ASTROPHYSICS REVIEW

The Solar System

The Sun  Mass: 1.99 x kg  Radius:6.96 x 10 8 m  Surface temperature: 5800 K  Mass: 1.99 x kg  Radius:6.96 x 10 8 m  Surface temperature: 5800 K

PlanetPictureDistance to the Sun (km) Radius (km)Orbital period around its axis Orbital period Surface day temp (ºC) Density (water=1) Satellites Mercury58 million4 878 km59 days88 days1675,430 Venus108 million km-243 days225 days4645,240 Earth149,6 million km23, 93 h365,2 days155,521 Mars228 million6 794 km24h 37min687 days-653,042 Jupiter778 million km9h 50min 30s12 years-1101,32+63 Saturn1 427 million km10h 14min29,5 years-1400,69+56 Uranus2 870 million km16h 18min84 years-1951,2727 Neptune4 497 million km15h 48min164 years-2001,7713 Pluto5 900 million2 400 km6 days248 years Planets Data

Galaxies A galaxy is a collection of a very large number of stars mutually attracting each other through the gravitational force and staying together. The number of stars varies between a few million and hundreds of billions. There approximately 100 billion galaxies in the observable universe. There are three types of galaxies: - Spiral (Milky Way) - Elliptical (M49) - Irregular (Magellanic Clouds)

Constellations A group of stars in a recognizable pattern that appear to be near each other in space. Orion

A star is a big ball of gas, with fusion going on at its center, held together by gravity! There are variations between stars, but by and large they’re really pretty simple things. Massive Star Sun-like Star Low-mass Star

What is the most important thing about a star? MASS! The mass of a normal star almost completely determines its LUMINOSITYTEMPERATURE The mass of a normal star almost completely determines its LUMINOSITY and TEMPERATURE!  Note: “normal” star means a star that’s fusing Hydrogen into Helium in its center (we say “hydrogen burning”).

Luminosity The Luminosity of a star is the energy that it releases per second. Sun has a luminosity of 3.90x10 26 W (often written as L  ): it emits 3.90x10 26 joules per second in all directions. The energy that arrives at the Earth is only a very small amount when compared will the total energy released by the Sun.

Apparent brightness  When the light from the Sun reaches the Earth it will be spread out over a sphere of radius d. The energy received per unit time per unit area is b, where: d b is called the apparent brightness of the star

Black body radiation  A black body is a perfect emitter. A good model for a black body is a filament light bulb: the light bulb emits in a very large region of the electromagnetic spectrum.  There is a clear relationship between the temperature of an object and the wavelength for which the emission is maximum. That relationship is known as Wien’s law:  A black body is a perfect emitter. A good model for a black body is a filament light bulb: the light bulb emits in a very large region of the electromagnetic spectrum.  There is a clear relationship between the temperature of an object and the wavelength for which the emission is maximum. That relationship is known as Wien’s law:

Black body radiation and Wien Law

Black body radiation  Apart from temperature, a radiation spectrum can also give information about luminosity.  The area under a black body radiation curve is equal to the total energy emitted per second per unit of area of the black body. Stefan showed that this area was proportional to the fourth power of the absolute temperature of the body.  The total power emitted by a black body is its luminosity.  According to the Stefan-Boltzmann law, a body of surface area A and absolute temperature T has a luminosity given by:  Apart from temperature, a radiation spectrum can also give information about luminosity.  The area under a black body radiation curve is equal to the total energy emitted per second per unit of area of the black body. Stefan showed that this area was proportional to the fourth power of the absolute temperature of the body.  The total power emitted by a black body is its luminosity.  According to the Stefan-Boltzmann law, a body of surface area A and absolute temperature T has a luminosity given by: where, σ = 5.67x10 8 W m -2 K -4

The Spectral Sequence ClassSpectrumColorTemperature O ionized and neutral helium, weakened hydrogen bluish31,000-49,000 K B neutral helium, stronger hydrogen blue-white10,000-31,000 K A strong hydrogen, ionized metals white ,000 K F weaker hydrogen, ionized metals yellowish white K G still weaker hydrogen, ionized and neutral metals yellowish K K weak hydrogen, neutral metals orange K M little or no hydrogen, neutral metals, molecules reddish K L no hydrogen, metallic hydrides, alkalai metals red-infrared K T methane bands infraredunder 1200 K

“If a picture is worth a 1000 words, a spectrum is worth 1000 pictures.”  Spectra tell us about the physics of the star and how those physics affect the atoms in it

Types of Stars  Red Giants Very large, cool stars with a reddish appearance. All main sequence stars evolve into a red giant. In red giants there are nuclear reactions involving the fusion of helium into heavier elements.  Red Giants Very large, cool stars with a reddish appearance. All main sequence stars evolve into a red giant. In red giants there are nuclear reactions involving the fusion of helium into heavier elements.

Types of Stars  Cepheid variables Cepheid variables are stars of variable luminosity. The luminosity increases sharply and falls of gently with a well-defined period. The period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star. A Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity. The luminosity of Cepheid stars range from 10 3 to 10 4 times that of the Sun.  Cepheid variables Cepheid variables are stars of variable luminosity. The luminosity increases sharply and falls of gently with a well-defined period. The period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star. A Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity. The luminosity of Cepheid stars range from 10 3 to 10 4 times that of the Sun.

Types of Stars  Binary stars A binary star is a stellar system consisting of two stars orbiting around their centre of mass. For each star, the other is its companion star. A large percentage of stars are part of systems with at least two stars. Binary star systems are very important in astrophysics, because observing their mutual orbits allows their mass to be determined. The masses of many single stars can then be determined by extrapolations made from the observation of binaries.  Binary stars A binary star is a stellar system consisting of two stars orbiting around their centre of mass. For each star, the other is its companion star. A large percentage of stars are part of systems with at least two stars. Binary star systems are very important in astrophysics, because observing their mutual orbits allows their mass to be determined. The masses of many single stars can then be determined by extrapolations made from the observation of binaries. Hubble image of the Sirius binary system, in which Sirius B can be clearly distinguished (lower left).

Binary stars There are three types of binary stars  Visual binaries – these appear as two separate stars when viewed through a telescope and consist of two stars orbiting about common centre. The common rotation period is given by the formula: There are three types of binary stars  Visual binaries – these appear as two separate stars when viewed through a telescope and consist of two stars orbiting about common centre. The common rotation period is given by the formula: where d is the distance between the stars. Because the rotation period can be measured directly, the sum of the masses can be determined as well as the individual masses. This is useful as it allows us to determine the mass of singles stars just by knowing their luminosities. where d is the distance between the stars. Because the rotation period can be measured directly, the sum of the masses can be determined as well as the individual masses. This is useful as it allows us to determine the mass of singles stars just by knowing their luminosities.

Binary stars  Eclipsing binaries – some binaries are two far to be resolved visually as two separate stars (at big distances two stars may seem to be one). But if the plane of the orbit of the two stars is suitably oriented relative to that of the Earth, the light of one of the stars in the binary may be blocked by the other, resulting in an eclipse of the star, which may be total or partial

Doppler effect In astronomy, the Doppler effect was originally studied in the visible part of the electromagnetic spectrum. Today, the Doppler shift, as it is also known, applies to electromagnetic waves in all portions of the spectrum. Also, because of the inverse relationship between frequency and wavelength, we can describe the Doppler shift in terms of wavelength. Radiation is redshifted when its wavelength increases, and is blueshifted when its wavelength decreases.

Binary stars  Spectroscopic binaries – this system is detected by analysing the light from one or both of its members and observing that there is a periodic Doppler shifting of the lines in the spectrum.

Types of Stars  White dwarfs A red giant at the end stage of its evolution will throw off mass and leave behind a very small size (the size of the Earth), very dense star in which no nuclear reactions take place. It is very hot but its small size gives it a very small luminosity. As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense.  White dwarfs A red giant at the end stage of its evolution will throw off mass and leave behind a very small size (the size of the Earth), very dense star in which no nuclear reactions take place. It is very hot but its small size gives it a very small luminosity. As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense. A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of 35,500 K.

The Hertzsprung-Russell diagram You are here This diagram shows a correlation between the luminosity of a star and its temperature. The scale on the axes is not linear as the temperature varies from 3000 to K whereas the luminosity varies from to 10 6, 10 orders of magnitude.

H-R diagram  The stars are not randomly distributed on the diagram.  There are 3 features that emerge from the H-R diagram:  Most stars fall on a strip extending diagonally across the diagram from top left to bottom right. This is called the MAIN SEQUENCE.  Some large stars, reddish in colour occupy the top right – these are red giants (large, cool stars).  The bottom left is a region of small stars known as white dwarfs (small and hot)  The stars are not randomly distributed on the diagram.  There are 3 features that emerge from the H-R diagram:  Most stars fall on a strip extending diagonally across the diagram from top left to bottom right. This is called the MAIN SEQUENCE.  Some large stars, reddish in colour occupy the top right – these are red giants (large, cool stars).  The bottom left is a region of small stars known as white dwarfs (small and hot)

Astronomical distances  The light year (ly) – this is the distance travelled by the light in one year. 1 ly = 9.46x10 15 m c = 3x10 8 m/s t = 1 year = x 24 x 60 x 60= 3.16 x 10 7 s Speed =Distance / Time Distance = Speed x Time = 3x10 8 x 3.16 x 10 7 = 9.46 x m

Astronomical distances  The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond. 1 pc = 3.086x10 16 m or 1 pc = 3.26 ly “Parsec” is short for parallax arcsecond

The Magnitude Scale  Magnitudes are a way of assigning a number to a star so we know how bright it is  Similar to how the Richter scale assigns a number to the strength of an earthquake  Magnitudes are a way of assigning a number to a star so we know how bright it is  Similar to how the Richter scale assigns a number to the strength of an earthquake This is the “8.9” earthquake off of Sumatra Betelgeuse and Rigel, stars in Orion with apparent magnitudes 0.3 and 0.9

Later, astronomers quantified this system.  Because stars have such a wide range in brightness, magnitudes are on a “log scale”  Every one magnitude corresponds to a factor of 2.5 change in brightness  Every 5 magnitudes is a factor of 100 change in brightness (because (2.5) 5 = 2.5 x 2.5 x 2.5 x 2.5 x 2.5 = 100)  Because stars have such a wide range in brightness, magnitudes are on a “log scale”  Every one magnitude corresponds to a factor of 2.5 change in brightness  Every 5 magnitudes is a factor of 100 change in brightness (because (2.5) 5 = 2.5 x 2.5 x 2.5 x 2.5 x 2.5 = 100)

Absolute Magnitude (M)  The Sun is in apparent magnitude, but would be 4.4 if we moved it far away  Aldebaran is farther than 10pc, so it’s absolute magnitude is brighter than its apparent magnitude  The Sun is in apparent magnitude, but would be 4.4 if we moved it far away  Aldebaran is farther than 10pc, so it’s absolute magnitude is brighter than its apparent magnitude Remember magnitude scale is “backwards” removes the effect of distance and puts stars on a common scale

Absolute Magnitude (M) Knowing the apparent magnitude (m) and the distance in pc (d) of a star its absolute magnitude (M) can be found using the following equation: Example: Find the absolute magnitude of the Sun. The apparent magnitude is The distance of the Sun from the Earth is 1 AU = 4.9x10 -6 pc Therefore, M= – log (4.9x10 -6 ) + 5 = = +4.8

So we have three ways of talking about brightness:  Apparent Magnitude - How bright a star looks from Earth  Luminosity - How much energy a star puts out per second  Absolute Magnitude - How bright a star would look if it was 10 parsecs away  Apparent Magnitude - How bright a star looks from Earth  Luminosity - How much energy a star puts out per second  Absolute Magnitude - How bright a star would look if it was 10 parsecs away

Spectroscopic parallax  Spectroscopic parallax is an astronomical method for measuring the distances to stars. Despite its name, it does not rely on the apparent change in the position of the star.  This technique can be applied to any main sequence star for which a spectrum can be recorded.  Spectroscopic parallax is an astronomical method for measuring the distances to stars. Despite its name, it does not rely on the apparent change in the position of the star.  This technique can be applied to any main sequence star for which a spectrum can be recorded.

Spectroscopic parallax  The temperature of a star can be found using an absorption spectrum.  Using its spectrum a star can be placed in a spectral class.  Also the star’s surface temperature can determined from its spectrum (Wien’s law)  Using the H-R diagram and knowing both temperature and spectral class of the star, its luminosity can be found.

Cepheid variables The relationship between a Cepheid variable's luminosity and variability period is quite precise, and has been used as a standard candle (astronomical object that has a know luminosity) for almost a century. This connection was discovered in 1912 by Henrietta Swan Leavitt. She measured the brightness of hundreds of Cepheid variables and discovered a distinct period- luminosity relationship.

Cepheid variables

Parallax angle, p d = 1 / p Luminosity L = 4πd 2 b Apparent brightness Spectrum Wien’s Law ( surface temperature T ) Chemical composition of corona L = 4πR 2 σT 4 Stefan-Boltzmann Radius Distance measured by parallax:

Apparent brightness Distance (d) b = L / 4πd 2 Luminosity class Spectrum Surface temperature (T) Wien’s Law Chemical composition Stefan-Boltzmann L = 4πR 2 σT 4 Radius Distance measured by spectroscopic parallax / Cepheid variables: H-R diagram Spectral type Luminosity (L) Period Cepheid variable

Measuring Astronomical Distances (summary DistanceMethod up to 100 pcParallax and Cepheid variables and spectroscopic parallax up to 10 MpcCepheid variables and spectroscopic parallax up to 60 MpcCepheid variables up to 250 MpcSuper red giants and super blue giants and supernovae up to 900 MpcGlobular clusters and supernovae Beyond 900 MpcSupernovae

Obler’s paradox Why isn't the night sky as uniformly bright as the surface of the Sun? If the Universe has infinitely many stars, then it should be. Why is the night sky dark? or

Obler’s paradox If the Universe is eternal and infinite and if it has an infinite number of stars, then the night sky should be bright. Very distant stars contribute with very little light to an observer on Earth but there are many of them. So if there is an infinite number of stars, each one emitting a certain amount of light, the total energy received must be infinite, making the night sky infinitely bright, which is not.

Obler’s paradox If we consider the Universe finite and expanding, the radiation received will be small and finite mainly for 2 reasons: There is a finite number of stars and each has a finite lifetime (they don’t radiate forever) and Because of the finite age of the Universe, stars that are far away have not yet had time for their light to reach us. Also, The Universe is expanding, so distant stars are red-shifted into obscurity (contain less energy).

Doppler effect In astronomy, the Doppler effect was originally studied in the visible part of the electromagnetic spectrum. Today, the Doppler shift, as it is also known, applies to electromagnetic waves in all portions of the spectrum. Astronomers use Doppler shifts to calculate precisely how fast stars and other astronomical objects move toward or away from Earth.

Big Bang The Big Bang Model is a broadly accepted theory for the origin and evolution of our universe. It postulates that 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimetres across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit. We can see remnants of this hot dense matter as the now very cold cosmic microwave background radiation which still pervades the universe and is visible to microwave detectors as a uniform glow across the entire sky.

Big Bang The singular point at which space, time, matter and energy were created. The Universe has been expanding ever since. Main evidence: Expansion of the Universe – the Universe is expanding (redshift)  it was once smaller  it must have started expanding sometime  “explosion” Background radiation  evidence of an hot Universe that cooled as it expanded He abundance  He produced by stars is little  there is no other explanation for the abundance of He in the Universe than the Big Bang model.

Doppler effect Why is Doppler effect so important? In 1920’s Edwin Hubble and Milton Humanson realised that the spectra of distant galaxies showed a redshift, which means that they are moving away from Earth. So, if galaxies are moving away from each other then it they may have been much closer together in the past Matter was concentrated in one point and some “explosion” may have thrown the matter apart.

Background radiation In 1960 two physicists, Dicke and Peebles, realising that there was more He than it could be produced by stars, proposed that in the beginning of the Universe it was at a sufficiently high temperature to produce He by fusion. In this process a great amount of highly energetic radiation was produced. However, as the Universe expanded and cooled, the energy of that radiation decreased as well (wavelength increased). It was predicted that the actual photons would have an maximum λ corresponding to a black body spectrum of 3K. So, we would be looking for microwave radiation.

Background radiation In every direction, there is a very low energy and very uniform radiation that we see filling the Universe. This is called the 3 Degree Kelvin Background Radiation, or the Cosmic Background Radiation, or the Microwave Background. These names come about because this radiation is essentially a black body with temperature slightly less than 3 degrees Kelvin (about 2.76 K), which peaks in the microwave portion of the spectrum.

Fate of the Universe Universe ClosedOpen Not enough matter  density is not enough to allow an infinite expansion  gravity will stop the Universe expansion and cause it to contract (Big Crunch) Enough matter  density is such that gravity is too weak to stop the Universe expanding forever Flat Critical density  Universe will only start to contract after an infinite amount of time

Critical density The density of the Universe that separates a universe that will expand forever (open universe) and one that will re- colapse (closed universe). A universe with a density equal to the critical density is called flat and it will expand forever at a slowing rate. So, how do we measure the density of the Universe?

Critical density If we take in account all the matter (stars) that we can see then the total mass would not be enough to keep the galaxies orbiting about a cluster centre. So, there must be some matter that can not be seen – dark matter. This dark matter cannot be seen because it is too cold to irradiate. According to the present theories dark matter consists in MACHO’s and WIMPS

MACHO’s WIMP’s Massive compact halo objects – brown and black dwarfs or similar cold objects and even black holes. Non-barionic weakly interacting massive particles (neutrinos among other particles predicted by physics of elementary particles) It seems that there is also what is called “dark energy”…