Chapter 9. Stars. The Hertzsprung-Russell Diagram. Topics for Today s Class. Phys1411 Introductory Astronomy Instructor: Dr.

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1 Foundations of Astronomy 13e Seeds Phys1411 Introductory Astronomy Instructor: Dr. Goderya Chapter 9 Stars Cengage Learning 2016 Topics for Today s Class HR Diagram Variable Stars Intrinsic Variables Cepheids and RR Lyrae type Extrinsic Eclipsing Variable Stars Mass of Stars Binary Stars Estimating mass from Binary Stars Spectroscopy and Radial Velocity measurements Life Cycles of Star Evolutionary Track on HR Diagram White Dwarfs Chandrashekar Limit on Mass Neutron Stars Black Holes Topics for Today s Class Luminosity and Absolute Magnitude Brightness, flux, luminosity, what's the difference? Distance Trigonometric parallax method Distance modulus method Radius Radius and surface area of stars Radius affects luminosity H-R Diagram The Hertzsprung-Russell Diagram In an H R diagram, a star is represented by a dot at a position that shows the star s luminosity and temperature. The background color in this diagram indicates the temperature of the stars. The Sun is a yellow-white G2 star. Most stars including the Sun have properties along the mainsequence strip running from hot high-luminosity stars at upper left to cool low-luminosity stars at lower right. Fig. 9-8, p

2 The Hertzsprung-Russell Diagram The Hertzsprung-Russell Diagram Same temperature, but much brighter than MS stars Must be much larger Giant Stars Same Luminosity but hotter than Sun The Relative Sizes of Stars in the HR Diagram An H R diagram showing the luminosity and temperature of many well-known stars. Individual stars that orbit each other are designated A and B, for example Spica A and Spica B. The dashed lines are lines of constant radius; star sizes on this diagram are not to scale. To visualize the size of the largest stars, imagine that the Sun is the size of a tennis ball. Then, the largest supergiant's would be the size of a sports stadium and white dwarfs the size of grains of sand. Comparison of Spectral Lines These model spectra show how the widths of spectral lines reveal a star s luminosity class. Supergiant's have very narrow spectral lines, and main-sequence stars have broad lines. Certain spectral lines are more sensitive to this effect than others; Careful inspection of a star s spectrum can determine its luminosity classification. Luminosity Class See Figure 9-12 Ia Bright Supergiant's Ib Supergiant's II Bright Giants III Giants IV Subgiants V Main-Sequence Stars Our Sun: G2 star on the Main Sequence: G2V 2

3 Example Luminosity Classes Luminosity Classes and H-R Diagram Our Sun: G2 star on the Main Sequence: G2V Polaris: G2 star with Supergiant luminosity: G2Ib Ia Bright Supergiant's Ia Ib II III IV V Ib Supergiant's II Bright Giants III Giants IV Subgiants V Main-Sequence Stars Variable Stars Variability in Light Curve Some stars show changes in their apparent magnitude as a function of time, that can be periodic, irregular or one time event. Stars that show periodic changes can be intrinsic or extrinsic. Intrinsic means changing due to some mechanism inside the star Extrinsic means changing because of blocking of star light. Intrinsic Variables Pulsating Stars If the star is pulsating (getting bigger or smaller in size periodically). Its light output will vary with time. Such stars are called intrinsic variables (examples, Cepheid and RR Lyra variables). Pulsating Stars Stars that grow and shrink in diameter periodically Cepheid Variables (period less than 100 days) RR Lyrae variables (period less than 1 day) Mira variables (period greater than 100 days) They are also used as standard candles (distance calibrators) On HR diagram found in the instability strip Pulsating Variables: The Valve Mechanism Partial He ionization zone is opaque and absorbs more energy than necessary to balance the weight from higher layers. => Expansion Upon expansion, partial He ionization zone becomes more transparent, absorbs less energy => weight from higher layers pushes it back inward. => Contraction. RR Lyra Variable Cepheid Variable Upon compression, partial He ionization zone becomes more opaque again, absorbs more energy than needed for equilibrium => Expansion 3

4 Extrinsic Variables - Binary Stars Binary stars are system of two stars that are bound by the mutual gravitation of the two stars. Both star orbit a common center of mass The Orbital Period P is the amount of time in years it takes for one star to orbit the other at a separation a in AU. Eclipsing Variable and its light Curve Binary Stars Optical Double Stars Skyandtelescope Mass of Stars Mass is the most FUNDAMENTAL parameter of Stars. It tells us how stars will live their lives, evolve and die. How do we find the Mass of a Star? Mass of Stars One sure way of doing this is to use Binary Stars? More than 50 % of all stars in our Milky Way are pairs or multiple systems of stars which orbit their common center of mass Probably same is true for other Galaxies Estimating Stellar Masses, Part 1 Recall the general version of Kepler s 3rd Law: Estimating Stellar Masses, Part 2 Binary system with period of P = 32 years and separation of a = 16 AU: We find almost the same law for binary stars with masses M A and M B different from 1 solar mass: Any binary system with a combination of period P and separation a that obeys Kepler s 3 rd Law must have M A + M B = 1 solar mass (M A and M B in units of solar masses) 4

5 Radial Velocity From Doppler Shift Evolution of Stars on the HR Diagram Doppler shift Measurement of radial velocities Estimate of separation a Estimate of masses Fusion proceeds; formation of Fe core. M > 8 M sun Fusion stops at formation of C,O core. M < 4 M sun M < 0.4 M sun Supernova Evolution of 4-8 M sun stars is still uncertain. Mass loss in stellar winds may reduce them all to < 4 M sun stars. Red dwarfs: He burning never ignites The Final Breaths of Sun-Like Stars: Planetary Nebulae Characteristics of White Dwarfs Degenerate stellar remnant (C-O core) Extremely dense Remnants of stars with ~ 1 a few M sun Radii: R ~ light years Expanding at ~10 20 km/s ( Doppler shifts) Less than 10,000 years old Have nothing to do with planets! The Helix Nebula White dwarfs: Mass ~ M sun Temp. ~ 25,000 K Luminosity ~ 0.01 L sun 1 teaspoon of WD material: mass 11 tons! The degenerate matter inside a white dwarf is so dense that a lump the size of a beach ball would, transported to Earth, weigh as much as an ocean liner. Chandrashekhar Limit A mathematical condition on the mass of a star for it to become a white dwarf, neutron star or black hole The Famous Supernova of 1987: SN 1987A Before At maximum M core < 1.4 M sun ----> White Dwarf 1.4M sun < M core < 3.0 M sun ----> Neutron Star 3.0 M sun < M core < 5.0 M sun ----> Black Hole Supernova in the Large Magellanic Cloud in Feb

6 Pulsars / Neutron Stars are very Hot Neutron star surface has a temperature of ~ 1 million K. Cas A in X-rays Lighthouse Model of Pulsars A Pulsar s magnetic field has a dipole structure, just like Earth. Wien s displacement law, max = 3,000,000 nm / T[K] gives a maximum wavelength of max = 3 nm, which corresponds to X-rays. Radiation is emitted mostly along the magnetic poles. Properties of Neutron Stars Typical size: R ~ 10 km Mass: M ~ M sun Density: ~ g/cm 3 Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!! Escape Velocity Velocity needed to escape Earth s gravity from the surface: v esc 11.6 km/s. Now, gravitational force decreases with distance (~ 1/d 2 ) => Starting out high above the surface => lower escape velocity. If you could compress Earth to a smaller radius => higher escape velocity from the surface. v esc v esc v esc Black Holes Just like white dwarfs (Chandrasekhar limit: 1.4 M sun ), there is a mass limit for neutron stars: Neutron stars can not exist with masses > 3 M sun We know of no mechanism to halt the collapse of a compact object with > 3 M sun. It will collapse into a single point a singularity: => A Black Hole! Acknowledgment The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only Images and text material have been borrowed from various sources with appropriate citations in the slides, including PowerPoint slides from Seeds/Backman text that has been adopted for class. 6