Basic Properties of Stars

1. Basic Properties of Stars

2. � Sierra College Astronomy Department 2 Lecture 10a: Measuring the Properties of StarsStellar Brightness and Magnitude Power is the rate at which energy is transferred, or the amount of energy transferred per unit time. Luminosity is the rate at which electromagnetic energy is being emitted - the total amount of power emitted by a star. Brightness refers to the power/area of a star as seen at the Earth and which follows the inverse square law.

3. � Sierra College Astronomy Department 3 Lecture 10a: Measuring the Properties of StarsStellar Brightness and Magnitude We use the magnitude scale to label the apparent visual brightness or intensity of the stars Scale developed by the ancient Greek Hipparchus in the second century B.C. The first stars seen at night were 1st magnitude stars, the next 2nd magnitude and so forth to 6th magnitude. Lower magnitudes means brighter! (Kind of like golf scores)

4. � Sierra College Astronomy Department 4 Lecture 10a: Measuring the Properties of StarsStellar Brightness and Magnitude Modern development of magnitude scale Five magnitudes = 100 fold in brightness Hence, one magnitude = 2.512 fold so that (2.512)5 = 100 e.g. a 3rd magnitude star is 2.512 times brighter than a 4th magnitude star A 5th magnitude star is 2.512 x 2.512 = 6.25 times fainter than a 3rd magnitude star Scale can use decimal numbers (i.e. 3.6, 4.1) This is referred to as the apparent magnitude, designated by the letter m

5. � Sierra College Astronomy Department 5 Lecture 10a: Measuring the Properties of Stars Stellar Brightness and Magnitude Modern measuring devices allow astronomers to determine magnitudes to an accuracy of 0.001 or better. A few stars (e.g., Sirius) are so bright that they have negative magnitudes. Sirius�s apparent magnitude is �1.47. Scale can be below 0 and above 6 Modern, large telescopes equipped with CCD devices can image objects as dim as 25th magnitude or better.

6. � Sierra College Astronomy Department 6 Lecture 10a: Measuring the Properties of StarsDistances to Stars - Parallax Stellar parallaxes were not observed until the mid-1800s (need good telescope). Parallax angle is half the maximum angle that a star appears to be displaced due to the Earth�s motion around the Sun. The maximum angle of the nearest star is only about 1.52 seconds of arc, but astronomers define the parallax angle as half that value, or 0.76 seconds.

7. � Sierra College Astronomy Department 7 Lecture 10a: Measuring the Properties of StarsDistances to Stars - Parallax Parallax distance formula (in light-years): Distance to star (ly) = 3.26 ly/parallax angle in arcsec Parallax distance formula (in parsecs): Distance to star (pc) = 1 pc/parallax angle in arcsec A parsec is the distance of an object that has a parallax angle of one arcsecond. One parsec is equal to 3.26 ly or 206,265 AU or 3.09 x 1013 km.

8. � Sierra College Astronomy Department 8 Lecture 10a: Measuring the Properties of StarsDistances to Stars - Parallax Only stars within about 120 parsecs (400 light-years) have parallax angles great enough to allow accurate calculations of their distances. The satellite Hipparcos (1989-1993) measured positions and parallaxes to an accuracy of 0.002 arcsecond for over 100,000 stars and extended accurate calculations of distance to 300 pc (1000 ly) Accurate stellar distances help to determine the physical quantities of stars

9. � Sierra College Astronomy Department 9 Lecture 10a: Measuring the Properties of StarsAbsolute Magnitude & Luminosity Absolute Magnitude The intrinsic luminosity of a star is usually given as its absolute magnitude and designated with a capital M. M is defined as the apparent magnitude a star would have if it were at a distance of 10 parsecs. Sirius�s apparent brightness (�1.47) is due to its closeness (2.7 parsecs from Earth). Its absolute magnitude is +1.45 (determined by using inverse square law). Demo with SC001 & SC006 star charts.Demo with SC001 & SC006 star charts.

10. � Sierra College Astronomy Department 10 Measuring the Properties of StarsTemperature and Spectral Classes A star�s color is determined by its temperature. An absorption spectrum - the absorption of radiation at various wavelengths - can be used to determine a star�s temperature. Harvard astronomers, lead by Edward Pickering and his women �computers� developed the first stellar classification system using letters A-O, in alphabetical order. In particular, Williamina Fleming based the system on the strength of the stars� hydrogen absorption lines (A strong, O weak)

11. � Sierra College Astronomy Department 11 Measuring the Properties of StarsTemperature and Spectral Classes The A-O scheme was eventually found to be inadequate. Another �computer�, Annie Jump Cannon, discovered that a reordering and elimination of some of the letters gave a better scheme, which is still used today. Cannon�s system was thought to reflect stellar composition, but �computer� Cecilia Payne-Gaposchkin showed that the system was a consequence of the stars� surface temperatures.

12. � Sierra College Astronomy Department 12 Lecture 10a: Measuring the Properties of StarsSpectral Classes Spectral types used today (from hottest to coolest) are designated as O B A F G K M. O stars range in temperature from 30,000�K to 60,000�K. M stars have temperatures less than 3,500�K. Within each spectral class, stars are subdivided into 10 categories by number (0 to 9). The Sun is a G2 star, for example There are also other spectral types which have come and gone typically appear after the M type. The two recognized now are types L and T which have dust grains in their atmosphere

13. � Sierra College Astronomy Department 13 Lecture 10a: Measuring the Properties of StarsThe Hertzsprung-Russell Diagram Hertzsprung-Russell diagram is a plot of absolute magnitude (or luminosity) versus temperature (or spectral class) for stars. About 90% of all stars fall into a group running diagonally across the diagram called main sequence stars. Stars on the H-R diagram fall into categories such as main sequence stars, white dwarfs, red giants, and supergiants. The key in getting an accurate H-R diagram is to get accurate distances to the stars

14. � Sierra College Astronomy Department 14 Measuring the Properties of StarsLuminosity Classes In the 1880s Antonia Maury and Ejnar Hertzsprung discovered that the width of a star�s absorption lines was directly related to the star�s luminosity (which in turn is related to a star�s surface density). Luminosity classes are one of several groups into which stars can be classified according to the characteristic widths of their spectra. The luminosity classes are: Ia (supergiants), Ib (dimmer supergiants), II (bright giants), III (ordinary giants), IV (subgiants), and V (main-sequence). Complete Stellar Classification: A star is fully classified if its spectral class and luminosity class are specified (e.g., the Sun is designated as a G2 V star)

15. � Sierra College Astronomy Department 15 Lecture 10a: Measuring the Properties of StarsTowards a �Distance Ladder� Spectroscopic Parallax Knowing a star�s luminosity class and temperature (spectral class) gives its absolute magnitude. Knowing a star�s absolute magnitude and apparent magnitude gives its distance. The distances to stars too far away for parallax measurements can be determined using this procedure. Spectroscopic parallax represents the second rung (geometric parallax being the first) in the distance ladder created and used to scale the Universe.

16. � Sierra College Astronomy Department 16 Lecture 10a: Measuring the Properties of StarsThe Hertzsprung-Russell Diagram Spectroscopic Parallax � Final Touch Knowing a star�s luminosity class and temperature gives its absolute magnitude (i.e. luminosity). Knowing a star�s absolute magnitude and apparent magnitude gives its distance. The distances to stars too far away for parallax measurements can be determined using this procedure.

17. � Sierra College Astronomy Department 17 The Sizes of Stars (directly) The sizes of a few very large stars have been measured directly by interferometry. The Sizes of Stars (indirectly) Knowing the temperature of a star gives its energy emitted per square meter. Knowing the total energy emitted (from the absolute magnitude) one can then calculate the surface area of the star. From that the diameter of the star can be determined Lecture 10a: Measuring the Properties of StarsThe Hertzsprung-Russell Diagram

18. � Sierra College Astronomy Department 18 Lecture 10a: Measuring the Properties of StarsMultiple Star Systems and Binaries Multiple Star Systems and Binaries More than half of what appear as single stars are in fact multiple star systems. Optical doubles are two stars that have small angular separation as seen from Earth but are not gravitationally linked. Binary star system is a system of two stars that are gravitationally linked so that they orbit one another.

19. � Sierra College Astronomy Department 19 Lecture 10a: Measuring the Properties of StarsMultiple Star Systems and Binaries A visual binary is an orbiting pair of stars that can be resolved (normally with a telescope) as two stars. If one uses large telescopes, about 10% of the stars in the sky are visual binaries. Binaries can be confirmed by observing the system over time and looking for signs of revolution. Spectroscopic binary is an orbiting pair of stars that can be distinguished as two due to the changing Doppler shifts in their spectra. Inclination of orbit will affect results

20. � Sierra College Astronomy Department 20 Lecture 10a: Measuring the Properties of StarsMultiple Star Systems and Binaries Algol, discovered by Goodricke in 1783, is an eclipsing binary in which one star moves in front of the other as viewed from Earth. Algol�s light curve - a graph of the numerical measure of the light received from a star versus time - shows peaks and dips that indicate an unseen companion.

21. � Sierra College Astronomy Department 21 Lecture 10a: Measuring the Properties of StarsMasses and Sizes from Binary Stars Binary stars are important because they allow one to measure masses of stars using Newton�s version of Kepler�s laws. Knowledge of the size of one of the star�s ellipses, along with knowledge of the period of its motion, permits calculation of the total mass of the two stars. To determine how the system�s total mass is distributed between the two stars, one need only consider the ratio of the two stars� distances to the center of mass.

22. � Sierra College Astronomy Department 22 Lecture 10a: Measuring the Properties of Stars Masses and Sizes from Binary Stars Because the inclination of spectroscopic binary orbits are usually not known, exact mass calculations cannot be done. However, assuming an average inclination can provide information about average masses of spectroscopic binary stars. Eclipsing binaries that are also spectroscopic binaries provide us with a way of measuring not only the masses of the two stars but also their sizes. We derive this information using measurements of their Doppler shifts.

23. � Sierra College Astronomy Department 23 Measuring the Properties of StarsMain-Sequence Lifetimes The lifetime on the main-sequence depends on how much fuel (hydrogen) the star has and how fast the star is consuming it. The more massive stars do this the fastest. This lifetime can be expressed as: Where t?= 10 billion years Examples: A 10 M? will last about 10 million years, whereas a 0.3 M? star will last 300 billion years

24. � Sierra College Astronomy Department 24 Measuring the Properties of StarsStar Clusters and Aging Open (galactic) cluster is a group of stars that share a common origin and are located relatively close to one another. Globular cluster is a spherical group of up to hundreds of thousands of stars found primarily in the halo of the Galaxy. Clusters are important for two reasons: All stars in a cluster are at about the same distance from us, so their apparent magnitude is a direct indication of their absolute magnitude. All the stars within a cluster formed at about the same time (more or less). Age of cluster determined from main-sequence turnoff Much of our knowledge of star formation has come from examination of clusters

25. � Sierra College Astronomy Department 25 Lecture 10b: Interstellar Matter and Stellar EvolutionA Brief Woodland Visit If you were alien from a treeless world and were sent to Earth for one day to gather data from a forest, what do you think your chances are of developing the correct theory for the growth history of a tree? How would your chances change if you were given a basic knowledge base of Earth biology? Astronomers are in a similar position with the life cycle of stars. They tackle the problem by observing tremendous numbers of stars in various stages of development.

26. � Sierra College Astronomy Department 26 Lecture 10b: Interstellar Matter and Stellar EvolutionStar Birth The Collapse of Interstellar Clouds Stars are born in the cold (10 K), giant molecular clouds (GMCs) found in the Galaxy. Astronomers estimate that our Galaxy contains 5,000 GMCs. The average density of a GMC is about 200 molecules/cm3 over some 100 parsecs. A GMC may contain as much as a million solar masses of material.

27. � Sierra College Astronomy Department 27 Lecture 10b: Interstellar Matter and Stellar EvolutionStar Birth Theories about star birth began with Russell (and the H-R diagram) early in the 20th century. However, the exact mechanism that begins the collapse of part of a GMC is not well understood. Collapse could be triggered by colliding GMCs or by a shock wave in the interstellar medium. Shock waves could be produced by stellar winds from massive stars, supernova explosions, or from the rotation of galactic arms.

29. � Sierra College Astronomy Department 29 A protostar is a star in the process of formation before it reaches the main sequence The eventual contraction of a gas cloud is unstopped by internal pressure (i.e. gravity wins) Conservation of angular momentum increase rotation speed as cloud collapses This infall of material heats up the internal dusty gas (to about 1500K; surrounded and blocked by cocoon nebula) Gravitational potential energy converted to thermal energy Bipolar flows clear away some of the outlying material

30. � Sierra College Astronomy Department 30 Lecture 10b: Interstellar Matter and Stellar EvolutionStar Birth During these later stages of a protostar�s evolution, streams of material flow from the poles of the protostar (jets) These flows are called bipolar flows and astronomers theorize they may help reduce the angular momentum of stars. Bipolar flows clear away most of the cocoon�s gas and dust allowing astronomers to finally see the new star in the visible part of the spectrum.

31. � Sierra College Astronomy Department 31 Lecture 10b: Interstellar Matter and Stellar EvolutionStar Birth Times spent as protostars: M-class stars may remain protostars for hundreds of millions of years. G stars (like the Sun) spend about 30 million years in the protostar phase. Massive O- and B-type stars may spend only 100,000 years as protostars before joining the main sequence. Evolutionary track is the path on the H-R diagram taken by the star (and its precursor cocoon and protostar) as its luminosity and color change.

32. � Sierra College Astronomy Department 32 Lecture 10b: Interstellar Matter and Stellar EvolutionStar Birth Upper limit of Star�s Mass: Astronomers calculate that a star with a mass greater than 100 solar masses will emit radiation so intense that it will prevent more material from falling into the star, thereby limiting the star�s size. Lower limit of Star�s Mass: Protostars with masses of less than 0.08 solar masses do not have enough internal pressure to ignite hydrogen fusion. What about those stars whose masses are between this and Jupiter?

33. � Sierra College Astronomy Department 33 Lecture 10b: Interstellar Matter and Stellar EvolutionStellar Maturity Stellar Nuclear Fusion Stars of low mass like the Sun (<1.5 M?) use the proton-proton chain to generate energy. Stars of mass greater than 1.5 M? have higher core temperatures that allow the CNO cycle to fuse of hydrogen into helium (4H ? He). The CNO cycle is more efficient at the higher core temperatures of these stars This series of reactions involves hydrogen with carbon, nitrogen, and oxygen as catalysts. Hydrostatic equilibrium (pressure balances gravity) maintains fusion at a uniform rate.

34. � Sierra College Astronomy Department 34 Lecture 10b: Interstellar Matter and Stellar EvolutionStellar Maturity Towards Star Death Until their lives end on the main sequence, the main difference between the evolution of stars of various masses is the amount of time they spend as protostars and main sequence stars. Stars can be grouped by mass as low-mass or high-mass depending on their eventual end state. ? STAR�S LIFETIME ON MAIN SEQUENCE DEPENDS THE STAR�S INITIAL MASS

35. � Sierra College Astronomy Department 35 Lecture 10b: Interstellar Matter and Stellar EvolutionVery-Low-Mass Stars Very-Low-Mass Stars In stars with a mass of less than about 0.4 solar masses, convection occurs throughout most or all of the volume of the star. Hydrogen from throughout the star is cycled through the core, and the entire star runs low on hydrogen at the same time. A very-low-mass star will take 20+ billion years to completely burn its hydrogen.

36. � Sierra College Astronomy Department 36 Lecture 10b: Interstellar Matter and Stellar Evolution Very-Low-Mass Stars Ultimately, very-low-mass stars will (should?) become white dwarfs through gravitational shrinkage. The hypothetical lifetime of a very-low-mass star is more than the assumed age of the universe. Consequently, white dwarfs currently observed must have originated in a different manner.

37. � Sierra College Astronomy Department 37 Low-Mass Stars Low-mass stars include stars with masses between 0.4 and 6 solar masses (includes Sun). The core shrinks as hydrogen is depleted. Heat from contraction of the core then heats a shell surrounding the core to temperatures that permit fusion of hydrogen to begin. These two sources of energy (gravitational and nuclear) cause the outer portions of the star to expand and cool. Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars

38. � Sierra College Astronomy Department 38 Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars Consequently, the star moves to the right on the H-R diagram and upward (due to increasing luminosity) becoming a red giant. A red giant can have a lower surface temperature (less radiation per square meter) but a higher luminosity because its diameter will expand 200 times or more. As a red giant evolves and hydrogen burning takes place in outer layers of the star, the helium �ashes� are dumped back onto a degenerate core, raising the temperature of the core.

39. � Sierra College Astronomy Department 39 Electron Degeneracy The core of a red giant will not continue to contract indefinitely because of electron degeneracy. Electron degeneracy is a quantum state of a gas in which its electrons are packed as densely as nature permits. The temperature of such a high-density gas is not dependent on the pressure as it is in a �normal� gas. Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars

40. � Sierra College Astronomy Department 40 Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars When the degenerate core temperature reaches 100 million K, helium nuclei begin to combine through the triple alpha process forming carbon. The initial fusion of helium proceeds in a runaway process called the helium flash, expanding the core, returning the core to a non-degenerate state, and shrinking the star to a yellow giant. Following the helium flash, the center of the star forms three layers - an inner degenerate carbon core, a layer of helium that fuses to carbon in a conventional manner, and an outer hydrogen-fusing shell.

41. � Sierra College Astronomy Department 41 Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars Yellow Giants and Pulsating Stars Many yellow giants (whether an aging high-mass or low-mass star) swell and shrink rhythmically: they pulsate. These pulsating yellow giants are located in the instability strip of the H-R diagram. High-mass pulsating giants are Cepheid variables (periods of about 1-70 days). Low-mass pulsating giants are RR Lyrae variables (periods of about 12 hours).

42. � Sierra College Astronomy Department 42 Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars The cause for the pulsation is a special situation where the yellow giant�s atmosphere can trap some of its radiated energy. This heats the atmosphere which then expands to a point that the star�s trapped radiation can escape. This causes the atmosphere to cool, shrink to its original size, and start the process all over again. The regular pulsation process of variable stars has led to the period-luminosity relation: higher average luminosity leads to longer periods.

43. � Sierra College Astronomy Department 43 Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars Post Helium Flash After the helium flash, a yellow giant then expands again into a red giant. Stars more massive than 2 solar masses do not experience a helium flash, but will simply expand through the yellow giant stage to its one and only red giant stage.

44. � Sierra College Astronomy Department 44 Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars Mass Loss In Stars The solar wind carries away about 10�14 of the Sun�s mass each year. Over the course of 10 billion years, the Sun will lose only 0.01% of its mass this way. In red giant stars, it is thought that core instabilities and pulsations are responsible for the large mass loss. A typical red giant loses 10�7 solar masses a year and hence can last at most 10 million years.

45. � Sierra College Astronomy Department 45 Lecture 10b: Interstellar Matter and Stellar Evolution Low-Mass Stars Planetary Nebulae A Planetary nebula is a spherical shell of gas that is expelled by a red giant near the end of its life. The material in the shell glows because UV radiation from the central hot star causes it to fluoresce. Pulsations and/or stellar winds are thought to cause planetary nebulae.

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47. � Sierra College Astronomy Department 47 The End