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CLEMSON / Astronomy / ASTR 1020 / What is the structure of a neutron star?

What is the structure of a neutron star?

What is the structure of a neutron star?

Description

School: Clemson University
Department: Astronomy
Course: Stellar Astronomy
Professor: Flower
Term: Winter 2016
Tags: astronomy
Cost: 50
Name: Astronomy Unit 4A
Description: These notes cover the learning objectives as seen on blackboard AND more, including the sample questions and explanations on blackboard.
Uploaded: 03/22/2016
15 Pages 157 Views 16 Unlocks
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What is the structure of a neutron star?



Astronomy Unit 4A 

Neutron Stars 

∙ Neutron star- the remnant core of the exploded star

o Extremely compact/dense and tiny

o Diameters (size) are less than 35 km, the size of a large city (still tiny in  comparison to other stars)

o Difficult to detect

o The largest mass is about 3 M, but scientist don’t know for sure. o In binary stars, the maximum is about 2M.

o The average mass is about 1.5M, slightly more massive than white dwarfs o It’s surface gravity is 100 billion times greater than Earth’s


What are magnetic fields and pulsars for?



If you want to learn more check out What kind of social media platform is twitter?

∙ Composition of the Neutron Star

o The crust is about 1-2km thick

▪ Consists of an iron nuclei

o The core is a neutron superfluid in which the sea of neutrons become  frictionless fluid

▪ Very dense region

∙ Pulsars- celestial radio sources

o Rotation increases as the core shrinks and the magnetic field increases in  strength.

o Produce radio waves

o Discovered these signals from the Crab Nebula Don't forget about the age old question of Where do beta-oxidation and fa synthesis take place?

o Glitches are rare speed ups, and about 30 of the 1500 known pulsars  exhibit these


What is the role of bulge as a part of the milky way's structure?



▪ This means they spin more rapidly

▪ Glitches are produced when the rotational motion of vortexes is  deposited to the crust, speeding up its rotation

▪ Happens every few years

o The slowing down of pulsars is probably the result of strong magnetic  fields surrounding pulsars.

∙ Magnetic fields and Pulsars

o 2 observational effects: they slow down pulsar rotations and provide a  mechanism for pulsars to emit radiation in concentrated beams.

o The slow-down rate suggests that the fastest rotators are the youngest,  most recently formed pulsars.

▪ This means their magnetic field strength decreases in time

∙ Synchrotron radiation- The type of radiation and electrons emit when they  move at speeds close to the speed of light

o The radiation emitted is directional(in the direction they are accelerating) o Faster moving electrons emit more directly in the forward direction o Spiraling electrons produce forward-oriented emission If you want to learn more check out What does demographic transition entail?

∙ Pulsars in Binary Systems

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o Exhibit X-ray pulsars as well as radio pulses

o Binary pulsars- normal radio pulsars in binary systems in which their  companions are either neutron stars of white dwarfs

▪ Sometimes emit burst of X-rays and are called X-ray bursters result from nuclear reactions on the surfaces of neutron stars and  are not associated with the rotation of the neutron star

o Magnetars- one of the first in a class of X-ray pulsars with relatively slow  rotations (6-11 seconds) and with extreme magnetic fields.

▪ Slow down so fast that they reach the slow rotational rates in only  10,ooo years

▪ Thought to be neutron stars that rotated so fast when they formed  that convective motions in the superfluid core created an additional  magnetic field by they dynamo effect If you want to learn more check out Wich technique can be used to analyze direction fields?
Don't forget about the age old question of Why is understanding newborn reflex extremely important?

o Millisecond Pulsars- the fastest rotating pulsars

▪ Spin thousands of times in a second

▪ Have extremely weak magnetic field, which is weird because this  usually means they spin slowly

o Abating pulsar- the intense radiation from the neutron star slowly  Evaporates a white dwarf companion

∙ X-Ray Binaries

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o Accretion disk- a thin disk in the orbital plane of the binary system. Gas  in the disk develops a spiraling motion. Mass transfer deposits the gas to  the inner edge, where it eventually falls onto the hot, neutron star surface.

Milky Way Galaxy 

∙ Milky Way- a luminous band that arches across the sky on a winter’s evening. o Milky white appearance is due to innumerable stars If you want to learn more check out On which ground was al capone arrested then?

o The sun is located on the edge of the milky way far from the center o The center is nearly 10 parsecs away from the sun, and 8500 parcecs (8.5  kpc) for the distance from earth to the center.

Structure of the Milky Way 

o Halo- a roughly spherical volume of stars made up of the 170 known  globular clusters

▪ Included in the halo are old red stars and individual RR Lyrae  

variables

▪ The oldest halo stars appear to be about 12 billion years old

o Flat Disk Structure

▪ The length of the disk reveals the stars of the milky way

▪ Looking above or below the disk reveals relatively few stars.

o Nucleus- The center of the Milky Way Galaxy

▪ 8.5 kpc from the sun  

▪ Has a very large mass despite its small volume

▪ Is about 100pc across and contains about 100 million suns

o Bulge- a huge oval-shaped concentration of stars that surrounds the  nucleus  

▪ When viewed edge-on it projects above the flat disk

▪ Proposed that it consists of an elongated, or bar shaped, structure  instead of a spherical distribution of stars.

o Spiral Arms- concentrations of young objects such as H II regions, O and  B stars, and molecular clouds

▪ The sun lies in a populated region of young stars near one of the  spiral arms 

o Dark halo- motions of stars and gas in and near the Galaxy suggest that  the halo and disk lie within a huge invisible dark halo

▪ 200 kpc  

across with a  

mass more  

than twenty  

times what is  

visible

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∙ Stellar populations 

o Disk clusters contain fewer stars than globular clusters

o Open Cluster- term used to refer to star clusters in the disk because they  often appear as loose, open structures

▪ Younger than global clusters

▪ Have a higher metal abundance than globular cluster stars.

∙ Population I- consists of individual stars with characteristics similar to open  cluster stars, such as Type 1 Cepheids and the sun

o Have a higher metal abundance

o Population I objects confine themselves to a disk less than a thousand  parsecs thick

o Motions of Population 1 stars within the disk are highly organized ∙ Population II- consists of global clusters and old stars such as RR Lyrae  variables and Type II Cepheids

o Low metalicities

o Population II objects sparsely fill a spherical volume centered on the  nucleus  

o The disk of the Milky Way Galaxy lies inside the Population II halo o High velocity stars are part of the halo, but do not partake in the  rotation of the Milky Way’s disk

∙ The Sun’s Motion 

o Disk structures exhibit circular motion around a concentration of mass o Stars closer to the galactic center move slightly faster than the sun, and  those further away move slightly slower

o High velocity stars are part of the halo, but do not partake in the  rotation of the Milky Way’s disk

∙ Rotation Curve- the plot of orbital velocities and distances from the galactic  center

o Represents the orbital velocities of gas, dust, stars, and star clusters  orbiting in the disk of the Galaxy.

o Allows us to calculate the expected radial velocities of objects in any orbit  along any line of sight.

∙ The Nature of Spiral Arms 

o Spiral arms are visible because of the presence of H II regions, O and B  stars, and young star clusters within the curved segments.  

o These are the most luminous objects in the galaxy  

o The outer edges of a star forming region lags behind the inner edges,  making a star forming spiral arm

o The arms start near the central regions of the galaxy and spiral outward  through the disk

o Double spiral arms are an increase in the density of stars, gas, and dust in  a spiral pattern in the disk. Their orbits of stars are slightly perturbed

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(changed) which can lead to precession of the orbits of individual stars in  molecular clouds

o Spiral patterns form from perturbations

▪ Due to the gravitational influence of the galaxy, or nearby stars, and  the spiral arms

▪ Allow matter in the disk to linger closer together in certain parts of  their orbits than in other parts

▪ It as a wave pattern called a spiral or density wave

▪ High densities are close correspond to the crest of the wave, and  low densities between the arms where orbits are farther apart are  

the troughs.

∙ High Velocity clouds- Do not partake in the rotation of the galaxy, and appear  to be falling into the disk at high speeds.

o Dilute the interstellar medium wherever they merged with disk dust and  gas

∙ The Galactic Center 

o Hard to see because of interstellar dust and gas

o The number density of stars near the center is about 1000 stars per cubic  parsec, or a million times the sun.

o Supermassive black hole

▪ A Sgr A* is a supermassive black hole because of the high mass  

inferred from the velocity of stars and ionized gas close to the  

nucleus.

Black Holes 

Background:

∙ Scientists coined the term black holes in the early 1960s

∙ John Michell suggested that particles of light might not be able to escape from  surfaces of completely compact stars

∙ Pierre Laplace expressed this same idea decades later

∙ Both scientists reasoned that objects of high mass and small size could have an  escape velocity that is greater than the speed of light

What are black holes? : 

∙ Simple objects whose only characteristics are size, mass, and spin

∙ They have no spectral type or magnitude or color or other properties astronomers  generally compile  

∙ Represent one of the ends of the nuclear lives of stars, but only the most massive  stars

∙ Represent the end to an intense battle between gravity and thermodynamics  (tries to support stars through gas pressure)-- gravity wins in massive stars

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∙ Astronomers have found evidence that black holes reside at the centers of  galaxies and have masses of millions of solar masses

∙ Astronomers don’t know of any black holes close enough to explore directl The radius of a black hole: 

∙ For a star of mass M and a radius R, the surface gravity is proportional to M/R2  

∙ If a star collapses without losing mass, its surface gravity increases (the mass is  no longer being divided by the radius)

o Ex: This happens to the cores of stars when they contract after each loss of a  nuclear fuel source  

∙ Increasing surface gravity makes it more difficult for gas to escape from a star  o The effect is more severe for smaller objects

o Since nothing can travel faster than the speed of light, nothing can escape  from its surface, not even light itself

o If no light escapes from the surface of such a star, observers could not see it-- it would be invisible

o ***This is the original concept of the black hole****

∙ The greater the mass of the star, the greater the distortion of space  ∙ The distortion is even greater if the mass is compressed into a small volume

∙ An iron core with a mass greater than about 2-3 M. could collapse with a radius  of 4 km

∙ Schwarzschild radius:

o At a radius during collapse, surface gravity reaches the point where the escape  velocity is the speed of light  

o The distortion of space becomes so severe the even the photons can’t climb  out of the deep gravitational well

o Any object that reaches this radius becomes a black hole

o No light or any electromagnetic radiation can escape its surface o The radius is only a few kilometers

o The radius depends on mass (large collapsing mass reaches the escape  velocity at a larger radius than a small mass)

o Equation: 3 X (M/M.) km

∙ A million solar mass black hole would have a radius of 3 million km, or  about .002 AU

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o This is 4 times the size of the sun and much smaller than the solar system,  yet contains a million times the mass of the solar system

∙ High concentrations of mass in tiny volumes severely distort space near the  concentrations

Newtonian problems with black holes: 

∙ Since photons have a velocity limit, it is easy to visualize photons not escaping  from the hypothetical neutron star

∙ Newton’s theory of gravity, though, states that matter experiences and generates  gravitational forces that are proportional to the product of masses involved

∙ Since photons have no mass, how can gravity influence them?

∙ How can photons experience gravitational force that inhibits their escape?? Einstein’s concept of black holes (Curvature): 

∙ Einstein replaced Newton’s concept of force with the geometry of space and time  in his theory of general relativity  

∙ Einstein described the path of a rock as following the “curvature of space”

∙ The coordinate system describing space curves near the surface of the Earth and  the rock follows this curvature  

∙ Curvature replaces the pull of gravity

∙ Einstein believed the curvature of space causes the curved path of an asteroid  (dips in a putting green)

∙ Matter generates the curvature  

∙ The curvature of space refers to the curvature of our 3D space and implies a  fourth dimension  

∙ Embedding Diagrams:

o One of the dimensions is embedded and not shown

o The “space” perpendicular to the curved surface has no meaning; it is not the  3rd dimension  

o Far away from the object, the space is relatively flat

o The closer to the source of gravity, the more curved space becomes  o The amount of curvature is a measure of surface gravity and escape of velocity  o Falling means following the curvature downward to the surface

o Upward motion requires expending energy  

o The path of any particle is independent from its mass

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Near and In the Black Hole: 

∙ The surface of the sphere defined by Schwarzchild is called the event horizon

∙ The collapse of an iron core of a massive star continues after the surface of the  core reaches the event horizon

∙ Singularity- The collapsing core forms a singularity at the center of the black  hole

o it represents an infinite density and curvature of space

o The laws of science break down here

∙ Objects cannot escape a black hole once inside the event horizon, but they can  orbit the black hole

∙ Photon sphere- the radius at which circular orbits of photons are possible  defines the radius of a volume around a black hole

o The variety of orbits at and near the photon spheres can give observers  fantastic views

o As photons from stars and galaxies swing around the black hole and out again,  observers would be able to see light from around the universe

∙ If an astronaut tried to go into a black hole, differential forces would stretch the  astronauts apart  

∙ The black hole only has one characteristic that determines all of its properties-- mass

∙ The size of the mass determines the event horizon, photon sphere, and the  behavior of orbiting objects  

∙ Kerr black holes- rotating black holes that can drag space around with it when  collapsed  

o The funnel twists in the direction of the rotation

o The spinning black hole pulls objects inward and drags it around itself o Black holes can lose mass (can cause it to explode)

Black Hole Evaporation: 

∙ Black holes can “emit” particles

∙ The lower the mass, the higher the temperature

∙ Laws of quantum mechanics allow pairs of particles to appear and disappear

∙ Virtual Particles- particles that cannot be detected by particle detectors over  short periods of time

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∙ Example: Electron-positron pairs  

∙ Mass loss from black holes involves virtual particles and occurs just outside the  event horizon

o As the mass decreases, the black hole becomes smaller and hotter, and mass  loss accelerates

o The rapid accelerated loss may produce a cataclysmic explosion

o Predictions suggest that in the last tenth of a second the black hole converts  the rest of its mass into energy in a burst of gamma rays

Worldlines: 

∙ Trajectories of particles in space-time

∙ The worldline of the Sun is a vertical straight line

∙ The Earth’s worldline traces out a spirical pattern

Gravitational Waves: 

∙ Waves in the curvature of space that are generated by gravitational sources

∙ The strength of these waves is much smaller in magnitude than electromagnetic  waves

∙ The implosion of a massive iron core would generate incredible acceleration of  mass, which would produce a flash of gravitational waves

∙ The same would happen if two black holes collided  

Existence of Black Holes:

∙ Gravitational lensing- the focusing of the light by a black hole, or any object  capable of severely distorting space

∙ The lensed objects are distant galaxies and the spectra of two or more images are  identical

∙ No stars have been identified as lensed objects

∙ The greater the mass of the lens, the greater the separation of the images  ∙ Microlensing- lensing by small objects, like stellar black holes

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Stellar Evolution and End States: 

∙ Stars evolve starting from the far left as main sequence stars and end up on the  right

∙ The collapse of massive cores may prevent a supernova from occurring as all the  mass of the star could fall into the black hole  

Sample Test Answers: 

1. Pulsars are pulsating neutron stars. T/F?

A: False- Pulsation refers to a star moving in and out - its radius increased and  decrease like Cepheid variables. The term pulsar is the combination of a pulse of  radiation from a star. The star in this case is a neutron star.

2. What observation proved that pulsars were neutron stars?

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A: The Crab supernova remnant included a pulsar at its center.- The  structure of a supernova remnant is a cloud of the ejected envelope of the star that  exploded plus a star in the center of the envelope. We know that the result of a  supernova is a neutron star. Since it emits radiation we can view in visible light.

3. Glitches refer to the mechanism that slows the spinning of neutrons stars (NS) T/F?

A: False- A glitch is a sudden speed of the rotation rate of a pulsar. Figure 26.6 s a  graph of rotation period over a period of time of 8 years. It shows the rotation period on  the left axis as decreasing upward. the line in the figure show the general slowing down  of a pulsar. The jagged points represents a slight speed up (smaller period) of the pulsar.  The mechanism is complicated and uncertain, so all you have to know is that some  interior rotation transfers to the surface, causing the slight spin up.

4. If the magnetic axis of a neutron star is aligned with it rotational axis, then

A: we would detect a constant pattern of beam of radiation towards  us, no pulses- The reason we see what appears as a light house effect of  electromagnetic radiation (pulses) from pulsars is that the magnetic axis does not align  with its rotational axis. The radiation for a pulsar comes from the north and south poles  of the magnetic axis.

5. If the maximum mass for a white dwarf is 1.4 solar masses and the maximum mass of  a neutron star is 3 solar masses, what kind of object must be in an X-ray binary system if  the mass of the invisible object was 2 solar masses:

A: Neutron Stars (NS)- Since white dwarfs can only support masses less than  1.4 solar masses, the object must be a neutron star since the mass of the object is  between the maximum mass for a neutron but greater than that of a white dwarf.

6. What is the radius of a 10 solar mass black hole?

A: 30 km- Radius of a black hole is its mass times 3.

7. Which binary system described below must have a black hole (BH) as one of the two  stars:

A: An X-ray binary system in which the fainter or invisible companion  has a mass of 5 solar masses- In a spectroscope binary, we can see only one star but  we can determine the upper limit to the mass of the invisible star. This star could be of  any mass, it could also be a white dwarf or a normal star. Both neutron stars and black  holes produce x-ray radiation in binary systems.

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8. Newton's theory of gravity explains the curved path of a photon as due to the  gravitational force pulling it. T/F?

A: False- What property of a particle does it have to have for the gravitational  force to operate on it that the photon does not have - mass.  

9. Stars in the disk:

A: Are metal rich relative to the halo stars- See Table 28.1.

10. The galactic center:

A: Is visible to us in radio and infrared radiation but not seen with  optical telescopes.- There is some dust between us and the center of the galaxy, that  no visible radiation reaches the Earth. This is true because we are in a spiral are and  spiral arm contain lots of dust because they are part of regions of star formation, which  occurs in spiral arms.

11. The halo component of our galaxy:

A: Is a sphere of old stars and star clusters.- See table 28.1

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12.  

13. What is one way to generate spiral structure in a galaxy?

A: Star-forming spiral arms.- Since molecular clouds partake in the rotation  of the galaxy and since the inner parts of them move faster than the outer parts, then  tend to elongate in a curve. The combination of many clouds forming stars produces  spiral arms. See Figure 28.1.

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14.  

15. Which of the following correctly describes an orbital characteristic of the Sun in the  Galaxy?

A: It orbits at a speed of about 220 km/s.- The Sun orbits the center of the  galaxy. Thus it has a semimajor axis (distance form the center), a speed, and an orbital  period. For the Sun these are 8.5 kpc, 200 km/s, and 240 millions years. See page 180.

16. Why would older stars in the disk be metal poor (low Z) compared to younger stars  in the disk?

A: The older stars in the disk were formed before star formation  enriched the gas and dust in the disk.- The process of star formation ends with the  ejection of envelopes with iron group and heaver elements either gently (planetary  nebulae) or violently (supernova). In either case, elements that contributes to the Z in  the disk increases with time as more and more star formation occurs over the history of  the galaxy.

17. What kind of object near the Sun would not be part of a spiral arm:

A: Globular clusters- Globular clusters are part of the metal-poor halo, The  orbit the galactic center and sometimes pass near the Sun. HII regions and young stars  form in the spiral arms, so we expect them near the Sun because the Sun is in a spiral  arm.

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18. Population II:

A: Consists of the old stars in the halo and bulge.- Table 28.1

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