Module 8: Understanding Stars: Properties and Classification

Pioneers of stellar classification

(A) Annie Jump Cannon and the "calculators" at Harvard College Observatory in 1913 laid the foundation of modern stellar classification. (B) Annie Jump Cannon (1863-1941)in 1929. She personally cataloged over 350,000 stellar spectra.

Parallax for Mars

(A) Giovanni Domenico Cassini (1625-1712) was an Italian mathematician, astronomer, astrologer, and engineer. (B) In the late 17th century, Cassini used the parallax technique to measure the distance to Mars. Cassini knew that a larger parallax would be easier to measure, but this required a larger baseline. He took measurements of the position of Mars from Paris and sent a colleague to French Guiana in South America to do the same. This gave him a baseline of several thousand kilometers. Using geometry, he was able to calculate a distance for Mars that is only 7% off from our current more accurate measurement.

Examples of a Parallax

(A) If an object is at close distance, your left eye and your right eye will give two different views. Nature knows this effect, in fact this is how we are able to estimate distances. If you hold a pencil at a short distance in front of your eyes, you may observe an effect like the one shown above. Note that if you move the close-by pencil out to large distances, this parallax-effect will become smaller and smaller, and at some time it will approach zero and vanish. The church is too far away to give any noticeable parallax. (ESO) (B) This animation is an example of parallax. As the viewpoint moves side to side, the objects in the distance appear to move more slowly than the objects close to the camera.

Open Cluster: The Hyades with the Bright Star Aldebaran

(A) Image of the Hyades, a V-shaped open star cluster that forms the face of Taurus and is the nearest open cluster to the solar system. The cluster's center is about 153 l-y (46.9 pc) distant. The cluster consists of a roughly spherical group of hundreds of stars sharing the same age, place of origin, chemical content, and motion through space. The Hyades cluster is about 625 million years old, and diameter is about 17.6 l-y. Note that red giant Aldebaran (the "eye" of Taurus) is not related to the Hyades. (B) Close-up of the Hyades generated from Starry Night.

The Trapezium in M42

(A) Plotted here are the locations of the stars in the Trapezium, their separations, and magnitudes. The Trapezium open cluster is about 1,600 l-y (490 pc) away. Galileo discovered the Trapezium in 1617. (B) The Trapezium (circled) is a small star cluster in M42. (C) The Trapezium imaged in the near-infrared by the Hubble Space Telescope.

Stars of the Pleiades

(A) The Pleiades is also known as the Seven Sisters. The cluster, only 440 light-years (134.8 pc) away, actually contains at least 500 stars. Recent calculations put the age of the hottest bright members at about 100 million years. (B) The Pleiades as it would appear viewed in a small scope or binoculars. A finder chart for the Pleiades (M45), which sits in the shoulder of Taurus. The Pleiades are the closest open cluster to Earth and are thus easily naked-eye visible.

Double Cluster in Perseus (NGC869 and NGC884)

(A) This double open cluster can just be seen with the unaided eye from a dark site. (B) A finder chart for the Double Cluster. Though always visible, the Double Cluster is best viewed from mid-August until mid-April.

Visual Binary Stars

(A) When astronomers can actually see the two stars orbiting each other, the binary is called a visual binary. This binary system is Kruger 60 in the constellation Cepheus and has an orbital period of 44.5 years. (NASA) (B) Two telescopic views of the double star Albireo, which many consider the most beautiful double visible in the northern hemisphere. Albireo is found in the constellation Cygnus, often referred to as the Northern Cross.

Remembering Spectral Types

(Hottest) O B A F G K M (Coolest)

Properties of Thermal Radiation

1.Hotter objects emit more light per unit area at all frequencies. 2.Hotter objects emit photons with a higher average energy. 3.Peaks of the blackbody curves move toward shorter wavelengths as the objects get hotter. Humans emit thermal radiation in the infrared (310 K), which our eyes cannot detect.

H-R Diagram

A Hertzsprung-Russell diagram (H-R diagram) plots stellar luminosities on one axis (usually the y-axis) and spectral types—stellar temperatures—on the other axis (usually the x-axis). Note two things about the y-axis: (1) luminosity is usually given in units of the Sun's luminosity and (2) each tick mark represents a jump in luminosity 10 times that of the prior tick mark (the y-axis does not increase linearly but rather logarithmically, or by powers of ten). The H-R diagram provides direct information about stellar radii because a star's luminosity depends on both its surface temperature and its surface area or radius. An H-R diagram plots the luminosity (on the y-axis) and the surface temperature (on the x-axis) of stars. Note that temperature is equivalent to a star's color and spectral class. The main sequence plots stars that are hydrogen fusing. Stellar masses go from low at bottom right to high at upper left. Note that mass is also associated with lifespan (small stars live long lives while massive stars do not) and radius. As stars age, they move off the main sequence to become giants and supergiants, and most eventually become white dwarfs. The H-R diagram is a bit different from conventional graphs. On the x-axis, temperature is read from right to left. On the y-axis, the luminosity scale is a logarithmic scale that moves by powers of ten.

Globular Star Cluster M80

A globular cluster contains from 100,000 up to a million or more stars in a dense ball bound together by gravity. (A) Globular cluster M80, in Scorpius, was discovered by Charles Messier in 1781 and is 32,600 l-y (10 kpc) distant. It is best viewed from June 1 to September 1.

Parallax and distance

A parsec is the distance from the Sun to an astronomical object which has a parallax angle of one arcsecond. The term parsec is a distance corresponding to a parallax of one second. It was coined in 1913 at the suggestion of British astronomer Herbert Hall Turner. A parsec is the distance from the Sun to an astronomical object which has a parallax angle of one arcsecond. 1 parsec= 3.26 light years = 206265AU= 3.085678 x 10<16 m 1 kiloparsec= 1,000 pc; 1 megaparsec (Mpc)= 1 million pc

Absolute Magnitude

A star's absolute magnitude is the apparent magnitude a star would have if it were observed at a distance of 10 parsecs from Earth.

Stellar Classification (slide 74)

A star's full classification includes spectral type (line identities) and luminosity class (line shapes, related to the size of the star) The surface of Betelgeuse (class I supergiant) showing convection spots was imaged in near infrared at 1.64 micron and was obtained using the IOTA interferometer in Arizona. The star diameter is about 40 mas (milli-arcsecond), and details as small as 9 mas are shown. The two giant bright spots, whose size is equivalent to the Earth-Sun distance, is the first direct indication of the presence of convection in a star other than the Sun.

Main-Sequence Lifetime

A star's main-sequence lifetime is the time the star spends on the main sequence as a hydrogen-fusing star. The Sun's lifetime is about 10 billion (10<10) years. A 30-solar-mass star has a luminosity that is 300,000 times greater, so its lifetime is 30/300,000 or 1/10,000 as long or about 10<10 y/10<4 = 10<6 y or 1 million years (this is a rough estimate). A star's surface temperature and luminosity typically increase gradually during its time on the main sequence. As mass and luminosity increase, lifetime decreases.

Reduction in Intensity of Radiation with Distance Traveled

A typical inverse-square curve. Radiation (i.e., light) and gravity both obey inverse-square laws.

Stellar Absorption Lines

Absorption lines in a star's spectrum tell us its ionization level.

Algol

Algol (β Persei) is a triple-star system (Algol A, B, and C) in the constellation Perseus, in which the large and bright primary Algol A is regularly eclipsed by the dimmer Algol B every 2.87 days. The eclipsing binary pair is separated by only 0.062 AU from each other, so close in fact that Algol A is slowly consuming the less massive Algol B by continually stripping off Algol B's outer layers. This animation was assembled from 55 images of the CHARA interferometer in the near-infrared H-band, sorted according to orbital phase. Because some phases are poorly covered, B jumps at some points along its path. The phase of each image is indicated at the lower left. The images vary in quality, but the best have a resolution of 0.5 milliarcseconds, or approximately 200 times better than the Hubble Space Telescope. (A milliarcsecond is about the size of a quarter atop the Eiffel Tower as seen from New York City.) Tidal distortions of Algol B giving it an elongated appearance are readily apparent. Tidal distortions also result in "gravity darkening" effects, whereby in a significant number of images of Algol B, the edge or limb of the image is actually brighter than the center.

Stars

All stars form in great clouds of gas and dust. All stars form with roughly the same composition: 75% H / 23% He / 2% other elements. Stars appear different because of differences in their masses and the stage at which we observe them. The "key" to understanding stars was an appropriate classification system. Today, stars are classified by luminosity and surface temperature. Betelgeuse, a red supergiant star in Orion (aka Alpha Orionis), has a high luminosity (90,000-150,000 L) due to its large diameter but a low surface temperature (3,500 K). Betelgeuse is of spectral class M1-M2 and appears at apparent magnitude of 0.50. (This is an average since Betelgeuse is a variable star.)

Using Magnitudes

Amateur astronomers rate how dark the sky is by the dimmest apparent magnitude star one can see with the naked eye. An extremely dark sky has a limiting magnitude of 7.0 or better. A very dark sky will be mag 6.0-7.0. A reasonably dark sky—like those we can get in parts of southern New Jersey will be magnitude 5.5-6.0. (The Milky Way is visible.) Because of light pollution, suburban skies will have limiting magnitudes of 4.0-5.0 and even less. (The Milky Way is not visible.) The Sun has an apparent magnitude of -26.7 but an absolute magnitude of 4.8. The full Moon's apparent magnitude is -12.6, Venus at its brightest is -4.6, and Mars at its brightest is -2.8. Sirius, the brightest star at visible wavelengths, has an apparent magnitude of -1.46. The Bortle scale is a nine-level numeric scale that measures the night sky's brightness of a particular location.

M45, The Pleiades

An open cluster contains several hundred to a few thousand loosely packed stars. Most of the stars in open clusters are young. The hot B-type stars in the Pleiades, which are about 100 million years old, create the blue reflection nebulosity. (A) The Pleiades (M45) look somewhat like a small version of the dippers. The Pleiades are visible after 9 pm from mid-October until mid-April. The Pleiades (Subaru in Japanese) is easily seen with the unaided eye and is spectacular in binoculars. (Rochus Hess) (B) The logo on Subaru cars reflects the connection to the Pleiades star cluster.

Variable Stars

Any star that varies significantly in brightness with time is called a variable star. Some stars vary in brightness because they cannot achieve proper balance between power welling up from the core and power radiated from the surface. Such a star alternately expands and contracts, varying in brightness as it tries to find a balance.

Apparent brightness and luminosity

Apparent brightness of any star is the amount of light per unit area that reaches us. Apparent brightness obeys the inverse square law. A star's luminosity is the total amount of power it radiates into space, which is stated in watts. (A) This map of Canis Major uses dot size to indicate apparent magnitude (Mapp). (B) This map of Canis Major uses dot size to indicate absolute magnitude (Mabs)—a measure of intrinsic stellar luminosity.

Stellar Brightness: Magnitudes

Apparent magnitude is the relative brightness of stars as seen with the naked eye from Earth. Hipparchus (135 B.C.) was the first to classify stars from magnitude 1 (bright) to magnitude 6 (dim). Magnitude 1 is 100X brighter than magnitude 6, so each magnitude change is ≈2.512 (1001/5 ≈ 2.512). In modern times, we know of stars brighter than magnitude 1, so we use 0 and negative numbers (which the ancient Greeks did not have) to indicate the brightest stars and numbers greater than 6 to indicate dim stars. Under very dark skies, the human eye can see to magnitude 6.5-7.0.

Eclipsing Binary

Both the timing and magnitude changes of an eclipsing binary system can be measured and graphed. (1)Only the light from star A is visible as star B is in eclipse. (2)Both star A and star B are visible, giving the maximum light output of the system. (3)Star B is transiting star A, which slightly reduces the total light output of the system. (4)Again, stars A and B are both visible, giving the baseline light output. (5)The eclipse cycle begins again.

Distance Measurements & Eclipsing Binaries

Careful observations of a rare class of double star have produced a more precise value for the distance to the Large Magellanic Cloud (LMC)—163,000 l-y. The distance to the LMC was determined by observing eclipsing binaries. As these stars orbit each other they pass in front of each other. When this happens, as seen from Earth, the total brightness drops, both when one star passes in front of the other and, by a different amount, when it passes behind. By tracking these changes in brightness and also measuring the stars' orbital speeds, the size of the stars, their masses, and other information about their orbits can be determined. When this is combined with measurements of the total brightness and colors of the stars, very accurate distances can be found. This method has been used before, but just with hot stars. However, certain assumptions have to be made in this case and such distances are not as accurate as is desirable. But now, for the first time, eight extremely rare eclipsing binaries where both stars are cooler red giant stars have been identified. Careful study of these stars yield distance values accurate to about 2%.

Cepheid Variable Stars

Cepheid periods are closely related to their luminosities: the longer the period, the more luminous the star. This period-luminosity relation holds because larger (more luminous) Cepheids take longer to pulsate in and out in size. Measuring the period of a Cepheid variable, one can use the period-luminosity relation to determine its luminosity. In turn, its distance can be determined with the luminosity-distance formula. Polaris is a Cepheid variable as well as being a triple star system. Polaris is an odd case as it pulsates very little. Most pulsating variable stars inhabit an instability strip on the H-R diagram. The most luminous ones are known as Cepheid variables. Star trails surround the Cepheid variable star Polaris. Cepheid variable stars are found in what is known as the instability strip, which is off of the main sequence.

Dwarf Star

Coined in 1906 by Danish astronomer Ejnar Hertzsprung noticed that the reddest stars-classified as K and M in the Harvard scheme-could be divided into two distinct groups. They are either much brighter than the Sun, or much fainter. To distinguish these groups, he called them "giant" and "dwarf" stars. The dwarf stars are fainter and the giant stars are brighter than the Sun. The scope of the term "dwarf was later expanded to include any main-sequence star of luminosity class V. dwarf stars can be up to 200 times the mass of the Sun and up to 20,000X brighter. Our Sun is a dwarf star. Dwarf stars are the main sequence stars that fuse hydrogen. Most stars fall along the main sequence. By definition, all stars along the main sequence are fusing hydrogen into helium in their cores. Note that of the four main parts of the H-R diagram, only stars on the main sequence are fusing hydrogen in their cores.

Balancing Gravity in High Mass Stars

Core pressure and temperature of a higher-mass star need to be larger in order to balance gravity. A higher core temperature boosts the fusion rate, leading to larger luminosity. High-mass stars have a larger luminosity as a result of having a greater surface area. This larger luminosity means that high-mass stars live shorter lives.

Double star system SS Leporis

Double star system SS Leporis (17 Lep), created from observations made with the VLT Interferometer at ESO's Paranal Observatory using the PIONIER instrument. The system consists of a red giant star orbiting a hotter companion. The remarkable image sharpness—50 times sharper than those from the NASA/ESA Hubble Space Telescope—not only allows the stars to be clearly separated and their orbital motion followed, but also allowed the size of the red giant to be measured more accurately than ever before. Note that the stars have been artificially colored to match their known temperatures. (ESO/PIONIER/IPAG)

Thermal Radiation

Every object emits thermal radiation with a spectrum that depends on its temperature. An object of fixed size grows more luminous as its temperature rises. A metal poker left in a fire allows us to see that continued heating causes the poker to grow more luminous.

Hyades finder chart

Finder chart for the Hyades open star cluster in the constellation Taurus (the bull). Note the position of the bright open cluster M45, also known as the Pleiades.

Inverse Square Law-1

For light, the inverse square law tells us that the apparent brightness of a star declines with the square of its distance. Inverse square law: the luminosity-distance formula is given in watts per square meter: apparent brightness=luminosity/4(pi)(distance)<2 This relationship is correct only if there is no intervening interstellar dust to scatter or absorb the incoming starlight. As light moves away from a source, it spreads out over an area that is the square of the distance traveled.

Parallax

For nearby stars, we can measure their distances through stellar parallax, where the star's parallax angle is defined as half the star's annual back-and-forth shift. Parallax angles are very small even for nearby stars We can measure stellar parallaxes for stars only within a few hundred light years of Earth We have measured the parallaxes of more than 300 stars within 33 light years (10 parallaxes) of the sun. Distance to an object with a parallax of 1 arcsecond is 1 parsec (1pc) 1 pc= 3.26 light years = 206,265 AU = 3.09 x 10<13 km 1 kpc= 1,000 pc and 1 Mpc= 1,000,000 pc An observer on Earth sees the apparent motion of a nearby star as a small ellipse in the sky relative to the background stars over the period of a year. This apparent motion is the parallax of the star. (1 AU and 1 pc are not to scale.)

M4, Globular Cluster in Scorpius

Globular clusters contain hundreds of thousands of stars and form a halo around the nuclear bulge of our galaxy. The stars in globular clusters are very old, between 9 and 12 billion years old. M4 is the closest globular cluster to us at 7,000 l-y (2.1 kpc). M4 is found near Antares in the constellation Scorpius and is visible in the southern sky at 10:00 pm from June 1 to September 1.

Globular Star Clusters

Globular clusters... Are found in halo of the galaxy (though some are in the disk). Contain from hundreds of thousands of stars to over a million stars. Span from 60 to 150 light-years (spherical shape). In their innermost portion 10,000 stars can be packed into a few light-years across. Usually are composed of very old stars. Contain little gas or dust. Globularstar cluster M55 contains 100,000 stars, is 100 light-years across, and is located 20,000 l-y (6 kpc) away in Sagittarius.

Main sequence: star summary

High Mass: High luminosity Large radius Short-lived Blue Low Mass: Low luminosity Small radius Long-lived Red Main-sequence stars from large blue stars to tiny red stars. All are considered to be dwarf stars because all are fusing hydrogen in their cores. Note that the smaller a star's mass (and hence its radius), the longer the star lives. Conversely, a higher mass star has a larger radius that radiates energy away at a faster rate, thus shortening its life span.

Surface Temperature of Stars

Hottest stars:0050,000 K Coolest stars:00<3,000 K Sun's surface temperature is 5,800 K. The surface temperature and color of stars are related to their black-body curves.

Cecilia Payne-Gaposchkin

In 1925, Cecilia Payne-Gaposchkin was the first to show that the Sun is mainly composed of hydrogen, contradicting accepted wisdom at the time. Shediscovered that a star's surface temperature determines the strength of its spectral lines and applied the newly developed science of quantum mechanics to show that spectral differences reflected changes in the ionization level of the emitting lines. Cecilia Payne-Gaposchkin (1900-1979). Noted astronomer Otto Struve characterized her Ph.D. thesis as "undoubtedly the most brilliant Ph.D. thesis ever written in astronomy."

Size Comparisson

Jupiter, Saturn, Uranus, Neptune, Earth, Venus, Mars, and Mercury. A comparison of the Sun with Sirius (the brightest star we see in our night sky), Pollux (the brightest star in Gemini), and Arcturus, the brightest star in Boötes. The radius of the star Antares is 271% larger than the radius of the orbit of Mars and about 79% the radius of the orbit of Jupiter. A comparison of star diameters ranging from a supergiant to a white dwarf. Earth is approximately the same diameter as a white dwarf.

More on Magnitudes

Larger apertures can see dimmer stars, i.e., stars with higher magnitude numbers Light pollution limits the faintest stars one can see; suburban skies: magnitude 3-4; dark skies: magnitude 5.5-7 Some apparent magnitudes: 26.80 Sun 1.46 Sirius 12.74 Moon (full) 0.74 Canopus 04.60 Venus (at max) 0.03 Vega 02.80 Mars (at max) 1.97 Polaris Apparent magnitudes and distances of the 10brightest stars: Sirius −1.46 (8.6 l-y); Canopus−0.72 (74 l-y); Alpha Centauri−0.27 (4.3 l-y); Arcturus−0.04 (34 l-y); Vega 0.03 (25 l-y); Capella 0.08 (41 l-y); Rigel 0.12 (1,400 l-y); Procyon 0.38 (11.4 l-y); Achernar 0.46 (69 l-y); Betelgeuse 0.50 (1,400 l-y) A conjunction of Venus (left), Moon (middle), and Jupiter (right) taken on December 1, 2008. Moon's apparent magnitude varies from −12.74 (full) to −10.0 (quarter) to −6 (crescent) to −2.5 (new Moon illuminated by earthshine). Venus's apparent magnitude varies from −4.6 (crescent) to −3.8 (full). Jupiter's apparent magnitude varies from −2.94 to −1.6.

The Beehive Cluster (M44)

Like the Pleiades, M44 has been known since prehistoric times as it is visible to the naked eye. Commonly called the Beehive, this open cluster is also known as Praesepe (Latin for "manger"). M44 contains more than 200 stars, is 577 light-years (176.8 pc) away, and astronomers estimate its age at 730 million years. Best observed with binoculars, M44 is found in the constellation Cancer. M44, the Beehive cluster is best viewed from mid-December until June 1

A star's spectral lines

Lines in a star's spectrum correspond to a spectral type that reveals its temperature. Very hot stars have few spectral lines while cool stars have many. Spectral type or class directly tells us how hot a star is.

Stellar spectra compared

Low-temperature M class stars show many lines. These stars are cool enough that molecular compounds can form. The abbreviations to the right represent different star catalogs: HD = Henry Draper Catalogue; BD = Bonner Durchmusterung; SAO = Smithsonian Astrophysical Observatory; Yale = Yale Observatory Zone Catalog.

Luminosity and Surface Area

Luminosity is proportional to the surface area of a star. For two stars of the same surface temperature but different diameters, the larger star will be more luminous. A comparison of the surface area and luminosity of two stars of the same temperature but differing radii. The bigger one will have a greater intrinsic luminosity

Luminosity vs. Brightness

Luminosity is the total amount of power a star radiates and is defined as: energy per second = joules/s = watts. Though most of the power output for our Sun is in visible wavelengths, the Sun also produces continuously flowing energy in X-ray, ultraviolet, and infrared. Apparent brightness is the amount of starlight that reaches Earth and is defined as: energy per second per square meter or w/m2. The amount of visible light from a star that reaches an individual's eyes on Earth is a small fraction of the total power output of that star.

Radiation and the Inverse Square Law

Luminosity passing through each segment of a sphere is the same. Divide luminosity by area to get brightness. The red lines represent the radiative flux (the amount of power radiated through a given area, in the form of photons, typically measured in W/m2) emanating from the source, S. The total number of flux lines depends on the strength of the source and is constant with increasing distance. A greater density of flux lines (lines per unit area) means a stronger field. The density of flux lines is inversely proportional to the square of the distance from the source because the surface area of a sphere increases with the square of the radius. Thus, the strength of the field is inversely proportional to the square of the distance from the source. Area of sphere: 4π (radius)2

Stellar Properties Review

Luminosity: from brightness and distance, range is (0.08 M-sun symbol) 10<-4L (sun symbol) - 10<6 L (sun symbol) (120-150 M sun symbol) Temperature: from color and spectral type, range is (0.08M sun symbol) 3,000K - 50,000K (120-150 M sun symbol) Mass: from period (p) and average separation (a) of binary-star orbit, range is 0.08 M (sun symbol) - 120 to 150 M (sun symbol)

Finder chart for M35 in Gemini

M35 and NGC 2158 are visible at 9:00 pm from November 10 to May 10. NGC 2158 sits below M35, with the two clusters separated by a little over 26 arcminutes.

M7, Ptolemy Cluster

M7 (NGC 6475), sometimes known as the Ptolemy Cluster, is an open cluster of stars in the constellation of Scorpius. Look for it close to the "stinger" of Scorpius. It was first recorded by the 1st-century astronomer Ptolemy in 130 AD. Charles Messier catalogued the cluster in 1764. Telescopic observations of the cluster reveal about 80 stars within a field of view of 1.3° across. At the cluster's estimated distance of 800-1,000 l-y (245-306 pc), this corresponds to an actual diameter of 18-25 light-years. The age of the cluster is around 220 million years. Open cluster M7 is visible at 10:00 pm from July 1 to September 1.

Main sequence stars

Main-sequence stars are fusing hydrogen into helium in their cores like the Sun. Luminous main-sequence stars are hot (blue). Less luminous ones are cooler(yellow yellow or red). Main sequence stars are in hydrostatic equilibrium

Measuring Stellar Masses

Mass is a star's most important property; stellar masses are harder to measure than luminosities or surface temperatures. Stellar masses are relatively easy to measure only in binary star systems, but you still need to know the orbital periods of both stars as well as their separation. A binary system of stars orbit around their common center of mass (barycenter) indicated by the "+."

Mass and Main sequence stars

Mass measurements of main-sequence stars show that the hot, blue stars are much more massive than the cool, red ones. The mass of a normal, hydrogen-burning star determines its luminosity and spectral type! Also, the more massive a star, the shorter is its lifespan.

Mizar and Alcor

Mizar and Alcor's proper motions show they move together (they are both members of the Ursa Major Moving Group), raising the question of whether they are gravitationally bound. In 2009, it was independently reported by two groups of astronomers (Mamajek et al. and Zimmerman et al.) that Alcor actually is itself a binary, consisting of Alcor A and Alcor B, and that this binary system is most likely gravitationally bound to Mizar, bringing the full count of stars in this complex system to six. These studies also demonstrated that the Alcor binary and Mizar quadruple are somewhat closer together than previously thought: approximately 74,000 ± 39,000 astronomical units or 0.5-1.5 light years. (A) Mizar and Alcor are separated by about 10 arcmin. (B) The bowl and a portion of the handle stars of the Big Dipper are visible in this photograph taken by astronaut Donald R. Pettit, NASA ISS science officer, on board the International Space Station.

Mizar: An Example of a Double Spectroscopic Binary

Mizar—in the handle of the Big Dipper—is an optical double with Alcor (though current research indicates the two are gravitationally interacting, which would make them a true double), a visual binary itself (Mizar A and B), and a double spectroscopic binary. Alcor is also suspected of having an unseen companion. The two inset images of Mizar/Alcor and Mizar A/B are telescopic images.

Stellar Masses

Most massive stars: 120-150 M(sun symbol) (exact limit is not well established) Least massive stars:0.08 M(sunspot) M(sunspot)is the mass of the Sun, which is defined as 1 solar mass. Size and mass of very large stars: Most massive example is the blue Pistol Star (150 Msunspot). Others are Rho Cassiopeiae (40 Msunspot), Betelgeuse (20 Msunspot), and VY Canis Majoris (30-40 Msunspot). The Sun (1 Msunspot), which is not visible in this thumbnail, is included to illustrate the scale of example stars. Earth's orbit (grey), Jupiter's orbit (red), and Neptune's orbit (blue) are also given.

Patterns in the H-R Diagram

Most stars fall along the main sequence. Most of these are called dwarf stars. Stars at the top are supergiants—very large and very bright. Below supergiants are giants—smaller and less luminous but still brighter than main-sequence stars of the same spectral type. White dwarfs are stars near the lower left that are small in radius and appear white in color because of their high temperature.

Stellar Temperatures

Note that stellar interior temperatures cannot be measured and are determined as the result of theoretical models. The emission and absorption lines in a star's spectrum provide an independent and more accurate way to measure its surface temperature. Stars that show spectral lines of ionized elements will be hotter than stars that show spectral lines of molecules.

Open star clusters

Open clusters... Are found in disk of the galaxy. Contain up to several thousand stars. Span up to 30 light-years. Usually are composed of young stars. Contain much gas and dust. Open star clusters M35 (upper left) and NGC 2158 (lower right). These clusters can be found at the foot of Gemini. M35 is 2,800 l-y (0.9 kpc) away, and NGC 2158 is 11,000 l-y (3.4 kpc) distant.

Magnitude System

Originally, the magnitude system of describing stellar brightness was strictly a visual one, i.e., naked eye. We now call these apparent magnitudes because this is how bright stars appear to us on Earth. The modern magnitude scale precisely defines absolute magnitude in terms of a star's true luminosity. A star's absolute magnitude is the apparent magnitude a star would have if it were observed at a distance of 10 parsecs from Earth. The modern magnitude scale is defined so that each difference of 5 magnitudes corresponds to a factor of 100 in brightness. Thus a single magnitude corresponds to a factor of (100)1/5which is approximately equal to 2.512. The apparent magnitudes of large asteroid 65 Cybele (11.6) and stars HD 217121 (8.7) and HD 216932 (9.1) are shown on this image. The two bright stars would be near the limit of typical 50-mm binoculars. Also visible towards the upper right are the galaxies PGC194570 and PGC1016451

Parallax Defined

Parallax is the apparent shift in position of a nearby object against a background of more distant objects. The term parallax is derived from the Greek παραλλαγή (parallagé), meaning "alteration."

How Parallax works

Parallax uses trigonometry and the relation between angles and sides of a right triangle. The baseline of the right triangle is the Earth-Sun distance or 1 AU. As Earth orbits the Sun, the position of a nearby star appears to shift against the background of more distant stars. This principle of stellar parallax was known to the ancient Greeks, but they lacked the technology to detect it.

Two types of star clusters

Pleiades (M45), an open cluster An open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud, and are still loosely gravitationally bound to each other. Open clusters are found only in spiral and irregular galaxies, in which active star formation is occurring. They are usually less than a few hundred million years old. M80, a globular cluster A globular cluster is a spherical collection of stars that orbits a galactic core. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes. Globular clusters are found in the halo of a galaxy and contain many more stars and are much older than the less dense galactic, or open clusters, which are found in the disk.

Polaris is a triple star system

Polaris or α Ursae Minoris—the North Star—is actually a triple star system 433 light-years (132.7 pc) from Earth. It took the Hubble Telescope to "see" the third close-in companion (AB). Polaris A is a supergiant variable star known as a Cepheid variable.

Pulsating Variable Stars

Pulsating variable stars expand and contract their outer atmospheres, resulting in a rise and fall in luminosity. Most pulsating variable stars inhabit a strip (the instability strip) on the H-R diagram between the main sequence and the red giants. Cepheid variables are a special group of very luminous pulsating variables that can be employed as standard candles to determine distances to nearby galaxies. (A) Mira (aka Omicron Ceti) is a red giant star estimated to be 300 l-y (92 pc) away in Cetus. Mira is a binary star (red giant Mira A + Mira B). Mira A is also a pulsating variable star. (NASA/ESA) (B) HST image of the galaxy M100 showing a Cepheid variable.

R136a1: Most Massive Star

R136a1—the most massive star yet found—is located in the Tarantula nebula in the Large Magellanic Cloud, which is 163,000 l-y (50 kpc) distant.

Range of Pleasmas

Range of plasmas. Density increases upwards, temperature increases towards the right. The free electrons in a metal may be considered an electron plasma. Note that plasma temperature can be given in either electron-volts (eV) or kelvins (K).

Spectral Types

Stars are classified according to surface temperature by assigning a spectral type. Annie Jump Cannon (1863-1941; from Delaware; she worked at Harvard) classified over 350,000 stellar spectra. Cannon developed the spectral class system and sub-system, and her system is what is used today. O B A F G K M ("Oh Be AFine Girl Kiss Me") Subdivisions are numbered from 0 (hottest) to 9 (coolest). The Sun is a G2 star (a hot G-type star). L and T stars are very cool and in some instances are brown dwarfs (above L2.5) Spectrum of a O5v-class star. Wavelengths are given in angstroms.

White Dwarfs

Stars with higher T and lower L than main-sequence stars must have smaller radii: these are White dwarfs.

Giants and Super giants

Stars with lower T and higher L than main-sequence stars must have larger radii: these are Giants and Supergiants.

Stellar Luminosities

Stellar luminosities cover a range of 10 orders of magnitude (10 billion). Most luminous stars:106L (sun symbol) Least luminous stars:10−4L(sun symbol) L(Sun symbol) is "luminosity of Sun" (defined as 1 solar luminosity).

Off the main sequence

Stellar properties depend on both mass and age: those that have finished fusing H to He in their cores are no longer on the main sequence. All stars become larger and redder after exhausting their core hydrogen: giants and supergiants. A giant with a mass similar to that of the Sun will form a white dwarf, no larger in size than our Earth. Larger-mass supergiants will explode, leaving behind neutron stars or, in rare cases, black holes.

Mass and Life Expectancy

Sun's life expectancy: 10 billion years ----> Until core hydrogen (10% of total) is used up Life expectancy of 10 M(sun symbol) star: 10X as much fuel, use it 10<4 (10,000) times as fast 10 million years~10 billion years x 10/10<4 10<10 x 10/10<4 = 10<11/10<4=10<7= 10 million years Life expectancy of 0.1 M (sun symbol) star: 0.1 (1/10th) times as much fuel, uses it 0.01 (1/100th) times as fast 10 billion years~10 billion years x 0.1/0.01 10<10 x 10<-1/10<-2= 10<9/10<-2=10<11=100 billion years

The H-R Diagram Depicts

Temperature Color Spectral type Luminosity Radius Mass Lifespan The H-R diagram is the single most important graph in astronomy.

Cassiopeia & the Double Cluster

The Double Cluster (NGC 884 and NCG 869) is always above the horizon but is best viewed from mid-August to mid-April. NCG 884 and 869 both lie at a distance of 7,300 l-y (2.2 kpc) and both are about 12.6 million years old. The clusters are also blueshifted, with NGC 869 approaching Earth at a speed of 39 km/s (24 mi/s) and NGC 884 approaching at a similar speed of 38 km/s (24 mi/s). Their hottest main sequence stars are of spectral type B0.

M11 Wild Duck Cluster

The Wild Duck Cluster (also known as Messier 11, or NGC 6705) is an open cluster in the constellation Scutum. It was discovered by Gottfried Kirch in 1681. Charles Messier included it in his catalogue in 1764. The Wild Duck Cluster is one of the richest and most compact of the known open clusters, containing about 2,900 stars. Its age has been estimated to about 220 million years. The cluster is 6,200 l-y (1.9 kpc) distant. Its name derives from the brighter stars forming a triangle that could represent a flying flock of ducks. The Wild Duck Cluster is visible at 10:00 pm from June 20 to October 15.

Brightness of a Star = Distance and Luminosity

The brightness of a star depends on both distance and luminosity.

Adaptive Optics & Binary Stars

The double star GJ263 as observed by the Very Large Telescope using the NACO adaptive optics system. The angular distance between the two stars is only 0.030 arcsec. Adaptive Optics (AO) System: Light from the telescope is sent to a deformable (adaptive) mirror, then to a beamsplitter, where part of the light is reflected to the wavefront sensor. The wavefront sensor measures the distortion in the wavefront and sends a correction signal to the deformable mirror. The deformable mirror changes shape to remove the distortions in the lightwave before the light goes to the camera.

Mizar A's Companion revealed

The first spectroscopic system discovered was Mizar or ζ Ursae Majoris in 1889. (The initial spectrograms were taken in 1887.) Actually Mizar was already known as a visual binary but spectroscopic analysis of the brighter of the two stars, Mizar A, showed that it was in fact a spectroscopic binary. Subsequent observations revealed that Mizar B was also a spectroscopic binary; thus the whole system comprised four stars. With recent improvements in optical interferometry and imaging techniques, modern astronomers can now "split" or resolve Mizar A into its component stars as is shown in the image.

The Largest Known Star

The largest known star—V1489 Cygni—has a diameter 1,650 times that of the Sun. Its edge would reach to 80% of the distance to the orbit of Saturn. This star has a mass of about 25-40 M

Ionization

The level of ionization also reveals a star's temperature. The spectral class of a star describes the ionization of the star's chromosphere, which gives an objective measure of the chromosphere's temperature. In the 1920s, the Indian physicist Meghnad Saha derived a theory of ionization. First applied to the solar chromosphere, he then applied it to stellar spectra. Harvard astronomer Cecilia Payne-Gaposchkin then demonstrated that the OBAFGKM spectral sequence developed between 1890 and 1912 is actually a sequence in temperature. As more heat is added to a substance, the molecules and atoms move more freely and with increasing speed. At high enough temperatures, ionization occurs: outer electrons are removed from atoms. Most plasmas are at temperatures above 1,000 K.

Light Curve of a CepheidPulsating Variable

The light curve of M31-V1, a Cepheid variable star in the Andromeda Galaxy. The star's period is 31.4 days.

Luminosity Classes on the H-R Diagram

The luminosity classes are specified with Roman numerals: Classes I and II: Supergiants* Class III: Giants Class IV: Subgiants Class V: Dwarfs *Note Class II stars are technically called "bright giants," but they are also massive stars, like supergiants.The Sun is a dwarf star, so it is a GV star. All main sequence stars are dwarfs

Mass-Luminosity Relation

The luminosity of a main-sequence star increases roughly as the mass is raised to the 3.5 power. (A,B) The mass-luminosity relation is nearly a linear function. For example, doubling the mass of a main sequence star increases its luminosity by a factor 23.5, or approximately 11.3. Thus, stars like Sirius that are about twice as massive as the Sun are more than 10 times as luminous. This particular relation between mass and luminosity holds only for stars on the main sequence.

Significance of the main sequence

The orderly arrangement of stellar masses along the main sequence tells us that mass is the most important attribute of a hydrogen-burning star. A 10 M(Sun symbol) star on the main sequence is about 10,000 (10<4) times more luminous than the Sun. Mass determines how much hydrogen fuel the star initially contains in its core. Luminosity determines how rapidly the star uses up its fuel.

Measuring Stellar Temperature

The second basic property of stars is surface temperature, which is determined directly from the star's color or spectrum. (7 major spectral classes)

The Magnitude Scale

These mathematical expressions are used to determine the relative apparent brightness and luminosity of two stars. m= apparent magnitude M= absolute magnitude apparent brightness of star 1/ apparent brightness of star 2 =(100 1/5) <m1-m2 luminosity of star 1/ luminosity of star 2= (100 1/5)< M1-M2 The apparent magnitude scale is used to describe the relative brightness of stars.

R136 Cluster in the LMC

This montage shows a visible-light image of the Tarantula nebula (in the Large Magellanic Cloud) as seen with the Wide Field Imager on the MPG/ESO 2.2-meter telescope (left) along with a zoomed-in visible-light image from the Very Large Telescope (middle). A new image of the R136 cluster, obtained with the near-infrared MAD adaptive optics instrument on the VLT is shown in the right-hand panel, with the cluster itself at the lower right (circled). The MAD image provides unique details on the stellar content of the cluster. (slide 97)

Three cluster in Auriga

Three open clusters—M36, M37, M38—visible in binoculars and small telescopes can be found in Auriga ("charioteer"). Auriga is a late fall and winter constellation and can be viewed from November 1 to May 1.

Mizar A's companion found

Two of the spectra of Mizar A taken at Harvard College Observatory in spring 1887 by Antonia C. Maury. While the K line (393.4 nm) of singly ionized calcium is double on the detail of the first plate (of March 27), it became single by April 5, when the second spectrogram was taken. The other line is H-ε of hydrogen. The only satisfactory explanation found was that Mizar A is itself a binary star with the components nearly equal in brightness and too close to split visually.

2nd Larget Star

VV Cephei A—the second largest star known—is a red super-giant and is part of an eclipsing binary system. This star is 1,050-1,900 times the diameter of the Sun. At its smallest estimated size, its outer edge would reach to within 95% of the orbit of Jupiter. Its mass is not well known and is estimated to be less than 25 times the Sun's mass.

Types of Binary Star Systems

Visual binary: pair of stars we can see distinctly with a telescope as the stars orbit each other. Eclipsing binary: a pair of stars that orbit in the plane of our line of sight; Algol is the most famous example. Spectroscopic binary: neither visual nor eclipsing, we detect these by observing Doppler shifts in its spectral lines. About half of all stars are in binary systems. (A) Astronomers can plot the orbits of the stars in a visual binary. This illustration shows the orbit of a faint visual double star in the constellation Ophiuchus. (NASA) (B) An artist's impression of an eclipsing binary system. (C) In a double-line spectroscopic binary, each star is alternatively moving toward the observer and then away.

Inverse Square Law-2

We can determine a star's luminosity if we can measure its distance and apparent brightness: luminosity=4(pi)(distance)<2 x (brightness) Convenient to use comparative units of solar luminosity, where L(sun symbol)= 3.8 x 10<26 watts total luminosity or total apparent brightness describes the luminosity and apparent brightness we would measure if we could detect photons across the entire electromagnetic spectrum Tucanae (NGC 104) is the second most luminous globular cluster in the Milky Way after Omega Centauri. (ESA/Hubble) Beyond 80 million l-y (24.5 Mpc), even the brightest blue supergiants are not visible. Astronomers turn to entire star clusters for luminosity measurements using the globular cluster luminosity function (GCLF). The brightest globular clusters have total luminosity of about absolute magnitude −7.5 and can be seen out to 326 million l-y (100 Mpc).

Doppler Shift and Spectroscopic Binary

We can determine the orbit of a spectroscopic binary by measuring Doppler shifts. Star A orbits Star B and has a radial velocity. Because of the Doppler effect, as Star A approaches the observer, spectral lines in Star A's spectrum are blueshifted. As Star A moves across the line of sight, there is no Doppler shift, and the observer sees a zero radial velocity spectrum. As Star A begins to move away from the observer, the change in radial velocity causes the lines to redshift.

Mass and gravity

We measure mass using gravity.Direct mass measurements are possible only for stars in binary star systems. p = period a = average separation p<2=4(pi)<2/G(M1+M2)a<3

Measuring Mass

We need 2 out of 3 observables to measure mass in a two-body system: Orbital Period (p) Orbital Separation (a or r = radius) Orbital Velocity (v)For circular orbits, v = 2πr / p

Low Mass vs. High Mass

We see fewer high-mass stars because most have died; low-mass stars are easier to form so we see many more of them, and they live much longer. A low-mass star (0.3 solar masses) has a luminosity 0.01 that of the Sun and thus lives 0.3/0.01 = 30 times longer than the Sun or about 300 billion years (contrast with the age of the universe at 13.8 billion years). As a star begins to run out of fuel, it grows more luminous and expands in size. Many of the brightest stars visible to the naked eye are giants and supergiants.

Spectroscopic Binary

You do not need to see two spectra; only the motion of one of the stars is needed. Typical velocities between binaries are 3 to 5 km/s, so very high- resolution spectra must be taken to observe this phenomenon. (A) Spectra of a spectro-scopic binary as one component of the system orbits the other. Note how spectral lines are redshifted or blueshifted depending on the direction one of the stars is moving. The circled spectral line illustrates this Doppler effect. When the star is crossing our line of sight, the velocity is zero, and we do not see either a redshift or blueshift. (B) The position of the orbiting star as each spectrum is recorded. When the two stars are along the same line of sight (i.e., at minimum separation), only one set of spectral lines is visible. When both stars are seen side by side (i.e., at maximum separation), double the number of spectral lines are observed.

Betelgeuse

α-Orionis—more commonly known as Betelgeuse—is a semi-regular, supergiant variable star in the constellation Orion, about 600 light years from Earth. Betelgeuse is the ninth largest star known, with a diameter 950-1,000 times that of the Sun and a mass 20X that of the Sun. This rendering is in scale with the previous drawings.