1. Radial velocity of the pulsar depending on the orbital phase
1. Radial velocity of the pulsar depending on the orbital phase
Was Einstein right ?: putting general relativity to the test. New York, 1986; the corresponding chapter of this book, translated by Konstantin Postnov, was published in the journal Uspekhi fizicheskikh nauk ).
Joseph Taylor. Photo from phy.princeton.edu
Princeton University professor Joseph Taylor got his student Russell Huls to work on the Arecibo radio telescope during the 1974 summer break. The work was quite routine, but on July 2, Hals discovered a weak periodic signal in the fresh data – it was only 4% higher than the registration threshold. Moreover, the period of pulsations was the second smallest after the pulsar in the Crab Nebula – 0.059 seconds (before the discovery of millisecond pulsars, also at the Arecibo telescope, it was still far away). The pulsar received a standardized name ("telephone number", as astrophysicists say) PSR1913 + 16 (coordinates in the sky).
Hulse resumed sightings of the object on 25 August to clarify the period. Moreover, in just two hours, the period increased by 30 microseconds. This is an unthinkable value for a pulsar! Then Hals discovered that the rate of change of the period and even its sign change over time. According to the testimony of Leonid Hurvits (he was told about this by the participants in the events), Russell pestered the observatory staff with a request to find with a fresh eye an error in his processing algorithm, leading to a period drift.
Soon the picture in fig. 1. The period changed periodically! The interpretation was obvious and unique: the period floats due to the Doppler effect when the pulsar moves orbiting around a common center of gravity with another heavy object. The orbital period is 7 hours 45 minutes, the maximum speed of approaching us is 300 km / s, the maximum speed of removal is 75 km / s. The radial velocity curve is radically different from the sinusoid because the orbit of the pulsar (and, accordingly, its invisible companion) is highly elongated. It was immediately possible to estimate the eccentricity (0.6) and the length of the orbit (6 million km – this is close to the length of the equator of the Sun). The only thing that could be said about the second object was that it was not an ordinary star — either a white dwarf or a second neutron star; in any case, it is a rather compact object, otherwise the effects associated with the dragging of matter from the star to the pulsar and distortion of radio pulses due to the influence of plasma would appear.
Fig. 1. Radial velocity of the pulsar depending on the orbital phase
The orbital parameters and masses of both objects were not immediately measurable. The point is that the inclination of the orbital plane to the line of sight is unknown. More subtle effects came to the rescue, however.
The people immediately appreciated the discovery of the double pulsar from the point of view that they found an excellent tool for testing general relativity, and Joseph Taylor was the main enthusiast of this idea. The contribution of relativistic effects, proportional to the square of the orbital velocity and the gravitational potential, turned out to be one and a half to two orders of magnitude higher than for Mercury.
Russell Huls. Photo from "Wikipedia"
But this is not the only point: the pulsar’s fast, stable rotation and short orbital period make it possible to measure these effects with amazing accuracy. From the drift of the periastron of the system, the previously unknown mass of the system was measured: 2.82843 solar masses (M☉) (all figures are significant). To establish the ratio of the masses of the two objects, we measured the contribution of the gravitational time dilation during the rotation of the pulsar. At the moment of their closest approach, this effect is 10−6, which is a thousand times less than the Doppler shift, but still measurable with good accuracy. First results: the masses of the two objects are close to each other; a pulsar – 1.42 M☉, an invisible companion – 1.4 M☉. Subsequently, these figures were revised to 1.4411 M☉ and 1.3874 M☉, respectively. The companion mass turned out to be very close to the Chandrasekhar limit, at which the white dwarf loses stability and collapses into a neutron star. In theory, it could be a white dwarf (the exact value of the Chandrasekhar limit depends on the chemical composition), but it is much more likely that it is also a neutron star. Simulation of the evolution of a pair system speaks in favor of two neutron stars. The following scenario is most likely. The observable pulsar was the first to form after the explosion of one of the stars in the system. Then it was spun by the falling substance from the companion – this explains its short period. Then a companion exploded to form a second neutron star.
And now the most important thing. Until now, general relativity has figured as a tool for measuring system parameters. It’s time to talk about the importance of a pulsar for testing general relativity. In theory, there is a nontrivial effect: the emission of gravitational waves during the orbital motion of a massive body. Energy is spent on radiation, the orbit contracts, the period decreases. The effect is negligible even for such a heavy and tight system of two bodies: in theory, the period decreases by 76 microseconds per year. But thanks to the accuracy of the rotation of the pulsar, it turned out to be measurable. The first significant results on period shortening were reported by Taylor and Hulse in 1978. Then the deceleration became statistically significant and coincided with the predictions of general relativity with an accuracy of 20%. A later picture is shown in Fig. 2. Accuracy, as they say, is evident.
Fig. 2. Advance of the orbital phase of the pulsar (time of passage of the periastron) relative to the constant period (point; measurement errors are less than the sizes of points). Curve shows predictions of general relativity
For 30 years of observations, the orbital phase of the pulsar has drifted away by 40 seconds. Thus, the existence of gravitational waves was demonstrated almost 40 years before they were recorded by the LIGO detector. After 300 million years, two neutron stars will merge, losing their orbital angular momentum to the radiation of gravitational waves. There will be a noble fireworks display – tens of seconds of strong gravitational waves, a short but powerful gamma-ray burst, a kilonova glow, hundreds of millions of times brighter than the Sun.
Taylor and Hulse received the Nobel Prize in 1993. Since then, dozens of double pulsars have been discovered. The coolest of them in terms of general relativity effects – PSR1534 + 12 – was discovered by the hero of our next essay, Alexander Wolschan, a radio astronomer from the University of Pennsylvania, who began his scientific career in Poland.
Pulsar Horror Planets
In 1990, Alexander Volschan and Dale Frail, working at the Arecibo telescope, discovered the millisecond pulsar PSR1257 + 12. Its period (6.2 milliseconds) was not a record short, but a year later Wolschan discovered  a feature that made the object unique: its phase relative to the phase of a strictly constant period swam back and forth for a couple of milliseconds over the course of months. Moreover, the phase drift curve was rather complicated (Fig. 3): it was decomposed into the sum of two Keplerian orbits paired with two planets with masses several times greater than the mass of the Earth. Later, analyzing the phase drift curve, they "pulled out" the third, light planet: its mass is comparable to the mass of the Moon. The orbital periods of the planets are 98, 66 and 25 days, the orbital radii are 0.46, 0.36 and 0.19 astronomical units, the orbits are close to circular, the two heavy planets are in a 3: 2 resonance. Later, the phase drift curve was measured so accurately that it was possible to determine the gravitational influence of the planets on each other and determine the exact masses: 3.9, 4.3 and 0.02 of the Earth’s masses.
Fig. 3. Phase drift (pulse arrival time) PSR1257 + 12. The triangles are the values measured by Wolschan. The curve is the result of an orbital fit with two planets. Source: 
The planets were given names from mythological horror films: Draugr (the revived dead, Old Greek), Fobetor (the scarecrow, Old Greek) and Poltergeist (knocking spirit, German). Indeed, hair stands on end when trying to imagine the conditions on these planets. But seriously, their very existence is mysterious: in a supernova explosion, which inevitably accompanies the formation of a neutron star, planetary systems collapse – the planets either evaporate or are thrown into interstellar space. These planets should have formed after a supernova explosion.
Alexander Volschan. Photo from "Wikipedia"
At the moment, the most plausible scenario for the formation of this "terrible" planetary system is as follows. The pulsar was formed as a result of the merger of two white dwarfs. Modeling shows that as a result of such a merger, in addition to a neutron star, a massive ring of ejected matter should form. Then a planetary system was formed from this ring. Later, other planetary systems were found near pulsars, but there the planets were much more massive or more distant.
Alexander Volschan did not receive the Nobel Prize, although he was a centimeter away from it. These were the first firmly established planets outside the solar system – exoplanets; however, the "wrong" planets are near the "wrong" star. Half of the 2019 Nobel Prize in Physics was awarded to Major and Kelo for the later discovery of the exoplanet. And there was a "wrong" planet – hot Jupiter, but the "right" star like the Sun was there. I think if that prize was awarded in its entirety for the discovery of exoplanets and Wolschan, the leader in the PSR1257 + 12 study, turned out to be the third laureate, then a significant part of the scientific community would have perceived such an outcome with great understanding.
The author is grateful to Leonid Gurvits for useful clarifications and additions.
Literature1. Hulse R. A., Taylor J. H. Discovery of a pulsar in a binary system // Astrophysical Journal. 1975. Vol. 195. P. L51 – L53.2. Will KM Double Pulsar, Gravitational Waves and the Nobel Prize // Phys. 1994. Issue. 164, pp. 765–773.3. Wolszczan A., Frail D. A planetary system around the millisecond pulsar PSR1257 + 12 // Nature. 1992. 355. P. 145-147.4. Malhotra R. Three-body effects in the PSR1257 + 12 planetary system // Astrophysical Journal. 1993. Vol. 407. P. 266-275.
Alexey Byalko"Nature" # 6, 2020
Fig. 1. Zodiacal light against the background of the Milky Way. The panorama is composed of four separate shots taken on March 10, 2010 in Teide National Park on the island. Tenerife. Photo by Daniel López, apod.nasa.gov
about the author
Alexey Vladimirovich Byalko – Doctor of Physical and Mathematical Sciences, Associate Researcher at the Institute of Theoretical Physics named after V.I. LD Landau RAS, deputy editor-in-chief of the journal "Nature". Research interests – theoretical physics, earth sciences.
Zodiacal light is a white, glowing cone visible in the west a few hours after sunset or in the east before dawn (Fig. 1). Its brightness is comparable to that of the Milky Way. The zodiacal light extends upward from where the sun has gone under the horizon in the evening or is about to rise in the morning. Its direction coincides with the ecliptic – the path of the Sun and planets through the starry sky, on which the zodiacal constellations are located. The best places to observe the zodiacal light are in subtropical latitudes far from city illumination, the most successful observation time is clear moonless nights around the spring and autumn equinox, when the ecliptic is perpendicular to the horizon.
From the spectrum of the zodiacal light, it is clear that this is reflected radiation from the Sun, although it is not known exactly where the scattering objects are located. This problem could be called half-forgotten, since more than half a century has passed since the review publication of NB Divari , although the importance of the author’s research is emphasized by the fact that his book was recently published in English . Subsequent works  refined the measurement data, but did not add anything fundamental to the understanding of the nature of this phenomenon. So let’s turn to Divari’s review.
What observations show
Let us quote the beginning of the article: “At present, the generally accepted, although not the only, hypothesis is that the zodiacal light is caused by the scattering of solar radiation on particles of interplanetary dust https://123helpme.me/ concentrated in the form of a lenticular cloud, elongated along the ecliptic. The possibility of such an explanation was pointed out as early as 1683 by J. Cassini, who gave the first scientific description of the zodiacal light. "
Further, Divari describes in detail the history of observations of the zodiacal light, then analyzes the dependence of its brightness on elongation – the angular distance along the ecliptic, as well as in the direction perpendicular to it. He gives an analysis of spectral measurements, showing a sufficient closeness of the radiation of the zodiacal spectrum to the solar one, but notes that the deep Fraunhofer lines turned out to be slightly blurred. Polarization measurements have found that it has a maximum of about 0.25 at elongation values of about 60 °. Various researchers noted fluctuations in the brightness of the zodiacal light, but they failed to come to a confident conclusion about the presence of seasonal and interannual fluctuations.
In conclusion, Divari discusses various hypotheses regarding where exactly the scattering dust is in outer space. Summing up his review, he writes: "Observational facts do not exclude the possibility that the zodiacal light is due to the dust cloud surrounding the Earth."
A significant contribution to understanding the nature of the zodiacal light was made by W. T. Reach of NASA’s Goddard Space Flight Center [4–7]. His analysis of microwave observations at wavelengths of 5–16 µm showed that the particles responsible for the zodiacal light have dimensions exceeding 10 µm and are located within 1 AU. e. from the Earth. The spectra of reflected solar radiation correspond to different silicates, which are similar in composition to carbonaceous chondrites. The temperatures of dust particles correspond to equilibrium radiation temperatures with an albedo not exceeding 8%. As for the volume distribution of dust, then, according to Rich’s assumption, it is an ellipsoidal cloud near the earth’s orbit, possibly with a power-law decrease in the concentration of particles with distance. I will put forward a different hypothesis based on the dynamics of the motion of dust particles.
I’ll make a reservation that the explanation of the zodiacal light was not an end in itself. The hypothesis, which will be further stated, did not arise as an independent task, but as a side effect of the study of another problem, it will have to be briefly described.
Recently, together with Academician MI Kuzmin, I posed and solved the problem  about the further fate of those fragments of the formation of the Moon, which in the process of the Giant collision of Proto-Earth with Tefia acquire speeds sufficient to escape from the Earth’s gravitational field to infinity. But this infinity is not that far away. These fast debris begin their movement around the Sun in elliptical orbits and, after one or several orbital periods, return to that very narrow region of the Solar System, where the Giant Collision took place. The mathematical approach to the problem was to find a numerical solution to the restricted three-body problem.
A significant proportion of these debris then collide with the Earth, and their volatile constituents form the primary atmosphere and ocean. However, in our article it was also suggested that some of the fragments may be near the so-called triangular Lagrange points (L4 and L5) of the Sun-Earth system.
Fig. 2. Scheme of the Lagrange points of the Sun – Earth system.