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presentsa production STELLAR DISTANCES based on the IB Astrophysics option 1
STELLAR DISTANCESHow far away are stars and galaxies? Parsec Stellar Parallax Spectroscopic parallax Cepheid variables Apparent magnitude Absolute magnitude Image: Carina Nebula by ESO
Measuring distances By observation, we can measure how bright an object appears. In order to calculate the actual magnitudes orluminosities of stars, we must know how far away they are. There are several ways of doing this depending on how great the distance is.
Astronomical units Reminders1 Astronomical unit = 150 million km(average Sun-Earth distance)1 light year = 10 000 billion km(distance light travels in 1 year)
Angle facts360 degrees in a circle60 arc-minutes in adegree60 arc-seconds in anarcminute There are approx. 1.3 million arc-seconds in a full circle
The parsec One parsec = 3.26 light years = 30 000 billion km “Parsec” is short forThe parsec (pc) – this is parallax arc-secondthe distance at which 1AU subtends an angle of 1 arc-second. Nearest star is approx 1.3 pc away
Stellar Parallax The method of measuring distance using the apparent change in position of nearby starsEvery six months, theEarth is at the oppositeside of its orbit and nearbystars shift position relativeto faraway stars. We canmeasure the angle, p.For very small angles, p = angle in arcsectan p ≈ p (angles in R = base in AUrads) d = distance in pc
Measurement of parallaxFor parallax measurementsfrom the Earth, R is 1 AU, so Proxima Centauri subtends a parallax angle of 0.769 arc sec, so its distance is 1/0.77 = 1.30 pc
The limit of parallax The farther awayan object gets, the smaller its shift. A parallax angle of 0.005 arc-sec isEventually, the shift is near the limit of measurability from too small to see. the Earth, which corresponds to a distance of 200 pc. Space telescopes are increasing the range of parallax, but there will always be limits due to the tiny angles involved.
Spectroscopic parallaxThe method of measuring distance using the HR diagram.Absorption spectrum of the starThis may tell us the type of star, eg main sequence, dwarf or giantWien’s lawCalculate the temperature fromthe most intense wavelength Finally, use LH-R diagram and b to find dIdentify the luminosityof the star using thetemperature
The limit of spectroscopic parallax Beyond 10 mega-parsecs (30 million light years), stars are too distant to give enough light to determine the temperature. 11
Cepheid variables The method of measuring distances using stars whose brightness changes predictably Their temperature and luminosity place them here on the HR diagram. A Cepheid variable is avery bright, unstable star which pulsates brighter and dimmer. 12
Cepheid calculationCepheids in another galaxy can be used to measure its distance. The period of the Cepheid variable is related to its luminosity: the brighter it is, the slower it pulses. The graph of log L vs log T is linear. From observing the period, use the graph to find the luminosity (L). From L and apparent brightness (b), find 13 the distance, d.
Different distances require different methods of measurement 14
Apparent magnitude Apparent magnitude (m) assigns a number to an object to describe how bright it appears from Earth Faintest objects areBetelgeuse and Rigel, larger positive numbers stars in Orion withapparent magnitudes 0.3 and 0.9 Brightest objects are smaller positive and even negative numbers
Magnitude scaleEach magnitude corresponds to a factorof 2.5 change in brightness (a log scale)Every 5 magnitudes is a factor of 100 change in brightness 5 b +1 = 2.5 ≈ 100 b +6 1 where b+m is brightness of star magnitude m
Absolute Magnitude (M) The magnitude an object would have if we put it 10 parsecs away from EarthApparent magnitude, m depends on the position of theobject. Absolute Magnitude, M puts them all on thesame scale. For the Sun, m = -26.7 M = +4.8Not forgetting that a bright star has a low magnitude number
Relation of M and m Knowing the apparent magnitude (m) and thedistance in pc (d) of a star, its absolute magnitude (M) can be found using the equation: What is the absolute magnitude of the Sun (m=-26.7)? The distance of Sun from Earth is 1 AU = 4.9x10-6 pc M = -26.7 – 5*log (4.9x10-7)= +4.8
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