Astro 101 Fall 2013 -- Lecture #3 T. Howard
Using Light to Sample the Universe Light is a mutual oscillation of electric and magnetic fields, travelling through space. Light is also a stream of fundamental particles (photons) that can be detected individually. Both interpretations are correct. It is electromagnetic radiation. Light from stars starts out like this … … and reaches us like this. Spherical wave wavefronts (lines of constant phase) Plane wave Why? Because stars are very, very far away. The curved wave flattens out with distance.
But, the amount of light we can collect … (with our telescopes) … falls off as 1/distance2 • Why? Three simple reasons: • The total energy = amount of light is conserved • As the light flows away from the star, that light • is spread over an imaginary sphere of area • 4pR2, where R is the distance from the star • C. Our telescope samples only a very small part • of the area of that imaginary sphere that • surrounds the distant star. distant star R Telescope (just the front aperture is shown) We can use this to find either (a) the absolute amount of light that the star emits, or (b) its distance, if we know the other quantity.
Since light is a wave, it has wave properties … Direction of wave travel “Amplitude” of the wave = height of the Electric field vibration “Wavelength” = distance between two successive peaks This defines the color of the light wave • Most light we see with our eyes has a spread of many colors mixed • Generally, some colors stronger than others, so we see objects • in different colors • White light is a nearly uniform mix of all the colors that we can see • with our eyes • There are many other colors (= wavelengths) that we can’t see • Our eyes just not sensitive to vibrations at those wavelengths • But, electronic detectors and telescopes can see them
So, almost all light reaches us with a spectrum Spectrum = spread of light wavelengths, mixed in varying strengths, that reaches our eye / telescope / camera (plural = spectra) Spectra can be continuous … (like this) or discrete … (like this) Continuous spectra come from warm objects (everything in the Universe, almost). The color extent and intensity of the spectrum depends on the temperature of the object. This is known as thermal or blackbody radiation. Even you are emitting thermal radiation, right now.
Example • The astronaut’s space suit is: • Reflecting light from its surroundings • … and … • Emitting infrared (thermal) radiation • (that we can’t see because our eyes • aren’t sensitive to those colors) • Q: What about the light coming • from the lunar surface? Which is it? • Q: Is the light from the Sun thermal radiation? If so, why • can we see it with our eyes? If not, what is it? incoming sunlight
The visible spectrum 700 nm 400 nm The human eye is sensitive only to the range 400 – 700 nanometers. (1 nanometer = 10-9 meter = one-billionth of a meter.) Blue wavelengths are shorter than red wavelengths. The visible spectrum is only a small part of the overall possible electromagnetic spectrum. Other regions of the spectrum correspond to … gamma rays (very short) x-rays (pretty short wavelengths) UV (ultraviolet, shorter than visible blue light) infrared or IR (long wavelengths, beyond the visible) radio waves (longer than infrared)
3x1025 1024 1023 1022 1021 1020 1019 1018 1017 1016 1015 1014 1013 1012 1011 1010 109 108 107 106 105 104 103 Electromagnetic Radiation Temperature of Blackbody with Peak emission at l 2900K 29K 290K LWIR 8-12 microns MWIR 3-5 microns NIR < 2 microns VLWIR • 10 100 • Wavelength [microns] Frequency [Hz] Infrared e- e+ annihilation 0.511 MeV Broadcast AM 0.8 MHz X-band 10 GHz Radio 1 eV 1.24 microns Gamma Rays frequency [Hz] 10-18 10-17 10-16 10-15 10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105 wavelength [m] Shortwave 10 MHz Cellphones (AMPS, USDC) 850 MHz X-rays UV Peak of Cosmic Microwave Background (CMB) [T =2.736 K] Broadcast TV 60 MHz UV “A” 320-400 nm UV “B” 290-320 nm Medical x-rays 0.1 - 0.5 Angstroms Wavelength [m] Photon energy: E = hn = hc/l ln = c Visible 400 nm [0.4 microns] 4000 Angstroms 700 nm [0.7 microns] 7000 Angstroms micron = mm = 10-6 m nanometer = nm = 10-9 m Angstrom = 10-10 m Peak Dark response 510 nm Peak Day response 570 nm
Light of a certain color also has a characteristic frequency Frequency = number of waves passing an arbitrary location (any convenient reference point) per second. Frequency and wavelength are inversely related: Longer wavelength = lower frequency = slower vibrations Shorter wavelength = higher frequency = faster vibrations Most of the time, in this class, we will talk about wavelength rather than frequency. But if you specify one, you know the other. The energy of the light is also related to wavelength and frequency.
Some typical wavelengths, temperatures, and frequencies Object Temperature Wavelength or frequency Dental narrow line near 5 nm X-rays Sun 5700 K Peak at about 500 nm Your skin about 70F Peak at about 10000 nm = 10 microns WiFi signal narrow signals at 2.4 GHz or 5 GHz (approx.) 1 GHz = 109 waves/sec. AM Radio 530 – 1070 kHz wavelength 280 – 560 m
What about discrete spectra ? • Narrow, well-defined spectral lines are phenomena caused by • energy transitions in individual atoms or molecules • These narrow lines correspond to specific light energies • Both atoms and molecules can exist in many possible energy states • Only certain energy states are physically possible (“allowed”) • So, the transition of an atom or molecule from energy state 1 • to energy state 2 has a fixed energy difference • That difference is characteristic of the atom or molecule • The energy either absorbs light of a certain color, or • emits energy of a certain color • Low High energyHigh Low energy • (absorbs light) (emits light)
Spectroscopy and Atoms • How do we know: • - Physical states of stars, e.g. temperature, density. • - Chemical make-up and ages of stars, galaxies • - Masses and orbits of stars, galaxies, extrasolar planets • expansion of universe, acceleration of universe. All rely on taking and understanding spectra: spreading out radiation by wavelength.
Types of Spectra and Kirchhoff's (1859) Laws 1. "Continuous" spectrum - radiation over a broad range of wavelengths (light: bright at every color). Produced by a hot opaque solid, liquid, or dense gas. 2. "Emission line" spectrum - bright at specific wavelengths only. Produced by a transparent hot gas. 3. Continuous spectrum with "absorption lines": bright over a broad range of wavelengths with a few dark lines. Produced by a transparent cool gas absorbing light from a continuous spectrum source.
The pattern of lines is a fingerprint of the element (e.g. hydrogen, neon)in the gas. For a given element, emission and absorption lines occur at the same wavelengths. Sodium
The Particle Nature of Light On microscopic scales (scale of atoms), light travels as individual packets of energy, called photons. (Einstein 1905). c photon energy is proportional toradiation frequency: E(or E ) example: ultraviolet photons are more harmful than visible photons. 1
The Nature of Atoms The Bohr model of the Hydrogen atom (1913): electron _ _ + + proton "ground state" an "excited state" Ground state is the lowest energy state. Atom must gain energy to move to an excited state. It must absorb a photon or collide with another atom.
But, only certain energies (or orbits) are allowed: _ _ _ a few energy levels of H atom + The atom can only absorb photons with exactly the right energy to boost the electron to one of its higher levels. (photon energy α frequency)
When an atom absorbs a photon, it moves to a higher energy state briefly When it jumps back to lower energy state, it emits a photon - in a random direction
Other elements Helium Carbon neutron proton Atoms have equal positive and negative charge. Each element has its own allowed energy levels and thus its own spectrum. Number of protons defines element. Isotopes of element have different number of neutrons.
Ionization Hydrogen _ + Energetic UV Photon _ Helium + + Energetic UV Photon _ Atom "Ion" Two atoms colliding can also lead to ionization. The hotter the gas, the more ionized it gets.
So why do stars have absorption line spectra? Simple case: let’s say these atoms can only absorb green photons. Get dark absorption line at green part of spectrum. “atmosphere” (thousands of K) has atoms and ions with bound electrons hot (millions of K), dense interior has blackbody spectrum, gas fully ionized
Stellar Spectra Spectra of stars differ mainly due to atmospheric temperature (composition differences also important). “hot” star “cool” star
So why absorption lines? . . . . . cloud of gas . . . . . . The green photons (say) get absorbed by the atoms. They are emitted again in random directions. Photons of other wavelengths go through. Get dark absorption line at green part of spectrum.
Why emission lines? hot cloud of gas . . . . . . - Collisions excite atoms: an electron moves to a higher energy level - Then electron drops back to lower level - Photons at specific frequencies emitted.
Molecules Two or more atoms joined together. They occur in atmospheres of cooler stars, cold clouds of gas, planets. Examples H2 = H + H CO = C + O CO2 = C + O + O NH3 = N + H + H + H (ammonia) CH4 = C + H + H + H + H (methane) They have - electron energy levels (like atoms) - rotational energy levels - vibrational energy levels
Types of Spectra 1. "Continuous" spectrum - radiation over a broad range of wavelengths (light: bright at every color). 2. "Emission line" spectrum - bright at specific wavelengths only. 3. Continuous spectrum with "absorption lines": bright over a broad range of wavelengths with a few dark lines.
Kirchhoff's Laws (1859) 1. A hot, opaque solid, liquid or dense gas produces a continuous spectrum. 2. A transparent hot gas produces an emission line spectrum. 3. A transparent, cool gas absorbs wavelengths from a continuous spectrum, producing an absorption line spectrum.
Happens for all wave phenomena: sound => change of pitch light => change of wavelength (or color) Doppler shifts where V is the velocity of the emitting source (m/s), c is the speed of light (m/s).
Redshift if receding, blueshift (negative sign) if approaching. Spectral lines are used to measure Doppler shift => gives us information about the motion of an object.
A spectral line normally seen at 400nm is shifted to 401nm due to relative motion of the source. What is the velocity of the source? Is it approaching or receding? Example Doppler shift
Star wobbling due to gravity of planet causes small Doppler shift of its absorption lines. Amount of shift depends on velocity of wobble. Also know period of wobble. This is enough to constrain the mass and orbit of the planet.
Final note: the Sun’s surface temperature of about 5800 K produces peak emission at 500 nm. Sun is not yellow-green! What’s going on?
The Earth’s atmosphere scatters short wavelength blue light more efficiently than red light. Sun appears redder because blue light scattered away into the sky. Sun even appears red at sunset.
Basic function of a telescope: extend human vision Collect light from celestial object Focus light into an image of the object Human eye works from 400 – 700 nm or so and uses a lens to form an image on the retina. Astronomical objects emit at much larger range of wavelengths, and can be very faint! Telescopes
Kinds of optical telescopes Refractor – uses a lens that light passes through, to concentrate light. Galileo’s telescope was a refractor. Optical telescopes
Large objective lens at the front of the telescope forms the image, the eyepiece lens at the back of the telescope magnifies the image for the observer. Focal length, f, is distance from the lens to the focal point.
Problem with refractors: big diameter objective lens means huge telescope! Tube here is 64 ft, biggest lens ever was 40 inches in diameter.
Solution: use concave mirror, not lens, to focus light. Reflecting telescope. Reflector – uses a mirror (shape is conic section– typically parabolic). Big, modern research telescopes are reflectors.
Observing with Your Eye vs. Telescope Photography Eye Eyepiece Objective Q: Why the difference? A: Because your eye has its own “detector” inside (the retina) Eyepiece provides magnification Your eye lens focuses the light onto the retina Detector (or film) Objective
Aligning the Telescope Axes … It Makes a Difference “Alt-Az” mounting : Vertical axis (sweep around horizon) Horizontal axis (up and down) “Equatorial” mounting : Main axis is parallel to Earth N-S axis Other axis goes up and down in ;atitude Advantage: Clock motor turns the telescope to match the Earth rotation, so long exposures possible Problem: Stars (& moon, etc.) drift through Image as Earth rotates No good for Photography, Spectroscopy !! X
100 inch Telescope, Mt. Wilson Observatory A small amateur telescope
Mirrors can be large, because they can be supported from behind. Largest single mirror built: 8.4 m diameter for the Large Binocular Telescope There are 10 m telescopes, but in segments Reflector advantages
Light gathering power: LGP area, or D2 Main reason for building large telescopes! Reasons for using telescopes
Magnification: angular diameter as seen through telescope/angular diameter on sky: m=fobj/feyepiece Typical magnifications 10 to 100 Resolution: The ability to distinguish two objects very close together. Angular resolution: = 2.5 x 105 /D, where is angular resolution of telescope in arcsec, is wavelength of light, D is diameter of telescope objective, both typically in meters. Reasons for using telescopes, cont.
Two light sources with angular separation much larger than angular resolution vs. equal to angular resolution