Distance and Brightness Stellar Parallax The Magnitude Scale

Stellar Parallax Trigonometric Parallax: Determine distance from “triangulation” Parallax Angle: One-half the maximum angular displacement due to the motion of Earth about the Sun (excluding proper motion) With p measured in radians

PARSEC/Light Year 1 radian = 57.2957795 = 206264.806” Using p” in units of arcsec we have: Astronomical Unit of distance: PARSEC = Parallax Second = pc 1pc = 2.06264806 x 105 AU The distance to a star whose parallax angle p=1” is 1pc. 1pc is the distance at which 1 AU subtends an angle of 1” Light year : 1 ly = 9.460730472 x 1015 m 1 pc = 3.2615638 ly Nearest star proxima centauri has a parallax angle of 0.77” Not measured until 1838 by Friedrich Wilhelm Bessel Hipparcos satellite measurement accuracy approaches 0.001” for over 118,000 stars. This corresponds to a a distance of only 1000 pc (only 1/8 of way to centerof our galaxy) The planned Space Interferometry Mission will be able to determine parallax angles as small as 4 microarcsec = 0.000004”) leading to distance measurements of objects up to 250 kpc.

The Magnitude Scale Apparent Magnitude: How bright an object appears. Hipparchus invented a scale to describe how bright a star appeared in the sky. He gave the dimmest stars a magnitude 6 and the brightest magnitude 1. Wonderful … smaller number means “bigger” brightness!!! The human eye responds to brightness logarithmically. Turns out that a difference of 5 magnitudes on Hipparchus’ scale corresponds to a factor of 100 in brightness. Therefore a 1 magnitude difference corresponds to a brightness ratio of 1001/5=2.512. Nowadays can measure apparent brightness to an accuracy of 0.01 magnitudes and differences to 0.002 magnitudes Hipparchus’ scale extended to m=-26.83 for the Sun to approximately m=30 for the faintest object detectable

Flux, Luminosity and the Inverse Square Law Radiant flux F is the total amount of light energy of all wavelengths that crosses a unit area oriented perpendicular to the direction of the light’s travel per unit time…Joules/s=Watt Depends on the Intrinsic Luminosity (energy emitted per second) as well as the distance to the object Inverse Square Law:

Absolute Magnitude and Distance Modulus Absolute Magnitude, M: Defined to be the apparent magnitude a star would have if it were located at a distance of 10pc. Ratio of fluxes for objects of apparent magnitudes m1 and m2 . Taking logarithm of each side Distance Modulus: The connection between a star’s apparent magnitude, m , and absolute magnitude, M, and its distance, d, may be found by using the inverse square law and the equation that relates two magnitudes. Where F10 is the flux that would be received if the star were at a distance of 10 pc and d is the star’s distance measured in pc. Solving for d gives: The quantity m-M is a measure of the distance to a star and is called the star’s distance modulus

The Continuous Spectrum of Light The Nature of Light Blackbody Radiation The Color Index

(will come back to this topic..soon) Speed of Light Ole Roemer(1644-1710) measured the speed of light by observing that the observed time of the eclipses of Jupiter’s moons depended on how distant the Earth was from Jupiter. He estimated that the speed of light was 2.2 x 108 m/s from these observations. The defined value is now c=2.99792458 x 108 m/s (in vacuum). The meter is derived from this value. Measurement of speed of light is the same for all inertial reference frames!!! Special Relativity (will come back to this topic..soon) Takes an additional 16.5 minutes for light to travel 2AU

The Nature of Light Newton believed that like was “corpuscular”, particle-like in nature…due to sharpness of shadows. Christian Huygens (1629-1695) believed that light was wave-like, with a distance between succesive peaks (troughs) of wavelength and that the number of waves per second that pass a point in space is the frequency of the wave. The speed of light is then given by : Particle and wave models could explain reflection and refraction of light…wave nature of light demonstrated by Thomas Young’s double slit experiment…

The Wave Nature of Light Light impinging on double slit Exhibits Inerference pattern Interference condition (n=0,1,2,…for bright fringes) (n=1,2,…for dark fringes) INTERFERENCE WAVE http://vsg.quasihome.com/interfer.htm

And God said…let there be light What is Light? And God said…let there be light Maxwell’s Equations in Free space Electromagnetic Wave equation and there was light….

Wavelike Nature of light Light is an electromagnetic phenomenon Heinrich Hertz’s Apparatus for the production and detection of radio waves Deutsches Museum Munich Changing electric field Changing Magnetic Field Propagates through free space Nothing is waving!!!! EM waves created by accelerating charges (link)

Accelerating Charge causes Electromagnetic Waves Electric Field emanates from electric charges What happens to field when charge is accelerated? “Kink” in electro-magnetic field propagates with finite velocity http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=322.0

Electromagnetic Waves Electromagnetic Wave speed Light is indeed an Electromagnetic Wave Waves are Transverse

Electromagnetic Spectrum Region Wavelength Gamma Ray nm X-Ray 1 nm<10 nm Ultraviolet 10 nm<400 nm Visible 400 nm<700 nm Infrared 700 nm<1 mm Microwave 1mm<10 cm Radio 10 cm<

Radiation Pressure and the Poynting Vector The rate at which energy is carried by a light wave is described by the Poynting vector. Instantaneous flow of energy per unit area per unit time (W/m2) for all wavelengths. Points in the direction of the electromagnetic wave’s propagation. Radiant Flux: Time average (over one period) of the Poynting vector Because an electromagnetic wave carries momentum it can exert a force on a surface hit by light… Radiation Pressure Radiation Pressure is significant in extremely luminous objects such as: early main-sequence stars red supergiants Accreting compact stars Interstellar medium dust particles absorption) reflection)

Photon Flux Densities Light Source Photon Flux Density Photons/(sec m2) Laserbeam (10 mW,He-Ne 20um) Laserbeam (1 mW,He-Ne ) Bright Sunlight Indoor Light Level Twilight Moonlight Starlight

Particle-like nature of light Photons Photon = “Particle of Electromagnetic “stuff”” Blackbody Radiation Failure of Classical Theory Radiation is “quantized” Photo-electric effect (applet) Light is absorbed and emitted in tiny discrete bursts

Color/Temperature Relation Betelguese(3100-3900K) What does the color of a celestial object tell us?  Rigel (8000-13,000K)

Blackbody Radiation Any object with temperature above absolute zero 0K emits light of all wavelengths with varying degrees of efficiency. An Ideal Emitter is an object that absorbs all of the light energy incident upon it and re-radiates this energy with a characteristic spectrum.Because an Ideal Emitter reflects no light it is known as a blackbody. Wien’s Law: Relationship between wavelength of Peak Emission max and temperature T. Stefan-Boltzmann equation: (Sun example) Blackbody L:Luminosity A:area T:Temperature Blackbody Radiation Spectrum

Blackbody Radiation http://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.html