Presentation on theme: "Chapter 11 Stars Properties of Stars Classifying Stars"— Presentation transcript:
1Chapter 11 Stars Properties of Stars Classifying Stars Hertzsprung-Russel (H-R) DiagramStar ClustersOpen and Globular Clusters
2Properties of StarsMass – The single most important property that determines other properties of the star.Luminosity – The total amount of energy (light) that a star emits into space.Temperature – surface temperature, closely related to the luminosity and color of the star.Spectral type – closely related to the surface temperatureSize – together with temperature determine the luminosity
3What can we measure directly? The Easy Ones:Apparent brightness: a well-calibrated detector.Temperature: spectroscopySpectral type: spectroscopyThe Hard ones:Distance: stellar parallax, but the stars are so farrrrr away…Size: The stars are so far away. Their small angular size makes it really difficult to be measured directly.Mass: Newton’s version of Kepler’s Third LawNeed to find the right targets
4The Apparent Brightness The brightness of the a star as it appears to our eyes (or detectors).It depends on both the luminosity AND distance between the star and the Earth.The apparent brightness of a star is related to its luminosity and distance by the formula:The total energy in this cone is fixed…At a larger distance from the star, the same amount of energy is spread into a larger area. Thus, the apparent brightness of a star is lower if we are further away from it.
5The Magnitude SystemApparent magnitude describes the relative brightness of objects as they appears in sky.A difference of 5 magnitudes is equivalent to a factor of 100 difference in apparent brightness. 1st magnitude star is 100 times brighter than a 6th magnitude star.A difference of one magnitude is a factor of 2.51 difference in brightness.The larger the magnitude, the fainter the objectObjects with negative magnitude appear brighter than objects with positive apparent magnitude.Apparent magnitude mv of selected objects :The brightest star in the in night time sky, Sirius, is mv = -1.4The Sun: mv = -27The full Moon is -13Maximum brightness ofVenus: mv = -4.7Mars: mv = -2.9Jupiter: mv = -2.8Large Magellantic Cloud: mv = 0.9Andromeda galaxy: mv = 4.3Faintest star visible to human eyes: mv = 6
6The Absolute Magnitude A star’s absolute magnitude Mv is the apparent magnitude it would have if it were at a distance of 10 parsecs (32.6 light-years) from Earth.The Sun’s absolute magnitude is Mv = 4.8Sirius: Mv = +1.4Betelgeuse: Mv = -5.1Apparent magnitude tells us nothing about the luminosity of the objects, but it tell us how difficult it is to see the objects in the sky.Absolute magnitude, on the other hand, is directly related to the luminosity of the object. But it does not tell us how bright they appear in the sky.Astronomical Distance
7Measuring the Temperature of Stars Everything with a temperature emit thermal radiation. We can measure the temperature of the stars or any object by studying the shape of their overall spectra.Black BodyAn idealized perfect light absorber that absorbs all the photons that strikes it (no reflection). It re-emits the absorbed energy through thermal radiation, with a spectrum characterized by the blackbody spectrum.The shape of the blackbody spectrum is always the same, independent of its temperature.The peak position (in wavelength) of the blackbody spectrum depends only on the temperature, independent of the blackbody’s composition, or size, etc.
8Spectral Type of StarsSpectral type is closely related to temperature
9Spectral Type and Temperature The spectral features of the stars are closely related to the surface temperature of the star because the formation of ionized atoms, the excitation state of the atoms, and the existence of molecules in the stellar atmosphere strongly depends on the temperatureHigh temperature Ionized atomsMedium temperature Neutral atomsLow temperature Molecules
10Determination of Distance Stellar ParallaxKnowledge of the distance to the stars is crucial for our determination of the luminosity of stars…Current technology allows us to determine the distance accurately to within a few hundred light-years.Hipparcos mission (European Space Agency) measured the stellar parallax of roughly 100,000 stars with precision of a few milli-arcseconds. So, it can measure distance of star up to 1,000 light-years away…Simulation of Stellar Parallax…
11Astronomical Distance Units Light-year:The distance light travels (in vacuum) in one year.one light-year is 10 trillion (1013) kmParsec: parallax & arcsecondOne parsec: the distance to an object with a parallax angle of 1 arcsecond.One parsec equals to 3.26 light-year.kiloparsecs: 1,000 parsecs.megaparsecs: 1,000,000 parsec.Absolute Magnitude
12Determination of Stellar Mass Mass is the single most important property of a star. But it is also difficult to measure…The most dependable method we have for measuring the mass of distant stars is Newton’s version of Kepler’s Third Law of orbital motion (Problem 33, Chapter 4).Recall thatSo, if we can findtwo stars (binary star system) orbiting each other, andif we can measure theirrotational period p, andsemi-axis a of the orbit,then we can determine their masses.
13Binary Star SystemsBinary star systems are formed by two stars that are gravitationally bounded, and they orbit each other.About 50% of the stars are in binary star system. There are three categories of binary star systems:Visual Binary: a pair of stars that we can see distinctly (with a telescope) as the stars orbit each other.Eclipsing Binary: is a pair of stars that orbit in the plane of our line of sight. The stars are not resolved, but we can see the effects of the stars blocking each other in their combined light-curve.Spectroscopic Binary: in some binary system, we cannot see the two stars, nor can we see their light curve changes, but we can see the motion of the stars from Doppler effect measurement of the spectra.BCenter of massATrue Binary Star System
14Binary Star SystemsTwo stars appearing close to each other in the sky do not necessarily means that they are a binary system.BLine-of-SightAIf A and B are notgravitationally bounded with each other, then, although they may appears to be very close in the sky, they do not constitute a binary system!AB
15Visual Binary – SiriusSirius (in constellation Canis Major) is the brightest star in the night-time sky (magnitude -1.4). It is a visual binary system. Sirius A (the larger of the two) is a main sequence star with spectral type A0, and Sirius B is a white dwarf.Hubble Space Telescope image ofSiriusSirius A & B time sequenceWhite Dwarf
16Eclipsing BinaryAbout 50% of the stars are in binary star system. There are three categories of binary star systems:Eclipsing Binary: is a pair of stars that orbit in the plane of our line of sight, (measuring the time curve)Animations source:
17Algol – Eclipsing Binary Algol (the demon star) is in the constellation of Perseus.Algol A: main sequence star, more massive.Algol B: subgiant, less massive.The Algol Paradox:Why is the more massive Algol A evolve slower than the less massive Algol B? (Next chapter).
18Spectroscopic BinarySometimes only the spectrum from one star is seen, the other star is too dim.Sometimes two sets of spectra can be seen at the same timeSometimes more than two sets of spectra can be seenMizar is a visual binary system in the constellation of Big Dipper.Each ‘star’ in the visual binary system is also a spectroscopic binary!
19Eclipsing Binary and Stellar Mass Measurements Among the three types of binary star systems, the eclipsing binary system is most important for the determination of stellar mass, becauseDetermination of the stellar mass requires knowledge of the orbital period and distance (in real distance unit, not in angular separation).Orbital period is easy to measure, but distance between the stars is difficult to determine.For visual binary, we need to know the distance from Earth to the stars before we can determine the separation between the stars in the binary system.For spectroscopic binary, we can calculate the separation between the stars if we know their orbital speed. However, we can only determine the line-of-sight speed of the binary system from Doppler measurement. If the orbits are tilted with respect to our line-of-sight, then we under estimate the orbital speed.If an eclipsing binary is also a spectroscopic binary, then we know its true orbital speed, and can determine the separation between the two stars. Then, the masses of the stars can be determined!
20LuminosityTo directly measure the luminosity of a star (let’s say, the Sun), we will need to surround the Sun completely with detectors, which is impossible.We can infer the luminosity of the Sun if we knowthe distance to the star, andthe star’s apparent brightnessFurther more, we need to assume thatthe star emits energy uniformly in all direction…Then we can calculate its luminosity by the formula:dThe total area of the sphere with a radius of r is 4d2
21Quiz: Which Star Has Higher Luminosity? Apparent Brightness BDistance dA101BThe apparent brightness decrease as d 2The brightness of star A is 10 × 1 = 10The brightness of star B is 1 × 102 = 100 if observed at distance 1 Star B is 10 times more luminous than A!The photons contained in box A are spread into an area 4 times as large in box Y which is twice the distance from the star as X.XY
23Luminosity and Distance — Chicken and Egg Most of the time, we need measurement of distance to calculate the luminosity. Howver, if we can determine the luminosity of an object with other methods (independent of distance measurement, such as the luminosity of supernovae), then we can derive the distance to the object from measurement of their apparent brightness.
24Direct Measurement of the Size of the Stars Except for the Sun, all the stars in the sky are very far away, and their angular sizes (the size of the star as it appears to observers on Earth, not the physical size) are all very small. Although the theoretical resolving power of modern large telescopes (such as the Keck telescope with 10-meter aperture) is about 0.01 arcseconds in the visible wavelength, it is difficult to realize the full resolution of the large telescopes due to atmospheric seeing effects.Interferometry have directly measure the angular size of stars. Direct measurement by interferometry can achieve about 0.01 arcseconds angular resolution.The angular size of Betelgeuse was first observed using interferometry in 1921…0.051 arcseconds.R Doradus (in constellation Dorado in the southern hemisphere) is the star with the largest observed angular size: arcseconds.0.057 arcseconds is equal to degrees!If we know the angular size and the distance of a star, we can derive its physical sizeSize of star = angular size [radian] distance
25Optical Interferometry The technique of combining images from multiple telescopes to obtain very high resolution images…Recall that the resolving power of telescopes is fundamentally limited by the size of the telescope.However, it is not necessary to build a single telescope with sufficient size to achieve the required resolution. Theoretically, multiple small telescopes separated by a large distance can achieve the same resolution of that of a single large telescope.The two 10-meter Keck Telescopes at Mauna Kea are separated by 85 meters distance. When they are used together as an interferometer, the theoretical resolution is equivalent to that of a single 85-meter diameter telescope.Interferometry is routinely used for observation in radio frequency.
26Betelgeuse and R Doradus The physical size of Betelgeuse (a red supergiant) is roughly 500 times the size of the Sun, or 4.6 AU (radius of 2.3 AU, or 345 million km).The size of R Doradus (a red giant) is 370 times the size of the Sun, or 3.4 AU (radius of 1.7 AU).If R Doradus or Betelgeuse are placed at the center of our solar system, then their surface would extends beyond the orbit of Mars (1.5 AU, or 225 million km).Image of hot spots on Betelgeuse fromusing interferometric technique.Giants and Supergiants
27Indirect Determination of the Size of Stars Since the stars are so far away, we can only directly measure the angular size of just about 10 stars by interferometric technique so far. However,if we know the luminosity (from apparent brightness and distance measurements) and the temperature of the stars, then we can calculate their physical size:Assuming that stars are blackbodyThe energy output of a unit surface area on the surface of the star is determined by its temperature (Stefan-Boltzman Law)The total energy output (luminosity) therefore depends on the temperature and its total surface area, which is related to its size.where r is the radius of the star.We can then calculate the size of the star by
28Properties of Stars: Summary Mass range: 0.08 Msun to 100 MsunLuminosity range: Lsun to 1,000,000 LsunSize range: 0.01 Rsun for white dwarf to 1,000 Rsun for supergiants.Temperature range: 3,000 K for M star to 40,000 for O stars.
29Properties of StarsClassifying StarsSpectral Type and Luminosity ClassHertzsprung-Russel (H-R) DiagramMain Sequence StarsGiants and SupergiantsWhite DwarfStar ClustersOpen and Globular Clusters
30Clues to Relationships Between the Properties of Stars General trends of the stars…Most of the very brightest stars are reddish in color.If we ignore those relatively few bright red stars, there’s a general trend to the luminosities and colors among all the rest of the stars:The brighter ones are white with a little bit of blue tint,the more modest ones are similar to our Sun in color with a yellowish white tint, andthe dimmest ones are barely visible specks of red.
31Hertzsprung-Russell Diagram Sizes scale1 Rsun10 Rsun100 Rsun1000 RsunSince there appears to be a strong correlation between luminosity and color (temperature), we put all the stars on a Luminosity – Temperature plot, and this is what it looks like:Properties of Stars shown in the H-R Diagram:Luminosity (log scale).Temperature and spectral typeSizeMass of the main sequenceLifetime
32Hertzsprung-Russell Diagram Sizes scale1 Rsun10 Rsun100 Rsun1000 RsunNotice that…Temperature scale decreases from left to right.The scale of luminosity is in power of 10 (log scale).Mass increases from lower right to upper leftSize increases from lower left to upper right.
33Classification of Stars in H-R Diagram Sizes scale1 Rsun10 Rsun100 Rsun1000 RsunThe Main Sequence starshealthy stars, fusing hydrogen in the core.High-mass, high-luminosity, high-temperature, and short-lived stars on the upper-left-hand cornerLow-mass, low-luminosity, low-temperature, and long-lived stars on the lower-right-hand cornerThe Supergiants,The Giants,Supergiants and giants are dying stars, fusing helium and heavier elements.The White Dwarfs.dead stars, exposed core of dead main-sequence stars.
34Classification of Stars Full classification of stars includes both spectral type and luminosity class:Spectral type: OBAFGKMLuminosity Class in descending order:I: SupergiantsII: Bright giantsIII: GiantsIV: SubgiantsV: Main-sequence starsThe full classification of a star includes both a spectral type and a luminosity class:The Sun is a G2 VProxima Centauri is M5 VBetelgeuse is M2 ISirius A: A1 VSirius B: DA2 V