DEGREES OF COMPARISON OF ADJECTIVES In English, as in Russian, ...
X-ray pulsars
X-ray pulsars are close binary systems in which one of the stars is a neutron star and the other is a bright giant star. About two dozen of these objects are known. The first two X-ray pulsars - in the constellation of Hercules and in the constellations of Centaurus - were discovered in 1972 (three years before the discovery of bursters) with the help of the American research satellite "Uhuru". The pulsar in Hercules sends out pulses with a period of 1.24 s. This is the rotation period of a neutron star. There is one more period in the system - the neutron star and its companion rotate around their common center of gravity with a period of 1.7 days. The orbital period was determined in this case due to the (accidental) circumstance that, in its orbital motion, the "ordinary" star regularly appears on the line of sight connecting us and the neutron star, and therefore it obscures the X-ray source for a while. This is obviously possible when the plane of stellar orbits makes only a small angle with the line of sight. X-ray radiation stops for about 6 hours, then reappears, and so on every 1.7 days.
(By the way, the observation of X-ray eclipses for bursters until recently was not successful. And this was strange: if the orbits of binary systems are randomly oriented in space, then one should expect that out of more than three dozen bursters, at least a few have orbital motion planes, approximately parallel to the line of sight (like a pulsar in Hercules) so that an ordinary star can periodically cover a neutron star from us.It was not until 1982, i.e. 7 years after the discovery of bursters, that one example of an eclipsing burster was finally discovered.) Long-term observations made it possible to establish one more - third - period of the X-ray pulsar in Hercules: this period is 35 days, of which 11 days the source shines, and 24 days do not. The reason for this phenomenon remains unknown. The pulsar in the constellation Centaurus has a period of pulsations of 4.8 s. The period of orbital motion is 2.087 days - it is also found from X-ray eclipses. Long-term changes similar to the 35-day period of the pulsar in the constellation Hercules are not found in this pulsar. The companion of a neutron star in the binary system of this pulsar is a bright visible giant star with a mass of 10-20 Suns. In most cases, the companion of a neutron star in X-ray pulsars is a bright blue giant star. In this they differ from bursters, which contain faint dwarf stars. But, just like in bursters, in these systems the flow of matter from an ordinary star to a neutron star is possible, and their radiation also arises due to the heating of the surface of a neutron star by the flow of accreted matter.
This is the same physical radiation mechanism as in the case of the background (non-flare) burster radiation. In some of the X-ray pulsars, the matter flows to the neutron star in the form of a jet (as in bursters). In most cases, a giant star loses matter in the form of a stellar wind - a stream of plasma, ionized gas, emanating from its surface in all directions. (A phenomenon of this kind is also observed in the Sun, although the solar wind is weaker - the Sun is not a giant, but a dwarf.) Part of the stellar wind plasma falls into the vicinity of a neutron star, into the zone of its gravitational predominance, where it is captured by it.
However, when approaching the surface of a neutron star, charged plasma particles begin to experience the action of yet another force field of the magnetic field of the neutron star-pulsar. The magnetic field is capable of rearranging the accretion flow, making it non-spherically symmetrical, but directed. As we will see in a moment, this is what causes the effect of radiation pulsations, the beacon effect. There is every reason to believe that the neutron stars of X-ray pulsars have a very strong magnetic field, reaching magnetic induction values of 10 8 - 10 9 T, which is 10 11 - 10 12 T times greater than the average magnetic field of the Sun. But such fields are naturally obtained as a result of strong compression during the transformation of an ordinary star into a neutron one. According to the general relations of electrodynamics, magnetic induction In fields, lines of force. which permeate a given mass of matter, increases with a decrease in the geometric dimensions R of this mass.
This relation follows from the law of conservation of magnetic flux. It is worth paying attention to the fact that the magnetic induction increases when the body is compressed in exactly the same way as its rotation frequency. When the radius of a star decreases from a value equal, for example, to the radius of the Sun, 10 9 m, to the radius of a neutron star, 10 4 m, the magnetic field increases by 10 orders of magnitude. A magnetic field with an induction of B=10 -4 T, comparable to the field of the Sun, is considered more or less typical for ordinary stars; some "magnetic" stars have fields several thousand times greater, so it can be expected that a certain (and not too small) fraction of neutron stars should indeed have a very strong magnetic field. This conclusion was reached by the Soviet astrophysicist N. S. Kardashev back in 1964.
In its structure, i.e., in the geometry of the lines of force, the magnetic field of a pulsar is similar, as one might expect, to the magnetic field of the Earth or the Sun: it has two poles, from which lines of force diverge in different directions. Such a field is called a dipole.
The matter accreted by a neutron star is the stellar wind, it is ionized, and therefore interacts with its magnetic field during its motion. It is known that the movement of charged particles across the field lines is difficult, while the movement along the lines of force is unhindered. For this reason, the accreted matter moves near the neutron star practically along the lines of force of its magnetic field. The magnetic field of a neutron star, as it were, creates funnels at its magnetic poles, and the accretion flow is directed into them. This possibility was pointed out back in 1970 by the Soviet astrophysicists G. S. Bisnovaty-Koganta. A. M. Fridman. Due to this, the heating of the surface of a neutron star turns out to be uneven: the temperature at the poles is much higher than on the rest of the surface. The hot spots near the poles are estimated to be about one square kilometer in area; they create mainly the radiation of the star - after all, the luminosity is very sensitive to temperature - it is proportional to the temperature to the fourth power.
Like the Earth, the magnetic axis of a neutron star is tilted to its axis of rotation. Because of this, a beacon effect arises: a bright spot is sometimes visible, sometimes not visible to the observer. The radiation of a rapidly rotating neutron star appears to the observer as discontinuous, pulsating. This effect was theoretically predicted by the Soviet astrophysicist V. F. Shvartsman several years before the discovery of X-ray pulsars. In fact, the radiation of a hot spot occurs, of course, continuously, but it is not uniform in directions, not isotropic, and the X-rays from it are not directed at us all the time, their beam rotates in space around the axis of rotation of a neutron star, running through the Earth once for the period.
Burster-like flares have never been observed from X-ray pulsars. On the other hand, regular pulsations have never been observed from bursters. Why don't bursters pulsate and pulsars don't flare? The point is probably that the magnetic field of neutron stars in bursters is noticeably weaker than in pulsars, and therefore it does not noticeably affect the accretion dynamics, allowing more or less uniform heating of the entire surface of the neutron star. Its rotation, which can be as fast as that of pulsars, does not affect the X-ray flux, since this flux is isotropic. On the other hand, it is assumed that a field with a magnetic induction of B=10 -8 T is capable of suppressing thermonuclear explosions in the subpolar zones of neutron stars somehow - although, however, it is not entirely clear yet how exactly. The difference in the magnetic field is probably due to the difference in the age of bursters and pulsars. The age of a binary system can be judged from an ordinary companion star.
Neutron stars in X-ray pulsars have bright giant stars as companions; in bursters, the companions of neutron stars are low-mass stars of low brightness. The age of bright giants does not exceed several tens of millions of years, while the age of faint dwarf stars can be billions of years: the former consume their nuclear fuel much faster than the latter. It follows that bursters are old systems in which the magnetic field has weakened to some extent over time, and pulsars are relatively young systems and therefore magnetic fields in them. stronger. Maybe bursters once pulsated in the past, but pulsars have yet to flare in the future.
It is known that the youngest and brightest stars of the Galaxy are located in its disk, near the galactic plane. Therefore, it is natural to expect that X-ray pulsars with their bright giant stars are located predominantly near the galactic plane. Their general distribution over the celestial sphere should be different from the distribution of bursters, old objects that - like all old stars of the Galaxy - are concentrated not towards its plane, but towards the galactic center. Observations confirm these considerations: X-ray pulsars are indeed located in the disk of the Galaxy, in a relatively narrow layer on both sides of the galactic plane. The same distribution in the sky is also found by pulsars emitting radio pulses - radio pulsars.
X-RAY PULSARS- sources of alternating periodic. x-ray , which are rotating neutron stars with strong magnet. field, radiating due to accretions. Magn. field on the surface of R. p. ~ 10 11 -10 14 gauss. Luminosities most R. p. from 10 35 to 10 39 erg / s. Pulse periods R from 0.07 s to several thousand seconds. R. p. are included in close binary star systems (see. close binary stars), the second component of which is a normal (non-degenerate) star that supplies the matter necessary for accretion and normal functioning of the R. p. If the second component is at the stage of evolution, when the mass loss rate is low, the neutron star does not manifest itself as a R. p .X-ray pulsars are found both in massive young binary star systems belonging to population I galaxies and lying in its plane, and in low-mass binary systems belonging to the population of the II Galaxy and belonging to its spherical. component. R. p. also discovered in the Magellanic Clouds. Total open approx. 30 R. p.
Rice. 1. Recording of X-ray pulsar radiation Centaur X-3, received from the Uhuru satellite on May 7, 1971. On the vertical axis - the number of readings per time interval 1 bin = 0.096 s, on the horizontal - time in bins. The registered flux is maximum when the source is in the center of the field of view of the counter, limited by the collimator. Due to the rotation of the satellite, the recorded average flux first increases and then decreases. Superimposed on this simple time dependence are periodic pulsations associated with the intrinsic variability of the source.
Rice. Fig. 2. Long-term variability of the X-ray emission from the Centaur-X-3 source (lower graph, N - number of readings, s -t). Characteristic X-ray eclipses are visible. The upper graph shows the changes in the period P, proving the movement of the pulsar around the center of mass of the binary system (A 1.387-10 -3).
At the beginning stage of X-ray research. objects were given names according to the constellations in which they are located. For example, Hercules X-1 means the first in X-ray. brightness object in the constellation Hercules, Centaur X-3 - the third brightest object in the constellation Centaur. R. p. in the Small Magellanic Cloud is designated as SMC X-1, in the Large Magellanic Cloud - LMC X-4 [often found in X-ray notation. sources letter X - from English. X-rays (X-rays)]. Detection from satellites of a large number of X-rays. sources required another system of notation. For example, 4U 1900-40 corresponds to the designation of R. p. Sails X-1 in the fourth catalog of the Uhuru satellite (USA). The first four digits indicate the right ascension (19:00), the second two together with the sign give the declination of the object (see Fig. Astronomical coordinates). The numbers in the designation of sources discovered by the Ariel satellite (Great Britain) have a similar meaning, for example. A0535 + 26. Type designations GX1+4 refer to sources in the center. regions of the galaxy. The numbers correspond to the galactic coordinates l and b(in this case l = 1°, b=+4°). Other designations are also used. Thus, a flashing RP with a period of about 8 seconds, discovered from the board of the Soviet AMS Venera-11, -12 in the Cone experiment, was named FXP0520-66.
Variability of radiation of X-ray pulsars. short period x-ray variability. radiation R. p. illustrates fig. 1, on Krom there is a recording of the radiation of one of the first discovered R. p. - Centaur X-3 (May 1971, satellite "Uhuru"). Pulse period P = 4.8 s
On fig. 2 shows a long period. variability R. n. Centaur X-3. Once every two days, R. p. periodically "disappears" (eclipsed) at 11 a.m. (lower graph). Careful research has also shown that R depends on the phase of the two-day period T= 2.087 days according to harmonics. law (upper graph): where - change R, R 0- unperturbed value R, A- amplitude refers. changes Р, t0 corresponds to one of the moments when the period deviation is maximum. These two facts are interpreted unambiguously: R. p. enters a binary system with an orbital period equal to T. The "disappearances" are explained by the eclipses of the R. p. the second component of the binary system. Based on the duration of the eclipse, we can conclude that the second (eclipsing) component fills its Roche cavity.Periodic changes R are due to the Doppler effect during the orbital motion of the R. p. around the center of mass of the binary system. Period change amplitude 
, where i is the inclination angle of the orbit of the binary system (in this system it is close to 90°), v- the speed of the orbital movement of R. p.; v sin i= 416 km/s, the orbital eccentricity is small. X-ray eclipses have not been found in all binary systems with RP (to observe eclipses, it is necessary that the line of sight be close to the orbital plane of the binary system), but periodic. changes R- in most binary systems with R. p.
Rice. 3. Simplified picture of accretion onto a magnetized neutron star in a binary system. Gas enters the star both in a geometrically thin disk and in a spherically symmetrical manner. The real magnetosphere has a more complex shape than is shown in Fig. a ( and M are the angular velocity of rotation and the magnetic moment of the neutron star). The conditions for plasma freezing into the magnetosphere are not favorable over its entire surface. Frozen plasma flows along magnetic field lines to magnetic poles (arrows). Near the poles, the accretion channel is an open crown (b).
After the discovery of R. p. in its vicinity, a variable optical is usually quickly found. a star (the second component of a binary system), the brightness of which changes with a period equal to the orbital or half as long (see below). In addition, the spectral lines of the optical components experience a Doppler shift that varies periodically with the orbital period of the binary system. optical the variability of binary systems with RP is due to two effects. The first effect (reflection effect) is observed in systems in which the luminosity of the optical. stars are less than the luminosity of the R. p. The side of the star facing the R. p. is heated by its X-ray. radiation and in optical. rays appear brighter than the opposite side. The rotation of the binary system leads to the fact that the brighter, then less bright side of the star is observed. Such an effect is clearly manifests itself in a system that includes R. p. Hercules X-1 and the star HZ Hercules. Per unit surface of this star facing X-ray. source, falls thirty times more energy in the form of X-rays. radiation than comes from the interior of the star. As a result, the amplitude of the optical variability exceeds 2 t in the filter AT(cm. Astrophotometry).X-ray part. radiation is reflected by the star's atmosphere, but DOS. the share is absorbed by it and processed into optical. radiation, which pulsates weakly with a period R. Part of the energy goes to eff. heating of a substance on the surface, accompanied by the formation of the so-called. induced. stellar wind. The second effect, called the ellipsoidal effect, is related to the fact that the shape of the star filling the Roche lobe differs markedly from a spherical one. As a result, b. h. surface and two times - smaller. Such variability with a period half the orbital period is observed in binary systems where the luminosity of the optical. component is much larger than the roentgen. the luminosity of the R. p. In particular, it is precisely because of this variability that the normal component of the Centaur X-3 source was discovered.
Accretion onto a neutron star with a strong magnetic field. In close binary stellar systems, there are two main possibilities. types of accretion: disk and spherically symmetrical. If the flow of matter goes preim. through the internal Lagrange point (see Art. Roche cavity), then the flowing substance has a means. beats moment of momentum and an accretion disk is formed around the neutron star. If a normal star loses matter through the stellar wind, then the formation of a shock wave and close to spherically symmetric accretion behind it are possible.
Rice. 4. Pulse profiles of a number of X-ray pulsars. The energy intervals for which the data were obtained and the periods Р.
Rice. 5. Energy dependence of the pulse profile for two X-ray pulsars.
Rice. 6. Spectra of a number of X-ray pulsars. Noticeable X-ray line of iron with hv 6.5-7 keV.
Free fall (with spherically symmetric accretion) is possible only at large distances R from a star. At a distance L m ~ 100-1000 km (radius of the magnetosphere), the pressure of the magnet. field of a neutron star is compared with the pressure of the accreting flow of matter 
( - substances) and stops it. In the zone R< R M
the closed magnetosphere of a neutron star is formed (Fig. 3, a), near R M arises in which the plasma is cooled by the radiation of the RP due to Compton scattering. Due to the Rayleigh-Taylor instability, it becomes possible for plasma droplets to penetrate into the magnetosphere, where they are further crushed and frozen into the magnetic field. field. Magn. the field channels the accreting plasma flow and directs it to the magnetic field. poles (Fig. 3, b). The zone on which the substance falls, apparently, does not exceed 1 km 2 in area. On the surface of a neutron star, gravitational binding energy per unit mass. The flux of matter falling onto the star, necessary to maintain the luminosity L x ~ 10 35 -10 39 erg/s, is equal to a year. More than a ton of matter per second falls on 1 cm 2 of the surface. Free fall speed is 0.4 With.
In R. p. with luminosity L x < 10 36 эрг/с падающие протоны и электроны тормозятся в атмосфере (образованной веществом, выпавшим на нейтронную звезду за ничтожные доли секунды до этого) за счёт ядерных и кулоновских столкновений. Выделяющаяся энергия излучается слоем, к-рого ок. 10-20 г/см 2 , а толщина - неск. метров. Существует предположение, что может возникнуть тонкая (неск. см) бесстолкновительная ударная волна, в к-рой выделяется вся кинетич. энергия аккрецирующего потока.
Rice. 7. Period P (in s) as a function of time for a number of X-ray pulsars.
In R.p. with a luminosity close to 5 * 10 36 erg / s, a colossal energy release in the magnetic zone. poles leads to the fact that the radiation pressure force (see. light pressure) to incident electrons is able to stop the flow of accreting matter. Near the surface of a neutron star (at a height of less than 1 m), radiation-dominants can form. shock wave. In such a shock wave, the radiation pressure is much higher than the plasma pressure. The electrons incident on the star are decelerated by the pressure force of the radiation due to the Thomson scattering of the radiation coming from below. At the same time, the electrostatic processes associated with electrons stop. forces of protons carrying DOS. kinetic energy. This energy is spent on increasing the energy of photons due to their multiple scattering by high-speed electrons (comptonization). Some of the "hard" photons go to the observer, and some get into the dense layers of the atmosphere (neutron star), heating it. In these layers, as a result, many are born. "soft" photons, to-rye, experiencing Thomson scattering on the incident electrons, slow down the incident matter.
If the luminosity of the R. p. exceeds 10 37 erg / s, then above the surface of a neutron star in the region of the magnetic. poles an accretion column is formed. Radiation dominant the shock wave occurs at a high altitude above the surface of a neutron star (hundreds of meters and even kilometers). It slows down the flow. Under the shock wave, the subsidence mode occurs. The radiation escapes through the side surface of the column, while the substance in it slowly settles, releasing gravity. energy is converted into heat and radiation. The gravitational forces are counteracted by the pressure gradient of the radiation trapped in the radiation-dominants. column. The column can provide luminosity far greater than critical luminosity, because from the sides it is held magnetically. field, not gravity. Moreover, if the magnetic Since the field of a neutron star exceeds 10 13 G, then at the base of the column the temperature of plasma and radiation reaches 10 10 K. At such temperatures, the processes of creation of electron-positron pairs also occur. Neutrinos produced in a reaction 
, take away the main share of luminosity. X-ray the luminosity (exceeding the critical one) is a small fraction of the neutrino luminosity, and the luminosities of SMC X-1 and LMC X-4 ~ 10 m erg / s, i.e., they are much higher than the critical one. These objects have, apparently, and mean. neutrino luminosity. The emitted neutrinos heat the interior of the neutron star and, being absorbed in the interior of the normal component of the binary system, make a small contribution to its optical. luminosity. The flux of accreting matter in such objects can reach (10 - 6
-10 - 5
) in year. In this case, a situation is possible when, during 10 6 -10 5 years of "work" of R. p., approx. 1 matter, the stability limit for neutron stars will be exceeded, there will be gravitational collapse accompanied by an explosion supernova rare type and education black hole. This can only happen with disk accretion, when the radiation pressure does not prevent accretion at large distances from the gravitating center.
Formation of pulse profiles and emission spectra of X-ray pulsars. The release of energy in limited. zone near the poles of a neutron star, together with its rotation, leads to the phenomenon of a pulsar: the observer sees the radiating zone at different angles and receives a time-varying X-ray flux. radiation. Period R equal to the rotation period of the neutron star. The presence of a strong magnet. fields can lead to radiation directivity. Depending on the ratio between the energy of photons hv, magnetic strength. fields H and plasma swarm T e both "pencil" and "knife" patterns can be formed. The most important parameter is the gyrofrequency (frequency) of the electron. The degree of orientation is a function of relations. The radiation pattern determines the shape of the pulse profile of the R. p. The pulse profiles of the R. p. 4. The shape of the profiles for many R. p. changes with increasing photon energy (Fig. 5).
The emission spectrum of a neutron star must be multicomponent. The shock wave, the accretion column, the surface of the neutron star near the base of the column, and the plasma flowing through the magnetosphere to the poles of the neutron star radiate. This plasma absorbs the hard radiation of the column and re-radiates it in the "soft" X-ray. range both in the continuum (continuous spectrum) and in x-rays. lines (characteristic and resonant) of ions of heavy elements. The spectra (Fig. 6) depend decisively on the luminosity of the R. p. and the strength of the magnetic field. fields, so they are very different from each other.
If plasma flows on the magnetosphere of a high-luminosity RP do not cover its entire surface, then “windows” are formed, into which “hard” radiation freely escapes, while other directions are closed to it due to the large optical radiation. thicknesses of plasma flows. The rotation of a neutron star should lead to radiation pulsations. This is another mechanism for the formation of the X-ray profile. impulses.
The most important step in the study of R. p. was the discovery of a gyroline [spectral line due to cyclotron radiation (or absorption) of electrons] in the spectrum of R. p. Hercules X-1. The discovery of the gyroline gave the method of direct experimentation. definitions of magnet. fields of neutron stars. The gyroline in the spectrum of R. p. Hercules X-1 corresponds to hv H= 56 keV. According to the relation hv H = 1,1 (H/10 11 G) keV, magnetic strength. the field on the surface of this neutron star is 5*10 12 G.
Acceleration and deceleration of the rotation of neutron stars. Unlike radio pulsars (some of them, in particular pulsars in Crab and Sails, radiate in X-ray. range) that radiate due to the rotational energy of a magnetized neutron star and increase their period with time; RPs that radiate due to accretion accelerate their rotation. Indeed, during disk accretion, the matter falling onto the magnetosphere has a noticeable sp. moment of the number of motion. Freezing into the magnet. field, the accreting plasma moves to the surface of the star and transfers its angular momentum to it. As a result, the rotation of the star accelerates and the pulse repetition period decreases. This effect is characteristic of all R. p. (Fig. 7). However, sometimes there is also a slowdown in rotation. This is possible if the accretion rate or the direction of the momentum of the accreting matter's motion changes. Among the mechanisms leading to an increase in the period, the so-called. propeller mechanism. It is assumed that the asymmetric atmosphere of a neutron star rotates in an atmosphere created by gas accreting at a sound speed, while sound or shock waves are generated, convective currents are excited, diverting the angular momentum from the magnetosphere to the stellar wind flowing around the neutron star. R. A. Sunyaev.
X-RAY PULSARS
- sources of alternating periodic. x-ray neutron stars with a strong magnetic field. field, radiating due to accretions. Magn. field on the surface R. p. ~ 10 11 -10 14 gauss. Luminosities most R. p. from 10 35 to 10 39 erg / s. Pulse periods R from 0.07 s to several thousand seconds. R. p. are included in close binary star systems (see. close binary stars) the second component to-rykh is a normal (non-degenerate) star, which supplies the substance necessary for the accretion and normal functioning of the R. p. of the Galaxy and those lying in its plane, as well as in low-mass binary systems belonging to the population of the II Galaxy and belonging to its spherical. component. R. p. also discovered in the Magellanic Clouds.
Rice. 1. Recording of X-ray pulsar radiation Centaur X-3, obtained from the satellite "Uhuru" on May 7, 1971. On the vertical axis - the number of readings per time interval 1 bin = 0.096 s, on the horizontal - time in bins. 
Rice. Fig. 2. Long-term variability of X-ray emission from the Centaur-X-3 source (lower graph, N - number of readings, s -t). Characteristic X-ray eclipses are visible. The upper graph shows the changes in the period P, proving the motion of the pulsar around the center of mass of the binary system (A 1.387-10 -3).
At the beginning stage of X-ray research. objects were given names according to the constellations in which they are located. For example, Hercules X-1 means the first X-ray. brightness object in the constellation Hercules, Centaur X-3 - the third brightness in the constellation Centaur. R. p. in the Small Magellanic Cloud is designated as SMC X-1, in the Large Magellanic Cloud - LMC X-4 [often found in X-ray notation. sources letter X - from English. X-rays (X-rays)]. Detection from satellites of a large number of X-rays. other sources required. Astronomical coordinates). The numbers in the designation of sources discovered by the Ariel satellite (Great Britain) have a similar meaning, for example. A0535 + 26. Type designations GX1+4 refer to sources in the center. regions of the galaxy. The numbers correspond to the galactic coordinates l and b(in this case l = 1°, b=+4°). Other designations are also used. Thus, the flashing RP with a period of about 8 seconds, discovered from the board of the Soviet AMS Venera-11, -12 in the Cone experiment, was named FXP0520-66.
Variability of radiation of X-ray pulsars. short period x-ray variability radiation R. p. illustrates fig. 1, on Krom there is a record of the radiation of one of the first discovered R. p. - Centaur X-3 (May 1971, satellite "Uhuru"). Pulse repetition period P = 4.8 s
On fig. 2 shows a long period. variability R. n. Centaur X-3. Once in two days, R. p. periodically "disappears" (eclipsed) for 11 hours (lower. R. depends on the phase of the two-day period T= 2.087 days according to the harmonic law (upper graph): where is the change R, R 0- unperturbed value R, A - amplitude relative. changes Р, t0 corresponds to one of the moments when the period deviation is maximum. These two facts are interpreted unambiguously: R. p. enters a binary system with an orbital period equal to T."Disappearances" are explained by eclipses of R. p. Roche lobe. Periodic changes R are due to the Doppler effect during the orbital motion of the R. p. around the center of mass of the binary system. ,where i- the orbital inclination angle of the binary system (in this system is close to 90°), v- the speed of the orbital movement of R. p.; v sin i= 416 km/s, the orbital eccentricity is small. X-ray eclipses have been discovered in far from all binary systems with R. p.
Rice. 3. Simplified picture of accretion onto a magnetized neutron star in a binary system. The gas enters the star as in a geometrically thin disk, and M is the angular velocity of rotation and the magnetic moment of the neutron star. The conditions for plasma freezing into the magnetosphere are not favorable on its entire surface.
After the discovery of R. p. in its vicinity, a variable optical is usually quickly found. a star (the second component of a binary system), the brightness of which changes with a period equal to the orbital or half as long (see below). In addition, the spectral lines of the optical components experience Doppler shift, 2 t in filter AT(cm. astrophotometry). Part of the X-ray radiation is reflected by the star's atmosphere, but DOS. the share is absorbed by it and processed into optical. R. Part of the energy is spent on eff. heating of a substance on the surface, accompanied by the formation of m. n. induced. stellar wind. The second effect, called the ellipsoidal effect, is related to the fact that the shape of the star filling the Roche lobe differs noticeably from a spherical one. As a result, b. h. surface and two times - smaller. Such variability with a period half the orbital period is observed in binary systems where the luminosity of the optical. component is much higher than Rg. the luminosity of the R. p. In particular, it is precisely because of this variability that the normal component of the Centaur X-3 source was discovered.
Accretion onto a neutron star with a strong magnetic field. In close binary star systems, two basic systems are possible. types of accretion: disk and spherically symmetrical. Roche lobe), then the flowing substance has a mean. beats 
Rice. 4. Pulse profiles of a number of X-ray pulsars. The energy intervals for which the data were obtained and the periods P are given.
Rice. 5. Energy dependence of the pulse profile for two X-ray pulsars.
Rice. 6. Spectra of a number of X-ray pulsars. The X-ray line of iron with hv6.5-7 keV is noticeable.
Free fall (with spherically symmetric accretion) is possible only at large distances R from a star. At a distance L m ~ 100-1000 km (radius of the magnetosphere), the pressure of the magnet. field of a neutron star is compared with the pressure of the accreting flow of matter 
( - substance density) and stops it. In the zone R< R M
the closed magnetosphere of a neutron star is formed (Fig. 3, a), near R M a shock wave arises, in which the plasma is cooled by the radiation of the RP due to Compton scattering. Due to the Rayleigh-Taylor instability, it becomes possible for plasma droplets to penetrate into the magnetosphere, where they are further crushed and frozen into the magnetic field. field. Magn. field-channelizes the flow of accreting plasma and directs it to the magnetic region. b). The zone, on which the substance falls, apparently, . The flux of matter falling onto the star, necessary to maintain the luminosity L x ~ 10 35 -10 39 erg/s, is equal to a year. More than a ton of matter falls per 1 cm 2 of the surface every second. Free fall speed is 0.4 With.
In R. p. with luminosity L x < 10 36 эрг/спадающие протоны и электроны тормозятся в атмосфере (образованной веществом, 
Rice. 7. Period P (in s) as a function of time for a number of X-ray pulsars.
In R. The pressure of light) on incident electrons is capable of stopping the flow of accreting matter. Near the surface of a neutron star (at a height of less than 1 m), radiation-dominants can form. shock wave. If the luminosity of the R. p. exceeds 10 37 erg / s, then above the surface of a neutron star in the region of the magnetic. poles an accretion column is formed. critical luminosity, because from the sides it is held magnetically. field, not gravity. Moreover, if the magnetic Since the field of a neutron star exceeds 10 13 G, then at the base of the column the temperature of plasma and radiation reaches 10 10 K. At such temperatures, the processes of creation and annihilation of electron-positron pairs occur. Neutrinos produced in a reaction 
, take away the main share of luminosity. X-ray the luminosity (exceeding the critical one) is a small fraction of the neutrino luminosity, and the luminosities of SMC X-1 and LMC X-4 ~ 10 m erg / s, i.e., they are much higher than the critical one. These objects have, apparently, and mean. neutrino luminosity. The emitted neutrinos heat the interior of the neutron star and, being absorbed in the interior of the normal component of the binary system, make a small contribution to its optical. luminosity. The flux of accreting matter in such objects can reach (10 - 6
-10 - 5
)in year. In this case, a situation is possible when, during 10 6 -10 5 years of "work" of R. p., approx. 1substance, the stability limit for neutron stars will be exceeded, there will be gravitational collapse, accompanied by an explosion supernova rare type and education black hole. This can happen only with disk accretion, when the radiation pressure does not prevent accretion at large distances from the gravitating center.
Formation of pulse profiles and emission spectra of X-ray pulsars. P is equal to the rotation period of the neutron star. The presence of a strong magnet. fields can lead to radiation directivity. Depending on the ratio between the energy of photons hv, magnetic strength. fields H and plasma swarm T e both "pencil" and "knife" patterns can be formed. The most important parameter is the gyrofrequency (cyclotron frequency) of the electron. The degree of directivity is a f-tion of relations. The directivity pattern determines the shape of the pulse profile of R. p. 4. The shape of the profiles of many R. p. changes with increasing photon energy (Fig. 5).
The emission spectrum of a neutron star must be multicomponent. They emit a shock wave, an accretion column, the surface of a neutron star near the base of the column, and plasma flowing through the magnetosphere to the poles of a neutron star. This plasma absorbs the hard radiation of the column and re-radiates it in the "soft" X-ray. range both in the continuum (continuous spectrum) and in x-rays. lines (characteristic and resonant) of ions of heavy elements. If plasma flows on the magnetosphere of a high-luminosity RP do not cover its entire surface, then “windows” are formed, into which “hard” radiation freely escapes, while other directions are closed to it due to the large optical radiation. thicknesses of plasma flows. The rotation of a neutron star should lead to radiation pulsations. This is another mechanism for the formation of the X-ray profile. The most important stage in the study of R. p. was the discovery of a gyroline [spectral line due to cyclotron radiation (or absorption) of electrons] in the spectrum of R. p. Hercules X-1. The discovery of the gyroline gave the method of direct experimentation. hv H = 56 keV. According to the relation hv H = 1,1 (H/10 11 G) keV, magnetic strength the field on the surface of this neutron star is 5*10 12 G.
Acceleration and deceleration of the rotation of neutron stars. Unlike radio pulsars (some of them, in particular pulsars in the Crab and Sails, radiate in X-ray. range) that radiate due to the rotational energy of a magnetized neutron star and increase their period with time; RPs that radiate due to accretion accelerate their rotation. Indeed, during disk accretion, the matter falling onto the magnetosphere has a noticeable sp. the moment of the amount of movement. Freezing into the magnet. field, the accreting plasma moves towards the surface of the star and transfers its angular momentum to it. As a result, the rotation of the star accelerates and the pulse repetition period decreases. This effect is characteristic of all R. p. (Fig. 7). However, sometimes slowdown is observed. This is possible if the rate of accretion or the direction of the moment of the amount of movement of the accreting matter changes. Among the mechanisms leading to an increase in the period, the so-called. propeller mechanism. It is assumed that R. A. Sunyaev.
"X-RAY PULSARS" in books
author Panysheva Lidia VasilievnaX-ray machines by E. I. Lipina
From the book Diseases of Dogs (Non-Contagious) author Panysheva Lidia VasilievnaX-ray devices E. I. Lipina Each X-ray device, regardless of its purpose, must necessarily have the following main components: autotransformer, step-up transformer, X-ray tube helix filament transformer (step-down)
X-RAY RAYS OR STREAMS*
From the book of Nikola Tesla. LECTURES. ARTICLES. by Tesla NikolaX-RAY RAYS OR STREAMS* In the first account of his landmark discoveries, Roentgen expressed his conviction that the phenomena he observed were the result of some new perturbations in the ether. This point of view requires more careful consideration, since it is likely
author Shklovsky Iosif SamuilovichChapter 21 Pulsars as Sources of Radio Emission Perhaps the most difficult thing for pulsars to determine are the two main characteristics of any "normal" source of radio emission - flux and spectrum. These difficulties are associated primarily with the very nature of pulsars. The fact,
Chapter 23 X-Ray Stars
From the book Stars: Their Birth, Life and Death [Third Edition, revised] author Shklovsky Iosif SamuilovichChapter 23 X-Ray Stars As already indicated in the introduction to this book, the rapid development of extra-atmospheric astronomy, as well as radio astronomy, led in the postwar years to a revolution in our science. Perhaps the most impressive achievements of extra-atmospheric
6. Pulsars - sensation number 2
From the book Interesting about astronomy author Tomilin Anatoly Nikolaevich6. Pulsars - sensation No. 2 Everything started normally. A group of Cambridge radio astronomers, scanning the sky at a frequency of 81.5 megahertz, in June 1967 came across four unusual pulsed sources of cosmic radio emission. The respectable "Nature" brought not without pleasure
76. What are neutron stars and pulsars?
From the book Tweets About the Universe by Chown Marcus76. What are neutron stars and pulsars? Amazing fact: you can fit the whole of humanity into the volume of a sugar cube. Why? Because matter can be mind-blowingly empty. In primitive terms, you can think of an atom as
What are x-rays?
From the book All About Everything. Volume 1 the author Likum ArkadyWhat are x-rays? X-rays were discovered in 1895 in Germany by Wilhelm Roentgen, after whom they are named. These rays, like light rays, have a penetrating power. They differ from light rays in wavelength and energy. The shortest
From the book Great Soviet Encyclopedia (PU) of the author TSBPulsars
From the book Dark Mission. NASA Secret History author Hoagland Richard CaulfieldPulsars
5. Supernovae, pulsars and black holes
From the book Universe, life, mind author Shklovsky Iosif Samuilovich5. Supernovae, Pulsars and Black Holes In the previous chapter, a picture of the evolution of a "normal" star was sketched from the moment of its birth in the form of a bunch of shrinking gas and dust nebula to deep "old age" - a superdense cold "black" dwarf. However
§ 2.19 Pulsars
From the book Ritz Ballistic Theory and the Picture of the Universe author Semikov Sergey Alexandrovich- these are cosmic sources of radio, optical, x-ray and / or gamma radiation coming to Earth in the form of periodic bursts (pulses).
Therefore, according to the type of radiation, they are divided into radio pulsars, optical pulsars, X-ray and / or gamma-ray pulsars. The nature of the emission of pulsars has not yet been fully disclosed, models of pulsars and the mechanisms of energy emission by them are studied theoretically. Today, the prevailing opinion is that pulsars are rotating neutron stars with a strong magnetic field.
Discovery of pulsars
This happened in 1967. The English radio astronomer E. Hewish and his collaborators discovered short radio pulses coming as if from an empty place in space, repeating stably with a period of at least a second. At first, the results of observations of this phenomenon were kept secret, because. it could be assumed that these radio emission pulses are of artificial origin - perhaps these are signals from some extraterrestrial civilization? But no source of radiation making orbital motion was found, but Hewish's group found 3 more sources of such signals. Thus, the hope for signals from an extraterrestrial civilization disappeared, and in February 1968 a report appeared on the discovery of rapidly variable extraterrestrial radio sources of an unknown nature with a highly stable frequency.
This message caused a real sensation, and in 1974 Hewish received the Nobel Prize for this discovery. This pulsar is called PSR J1921+2153. Currently, about 2 thousand radio pulsars are known, they are usually denoted by the letters PSR and numbers that express their equatorial coordinates.
What is a radio pulsar?
Astrophysicists have come to the consensus that the radio pulsar is neutron star. It emits narrowly directed streams of radio emission, and as a result of the rotation of a neutron star, the stream enters the field of view of an external observer at regular intervals - this is how pulsar pulses are formed. Most astronomers are convinced that pulsars are tiny neutron stars with a diameter of several kilometers, rotating with periods of a fraction of a second. They are sometimes even called "star tops". Due to the magnetic field, the radiation of a pulsar is similar to a searchlight beam: when, due to the rotation of a neutron star, the beam hits the antenna of a radio telescope, bursts of radiation are visible. Pulsar signals at different radio frequencies propagate in the interstellar plasma at different speeds. By the mutual delay of the signals, the distance to the pulsar is determined, and their location in the Galaxy is determined. The distribution of pulsars roughly corresponds to the distribution of supernova remnants.
X-ray pulsars
The X-ray pulsar is close binary system, one of the components of which is neutron star, and the second - normal star, resulting in the flow of matter from an ordinary star to a neutron one. neutron stars- these are stars with very small sizes (20-30 km in diameter) and extremely high densities exceeding the density of the atomic nucleus. Astronomers believe that neutron stars are the result of supernova explosions. During a supernova explosion, the core of a normal star rapidly collapses, which then turns into a neutron star. During compression, due to the law of conservation of angular momentum, as well as conservation of the magnetic flux, there is a sharp increase in the speed of rotation and the magnetic field of the star. Thus, it is precisely these two features that are important for an X-ray pulsar: fast rotation speed and extremely high magnetic fields. Matter, hitting the solid surface of a neutron star, is strongly heated and begins to radiate in x-rays. Close relatives of X-ray pulsars are polars and intermediate polars. The difference between pulsars and polars is that a pulsar is a neutron star, while a polar is a white dwarf. Accordingly, they have lower magnetic fields and rotation speed.
Optical pulsars
In January 1969, the region of the pulsar in the Crab Nebula was surveyed by an optical telescope with photoelectric equipment capable of detecting rapid brightness fluctuations. The existence of an optical object with brightness fluctuations having the same period as the radio pulsar in this nebula was noted. This object turned out to be a 16th-magnitude star at the center of the nebula. She had some kind of illegible spectrum without spectral lines. While investigating the Crab Nebula in 1942, W. Baade pointed to it as a possible stellar supernova remnant, and I.S. Shklovsky in later years suggested that it is a source of relativistic particles and high-energy photons. But these were all just guesses. And here is the star optical pulsar, which has the same period and interpulses as a radio pulsar, and physically it should be a neutron star, the energy consumption of which is sufficient to maintain the glow and all types of radiation from the Crab Nebula. After the discovery of the optical pulsar, searches were also carried out in other supernova remnants, especially in those where radio pulsars had already been found. But only in 1977, using special equipment, Australian astronomers managed to find a pulsation in the optical range of an extremely faint star of the 25th magnitude in the remnant of the supernova Sails X. The third optical pulsar was found in 1982 in the constellation Vulpecula by radio emission. No supernova remnant found.
What is an optical pulsar? The central components of the spectral lines of SS 433 show movements with a period of 13 days and changes in the speed of movement from -73 to +73 km/s. Apparently, there is also a close binary system here, consisting of an optically observable hot supergiant of classes O or B and an X-ray component invisible in optics. The supergiant has a mass of more than ten solar masses, it has swelled up to the limiting boundaries of its own gravitational zone, replenishes with its gas the disk surrounding the X-ray component along the equator of rotation. The plane of the disk is perpendicular to the axis of rotation of the compact object, which is the X-ray component, and does not lie in the orbital plane of the binary system. Therefore, the disk and both gas jets behave like an obliquely rotating top, and the axis of their rotation precesses (describes a cone), making one revolution in 164 days (this is a well-known phenomenon of precession of rotating bodies). The X-ray component that devours disk gas and ejects jets could be a neutron star.
They are among the most powerful cosmic sources of gamma radiation. Astrophysicists are eager to find out how these neutron stars manage to shine so brightly in the gamma range. Before the launch of the Fermi telescope, only about a dozen gamma-ray pulsars were known, while the total number of pulsars was about 1800. Now the new observatory began to discover dozens of gamma-ray pulsars. Scientists hope that her work will provide a wealth of valuable information that will help to better understand the nature of gamma-ray pulsars and other cosmic gamma-ray generators.
In 2012, using the Fermi orbiting gamma-ray telescope, astronomers discovered the fastest gamma-ray pulsar in the constellation Centaurus to date, making one revolution in 2.5 milliseconds and devouring the remains of a companion star the size of Jupiter. ( Gamma radiation (gamma rays, γ rays) - a type of electromagnetic radiation with an extremely short wavelength -< 5·10 −3 нм и, вследствие этого, ярко выраженными корпускулярными и слабо выраженными волновыми свойствами. На картинке гамма-излучение показано фиолетовым цветом.
To summarize...
neutron stars are amazing objects. They have recently been observed with particular interest, because. not only their structure is a mystery, but also their huge density, strong magnetic and gravitational fields. Matter there is in a special state resembling a huge atomic nucleus, and these conditions cannot be reproduced in terrestrial laboratories.
A pulsar is just a huge magnetized top spinning around an axis that does not coincide with the axis of the magnet. If nothing fell on it and it did not emit anything, then its radio emission would have a rotation frequency and we would never hear it on Earth. But the fact is that this top has a colossal mass and high surface temperature, and the rotating magnetic field creates an electric field of enormous intensity, capable of accelerating protons and electrons almost to the speed of light. Moreover, all these charged particles rushing around the pulsar are trapped in a trap from its colossal magnetic field. And only within a small solid angle near the magnetic axis, they can break free (neutron stars have the strongest magnetic fields in the Universe, reaching 1010-1014 gauss. Compare: the earth's field is 1 gauss, the solar field is 10-50 gauss). It is these streams of charged particles that are the source of the radio emission, according to which pulsars were discovered, which later turned out to be neutron stars. Since the magnetic axis of a neutron star does not necessarily coincide with the axis of its rotation, when the star rotates, a stream of radio waves propagates in space like a beam from a flashing beacon - cutting through the surrounding darkness only for a moment.
At the initial stage of research, an open X-ray. objects were given names according to the constellations in which they are located. For example, Hercules X-1 means the first X-ray. brightness object in the constellation Hercules, Centaur X-3 - the third brightest object in the constellation Centaur. R.p. in the Small Magellanic Cloud it is designated as SMC X-1, in the Large Magellanic Cloud - LMC X-4. Detection from satellites of a large number of X-rays. sources required another system of notation. For example, 4U 1900-40 corresponds to the designation R.p. Sails X-1 in the fourth catalog "Uhuru". The first four digits indicate the right ascension (19:00), and the second two, together with the sign, give the declination of the object. The numbers in the designation of sources discovered by the Ariel satellite (Great Britain) have a similar meaning, for example. A 0535+26. Designations such as GX 1+4 refer to sources in the central region of the Galaxy. The numbers correspond to the galactic coordinates (see ) l and b (in this case l=1o, b=+4o). Other designations are also used. Thus, the flashing R.p. with a period of 8 s (see ) received the name FXP 0520-66.
Radiation variability R.p.
, where i is the inclination angle of the orbit of the binary system (in this system it is close to 90 o), v is the velocity of the orbital motion R.p.; v sin i=416 km/s, orbital eccentricity is small. X-ray eclipses have not been found in all binary systems with R.p. (to observe eclipses, it is necessary that the line of sight be close to the plane of the orbit of the binary system), and periodic. changes P- in most binary systems with R.p. After the opening of R.p. in its vicinity, the optical variable is usually quickly found. a star (the second component of a binary system) whose brightness changes with a period equal to the orbital period or half as long (see below). Also, spectrum. optical lines. components experience a Doppler shift that periodically changes with the orbital period of the double system. optical variability of binary systems with R.p. due to two effects. The first effect (reflection effect) is observed in systems in which the luminosity of the optical. stars less than the luminosity R.p. The side of the star facing R.p. is heated by its X-ray. radiation and in optical. rays appear brighter than the opposite side. The rotation of the binary system leads to the fact that the brighter, then less bright side of the star is observed. This effect is most clearly manifested in a system that includes R.p. Hercules X-1 and the star HZ Hercules. per unit surface of this star, facing the x-ray. source, falls thirty times more energy in the form of X-rays. radiation than comes from the interior of the star. As a result, the amplitude of the optical variability exceeds 2 m in filter B. Part of X-ray. radiation is reflected by the star's atmosphere, but DOS. the share is absorbed by it and processed into optical. radiation. This radiation weakly pulsates with a period P. Part of the energy is spent on efficient heating of the substance on the surface, accompanied by the formation of the so-called. induced stellar wind.
The second effect, called the ellipsoidal effect, is due to the fact that the shape of the star that fills the critical the Roche lobe differs markedly from a spherical one. As a result, twice during the orbital period, a large part of the surface faces the observer, and two times less. Such variability with a period half the orbital period of a binary system is observed in binary systems where the luminosity of the optical. component is much larger than the roentgen. luminosity R.p. In particular, it is due to this variability that the normal component of the Centaur X-3 source was discovered.
Accretion onto a neutron star with a strong magnetic field.
In close binary stellar systems, two mains are possible. types of accretion: disk and spherically symmetrical. If the flow of the substance goes mainly through the internal. Lagrange point, then the flowing substance has a mean. beats angular momentum and is formed around the neutron star. If ok. the star loses matter through the stellar wind, then the formation of a shock wave and close to spherically symmetric accretion behind it is possible.
 |
|
Rice. 3. Simplified picture of accretion onto a magnetized neutron star in a binary system. The gas goes to star both in a geometrically thin disk and spherically symmetrical. Real magnetosphere has a more complex shape than shown in Fig. a (, M- angular velocity of rotation and magnetic neutron star moment). Plasma freezing conditions into the magnetosphere are not favorable on its entire surface. Frozen plasma flows along lines to magnetic poles (arrows). An accretion channel near the poles represents an open crown (b). |
In R.p. with luminosity L X
In R.p. with a luminosity close to erg/s, a colossal energy release in the magnetic zone. poles leads to the fact that the force on the incident electrons is able to stop the flow of accreting matter. Near the surface of a neutron star (at a height of 1 m), a radiation-dominated shock wave can form. In such a shock wave, the radiation pressure is much higher than the plasma pressure. The electrons incident on the star are decelerated by the pressure force of the radiation due to the Thomson scattering of the radiation coming from below. At the same time, the electrostatics associated with electrons are stopped. forces of protons, carrying the main kinetic. energy. This energy is spent on increasing the energy of photons due to their multiple scattering by high-speed electrons (comptonization). Some of the "hard" photons go to the observer, and some get into the dense layers of the atmosphere (neutron star), heating it. As a result, numerous "soft" photons are born in these layers, which (experiencing Thomson scattering on incident electrons) slow down the incident matter.
If the luminosity of R.p. exceeds 10 37 erg / s, then above the surface of a neutron star in the region of magn. poles an accretion column is formed. A radiation-dimonated shock wave occurs at a high altitude above the surface of a neutron star (hundreds of meters and even kilometers). It slows down the flow. Under the shock wave, the subsidence mode occurs. The radiation escapes through the side surface of the column, while the substance in it slowly settles, releasing gravity. energy is converted into heat and radiation. The forces of gravity are counteracted by the pressure gradient of the radiation trapped in the radiation-dimonated column. An accretion column can provide a luminosity much greater than , since from the sides of the column is held magnetically. field, not gravity. Moreover, if the magnetic Since the field of a neutron star exceeds 10 13 G, then at the base of the column the plasma temperature reaches 10 10 K. At such temperatures, the processes of creation and annihilation of electron-positron pairs occur. Neutrinos produced in reactions carry away the main. share of luminosity. X-ray luminosity (exceeding the critical) is a small fraction of the neutrino luminosity. In this connection, we note the existence of R.p. SMC X-1 and LMC X-4 with X-ray luminosity ~ 10 39 erg/s, i.e. much higher than the critical one. These objects apparently also have significant neutrino luminosity. The radiated neutrinos heat up the interior of the neutron star and are absorbed in the interior of the norms. component of the binary system, give a small contribution to its optical. luminosity. The flow of accreting matter in such objects can reach
in year. In this case, a situation is possible when for 10 6 -10 5 years of R.p. approx. matter, the stability limit for neutron stars will be exceeded, will occur, accompanied by a supernova explosion of a rare type and the formation of a black hole. This can happen during disk accretion, when the radiation pressure does not prevent accretion at large distances from the gravitating center. Formation of pulse profiles and emission spectra R.p. The release of energy in a limited zone near the poles of a neutron star, together with its rotation, leads to the pulsar phenomenon: the observer sees the radiating zone at different angles and receives a time-varying X-ray flux. radiation. The period P is equal to the rotation period of the neutron star. The presence of a strong magnet. fields can lead to radiation directivity. Depending on the ratio between photon energy, magnetic strength. fields and temperature of the plasma can be formed as a pencil and knife patterns. The most important parameter yavl. gyrofrequency (cyclotron frequency) of an electron. The degree of orientation yavl. relationship function and . The radiation pattern will determine the shape of the R.p. pulse profile. Pulse profiles of the R.p. shown in fig. 4. View of the profiles of many Pn. changes
