Introduction to Space Science
Stars
Ahmed Waqas Zubairi
Institute of Space Technology, Islamabad
pptx courtesy: Dr Saeeda Sajjad
What is a star?
A star is a huge sphere of gas held together by gravity
→ mainly Hydrogen and Helium
The core is so hot and dense that nuclear fusion can occur
→ releasing energy that radiates into space
Visually
• Stars appear like points to us
• Yet, we have come to know a lot about them.
• We know various parameters of stars such as temperature, radius, mass, luminosity, composition, etc.
• Complex models – so complex they can only be worked with numerically
Course content on stars
1. How do we gather information about stars?
2. We know a lot from the Sun, but we have other means to gather information too.
3. The life cycle of stars
i. Different stages from birth till death.
How do we know about stars?
• Point like sources of light for us.
• The main source of information from stars is the light they emit.
• A lot of information can be gathered through that light.
Spectroscopy
• Light, even from a point source, can be broken down into its spectrum.
Spectrum: distribution of light/electromagnetic radiation as a function of wavelength/frequency/energy
Obtaining and analysing the spectrum of light/electromagnetic radiation from a distant star is called spectroscopy.
Spectroscopy is a key tool in astronomy.
Spectroscopy
Absorption and Emission spectra are also called line spectra Three types of spectra
Continuous Spectrum
Black body radiation
-Example of a metal that is heated -starts turning red
-then orange -then yellow
-then white hot,
as the temperature rises.
Continuous Spectrum Black body radiation
Such a body, emits light over a wide range of wavelengths
Continuous Spectrum
• Typical spectrum of a black body
• Emission over a wide range of wavelengths.
• But intensity varies with wavelength.
Continuous Spectrum
Continuous Spectrum
• Peaks around a certain wavelength
• The position of this peak depends on the temperature of the body
Continuous Spectrum
-Peaks around a certain wavelength
-The position of this peak depends on the temperature of the body
The shift in the peak is given by Wien’s law
λ =2.93 X 10-3 / T
max
λ is in metres T is Kelvins
Continuous Spectrum
• Stars behave almost like black bodies
• Therefore, the colour or peak emission wavelength of a star is related to its surface temperature.
• Stars have different colours Effect noticeable even to the naked eye
• This means that if the continuous spectrum from a star is obtained, we can find out the surface temperature of the star from the peak emission wavelength.
=> The spectrum of a star can be used to calculate its surface temperature.
Exercise
The Sun’s maximum intensity is at a wavelength of 500 nm. Calculate the Sun’s surface temperature using Wien’s law.
=> The spectrum of a star can be used to calculate its surface temperature.
Exercise
The Sun’s maximum intensity is at a wavelength of 500 nm. Calculate the Sun’s surface temperature using Wien’s law.
The shift in the peak is given by Wien’s law λmax =2.93 X 10-3 / T
λ Is in metres T is Kelvins
Temperature of Sun’s surface 5860K
Exercise
Continuous Spectrum
• Stars are classified based on their colour
• Hotter stars are blue and cooler stars, reddish.
Effect noticeable even to the naked eye
Absorption Spectrum
(one type of line spectrum)
Light is emitted by a source (for instance the core of a star) (continuous spectrum)
→ Passes through colder gas
→ Excitation of the atoms of the gas
→ Electrons jump from one low energy orbit to a high energy orbit
→ Absorption of light at fixed wavelengths, corresponding to the difference between two orbits
(appears as dark gaps on the continuous spectrum) -absence of light at those wavelengths
Absorption Spectrum
Each element has unique signature lines at fixed wavelengths
Absorption Spectrum
• Thousands of lines corresponding to different elements have been identified.
• Each element has unique signature lines at fixed wavelengths
• Implication: By looking at the absorption lines in the spectrum of a star, we can identify the elements in it.
Absorption Spectrum
Sun’s absorption spectrum
Example of hydrogen absorption spectrum superimposed on the black body curve
Absorption Spectrum
Emission Spectrum
• Each element has unique signature lines at fixed wavelength
• Same lines as Absorption spectrum
• But this time, emitted from a gas in excited state (no other source of electromagnetic radiation necessary).
How do we know about stars?
1. Spectroscopy
2. Photometry (measuring the luminosity and brightness of stars)
Brightness and Luminosity
The luminosity of a star is the total amount of energy radiated by the star.
→ For a bulb, this is given in Watts.
→ For stars, it is given in units/multiples of solar luminosity L sol
The Sun outputs: 380,000,000,000,000,000,000,000,000 Watts
→ 3.8 x 1026 Watts
• The brightness of a star is the energy/light we receive from it, which is a fraction of what it emits.
• For a star of given luminosity, the brighness we receive/measure, depends on its distance from us.
• If we know the distance, and measure the brightness, we can deduct, the luminosity.
Brightness and Luminosity
Relationship between luminosity, brightness and distance
b=L/4πd2 4πd2 is the surface of the spherical shell with radius d L=luminosity
d=distance to star
b=observed brightness
if we measure the brightness b of the star, we also need its distance d from us, in order to find out the luminosity L.
Distance of stars
Different methods
One of them is the method of parallax
Distance of stars
Parallax
Angle p is the parallax
tan p= 1 AU/d
By simple geometry
Recall: 1 AU = distance Sun-Earth
= 150 million km AU is a unit of distance.
Information about stars
So far we have seen
Temperature T – continuous spectrum Composition – line spectrum
Distance D – Parallax (other methods exist)
Luminosity L – calculated from measurements of brightness and distance
Radius R: We can also deduct the of the star from the temperature T and Luminosity L.
Based on Stefan-Boltzman law for black bodies.
Luminosity, Temperature and Radius Relationship
Stefan-Boltzman law for black bodies
(experimentally determined)
Dependence of energy emitted per unit area on temperature
F=σT4
F is the energy flux: energy emitted per unit area (of the star/black body).
The constant σ is Stefan Boltzman constant
Stefan-Boltzman law for black bodies F=σT4
For the entire surface of the star: the surface area is 4πR2 where R is the radius.
The Luminosity is the energy emitted by the entire star.
L=F. 4πR2
= σT4. 4πR2
The luminosity depends on -temperature
-radius
Luminosity, Temperature and Radius Relationship
Stefan-Boltzman law for black bodies L = σT4. 4πR2
If we know L and T, we can deduct R.
Luminosity, Temperature and Radius Relationship
• The determination of mass is more complicated. We won’t go into it here.
• In some cases, the mass can be determined through gravitational effect on another star.
• For stars burning H into He, there is also a linear relationship between mass and luminosity.
• Complex models are also used to find out the mass
• Masses of stars are given in units of solar masses M sol
Mass
Information about stars
There are also ways to find out the mass – a bit more complex Masses of stars are given in units of solar masses M sol
The Sun is an average star.
Masses can go up to 60 M sol or more.
Luminosities can go up to 106 L sol
Temperatures can go up to 30 000 K
The temperature of the Sun is 5800 K.
Bottom line: information gathered through just the light of stars, combined with models
Remember this?
Colour and radius of stars
Life cycles of stars
We saw how the Solar System was formed – Solar System lecture
-the birth of the Sun
Recap: Formed from a gas and dust cloud.
Stars go through different phases in their life time.
1. Protostar – Stage before fusion starts.
2. Fusion: Hydrogen into Helium - Most of a star’s life
- Known as the Main Sequence
3. Red Giant – Dying star
4. Planetary Nebula – Fusion ends 5. White Dwarf – remains of the star.
6. Neutron Star 7. Black Hole
Discovering the Universe Ninth Edition Discovering the Universe Ninth Edition Neil F. Comins William J. Kaufmann III
Protostar: before fusion has started
• Collapsing cloud – dense core - growing
• Temperature starts rising due to compression
• Emit radiation in infrared
– not hot enough to be seen in visible light.
http://hubblesite.org/news_release/news/1997-13
← Infrared image
The protostar keeps on contracting
When the temperature at the core reaches 107K
→ fusion starts (not a protostar any longer)
→ large amounts of energy released Hydrostatic Equilibrium is achieved
It is called a Main Sequence Star
Most of the star’s life is spent in this stage
Main Sequence
• Stage in which stars convert Hydrogen in Helium through fusion.
• Note: Fusion takes place in the core, where the temperatures are high enough (107K or more).
• After a long time, the hydrogen runs out.
• The time this takes depends on
• the amount of fuel available: mass
• the luminosity (rate at which fuel is burnt)
• More massive stars burn energy at a higher rate.
• As a result, instead of having longer lifetimes, they have shorter lifetimes.
• The lifetime of the Sun = 1010 years
Red Giant Phase: Running out of Hydrogen (in the core)
After spending most of its lifetime burning Hydrogen into
Helium, the star eventually runs out of Hydrogen in the core.
→ Enters the Red Giant Phase
Running out of Hydrogen (in the core)
-As the hydrogen in the core runs out, the energy released from fusion decreases and the gravity causes the core of the star to collapse.
-The external shell, where there is still Hydrogen contracts too.
-This causes it to heat up.
→Fusion stars in the Hydrogen shell.
-More energy is released
→The gases on the outside expand
→The star becomes giant
-The outer most layers are far from the fusing shell therefore cooler
→ star turns red
Red Giant Phase
Red Giant Phase
Eventually, a star like the Sun will expand up to 1 AU.
→ Up to the Earth’s orbit.
NB: this is a simplified presentation
→ In reality, this several steps are involved The Helium in the core fuses to
Carbon -Oxygen too at some point.
https://maas.museum/app/uploads/sites/6/2013/07/Present-Sun-Earth-orbit-and-the-future-red-giant_Nick-Lomb.jpg
Red Giant to Planetary Nebula
In the Red Giant phase, the outer most layers of the star lose mass constantly.
At some point, the mass loss is so great that fusion in the shell stops.
Ejected material → expands → cools
→ electrons and ions recombine
→ dust and gas condense
→ eventually, the interior of the star is revealed
→ This is known as a Planetary Nebula
Planetary Nebula
-The hot interior of the star is revealed.
The name Planetary Nebula does not have anything to do with planets →historical
Planetary Nebula
-Some can be spectacular
-The central star can be seen at the centre of the nebula -They are very common in our Galaxy
Planetary Nebula → White dwarf
-After about 50 000 years, the gases of the nebula spread so far from the cooling central star that they are not visible any longer.
-All that remains is the slowly cooling core of the original star.
-This is known as a White Dwarf.
It is white because once the outer gases spread away, the cooling core that is revealed is at higher temperature.
White dwarf
-Typically, the size of the Earth but much denser.
-Some H and He may remain (but mostly converted to Carbon-Oxygen after fusion.
-Its luminosity decreases further as it cools down.
-Calculations predict that it takes billions of years for a white dwarf to cool down.
-Currently, the oldest white dwarfs still radiate at a few thousand Kelvin.
-Because of their low luminosity, they are hard to observe.
For more massive stars
If the star is massive enough, then the temperature increases enough in the core to allow carbon fusion.
8 solar masses and above
The cycle can repeat itself, fusing heavier elements each time provided the temperature required is reached
Heavier elements fusion
-Carbon, Neon, Oxygen, Silicon
The cycle repeats, fusing heavier elements each time, until the core temperature cannot rise any higher.
A Red Supergiant is formed – size of Jupiter’s orbit Iron core
-At some point, the core cannot sustain the pressure from above and collapses violently.
→ Massive explosion occurs as a result.
This is known as a Supernova explosion
• Star can brighten to 1010 Lsol within minutes
• Can outshine an entire galaxy
• Among the most violent phenomena in the universe
• Neutron stars, pulsars, black holes can be formed as a result of supernova explosions
• Elements heavier than iron are forged in supernova explosions
The gas and dust will eventually be recycled into new star and solar systems
→We come back full circle to the birth of stars
Life cycle of stars
Black hole
• Generally, stars having mass > 3 times than the solar mass is regarded as massive stars.
Question: Why massive stars burns quickly?
• This can be defined by Eddington limit as Balance between gravity and radiative pressure.
• Massive stars have more gravitational potential energy, so they can collapse faster.
• Massive stars, even when they start nuclear fusion, have relatively higher pressures in their centers (because the larger mass is exerting a relatively higher pressure), thus higher central temperatures.
HR Diagram
