IB Physics/Astrophysics HL

Thanks to Tímea Garlati and a little help from Mephistophyles

Binary Stars

A binary star system is the orbiting of two stars around a common center. There are three classes of binary stars: visual, eclipsing, and spectroscopic.

Visual binaries

Appear as two separate stars as they orbit their common center. The center is know to be the mass of the two stars. The common period of rotation can be found with the equation

T²=4π²d³/G(M₁+M₂)

where d stands for the distance between the stars. Note that these stars will always remain diametrically opposite of each other. This is due to the gravity each star produces and contains.

Eclipsing binaries

This binary system occurs when the stars are oriented to a degree that when viewed from earth, one star will appear to stand in front of the second star. This will result in an eclipse, which may be total or partial. Depending on the stars, the light will bend around it, which will create a light curve pattern. This can be measured by the temporary increase of the luminosity , as the stats light emission is distorted.

Spectroscopic binaries

This binary system can only be defined if the light from one or both of the stars is observed as suffering from the Doppler effect. This shifting will cause the star to fall under two categories: the blue shift, which means moving towards the earth, and redshift, meaning moving away from the earth. The change is determined by

z=[λ-λ₀/λ₀]

were z represents the shift, and y is the wavelength of the spectral line and y is the wavelength earth observes.

In addition, the stars relatives speed in contrast to that of light will illustrate that there is a correlation between the shift and the speed of the star.

E.H. and J.N.

F.4 Cosmology

The Olbers Paradox

The Olbers Paradox questions why the night sky is dark. If the universe was infinite and thereby contained an infinite amount of stars, then theoretically there would be an infinite amount of energy radiating from the stars making the night sky infinitely bright. The Olbers Paradox applies to all infinite models, but does not apply to finite models. This is due to the fact that:

     1) There is a finite number of stars and each star has a finite lifetime. 
     2) The universe has a finite age and stars that are beyond the event horizon 
         have not yet had time for their light to reach Earth. 
     3) The radiation received is redshifted and so contains less energy.

/M.H.

The Development of the Universe

There is still a relatively large argument about how the universe actually came to be. In physics, the development reaches one conclusion through the Big Bang theory, but new theories are in speculation. The expansion of the universe can be described in mathematical terms. Consider

x(f)=R(t)x₀

if the distance between two galaxies was once x₀ , their separation after some time would described by (t).

Function R(t) is known as the scale factor of the universe. The scale factor could be loosely interpreted as the radius of the universe.

While the function is convenient enough, it leaves scientists with a large obstacle. The challenge of finding what the scale factor actually comes to leaves only three possibilities. They work in relation with the laws of general relativity.

[clearly not finished yo] E.H. and J.N.

F.5 Measuring radiation

F.5.1

The longer the period of light variation of a Cepheid, the greater is the luminosity. Observing the luminosity and the period the absolute magnitude can be determined. Comparing the absolute luminosity to the apparent luminosity we can calculate the distance to the Cepheid and surrounding stars. They serve therefore as 'distance markers' for distant stars where parallax can not be applied.

E.H. and J.N.

F.6 The expanding universe

Movement of Constellations/Stars over night/year

During the night, stars and constellations seem to be moving from east to west. But the relative position of the constellations do not change. The celestial sphere is the area around earth where the stars and constellations are located. The North Star, Polaris, is on the north celestial pole and doesn't seem to move at all. The rest of the stars and constellations seem to rotate around the North Star. Stars seem to move less the further north or south they are located. As the Earth rotates, the hemispheres receive different views of the stars and constellations.

For the Earth to make one revolution per year there must be a small change every day. The change per night is 0.986 degrees and is not easily detected.

www.astro.psu.edu/users/rbc/a1/lec2_2d.html

F.7 General relativity

F.7.1

'No observer can determine by experiment whether he or she is accelerating or is rather in a gravitational field.' For example, a pilot in fog, while making a steep turn can not tell whether he is accelerating by gravity or by the plane's thrust without looking at his instruments.

inertial mass = gravitational mass.

F.7.2

The effect of gravity upon time can be visualized as a stretched rubber-sheet, representing the 3 dimensions of space and one of time that is deformed by gravity. The more massive the object, the greater the deformation.

Does it mean that we don't know whether we are accelerated through time or pulled backwards by gravity?

F.7.3

The effect of gravity upon time can be visualized as a stretched rubber-sheet, representing the 3 dimensions of space and one of time that is deformed by gravity. The more massive the object, the greater the deformation.

Does it mean that we don't know whether we are accelerated through time or pulled backwards by gravity?

EDIT: It is actually the fabric of space-time that can be visualized as a rubber-sheet. When massive celestial bodies such as planets are placed on this fabric, they bend it inwards. This curvature on the fabric can be defined as the effect of gravity. When smaller objects go into this curvature, they start spiraling around the central planet and get closer to the core as they sprial. You can visualize this motion as the water that spirals down the drain.

Therefore, we can say that gravity causes acceleration on the space-time fabric.

F.7.5

Light is bent by strong gravitational fields. This was observed when light from distant star could be observed although the Sun stood in its way.

F.8 Stellar evolution

F.8.1

Stars undergo changes as their hydrogen is used up, first off they try to fuse the heavier elements, but this only works under certains circumstances and for a finite time. They either red giants after they go supernova, or they release a planetary nebula (nothing to do with planets, another form of expansion not as bad as going supernova). After going supernova stars become red giants, due to their large masses, or they decay into a neutron star. If they release a planetary nebula, they become a white dwarf or a brown dwarf, all depending on their mass.

(See also F.1.1)

F.8.2

Clouds of hydrogen and helium forms into 'Main sequence' stars.

Nuclear fusion takes place: H + H -> He , then He + He -> Be.

Further fusion takes only place in heavier stars, otherwise the pull of gravity forces the star to contract and cool to a red dwarf. If further fusion takes place the star becomes a red giant.

Small mass red giants : 1.4 solar masses (Chandraseka limit) can not withstand the pull of gravity, so it shrinks, becomes extremely hot, till it finally cools into a white dwarf.

Large red giants : Fuse until the formation of iron, but thereafter no fusion can take place without energy addition. So the star contracts, and heats up because of the large KE in the particles. When it can't be compressed further it explodes in a supernova. Such a great explosion may leave behind a very dense star made up of mostly neutrons, i.e. a neutron star.

Lighter neutron stars : With solar masses below 2-3 solar masses are thought to form Black holes because the gravitational force, which increases with mass, doesn't even allow light to leave the surface. Note, it is not a hole as such just a small extremely dense mass.

F.8.3

Pulsars are neutron stars that radiate energy at regular periods (See F.1.1)

Quasars suggest the existence of black holes, since the accelerated matter that black holes draw in could release its energy in the form large amounts of light.

X-ray is possibly produced as the accelerated matter due to Black holes is compressed and heated to millions of degrees.

F.8.4

Since black holes are really massive the 'stretched rubber sheet' of space-time becomes very deformed.

The Schwarzhild equation tells that R_s = 2GM/c² meaning that there's a critical radius when a mass becomes a black hole. (G is the gravitational constant, M is mass and c is the speed of light). For Earth this radius is 1cm.

The event horizon is the boundary at which light can not escape from the black hole. The singularity is a spot in the middle of the event horizon to which the mass shrinks, since no known force can stop the contraction. Here all time, space, matter and energy end.

Wormholes should allow us to disregard the curvature of space-time and let us travel through space instantaneously.

Not exactly; wormholes allow us to travel faster between two points than would be possible over the plane of space-time. The problem with relativity in it is that it views space-time as a flat plane with holes or dents that represent large masses. But for wormholes to effectively work, space-time needs to be curved or even spherical (like a soccer ball). Also, if you appear on the other end faster than light could travel all the way around, you are effectively violating (in some complicated way) causality.

But how does this link to general relativity

General relativity states space-time curves because of mass, yadda yadda. A singularity has such high mass that it can curve space time in on itself creating wormhole. Or it can cause a tear in the continuum, into which everything in the event horizon is eventually pulled, out of the universe itself.

not exactly, black holes have very high density areas called singularities, they are very curved, but they don't have infinite mass, but high enough to curve light into it, the event horizon is found using The Schwarzhild equation (see above). The wormhole thing is something entirely different, it's not a rip in the fabric, more like a tunnel between two black holes. Einstein did some work on this and it led to a recent discovery at CalTech where they found it was theoretically possible to time travel, but you need to be REALLY small and REALLY fast. Anyhow, that should cover that, any more questions, just post them. The only thing on the syllabus as far as I know is the Schwarzhild equation.