PHY– Pulsars – Report

II – Characteristics of Pulsars

Part A – the Sizes of Pulsars

• Figure 23.3 shows a plot of observed radio emission by a typical pulsar versus time. The periodicity of its emission is 0.5 seconds (every half second the pulsar sends a radio signal). There are other objects whose light emission varies with time. Among these are the Cepheid variables, stars that vary in diameter and temperature, which produces changes in their brightness with a well-defined periodicity. Figure 23.4 shows the period luminosity relation for Cepheids. How does the period of the typical pulsar compare with the period of most variable stars?

• The short period of pulsation is one of the characteristics used by radio astronomers when looking for pulsars. The general rule is that, the shorter the period of a variable, the smaller the object is. Based on this rule, are pulsar (LARGER, SMALLER) than normal variable stars? [Highlight your choice]

• Another rule is that no astronomical object can have a period that is shorter than the time it takes light to travel across its diameter. Consider a pulsar with a period T = 0.02 seconds. Given that the speed of light is c = 300,000 km/second, calculate the maximum size of this pulsar (in kilometers).

Max size of pulsar = T x c =

• The Earth’s diameter is 12,742 km. The Moon’s diameter is 3,474 km. How does this pulsar compare in size to the Earth and the Moon?

• The pulsar in Fig. 23.3 has a longer period, T = 0.5 seconds. How does this pulsar compare in size to the Earth and the Moon?

• Some pulsars have a time variation of just 0.002 seconds. The largest asteroids in our solar system are Ceres (now upgraded to a dwarf planet) and Vesta. These are respectively 946 km and 530 km in diameter. How do these pulsars compare in size to Ceres and Vesta?

Part B – the Pulsar ‘Clock’

• Two hypotheses were initially put forward as explanations for the periodicity of pulsars. One was that pulsars might be pulsating, like normal variable stars. The other was that they might be rotating, and a narrow beam of radiation would strike the Earth during each rotation (the lighthouse effect). Figure 23.5 shows an artist’s conception of the Crab Nebula Pulsar. According to the first hypothesis, the period of a pulsar should remain constant (or slightly decrease) as it ages. The lighthouse effect instead predicts that, as the rotating object loses energy, it will slow down, and the period should increase. It has been found that the periods of all pulsars are increasing. What do you think is the cause of the periodicity of a pulsar, PULSATION or ROTATION? [Highlight your choice]. Explain your reasoning.

Part C – the Density of Pulsars

It is now believed that pulsars are neutron stars. Neutron stars are formed by the gravitational collapse of the remnant of a massive star after a supernova explosion. In the collapse, atoms implode. The electrons merge with the protons in the nuclei of atoms, forming neutrons. This star is basically as dense as the nuclei of atoms.

The density of an object can be calculated as the ratio between its mass and its volume. The mass is measured in grams and the volume in cubic centimeters.

• The mass of the Sun is 2 x 1033 grams, and its volume is 1.4 x 1033 cm3. What is its density?

Density of Sun = Mass/Volume =

• How does the density of the Sun compare to the density of water, which is 1.0 g/cm3?

• Suppose a typical pulsar has half the mass of the Sun and a radius of 20 km, corresponding to a volume of about 1019 cm3. What is its density?

Density of pulsar =

• As you saw, the density of pulsars is enormous. To get a feeling for it, let’s compare the weight of one thimbleful of pulsar (the volume of a thimble is 1 cm3) to the weight of the ocean liner Queen Mary. The Queen Mary weighs 83,000 tons, or about 1011 How do the two compare?

• The tallest mountains on a pulsar are about 1 centimeter in height. Based on your findings, do you think this statement is TRUE or FALSE? [Highlight your choice]

III – Locations and Brightness of Pulsars

• Figure 23.6 shows the locations of 84 randomly selected pulsars with respect to the plane of our galaxy. Galactic longitude is indicated by ‘l’, and latitude by ‘b’. The horizontal line represents the galactic plane, which is at latitude b = 0. The Sun and the spiral arms of the galaxy lie near the galactic plane. Do most pulsars lie CLOSE to the galactic plane or FAR AWAY from it? [Highlight your choice]
• We believe, from observing other galaxies, that the stars that explode to become supernovae lie in or near the spiral arms of galaxies. For example, we have seen that a pulsar lies at the center of the Crab Nebula, which is the remains of the supernova observed by the Chinese astronomers in the year 1054 A.D. The search for remnants of other historic supernovae resulted also in the identification of the radio source 3C58 as the remains of the 1181 A.D. supernova. If all pulsars originate the same way, what can we infer about their origin?

• Back to Figure 23.6, the pulsars that appear to lie close to the galactic plane must be, in general, the farthest away. At great distances, only the brightest pulsars will be visible. Therefore, we can generalize that the pulsars seen near the plane of the galaxy will be the intrinsically bright ones, while the pulsars away from the plane will be nearby faint ones. In Table 23.1 the pulsars in Figure 23.6 that are nearer than 6o from the plane are listed and their periods given. Find the average of the periods of these pulsars:

Average Period (latitude < 6o) =

Table 23.2 instead lists the pulsars that are farther than 6o from the plane. Find the average of the periods of these pulsars:

Average Period (latitude > 6o) =

• On average, the pulsars that lie closer to the galactic plane have (LONGER, SHORTER) period than those farther away from the plane. Thus, the brightest pulsars tend to have (SHORTER, LONGER) periods. [Highlight your choices]

• In conclusion, we have seen that pulsars are probably connected with (LARGE, SMALL), (ROTATING, PULSATING) neutron stars. They seem to be the remnants of ____________ explosions in or near the spiral arms of our galaxy. The brightest pulsars have (LONGER, SHORTER) periods than the fainter ones. [Highlight your choices and fill the blank]