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 …)

Next: How Does the Sun Work?

How Does the Sun Work? Some useful numbers:  The mass of the Sun is 2x10 30 kg.  The luminosity of the Sun is 4x10 26 Watts.  The first question to ask is: What is the energy source inside the Sun?

Energy Sources A definition: Efficiency = energy released/(fuel mass x [speed of light] 2 ) Chemical energy (e.g. burning wood, combining hydrogen and oxygen to make water, etc.).  Efficiency = 1.5 x  Solar lifetime = 30 to 30,000 years, depending on the reaction. Too short!

Energy Sources A definition: Efficiency = energy released/(fuel mass x [speed of light] 2 ) Gravitational settling (falling material compresses stuff below, releasing heat).  Efficiency = 1 x  Solar lifetime = 30 million years. Too short, although this point was not obvious in the late 1800s.

Energy Sources A definition: Efficiency = energy released/(fuel mass x [speed of light] 2 ) Nuclear reactions: fusion of light elements (as in a hydrogen bomb).  Efficiency =  Solar lifetime = billions of years.

How to get energy from atoms Fission: break apart the nucleus of a heavy element like uranium. Fusion: combine the nuclei of a light element like hydrogen.

More Nuclear Fusion Fusion of elements lighter than iron can release energy (leads to higher BE’s). Fission of elements heaver than iron can release energy (leads to higher BE’s).

Nuclear Fusion Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). Why does this produce energy?  Before: the mass of 4 protons is 4 proton masses.  After: the mass of 2 protons and 2 neutrons is 3.97 proton masses.  Einstein: E = mc 2. The missing mass went into energy! 4H ---> 1He + energy

Nuclear Fusion The CNO cycle (left) and pp chain (right) are outlined.

Models of the Solar Interior The interior of the Sun is relatively simple because it is an ideal gas, described by three quantities: 1.Temperature 2.Pressure 3.Mass density The relationship between these three quantities is called the equation of state.

Ideal Gas For a fixed volume, a hotter gas exerts a higher pressure: Image from Nick Strobel’s Astronomy Notes (

Hydrostatic Equilibrium The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance: Image from Nick Strobel’s Astronomy Notes (

Hydrostatic Equilibrium The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun. Image from Nick Strobel’s Astronomy Notes (

Hydrostatic Equilibrium The Sun (and other stars) does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun. The temperature increases as you go deeper and deeper into the Sun!

Models of the Solar Interior The pieces so far:  Energy generation (nuclear fusion).  Ideal gas law (relation between temperature, pressure, and volume.  Hydrostatic equilibrium (gravity balances pressure).  Continuity of mass (smooth distribution throughout the star).  Continuity of energy (amount entering the bottom of a layer is equal to the amount leaving the top).  Energy transport (how energy is moved from the core to the surface).

Models of the Solar Interior Solve these equations on a computer:  Compute the temperature and density at any layer, at any time.  Compute the size and luminosity of the star as a function of the initial mass.  Etc…….

Solar Structure Models

Here is the model of the structure of the Sun.

Next: Characterizing Stars

The Sun and the Stars The Sun is the nearest example of a star. Basic questions to ask: –What do stars look like on their surfaces? Look at the Sun since it is so close. –How do stars work on their insides? Look at both the Sun and the stars to get many examples. –What will happen to the Sun? Look at other stars that are in other stages of development.

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

Observing Other Stars Recall there is basically no hope of spatially resolving the disk of any star (apart from the Sun). The stars are very far away, so their angular size as seen from Earth is extremely small. The light we receive from a star comes from the entire hemisphere that is facing us. That is, we see the “disk-integrated” light.

Observing Other Stars To get an understanding of how a star works, the most useful thing to do is to measure the spectral energy distribution, which is a plot of the intensity of the photons vs. their wavelengths (or frequencies or energies). There are two ways to do this:  “Broad band”, by taking images with a camera and a colored filter.  “High resolution”, by using special optics to disperse the light and record it.

Broad Band Photometry There are several standard filters in use in astronomy. The filter lets only light within a certain wavelength region through (that is why they have those particular colors).

Color Photography The separate images are digitally processed to obtain the final color image.

Color Photography

Broad Band Photometry Broad band photometry has the advantage in that it is easy (just need a camera and some filters on the back of your telescope), and it is efficient (relatively few photons are lost in the optics). The disadvantage is that the spectral resolution is poor, so subtle differences in photon energies are impossible to detect.

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.

High Resolution Spectroscopy Using a good high resolution spectrum, you can get a much better measurement of the spectral energy distribution. The disadvantage is that the efficiency is lower (more photons are lost in the complex optics). Also, it is difficult to measure more than one star at a time (in contrast to the direct imaging where several stars can be on the same image).

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.

The Distance How can you measure the distance to something?  Direct methods, e.g. a tape measure. Not good for things in the sky.  Sonar or radar: send out a signal with a known velocity and measure the time it takes for the reflected signal. Works for only relatively nearby objects (e.g. the Moon, certain asteroids).

The Distance How can you measure the distance to something?  Direct methods, e.g. a tape measure. Not good for things in the sky.  Sonar or radar: send out a signal with a know velocity and measure the time it takes for the reflected signal. Works for only relatively nearby objects (e.g. the Moon, certain asteroids).  Triangulation: the use of parallax.

The Parallax Parallax is basically the apparent shifting of nearby objects with respect to far away objects when the viewing angle is changes. Example: hold out your finger and view it with one eye closed, then the other eye closed. Your finger shifts with respect to the background.

The Parallax Example: hold out your finger and view it with one eye closed, then the other eye closed. Your finger shifts with respect to the background.

The Parallax A better example: place an object on the table in front of the room and look at its position against the back wall as you walk by. In most practical applications you will have to change your position to make use of parallax.

Triangulation Triangulation is based on trigonometry, and is often used by surveyors. Image from Nick Strobel’s Astronomy Notes (

Triangulation Triangulation is based on trigonometry, and is often used by surveyors. The length B and the angle p can be measured, so the distance can be computed: d=B/tan(p) Image from Nick Strobel’s Astronomy Notes (

Triangulation Triangulation is based on trigonometry, and is often used by surveyors. This technique can be applied to nearby stars. Image from Nick Strobel’s Astronomy Notes (

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 (

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 (

Triangulating the Stars Here are two neat Java tools demonstrating parallax:

Triangulating the Stars When viewed at 6 month intervals, a relatively nearby star will appear to shift with respect to distant stars. The angle p for the nearest star is 0.77 arcseconds. One can currently measure angles as small as a few thousands of an arcsecond. Image from Nick Strobel’s Astronomy Notes (

Triangulating the Stars For very tiny angles, use the approximation that tan(p)=p, when p is in radians. Then d=B/tan(p) becomes d=B/p.

Triangulating the Stars For very tiny angles, use the approximation that tan(p)=p, when p is in radians. Then d=B/tan(p) becomes d=B/p. B=1 “astronomical unit” (e.g. the Earth-Sun distance). Define a unit of distance such that d=1/p, if the angle p is measured in arcseconds.

Triangulating the Stars For very tiny angles, use the approximation that tan(p)=p, when p is in radians. Then d=B/tan(p) becomes d=B/p. B=1 “astronomical unit” (e.g. the Earth-Sun distance). Define a unit of distance such that d=1/p, if the angle p is measured in arcseconds. This unit is the parsec, which is 3.26 light years.

Distances and Brightness What do we do with the distance measurement?

Distances and Brightness What do we do with the distance measurement? We need the distance to compute the star’s luminosity. Note the distinction between how bright a star appears and how luminous it actually is. Let’s review how to quantify brightness…

Magnitudes as a Measure of Brightness Historically (e.g. Hipparcos in the First Century), the brightness of stars as seen by the eye have been measured on a magnitude scale: –The brightest stars were “first magnitude”. –The faintest stars were “sixth magnitude”. Brighter objects have smaller magnitudes.

Magnitudes as a Measure of Brightness In modern times, it was discovered that the human eye has a nonlinear response to light: if one source of light has twice the photons as a second source, then the first source would not appear by eye to be twice as bright. The response of the eye is logarithmic, so that differences of magnitudes correspond to ratios of flux.

The Magnitude Scale The modern of the magnitude scale is set up so that a difference of 5 magnitudes corresponds to a ratio of brightnesses of 100. Bright objects can have negative apparent magnitudes.

The Magnitude Scale The modern of the magnitude scale is set up so that a difference of 5 magnitudes corresponds to a ratio of brightnesses of 100. Bright objects can have negative apparent magnitudes.

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 Imagine a source emitting light uniformly over all directions. Also imagine a series of concentric spheres centered on the light source. The energy passing through each sphere is the same!

The Inverse Square Law 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 flux through the first sphere is 72 W/m 2. 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 flux through the first sphere is 72 W/m 2. The surface area of the second sphere is 4 m 2. 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 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 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 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 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 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 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 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.

The Inverse Square Law Here is a neat Java tool demonstrating the inverse square law:

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 Type Sequence Mnemonics Oh Boy, An F Grade Kills Me Oh, Be A Fine Girl, Kiss Me

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