ASTRO 101 Principles of Astronomy

Instructor: Jerome A. Orosz (rhymes with “boris”) Contact: Telephone: WWW: Office: Physics 241, hours T TH 3:30-5:00

Homework/Announcements Homework due Tuesday, April 16: Question 4, Chapter 8 (Describe the three main layers of the Sun’s interior.) 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)  Temperature at the “surface”  Radius  Mass  Chemical composition

The Luminosity Luminosity (or power) is a measure of the energy emitted at the surface of the star per second. –We are not at the surface of the star, so we need to extrapolate from measurements we can do. –We can measure the energy received from the star at the Earth. –If we can measure the distance to the star, then we can figure out the energy that the star emitted.

Triangulation Triangulation is based on trigonometry, and is often used by surveyors. Here is another diagram showing the technique. This technique can be applied to other stars! Image from Nick Strobel’s Astronomy Notes (

Triangulating the Stars The largest baseline one can obtain is the orbit of the Earth! When viewed at 6 month intervals, a relatively nearby star will appear to shift with respect to distant stars.

Triangulating the Stars The largest baseline one can obtain is the orbit of the Earth! When viewed at 6 month intervals, a relatively nearby star will appear to shift with respect to distant stars. Image from Nick Strobel’s Astronomy Notes (

The Luminosity of Stars An important physical characteristic of a star is its luminosity, which is a measure of the amount of energy emitted by the star at its surface per unit time. We can measure the amount of energy received from the star per unit time (we call this the flux). How do we relate the luminosity to the flux?

The Inverse Square Law The flux through the first sphere is 72 W/m 2. The surface area of the second sphere is 4 m 2. The flux through the second sphere is (72 W)/(4 m 2 ) = 18 W/m 2. The surface area of the third sphere is 9m 2. The flux through the third sphere is (72 W)/(9 m 2 ) = 8 W/m 2. The flux decreases as the square of the distance. The energy passing through each sphere is the same. Suppose the light source has a luminosity of 72 watts. Suppose the inner sphere has a surface area of 1 m 2. Recall the area of a sphere is 4  R 2.

The Inverse Square Law The car’s headlights give off the same amount of light no matter where you stand. Obviously you will see more light if you are closer.

The Inverse Square Law Image from Nick Strobel’s Astronomy Notes (

The Inverse Square Law Image from Nick Strobel’s Astronomy Notes (

The Inverse Square Law The received flux from a source depend inversely on the square of the distance. If you want to know the intrinsic luminosity of your source, you must measure the flux and the distance.

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”  Radius  Mass  Chemical composition

Stellar Properties There are two ways to measure the temperature of a star:  Measure its “color”.  Measure its absorption line spectrum.

Stellar Temperatures Recall from the discussion of black bodies that a hotter black body looks bluer than a cooler black body. This works for stars also…

Stellar Temperatures The redder stars in this image are relatively cool, and the bluer stars are relatively hot.

Stellar Temperatures As the temperature goes up, the peak of the spectrum goes towards the blue.

Stellar Properties There are two ways to measure the temperature of a star:  Measure its “color”.  Measure its absorption line spectrum.

High Resolution Spectroscopy To obtain a high resolution spectrum, light from a star is passed through a prism (or reflected off a grating), and focused and detected using some complicated optics.

Spectral Classification In the early 1800s, Joseph Fraunhofer observed the solar spectrum. He saw dark regions, known as spectral lines (these tell us what elements are there). Starting in the late 1800s, it became possible to take the spectra of stars with similar detail.

Spectral Classification At first, there was no physical understanding. The earliest classification scheme was based on the strength of the hydrogen lines, with classes of: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. Class A had the strongest hydrogen lines, class O the weakest. Later on, only a few of these classes were kept. Then, subclasses were added (e.g. G2), based on other elements.

Spectral Classification At first, there was no physical understanding. The earliest classification scheme was based on the strength of the hydrogen lines, with classes of: A, B, F, G, K, M, O. Eventually, physical understanding came. It was discovered that the spectral type was a temperature indicator. As a result, a more natural ordering of the spectral types became: O, B, A, F, G, K, M (the old classes were retained).

Spectral Classification Here are digital plots of representative stars in the spectral sequence. Note the variation in the strength of the hydrogen lines.

Spectral Classification This is a computer simulation of the different types.

Spectral Classification A measurement of the spectral type gives the “surface” temperature of the star. O-stars are the hottest, with surface temperatures of up to 60,000 K. M-stars are the coolest, with temperatures of only 3000 K. The temperature of the Sun (a G2 star) is 5770 K.

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

Stellar Properties We can measure the apparent brightnesses of stars relatively easily (e.g. broad-band photometry). We can measure the color index and/or the spectral type of stars. This gives us the temperatures. We can measure the distances to the relatively nearby stars. Thus we can compute intrinsic brightnesses or luminosities for these stars. What do you do with these data?

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

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.

Temperature-Luminosity Diagrams The stars do not fall on random locations in this diagram!

Temperature-Luminosity Diagrams The stars do not fall on random locations in this diagram! Image from Nick Strobel’s Astronomy Notes (

Temperature-Luminosity Diagrams 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 (

Temperature-Luminosity Diagrams The stars do not fall on random locations in this diagram! There is some specific physical process that limits where a star can be on this diagram. Image from Nick Strobel’s Astronomy Notes (

Temperature-Luminosity Diagrams The stars do not fall on random locations in this diagram! Furthermore, the location of a star on this diagram is an indicator of its size. Image from Nick Strobel’s Astronomy Notes (

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.

Temperature-Luminosity Diagrams Temperature is on the x-axis: hotter stars are on the left, cooler ones on the right. Luminosity is on the y-axis, more luminuous ones are at the top, the less luminuous ones are at the bottom. Image from Nick Strobel’s Astronomy Notes (

Temperature-Luminosity Diagrams 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. Image from Nick Strobel’s Astronomy Notes (

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

Temperature-Luminosity Diagrams These regions in the H-R diagram are useful when considering the evolution of stars (more later).

Temperature-Luminosity Diagrams 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

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:  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.

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.

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?

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?

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!

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

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 M 1 = 2M 2.

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 M 1 >> M 2, for example the Sun and Earth.

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.

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. These are “visual binaries.”

Binary Stars

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

Center of Mass A star will appear to “wobble” when it is orbiting another body.  If the other body is another star, the wobble will be relatively large.  If the other body is a planet, the wobble will be very small.

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”). For a binary star, the decomposition depends on the orientation of the orbit:  For an orbit seen face-on, all motion is in the plane of the sky.  For an orbit seen edge-on, the motion is also in the radial direction. The size of the radial velocity variations depend on the inclination of the orbit (the radial velocity is the true velocity times the sine of the inclination.)

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.

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. One can see Sirius wobble over the course of decades (it has a very massive, but dark, companion).

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. We can’t detect this motion in most binaries.

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. 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:

Detecting Radial Velocities Recall that radial velocities can be measured from Doppler shifts in the spectral lines: Motion towards us gives a shorter observed wavelength.

Detecting Radial Velocities Recall that radial velocities can be measured from Doppler shifts in the spectral lines: Motion towards us gives a shorter observed wavelength. Motion away from us gives a longer observed wavelength.

Spectroscopic Binaries Recall that radial velocities can be measured from Doppler shifts in the spectral lines: 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: Image from Nick Strobel’s Astronomy Notes (

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.

Binary Stars A binary system is when two stars are bound together by gravity. They orbit their common center of mass. In some cases, we can use binary stars to measure precise masses and radii for stars.

Center of Mass Recall that m 1 r 1 =m 2 r 2 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 m 1 v 1 =m 2 v 2, or m 1 /m 2 =v 2 /v 1 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.). Image from Nick Strobel’s Astronomy Notes (

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.

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. How do you find the viewing angle?

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. 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.

Eclipsing Systems and Stellar Radii The relative radii can be found by studying how much light is blocked, and for how long. Image from Nick Strobel’s Astronomy Notes (

Eclipsing Systems and Stellar Radii The “light curve depends on the relative sizes and brightnesses of the stars, and on the orientation.

Eclipsing Systems and Stellar Radii 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! Image from Nick Strobel’s Astronomy Notes (

Mass-Luminosity Relation The stars form a tight sequence. This is another clue to the inner workings of stars!

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:  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.