Homework and quiz question AST Midterm II

absorption lines

A hot, glowing, opaque solid surrounded by a cool gas will show

Two images of the star, one on each side of the black hole.

A solar-mass black hole lies halfway between us and a solar-type star, but it is not lined up exactly. What do you predict that we will see when we observe the star?

hydrogen is exhausted in the core of the star.

A star evolves off the main sequence when

The star is hotter and more luminous than the Sun.

A star is burning hydrogen to helium in its core and has 10 times the mass of the Sun. Which of the following is true?

On the main sequence, the more massive stars are also hotter. The hottest main sequence star is Spica, so it must be the most massive.

Among the main-sequence stars listed, which one is the most massive?

The Chandrasekhar limit is the mass limit of a white dwarf. It is equal to 1.4 solar masses. When the mass of a white dwarf reaches this limit, the speed of the electrons are approaching the speed of light.

Chandrasekhar limit

more gas in the disk.

Compared to the present-day Milky Way Galaxy, the Milky Way of 3 billion years ago would have had

lower energy and longer wavelength

Compared to visible light, radio waves have

Because the Hydrogen fuel is used up in the core, there is no energy production and, thus, no thermal pressure to counteract the crush of gravity. So, the core contracts! The shell of fresh Hydrogen above the core contracts as well, becoming more dense and hotter until it reaches a point where Hydrogen burning begins in the shell. Because of the high temperatures and increased fusion rates, the thermal pressure increases significantly. Because the pressure created by shell burning only has to counteract the gravity from a smaller percentage of the star's mass (much of the original mass is now locked in the inert core below), the huge pressure causes the outer layers of the star to expand enormously.

Explain how it is possible for the core of a red giant to contract at the same time that its outer layers expand.

an object that emits flashes of light several times per second or more, with near perfect regularity

From an observational standpoint, what is a pulsar?

iron nuclei are the most tightly bound of all nuclei, so iron fusion does not release energy.

Fusion in the core of a stable massive star cannot proceed beyond iron because

an interstellar gas and dust cloud.

If one region of the sky shows nearby stars but no distant stars or galaxies, our view is probably blocked by

Helium fuses into carbon by combining three helium nuclei (atomic number 2) into one carbon nucleus (atomic number 6), therefore bypassing the elements lithium, beryllium, and boron with atomic numbers 3 through 5. Thus, fusion processes in the cores of stars do not form these three 3 elements.

Lithium, beryllium, and boron are elements with atomic numbers 3, 4, and 5 re- spectively. Despite their being three of the five simplest elements, the graph of the observed relative abundances of elements in the galaxy in comparison to the abun- dance of hydrogen shows that they are rare compared to many heavier elements.

The parallax i.e. the parallactic angle (p), of A would be twice as small as the angle for B based on the equation relating parallax angle and distance, d (in pc) = 1 / p (in arcseconds)which is derived from the small angle formula.

Star "A" is twice as far away as star "B". How would the parallaxes of these two stars compare?

are all about the same age and distance.

Star clusters are useful to stellar astronomers because the clusters contain stars that

- an object is fighter farther away, so A is farther than B -A need to to be grater luminosity (25x because 5 times away than B, apparent brightness = luminosity/4πd2)

Stars A and B are both equally bright (that is, they have the same apparent brightness) as seen from Earth, but A is 50 pc away while B is 10 pc away. Which star has a greater luminosity? How many times greater is it?

- since D is closer look brighter than C -D (4 times closer- 16x brighter than C)

Stars C and D both have the same luminosity, but C is 36 pc from Earth while D is 9 pc from Earth. Which star appears brighter as seen from Earth. How many times brighter is it?

This statement is not sensible. If fusion in the core ceased, the photons would continue to percolate out of the Sun at about the same rate for many thousands of years. No dimming would be possible to measure the day after such an event.

T or F If fusion in the solar core ceased today, worldwide panic would break out tomorrow as the Sun began to grow dimmer.

This statement is not sensible. Neutrinos pass right through the Earth and would not be diminished at all by a lead vest.

T or F Neutrinos probably can't harm me, but just to be safe I think I'll wear a lead vest.

This statement is sensible. The Sun produces neutrinos consistently at about the same rate as a result of nuclear fusion. Since neutrinos pass right through Earth, there is no different between the number passing through your body during the day and during the night.

T or F The number of neutrinos passing through your body at night is the same as the number of neutrinos passing through your body during the day.

This statement is sensible. The Sun's core acts as a thermostat; thus, if the inner core tempera- ture increases, the reaction rate increases too, but the extra energy expands the core and cools it, thus reducing the nuclear reaction rates.

T or F A sudden temperature rise in the Sun's core is nothing to worry about, because conditions in the core will soon return to normal.

-peak wavelength is plaint constant divided by Temperature -However, because the Sun also radiates other colors of the visible spectrum and the atmosphere scatters the bluer light, it appears white or yellow to our eyes.

The Sun's average surface temperature is about 5,800 K. Use Wien's law (see Math- ematical Insight 5.2) to calculate the wavelength of peak thermal emission from the Sun. Why do you think the Sun appears white or yellow to our eyes?

the photon is bounced around, absorbed, and re-emitted countless times along the way.

The energy of a photon emitted by thermonuclear processes in the core of the Sun takes millions of years to emerge from the surface because

a planetary nebula.

The event that marks the end of a star's evolutionary life before becoming a white dwarf is

These stars are younger than the Sun because their lifetimes on the main sequence are shorter than the present age of the Sun (about 5 billion years old).

The main sequence stars Sirius (spectral type A1), Vega (A0), Spica (B1), Fomalhaut (A3), and Regulus (B7) are among the 20 brightest stars in the sky. Are all of these stars younger or older than the Sun?

One cannot tell the age of Alpha Centauri A from the information given. The only certainty is that Alpha Centauri A is not older than 1010 years which is the main-sequence lifetime of a G star.

The third-brightest star in the sky, although it can be seen only south of 29o north latitude, is Alpha Centauri A. It is a main-sequence star of spectral type G2, the same as the Sun. Can you tell from this whether Alpha Centauri A is younger than the Sun, the same age, or older?

10,000 times fainter

Two stars are exactly the same (same chemical composition, surface temperature, luminosity etc), but one is 10 lightyears from Earth and the other is 1000 light years from Earth. The farther star appears to be

The brightest stars in a young cluster like this one will be the O stars, which are blue because of their high surface temperature. The faintest stars will be the red stars at the bottom of the main sequence.

What color will the brightest stars in the cluster from part (a) be? How about the faintest stars?

Degeneracy pressure is when the electrons (or neutrons) are so closely packed together that they cannot get any closer, due to the Pauli exclusion principle. Their resistance to compression is pressure!

What is degeneracy pressure (as in electron degeneracy pressure or neutron degeneracy pressure)?

he overall reaction involved in helium burning is to combine three helium nuclei into one carbon nucleus. Because helium nuclei have two protons, and therefore twice the charge of hydrogen nuclei, they repel one another more strongly. Therefore, the nuclei must slam into one another at much higher speeds than is needed for fusion, requiring much higher temperatures.

What is the helium fusion reaction, and why does it require much higher tem- peratures than hydrogen fusion?

An elliptical galaxy lacks a disk component.

What is the major difference between an elliptical galaxy and a spiral galaxy?

Supernovae would be more common. For stars that are as massive (or less massive) than our Sun, no problem. They would just end up with the Carbon core. However, for the stars that start out more massive than the Sun, their strong gravitational pull would continue to contract the core! Since fusion could not proceed beyond Carbon, those stars would go supernova! So, there would be more supernova since lower mass stars (which are more numerous) would reach this end state where they cannot burn any fuel.

What would stars be like if carbon had the smallest mass per nuclear particle?

Nuclear fusion would not occur in stars of any mass.

What would stars be like if hydrogen had the smallest mass per nuclear particle?

the sudden collapse of an iron core into a compact ball of neutrons.

Which event marks the beginning of a massive star supernova?

A red supergiant is undergoing advanced nuclear burning, which requires higher temperatures, even if it is not currently burning anything in its core.

Which of these stars has the hottest core, and why? A blue main-sequence star, a red supergiant, or a red main-sequence star.

apparent magnitude(m_v )Therefore, Sirius appears brightest because it has the smallest (most negative) apparent magnitude (-1.4).

Which star appears brightest in our sky?

apparent magnitude(m_v )Regulus appears the faintest to our eyes because it has the largest apparent magnitude (+1.4). (most positive)

Which star appears faintest in our sky?

absolute magnitude (MV ). Smaller numbers are brighter; therefore, Antares has the highest luminosity because it has the smallest (most negative) absolute magnitude. It is also a luminosity class I star which have the highest luminosity (supergiants).

Which star has the greatest luminosity

The surface temperature is described by the star's spectral type, with classes OBAFGKMLT in order from hottest to coolest. On this list, the highest spectral type is a B1 star, Spica.

Which star has the highest surface temperature?

As we move up in luminosity class (to smaller numbers), stars get bigger. Since Antares is the only supergiant, it must have the largest radius.

Which star has the largest radius?

Alpha Centauri A has the smallest luminosity because it has the largest absolute magnitude. (most positive) The stars at the cool end of the main sequence have the lowest luminosity. Of the stars in this list, Alpha Centauri A is a main sequence star (luminosity class V). It's spectral class is a G type star; the others are A and B type stars which are hotter.

Which star has the least luminosity?

Again, we look at spectral type. The coolest stars are M type stars such as Antares.

Which star has the lowest surface temperature?

Supergiants are luminosity class I. Red stars are M or K stars. Antares fits both of those criteria.

Which star is a red supergiant?

The sun is a G2 V star. Alpha Centauri A is also a G2 V star.

Which star is most similar to the Sun?

Any star that has left the main sequence has finished core hydrogen burning. So stars of lumi- nosity classes I-IV have finished core hydrogen burning i.e. Aldebaran, Antares, and Canopus.

Which stars have finished burning hydrogen in their cores?

The O stars will have the shortest lifetime on the main sequence. Although they are the most massive stars, they are also the most luminous. They are burning hydrogen to helium in their cores at a furious rate and will use up their available fuel the fastest.

Which stars in this cluster will have the shortest lifetime on the main sequence?

High-mass stars have shorter lifetimes than those of lower mass because they burn their fuel at much faster rates. Because of their large masses, they must sustain higher nuclear fusion rates to maintain gravitational equilibrium.

Why do high-mass main sequence stars have shorter lifetimes than those of lower mass?

Fusion of elements heavier than helium (which fuses to form carbon) occurs only in high-mass stars because of the very high temperatures required to overcome the large electromagnetic repulsion of the highly positively-charged heavy elements. Only high-mass stars have enough mass to produce the immense gravitational crush on the star's core that is req'uired to contract the core and reach the necessary core temperatures for fusion.

Why does advanced nuclear burning (to heavier elements up to Iron) occur in high-mass stars but not in low-mass stars?

X-ray binaries are bright, constant X-rays sources. They come from neutron stars in close binary systems accreting material from their companion. The material in the accretion disk becomes so hot that it emits X-rays. The neutron star is the remnant of a massive main sequence star.

X-ray binaries

The star cluster is a young cluster because we see O stars in it. The lifetime of an O star on the main sequence (i.e. how long it is burning hydrogen to helium in the core) is very short and, therefore, any star cluster which contains O stars must be young.

You plot a HR diagram of a cluster of stars and see a clear main sequence which includes stars from type O to type M. Is this a young cluster or an old cluster?

The least massive stars live the longest. The main sequence star of the least mass is Alpha Centauri A, as based on it's spectral class (cooler stars have less mass on the main sequence).

mong main-sequence stars listed, which one has the longest lifetime?

0.5

ssume that a star behaves as a blackbody (thermal emitter). If the surface temperature of that star doubles, then the wavelength of maximum intensity will be ____ times the original wavelength?