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6–1 Transformation of Astronomy Antiquity – 1700s: Most astronomers were interested in the planets: Stars remain fixed—it was the planets which moved in interesting ways. With the telescope planets could be resolved but stars still looked like points of light. Interest in the stars started to emerge in the 1700s: Telescopic sights allowed the determination of stellar positions with increasing accuracy. Proper motions of the stars became measurable. Astronomers actively searched for stellar parallax. Astronomy shifted decidedly away from planets in the 1800s and 1900s: Advances in physics allowed astronomers to determine various properties of stars (e.g. temperature, composition) from their spectra. Astronomy ==> Astrophysics Only with the space program has there been renewed interest in the solar system. Astronomy: An Observational Science Except for a few samples from planets, we have no samples we can study in the lab. Almost all the information we have about astronomical objects comes from studying the light (and other electromagnetic radiation) they emit. Fortunately, quite a lot of information can be gleaned from the light they emit. For example: Atoms: Temperature An element is a substance which cannot be broken down into other substances by chemical means. Composition Velocities Size Poor medieval alchemists! An atom is the smallest possible particle which retains the properties of an element. Atoms are composed of two main parts: To see how we can determine these properties we need to explore the physics of the very small. 6–2 Quantum Mechanics Excitation of Atoms The behavior of things at small scales differs from that at the larger scales of our common experience. Atoms in which the electrons are in the lowest energy level are said to be in the ground state. e.g., planets can orbit the sun at any distance. While electrons cannot be at intermediate energy levels, they can jump from one permitted energy level to another. Not true of electrons in an atom: They can only occupy certain orbits in an atom called permitted orbits. ==> Electrons can only have certain amounts of energy in atoms. Electrons cannot have other energies. Atoms can be excited from the ground state to higher energy states in two major ways: 1. Collisions between atoms can excite electrons. 2. Electrons can absorb light (photons) if the photon has just the right amount of energy. The permitted energies are different for different elements. The energy of a photon of light depends on its wavelength: Atomic Spectra E = hc/wavelength As noted above, atoms are only good at absorbing or emitting light of very specific wavelengths. The shorter the wavelength, the more energetic the photon. Thus, atoms in a gas in front of a light source will remove very specific wavelengths of light from the source creating absorption lines: Thus, because an atom can only absorb a photon of just the right energy to excite an electron to a higher energy level, it can only absorb light of just the right wavelength. Eventually, an excited atom will tumble back to its ground state by emitting a photon of energy equal to the difference in energy between the energy levels. Alternatively, away from a light source, the atoms will emit light at the same specific wavelengths creating emission lines. 6–3 Recall that different elements have unique permitted energy levels. Blackbody Radiation: ==> Each element has a unique set of absorption or emission lines. As discussed earlier, the spectrum from a gas of atoms will yield very specific wavelengths of light (either in absorption or emission). Thus spectral lines can be used much like a fingerprint: Not true of solid or liquid objects (or gases at high density). If a person’s fingerprint (or DNA) is present at a crime scene it indicates they were there. Such objects emit a continuous spectrum of light. In just the same way the presence of an element’s spectral lines in a spectra indicate it must be present as well. A blackbody is an ideal body which is a perfect absorber (and emitter) of light. While real objects are not perfect absorbers, most objects emit light approximately like a blackbody. Thus, it is useful to study how blackbodies emit light. Characteristics of Blackbody radiation: Both very short (energetic) and very long (low energy) wavelength photons are rare. Most of the light is emitted at intermediate wavelengths. Wien’s Law: Specifically, the wavelength of the peak intensity is inversely proportional to the temperature: λ max (nm) = 3,000,000/T(K) The amount of light emitted depends on the temperature: Do you think that hotter objects emit more or less light than cool objects? Examples? Examples of the peak intensity wavelengths: The sun (6000K): λmax = ? Cool star (3000K): λmax = ? The peak wavelength of intensity also depends on the temperature: As a body is heated, the peak intensity occurs at shorter (more energetic) wavelengths. You (310K): λmax = ? 6–4 This explains why, for example, as iron is heated in a forge it goes from emitting no light, to glowing a dull red to glowing a brilliant white at very high temperatures. Stefan-Boltzman Law: The power of light emitted per unit area by an object depends strongly on its temperature: It also explains the different colors of stars: Cool stars (e.g. 3000K) will emit their light at what wavelength (relatively short or long)? E = σ T4 For example: doubling the temperature would lead to how much more energy being emitted? Thus they will appear what color? tripling the temperature? Somewhat warmer stars (like the sun)? Hot stars? ==> a small change in the temperature can lead to a large change in the energy emitted. Color of a star can be used to determine temperature! Formation of Spectra: 2. An excited low density gas will emit an emission spectrum. Kirchhoff’s Laws: Example: Emission Nebula 1. A hot solid, liquid, or dense gas will emit a continuous spectrum. Examples would include the filaments of light bulbs and “red hot” metals. Hot Star Emission Nebula Observer 6–5 3. A cool, low density gas between a continuum light source and the observer will produce an absorption spectrum. Example: Most stars (including the sun) show an absorption spectrum. Spectral Classification We expect that stars of similar temperatures will have similar spectral features. Stars have been classified into 7 major categories based on the relative strength of their spectral lines. Stellar Atmosphere From hottest to coolest stars these are: Star O, B, A, F, G, K, and M Observer The main categories are subdivided into ten subcategories: For example, class A is subdivided into A0, A1, A2...A8, A9 Most stars show absorption spectra, what does this suggest about how temperature varies in such stars? Determining Stellar Velocities: For example, the sun is a typical G2 class star. Stars The Doppler Effect Wavelength emitted by an object will be shortened if approaching and lengthened if receding: For the next couple of weeks or so we will be discussing stars. Following the scientific method we will first discuss the properties of stars (initial observations). Red Shifted Blue Shifted True of any waves including sound or light waves. Shift in wavelength of spectral lines can be used to measure the velocity of stars. Also how radar guns determine the speed of cars. How do we measure stellar properties? Are there any patterns? If so, how can we categorize stars? We will then use these observed properties in examining theories of stellar evolution. 6–6 Stellar Properties Luminosity Unfortunately, most properties of stars cannot be determined directly. It is straightforward to measure how bright a star appears on the sky (apparent magnitude). e.g. how would you measure the length of a table? Is this enough? We have seen how stellar spectra can be used to determine stellar composition and temperature. Here we will see how we can determine some other stellar properties: Luminosity: Energy emitted by a star per unit time. Radius of a star Measuring Distances: Definition of the Parsec Trigonometric (or Stellar) Parallax Measuring distances to stars in AUs is unwieldy. If one can determine the parallax of an object, one can determine its distance. A more convenient unit to use, especially when measuring distances using parallax, is the Parsec: “Triangulation” It is defined as the distance at which a star would exhibit a parallax angle of one arc second: Technique used by surveyors to determine distance: 1 Parsec = 206,265 AU With this definition, the distance to a star (in parsecs) is given simply as: d (Parsecs) = 1/p(") 6–7 Light Year Another unit of distance which is often used is the light year. It is the distance light travels in a year: 1 Parsec = 3.26 light years From the ground parallax angles can be measured down to ~0.02". Thus distances of stars out to what distance can be reasonably accurately determined? Hippacos satellite has done better measuring the parallax angle down to about 0.001". Once we have determined the distance to a star, we can correct for the distance to the star and determine its luminosity. Absolute Magnitude: The apparent magnitude of a star depends only on the brightness of a star on the sky without regard to its distance. The absolute magnitude of a star is defined as the apparent magnitude a star would have if it were at a distance of 10 parsecs. Provides a convenient way to compare the intrinsic brightness of stars. Absolute magnitude is basically a measure of stellar luminosity. Out to what distance can it accurately measure? Stellar Sizes: Because stars are nearly spherical, we can use the surface area of a sphere, 4πR2: As noted before, it is almost impossible to measure the size of stars directly. L = Area × Flux = 4πR2 × σT4 However, it can be inferred from the luminosity and temperature of a star. This equation can be simplified somewhat if we compare the star to the sun: The luminosity depends on two properties of the stars: the temperature and the radius of a star. RStar 2 T Star 4 L Star = LSun RSun TSun The amount of energy per second flowing through a given area of a star’s surface (the flux) is given by the Stefan-Boltzman equation: We can determine the temperature of a star from its color. Flux = σT4 In order to get the total energy flowing out of a star per second (the luminosity) we need to multiply the flux by the surface area of the star. We can determine the luminosity from the apparent brightness and distance to a star. Given these two quantities we can determine the radius of a star from the above equation. 6–8 H-R Diagram Early last century reliable distances and spectral classifications were determined for the first time for a significant number of stars. Summary We have examined how various properties of stars can be determined: Composition: Strength and presence of spectral lines. From these data, Russell plotted the luminosity vs. temperatures of these stars. Hertzsprung had done similar work looking at stars in the Pleiades and Hyades star clusters. Temperature: Color or strength of spectral lines. Luminosity: Apparent brightness and distance measurements (parallax). Radius: Luminosity and Temperature. Such a diagram is now known as a HertzsprungRussell, or H-R, diagram. Do stars fall into distinct groups or are their properties random? HR-Diagram: Different classes of stars found from plots of stellar temperatures vs. luminosity. Why do stars have the properties they do?