Disclaimer: links to web sites are ever-changing.  It turns out to be a Sisyphus task to keep them updated all the time.  Therefore, either try a different "spelling" of the hyperlink, look for it on google.com and/or let me know about an outdated link by writing an e-mail to aveh@wncc.net .

Look ahead ... the answer to my little questions is usually hidden in the text right after the question.
(Arny ch.12, Chaisson/McMillan ch.12, Pasachoff ch.23-25, Arny ch.12)

Measuring the Stars

The planets in our solar system are the only objects in the universe to which we can send spacecraft and probe them.
So what kind of information do we get from the stars (and other objects, i.e. nebulae, dust clouds, galaxies, quasars, etc.)?
 
 

Well, we can't perform experiments or alter conditions ..., so all we can do is to rely on

 Observations.

What can we directly observe?

- ?
- ?
- ?
- ?
- ?
- ?

(Take quiz 13a Measuring Stars, which is not graded; look at the results and feedback when you're done with it because the information presented in that quiz belongs right here.)

Does that seem to be a lot?

Well, compare this with what we know about the universe: (Ch/Mc, ch.13-16; Pasa ch.21-28; Arny ch.12-14) Stars, their structure and their evolution, (Ch/Mc, ch.17-19; Pasa 31-35; Arny 15-16) Galaxies and their structure, (Ch/Mc, ch.20, Pasa 36; Arny ch.17) Cosmology, and my scripts.  That's quite a bit what we learn from pretty pictures, brightness, spectra, position and changes of brightness, spectra and position!

 While going through these chapters, beware that the basics are known very well and have been confirmed over and over again, while there are still disagreements about details and some conclusions.

 During today's lecture you will learn some of the basics, i.e. the following is fact, take it for granted, swallow it, pin it on your wall, file it,  ...

 Besides observing the stars, we need to know and rely on three sciences for analysis: Physics, Chemistry, Human Relations, and Mathematics.
 


So what do we know about the stars?

Directly Observed Properties -> distance, absolute brightness and luminosity, size, mass, composition, color and temperature, rotation (Arny ch.12.3), magnetic field (Arny ch.11.4); Stellar Structure -> pressure, density, temperature, composition, opacity, energy transfer at radii from center to surface; evolution - birth, life, death, stage each star is in - , lifetime, angular separation between double stars, distance between binary stars, number of stars in a cluster, energy source, proper and radial motion,  ...

 Note that structure and evolution cover four chapters!

 Does that seem to be a lot? Well, how do you measure distance without a yardstick, temperature without a thermometer, mass without a scale, evolution without observing one star through its entire life?

We can do that with the seemingly few information we receive, spectra, brightness, position, changes of these, pretty pictures.  And we astronomers are doing a really good job at that!

 The following will tell us how.

In advance Summary - how do we get ...

Distance: parallax (triangulation), or apparent -> absolute magnitude
Radial velocity: Doppler shift
Proper motion: change of position
Chemical composition: details of spectral lines
Temperature: spectral type, or color (Wien's law)
Luminosity: apparent magnitude -> distance, or spectral type (Main Sequence stars only)
Size: luminosity & temperature, or eclipsing binaries, or details in spectral lines reveal giant or dwarf
Mass: binary stars & Kepler 3
Age: globular clusters

Check also (Arny, ch.12) for very nice summaries.  What I really like about Arny's book is how well he outlines figures with colors emphasizing causal relationships.  Pay attention to those figures especially in ch. 12-14.
 



Proper Motion

This diagram shows real (so-called proper) motion (i.e. not parallax) of the fastest moving star: Barnard's star (each dot is a star). Subtle measurements? Sure, but possible. There are some really fantastic astronomers out there, including a myriad of amateurs. (c) Hipparcos, ESA/NASA.  Another method of determining a star's (radial) velocity is the Doppler effect: The absorption lines of a star's spectrum are shifted towards the red (a  ____________ ) or blue (a  ____________ ).  (For the Doppler effect see also these web sites: Exploratorium and Snow's Universe (Snow's Universe is temporarily offline).  Check also my lab M4 Proper motion.)

Proper motion and radial velocity make up a star's velocity as it cruises through our Milky Way Galaxy.

 The above needs physics and geometry.


Apparent Brightness






...
Photos of cars's headlights: the apparent brightness of a car's headlights depends on its distance and its true brightness.

In order to make a convenient scale, the Greeks came up with the magnitude system, one more name for brightness. They classified the brightest stars at 1 mag and the faintest detectable ones (that is of course without a telescope) as 6 mag. What's the main purpose of a telescope? ____________________

Right, so fainter stars were detected, going all the way to about 25 (equivalent to a 60 Watt light bulb at a distance of 1 million miles, which the largest telescopes would be able to detect). Unfortunately, the scale backwards: The smaller the magnitude (including negative numbers), the brighter a star. Oh well, astronomers are a strange breed. You'll see more of that.
 



Absolute Brightness / Luminosity


(Ch/Mc Figs. 12.6 and 12.7; Pasa p.385ff; Arny ch.12.2) show that the apparent brightness of a star depends on both its absolute brightness (luminosity) and its distance to us. This makes sense: How bright a candle, car headlight, street light, etc. appear to us, depends on their true brightness and how far they are away.

Absolute brightness is defined as if you were to look at the star from 10 parsec (= 32.6 light-years) away. Who knows, who came up with 10 pc ...  (I don't know who, but the parsec is defined as the 'par'allax of a star being one arc-'sec'ond.)

So, knowing two of the above yields the third.

Again, brightness decreases with distance. Surprise? Hope not.

Some math and of course observations were needed. However, even though the apparent magnitude is obvious, we still need either distance or luminosity to determine the other.



Stellar Spectra, Color, Surface Temperature

A star's spectrum is probably the most important observational information we get from stars.  That's because it contains a wealth of information.  You'll notice that as you read through my scripts and labs and the kind of emphasis I put on spectra.  Check the intensity graphs of these VLT images.

This is all about surface temperature. Stellar structure will then tell us about the temperature inside (which steadily climbs to 10-100 mill. K).

Find An Atlas of Stellar Spectra here.

Go back to (Ch/Mc ch.3; Pasa ch.23; Arny ch.3.2&12.2) on light and see that temperature is correlated to the peak of the black body curve (Wien's law). For stars that means that red is cold (3000 K) and blue is hot (up to 50,000 K). See (Ch/Mc p.285; no equivalent in Pasa; Arny ch.3.2) about that or watch a craftsman heating up a metal, which first turns red, than yellow, than white, and finally blue.
 

Whew, we got surface temperature, using physics and the knowledge I gained while working at Korsch Manufacturing in Berlin (where I saw a craftsman heating up a flange until it glowed orange).

Spectrum of Regulus (a Leonis), (c) Martin Reble, Berlin.  Check Lab F5 Spectra to determine which spectral lines you see.  The absorption lines are from the element  _______________ .

Another means of getting temperature is by observing a star's spectrum.

First, let's have a look at this Line Intensity diagram which shows that the strength of - for both neutral (suffix I) or ionized (suffix II) - atomic absorption lines depends on a star's temperature. Two things are important: i) all stars have about 90% Hydrogen, 10% Helium (number of atoms), and only traces of most other elements (dubbed metals by astronomers; our Sun contains at least 87 other elements, familiar Oxygen and Neon, but also the not well known Lithium and Cerium).  ii) A first glance at a star's spectrum tells us its surface temperature, NOT its composition.  To determine a star's exact composition one has to do very careful analysis of the absorption line profiles (see next section).  Due to a star's surface temperature, certain absorption lines show up, others don't.  An example using the excitation diagram:  Our Sun (a yellow star) should show very strong lines of ionized Calcium (dominant lines in the violet for cooler stars), weak Hydrogen lines, some metal lines (neutral Calcium, Iron, ...), but virtually no Helium or molecule lines.  Check your textbook or my lecture on our Sun and confirm if this is indeed the case.  Is it?  ______ .  Cite a page number:  ______ .

In article 3193 on Sun, Apr. 2, 2000, 16:59, the student P.T. writes:
>Let's see if I understand this now (see end of sun script,
>part I of lab F6 Stellar Spectra).
>Looking at the line intensity diagram in Measuring Stars,
>for a G2 star, it looks like the Ca II would have the
>strongest lines with H I being next. While H I is
>relatively strong in our Sun's absorbtion lines, it would
>be relatively weak compared to an A star.
>
>Is this close?

yes, that's correct. -- instructor A.V.


 
 

The spectral sequence.  The diagram on the left shows each spectral type from purple to red (4000-7000 Å), the one on the right shows a part of the purple in more detail (3900-4500 Å - enlarge) which you need to compare the spectra in lab F6 Stellar Spectra with.

You probably wondered about the strange numbering of the lab manual. It's adopted from spectral classification. In the beginning ... a long, long time ago (i.e. around 1900) ... spectra were alphabetized (A, B, C .. Z for those who don't know) according to the strength of their hydrogen lines. But then astrophysicists noticed that another scheme would work better, according to their temperature. Starting with O-stars for T = 50,000 K, then B, A, F, G, K, and M-stars for T = 3,000 K: Oh, Be A Fine Guy (Girl), Kiss Me Right Now (Snow's Universe is temporarily offline)! (The latter 2 designate carbon stars - for combustion.)

Some examples (check your textbook's Appendix on the Brightest Stars):

Rigel - B (blue), Altair - A (white), Procyon - F (yellow), Sun - G (yellow), Arcturus - K (orange), Betelgeuse - M (red)

Here are very nice examples of the spectra of these types and good explanations.  (Link doesn't work.)

A photo of colors in Orion(It's somewhere on this web site too.)

Since there are subtle differences within a spectral type, numbers are assigned also and roman letters for luminosity classes.  Our Sun is a G2 V star (V means Main Sequence, in this case also "dwarf").  Rigel is B8 I and Betelgeuse M2 I, both are supergiants (designated by the Roman I).

Check my Appendix of Stellar Evolution and (Ch/Mc p.289, Fig.12.12; Pasa Appx. 7; Arny Appx. 9) on the Nearest Stars: Which spectral type dominates? _____ Why? Hint: Again, check the script (and Appendix) on Evolution ON the Main Sequence.

...

In all cases, we actually work "backwards", that is we identify a star's dominant lines, which leads to the star's surface temperature.  In our Sun's case that is 5,800 K (10,000 oF), just right for metal lines to show up, but not hot enough for Helium and too warm for molecules.

Why is temperature so important?

This diagram shows that once a star's temperature is known (which is always the case right away since the spectral type and the color can be determined immediately), then size or luminosity can be determined too if one or the other is known (see further down).
 
 
 
 
 

We used chemistry and physics.
 

Check this out as well:  John Talbot's Laser Star pages , Cren Frayer's atlas of stellar spectra .


Chemical Composition

High-dispersion spectrogram of the orange K1 III giant Arcturus.  This absorption line profile shows a very narrow portion of Arcturus’ spectrum (between 6552 Å and 6557 Å).  The H a line at 6563 Å is just to the right (about 2 inches).  The dispersion of this spectrum is so large that a print out of the entire visible light spectrum (4000 Å to 7000 Å) would be 100 feet long.

(see Arny p.110/1 & 363 top & 364 top)  A casual look at a star's spectrum gives us its temperature, not its composition!  We need to record a high-dispersion spectrum to determine a star's composition.  Actually, the spectrua we get from stars are the ones of their photospheres - we can’t peek further inside the star then that.  So what we actually analyze is a star’s atmospheric composition, not its over all composition.

The line profile is what a spectrograph measured in this portion of Arcturus’ spectrum.  I checked in the Handbook of Chemistry and Physics (containing 130 pages with a total of 60,000 spectral lines in UV, visible and near-IR for 99 elements) and was able to determine that of the depicted absorption lines three belong to neutral Titanium and one belongs to neutral Cerium.  (In lab F6 Stellar Spectra I ask you to do something similar with our Sun's spectrum.)

Now the task is to match this profile with a computer model.  The basic assumptions are that the atmosphere of the star contains 90% Hydrogen, 10% Helium and small percentages of many "metals" (see SEA 7).  What is known is the surface temperature.  Given the size of Arcturus one can make initial estimates for density and pressure.

Now computer modeling starts.  The variables of pressure, density, amounts and ionization of elements are adjusted until the model fits the measured line profile well (my overlay is the dashed blue curve).

Having done this (found exact values for pressure, density, amounts, and ionization of atoms for the stellar atmosphere), one makes computer models of how the star must look like inside (pressure, temperature, density distribution, all dependent on radius) to give rise to the spectral line profile of the atmosphere.  (Check Snow Fig. 14.29, with further links (Snow's Universe is temporarily offline).)
 



Distance by Parallax

Once again distance! Quote: "Knowing two of the above yields the third." Apparent magnitude (looking at it) and Distance (for a close star through parallax) gives Absolute magnitude.
 

 Now, this is about the solar neighborhood (Ch/Mc Fig.12.2; notice that they should have been more accurate: Take whiteout and draw a smaller yellow dot into the sun's place, since our Sun is just an ordinary star.)
Most of these nearby stars are red, which tells us that they are ... COLD (about 3000 K = 5000 oF).

They are all within 5 parsec from us (1 pc = 3.26 light-years = 19 trillion miles). For stars that are that close, we can use a method called Stellar Parallax (the original link doesn't work; see Arny, ch.12) to measure their distance: due to the Earth's orbit a close star seems to shift against the background of the stars that are farther away. (Geometry: Measure the angle the star shifted, know the diameter of the Earth's orbit and get the distance!  Check also my lab F0 Parallax.) This method works only up to 250 light-years distance, because beyond that the parallax is too small to be accurately measured. Our Milky Way is 100,000 ly across, therefore only one millionth of the stars in our Galaxy can be measured with this method. So what about the others? Let's see about that later.

Below is a diagram made from the Hipparcos satellite data of 100,000 stars as far as 250 ly, that is within the reach of parallax.  It collected the most accurate accumulation of parallax data (and associated distances) and proper motion ever.
 
Parallax and Distance of selected stars
Parallax 
[milliarcseconds]
Distance 
[1 parsec = 3.26 ly]
Barnard's star 550 1.8 pc =   6 ly
Sirius 380 2.6 pc =   9 ly
Procyon 290 3.5 pc = 11 ly
Altair 190 5.2 pc = 16 ly
Fomalhaut 130 7.7 pc = 25 ly
Vega 130 7.8 pc = 25 ly

 Auxiliary sciences used for the above are Human Relations and some Geometry.

PS  Close stars are measured by using the Earth's orbit's diameter as a baseline.  This can't work for our Sun since it's on that very same line.  Instead we use Earth's diamater as the baseline (one observer on one continent, the second on another continent).  There are several methods for the planets in our solar system.  One is based on their movement and our orbit, plotting their and our positions, and that way we get a ratio in A.U.
 
 
This styrofoam and beads model of Orion hangs under the ceiling in my classroom.  The above photo shows Orion as we see the constellation from Earth - notice though that my model isn't perfect as Orion's belt came out somewhat skewed; furthermore, the really bright stars are red Betelgeuse on the upper left and blue Rigel on the lower right.  The other five stars (Saiph, Alnitak, Alnilam, Mintaka, Bellatrix - bottom up) are blue as well but appear white since our eye loses color perception when looking at fainter objects.  
Here is a photo of colors in Orion.

The bottom photo shows Orion from another perspective in our Galaxy - a vantage point some 500 lightyears away which we can not get to.  One can easily see that the stars are indeed at different distances - one can also recognize each star.

The point is that we cannot perceive depth - and thus neither distance - from our only vantage point on Earth in our Solar System.  That's where parallax comes in: as we change our vantage point from one side of our Sun to the other, this gives us a baseline of 186 million miles or 0.000032 ly.  That's minuscule - compared to the hypothetical 500 ly in the bottom photo - but enough to determine the distances to stars that are close enough to yield a measureable parallax.

Check also my lab F0 Parallax.  See also Alan W. Hirshfeld's neat book "Parallax : The Race to Measure the Cosmos".




Hertzsprung-Russell Diagram

HR diagram of the closest 100,000 stars.  (c) The Hipparcos Space Astrometry Mission, ESA - European Space Agency.     See also Sky & Telescope (July 1997, p. 28-34 From Hipparchus to Hipparcos, by Catherine Turon).  This particular HR diagram from the Hipparcos mission is undoubtedly one of the greatest ever compiled.  However, it is not representative for the red, cold, faint K and M stars.  Why not?

....

Now the most ingenious diagram appears: the Ejnar-Henry Norris diagram, sorry, I mean the Hertzsprung-Russell diagram. Here, all stars are plotted into the same diagram. The y-axis can read luminosity, brightness or absolute magnitude (they mean nearly the same). Notice the numbers on the y-axis on the right. It's an interesting scale, but necessary, since having a normal scale would quench half the stars (the cold ones) into a tenth of an inch and the hot ones had to be above the ceiling (rather on the 24th floor).
The x-axis can read color, temperature, and spectral type, which are as we just learned related to each other. Once again, astronomers are weird, so the highest temperature is on the left.

What does the H-R diagram tell us? A star makes it, a planet doesn't, neutron stars neither, nor a light bulb.

Look at (above Hipparcos diagram; Ch/Mc Fig. 12.12 & 12.13; Pasa p.392; Arny ch.12.6): Holy smokes, most stars lie on a diagonal (the main sequence), some in the upper right (Red Giants), some in the lower left (white dwarfs), all of which become important for stellar evolution, the most important use of the H-R diagram.

 For the previous we used Darwin, Drawing skills, and physics (see Ch/Mc ch.13-16; Pasa ch.26-28; Arny ch.12).

The H-R diagram and the spectral sequence will haunt us for the rest of the semester.  Make sure you have these diagrams handy when you study!



Distance by absolute (HR diagram) and apparent magnitude

Apparent magnitude and Absolute magnitude (for Main Sequence stars through the H-R diagram) gives Distance.

The apparent brightness of a star is known anyway (goodness, go outside and look at the star!), the spectrum gives its spectral type, which in turn gives its temperature, which then gives its luminosity/absolute magnitude (go up from the x-axis to meet the Main Sequence, then to the left or right y-axis, read off the number) with Ejnar and Henry's help (only for Main Sequence stars, though). And now comparing the apparent with the absolute magnitude does indeed yield the distance!!!!!!!

An example:  the above Regulus spectrum shows strong Hydrogen lines (in aquamarine and violet) and is therefore probably an ... (check the excitation diagram or the colorful spectral sequence) ... A-star (more precisely: B7 V).  Using the H-R diagram this gives an absolute magnitude of about ... 0 mag (a luminosity of about 100 solar L !!!).  Compare this to Regulus' apparent magnitude ... (check your textbook's appendix) ... of 1.36 mag (it's #20 in apparent magnitude):  using the logarithmic formula from your textbook (similar to the ones in Lab K2) that relates apparent, absolute magnitude and distance, this gives an estimate of 60 ly (a more careful computation yields 80 ly; that's because actually M = - 0.6 mag, brighter than the casual read off 0 mag).

 Physics and common sense we needed (and a good slurp out of the bottle).


Luminosity





The diagram shows the relationship between temperature, size, and luminosity: if we know two of these, we can determine the third (using the Stefan-Boltzmann law).


 
 
 

Or, in other words: "knowing two of the above yields the third."  A star's brightness, its luminosity, depends on its size and the surface temperature: L ~ R2 T4 (Arny p.359).  The accompanying diagram illustrates that.  Of course, a hot and large star is bright(and blue since it's hot).  Of course, a cold and small star is faint(and red since it's cold).  A yellow star has medium size and temperature, therefore medium luminosity as well (since our Sun is the prototype, brightness is defined in the solar luminosity unit).
On the other hand a cold but very large star can be bright (and red because it's cold) and a hot but small star can be faint (and white because it's hot).
 
 
 
 
 
 
 
 


 
 
 

The Main Sequence only, (c) Redshift.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 



Size of Stars (radius)

(see Arny p.358-60) The standard method is to determine the radius by knowing the luminosity and temperature of the star (see above).

Photo of Betelgeuse, (c) AURA / STScI.     The radius (i.e. its size) can be measured directly. Really? - Recall that resolving power is the second most important property of a telescope. However, a star appears smaller than the turbulence of our atmosphere allows for best resolution (Ch/Mc p.279; Pasa p.403; Arny ch.12.2), which is 1 arcsec (= 1/3600 degree, the width of a penny at 1 mile distance). (Ch/Mc p.281; Pasa p.46; Arny ch.12.2) nevertheless describes a high speed photography method, how the red giant star Betelgeuse's radius is determined (the first time I read about this method), compare (Ch/Mc Fig. 12.5; Arny Fig.12.7 or 12.6).
 

Amore applicable method is to determine the size from the lightcurve of an eclipsing binary.  Check Terry Herter's animations at Cornell, the lightcurve of NN Serpens taken by the VLT and my discussion on binary stars in the section on luminosity via the HR-diagram.
 
 

This value for size can be confirmed in two ways: measure the size directly (see Betelgeuse above and of course our Sun).  And by eclipsing binaries (e.g. Algol).  A profile of the change in brightness (Arny ch.12.4) gives us a good value for bright blue Algol's size (3 solar R) and for its fainter orange sub-giant K2 IV companion (3.4 solar R). (Although they have about the same size, the orange companion is 30 times fainter (3.5 mag) because blue Algol is 2.5 times as hot.) Very nice graphics and animations of the Algol system are provided by the University of Tennessee.  Look for Algol at the AAVSO as well.

------------------------------------------------------

What we know right away is a star's temperature (through its spectral type).  If we know the distance (through parallax), and of course we know its apparent magnitude, we get its luminosity (same as absolute magnitude).  These two then give us the size of the star.


 
 

 Sciences used are physics and excellent photography.
 



Mass

Now comes the mass of a star and astronomers are so nice to tell us that it "is practically impossible to determine [...] the mass of an isolated star".

 Let's take another slurp. This time our science was frustration.
 
 

A close binary star, (c) AURA / STScI.     Thank goodness, there are binary stars, which are physically linked double stars. Stars that actually orbit each other. Stars with planets (probably they have some), on which life [as we know it] might be impossible if they're orbiting too close, because their orbits are so screwed up that evolution (of life this time) wouldn't even take place.
Binary stars.  Imagine that our vantage point on Earth is on the bottom.  As the red supergiant approaches (left), the weak H b (aquamarine) line is blueshifted (compared to the spectrum above it); as the RSG recedes (right), the line is redshifted.  Because of Kepler 2, velocities change, and therefore line shifts do, too. Try UT's animation and especially Terry Herter's animations at Cornell.
 
 
 


The first diagram shows the yellow star approaching: its spectral lines (the thinner ones) are blueshifted.  The middle diagram shows both stars perpendicular to our line-of-sight: no shift.  The third has the yellow star receding: the thin lines are redshifted.  The red star does the opposite of course.
In this last diagram the stars are not as far in their most receding/approaching position as in the first diagram.  Since the shift of spectral lines is a measure of a star's "radial velocity", they are not as far apart.
To appreciate this more:  move the page down until the orbits are off-screen, so that you only see the spectra.  Picture in your head how the stars orbit to produce those spectral lines that you see.  That's what astronomers use the spectra for.  Images (c) Redshift (name of an astronomy software).

Binary stars are great for astronomers. Watch their orbits, use the Doppler effect as one's coming close and the other recedes, the brightness change if they happen to eclipse each other and then use the modified version of Kepler's 3rd Law (Ch/Mc ch.2; Pasa ch.3; Arny ch.12.4; astronomers actually read their own textbooks) and at least the sum of the two stars masses is determined.
One more piece of information (I forgot which) yields their individual masses.
I remembered it: Knowing the distances of each star to their common center of mass yields the ratio of the masses (imagine to swirl a baton with a larger mass on one end). Now, knowing sum and ratio of the masses gives the individual masses. Unfortunately, the orbits of binary stars must be directly observable, which is seldom the case.  (A good account with diagrams is at the Univ. of Tennessee, and a Java applet of binary stars, again at UT.)

 For that, we pretty much used all of our scientific repertoire.

And, as they mention, mass determines a star's evolution (the most interesting is the way it dies). From then on, mass is responsible for size, luminosity, lifetime of the star, evolution, the way it dies, i.e. virtually everything.
Source: University of Oregon Introduction to Astrophysics, Mass–Luminosity Relation, Image ID: ml.gif

Note that the Mass-Luminosity diagrams are only valid for main sequence stars (Ch/Mc Fig. 12.17; Pasa Fig.25-7; Arny, Fig. 12.20 or 12.19); also at Snow (University of Colorado) (Snow's Universe is temporarily offline) and at the University of Tennessee.  Notice that the scaling on the x- and y-axes is quite different: the same distance is used for an increase of factor ten, e.g. on the x-axis from 0.1 to 1.0 and from 1.0 to 10.  This has the advantage of plotting very large and very small data points on the same graph.  And more important, one can easily figure out the relationship between the two variables.  From the accompanying diagram, it's seems to be L ~ M, i.e. the larger the mass, the larger the luminosity.  But as you can see from the scaling, both axes are logarithmic, and thus luminosity grows much quicker than mass, which means that the true relationship is about  L ~ M4 , i.e. luminosity increases with the fourth power of the mass.  Go to SEA-1 and compare the mass and luminosity data of an A5 and a M5 star with each other: 10 times more mass means about 10,000 times more luminosity which is about correct as the table indicates.

This means that a higher mass star has of course more fuel but it's burning it way, way faster.  In our example 10 times more fuel but 10,000 times faster.

With this knowledge read up on the discussion of our Sun's lifetime, then check SEA-5 and explain why the more massive stars have a shorter life span: ___________________________________________
 

Take a deep breath.



Age

If a star becomes cataloged, look at the data the star revealed to you and with the help of the H-R and the other diagrams you can get everything knowledgeable and of interest about the star, even if it's a foreigner.
 

Yet, what you don't know about a star is its age (I don't know yours either). Astronomers are weird and ingenious, so let's look at one piece of information that we get from stars but have neglected so far: their position in the sky.

What about it?  (Ch/Mc p.7; Pasa p.83; Arny ch.1.1) tells us that Orion's (Pasa: Big Dipper) stars just happen to be in the same direction, but otherwise are at completely different distances, so obviously they don't have anything to do with each other. The same holds for all constellations.
However, look at the Orion nebula (M 42). Here quite a few stars lie close together, embedded in a diffuse nebula - their nursery, believe it or not. There are other examples, like the gorgeous Pleiades (M 45) or the globular cluster M 13 in Hercules, which we couldn't find the last time observing.
 
 

..........................

Various Globular Clusters, (c) AURA / STScI.     So, many stars happen to be so close together that it is a fairly good assumption that they are also close in distance to each other. Assuming that, we can just determine one or two star's distances, take the other's to be at the same distance and with their apparent magnitude ("Knowing two yields ...") determine their absolute magnitude, plot them into the H-R diagram, and ...

 ... most of them end up on the main sequence. The latter confirms that a cluster's stars lie at the same distance. This in turn gives us a nice HR diagram, which outlines stellar evolution very nicely.
Now, look at the accompanying H-R diagram made from Lab K2 CLEA Photometry (or Ch/Mc, Fig. 12.18; Pasa p.411; not in Arny), it's hard to see, but the Pleiades' main sequence is branching off at the upper left. In (Ch/Mc, Fig. 12.19; Pasa p.413; not in Arny), another cluster's main sequence branches off in the middle. (Note that it was sufficient to graph apparent magnitude.  Since all stars in a cluster are at the same distance, apparent and absolute magnitude are directly correlated.)

 WHY?

 Simply the hotter stars are dying (they moved off the MS) ... don't get to close to that furnace. By the way, larger mass, larger temperature, larger luminosity, smaller lifetime.

 Now, mass and luminosity yield lifetime, so look at the branch-off and figure out that the last stars on there reveal the cluster's age, 20 mill. years for the Pleiades and 10 bill. years for the Omega Centauri cluster. See (Ch/Mc p.338ff; no equivalent in Pasa; Arny ch.13.9) on The Evolution of a Star Cluster (Strobel).

See the star clusters M67 and Praesepe.

 Wait a moment!!!! Who says that all stars in a cluster are of the same age to begin with?

 The Australian Society for Gerontology.

 Well, no. Read (Ch/Mc ch.13; Pasa ch.32; Arny ch.13) about the interstellar medium and it'll tell you that a cloud of matter needs at least a mass equivalent to 10,000 sun masses in order to gravitationally contract and form stars (some exceptions apply for smaller clouds hit by shock waves). Ouch, what a sentence.
So, they do form at approximately the same time (± a million years - who cares about that error on a scale of 10's and 100's of millions of years?).

 We sure needed all our knowledge to figure that and I try to cluster you to figure your age.

Look at the Evolution of star clusters at the University of Oregon!



Distance with Cepheids

The part not mentioned in this chapter is about variable stars and the information they yield, e.g. another means of determining distance via the Cepheids (and once more Cepheids and again Cepheids).

...


We are done, thanks for listening to one of my favorite topics.


For credits of AURA / STScI images see here.