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ASTROPHYSICS
REVIEW
ASTROPHYSICS
REVIEW
The Solar SystemThe Solar System
The SunThe Sun
Mass: 1.99 x 1030 kg
Radius:6.96 x 108 m
Surface temperature: 5800 K
Mass: 1.99 x 1030 kg
Radius:6.96 x 108 m
Surface temperature: 5800 K
Planet Picture Distance to the Sun (km)
Radius (km) Orbital period
around its axis
Orbital period
Surface day temp
(ºC)
Density (water=1
)
Satellites
Mercury
58 million 4 878 km 59 days 88 days 167 5,43 0
Venus 108 million 12 104 km -243 days 225 days 464 5,24 0
Earth 149,6 million 12 756 km 23, 93 h 365,2 days 15 5,52 1
Mars 228 million 6 794 km 24h 37min 687 days -65 3,04 2
Jupiter 778 million 142 800 km 9h 50min 30s
12 years -110 1,32 +63
Saturn 1 427 million 120 000 km 10h 14min 29,5 years -140 0,69 +56
Uranus 2 870 million 51 800 km 16h 18min 84 years -195 1,27 27
Neptune
4 497 million 49 500 km 15h 48min 164 years -200 1,77 13
Pluto 5 900 million 2 400 km 6 days 248 years -225 2 1
Planets DataPlanets Data
GalaxiesGalaxies
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)
ConstellationsConstellations
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!
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?
What is the most important thing about a star?
MASS!The The massmass of a normal star almost of a normal star almost
completely determines itscompletely determines its LUMINOSITYLUMINOSITY and TEMPERATURETEMPERATURE!
Note: “normal” star means a star that’s fusing Hydrogen into Helium in its center (we say “hydrogen burning”).
LuminosityLuminosity
The Luminosity of a star is the energy that it releases per second. Sun has a luminosity of 3.90x1026 W (often written as L): it emits 3.90x1026 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 brightnessApparent 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:
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
24 d
Lb
Black body radiationBlack 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:
K m 2.9x10T
constantT3-
max
max
Black body radiation and Wien Law
Black body radiation and Wien Law
Black body radiationBlack 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: 4σATL where, σ = 5.67x108 W m-2 K-4
The Spectral SequenceThe Spectral SequenceClass Spectrum Color Temperature
O ionized and neutral helium, weakened hydrogen
bluish 31,000-49,000 K
B neutral helium, stronger hydrogen
blue-white 10,000-31,000 K
A strong hydrogen, ionized metals
white 7400-10,000 K
F weaker hydrogen, ionized metals
yellowish white 6000-7400 K
G still weaker hydrogen, ionized and neutral metals
yellowish 5300-6000 K
K weak hydrogen, neutral metals
orange 3900-5300 K
M little or no hydrogen, neutral metals, molecules
reddish 2200-3900 K
L no hydrogen, metallic hydrides, alkalai metals
red-infrared 1200-2200 K
T methane bands infrared under 1200 K
“If a picture is worth a 1000 words, a spectrum is
worth 1000 pictures.”
“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
Spectra tell us about the physics of the star and how those physics affect the atoms in it
Types of StarsTypes 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 StarsTypes of Stars
Cepheid variablesCepheid 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 103 to 104 times that of the Sun.
Cepheid variablesCepheid 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 103 to 104 times that of the Sun.
Types of StarsTypes of Stars
Binary starsA 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 starsA 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 starsBinary 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:
)(
4
21
322
MMG
dT
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 starsBinary 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).
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 effectDoppler 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 starsBinary 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.
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 StarsTypes 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
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 25000 K whereas the luminosity varies from 10-4 to 106, 10 orders of magnitude.
H-R diagramH-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 distancesAstronomical distances
The light year (ly) – this is the distance travelled by the light in one year. The light year (ly) – this is the distance travelled by the light in one year.
1 ly = 9.46x1015
m
c = 3x108 m/st = 1 year = 365.25 x 24 x 60 x 60= 3.16 x 107 s
Speed =Distance / Time
Distance = Speed x Time = 3x108 x 3.16 x 107 = 9.46 x 1015
m
Astronomical distancesAstronomical distances
The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond.
The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond.
1 pc = 3.086x1016
m
or
1 pc = 3.26 ly
““ParsecParsec” is short for” is short forparparallax arcallax arcsecsecondond
The Magnitude ScaleThe 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.
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)Absolute Magnitude (M)
The Sun is -26.5 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 -26.5 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 magnitudeRemember magnitude scale is “backwards”
removes the effect of distanceand
puts stars on a common scale
Absolute Magnitude (M)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:
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:
5log5 dMm
Example: Find the absolute magnitude of the Sun.
The apparent magnitude is -26.7
The distance of the Sun from the Earth is 1 AU = 4.9x10-6 pc
Therefore, M= -26.7 – log (4.9x10-6) + 5 =
= +4.8
So we have three ways of talking about brightness: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 parallaxSpectroscopic 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 parallaxSpectroscopic 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 variablesCepheid variablesThe 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 variablesCepheid variables
Parallax angle, p
d = 1 / pLuminosity
L = 4πd2 b
Apparent brightness
Spectrum
Wien’s Law (surface
temperature T)
Chemical composition of corona
L = 4πR2 σT4
Stefan-Boltzmann
Radius
Distance measured by parallax:
Apparent brightness
Distance (d)
b = L / 4πd2
Luminosity class
Spectrum
Surface temperature (T)
Wien’s Law
Chemical compositio
n
Stefan-Boltzmann
L = 4πR2 σT4
Radius
Distance measured by spectroscopic parallax / Cepheid variables:
H-R diagram
Spectral type
Luminosity (L)
Period
Cepheid variable
Measuring Astronomical Distances (summary
Measuring Astronomical Distances (summary
Distance Method
up to 100 pc Parallax and Cepheid variables and spectroscopic parallax
up to 10 Mpc Cepheid variables and spectroscopic parallax
up to 60 Mpc Cepheid variables
up to 250 Mpc Super red giants and super blue giants and supernovae
up to 900 Mpc Globular clusters and supernovae
Beyond 900 Mpc Supernovae
Obler’s paradoxObler’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 paradoxObler’s paradoxIf 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 paradoxObler’s paradoxIf 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 effectDoppler 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 BangBig 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 BangBig BangThe 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 effectDoppler 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 radiationBackground 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 radiationBackground 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 UniverseFate of the Universe
Universe
Closed Open
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 densityCritical 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 densityCritical 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”…
