Stellar Composition. How do we determine what a star is made of?

Transcription

1 Stars

2 Essential Questions What are stars? What is the apparent visual magnitude of a star? How do we locate stars? How are star classified? How has the telescope changed our understanding of stars?

3 What are Stars?

4 Stars What are they? Stars are great balls of hot gas held together by their own gravity. If stars were not so hot, the gas would collapse into a small dense body.

5 Stellar Composition How do we determine what a star is made of?

6 Spectrograph an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify materials separates an incoming wave into a frequency spectrum

7 Spectral Absorption Lines The fingerprint elements create by allowing some wavelengths to pass while absorbing others Certain elements and molecules show up in a spectrum as absorption when they are heated

8

9 By comparing known absorption spectrum to those produced by a star, we can determine the elements and molecules present in that star

10 The Sun In the visible region of the electromagnetic spectrum, the Sun s s spectrum shows thousands of absorption lines. In studying these absorption lines, 67 elements have been identified in the Sun

11 Solar Elemental Abundances Element Hydrogen Helium Carbon Nitrogen Oxygen Neon Magnesium Silicon Sulfur Iron Number % Mass %

12 Classifying Stars: The Four Basic Characteristics of a Star Luminosity & Magnitude Size Mass Surface Temperature To discover these characteristics, distance to a star must be determined use parallax!

13 Characteristic 1 LUMINOSITY

14 Luminosity Luminosity (absolute magnitude) depends on distance and apparent magnitude Luminosity is the amount of electromagnetic energy a body radiates per unit of time. Luminosity does not depend upon the observer s s perspective

15 Magnitude is the logarithmic measure of the brightness of an object

16 Apparent or Visual Magnitude Is the fraction of energy emitted by a star that eventually reaches some source of detection device Varies with distance, the farther away the star the lower the apparent magnitude. Brighter objects have smaller magnitudes than fainter objects. Visual magnitude depends upon the observer s persepective

17 Development Hipparchus developed a 6 degree scale to define the brightness of stars 1 = brightest 6= just barely visible This scale continues to be used inan expanded form High numbers = fainter stars Negative numbers = brightest objects

18 Absolute Magnitude An object s s apparent magnitude when it is at a distance of 10parsecs from the observer.

19 Comparing Magnitudes A difference of 1 magnitude = a change of brightness of ~2.512 To determine how much brighter one star is then another you Determine the difference in magnitude Use the equation difference

20 Example 1 Star A has an apparent magnitude = 5.4 and star B has an apparent magnitude = 2.4 Which star is brighter and by how many times? Star B is brighter than star A because it has a lower apparent magnitude. Star B is brighter by = 3 magnitudes. In terms of intensity star B is ( ) = = approximately 15.8 times brighter than star A

21 Example 2 The Milky Way has an apparent magnitude of A local quasar has an apparent magnitude of Which is brighter and by how much? The quasar is brighter than the Milky way because it has a lower apparent magnitude. The quasar is brighter by = 5 magnitudes. In terms of intensity quasar is ( ) 20.5) = = approximately 100 times brighter than the Milky Way.

22 Sun = Full Moon = Venus = -4.4 Vega = 0 Deneb = 1.6 Faintest stars visible to naked eye = 6 HST can image a magnitude 30 star This is like detecting a firefly at a distance equal to Earth s diameter

23 I = r 1 2

24 Luminosity Luminosity depends on: 1) size of the star (bigger = more luminous!) 2) distance to the star (closer = more luminous!) 3) intervening matter (dust and gas can absorb light reduces luminosity and increases redness)

25 Calculating Luminosity If we know the distance to the star we can measure luminosity: L = 4πfd4 2 where the distance d to the star (m), the Flux f of the star (W/m 2 ) where flux measures light intensity the luminosity L of the star (Watts) 1 Parsec = meters

26 Example 1: Finding Luminosity What is the luminosity of our Sun which has a flux of 1360 W/m 2 and a distance of parsecs? Step 1: Change distance to m ( = x10 pc)x pc 11 m 16 m

27 Step 2: L = 4πfd4 2 L = 4π 4 (1360)( x L = 3.82 x Watts 11 ) 2

28 Luminosity By definition (using more accurate measurements): Lsun = 3.9 x W However, we can measure astronomical luminosity in Solar luminosity units, where Lsun = 1 Solar luminosity unit Solar luminosity units = L

29 Example 2: Changing into Solar Luminosity Units If a star has a luminosity of 1.3 x Watts, what is its luminosity in Solar luminosity units? Lstar = ( L = units 1Solar luminosityunit Watts) Watts

30 There is a Big Range of Stellar Luminosities Out there! Luminosity (in Star units of solar Luminosity) Sun 1 Proxima Centauri Rigel (Orion) 70,000 Deneb (Cygnus) 170,000

31 Example 3: Finding Distance from Luminosity You have a 100 W lightbulb in your laboratory. Standing at a distance of d from the lightbulb,, you measure flux of the lightbulb to be 0.1 W/m 2. How can you use this information to determine the distance from you to the lightbulb?

32 1) Rearrange d 2 = 4 L π f 2) Sub in values d 2 = 4 * 100 π * 0.1 d 2 = ) Solve for d d d = =

33 Luminosity The luminosity of stars ranges from 1*10-4 L to 1*10 6 L The Sun is not nearly as bright as the most luminous stars but is brighter than most stars. The Sun is gradually becoming more luminous (about 10% every 1 billion years). The Sun used to be fainter in the past, which is possibly the reason life on Earth has only existed for about 1 billion years on land.

34 The brightness of a visible star depends on both its luminosity and its distance. If brightness and distance are measured, luminosity can be calculated.

35 Characteristic 2 SIZE!

36 Stellar Size Stars are very spherical so we characterize a star s s size by its radius. We always compare to our Sun! R Stellar Radii vary in size from ~1500 R for a large Red Giant to R for a White Dwarf.

37 Examples Our Sun has a radius of 696,000Km A white dwarf has a radius of 0.01 R A dwarf star has a radius of 1 R A giant star has a radius of 10 A giant star has a radius of R 100 R A super giant has a radius of >100 R A super giant has a radius of >100 R

38 Size Equation L = 4πR4 2 s T 4, Where L is the luminosity in Watts R is the radius in meters s is the Stefan-Boltzmann constant 5.67x10 8 W 2 m K 4 T is the star's surface temperature in Kelvin NOTE: R is often given in Solar radii (radius of Sun)

39 Alternate Size Equation The luminosity-temperature temperature-radius radius relationship R = (L/4πθ)*(1/T 2 ) Where.. L = luminosity θ is a constant T is the surface temperature

40 Example 1 Find the Luminosity of Zeta Puppis which has a temperature of about 38,000 K and a radius of 18 R. R Then change this into Solar luminosity units. Step 1: Change units R = 18 x (6.955 x 10 8 m) = x m Step 2: Plug into equation L = 4πR4 2 s T 4 L = 4π( x ) 2 (5.67 x 10-8 ) (25000) 4 L = x W L = 597,038 L L

41 Example 2 Find the radius of a new star, VTURN, that has a luminosity of 5Lo and a temperature of 25,000K. Step 1: Change units R 5Lo x (3.9 x Watts/1Lo) = 1.95 x Step 2: Rearrange equation L = 4πR4 2 s T 4 R R = = = L 4πsT x10 4π 8 (5.67x10 )(25000) m 4

42 Characteristic 3 MASS!

43 Mass Stars fall into a narrow mass range because below 0.08 Solar masses, nuclear reactions cannot be sustained AND greater than 100 Solar masses stars are unstable. High mass stars burn their fuel at higher rates and live shorter lives than low-mass stars.

44 How do you weigh a star? By observing the star and anything that orbits it (maybe even another star) Use Doppler/Red shift to measure Use Kepler s Laws of Planetary Motion and Newton s s Law of Gravitation to determine mass

45 Doppler/Red Shift Red shift occurs when an object is moving away from the observer. Blue shift occurs when an object is moving towards the observer.

46 Doppler/Red Shift cont d Use the modified version of Kepler s 3 rd Law P 2 = 4π4 2 A 3 /G(m 1 +m 2 ) Rearrange: m 1 +m 2 =(4π 2 /G) (A 3 /P 2 ) (4π 2 /G) can be ignored as they never change m 1 (M )+m 2 (M ) =A 3 /P 2 Do Foundation 12.2 Worksheet

47 Formula A metric version of Kepler s Law! M = 4 ( GP 2 π 2 ) a 3 N Where: M = mass of star in kg N = mass of planet in kg a =distance from star to planet in m (average) G = gravitational constant ( m 3 kg - 1 s - 2 ) P = period of the orbit in seconds

48 What do I have to know? How to change from a mass in kg to a mass in Solar mass units Change 15 Mo into kg. Change 1.52 x kg into Mo.

49 Mass is important in determining the fate of the star and its life span Most stars travel in pairs called binary stars Binary stars orbit one another Using the orbital period, the size of the orbit, and Kepler s Third Law we can calculate the combined mass of both stars.

50 Characteristic 4 SURFACE TEMPERATURE

51 The Sun Although nuclear fusion needs heat of 1.5 x 10 7 K (core), the surface temperature of the Sun is about 5,700 K. The temperature of stars are between 3,000K to 30,000 K.

52 How do you measure the surface temperature of a star? Every element (when heated) will emit lines that lie along the visible light spectrum a.k.a. R-O-Y-G-B-I-VR Stars are mostly composed of hydrogen (and some helium)

53 b B / b V colour Brightness is measured through a filter Blue filter transmits light with wavelengths around 0.44µm Visual filter or yellow-green filter transmits light with wavelengths around 0.55µm Determine the ratio of brightness of a star as viewed through each filter b B / b V brightness through blue filter/ brightness through visual filter >1 = hot stars, <1 = cool stars Sun = 0.56, Vega = 1

54 A star s b B /b V colour depends on its temperature. The Plank spectra shown here are adjusted so they have the same brightness at 0.55 microns.

55 Example Star Temperatures Blue stars = 20,000K Yellow-white white star = 7,000K Yellow star = 6,000K Orange = 4,000K Red = 3,000K

56 Stefan-Boltzmann Law Hotter and the same size means more luminous Each square meter of the surface of a hot, blue star gives off more radiation than a square meter of the surface of a cool, red star Energy radiated each second by 1 m 2 of surface =θt= 4 Θ = a constant T = temperature

57 Stefan-Boltzmann Law cont d Total energy radiated by the star/second = (energy radiated by a m 2 /second)(# of m 2 of the star s s surface) J/s or L = [J/(m 2 /s)][4πr 2 ] L = θt 4 [4πR 2 ] Because 4, π,, and θ do not change L = T 4 R 2

58 Examples of Stefan-Boltzmann Law If a star is 3x as large as another 3 2 = 9, it has 9x the surface area If a star is 2x as hot as another 2 4 = 16, it has 16x as much energy

59 Wien s s Law Hotter means bluer T= 2,900µmK mk/ λpeak Λpeak = the wavelength at which the electromagnetic radiation from a star is most intense

60 The temperature and size of stars are measured by applying our understanding of Planck radiation.

61 Size Mass Taking the Measure of Stars Summary Property Distance Luminosity Temperature Composition Method Measure the parallax of the star over the course of the year For a star with a known distance, measure the brightness, then apply the inverse square law of radiation [L=(4πd 2 )(brightness)] Measure the colour of the star using the b B /b V or from the star s s spectrum Use Wien s s Law to relate the colour to a temperature For a star with a known luminosity and temperature, use Stefan s s Law Measure the motions of the stars in a binary system, use these to determine the orbits of the stars, then apply Newton s s form of Kepler s 3 rd Law Knowing the temperature of a star, analyze the lines in its spectrum to measure chemical composition

62 How do we locate stars?

63 Declination: : one of the two coordinates of the equatorial coordinate system. Comparable to Latitude. Expressed as an angle with respect to the celestial equator.

64 Declination Declination is measured in terms of the Celestial Equator The zenith is the direction pointing directly "above" a particular location A celestial object that passes over zenith has a declination equal to the observer's latitude.

65 Declination An object on the celestial equator has a declination of 0. 0 An object at the celestial north pole has a declination of +90 (North Star). An object at the celestial south pole has a declination of 90 (Southern Cross).

66 Declination A pole star therefore has the declination near to +90 or 90. Your latitude on Earth determines how much of the Southern or Northern sky you can see The Celestial Equator for us is = 45 latitude

67 Right Ascension: : a celestial longitude measured in the direction of the Earth s rotation. The notation adopted for right ascension is in terms of hours and minutes with 24 hours representing the full circle. The left-right coordinates.

68 Right Ascension Since the Earth is rotating constantly, the Right Ascension "value" changes continuously - every minute of the night. It also changes every day of the year as Earth goes around the Sun. We start this numbering system at the Vernal Equinox - i.e. the point in the sky where the Sun was at the time of the Spring Equinox. From that specific point on the Celestial Equator, they simply numbered the "hours" 0, 1, 2, 3, and so on up to 22, 23, and 24 was made the same as the 0 line. These are numbered East (i.e. to the left) to West (Sun rises in East and sets in West).

69 Circumpolar star: : a star that as viewed from a given latitude on Earth, never disappears below the horizon, due to its proximity to one of the celestial poles. Visible for the entire night (and throughout the day if it wasn t t for the sun s s glare) every night of the year.

70 Stellar Movement Based on 3 dimensions Transverse component Radial component Actual motion

71 Transverse Component Is perpendicular to our line of sight Is movement across the sky Can be measured by carefully comparing photographs of a given piece of sky taken at different times and measuring the angle of displacement of 1 star relative to the background stars (in arcsecond) A star s s distance can be used to translate the angular proper motion into a transverse velocity in km/s

72 Radial Component Is movement toward or away from the observer Is measured from the Doppler Shift apparent in a star s s spectrum Study the spectrum of the target star The frequencies of particular absorption lines are known if the source is at rest If the star is moving toward or away from us the lines will get shifted A fast moving star s s lines will be shifted more than a slow- moving one

73 Actual Motion Calculated by combining the transverse and radial components