Measuring Stars

1 Type Ia Supernova • The type of supernova discussed are called core collapse supernova. • Supernovas are classified into various classes, type I, type II etc., according to features of their spectrums. • One particular type called type Ia, has interesting and important properties.

Starts as a ordinary binary pair more massive star evolves faster and becomes a white dwarf

When the companion goes through the red giant White dwarf mass increase until it reaches the 1.4Mʘ phase it spills matter into the white dwarf Chandrasekhar limit and then explodes 2 SN SCP-0401 A supernova Ia in the pinwheel A supernova Ia in a galaxy galaxy (M101) 20 million ly away 10 billion ly away

• Since Type Ia Supernovae involve an explosion that occurs around a fixed mass (1.4Mʘ ), they are a very homogeneous events, and have about the same luminosity. • So they are like standard candles, wherever they occur, they have the same intrinsic luminosity. • If we see a type Ia supernova somewhere (in another galaxy), by comparing its observed brightness to intrinsic brightness we can estimate the distance to it using the inverse square law. (The inverse square law tells us that the brightness of an object falls off as one over the distance squared) • Since supernova are very bright, they can be seen at large distances, in galaxies billions of light years away. So provide a way to measure distance to far away galaxies. 3 Measuring the Stars: Distance

distant stars

• Nearby stars appear to move with respect to more distant background stars due to the motion of the nearby star Earth around the Sun

parallax • the line of sight to the star when the Earth is at A angle is different than at B, when the Earth is on the other side of its orbit.

• As seen from the Earth, the nearby star appears to move in the sky with respect to the distant stars.

A B • Half of this angle, is called the parallax of the star. • It is the angle subtend by a 1 AU distance at the Earth orbit star.

4 • Closer stars have a larger parallax

• Distant stars have a smaller parallax, if they are very far away parallax is too small to observe. • This gives a means to measure distances to nearby stars directly by measuring their parallaxes. • When the parallax is 1 arc second (1”), corresponding distance is called a parsec (parallax of an arc second) • 1 parsec is about 3.26 light years (or 3.086×1013 km) ퟏ • If a star has a parallax p its distance is parsecs is given by 푫 = 풑 • Parallax of Polaris (north star) is 0.0075” so its distance = 1 =133 parsecs 0.0075 5 • In 1838 Friedrich Bessel measured the parallax of Cygni 61 to be 0.33”, First time a parallax (distance) measured for an object outside the solar system. • Soon after Henderson measured the parallax of alpha Centauri to be 0.76 arc seconds and Struve measured the parallax of Vega to be 0.12 arc seconds.

6 • Even for nearby stars parallax is very small.

• The smallest parallax measurable from the ground is about 0.01-arcsec (100 parsec ) • Better resolution can be obtain from space, thus smaller parallax measurements. • Hipparcos Satellite, operated 1989-1993 had a resolution of 0.001” – Hipparcos measured parallaxes for over 100,000 stars – Got 10% accuracy distances out to about 100 pc – for bright stars out to 1000 pc.

7 Cepheid Variables

• Most stars undergo an unstable oscillations at the end of the red giant phase, later in their evolution. The star becomes a variable star, star with changing brightness. • There are many types of variable stars, and many reason why they change their luminosity periodically. • One type of variable stars called Cepheid Variables, which have periods from one to about 100 days show a direct relationship between their luminosity and the period of variation. • In 1912 Henrietta Leavitt working at the Harvard College Observatory was looking for variable stars in the Small Magellanic Cloud. • She noticed that one type of variable stars, Cepheids (named after delta Cepheus, first star of that type) had a longer period when they were brighter.

8 apparent brightness apparent

A Cepheid in the Andromeda galaxy. log(period)

• Since all stars in the Small Magellanic Cloud are at about the same distance, the brighter stars had longer periods suggested that period and luminosity were related. • Thus if a its period is known, its luminosity can be estimated . • Cepheids are bright supergiant stars (~1000 times brighter than the Sun), so they can be identified even in other galaxies. • In fact, in 1924 Edwin Hubble showed that Andromeda galaxy was an object outside the Mikey way by identifying few Cepheid variables in the Andromeda nebula (as it was called then) and estimating its distance.

9 Steller Temperature and Classification • In principal stellar temperature can be estimated by its color and the peak of the spectrum. • But due to absorption lines and bands in the spectrum it could get complicated. • Spectral lines in the spectrum provide a additional information about the temperature of a star. • Absorption line strength in a stellar spectrum is mostly controlled by the star temperature – Above 25000K show absorption lines of ionized helium and heavier elements appear, because at high temperatures those elements ionize – Hydrogen absorption lines of such stars is very weak, because hydrogen is totally ionized and there are no electrons to make transitions to produce light – At low temperatures (3000k) molecular abortion lines visible, since at low temperatures molecules can survive in the outer layers of the star, which breakdown at higher temperatures. 10 • Stars were first classified according to the strength of hydrogen absorption lines late 19th early 20th century. They used a scheme of classification A, B, C … • But later on in 1920s, with better understanding of atomic structure and spectra it was realized that original order of the scheme was not correct. • They were rearranged according to the temperature as O,B,A,F,G,K,M in descending order of the temperature. • Each class is sub divided 1-10, like B2, G8…

11 Hertzsprung–Russell Diagram O B A F G K M Blue giants 107years

10000 Red super giants 10M☉ 108years 100 R☉ 100 Red giants

1010years Sun 1 10 R☉ main sequenceA Luminosity (solar) Luminosity 1011years

1 R☉ 0.01 0.2M☉ white dwarfs red dwarfs 0.0001 0.1 R☉ 25000 10000 8000 6000 4500 3000 surface temperature • When luminosity of stars is plotted versus their surface temperature, stars appear to fall into few distinct groups, according to their stage of life cycle. • Main Sequence: The majority of stars (~90%), including the Sun, are in a diagonal band, going from upper left corner (hot, luminous, massive stars) to the lower right corner (cool, dim, low mass stars). Those are the stars fusing hydrogen in their cores. Since every star spend most of their life cycle in the hydrogen burning main sequence stage, it is the mostly populated region of the plot.

12 Evolutionary path of a star like Sun in the HR diagram

planetary nebula forms supergiant stage

helium burning 100 R☉

red giant stage 10 R main sequence ☉ helium core Sun contracting 1 R☉

white dwarf

0.1 R☉

13 Star Clusters

M92 M13

• Since a large interstellar cloud first fragments to smaller pieces when it collapses under gravity, end result is a cluster of stars. • All stars in a cluster are of the same age and composition, an ideal place to study the effect of mass on the stellar evolution.

• There are two main types of star clusters: – Globular clusters: A tight spherical collection of hundreds of thousands (or millions) of very old (over 10 billion years) stars. Most of them are in a spherical halo surrounding the galaxy, ~150

14 M44

NGC 3603, A young open cluster, radiation Pleiades pressure from the stars has cleared the M11 cavity in the cloud, few light years across

• Open clusters: A loose irregular group of stars up to few thousands, that originated from the same gas cloud. They are found in the plane (disk) of the galaxy where there is abundant gas and dust for new star formation.

15 Evolution of Stars in a Cluster

Shortly after the formation, massive stars already in the main sequence and burning hydrogen and with lower mass just beginning to arrive on the main sequence.

After 10 million years, the most massive stars have already evolved out the main sequence or exploded, while many of the least massive have not even reached there yet.

After 100 million years, stars larger than 4-5 solar masses have left the main sequence and there is a distinct main- sequence turnoff. Most of the low mass stars are now in the main sequence. 16 red giants

After 1 billion years, main-sequence turnoff is now at about 2 solar masses. Red giant branch associated with low mass is evident. White dwarfs are beginning to appear. white dwarfs

After 10 billion years, solar mass stars are evolving away from the main sequence. The red-giant, supergiant, and horizontal branches are all clearly populated. White dwarfs, indicating that solar-mass stars are in their last phases, also appear.

17 The double cluster in Perseus, H-R diagram shows that most young stars has not reached the MS and only most massive stars has left the MS, it is very young probably 10-15 million years

Pleiades, H-R diagram shows lo mass stars in the main sequence and more higher mass stars moved away from MS, likely it is 100 million years old. The Hyades cluster. Its H-R diagram shows that the MS cut off progressed further down, and few white dwarfs. Probably it is 600 million years old. 19

Globular cluster 47 Tucana, MS turnoff has reached Sun like stars well developed radiant and white dwarf branches. So it has to be more than 10 billion years old. 19 Binary Stars

CoM

• A binary star system consists of two stars which are gravitationally bound and orbit around their center of mass. • About half of the stars are binary, some systems even have more than two. • In some cases individual stars of the can be seen through a telescope, which are called Visual binaries. Many visual binaries have long orbital periods of several centuries or millennia. • In many cases a binary system is too far away, or the stars are too close, or one star is so much brighter than the other that we cannot distinguish the two stars visually. But still we can infer that the system is binary by several indirect methods. – Eclipsing binaries: In some binary systems orbital plane of the stars is oriented edgewise toward earth. So that one star passes directly in front of the other eclipsing its light Most famous example is Algol: 20 Algol: • A star in the constellation Perseus known for centuries which change its brightness. • A blue spectral class B8 star with a diameter of 3 solar diameters and red-yellow spectral class K2 star of about 3.5 solar diameters are in very close orbit around each other. • They are so close together that tidal forces are distorting the shape of the K2 star, into a teardrop shape.

21 • Spectroscopic binaries are systems in which the stars are so close together that they appear as a single star even in a telescope. • The only evidence of a binary star comes from the Doppler effect on its emitted light. • As the stars move through their orbits around the center of mass, their radial velocity toward Earth changes, which blue and red shift their spectral lines.

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