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.

2

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

When the companion goes through the red giant phase it spills matter into the white dwarf

White dwarf mass increase until it reaches the 1.4Mʘ

Chandrasekhar limit and then explodes

• 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

SN SCP-0401

A supernova Ia in a galaxy 10 billion ly away

A supernova Ia in the pinwheel galaxy (M101) 20 million ly away

Measuring the Stars: Distance

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

• the line of sight to the star when the Earth is at A 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.

• Half of this angle, is called the parallax of the star.

• It is the angle subtend by a 1 AU distance at the star.

4

A B

distant stars

nearby star

parallax angle

Earth orbit

5

• 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)

• If a star has a parallax p its distance is parsecs is given by 𝑫 =𝟏

𝒑

• Parallax of Polaris (north star) is 0.0075” so its distance = 1

0.0075=133 parsecs

• 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

• 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

log(period)

app

aren

t b

righ

tne

ss

A Cepheid in the Andromeda galaxy.

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

• 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

Lum

ino

sity

(so

lar)

main sequence

white dwarfs

Red giants

Red super giants

red dwarfs

25000 6000 4500 3000800010000

A

A

BO F G K MBlue giants

0.01

0.0001

1

100

10000

0.1 R☉

1 R☉

10 R☉

100 R☉

Sun

surface temperature

0.2M☉

10M☉

1010years

1011years

107years

108years

Evolutionary path of a star like Sun in the HR diagram

13

red giant stage

helium burning

planetary nebula forms

supergiant stage

Sun

0.1 R☉

1 R☉

10 R☉

100 R☉

white dwarf

main sequence

helium core contracting

Star Clusters

• 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

M13 M92

• 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

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

Pleiades

M44

M11

Evolution of Stars in a Cluster

16

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.

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.

17

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.

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.

white dwarfs

red giants

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.

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

19

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.

Binary Stars

• 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

CoM

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.

22