Astronomy test 3 summary PDF

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Study Guide for Test #3 Dr. J. R. Webb Stellar Astronomy Chapter 17. The Nature of Stars. 17-1 careful measurements of the parallaxes of stars reveal their distances: stellar parallax – apparent motion of stars caused by earths orbital motion around the sun. (the direction from earth to a nearby star changes as our planet orbits the sun, and the nearby star appears to move back and forth against the background of more distant stars). The distance d(parsecs) = 1./parallax angle in arc seconds. Closest other star – proxima Centauri – p = 0”.75 ~ 20 parsecs. Luminosity – The energy output per unit time. (how much energy the stars emit into space per second. (caused by the thermonuclear reaction occurring within the star) Parallax and the distances of stars: Parallax: is the apparent displacement of an object because of change in the observers point of view. – the closer the object is that you are viewing, the greater the parallax shift. 17-2 if a stars distance is known, its luminosity can be determined from its apparent brightness suns luminosity: 3.90 x 1026 W Brightness (b): the amount of energy that passes each second through a square meter of the sphere’s surface area. Brightness is the total luminosity of the source (L) divided by the total surface area of the sphere (equal to 4 d2) -> apparent brightness -> how bright a light source appears depends on how far away it is being observed. Brightness is measeard in Watts/Square meter2

the apparent brightness of light that an observer can see or measure is inversely proportional to the square of the observer’s distance (d) from the source Photometry: when astronomers measure the apparent brightness of a star

We can determine the luminosity of a star from its distance and apparent brightness. For a given distance, the brighter the star, the more luminous that star must be. For a given apparent brightness, the more distant the star, the more luminous it must be to be seen at that distance. 17-3 astronomers often use the magnitude scale to denote brightness

magnitude scale: denote the brightness of stars introduced by Hipparchus who called the brightest stars = 1st magnitude stars and dimmest 6th magnitude stars. Apparent magnitude (m)– How bright an object appears to be to an observer. If the change in magnitude, M , is 1, then the difference in brightness B, is 2.512.  In general, B = (2.512)M (e.g. M = 5, B = (2.512)5 = 100) Absolute Magnitude (M) - The magnitude a star would be if it were exactly 10 parsecs away. M = m–5log(d) +5, where d is the distance in parsecs. (Note: The Sun’s apparent magnitude from Earth is –26.5, its apparent brightness would be +4.8 if it were 10 parsecs from Earth, thus its absolute magnitude is +4.8. 17-4 a stars color depends on its surface temperature stars come in different colors even viewed with the naked eye. You can see the reddish in Betelgeuse and the blue tint in Bellatrix. - Colors are more evident for the brightest stars, because human color vision works poorly at low light levels. Magnitude difference related to brightness ratio M2 – M1 = 2.5 log (b1/b2)

M 1+ 2 = apparent magnitudes of stars 1 + 2 B 1 + 2 = apparent brightness of stars 1 + 2 Relation between a stars apparent magnitude and absolute magnitude: m – M = 5 log d – 5 m = stars apparent magnitude M = stars absolute magnitude D = distance from earth to the stars in parsecs. Color and temperature: Stars color is directly related to its surface temperature. The intensity of light from a relatively cool star peaks at long wavelengths, making the star look red. - A hot star’s intensity curve peaks at shorter wavelengths making the star look blue. - Intermediate temperatures: like the sun, it looks yellow. This all leads to an important rule: Red stars are relatively cold, with low surface temperatures; blue stars are relatively hot, with high surface temperatures, Astronomers use a set of filters in their telescopes to measure the surface temperature of stars. - Filtered light is collected by a light-sensitive device such as a CCD. - The stars image will have a different brightness through each colored filter, and by comparing these brightness’s, astronomers can find the wavelength at which the star’s intensity curve has its peak. And therefore the star’s temperature Most commonly used filters are; U, B, V -> technique is called = UBV Photometry To determine a stars temperature using UBV photometry, they first measure the stars brightness through each of the filters individually. This give 3 apparent brightness’s; Bu, Bb, Bv Then they compare the intensity of starlight in neighboring wavelength by taking the ratio (color ratios) of these brightness’s; BV/Bb and Bb/Bu a. A cool star with surface temp 3000 K emits much more red light than blue light, and so appears red. b. A warmer star with surface temp 5800 K (like the sun) emits a similar amount of visible wavelength and so appears yellow-white c. A hot star with surface temperature 10,000 K emits much more blue light than red light, and so appears blue.  Color Indices – U – B = mu – mv, and is called the U-B color index. It measures the amount of ultraviolet light relative to the amount of Blue light emitted by a star. B-V = mb – mv is the B-V color index. (Note: you can use either apparent magnitudes m, or absolute magnitudes M to compute the color index, since they are differences, the distance cancels out.) A graph of B-V versus temperature allows one to determine the temperature of a star by measuring just the mb and mv.

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Spectral Types – Originally Harvard astronomers classified stellar spectra into categories A through Q, but upon further study, realized that when they spectra arranged according to temperature, the classes became: O B A F G K M Hot Cool A stars spectrum is included in one of these categories based on the presence, absence, and strength of various spectral lines. (example: The Balmer lines of hydrogen or the H and K lines of Calcuim). (See Figure 19-10 and Box 19-4)

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Strengths of Absorption lines: See Figure 19-11. You MUST understand this table. Line strength means, how visible or how dark the lines are compared to the rest of the spectrum.

17-5 the spectra of stars reveal their chemical compositions as well as their surface temperatures to cope with the diversity, astronomers group similar-appearing stellar spectra into spectral classes. OBAFGKM Spectral types is further divided into 0 to 9 of the original letters by Cannon. Why surface temperatures affects stellar spectra:

Brow dwarfs: 1995 astronomers found a number of stars with surface temp even lower than those of spectral class M. these are not stars but Brown dwarfs. They are too small to sustain thermonuclear fusion in their cores; they have masses between 13 Mj and 80 mj (mj stands for mass of Jupiter ) - Brown dwarfs are so cold. That they primarily release heat from Kelvin-Helmholtz contraction. All stars have similar compositions: - By mass, almost all stars and brown dwarfs are about ¾ hydrogen, ¼ helium and 1% or less metals (elements heavier than helium) Our sun is no exception: 75% hydrogen with the remainder mostly consisting of 1.7% of heavier elements. 17-6 stars come in a wide variety of sizes and temperatures a stars radius can be calculated if we know its luminosity and surface temperature. - To determine size of star, they combine information about its luminosity (distance and apparent brightness) And its surface temperature (spectral type) relationship between a star's luminosity, radius and surface temp:

We can determine the radius of a star from its luminosity and surface temperature for a given luminosity; the greater the surface temperature, the smaller the radius must be for a given surface temperature; the greater the luminosity, the larger the radius must be. 17-7 Hertzsprung-Russel (H-R) diagram reveal different kinds of stars astronomers want to analyze their data to look for trends and underlying principles. Best way is to create a graph showing how one quantity depends on the other. Radius of a star related to its luminosity and surface temperature (equation p. 485)

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The Hertzsprung-Russell Diagram or (H-R diagram) IMPORTANT!!! – Plot absolute magnitude versus color index (or temperature or spectral type). Every phase of a stars evolution can be traced on this diagram.

Key Parts of the H-R Diagram 1. Main sequence – stars converting H to He, in hydrostatic equilibrium. Middle age of star. Luminosity class V, also called dwarfs. (90% of stars) -> extends from the hot, luminous blue stars in the upper left to cool, dim red stars lower right. 2. White Dwarf region – cores of dying stars. (no luminosity class) (Sirius) 3. Sub Giants – highly evolved low mass stars. Luminosity class IV. 4. Giants – highly evolved stars. Luminosity Class III. 5. Bright Giants – Highly evolved massive stars. Luminosity Class II. 6. Super Giants – Highly evolved massive stars. Luminosity class I. Betelgeuse and Antares are two supergiant’s Main Sequence is a Mass relationship – massive stars, upper left, less massive stars as you go toward lower right-hand side of HR diagram. - Main sequence stars gain their energy through conversion of hydrogen to helium in their cores.  Stellar Radius – Larger stars are brighter for a given temperature, thus occur higher on the H-R diagram than smaller stars. (e.g. White Dwarfs versus Supergiants.)  Binary Stars – used to determine stellar masses by applying Kepler’s 3rd Law. (refer to chapter 3, P2 = [ (42)/G(M1+M2)]a3 where P is sidereal period and a is the semi major axis.). 17-8 details of a stars spectrum reveal wheter it is giant, a white dwarf or a main sequence star. a. A supergiant star has a low-density, low pressure atmosphere; its spectrum has narrow absorption lines. b. A main-sequence star has a denser, higher-pressure atmosphere; its spectrum has broad absorption lines. Luminosity classes: based upon the subtle differences in spectral lines. When these luminosity classes are plotted on the H-R diagram, they provide useful subdivision of the star types. 

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. - Using spectroscopy to find the luminosity of stars. 17-9 observing binary star systems reveals the masses of stars for main-sequence stars, there is a direct correlation between mass and luminosity. Binary stars: - A pair of stars located at nearly the same positions in the night sky is called a double star. Herschel made the first organized search for these stars. - Optical Double stars– two stars that appear to be physically connected but are really far apart. - Many double stars are binary stars or binaries: pairs of stars that actually orbit each other. - visual binaries – can be seen as two distinct stars from Earth that orbit each other. Kepler’s third law for binary star system M1 + M2 = a3/p2 -

M1 + M2 = masses of two stars in binary systems, in solar masses a = semi major axis of one star’s orbit around the other, in AU P = orbital period, in years.

Each of the two stars in a binary system actually moves in an elliptical orbit about the center of mass of the system.

Main-sequence masses and the mass-luminosity relation: - The more massive a main-sequence star, the more luminous it is.

the greater the mass of a main-sequence star, the greater its luminosity, its surface temp and its radius. 17-10 spectroscopy makes it possible to study binary systems in which the two stars are close together 1. spectroscopic binaries – star systems where stars are to close together to be resolved from Earth, but can be detected by their spectral lines that shift as the stars orbit each other (Doppler shifts). 2. Eclipsing binaries – When the stars orbital plane is parallel to the line of sight, thus we see the stars “eclipse” each other. 3. What we get from Binaries: relative masses of stars from radial velocity curve, (radial velocity vs time) relative sizes of stars and relative brightness’s from eclipses. 

Main Sequence Lifetimes – Low mass. Later spectral types, G, K M, live longer than more massive O,B or A stars. Hot stars have more fuel, but burn hotter and use their fuel much faster than low mass stars.

17-11: light curves of eclipsing binaries provide detailed information about two stars some binary systems are oriented so that the two stars periodically eclipse each other as seen from earth. These eclipsing binaries can be detected even when two stars cannot be resolved visually as two distinct images in the telescope. - The apparent brightness of the image of the binary dims briefly each time one star blocks the light from the other.

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Using a sensitive detector at the focus of a telescope, they can measure the incoming light intensity quite accurately and create a light curve. The shape of light curve for an eclipsing binary reveals at a glance whether the eclipse is partial or total.

Chapter 18. The Birth of Stars. Gas and dust where stars are born Stars are visible to the naked eye due to thermonuclear reactions and they only have a finite amount of fuel available for these reactions. - They can not last forever. - They form from material in interstellar space, evolve over billions of years, and eventually die. Our sun consumes 6 x 1011 kg of hydrogen each second and convert it into helium. It isn’t infinite but it is vast. - Stars consume the material of which they are made, and so cannot last forever. - Sun has not been always shining, nor will it stay shining. This is true for all the mainsequence stars; same as sun, but different masses. 18-1 Understanding how stars evolve requires observation as well as ideas from physics stellar evolution: how stars are born, live their lives, and finally die. Gravity continuously tries to make a star shrink, while the star’s internal pressure tends to make the star expand. - When these two opposing forces are in balance, the star is in a state of hydrostatic equilibrium. 18-2 interstellar gas and dust pervade the galaxy where do stars come from? - Different types of nebulae emit, absorb, or reflect light. Interstellar medium: space between stars seem to be empty. Closer up, it is filled with a thin gas laced with microscopic dust particles. Combination of dust and gas is called Interstellar medium Nebula (nebulae or nebulosity): any interstellar cloud. a cloud of gas and dust in outer space, visible in the night sky either as an indistinct bright patch or as a dark silhouette against other luminous matter. The Orion nebula emits its own light, with the characteristic emission line spectrum of a hot, thin gas. -> emission nebula - Many small emission nebula can be seen with small telescope. - They are direct evidence of gas atoms in the interstellar medium. Emission nebulae are found near hot, luminous stars of spectral types O and B. - Astronomers use H 1 for neutral, un-ionized hydrogen atoms and H 2 for ionized hydrogen atoms, which is why they are also called H 2 regions.

H 2 regions emit red visible light when some of the free protons and electrons get back together to form hydrogen atoms, a process called, recombination 1. High-energy ultraviolet photons are emitted from a nearby hot star. 2. Hydrogen atoms in the nebula absorb the ultraviolet photons, which have enough energy to break the atoms into electrons and protons.

3. When electrons and protons recombine, the electron typically begins in a large, highenergy orbit around the proton. 4. The electron jumps to successfully lower-energy orbits. With each jump, the atom emits a photon; each of these photons has less energy and a longer wavelength than the ultraviolet photons in step q. these emitted photons give the hydrogen a characteristic visible glow. Stationary absorption lines: certain calcium and sodium lines are found to be at fixed wavelengths and these lines have captured the curiosity of observers. These are therefore not associated with the binary star. - Instead they are caused by interstellar gas between us and the binary system. Two kinds of evidence for larger bits of matter - Dust grains, in the interstellar medium They make their appearance in the dark nebulae and reflection nebulae. - A dark nebula; is so opaque that it blocks any visible light coming from starts that lie behind it. For example; Horsehead nebula, Barnard 86. They have relatively dense concentration of microscopic dust grains, which scatter and absorb light much more efficiently than single atoms. -

Reflection nebula: a haze kind of thing around a star., it is caused by fine grains of dust in a lower concentration than that found in dark nebulae. The light we see coming from a nebula is starlight that has been scattered and reflected by these dust grains. Grains are about 500 nm across no larger than a typical wavelength of visible light, and they scatter short wavelength. Blue more than red.

Interstellar extinction and reddening Robert Trumpler discovered two other convincing pieces of evidence for the existence of interstellar matter Interstellar extinction: intensity of light from remote stars is reduced as the light passes trough material in interstellar space. Interstellar reddening: the light from remote stars is also reddened as it passes through the interstellar medium, because the blue component of their starlight is scattered and absorbed by interstellar dust. (same effect makes the setting sun look red)

GRAVITY VERSUS INTERNAL PRESSURE!!!  

Gravity – depends solely on the mass of the star. Internal Pressure – 1. Temperature (gas and radiation pressure) 2. Rotation 3. Magnetic Fields

F= Gravity is pulling inward and internal pressure is pulling outwards. Gravity wins if: as collapse ensure center to heat up, causing pressure to increase. - Heat must be efficiently transported outward for the center to collapse. - If it gets cold within the region, pressure inside gets denser and denser causing collapse and star formation. So star formation regions must be cold. H 1 line in hydrogen. 18-3 protostars form in cold, dark nebulae how contracting cloud gives birth to a clump called a protostar: a future main-sequence star. - The only parts of the interstellar medium with high enough density and low enough temperature for stars to form are the dark nebulae. - Horsehead nebulae (Barnard 33) and Barnard 86 were discovered by Barnard in 1900 and are known as Barnard objects. M – few 1000 msun r – 10 parsecs - Bok Globules – small, round nebula r ~ 1-2 ly, M ~ 20-200 Mo, T ~ 5-15K named by Bart Bok. An bok globules resembles an inner core of a Barnard object with the outer, less dense portions stripped away. - Within these clouds, the densest portion can contract under their own mutual gravitational attraction and form clumps called Protostars. They eventually form into a main-sequence star. Think of dark nebula as a “stellar nurseries” The evolution of a protostar: - Protostar’s luminosity and surface temperature change at various stages in its contraction. When plotted on the H-R diagram, provides a protostar evolutionary track. - It shows how its appearance change because of changes in its interior. Protostar’s form within clouds that contain substantial amounts of interstellar dust. The dust in a protostar’s immediate surroundings is called cocoon nebula. - They absorb vast amounts of visible light emitted by the protostar and makes it very hard to detect using visible wavelengths. It can be seen using infrared wavelengths. The course of a protostars evolution depends on its mass. a. Mass more than about 4 M : energy flows by convection in the inner regions and by radiation in the outer regions b. Mass between about 4M and 0.4 M: energy flows by radiation in the inner regions and by convection in the outer regions c. Mass less than 0.4 M: energy flows by convection throughout the star’s interior. 18-5 during the birth proces...