Stellar Spectroscopy and Evolution: A Comprehensive Guide
Posted on Aug 20, 2024 in Physics
Chapter 8: Spectroscopy of Stars
- What does ‘luminosity’ mean?
Luminosity refers to the total energy radiated by a star per second. The larger a star’s surface area, the greater its luminosity. - What is the equation relating apparent brightness to luminosity? Which tells us more about a star: its luminosity or its brightness?
The equation is L = b/d², where L is luminosity, b is apparent brightness, and d is distance. Luminosity tells us more about a star’s intrinsic properties. To determine a star’s distance, we can use parallax or “standard candles.” - Can you determine a star’s luminosity just from its brightness alone?
No, we need to measure the apparent brightness and account for factors like atmospheric variations and interstellar gas and dust. - What is photometry?
Photometry is the science of measuring light intensity, particularly human visual response to light. The basic unit is the lumen (lm), related to watts (W) by: lm = 683 x W x Vλ, where Vλ is the relative luminosity. - Which color of star is hottest? Which is coolest?
Bluish stars are the hottest, while reddish stars are the coolest. - Which spectral type of star is hottest? Which is coolest?
Spectral types range from O (hottest) to M (coolest): O B A F G K M. - Which spectral type of stars is most ionized?
O-type stars are the most ionized. - Which spectral type of stars has the most molecules?
M-type stars have the most molecules. - If all stars contain hydrogen, why don’t we see H lines in ‘O’ type stars?
O-type stars are so hot that hydrogen is completely ionized, making it difficult to observe H lines. - The spectral types (OBAFGKMLT) are in what order?
They are in order of decreasing temperature: hottest to coolest. - Which spectral type has the strongest hydrogen spectrum?
A-type stars have the strongest hydrogen spectrum. - What are two ways to determine a star’s surface temperature?
Color and spectral type are two ways to determine a star’s surface temperature. - Why can’t you use these techniques to determine a star’s core temperature?
These techniques only probe the surface layers of a star. The core is hidden from direct observation. - How do you measure the rotation rate of stars?
The rotation rate of stars can be measured using the Doppler effect. As a star rotates, one side moves towards us while the other moves away, causing a broadening of spectral lines. - How do you measure the magnetic fields of stars?
The Zeeman effect and Doppler imaging are two techniques used to measure the magnetic fields of stars. - What is proper motion, and how do you measure it?
Proper motion is the apparent motion of a star across the sky, perpendicular to our line of sight. It is measured in arcseconds per year. - What is ‘radial velocity,’ and how do you measure it?
Radial velocity is the speed of a star towards or away from us, measured using the Doppler shift of spectral lines. A blueshift indicates motion towards us, while a redshift indicates motion away from us.
Chapter 9: Measurements of Stars & the H-R Diagram
- Which are more common: low- or high-mass stars?
Low-mass stars are more common. - Which are more common: low- or high-temperature stars?
Low-temperature stars are more common. - Which are more common: low- or high-luminosity stars?
Low-luminosity stars are more common. - How do we measure the mass of stars?
We need two things: binary stars and Kepler’s laws. By observing the period and average separation of a binary star system, we can calculate the masses of the stars. - What is the range of stellar masses possible?
The range of stellar masses is approximately 0.08 to 100 times the mass of the Sun. - What is the mass-luminosity equation (approximate)?
The approximate mass-luminosity equation is L ≈ M^3.5, where L is luminosity and M is mass. - How do we measure the diameters of stars? (2 ways)
We can measure the diameters of stars using eclipsing binary systems or by combining luminosity and temperature measurements. - What is the H-R diagram (and why do we abbreviate it)?
The Hertzsprung-Russell (H-R) diagram is a plot of stars’ luminosity versus their spectral type (or color or temperature). It helps us understand the lives of stars. - What are the two axes of the H-R diagram?
The two axes are luminosity (y-axis) and color or temperature (x-axis). - Which side of the H-R diagram is hottest?
The upper left side of the H-R diagram is the hottest. - Which side of the H-R diagram is bluest?
The upper left side is also the bluest. - Which side of the H-R diagram is most luminous?
The upper left side is the most luminous. - Which corner of the H-R diagram has stars with the largest diameter?
The upper right corner has stars with the largest diameter (red giants). - Which corner of the H-R diagram has the lowest mass main sequence stars?
The lower right corner has the lowest mass main sequence stars. - Where on the H-R diagram do we find: white dwarfs, red giants, high-mass main sequence stars, and low-mass main sequence stars?
– White dwarfs: lower left
– Red giants: upper right
– High-mass main sequence stars: upper left
– Low-mass main sequence stars: lower right - What is the main sequence?
The main sequence is a diagonal band on the H-R diagram where most stars spend the majority of their lives. These stars fuse hydrogen into helium in their cores. A star’s mass determines its position along the main sequence. - Which equation accompanies the H-R diagram? (Note: not in the book)
The equation L = R²T⁴ relates luminosity (L), radius (R), and temperature (T). - Ninety percent of all stars fall where on the H-R diagram?
Ninety percent of all stars fall on the main sequence. - What are ‘binary stars’?
Binary stars are systems of two stars that orbit around their common center of mass. - What are ‘spectroscopic binaries’?
Spectroscopic binaries are binary star systems that are too close together to be resolved visually. Their binary nature is revealed by observing the Doppler shifts in their spectral lines. - What is the difference between a star and a brown dwarf?
Brown dwarfs are objects that are not massive enough to sustain hydrogen fusion in their cores. They are often considered”failed stars” - What spectral types are brown dwarfs?
Brown dwarfs have spectral types of M, L, T, and Y. - If a star has high luminosity and a low temperature, what is its size?
A star with high luminosity and low temperature must be very large, such as a red giant. - Which stars are more massive: ‘upper main sequence’ or ‘lower’?
Upper main sequence stars are more massive than lower main sequence stars.
Chapter 12: Star Formation
- Where do stars form?
Stars form in giant molecular clouds, which are cold and dense regions of gas and dust in interstellar space. - Why is it so difficult to observe star formation?
Star formation is obscured by the surrounding gas and dust, making it difficult to observe directly. - Which stage of star formation occurs first?
The protostar stage occurs first. - What are the stages of star formation?
1. **Nebula:** A cloud of gas and dust begins to collapse under its own gravity.
2. **Protostar:** As the cloud collapses, it heats up and becomes more luminous, forming a protostar.
3. **Main Sequence:** When the core temperature and pressure are high enough, nuclear fusion begins, and the star enters the main sequence.
4. **Red Giant or Supergiant:** As the star runs low on hydrogen fuel, it expands and cools, becoming a red giant or supergiant.
5. **Ending Stages:** The star’s ultimate fate depends on its mass. Low-mass stars end as white dwarfs, while high-mass stars explode as supernovae, leaving behind neutron stars or black holes. - What is a ‘proto-star’?
A protostar is a young star that is still in the process of forming. It is surrounded by a disk of gas and dust. - What is the main difference between a proto-star and a main sequence star?
The main difference is that a protostar is not yet undergoing sustained nuclear fusion in its core, while a main sequence star is. - What is stellar wind, and when does it begin?
Stellar wind is a stream of charged particles ejected from a star’s atmosphere. It begins during the protostar stage. - What determines the rate of star formation (and stellar evolution)?
The mass of a star is the primary factor that determines its rate of formation and evolution. More massive stars form and evolve much faster than less massive stars. - Planets form from what part?
Planets form from the protoplanetary disk, which is a disk of gas and dust that surrounds a young star. - Why is observing planet formation so difficult?
Planet formation is difficult to observe because planets are much fainter than stars and are often obscured by the light of their host star. - Why is detecting extra-solar planets so difficult?
Extrasolar planets are difficult to detect because they are small, faint, and close to their much brighter host stars. - Why is detecting low-mass extra-solar planets especially difficult?
Low-mass planets have weaker gravitational effects on their host stars, making them harder to detect using radial velocity or transit methods. - Why is detecting large-orbit extra-solar planets especially difficult?
Large-orbit planets take longer to complete one orbit around their host star, making it more challenging to observe multiple transits or measure their orbital periods.
Chapter 13: Stellar Evolution
- Why do stars spend most of their time on the main sequence (M.S.)?
Stars spend most of their lives on the main sequence because this is the stage where they fuse hydrogen into helium in their cores, which is a very long-lasting process. - Which spectral type of star spends the most time on the M.S.?
Low-mass M-type stars have the longest main sequence lifetimes. - What is the equation for mass vs. life expectancy of stars? (approx.)
The approximate equation is Lifetime ≈ M/L ≈ M^-2.5, where M is mass and L is luminosity. - What is a red giant?
A red giant is a star that has exhausted the hydrogen fuel in its core and has begun to fuse helium in a shell around the core. This causes the star to expand and cool, giving it a reddish appearance. - What causes stars to turn into red giants?
Stars turn into red giants when they run low on hydrogen fuel in their cores. The core contracts and heats up, causing the outer layers of the star to expand and cool. - Where are red giants on the H-R diagram?
Red giants are located on the upper right side of the H-R diagram. - What happens to a star’s core when it runs low on hydrogen?
When a star runs low on hydrogen, its core contracts and heats up. This can eventually trigger the fusion of helium into heavier elements. - Then what happens to the shell of hydrogen around the core?
The shell of hydrogen around the core ignites and begins to fuse hydrogen into helium at a faster rate, causing the star’s outer layers to expand. - What does the inner core start ‘burning’ at 100 million K?
At 100 million K, the inner core of a star can begin to fuse helium into carbon through the triple-alpha process. - What happens if the star has very low mass?
Very low-mass stars will eventually exhaust their nuclear fuel and become white dwarfs. - After the inner core runs low on helium, what happens to it?
After the inner core runs low on helium, it contracts and heats up again. In stars massive enough, this can trigger the fusion of carbon into even heavier elements. - What happens to the shell of fresh helium around it?
The shell of fresh helium around the core ignites and begins to fuse helium into carbon. - What happens to the carbon core of low-mass stars (< 8 solar masses)?
In low-mass stars, the carbon core will not reach a high enough temperature to fuse carbon into heavier elements. The core will continue to contract and heat up, eventually becoming a white dwarf. - What’s the difference between the helium flash and the helium configuration?
The helium flash is a brief period of rapid helium fusion that occurs in the cores of low-mass stars. The helium configuration refers to the structure of a star’s core after it has exhausted its core hydrogen fuel and has begun to fuse helium. - Which types of stars experience the helium flash?
Low-mass stars experience the helium flash. - Stars over what mass can convert carbon into heavier elements?
Stars over about 8 solar masses can convert carbon into heavier elements. - What’s the heaviest element whose production gives off energy?
Iron is the heaviest element whose fusion releases energy. Fusing elements heavier than iron requires energy. - What happens when a star’s core is made out of that element?
When a star’s core is made of iron, it can no longer produce energy through fusion. The core collapses, leading to a supernova explosion. - What are the stages of evolution for a low-mass star?
1. Protostar
2. Main Sequence
3. Red Giant
4. Helium Flash
5. Horizontal Branch
6. Asymptotic Giant Branch
7. Planetary Nebula
8. White Dwarf - What are the stages of evolution for a high-mass star?
1. Protostar
2. Main Sequence
3. Supergiant
4. Supernova
5. Neutron Star or Black Hole - Which stages of evolution will the Sun go through?
The Sun will go through the following stages: protostar, main sequence, red giant, horizontal branch, asymptotic giant branch, planetary nebula, and white dwarf. - How can the H-R diagram tell you the age of a cluster of stars?
The H-R diagram can be used to estimate the age of a star cluster by looking at the main sequence turnoff point. The turnoff point is the point on the main sequence where stars are beginning to evolve off and become red giants. The age of the cluster is related to the mass of the stars at the turnoff point. - Why are there sometimes two ‘branches’ on the H-R diagram for star clusters?
There can be multiple branches on the H-R diagram for star clusters because stars of different masses evolve at different rates. For example, a cluster might have a main sequence branch and a red giant branch. - What is the upper branch called?
The upper branch is often called the red giant branch.
Chapter 7: The Sun – Nuclear Energy
- The Sun turns how many tons of matter into energy per second?
The Sun converts about 4 million tons of matter into energy per second. - The Sun turns how many tons of hydrogen into helium per second?
The Sun converts about 600 million tons of hydrogen into helium per second. - What are the three steps of the p-p chain?
The proton-proton (p-p) chain is the primary process by which the Sun fuses hydrogen into helium. The three steps are:
1. Two protons fuse to form deuterium, a positron, and a neutrino.
2. Deuterium fuses with another proton to form helium-3 and a gamma ray.
3. Two helium-3 nuclei fuse to form helium-4 and two protons. - Which particle produced in the p-p chain is “anti-matter”?
The positron is the antimatter particle produced in the p-p chain. - The CNO cycle involves which elements?
The CNO cycle is another process by which stars can fuse hydrogen into helium. It involves carbon, nitrogen, and oxygen as catalysts. - What are the steps of the CNO cycle?
1. A carbon-12 nucleus captures a proton to form nitrogen-13 and a gamma ray.
2. Nitrogen-13 undergoes beta decay to form carbon-13, a positron, and a neutrino.
3. Carbon-13 captures a proton to form nitrogen-14 and a gamma ray.
4. Nitrogen-14 captures a proton to form oxygen-15 and a gamma ray.
5. Oxygen-15 undergoes beta decay to form nitrogen-15, a positron, and a neutrino.
6. Nitrogen-15 captures a proton to form carbon-12 and a helium-4 nucleus. - Neutrino oscillation can produce light. Use it to calculate how much energy the Sun makes.
Neutrino oscillation itself doesn’t produce light. However, by studying solar neutrinos, we can learn about the nuclear reactions happening in the Sun’s core and confirm the energy production rate. - How long does it take for energy to move through the radiative zone?
It takes about 170,000 years for energy to move through the radiative zone. - How long does it take for energy to move through the convective zone?
It takes a few weeks for energy to move through the convective zone. - How long does it take for energy to move from the Sun to the Earth?
It takes about 8.3 minutes for energy (light) to travel from the Sun to the Earth. - What is the correct term for the study of the Sun using sound waves?
The study of the Sun using sound waves is called helioseismology. - List discoveries of the solar interior from helioseismology.
Helioseismology has helped us learn about:
– The Sun’s internal structure and rotation
– The depth and properties of the convective zone
– The existence and behavior of solar oscillations
– The transport of energy through the Sun - What is the approximate period of solar oscillations?
Solar oscillations have periods of around 5 minutes. - As a result of using sound waves to probe the interior of the Sun, we’ve discovered that differential rotation is linked to which solar phenomenon?
Differential rotation (the Sun rotating faster at its equator than at its poles) is linked to the solar cycle, which is the periodic variation in solar activity, including sunspots and solar flares.
