Presentation on theme: "OPTION E - ASTROPHYSICS E3 Stellar distances Parallax method"— Presentation transcript:
1OPTION E - ASTROPHYSICS E3 Stellar distances Parallax method
2Astronomical distances – recap The SI unit for length, the metre, is a very small unit to measure astronomical distances. There units usually used is astronomy:The Astronomical Unit (AU) – this is the average distance between the Earth and the Sun. This unit is more used within the Solar System.1 AU = kmor1 AU = 1.5x1011m
3Astronomical distances – recap The light year (ly) – this is the distance travelled by the light in one year.c = 3x108 m/st = 1 year = x 24 x 60 x 60= 3.16 x 107 sSpeed =Distance / TimeDistance = Speed x Time= 3x108 x 3.16 x 107 = 9.46 x 1015 m1 ly = 9.46x1015 m
4E3 - Stellar distancesE.3.1 Define the parsec.The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond.“Parsec” is short forparallax arcsecond1 pc = 3.086x1016 mor1 pc = 3.26 ly
5(206,000 times further than the Earth is from the Sun) E3 - Stellar distances1 parsec = X 1016 metresNearest Star1.3 pc(206,000 times further than the Earth is from the Sun)
6E3 - Stellar distancesE.3.2 Describe the stellar parallax method of determining the distance to a star.Bjork’s EyesSpaceWhere star/ball appears relative to backgroundAngle star/ball appears to shiftDistance to star/ball“Baseline”
7E.3.2 Describe the stellar parallax method of determining the distance to a star. Parallax, more accurately motion parallax, is the change of angular position of two observations of a single object relative to each other as seen by an observer, caused by the motion of the observer.Simply put, it is the apparent shift of an object against the background that is caused by a change in the observer's position over a period of 6 months.
8E3 - Stellar distancesE.3.2 Describe the stellar parallax method of determining the distance to a star.We know how big the Earth’s orbit is, we measure the shift (parallax), and then we get the distance…Parallax - p(Angle)Distance to Star - dBaseline – R(Earth’s orbit)
9E3 - Stellar distancesE.3.2 Describe the stellar parallax method of determining the distance to a star.For very small angles tan p ≈ pIn conventional units it means that
10E3 - Stellar distancesE.3.2 Describe the stellar parallax method of determining the distance to a star.
11Angular sizes 360 degrees (360o) in a circle E3 - Stellar distancesAngular sizes360 degrees (360o) in a circle60 arcminutes (60’) in a degree60 arcseconds (60”) in an arcminute
12E3 - Stellar distancesE.3.3 Explain why the method of stellar parallax is limited to measuring stellar distances less than several hundred parsecs.The farther away an object gets, the smaller its shift.Eventually, the shift is too small to see.Measurements from Earth only allow distances up to 300ly, or roughly 100pc, to be determined with the parallax method.With satellites, distances of around 500 pc can be determined.
13How Do We Measure the Distance to Stars? - Instant Egghead #46 https://www.youtube.com/watch?v=vyiauRjJBNQ
14Go to Option E – Astrophysics SL worksheet E.3.4 Solve problems involving stellar parallax.Go to Option E – Astrophysics SL worksheet
15OPTION E - ASTROPHYSICS E3 Stellar distances OPTION E - ASTROPHYSICS E3 Stellar distances Absolute and apparent magnitudes
16Another thing we can figure out about stars is their colours… E3 - Stellar distancesE.3.5 Describe the apparent magnitude scale.Another thing we can figure out about stars is their colours…We’ve figured out brightness, but stars don’t put out an equal amount of all light……some put out more blue light, while others put out more red light!
17E3 - Stellar distancesE.3.5 Describe the apparent magnitude scale.Usually, what we know is how bright the star looks to us here on Earth…We call this its Apparent Magnitude“What you see is what you get…”
18Betelgeuse and Rigel, stars in Orion with apparent magnitudes E3 - Stellar distancesE.3.5 Describe the apparent magnitude scale.Magnitudes are a way of assigning a number to a star so we know how bright it isSimilar to how the Richter scale assigns a number to the strength of an earthquakeBetelgeuse and Rigel, stars in Orion with apparent magnitudes0.3 and 0.9This is the “8.9” earthquake off of Sumatra
19The historical magnitude scale… E3 - Stellar distancesThe historical magnitude scale…Greeks ordered the stars in the sky from brightest to faintest……so brighter stars have smaller magnitudes.MagnitudeDescription1stThe 20 brightest stars2ndstars less bright than the 20 brightest3rdand so on...4thgetting dimmer each time5thand more in each group, until6ththe dimmest stars (depending on your eyesight)
20Later, astronomers quantified this system. E3 - Stellar distancesLater, astronomers quantified this system.Because stars have such a wide range in brightness, magnitudes are on a “log scale”Every one magnitude corresponds to a factor of 2.5 change in brightnessEvery 5 magnitudes is a factor of 100 change in brightness(because (2.5)5 = 2.5 x 2.5 x 2.5 x 2.5 x 2.5 = 100)
21Brighter = Smaller magnitudes Fainter = Bigger magnitudes E3 - Stellar distancesBrighter = Smaller magnitudes Fainter = Bigger magnitudesMagnitudes can even be negative for really bright objects!ObjectApparent MagnitudeThe Sun-26.8Full Moon-12.6Venus (at brightest)-4.4Sirius (brightest star)-1.5Faintest naked eye stars6 to 7Faintest star visible from Earth telescopes~25
22𝑏 𝑏 0 = 2.512 −𝑚 E.3.5 Describe the apparent magnitude scale. E3 - Stellar distancesE.3.5 Describe the apparent magnitude scale.Given a star of apparent brightness b, we assign that start and apparent magnitude m defined by:𝑏 𝑏 0 = 100 −𝑚 5Where 𝑏 0 =2.52× 10 −8 𝑊 𝑚 −2 is taken as the reference value for apparent brightnessOr:𝑚=− 5 2 𝑙𝑜𝑔 𝑏 𝑏 0The first equation can also be re-written as:𝑏 𝑏 0 = −𝑚
23E3 - Stellar distancesE.3.6 Define absolute magnitude.However: knowing how bright a star looks doesn’t really tell us anything about the star itself!We’d really like to know things that are intrinsic properties of the star like: Luminosity (energy output) and Temperature
24…we need to know its distance! E3 - Stellar distancesE.3.6 Define absolute magnitude.In order to get from how bright something looks…to how much energy it’s putting out……we need to know its distance!
25Absolute Magnitude (M): E3 - Stellar distancesE.3.6 Define absolute magnitude.The whole point of knowing the distance using the parallax method is to figure out luminosity…Once we have both brightness and distance, we can do that!It is often helpful to put luminosity on the magnitude scale…Absolute Magnitude (M):The magnitude an object would have if we put it 10 parsecs away from Earth
26Absolute Magnitude (M) E3 - Stellar distancesE.3.6 Define absolute magnitude.Absolute Magnitude (M)removes the effect of distance and puts stars on a common scaleThe Sun is in apparent magnitude, but would be 4.4 if we moved it far awayAldebaran is farther than 10pc, so it’s absolute magnitude is brighter than its apparent magnitudeRemember magnitude scale is “backwards”
27Absolute Magnitude (M) E3 - Stellar distancesAbsolute Magnitude (M)Knowing the apparent magnitude (m) and the distance in pc (d) of a star its absolute magnitude (M) can be found using the following equation:Example: Find the absolute magnitude of the Sun.The apparent magnitude is -26.7The distance of the Sun from the Earth is 1 AU = 4.9x10-6 pcTherefore, M= – log (4.9x10-6) + 5 == +4.8
28So we have three ways of talking about brightness: E3 - Stellar distancesSo we have three ways of talking about brightness:Apparent Magnitude - How bright a star looks from EarthLuminosity - How much energy a star puts out per secondAbsolute Magnitude - How bright a star would look if it was 10 parsecs away
29E.3.7 Solve problems involving apparent magnitude, absolute magnitude and distance. E.3.8 Solve problems involving apparent brightness and apparent magnitude.
30OPTION E - ASTROPHYSICS E3 Stellar distances Spectroscopic parallax
31E.3.9 State that the luminosity of a star may be estimated from its spectrum. Spectroscopic parallax is an astronomical method for measuring the distances to stars.Despite its name, it does not rely on the apparent change in the position of the star.This technique can be applied to any main sequence star for which a spectrum can be recorded.
32E.3.10 Explain how stellar distance may be determined using apparent brightness and luminosity. The Luminosity of a star can be found using an absorption spectrum.Using its spectrum a star can be placed in a spectral class.Also the star’s surface temperature can determined from its spectrum (Wien’s law)Using the H-R diagram and knowing both temperature and spectral class of the star, its luminosity can be found.
33E.3.11 State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc.E.3.12 Solve problems involving stellar distances, apparent brightness and luminosity.
34Distance measurement by parallax apparent brightness spectrum Distance measured by parallax:Distance measurement by parallaxapparent brightnessspectrumChemical composition of coronaWien’s Law (surface temperature T)LuminosityL = 4πd2 bd = 1 / pL = 4πR2 σT4Stefan-BoltzmannRadius
35OPTION E - ASTROPHYSICS E3 Stellar distances Cepheid variables
36E.3.13 Outline the nature of a Cepheid variable. Cepheid variablesCepheid variables are stars of variable luminosity.The luminosity increases sharply and falls of gently with a well-defined period.The period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star.A Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity.The luminosity of Cepheid stars range from 103 to 104 times that of the Sun.
37E.3.14 State the relationship between period and absolute magnitude for Cepheid variables. The relationship between a Cepheid variable's luminosity and variability period is quite precise, and has been used as a standard candle (astronomical object that has a known luminosity) for almost a century.This connection was discovered in 1912 by Henrietta Swan Leavitt. She measured the brightness of hundreds of Cepheid variables and discovered a distinct period-luminosity relationship.
39E.3.14 State the relationship between period and absolute magnitude for Cepheid variables. A three-day period Cepheid has a luminosity of about 800 times that of the Sun.A thirty-day period Cepheid is 10,000 times as bright as the Sun.The scale has been calibrated using nearby Cepheid stars, for which the distance was already known.This high luminosity, and the precision with which their distance can be estimated, makes Cepheid stars the ideal standard candle to measure the distance of clusters and external galaxies.
40E.3.14 State the relationship between period and absolute magnitude for Cepheid variables.
41E.3.15 Explain how Cepheid variables may be used as “standard candles”. The luminosity of a Cepheid variable can be determined from its period.The brightness of the Cepheid (b) can be determined from its apparent magnitude.Then, from the relationship𝒃= 𝑳 𝟒𝝅 𝒅 𝟐the distance to the Cepheid can be determined.If a Cepheid variable is located in a particular galaxy, then the distance to the galaxy may be determined.The Cepheids method can be used to find distances up to a few Mpc.
42Surface temperature (T) E.3.16 Determine the distance to a Cepheid variable using the luminosity–period relationship.Distance measured by spectroscopic parallax / Cepheid variables:Apparent brightnessLuminosity classspectrumChemical compositionCepheid variableSpectral typeH-R diagramSurface temperature (T)Wien’s LawPeriodLuminosity (L)Stefan-BoltzmannL = 4πR2 σT4b = L / 4πd2Distance (d)Radius