickness of the Galactic DiskThe Milky Way is so big (30,000 parsecs) that we areonly seeing a short distance into it. The density of stars(i.e. the count of stars seen in our telescope field) shouldbe roughly constant. However, at higher galactic --("latitudes, if the disk is thin, we will start to see "out" of Ithe galaxy where there are no stars. If the galactic diskhas thickness of "T", then the critical latitude this willoccur at is given by,

Tan(B)=T/(2D), (4a)

where D is our space penetration. Above this latitude,the number of stars seen will decrease, reaching aminimum at the galactic pole.

At galactic latitude "bIt above the critical value "B", N ---the depth of stars we are counting is less than D, its, 0

R = T/(2 sin b) .(4b)

The number of stars that we see is proportional to thevolume, which is proportional to R cuoed. Hence thenumber of stars we expect to see at latitude "bIt is,

N(b)=No[T/(2Dsinb)f, (5) : ,Where: No =N(O) is the count of stars seen at the -IQ (~/ClLftL ~-A-~~~ #Galactic equator. B

At the pole (b=90) we have the simplified relationship that Np=N (90) =No [T / (2D) ] 3, so we can estimatethe thickness of the galaxy by taking the cube root of the ratio of the count of the stars at the pole to that of theequator,

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(6)T = 2 D [N(90)/No]1/3 = 2D[Np/No] 1/3,

= 554 parsecs (very

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For my "starrnap" situation, we'd estimate then a thicImess of: 2 (400) (10/30) J./.j

close to accepted answer!).