Stars

Comparison of ground-based observation of the globular cluster M4 with an HST image showing white dwarfs. (Produced with the Wide-Field Planetary Camera 2, Hubble Space Telescope.)

Stars

The stars in the sky appear to be objects much like the sun although much, much further away. Can we get some kind of idea of how far away?

In the lab we will do an experiment demonstrating the parallax method for determining distances. This method actually works for the “nearer” stars.

Parallax

The basic idea behind parallax is trig: using known distances and angles to get unknown distances:

Line of sight to background stars very, very far away

2 AUs

Line of sight to background stars very, very far away

Change in angle of star from 6 months previous

Parallax

We actually have a unit of distance defined by the parallax method. It is called a parsec. A parsec is the distance a star is away if it has a change of angle of 1 arc second (which is 1/60th of an arc minute, which is 1/60th of a degree). A parsec can be converted into AU’s and another common unit of distance, the light year: 1 parsec = 3.26 lt. yrs = 200,000 AU’s.

Parallax

The nearest star has a parallax angle of about ¾ of a second of arc, and so is about 4/3 = 1.3 parsecs away (about 4 light years away, or about 266,000 AU’s away). Recall that Pluto was about 40 AU’s away, and the Oort Cloud is thought to be about 50,000 AU’s away.

We can effectively measure distances this way for about several thousand stars that are within about 90 parsecs (300 light years) from the earth.

Binary Stars – Get Mass

Because gravity is the force that keeps smaller objects going around bigger objects, we can determine the mass of the bigger object by measuring the radius and period of the smaller orbiting objects.

We use this in determining the masses of the planets by looking at their moons – or by putting our own moons (satellites) in orbit around them.

Binary Stars – Get Mass

We use this same system to get the mass of the sun – since we have the planets orbiting the sun.

We are only now being able to “see” other planets orbit other stars since those stars are so far away.

However, we notice that there are lots of stars that orbit each other – and we can use that to get the mass of the bigger (central) star.

Binary Stars

The most direct way of seeing binary stars is to really see them. This is possible for the nearer stars. We can actually see both stars individually and watch one orbit the other. These are called visual binaries.

We need to be careful here, since some stars only appear to be close due to our perspective. These are called “optical doubles” and not real binary systems at all. We can tell the difference by watching these over time or by noting that the distance to each of the two is quite a bit different.

Binary Stars

A second way is to look at the spectra. When the orbiting star comes toward us, its spectral lines are shifted (Doppler effect) a little towards the blue, and when it goes around and away from us, the spectral lines are shifted a little towards the red. This works well for binary systems that we view edge on.

Binary Stars

A third way of detecting binary stars is to notice the brightness of a star over time (light curves). When the orbiting star goes in front of the more massive central star, a bit of the central star will be “covered” by the orbiting star and the total light from the star system will decrease. A similar thing happens when the orbiting star goes behind the central star. These are called “eclipsing binaries”.

Binary Stars

For these “eclipsing binary” star systems, we can then determine it as binary and get some interesting information about the systems from these light curves.

Binary Systems

A fourth way of detecting binary systems is to notice that a star is “wobbling” as if it is swinging another heavy object around it – even if the heavy object can’t be seen. This can occur if the star is swinging a “dark” star or perhaps a “burned out” star. These are called “astrometric binaries”. This will have to be considered when looking at the birth and death of stars (stellar evolution).

Binary and Multiple Star Systems

By having these various methods available to detect binary systems, we notice that most stars are not single stars like the sun, but instead are either binary star systems or are in star groups with multiple stars mutually orbiting each other. We will have to take this fact of multiple star systems into consideration in looking at theories of stellar formation and evolution.

What we can measure1. Parallax (but only for the nearer stars)

2. Brightness3. Spectra - how much red versus blue

4. Spectra - emission and absorption lines

5. Binary systems: orbits of less massive stars around more massive stars

a) by direct viewing (seeing the stars orbit)b) by spectroscopy (seeing alternating blue and red shifts)

c) by light curves (seeing dips in light output due to stars eclipsing one another).

d) astrometric (by observing the wobble of a star)

Relations between quantities

• Spectra: amount of red versus blue gives surface temperature (T)

• Brightness (B) depends on luminosity (L) and distance (d): B L/d2

(Here the symbol means proportional to.)

• Luminosity (L) depends on temperature (T) and area (A): L A*T4

For the nearer stars1. Get distance (d) from parallax.2. Get temperature (T) from amount of red

versus blue in spectra.3. From brightness (B) and distance (d), useL B/d2 to get luminosity (L).4. From luminosity (L) and temperature (T),

use L A*T4 to get area (A).For the nearer stars, we then know their

surface temperature and size.

Farther stars

For the farther stars, we cannot use parallax to determine the distance.

Since we don’t know the distance, we can’t determine their luminosity.

Since we don’t know their luminosity, we can’t determine their area.

Stellar Classifications

Since there are several thousand stars close enough to use parallax, perhaps we can classify these stars, and then apply these classifications to further stars to try and get their luminosities based on their classifications.

If we can determine their luminosities, we can use B L/d2 to determine their distances, and we can use L A*T4 to get their areas.

The H-R diagram

One way to try and see relations between quantities for the purpose of developing a classification system is to plot one quantity versus another and see what it looks like.

It turns out that plotting Luminosity versus Temperature gives a very useful graph. This is called an H-R diagram. (The diagram name is actually the Hertzsprung-Russell diagram, but it is called the H-R diagram for short.)

LuminosityApparent Magnitude is a measure of brightness

and came from the attempt to classify stars by their brightness: 1 = brightest, 5 = dimmest (to the unaided eye).

Luminosity is often expressed in terms of Absolute Magnitude: the brightness (in Apparent Magnitude) a star would have if it were located at a standard distance of 10 parsecs away.

LuminosityWhen we started using the telescope, we had to extend the

apparent magnitude system to cover even lower brightnesses. In doing so and in using more sophisticated measuring devices than the eye, we noted that the original five units of apparent magnitude corresponded to 100 times in brightness. Thus we could extend the brightness system (apparent magnitude) down in brightness but up in value from 1 to 5 all the way to 1 to 15. (At this point, we about reach the limit of telescopes based on the light scatter in the atmosphere.) With the Hubble, we can extend it even lower still.

LuminosityBut after we started using this scale for

Absolute Magnitude (Luminosity) we saw that we needed even higher luminosities and so we needed even lower numbers. This meant we had to go below 1 (and even below 0) to reach as low (as high a luminosity) as -10 !

On this scale, our sun is rated as +4.8 . That is, at 10 parsecs (about 32 light years away), it would be just barely visible to the naked eye.

Spectral Classification (due to temperature)

We measure temperature of the star’s surface by measuring how much red versus how much blue there is in the spectra of the star. Thus we refer to the cooler stars as “red” stars and the hotter stars as “blue” stars. But we have developed a letter scale for this as well: From hotter to cooler we have:

O B A F G K M (O stars are the hottest and bluest, M stars are the coolest and reddest).

(Memory device: Oh Be A Fine Guy/Girl Kiss Me)

Temperature

We even got good enough that we could identify subclasses of these temperatures, with 0 being the hottest and 9 being the coolest in any letter category. According to this, an O0 star is the hottest and an M9 star is the coolest.

According to this scale, our sun is a G2 star (as far as temperature/color is concerned).

The H-R diagram

The vertical axis of the H-R diagram is Luminosity, with the lower luminosity at the bottom (+15 in Absolute Magnitude) and the higher luminosity at the top (-10 in Absolute Magnitude).

The horizontal axis of the H-R diagram is temperature/color, with the hottest/bluest stars (O) on the left and the coolest/reddest stars (M) on the right.

The H-R DiagramEverything else being equal, we might expect

that the stars would fall on a diagonal line from the upper left (high luminosity and high temperature) to the lower right (low luminosity and low temperature).

Detailed H-R diagrams can be found on the web if you search for H-R diagrams. Many stars do fall on a more or less diagonal line like we expected, and this line is called the Main Sequence.

H-R Diagramexpected results

Luminosi ty

Temperature / Color

+15

+10

+5

0

-5

-10

O0 B0 A0 F0 G0 K0 M0

Sun = G2 at +4.8 Magnitude

H-R Diagramresults for nearest stars

Luminosi ty

Temperature / Color

+15

+10

+5

0

-5

-10

O0 B0 A0 F0 G0 K0 M0

sun

H-R Diagrambrightest stars

Luminosi ty

Temperature / Color

+15

+10

+5

0

-5

-10

O0 B0 A0 F0 G0 K0 M0

sun

H-R diagram

The nearest stars should give us a good representation since it should count all the stars in the area. We can see that many if not most of the stars do fall on the predicted line. We’ll call this predicted line the “Main Sequence”.

There are significant number of stars that fall below the Main Sequence. Since they have lower luminosities than their temperature would normally suggest, we infer that they are much smaller. We call them white dwarfs.

H-R diagram

When we add in the brightest stars, we realize that this is NOT a representative sample because we can see those brighter stars at much greater distances.

Some of the bright stars do seem to fall on the expected “Main Sequence” line. But many of these stars have much higher luminosities than their temperature suggests, they much be much larger stars. We call these stars giant stars.

Size classificationThe stars furthest above the Main Sequence are called

Super Giants, and are classified as I or II (with I being the biggest).

The stars above but close to the Main Sequence are called Giants, and are classified as III (or IV for sub-giants).

The stars on the Main Sequence are classified as V.Stars below the Main Sequence are sometimes called

Dwarf stars, but they have low luminosities and so are hard to see.

Hence our sun is a G2-V star since it is on the Main Sequence.

Mass-Luminosity Relation

By using binary stars, we can get the mass of the central star. As we noted earlier, over half of the stars in the sky are part of binary or multiple star systems, so we have lots of stars to relate luminosity with brightness.

We find that higher mass stars on the main sequence also have higher luminosities.

Mass and Luminosity

This makes sense: • higher mass means more gravity; • more gravity means more compactness and

more heat;• more heat and compactness means more

energy production by fusion;• more energy production means more

luminosity.

Mass and Main Sequence Stars

The place a star has on the main sequence can be related to its mass.

We still have the problem with the stars that are off of the main sequence: why would they have different temperatures and different sizes when they have the same mass as other stars? Is this related to their age or development? This leads to the next topic: stellar evolution.

Brightest stars in North – basic infoStar constellation class App. Mag Abs. Mag dist in

ly

Sirius Canus Major A1 V -1.46 +1.4 9

Arcturus Bootes K2 III 0 -0.2 36

Vega Lyra A0 V 0 +0.5 26

Capella Auriga G8 III 0.1 +0.3 42

Rigel Orion B8 Ia 0.1 -7.1 900

Procyon Canus Minor F5 IV 0.4 +2.6 11

Betelgeuse Orion M2 Iab 0.5 -5.6 310

Altair Aquila A7 IV-V 0.8 +2.2 16