ASTRO 101

ASTRO 101

Principles of Astronomy

Instructor: Jerome A. Orosz (rhymes with “boris”)Contact:• Telephone: 594-7118• E-mail: [email protected]• WWW: http://mintaka.sdsu.edu/faculty/orosz/web/

• Office: Physics 241, hours T TH 3:30-5:00

Homework/Announcements

• Chapter 9 homework due April 23: Question 13 (Draw an H-R Diagram …)

Stellar Properties• The Sun and the stars are similar objects.

• In order to understand them, we want to try and measure as many properties about them as we can: Power output (luminosity) Measure distance and flux

Temperature at the “surface” color or spectral type

Radius Mass Chemical composition

Next:

• Temperature-Luminosity diagrams

• Binary stars

Temperature-Luminosity Diagrams

• When you have a large number of objects, each with several observed characteristics, look for correlations between the observed properties.

• Henry Norris Russell and Ejnar Hertzsprung were the first to do this with stars in the early 1900s.

• Some measure of the temperature is plotted on the x-axis of the plot, and some measure of the intrinsic luminosity is plotted on the y-axis.


• The stars do not fall on random locations in this diagram!



• What does this mean?

• This diagram gives us clues to inner workings of stars, and how they evolve.

Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)



• There is some specific physical process that limits where a star can be on this diagram.




• Furthermore, the location of a star on this diagram is an indicator of its size.


Black Body Radiation

• The luminosity, radius, and temperature of a black body are related: measure any two values, you can compute the third one.

• Since stars are approximately black bodies, their location in the CMD indicates their radii.


• Lines of constant radius go something like this:

• Cool and luminous stars: large radii.

• Hot and faint stars: small radii.

• Most stars are here, and there is not a large variation in radius.



• This diagram shows some well-known stars. Most of the bright stars you see without a telescope are giants.


• So far, we have found out that:1. Stars occupy specific regions of the

temperature-luminosity or color-magnitude diagram.

2. The inferred radii of stars spans a very wide range from “white dwarfs” with sizes similar to the Earth to “supergiants” with sizes equal to the Sun-Mars distance.

• This is related to the life cycles of stars. But first, we must discuss binary stars and stellar “populations”…

Next:Other Stellar Properties

Binary Stars


• In order to understand them, we want to try and measure as many properties about them as we can: Temperature at the “surface” ---use spectral types

Power output (luminosity) --- flux and distance

Radius Mass Chemical composition

Other Stellar Properties

• We can measure the temperature of a star relatively easily by its spectral type or color. If the distance is known, then we can measure its luminosity, and then compute its radius. Note, however, that the radius measured this way is not very accurate, owing to the uncertainty in the distance.

• Is it possible to measure the radius of a distant star accurately? Also, are there other properties we can measure? Yes, use binary stars!

Detour: The Two-Body Problem

• Use Newton’s Laws to describe the behavior of two objects under the influence of their mutual gravity. We will apply it to binary star systems (e.g. a system consisting of two stars).

Center of Mass

• For two point masses, the center of mass is along the line joining the two masses.

• The center of mass is closer to the more massive body.

Center of Mass

• Why is this useful? Two bodies acting under their mutual gravity will orbit in a plane about their center of mass.

• Here is the case for equal masses.

Center of Mass

• Why is this useful? Two bodies acting under their mutual gravity will orbit in a plane about their center of mass.

• Here is the case for M1 = 2M2.

Binary Stars• A binary system is when two stars are bound together by gravity. They orbit their common center of mass.

• In some cases, you can see two stars move around each other on the sky.


• In some cases, you can see two stars move around each other on the sky.

• These are “visual binaries.”

Binary Stars


• In a visual binary, you can see two stars.

• However, for most binary stars, their separation is very small compared to their distance, and from Earth they appear to be a single point.

• How do you observe these types of binaries? Use spectroscopy!

Viewing Angle

• The plane of the orbit is two dimensional, so depending on how that plane is tilted with respect to your line of sight you can see different things.

Detecting the Wobble• In Astronomy, any motion can be broken down into two groups: Motion in the plane of the sky (e.g. east-west and north-south motion).

Motion towards or away from us (e.g. “radial velocities”).

• Motions in the plane of the sky are usually small, and typically one has to wait many years to see a relatively big shift.



• Motions in the plane of the sky are usually small, and typically one has to wait many years to see a relatively big shift. One can see Sirius wobble over the course of decades (it has a very massive, but dark, companion).



• Motions in the plane of the sky are usually small, and typically one has to wait many years to see a relatively big shift. We can’t detect this motion in most binaries.

Detecting Radial Velocities

• Recall that radial velocities can be measured from Doppler shifts in the spectral lines:


• Recall that radial velocities can be measured from Doppler shifts in the spectral lines: Motion towards us

gives a shorterobserved wavelength.



Motion towards us gives a shorterobserved wavelength.

Motion away from us gives a longer observed wavelength.

Spectroscopic Binaries


• Here are two spectra of Castor B, taken at two different times. The shift in the lines due to a change in the radial velocity is apparent.

Spectroscopic Binaries• The radial velocity of each star changes smoothly as the stars orbit each other.

• These changes in the radial velocity can be measured using high resolution spectra.

Spectroscopic Binaries

• Recall from that radial velocities can be measured from Doppler shifts in the spectral lines:


Spectroscopic Binaries• In some cases, you can see both stars in the spectrum.

• In most cases, you can only see one star changing its radial velocity in a periodic way.


• In some cases, we can use binary stars to measure precise masses and radii for stars.

Center of Mass• Recall that m1r1=m2r2

• Also, note that velocity of the star is proportional to the distance to the center of mass since a star further from the COM has a greater distance to cover in the same amount of time. This implies m1v1=m2v2, or m1/m2=v2/v1

• The ratio of the velocities in inversely proportional to the mass ratio. Also, the same is true for radial velocities.

Center of Mass

• If you can see both stars in the spectrum, then you may be able to use Doppler shifts to measure the radial velocities of both stars. This gives you the mass ratio, regardless of the viewing angle (e.g. nearly face-on, nearly edge-on, etc.).

Stellar Masses• If you can see both stars in the spectrum, then you may be able to use Doppler shifts to measure the radial velocities of both stars. This gives you the mass ratio, regardless of the viewing angle (e.g. nearly face-on, nearly edge-on, etc.). This is usually useful information.

• If you can find the viewing angle, then you can compute true orbital velocities and use Kepler’s Laws and Newton’s theory to find the actual masses.

Viewing Angle

• The plane of the orbit is two dimensional, so depending on how that plane is tilted with respect to your line of sight you can see different things.


• If you can find the viewing angle, then you can compute true orbital velocities and use Kepler’s Laws and Newton’s theory to find the actual masses. How do you find the viewing angle?


• If you can find the viewing angle, then you can compute true orbital velocities and use Kepler’s Laws and Newton’s theory to find the actual masses. Find eclipsing systems!

Definition

• An eclipse, occultation, and transit essentially mean the same thing: one body passes in front of another as seen from earth.

Eclipsing Systems and Stellar Radii

• Eclipsing systems must be nearly edge-on, since the stars appear to pass in front of each other as seen from Earth.


• The relative radii can be found by studying how much light is blocked, and for how long.



• The “light curve depends on the relative sizes and brightnesses of the stars, and on the orientation.


• The “light curve depends on the relative sizes and brightnesses of the stars, and on the orientation.

• Algol was known to be variable for a long time, and its periodic nature was established in 1783.

Accurate Masses and Radii From Binary

Stars• The ideal binary systems are ones where both stars are seen in the spectrum (“double-lined”), and where eclipses are seen. Masses and radii accurate to a few percent can be derived from careful observations of these systems.

• There are on the order of 100 such well-studied systems with “main sequence stars”. What do you do with this information?

Mass-Luminosity Relation

• The stars form a tight sequence. This is another clue to the inner workings of stars!



• The stars form a tight sequence. This is another clue to the inner workings of stars!


• In order to understand them, we want to try and measure as many properties about them as we can: Temperature at the “surface” ---use spectral types

Power output (luminosity) --- flux and distance

Radius --- eclipsing binary stars Mass --- eclipsing binary stars Chemical composition

Next:

• Stellar Evolution.

Stellar Evolution

• Observational aspects– Observations of clusters of stars

• Theory– Outline of steps from birth to death

Stellar Groupings

• To understand how stars evolve, one must study groups of stars since an individual star takes a very long time to change.

Stellar Groupings

• To understand how stars evolve, one must study groups of stars since an individual star takes a very long time to change.

• One must choose samples of stars very carefully to avoid bias and to eliminate “variables”.

An Example of Bias• Suppose we had two samples of stars, one with the nearest stars, and one with the apparently brightest stars. What to the CMDs look like?


• Here are the nearest stars.


• Here are the nearest stars.

• Here are the brightest stars.

An Example of Bias• Suppose we had two samples of stars, one with the nearest stars, and one with the apparently brightest stars. What spectral types do the stars have?


• The nearby stars tend to be cooler, whereas the bright stars are hotter.

Image from Nick Strobel’s Astronomy Notes(http://www.astronomynotes.com)


• Which sample is more representative?

Image from Nick Strobel’s Astronomy Notes(http://www.astronomynotes.com)

Stellar Groupings

• One way to get around sample biases is to study groups of stars bound by gravity. Why?1 The distance across a group is

relatively small, which means the stars in the group have roughly the same distance from us. This in turn means that ratios in apparent brightness are the same as the ratios of intrinsic luminosities.

Stellar Groupings

• One way to get around sample biases is to study groups of stars bound by gravity. Why?2 The groups are loosely bound,

meaning that the stars must have formed together, rather than being “captured” after formation.

Stellar Groupings

• One way to get around sample biases is to study groups of stars bound by gravity. Why?2 The groups are loosely bound,

meaning that the stars must have formed together, rather than being “captured” after formation. This means the stars in the group all have the same age and the same chemical composition.

Star Clusters

• Star clusters can be roughly classified based on how “tight” they are.

Star Clusters

• Star clusters can be roughly classified based on how “tight” they are. “Open” clusters are less compact, and generally have relatively small numbers of stars (a few hundred).

Star Clusters

• Star clusters can be roughly classified based on how “tight” they are. “Globular” clusters are more compact, and generally have relatively large numbers of stars (a few hundred thousand).

Star Clusters

• The physical size of a cluster is only a few dozen light years, compared to typical distances of several hundred or a few thousand light years.

Star Clusters

• The physical size of a cluster is only a few dozen light years, compared to typical distances of several hundred or a few thousand light years. All of the cluster stars have the same distance from us to an accuracy of a few percent.

Star Clusters

• The physical size of a cluster is only a few dozen light years, compared to typical distances of several hundred or a few thousand light years. All of the cluster stars have the same distance from us to an accuracy of a few percent.

• You can plot the apparent brightness instead of the intrinsic luminosity on the temperature-luminosity diagram.

Star Clusters

• Here is a plot of apparent magnitude vs. the color. No pattern is seen since each star is at a different distance.

Figure from Michael Richmond (http://spiff.rit.edu/classes/phys230/phys230.html)

Star Clusters

• Here is a plot of luminosity (expressed as absolute magnitude) vs. the color. A clear pattern is seen since the luminosity is a physical property.


• Sometimes in order to understand how stars work, it is useful to compare two or more stars.

• Note you can sometimes compare properties without knowing the actual values, as in “The female rabbit of this species is larger than the male rabbit of the same species.”

• A simple question to ask is “Which star is more luminous than the others?”

Comparing Stellar Properties

• This large-area photograph shows the constellations of Orion, Canis Major, Canis Minor Taurus, and a few others.

• Which star is more luminous:Rigelor Sirius


• Looking up the distances, we find

• Rigel– d = 240 pc– L = 66,000 Lo

• Sirius – d = 2.64 pc– L = 25.4 Lo

• The ratio of the fluxes is not the ratio of the luminosities since the distances are different.


• A cluster is a group of stars bound by their own gravity. The size of the cluster is small compared to its distance from Earth.

• Which star is more luminous:Star AorStar B



• Comparing the apparent brightnesses does not help if the stars have different distances.



• Comparing the apparent brightnesses of stars in a cluster does help since each star in that cluster has the same distance from the Earth.

• The distance is still needed to compute the actual luminosities, and not just the relative ones.


Star Clusters

• Let’s plot the stars from several different clusters on the diagram and draw “tracks” where the stars are to clean it up…


Star Clusters

• The “sequences” occupied by cluster stars changes from cluster to cluster (within certain bounds).

Star Clusters

• The “sequences” occupied by cluster stars changes from cluster to cluster (within certain bounds). WHY????

Star Clusters

• The “sequences” occupied by cluster stars changes from cluster to cluster (within certain bounds). WHY????

• This is related to the life cycles of stars.

The Life Cycles of Stars

• To understand why different star clusters have different tracks in the temperature-luminosity diagram, we must return to a result found from eclipsing binaries…


• The luminosity of a star is related to its mass: L ~ Mp, where p is almost 4.


• The luminosity of a star represents the amount of energy emitted per second. There must be a source of this energy, and it cannot last forever.



• The amount of “fuel” a star has is proportional to its initial mass.




• The length of time the fuel can be spent is equal to the amount of fuel divided by the consumption rate.





• Age ~ mass/luminosity





• Age ~ mass/luminosity = mass/(mass)4=1/(mass)3

Mass-Age Relation

• Age ~ 1/(mass)3 (“age” means time on the main sequence, “mass” means initial mass).

Mass-Age Relation


• More massive stars “die” much more quickly than less massive stars. For example, double the mass, and the age drops by a factor of 8.

Mass-Age Relation


• More massive stars “die” much more quickly than less massive stars. For example, double the mass, and the age drops by a factor of 8.

• On the main sequence, O and B stars (the bluest ones) are the most massive. Their lifetimes are relatively short.

Mass-Age Relation• Detailed computations show:

Star Clusters• Large radii• Small radii

• High mass (main sequence)

• Low mass (main sequence)

Star Clusters

• The “sequences” occupied by cluster stars changes from cluster to cluster (within certain bounds).

Star Clusters

• Some clusters have “lost” only the bluest main sequence stars.

Star Clusters


• Others have lost main sequence stars down to type F.

Star Clusters


• Others have lost main sequence stars down to type F.

• The differences in the tracks are due to age differences of the clusters!

Star Clusters

• Here is an animation showing how a cluster ages:

http://spiff.rit.edu/classes/phys230/lectures/clusters/hr_anim_slow.gif

Star Clusters

• Here is a temperature luminosity diagram for the Hyades cluster.

• This one is relatively young.

Star Clusters

• Here are the temperature luminosity diagrams for a three clusters.

• These diagrams and others can be used to make a “movie” on how stars evolve.

Star Clusters• Here is a schematic diagram showing a cluster age from zero years (formation) to several billion years.

Stellar Evolution

• Observational aspects– Observations of clusters of stars

• Theory– Outline of steps from birth to death

ASTRO 101

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