An introduction to… Pulsars! Paulo César C. Freire Cornell University / Arecibo Observatory.

An introduction to… Pulsars! Paulo César C. Freire Cornell University / Arecibo Observatory

In this talk: 1930s: Neutron star basics. White dwarfs * The Chandrasekhar limit * The neutron * Neutron stars in supernovae. 1930s: Neutron star basics. White dwarfs * The Chandrasekhar limit * The neutron * Neutron stars in supernovae. The Crab Nebula. Supernovae * M1 * What powers the Crab nebula? * Pacini’s idea. The Crab Nebula. Supernovae * M1 * What powers the Crab nebula? * Pacini’s idea. 1967: The discovery of the first pulsar. Emission characteristics * Propagation effects * What is a pulsar? 1967: The discovery of the first pulsar. Emission characteristics * Propagation effects * What is a pulsar? 1968: The discovery of the Crab Pulsar. The discovery of the Crab pulsar * Pulsars are rotating neutron stars! * The basic pulsar emission model. 1968: The discovery of the Crab Pulsar. The discovery of the Crab pulsar * Pulsars are rotating neutron stars! * The basic pulsar emission model.

In this talk (continued): Pulsar Timing. Energy emission * Characteristic ages * Magnetic Fields * Glitches and timing noise. Pulsar Timing. Energy emission * Characteristic ages * Magnetic Fields * Glitches and timing noise. 1974: The discovery of PSR B1913+16. The discovery of the binary pulsar * pulsars as gravitational laboratories. 1974: The discovery of PSR B1913+16. The discovery of the binary pulsar * pulsars as gravitational laboratories. 1982: The discovery of PSR B1937+21. Discovery of PSR B1937+21 * Millisecond pulsars as probes of the equation of state * Formation of millisecond pulsars * Timing accuracy. 1982: The discovery of PSR B1937+21. Discovery of PSR B1937+21 * Millisecond pulsars as probes of the equation of state * Formation of millisecond pulsars * Timing accuracy.

Not in this talk: Pulsar signal detection. Filter banks * auto-correlators * baseband systems * incoherent de-dispersion * coherent dedispersion. Pulsar signal detection. Filter banks * auto-correlators * baseband systems * incoherent de-dispersion * coherent dedispersion. Pulsar surveys. Avoiding dispersion and scattering * Optimal survey parameters * Dedispersion and Fourier transforms * Harmonic folding * Confirmation observations * Accelerated surveys. Pulsar surveys. Avoiding dispersion and scattering * Optimal survey parameters * Dedispersion and Fourier transforms * Harmonic folding * Confirmation observations * Accelerated surveys. Historical surveys. The Hulse-Taylor surveys * Arecibo high-latitude surveys * The Molonglo survey * 20-cm surveys of the Galactic plane * Globular cluster surveys. Historical surveys. The Hulse-Taylor surveys * Arecibo high-latitude surveys * The Molonglo survey * 20-cm surveys of the Galactic plane * Globular cluster surveys. Applications of timing of millisecond pulsars. Applications of timing of millisecond pulsars.

1930’s: Neutron stars! At the end of the lives of most stars, the outer layers of the star are expelled and form a Planetary Nebula. The core of the star remains bound, and forms a white dwarf. At the end of the lives of most stars, the outer layers of the star are expelled and form a Planetary Nebula. The core of the star remains bound, and forms a white dwarf. The Helix Nebula, 450 light-years away in Aquarius.

Neutron stars! These Earth-sized objects have incredible densities, of the order of several ton/cm 3. These Earth-sized objects have incredible densities, of the order of several ton/cm 3. In the 1920’s, using Pauli’s exclusion principle for electrons, astronomers finally understood that white dwarfs are held against gravity by degeneracy pressure. In the 1920’s, using Pauli’s exclusion principle for electrons, astronomers finally understood that white dwarfs are held against gravity by degeneracy pressure. Sirius B (arrow), the first white Dwarf discovered, orbits the much brighter Sirius A with an orbital period of 50 years.

Neutron stars! In 1931, S. Chandrasekhar (1910-1995) predicts that above a mass of 1.4 solar masses, the gravitational field of a white dwarf star should make it collapse! (Ap.J., 74, 81-82). He was awarded the 1983 Nobel Prize in Physics for this fundamental prediction! In 1931, S. Chandrasekhar (1910-1995) predicts that above a mass of 1.4 solar masses, the gravitational field of a white dwarf star should make it collapse! (Ap.J., 74, 81-82). He was awarded the 1983 Nobel Prize in Physics for this fundamental prediction! 1983 Nobel Prize in Physics 1983 Nobel Prize in Physics This happens because relativistic electrons behave like photons!!! This happens because relativistic electrons behave like photons!!!

Neutron stars! Polytropic equation of state (EOS): Polytropic equation of state (EOS): p(r) = k. ρ(r) Γ For non-relativistic electrons, Γ = 5/3 For non-relativistic electrons, Γ = 5/3 For relativistic electrons, Γ = 4/3, as for photons. For relativistic electrons, Γ = 4/3, as for photons. Mass-radius relation for white dwarfs.

Neutron stars! What happens to a white dwarf with a mass over 1.4 solar masses? Does it just keep collapsing until it forms a black hole? What happens to a white dwarf with a mass over 1.4 solar masses? Does it just keep collapsing until it forms a black hole? …Or does it form something else? …Or does it form something else? In 1932, James Chadwick, then at the Cavendish Laboratory in Cambridge, England, discovers the neutron. He got the Nobel physics prize in 1935 for this discovery. In 1932, James Chadwick, then at the Cavendish Laboratory in Cambridge, England, discovers the neutron. He got the Nobel physics prize in 1935 for this discovery.

Neutron stars! In 1934, Walter Baade and Fritz Zwicky proposed on a paper about supernovae that extensive stellar collapse of a heavy star during a supernova event should lead to the formation of a dense core of neutrons (a neutron star!) at the center of the SN remnant. In 1934, Walter Baade and Fritz Zwicky proposed on a paper about supernovae that extensive stellar collapse of a heavy star during a supernova event should lead to the formation of a dense core of neutrons (a neutron star!) at the center of the SN remnant. The neutrons form through INVERSE BETA DECAY, which is possible under the enormous pressures in the collapsing core. The neutrons form through INVERSE BETA DECAY, which is possible under the enormous pressures in the collapsing core. This produces extreme amounts of neutrino emission!!! This produces extreme amounts of neutrino emission!!!

Neutron stars! This prediction has now been verified! The SN 1987A event created a shower of neutrinos in the world’s detectors. This accounts for 99% of the energy of the supernova! This prediction has now been verified! The SN 1987A event created a shower of neutrinos in the world’s detectors. This accounts for 99% of the energy of the supernova!

Neutron stars! No one knows what happened to the remnant of the star that exploded as SN 1987 A (Sanduleak –69 202). Was a neutron star formed? Should we be able to see it? No one knows what happened to the remnant of the star that exploded as SN 1987 A (Sanduleak –69 202). Was a neutron star formed? Should we be able to see it? Landau (1938) and Oppenheimer and Volkoff (1939) calculated the radius of these objects. They predicted radii of the order of 10 km! Such small objects should be undetectable by any telescope at the vast distances to the nearest supernova remnants (normally many thousands of light-years). Landau (1938) and Oppenheimer and Volkoff (1939) calculated the radius of these objects. They predicted radii of the order of 10 km! Such small objects should be undetectable by any telescope at the vast distances to the nearest supernova remnants (normally many thousands of light-years).

Neutron stars! The exact relation between mass and radius of a neutron star depends on the Equation of State for cold matter. This is still not very well known… The exact relation between mass and radius of a neutron star depends on the Equation of State for cold matter. This is still not very well known…

The Crab Nebula This was discovered in Taurus by John Bevis in 1731. This was discovered in Taurus by John Bevis in 1731. Charles Messier looked at it and thought he had found comet Halley in its 1758 return. To prevent such further occurrences, he compiled a list of all nebulosities known to him. For this reason, the Crab Nebula is also known as M1. Charles Messier looked at it and thought he had found comet Halley in its 1758 return. To prevent such further occurrences, he compiled a list of all nebulosities known to him. For this reason, the Crab Nebula is also known as M1.

The Crab Nebula In the 1940’s, it was found that the supernova event that resulted in the Crab Nebula was witnessed by Chinese astronomers in the year 1054. In the 1940’s, it was found that the supernova event that resulted in the Crab Nebula was witnessed by Chinese astronomers in the year 1054. Radio emission from the Crab nebula was first detected by Bolton, Stanley and Slee (1949). It is one of the most powerful radio sources known, with a flux of 1000 Jy at 1 GHz. Apart from M1, it is also known as Taurus A, 3C144 and G184.6-5.8. Radio emission from the Crab nebula was first detected by Bolton, Stanley and Slee (1949). It is one of the most powerful radio sources known, with a flux of 1000 Jy at 1 GHz. Apart from M1, it is also known as Taurus A, 3C144 and G184.6-5.8. The Crab nebula was the first known extra-solar X-ray source detected (Bowyer et al. 1964). It is used as an X-ray calibrator… The Crab nebula was the first known extra-solar X-ray source detected (Bowyer et al. 1964). It is used as an X-ray calibrator… Total emitted power at all wavelengths: 100,000 times the solar luminosity!!! Total emitted power at all wavelengths: 100,000 times the solar luminosity!!! Where does all this energy come from? Where does all this energy come from?

The Crab Nebula In 1942, Walter Baade identified a star with a peculiar spectrum near the center of the remnant; he proposed that such a star could be the power source of the nebula. In 1942, Walter Baade identified a star with a peculiar spectrum near the center of the remnant; he proposed that such a star could be the power source of the nebula. Radio scintillation studies led Hewish and Okoye (1964) to propose the existence of a compact radio source near the center of the nebula, with a steep spectrum. Radio scintillation studies led Hewish and Okoye (1964) to propose the existence of a compact radio source near the center of the nebula, with a steep spectrum. Pacini (1967) proposed the existence of a highly magnetized, rapidly spinning neutron star as the power source of the nebula. This would radiate a very powerful EM wave with the rotational frequency of the star. This is below the plasma frequency of the nebula, therefore all this energy will be absorbed and re- radiated by the plasma of the nebula. Pacini (1967) proposed the existence of a highly magnetized, rapidly spinning neutron star as the power source of the nebula. This would radiate a very powerful EM wave with the rotational frequency of the star. This is below the plasma frequency of the nebula, therefore all this energy will be absorbed and re- radiated by the plasma of the nebula.

The Crab Nebula The neutron star should be spinning fast due to conservation of angular momentum from the parent stellar core! The neutron star should be spinning fast due to conservation of angular momentum from the parent stellar core! It should be highly magnetized due to conservation of magnetic flux from the parent stellar core. It should be highly magnetized due to conservation of magnetic flux from the parent stellar core.

1967: The discovery of PSR B1919+21 In August 1967, Jocelyn Bell, then a graduate student at Cambridge, finds a radio signal in the constellation Sagitta (the Little Arrow) pulsating with a period of 1.33 seconds. She found this to appear 4 minutes earlier every day, indicating a sidereal source. In August 1967, Jocelyn Bell, then a graduate student at Cambridge, finds a radio signal in the constellation Sagitta (the Little Arrow) pulsating with a period of 1.33 seconds. She found this to appear 4 minutes earlier every day, indicating a sidereal source. For this discovery, Anthony Hewish earns the Nobel Prize in Physics 1974. For this discovery, Anthony Hewish earns the Nobel Prize in Physics 1974.Nobel Prize in Physics 1974.Nobel Prize in Physics 1974.

PSR B1919+21 The emission temperatures for pulsars are of the order of 10 30 K! Emission definitely not thermal, it must be coherent. The emission temperatures for pulsars are of the order of 10 30 K! Emission definitely not thermal, it must be coherent. The pulses were soon found to be arriving with extreme regularity, although no two individual pulses are alike. The average pulse, however, does not change with time. The pulses were soon found to be arriving with extreme regularity, although no two individual pulses are alike. The average pulse, however, does not change with time. Soon other pulsars were found, some with repetition periods as small as 0.25 s. Soon other pulsars were found, some with repetition periods as small as 0.25 s.

PSR B1919+21 All pulsars display different integrated pulse profiles! All pulsars display different integrated pulse profiles! These pulse profiles are characteristic of the frequency being used to make the observation. These pulse profiles are characteristic of the frequency being used to make the observation.

PSR B1919+21 The pulsed signal has no line features, except those resulting from absorption. It is normally stronger at about 100 MHz, decreasing with higher radio frequencies. No two pulsar spectra look alike! The pulsed signal has no line features, except those resulting from absorption. It is normally stronger at about 100 MHz, decreasing with higher radio frequencies. No two pulsar spectra look alike!

PSR B1919+21 The radio signal can be highly polarized, mainly at low frequencies. The radio signal can be highly polarized, mainly at low frequencies. No one knows what causes the radio emission! No one knows what causes the radio emission!

PSR B1919+21 The the pulses arrive at the Earth first at higher frequencies, then at the lower frequencies, with delays of many milliseconds (after traveling thousands of years in space). The the pulses arrive at the Earth first at higher frequencies, then at the lower frequencies, with delays of many milliseconds (after traveling thousands of years in space). This delay can be described by a single quantity, the Dispersion Measure, or DM, which is simply a measure of the column density of electrons between the telescope and the pulsar. This delay can be described by a single quantity, the Dispersion Measure, or DM, which is simply a measure of the column density of electrons between the telescope and the pulsar.

PSR B1919+21 The delay at a given frequency is given by: The delay at a given frequency is given by: Where Where It is because of this effect that we need spectrometers to observe pulsars! It is because of this effect that we need spectrometers to observe pulsars!

PSR B1919+21 Scintillation is a quasi-random variation of the intensity of the pulsed signal. Scintillation is a quasi-random variation of the intensity of the pulsed signal. It can be refractive or diffractive. The first is due to the geometry – if it produces amplification, it is because the interstellar medium is acting as a magnifying lens. Example: the caustics seen at the bottom of a pool. It can be refractive or diffractive. The first is due to the geometry – if it produces amplification, it is because the interstellar medium is acting as a magnifying lens. Example: the caustics seen at the bottom of a pool. The second results from the interference of the waves from the pulsars with themselves. Example: star twinkling. A distinguishing feature of this scintillation is its wavelength dependence – it affects color. The second results from the interference of the waves from the pulsars with themselves. Example: star twinkling. A distinguishing feature of this scintillation is its wavelength dependence – it affects color.

Scintillation is what Hewish was looking for, and that is what was found... PSR B1919+21

Faraday rotation: the different polarization angles at different frequencies (caused by the different velocities at which waves perpendicular and parallel to a magnetic field propagate in a plasma) indicate the strength and orientation of the magnetic field of the Galaxy along the line of sight. Faraday rotation: the different polarization angles at different frequencies (caused by the different velocities at which waves perpendicular and parallel to a magnetic field propagate in a plasma) indicate the strength and orientation of the magnetic field of the Galaxy along the line of sight. Scattering, or multi-path propagation. This is akin to “ghosts” in a TV image, caused, for instance, by reflection of the radio wave in a building. The “ghost” always arrives later than the original signal. Scattering, or multi-path propagation. This is akin to “ghosts” in a TV image, caused, for instance, by reflection of the radio wave in a building. The “ghost” always arrives later than the original signal.

PSR B1919+21 These five propagational effects (dispersion, refractive and diffractive scintillation, scattering and Faraday rotation) are very useful probes of the interstellar medium! These five propagational effects (dispersion, refractive and diffractive scintillation, scattering and Faraday rotation) are very useful probes of the interstellar medium! Hence, pulsars would be useful even if nothing else was known about them. Hence, pulsars would be useful even if nothing else was known about them. The question now is: WHAT ARE PULSARS? The question now is: WHAT ARE PULSARS?

PSR B1919+21 They are Galactic radio sources, as they are found mostly in the Galactic disk. They are Galactic radio sources, as they are found mostly in the Galactic disk. Pulsars also present proper motions that are on average much larger than those of stars (velocities are 100 times the Earth’s escape velocity!). Pulsars also present proper motions that are on average much larger than those of stars (velocities are 100 times the Earth’s escape velocity!). Evolution of 100 pulsars in the Galactic gravitational field over 200 Myr. Lateral view, 30 x 10 pc.

PSR B1919+21 The repetition rates imply that the source is very compact. A star pulsating with a period of 0.25 seconds cannot be larger than 0.25 x c (of 75.000 km). The repetition rates imply that the source is very compact. A star pulsating with a period of 0.25 seconds cannot be larger than 0.25 x c (of 75.000 km). This is confirmed by radio scintillation: extended objects do not scintillate, pulsars scintillate a lot. This is confirmed by radio scintillation: extended objects do not scintillate, pulsars scintillate a lot. Is the fundamental periodicity caused by… Is the fundamental periodicity caused by… White dwarf vibration? White dwarf vibration? White dwarf rotation? White dwarf rotation? White dwarf orbits? White dwarf orbits? Neutron star vibration? Neutron star vibration? Neutron star rotation? Neutron star rotation? Neutron star orbit? Neutron star orbit?

PSR B1919+21 If the periodicity was caused by some sort of orbital motion, then this should be decreasing in time, because of emission of gravitational waves. This is not observed! If the periodicity was caused by some sort of orbital motion, then this should be decreasing in time, because of emission of gravitational waves. This is not observed! Also, the orbital period for two white dwarfs in contact is about one second. Pulsars are observed with periods shorter than that. Also, the orbital period for two white dwarfs in contact is about one second. Pulsars are observed with periods shorter than that. White dwarf vibration? White dwarf vibration? White dwarf rotation? White dwarf rotation? White dwarf orbits? NO! White dwarf orbits? NO! Neutron star vibration? Neutron star vibration? Neutron star rotation? Neutron star rotation? Neutron star orbit? NO! Neutron star orbit? NO!

PSR B1919+21 The vibration periods of neutron stars are predicted to be a fraction of a millisecond. The vibration periods of neutron stars are predicted to be a fraction of a millisecond. The lower limits for white dwarf vibration and rotation periods are of the order of a second. So perhaps those might be an explanation... Except that the 0.25 second period is quite short… The lower limits for white dwarf vibration and rotation periods are of the order of a second. So perhaps those might be an explanation... Except that the 0.25 second period is quite short… White dwarf vibration? Perhaps, if you push it… White dwarf vibration? Perhaps, if you push it… White dwarf rotation? Perhaps, if you push it… White dwarf rotation? Perhaps, if you push it… White dwarf orbits? NO! White dwarf orbits? NO! Neutron star vibration? NO! Neutron star vibration? NO! Neutron star rotation? Neutron star rotation? Neutron star orbit? NO! Neutron star orbit? NO!

PSR B1919+21 In 1968, Tommy Gold writes that pulsars must be rotating neutron stars. He predicts a very slow and steady spin-down for these objects, based on the fact that they must be losing rotational energy due to their large EM emission. In 1968, Tommy Gold writes that pulsars must be rotating neutron stars. He predicts a very slow and steady spin-down for these objects, based on the fact that they must be losing rotational energy due to their large EM emission. If the pulsations were due to vibration, then the intensity of the oscillation should decrease, and the vibration period (a characteristic of the vibrating object) should remain constant. If the pulsations were due to vibration, then the intensity of the oscillation should decrease, and the vibration period (a characteristic of the vibrating object) should remain constant. He also predicts that faster pulsars might be found, “because the rotation rates of neutron stars are capable of going up to more than 100/s, and the observed periods would seem to represent the slow end of the distribution.” He also predicts that faster pulsars might be found, “because the rotation rates of neutron stars are capable of going up to more than 100/s, and the observed periods would seem to represent the slow end of the distribution.”

1968: The discovery of PSR B0531+21 (Crab Pulsar) In 1968, at the height of the “pulsar fever”, giant radio pulses originating in the Crab Nebula were detected (Staelin and Reifenstein). These extremely short bursts proved the existence of a pulsar at the center of the Nebula (PSR 0531+21). This is the compact radio source detected by Hewish and Okoye in 1964. In 1968, at the height of the “pulsar fever”, giant radio pulses originating in the Crab Nebula were detected (Staelin and Reifenstein). These extremely short bursts proved the existence of a pulsar at the center of the Nebula (PSR 0531+21). This is the compact radio source detected by Hewish and Okoye in 1964.

PSR B0531+21 Soon, Arecibo observations showed that the repetition period of the pulsar was only 33 ms! The pulsar showed measurable rotational slowdown within a single day! Soon, Arecibo observations showed that the repetition period of the pulsar was only 33 ms! The pulsar showed measurable rotational slowdown within a single day!

PSR B0531+21 PULSARS ARE NEUTRON STARS!!! No white dwarf can rotate so fast! And, the pulsar is slowing down, which excludes any kind of vibration. T. Gold was right! PULSARS ARE NEUTRON STARS!!! No white dwarf can rotate so fast! And, the pulsar is slowing down, which excludes any kind of vibration. T. Gold was right! NEUTRON STARS EXIST!!! The theorists were not just having a bad trip (although it looked like that…) NEUTRON STARS EXIST!!! The theorists were not just having a bad trip (although it looked like that…) PULSARS RESULT FROM STELLAR COLLAPSE IN SUPERNOVAE!!!! Baade and Zwicky were right!!!! PULSARS RESULT FROM STELLAR COLLAPSE IN SUPERNOVAE!!!! Baade and Zwicky were right!!!! THE ROTATIONAL ENERGY LOSS OF THE CRAB PULSAR IS EXACTLY THE SAME AS THE EMISSION OF THE CRAB NEBULA!!!! Pacini was right, neutron stars are fast, have large magnetic fields, and one of them powers the Crab Nebula. THE ROTATIONAL ENERGY LOSS OF THE CRAB PULSAR IS EXACTLY THE SAME AS THE EMISSION OF THE CRAB NEBULA!!!! Pacini was right, neutron stars are fast, have large magnetic fields, and one of them powers the Crab Nebula. However, no one predicted the feature that makes pulsars really shine, the radio emission. However, no one predicted the feature that makes pulsars really shine, the radio emission.

PSR B0531+21 After this event, the basic model of pulsar emission becomes established: pulsars are the radio equivalent of lighthouses on a neutron star. After this event, the basic model of pulsar emission becomes established: pulsars are the radio equivalent of lighthouses on a neutron star. Non-thermal radiation at a variety of wavelengths is emitted through the magnetic poles, which are generally misaligned with the spin axis. We see a pulse at the Earth every time this magnetic axis points towards us. Non-thermal radiation at a variety of wavelengths is emitted through the magnetic poles, which are generally misaligned with the spin axis. We see a pulse at the Earth every time this magnetic axis points towards us.

PSR B0531+21 Radakhrishnan and Cooke’s (1969) rotating vector model, explains the polarization characteristics of slow pulsars. It allows a basic determination of the geometry of pulsar emission! Radakhrishnan and Cooke’s (1969) rotating vector model, explains the polarization characteristics of slow pulsars. It allows a basic determination of the geometry of pulsar emission!

PSR B0531+21 Baade’s star is found to be the optical counterpart of the Crab pulsar. The optical pulsations have exactly the same period. This is the first pulsar seen at optical wavelengths! Baade’s star is found to be the optical counterpart of the Crab pulsar. The optical pulsations have exactly the same period. This is the first pulsar seen at optical wavelengths! X-ray pulses are also measured at the same frequency. X-ray pulses are also measured at the same frequency. A second pulsar was soon found in the Vela supernova remnant, (the Vela pulsar, or PSR 0833-45) which also shows optical and X-ray emission. A second pulsar was soon found in the Vela supernova remnant, (the Vela pulsar, or PSR 0833-45) which also shows optical and X-ray emission.

Listening… Let us take a break and listen to some pulsars: Let us take a break and listen to some pulsars: http://www.jb.man.ac.uk/~pulsar/Education/Sounds/

Pulsar timing How regularly do pulsars spin? How regularly do pulsars spin? Can we learn something from this rotation? Can we learn something from this rotation? For an isolated pulsar, the two main parameters measured by timing (apart from the position in the sky and the DM) are the rotational period and its first derivative. From these two parameters alone, one can learn a lot about a given pulsar. For an isolated pulsar, the two main parameters measured by timing (apart from the position in the sky and the DM) are the rotational period and its first derivative. From these two parameters alone, one can learn a lot about a given pulsar.

Pulsar timing Increase in P results from loss of rotational energy: Increase in P results from loss of rotational energy: Energy is radiated mostly as dipole radiation: Energy is radiated mostly as dipole radiation: Evolution of spin frequency: Evolution of spin frequency:

Pulsar timing The pulsar’s age τ can be estimated, integrating the spindown and assuming that P >> P 0 : The pulsar’s age τ can be estimated, integrating the spindown and assuming that P >> P 0 : Assumptions (n = 3, P >> P 0 ) may be wrong, but τ is normally a good estimator of the age. Assumptions (n = 3, P >> P 0 ) may be wrong, but τ is normally a good estimator of the age. For the Crab pulsar, real age is 949 years (in 2003), and τ is 1237 years! For the Crab pulsar, real age is 949 years (in 2003), and τ is 1237 years!

Pulsar timing The pulsar’s magnetic field can also be estimated: The pulsar’s magnetic field can also be estimated: We assumed: R = 10 km, I = 2/5 M R 2 = 10 38 kg m 2 We assumed: R = 10 km, I = 2/5 M R 2 = 10 38 kg m 2 α = 90 degrees. α = 90 degrees. Most pulsars have fields of 10 8 T, i.e., tens of millions of times more powerful than anything that can be produced on Earth. Most pulsars have fields of 10 8 T, i.e., tens of millions of times more powerful than anything that can be produced on Earth.

Pulsar timing Most pulsars show significant departures from simple, uniformly slowing rotation. The two main departures are: Most pulsars show significant departures from simple, uniformly slowing rotation. The two main departures are: Glitches. This corresponds to starquakes, caused by a sudden shrinkage in the star’s size, with corresponding spin up. Glitches. This corresponds to starquakes, caused by a sudden shrinkage in the star’s size, with corresponding spin up. Timing noise. The origin of this phenomenon is unknown. Timing noise. The origin of this phenomenon is unknown. The younger the pulsar, and the more intense its magnetic field, the larger are the torques applied to it surface. The phenomena listed above seem to be related to these torques… The younger the pulsar, and the more intense its magnetic field, the larger are the torques applied to it surface. The phenomena listed above seem to be related to these torques…

Pulsar timing The Crab pulsar is a particularly noisy one. For this reason, it has been monitored daily for more than 30 years. In 1999, it had already glitched 13 times. The Crab pulsar is a particularly noisy one. For this reason, it has been monitored daily for more than 30 years. In 1999, it had already glitched 13 times.

1974: The discovery of PSR B1913+16 Russel Hulse and Joe Taylor discovered PSR B1913+16, in the constellation Aquila (the Eagle), during a systematic 430-MHz survey of the Galactic plane at Arecibo. Russel Hulse and Joe Taylor discovered PSR B1913+16, in the constellation Aquila (the Eagle), during a systematic 430-MHz survey of the Galactic plane at Arecibo.

PSR B1913+16 It has a DM of 168.77 cm -3 pc and a rotational period of 59 ms. This was the second shortest period known at the time. It has a DM of 168.77 cm -3 pc and a rotational period of 59 ms. This was the second shortest period known at the time. This was the first binary pulsar to be discovered. This was the first binary pulsar to be discovered.

PSR B1913+16 The pulsar and the companion star are orbiting the common center of mass. The orbital period is 7 h 45 m and the eccentricity is 0.61. The pulsar and the companion star are orbiting the common center of mass. The orbital period is 7 h 45 m and the eccentricity is 0.61.

PSR B1913+16 When timing pulsars (or measuring radial velocities with the aid of spectral lines) one has access to the line-of-sight velocity, which causes a Doppler shift on the wavelength of the spectral line or a modulation on the period of the pulsar. When timing pulsars (or measuring radial velocities with the aid of spectral lines) one has access to the line-of-sight velocity, which causes a Doppler shift on the wavelength of the spectral line or a modulation on the period of the pulsar. In the case of pulsar timing, one can also measure the range relative to the center of mass of the binary, normally with a precision of the order of 1 km or less. In the case of pulsar timing, one can also measure the range relative to the center of mass of the binary, normally with a precision of the order of 1 km or less.

PSR B1913+16 Five Keplerian parameters can normally be measured from fitting the velocity (or, preferably, the delay) curves: orbital period (P b ), projected size of the orbit, in light seconds (x), eccentricity (e), longitude of periastron (ω) and time of passage through periastron (T 0 ). A non-changing Keplerian orbit is exactly what is predicted by Newtonian gravity. Five Keplerian parameters can normally be measured from fitting the velocity (or, preferably, the delay) curves: orbital period (P b ), projected size of the orbit, in light seconds (x), eccentricity (e), longitude of periastron (ω) and time of passage through periastron (T 0 ). A non-changing Keplerian orbit is exactly what is predicted by Newtonian gravity. Without access to information on transverse velocities, the individual masses of the components (m 1 and m 2 ) and the inclination of the system (i) cannot be measured, but… Without access to information on transverse velocities, the individual masses of the components (m 1 and m 2 ) and the inclination of the system (i) cannot be measured, but…

PSR B1913+16 The mass function, a relation between these three quantities, can be measured to excellent precision, as it depends on two observable parameters: The mass function, a relation between these three quantities, can be measured to excellent precision, as it depends on two observable parameters:

PSR B1913+16 For most binary pulsars, and spectroscopic binaries, there is no information on the transverse velocities, so this is as far as we can go. For most binary pulsars, and spectroscopic binaries, there is no information on the transverse velocities, so this is as far as we can go. However, the PSR B1913+16 system is so extreme, and pulsar timing is so precise, that some effects of general relativity became detectable! However, the PSR B1913+16 system is so extreme, and pulsar timing is so precise, that some effects of general relativity became detectable! Three such effects have been measured for PSR B1913+16: Three such effects have been measured for PSR B1913+16: 1. Periastron advance (ώ). 2. Rotational slowdown due to gravitational redshift and Lorenz time dilation (Einstein delay, γ). 3. Orbital decay due to emission of gravitational waves (dP b /dt).

PSR B1913+16 Perihelion advance due to general relativity had been observed for the orbits of several planets in the solar system, most notably Mercury. Perihelion advance due to general relativity had been observed for the orbits of several planets in the solar system, most notably Mercury. The periastron of PSR B1913+16 advances 4.226607(7) degrees/year. The daily periastron advance is the same as Mercury’s perihelion advance in a century… The periastron of PSR B1913+16 advances 4.226607(7) degrees/year. The daily periastron advance is the same as Mercury’s perihelion advance in a century…

PSR B1913+16 The Einstein delay was also measured: γ = 0.004294(1) s. The pulsar slows down visibly when it is near the companion, accumulating a delay relative to the prediction of constant rotational period. General relativity predicts that time itself slows down in an intense gravitational field (in this case, that of the companion object). The Einstein delay was also measured: γ = 0.004294(1) s. The pulsar slows down visibly when it is near the companion, accumulating a delay relative to the prediction of constant rotational period. General relativity predicts that time itself slows down in an intense gravitational field (in this case, that of the companion object). The pulsar also rotates more slowly due to special-relativistic time dilation – it is traveling faster near the companion object. The pulsar also rotates more slowly due to special-relativistic time dilation – it is traveling faster near the companion object.

PSR B1913+16 These two effects determine the mass and inclination of the system! This happens because, according to General relativity, they depend on the known Keplerian parameters and the masses of the two objects: These two effects determine the mass and inclination of the system! This happens because, according to General relativity, they depend on the known Keplerian parameters and the masses of the two objects:

PSR B1913+16 The masses of the individual components (and, from the mass function, the inclination of the system!) are only well determined if we assume that General relativity is right. The masses of the individual components (and, from the mass function, the inclination of the system!) are only well determined if we assume that General relativity is right. This is the most precise measurement of any mass outside the solar system. This is the most precise measurement of any mass outside the solar system.

PSR B1913+16 A third relativistic effect is measurable: The orbital period is becoming shorter. A third relativistic effect is measurable: The orbital period is becoming shorter. General relativity predicts this to be due to the loss of energy caused by emission of gravitational waves. This depends only on quantities that are already (supposedly) known: General relativity predicts this to be due to the loss of energy caused by emission of gravitational waves. This depends only on quantities that are already (supposedly) known: Prediction: the orbital period should decrease –2.40247 x 10 -12 s/s (or 75 μs per year!) Prediction: the orbital period should decrease –2.40247 x 10 -12 s/s (or 75 μs per year!)

PSR B1913+16 Value observed (after subtraction of the Galactic motion of the pulsar) is: Value observed (after subtraction of the Galactic motion of the pulsar) is: –2.4085(52) x 10 -12 s/s. –2.4085(52) x 10 -12 s/s. The agreement is perfect! The agreement is perfect! GENERAL RELATIVITY GIVES A SELF- CONSISTENT ESTIMATE FOR THE MASSES OF THE TWO COMPONENTS OF THE BINARY! GENERAL RELATIVITY GIVES A SELF- CONSISTENT ESTIMATE FOR THE MASSES OF THE TWO COMPONENTS OF THE BINARY! GRAVITATIONAL WAVES EXIST! GRAVITATIONAL WAVES EXIST!

PSR B1913+16 For this measurement, Hulse and Taylor were awarded the 1993 Nobel Prize in Physics. For this measurement, Hulse and Taylor were awarded the 1993 Nobel Prize in Physics.1993 Nobel Prize in Physics1993 Nobel Prize in Physics This is all very fine and beautiful, but are double neutron stars supposed to exist? This is all very fine and beautiful, but are double neutron stars supposed to exist? This was originally quite a puzzle… This was originally quite a puzzle…

1982: The discovery of PSR B1937+21 In 1982, at an Observatory near you, Don Backer and Shri Kulkarni found the first millisecond pulsar, PSR B1937+21, in the constellation Vulpecula (the Little Fox). The object is isolated. In 1982, at an Observatory near you, Don Backer and Shri Kulkarni found the first millisecond pulsar, PSR B1937+21, in the constellation Vulpecula (the Little Fox). The object is isolated.

PSR B1937+21 The pulsar was found in a search targeted at the location of a compact (scintillating) radio source with a steep spectrum in the radio nebula 4C21.53W. The pulsar was found in a search targeted at the location of a compact (scintillating) radio source with a steep spectrum in the radio nebula 4C21.53W. At first, it was thought to be rotating 1284 times a second! This was later found to be due to the fact that the profile has a double peak – the second Fourier component is the strongest! At first, it was thought to be rotating 1284 times a second! This was later found to be due to the fact that the profile has a double peak – the second Fourier component is the strongest! Still, a rotation of 642 times a second (or a period of 1.57 ms) implies that the equator is moving at 1/7 the speed of light! Still, a rotation of 642 times a second (or a period of 1.57 ms) implies that the equator is moving at 1/7 the speed of light!

PSR B1937+21 Is that possible? Why doesn’t the star fly apart? Is that possible? Why doesn’t the star fly apart? The gravity at the surface of a pulsar is about 10 12 times more powerful than at the Earth’s surface. The gravity at the surface of a pulsar is about 10 12 times more powerful than at the Earth’s surface. The rotational velocity introduces constraints on the equation of state: radii must be smaller than ~20 km, otherwise the centrifugal force would be larger than the gravitational force. The rotational velocity introduces constraints on the equation of state: radii must be smaller than ~20 km, otherwise the centrifugal force would be larger than the gravitational force. Some models of the behavior of nuclear matter at high densities have already been excluded by the discovery of PSR B1937+21, as they cannot predict a stable configuration rotating 642 times a second – such models tend to predict large stellar radii. Some models of the behavior of nuclear matter at high densities have already been excluded by the discovery of PSR B1937+21, as they cannot predict a stable configuration rotating 642 times a second – such models tend to predict large stellar radii.

PSR B1937+21 The rotational period derivative was found to be extremely small, which sets this pulsar completely apart from other young pulsars with small periods, like the Crab pulsar. The rotational period derivative was found to be extremely small, which sets this pulsar completely apart from other young pulsars with small periods, like the Crab pulsar. The magnetic field is ~1000 times weaker than that of normal pulsars, the age is of the order of billions of years! The magnetic field is ~1000 times weaker than that of normal pulsars, the age is of the order of billions of years! More than 100 other millisecond pulsars have been found to date! More than 100 other millisecond pulsars have been found to date!

PSR B1937+21 The formation of such stars was a mystery at first. In the same year, Alpar suggested that Millisecond Pulsars are formed in Low-Mass X-ray Binaries (LMXBs). The formation of such stars was a mystery at first. In the same year, Alpar suggested that Millisecond Pulsars are formed in Low-Mass X-ray Binaries (LMXBs). Under this suggestion, all MSPs should still be part of pulsar – white dwarf binaries. While this is true for most MSPs found since, PSR B1937+21 itself is isolated. Under this suggestion, all MSPs should still be part of pulsar – white dwarf binaries. While this is true for most MSPs found since, PSR B1937+21 itself is isolated. The formation of isolated millisecond pulsars is still not understood. The formation of isolated millisecond pulsars is still not understood.

PSR B1937+21 A distinctive feature of the formation model for MSP/white dwarf systems is the prediction that the orbits should be circular. This is observed to be true. A distinctive feature of the formation model for MSP/white dwarf systems is the prediction that the orbits should be circular. This is observed to be true.

PSR B1937+21 The rotation of most known millisecond pulsars is perfect, i.e., it can be described, to within observational accuracy, as a perfect, featureless slowdown. The rotation of most known millisecond pulsars is perfect, i.e., it can be described, to within observational accuracy, as a perfect, featureless slowdown. Millisecond pulsars have better long-term stability than atomic clocks! Millisecond pulsars have better long-term stability than atomic clocks! Uses are manifold… And have absorbed much time and effort over the last 21 years, with many delightful results: Uses are manifold… And have absorbed much time and effort over the last 21 years, with many delightful results: 1. Tests of General Relativity 2. Search for gravitational waves produced by giant black hole mergers. 3. Probe newtonian systems, like planetary systems and Globular clusters.

PSR B1937+21 Just an example of the precision of millisecond pulsar timing: PSR J1738+0333. Just an example of the precision of millisecond pulsar timing: PSR J1738+0333. Period is 5.8500957647881(5) ms, the projected semi-major axis of the pulsar’s orbit is 102,857,840 +/- 60 m Period is 5.8500957647881(5) ms, the projected semi-major axis of the pulsar’s orbit is 102,857,840 +/- 60 m Difference between semi-major axis and semi-minor axis of the pulsar’s orbit: 200 μm, or less than 1/100 of an inch! Difference between semi-major axis and semi-minor axis of the pulsar’s orbit: 200 μm, or less than 1/100 of an inch! Second most perfect circle known! Second most perfect circle known! Pulsar 1 kpc away… Pulsar 1 kpc away…

Listening to MSPs Millisecond pulsars sound decidedly different: Millisecond pulsars sound decidedly different: http://www2.naic.edu/~pfreire/47Tuc.html

Thank you for your time! Contact me at: pfreire@naic.edu, or visit my website at http://www2.naic.edu/~pfreire/. pfreire@naic.edu http://www2.naic.edu/~pfreire/pfreire@naic.edu http://www2.naic.edu/~pfreire/ The National Astronomy and Ionosphere Center is operated by Cornell University, under a cooperative agreement with the National Science Foundation.

An introduction to… Pulsars! Paulo César C. Freire Cornell University / Arecibo Observatory.

Similar presentations

Presentation on theme: "An introduction to… Pulsars! Paulo César C. Freire Cornell University / Arecibo Observatory."— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

An introduction to… Pulsars! Paulo César C. Freire Cornell University / Arecibo Observatory.

Similar presentations

Presentation on theme: "An introduction to… Pulsars! Paulo César C. Freire Cornell University / Arecibo Observatory."— Presentation transcript:

Similar presentations

About project

Feedback