Stars: Properties and Classification Announcements n n n Homework # 5 starts today. Due Tuesday, Nov 15th. Grades for Quiz # 4 are available in the OWL Gradebook In-class Exam # 2 will take place on Tuesday, Nov 8th. – Please check www.astro.umass.edu/~calzetti/astro100 for more infos Assigned Reading n Units 52.1-2-3, 54.1-2-3, 55, 56, 57.1-3 Goals for the Day n To begin a study of stars – what they re made of, what kinds are out there, how they are born, and how they die. Are all stars similar to our Sun? How far away are they? Where did they come from? What do they do? Do they live forever? How do they die? n There are four principal characteristics of a star: – Luminosity – Surface Temperature – Size – Mass Three of them (luminosity, size, and mass) require knowledge of the distance of the star from us. Stellar Parallax The measurements are taken six months apart. The baseline is the diameter of the Earth’s orbit. What is seen What is seen The ½ of the angle between the current location and the 6-month location is called the stellar parallax = P. Parallax Distance 1 (AU) D (in Parsecs) = P (in arcseconds) P, the parallax angle, is measured in arcseconds 60 arcseconds = 1 arcminute 60 arcminutes = 1 degree There are 3600 arcseconds in a degree The larger P, the smaller D The smaller P, the larger D 1 parsec = 3.26 light years = 3.086x1016 meter Parallax would be easier to measure if 1) the stars were further away. 2) Earth's orbit were larger. 3) Earth moved backwards along its orbit. 4) none of these. Parallax would be easier to measure if 1) the stars were further away. 2) Earth's orbit were larger. 3) Earth moved backwards along its orbit. 4) none of these. Star A has a parallax angle that is twice that of Star B. What is the relationship between their distances? n Star A is closer than Star B n Star B is closer than Star A n The stars are at the same distance n Not enough information is given Luminosity Luminosity is the total amount of power given off by a star. - Since it s a power, Luminosity is measured in Watts - For convenience, we often refer to the luminosity of a star in terms of the luminosity of the Sun. - Eg, - That star has a luminosity of 22LSun - That galaxy has a luminosity of 2x1012 LSun There is a Big Range of Stellar Luminosities Out there! Star Luminosity (in units of solar Luminosity) Sun 1 Proxima Centauri 0.0006 Rigel (Orion) 70,000 Deneb (Cygnus) 170,000 The Sun radiates an enormous amount of energy (LSun=4 x 1026 Watts). Only about 10-9 of this actually hits the Earth. Yet, the power of sunlight that illuminates a patch of desert 100 km x 100 km is equal to the total power consumption of the US. 4 x 1026 Watts radiated over entire surface 4 x 1026 Watts generated in core ~1017 Watts striking the Earth Recall the inverse square law…. Brightness is different from Luminosity n Luminosity – the total amount of power being released from a star (this is an intrinsic property of the star). n Brightness – the power from that star that actually gets to us. This is the quantity we measure with a telescope. A Star s brightness depends on its distance from us. - there are stars much more luminous than our sun in the sky, however, they are not nearly as bright because they are far away. A star s apparent brightness B = luminosity 4π (distance)2 L = 4π d2 Surface Temperature n We determine a star s surface temperature by examining its blackbody emission (a.k.a. it s continuous spectrum or color) n No information on distance is necessary! n For reference: the Sun s surface (photosphere) temperature is 5,800 K Surface Temperature Another (more accurate) method to measure Temperatures in Stars Using spectra (recall the Fraunhofer spectrum of the Sun): The `dark lines are created when the atoms in the photosphere have energy levels that match the photons that are emitted from the star. 1. They `reveal the composition of the star. 2. The strength of the lines (how `dark they are) depend on the stars surface temperature. Spectral Types For historical reasons, astronomers classify the temperatures of stars on a scale defined by spectral types, called O B A F G K M L T, ranging from the hottest (type O) to the coolest (type M) stars. The Sun has spectral type G2 Stellar Size n Stars are very spherical so we characterize a star s size by its radius. R Stellar Radii vary in size from ~1500xRSun for a large Red Giant to 0.008xRSun for a White Dwarf. Use Temperature and Luminosity to Measure Size A star s luminosity, surface temperature, and size are all related by the Stefan-Boltzmann Law: A refresher: the Stefan-Boltzmann Law L=4πR2 σT4 Luminosity Stellar radius Surface temperature L=4πR2 σT4 Survey Question Two stars have the same surface temperature, but the radius of one is 10 times the radius of the other. The larger star is 1) 10 times more luminous 2) 100 times more luminous 3) 1000 times more luminous 4) 1/10th as luminous 5) 1/100th as luminous L=4πR2 σT4 Survey Question Suppose two stars are at equal distance and have the same radius, but one has a temperature that is twice as great as the other. The luminosity of the hotter star is ____ as the other. 1) 1/2 as great 2) 1/4 as great 3) the same 4) 4 times as great 5) 16 times as great L=4πR2 σT4 Survey Question Suppose two stars are at equal distance and have the same radius, but one has a temperature that is twice as great as the other. The apparent brightness of the hotter star is ____ as the other. 1) 1/2 as great 2) 1/4 as great 3) the same 4) 4 times 5) 16 times as great Stellar Properties Survey Questions 1) Luminosity 2) Radius 3) Surface Temperature Question #1: Which property do we determine by first measuring the star s apparent brightness and distance? Stellar Properties Survey Questions 1) Luminosity 2) Radius 3) Surface Temperature Question #2: Which property do we determine by measuring the wavelength of peak emission (i.e., its color)? Mass: How do you measure the mass of a star? n Mass is the single most important property in determining how a star s life and death will proceed. n We can weigh stars that are in binary systems (two stars orbiting each other). Fortunately, most stars (about 70%) fall into this category. Center of Mass (or Barycenter) n n Stars orbiting each other orbit around their `center of mass or barycenter They behave like children on a seesaw Mb Ma C.M. (center of mass) is where: C.M. Rb Ra Ra Ma= Rb Mb Binary Stars: use the Generalized Kepler s Third Law Star A Ra C.M. Rb - Binary stars are in orbit around each other. - They orbit around their C.M. - Their orbital period depends on their separation and their masses. Generalized Kepler s Third Law Star B (Ma+Mb) P2 = a3 a= (Ra +Rb)/2 Kepler s Third Law G/4π2 Msun P2 = a3 Big P = Small Masses Small P = Big Masses I. Visual Binaries Summary n There are four principal characteristics of a star: – Luminosity (brightness and distance) – Surface Temperature (black-body spectrum) – Size (Stefan-Boltzmann Law) – Mass (generalized Kepler s Third Law) Are these quantities related with each other? Let s recall: Hydrostatic Equilibrium of Stars Thermal Pressure Gravitational Contraction The Stellar Thermostat Outward thermal pressure of core is larger than inward gravitational pressure Core expands Nuclear fusion rate rises dramatically Expanding core cools Contracting core heats up Core contracts Nuclear fusion rate drops dramatically Outward thermal pressure of core drops (and becomes smaller than inward grav. pressure) What happens if we increase the mass of the star? n More mass = more gravitational contraction n = need for more balancing pressure = higher temperature at the center (and on the surface) n Higher temperature = more hydrogen fusion = higher energy production = more luminous Thus… n More massive = n Higher Temperature (bluer color) = n More luminous L ~ M3.5 A star 10 times more massive than the Sun is ~3000 times more luminous! The Hertzsprung-Russell Diagram The Hertzsprung-Russell Diagram The Hertzsprung-Russell Diagram The Main Sequence - all main sequence stars fuse H into He in their cores - this is the defining characteristic of a main sequence star. - more massive stars are more luminous and hotter: L=4πR2 σT4 The Hertzsprung-Russell Diagram L=4πR2 σT4 Red Giants - Red Giant stars are very large, cool and quite bright. Ex. Betelgeuse is 100,000 times more luminous than the Sun but is only 3,500K on the surface. It s radius is 1,000 times that of the Sun. The Hertzsprung-Russell Diagram The Hertzsprung-Russell Diagram White Dwarfs - White Dwarfs are hot but since they are so small, they are not very luminous. L=4πR2 σT4 The Hertzsprung-Russell Diagram Mass of Star Size of Star