A correlation between the distributions of pulsars and emission measures in the galaxy

A correlation has been detected between the volume density of pulsars and the density of interstellar ionized gas on scales of more than 500 pc in Galactic longitude and 200 pc in Galactic latitude. On smaller scales, the correlation is present only for pulsars with ages less than 60000 years, which are located predominantly near supernova remnants and H II regions. This all indicates that pulsars are born in regions with high concentrations of interstellar gas. The minimum emission measures observed in the directions toward pulsars are inversely proportional to the pulsar ages. It is concluded that the ionized gas in the vicinities of a number of pulsars was formed during supernova explosions, and corresponds to Strömgren zones. The ionization of the gas in these zones requires a radiation energy on the order of 10⁵⁰–10⁵¹ erg.     

Strmömgren zones of type II supernovae

The emission measures EM in the directions of supernova remnants and pulsars are considered as functions of their ages t. The resulting plot has a well-defined lower boundary, which can be approximated by the expression EM_min∝1/t. The quantity EM_min increases with decreasing age t and does not level off or reach a maximum until t?500 yr. It is concluded that the bulk of the radiative energy that goes into ionizing and heating the interstellar gas is released at early stages of the supernova remnant’s evolution. We suggest that most of the kinetic energy of the supernova shell is converted into thermal energy and radiated at remnant ages t<100 yr, when the supernova shell, which is expanding at an enormous speed (about 10⁴ km/s), overtakes the shell produced by the presupernova in the supergiant stage. We have estimated the ionization energy E?10⁵¹ erg, diameter L?60 pc, and electron density N_e?7 cm^?3 of the HII regions around the supernovae (the supernova Strömgren zones). A list of objects that can be reliably identified as Strömgren zones of type II supernovae is presented. The plot of pulsar pulse broadening τ as a function of the pulsar age t also has a well-defined lower boundary, for which τ∝t^?2 when t≥1000 yr. This suggests that turbulence develops during the first thousand years after the supernova outburst. It is also concluded that turbulence plays an important role in the formation and evolution of the Strömgren zones of type II supernovae.     

Measurements of the scattering of pulsar radio emission

Measurements of the broadening of pulsar pulses by scattering in the interstellar medium are presented for a complete sample of 100 pulsars with Galactic longitudes from 6° to 311° and distances to three kiloparsec. The dependences of the scattering on the dispersion measure (τ _sc(DM) ∝ DM^α), frequency (τ _sc(v) ∝ v ^?γ ), Galactic longitude, and distance to the pulsar are analyzed. The dependence of the scattering on the dispersion measure in the near-solar neighbourhood can be represented by the power law τ _sc(DM) ∝ DM^2.2±0.1). Measurements at the low frequencies 111, 60, and 40 MHz and literature data are used to derive the frequency dependence of the scattering (τ _sc(v) ∝ V ^?γ ) over a wide frequency interval (covering a range of less than 10: 1) with no fewer than five frequencies. The index for the frequency dependence, γ = 4.1 ± 0.3, corresponds to a normal distribution for inhomogeneities in the turbulence in the scattering medium. Based on an analysis of the dependence of the scattering on the distance to the pulsar and on Galactic longitude, on average, the turbulence level C _n ² is the same in all directions and at all distances out to about three kpc, testifying to the statistical homogeneity of the turbulence of the scattering medium in the near-solar region of the Galaxy.     

Measurement of the inner turbulence scale of the interstellar plasma toward the pulsar PSR B2111+46

The pulsar PSR B2111+46 has been observed at 112 MHz, and a new approach to analyzing pulsar pulses scattered in turbulent interstellar plasma applied. This method is based on the dependence of the normalized energy in the trailing part of a pulse on the intrapulse time. Since the trailing edge of a pulse follow exponential law to high accuracy, the inner turbulence scale of the interstellar plasma exceeds the field coherence scale. The measured scattering parameter is τ _sc = 147 ± 1 ms. Analysis of the parameters of diffractive and refractive scintillations of the pulsar at 610 MHz together with the 112 MHz data shows that the spectrum of the interstellar plasma toward PSR B2111+46 is a piecewise power law: on scales of 10¹³–10¹⁴ cm, the exponent of the turbulence spectrum is n ≃ 4, whereas n = 3.5 on scales of 2 × 10⁸−10¹³ cm. The spectrum flattens with approach to the inner turbulence scale l: n = 3–3.2. The obtained inner turbulence scale is l = (3.5 ± 1.5) × 10⁷ cm. The distribution of the interstellar plasma toward the pulsar is close to statistically homogeneous. The local density (N _e = 0.4 cm⁻³) and filling factor (F = 0.04) of the interstellar plasma have been estimated. The similarity of N _e estimates obtained from the inner scale of the inhomogeneities and the ratio of the emission measure to the dispersion measure provides evidence that the inner turbulence scale corresponds to the ion inertial length.     

Anomalous frequency dependence of scattering of the radio emission from the Crab pulsar

The frequency dependence of scattering of the radio emission from the Crab pulsar at the low frequencies 111, 63, and 44 MHz has been measured and analyzed during sporadic enhancements of scattering and dispersion measure in October–December 2006 and December 2008. The frequency dependence of the scattering differs from the generally accepted dependence, τ _sc (ν) ∝ ν ^γ , where γ = −4.0 for Gaussian and γ = −4.4 for power-law Kolmogorov distributions of inhomogeneities of the scattering medium. In intervals of enhancement, the exponent of the frequency dependence γ decreased to −3.2(0.2) at the above frequencies. A model is proposed in which this is due to the presence of a dense plasma structure in the nebula in the line of sight toward the pulsar, in which scattering of the radio emission on turbulence differs from scattering in the interstellar medium. It is shown that the frequency dependence of scattering of the radio emission can be weaker in a dense plasma than in the rarefied interstellar medium.     

Peculiarities of α-element abundances in Galactic open clusters

A catalog compiling the parameters of 346 open clusters, including their metallicities, positions, ages, and velocities has been composed. The elements of the Galactic orbits for 272 of the clusters have been calculated. Spectroscopic determinations of the relative abundances, [el/Fe], for 14 elements synthesized in various nuclear processes averaged over data from 109 publications are presented for 90 clusters. The compiled data indicate that the relative abundances of primary α elements (oxygen and magnesium) exhibit different dependences on metallicity, age, Galactocentric distance, and the elements of the Galactic orbits in clusters with high, elongated orbits satisfying the criterion (Z_max² + 4e²)^1/2 > 0.40 and in field stars of the Galactic thin disk (Z_max is the maximum distance of the orbit from the Galactic plane in kiloparsec and e is the eccentricity of the Galactic orbit). Since no systematic effects distorting the relative abundances of the studied elements in these clusters have been found, these difference suggest real differences between clusters with high, elongated orbits and field stars. In particular, this supports the earlier conclusion, based on an analysis of the elements of the Galactic orbits, that some clusters formed as a result of interactions between high-velocity,metal-poor clouds and the interstellar mediumof theGalactic thin disk. On average, clusters with high, elongated orbits and metallicities [Fe/H] < -0.1 display lower relative abundances of the primary a elements than do field stars. The low [O, Mg/Fe] ratios of these clusters can be understood if the high-velocity clouds that gave rise to them were formed of interstellar material from regions where the star-formation rate and/or the masses of Type II supernovae were lower than near the Galactic plane. It is also shown that, on average, the relative abundances of the primary a elements are higher in relatively metal-rich clusters with high, elongated orbits than in field stars. This can be understood if clusters with [Fe/H] > -0.1 formed as a result of interactions between metal-rich clouds with intermediate velocities and the interstellar medium of the Galactic disk; such clouds could form from returning gas in a so-called “Galactic fountain.”     

Observational manifestations of gaseous baryon dark matter

The paper considers possible observational implications of the presence of dark matter in the Galaxy in the form of dense gas clouds—clumpuscules with masses M _c ～10^?3 M _⊙ and radii R _c～3×10¹³ cm. The existence of such clouds is implied by modern interpretations of extreme scattering events—variations in quasar radio fluxes due to refraction in dense plasma condensations in the Galactic halo. The rate of collisions between these clouds is shown to be rather high: from 1 to 10M _⊙ per year is ejected into the interstellar medium as a result of such collisions. The optical continuum and 21-cm emission from hot post-collision gas could be observable. Gas clouds composed of dark matter could be formed around O stars in an H II region with radius R～30 pc and emission measure EM?20 cm^?6 pc. They could also be observable in the H_α line. The evaporation of clumpuscules by external ionizing radiation could be a substantial source of matter for the interstellar medium. Assuming that the total mass of matter entering the interstellar medium over the Hubble time does not exceed the mass of luminous matter in the Galaxy, upper limits are found for the cloud radii (R _c<3.5×10¹² cm) and the contribution of clouds to the surface density of the Galaxy (<50M _⊙pc^?2). Dissipation of the kinetic energy of matter lost by clumpuscules could provide an efficient mechanism for heating gas in the Galactic halo.     

The radio pulsar J0205+6449 in the supernova remnant 3C 58

The detection of pulsed radio emission from the recently discovered X-ray pulsar J0205+6449 in the young supernova remnant 3C 58 is reported together with the results of first studies of this emission. The observations were carried out at 111 and 88 MHz on radio telescopes of the Pushchino Observatory. The pulsar period, 65.68 ms, and period derivative, \(\dot P = 1.9 \times 10^{ - 13} \), have been confirmed. The integrated pulse profile at 111 MHz has been obtained and the flux density and spectral index α=2.8 measured. The pulsar dispersion measure DM=141 pc cm^?3 has been confirmed. This dispersion measure yields a distance to the pulsar of d=6.4 kpc, a factor of two or more greater than the previously favored distance to the supernova remnant 3C 58 (2.6 kpc). The problem of the age and distance of the pulsar-SNR system is discussed. If the age of the pulsar J0205+6449 is equal to that of the SNR (820 years), this pulsar is the youngest known radio pulsar. The synchrotron mechanism for the radio and X-ray emission is proposed to explain the lower radio and X-ray luminosity of this new pulsar compared to the Crab pulsar, which is similar to it in many ways. Optical emission with luminosity L_opt=10³¹ erg/s and gamma-ray emission with L_γ=7×10³⁵ erg/s are predicted, and the steep radio spectrum (α≈3) can be explained.     

Magnetorotational supernova explosions and the formation of neutron stars in close binary systems

The formation of neutron stars in the closest binary systems (P _orb<12 h) gives the young neutron star/pulsar a high rotational velocity and energy. The presence of a magnetic field of 3×10¹¹–3×10¹³ G, as is observed for radio pulsars, enables the neutron star to transfer ～10⁵¹ erg of its rotational energy to the envelope over a time scale of less than an hour, leading to a magnetorotational supernova explosion. Estimates indicate that about 30% of all type-Ib,c supernovae may be the products of magnetorotational explosions. Young pulsars produced by such supernovae should exhibit comparatively slow rotation (P _rot>0.01 s), since a large fraction of their rotational angular momentum is lost during the explosion. The magnetorotational mechanism for the ejection of the envelope is also reflected by the shape of the envelope. It is possible that the Crab radio pulsar is an example of a product of a magnetorotational supernova. A possible scenario for the formation of the close binary radio pulsar discovered recently by Lyne et al. is considered.     

The outer turbulence scale in the interstellar plasma

The structure function for phase fluctuations on spatial scales from 10⁶ to 10¹⁷ m is constructed using data on diffractive and refractive scintillation of pulsars, scattering angles, variations in pulse arrival times, and differences in dispersion measures observed for close pairs of pulsars in globular clusters. For distances R>1 kpc (a sample of pulsars with DM≥30 pc/cm³), the fluctuations in the interstellar electron density on scales from 10⁶ to 10¹⁴ m are well described by a Kolmogorov spectrum with index 11/3. Analysis of variations in the dispersion measures for close pairs of pulsars in globular clusters indicates an outer turbulence scale of L ₀=10¹⁵ m. The relative level of turbulent fluctuations is determined for the interstellar plasma, and the important role of turbulence in the energy balance is demonstrated.     

The pulsar J1852+0040 in Kes 79 and the nature of central compact objects in supernova remnants

A possible model for the pulsar PSR J1852+0040 associated with the supernova remnant Kes 79 and detected in place of a central compact object in this remnant is discussed. The main observational properties of the pulsar can be understood as consequences of its weak surface magnetic field (B _s < 3 × 10¹¹ G) and short rotational period (P ～ 0.1 s). Its X-ray emission is thermal, and is generated in a small region near the surface of the neutron star due to cooling of the surface as the surface accretes matter from a relict disk surrounding the pulsar. The radio emission is generated in the outer layers of the pulsar magnetosphere by the synchrotron (cyclotron) mechanism. The optical luminosity of J1852+0040 is estimated to be L _opt < 10²⁸ erg/s. If the spectral features in another central compact object, 1E 1207.4+5209, are interpreted as electron cyclotron lines, this provides evidence for a weak surface magnetic field for this neutron star as well (B < 6 × 10¹⁰ G). The hypothesis that all central compact objects have weak surface fields makes it possible to explain the number of detected central compact objects, the absence of pulsar-wind nebulae associated with these objects, and the fact that no pulsar has yet been detected at the position of SN 1987a. We suggest that, after the supernova remnant has dissipated, the central compact object becomes a weak X-ray source (XDINS), whose weak emission is also due to the weakness of its magnetic field.     

The stellar epoch in the evolution of the Galaxy

We consider the astrophysical evolution of the Galaxy over large time scales, from early stages (an age of ～10⁸ yrs) to the end of traditional stellar evolution (～10¹¹ yrs). Despite the fact that the basic parameters of our stellar system (such as its size, mass, and general structure) have varied little over this time, variations in the characteristics of stars (their total luminosity, color, mass function, and chemical composition) are rather substantial. The interaction of the Galaxy with other stellar systems becomes an important factor in its evolution 100–1000 Gyr after its origin; however, we take the Galaxy to be isolated. In the model considered, the basic stages of Galactic evolution are as follows. The Galaxy forms as the result of the contraction (collapse) of a protogalactic cloud. The beginning of the Milky Way’s life—the relaxation period, which lasts about 1–2 Gyr—is characterized by active star formation and final structurization. The luminosity and colors of the Galaxy are correlated to the star formation rate (SFR). The young Galaxy intensely radiates high-energy photons, which are mostly absorbed by dust and re-emitted at IR wavelengths. In the subsequent period of steady-state evolution, the gas content in the Galactic disk gradually decreases; accordingly, the SFR decreases, reaching 3–5M _⊙/yr at the present epoch and decreasing to 0.03M _⊙/yr by an age of 100 Gyr. Essentially all other basic parameters of the Galaxy vary little. Later, the decrease in the SFR accelerates, since the evolution of stars with masses exceeding 0.4M _⊙ (i.e., those able to lose matter and renew the supply of interstellar gas) comes to an end. The Galaxy enters a period of “dying”, and becomes fainter and redder. The variation of its chemical composition is manifested most appreciably in a dramatic enrichment of the interstellar gas in iron. The final “stellar epoch” in the life of the Galaxy is completed ～10¹³ yrs after its formation, when the evolution of the least massive stars comes to an end. By this time, the supplies of interstellar and intergalactic gas are exhausted, the remaining stars become dark, compact remnants, there is no further formation of new stars, and the Galactic disk no longer radiates. Eventually, infrequent outbursts originating from collisions of stellar remnants in the densest central regions of the Galaxy will remain the only source of emission.     

The phenomenon of “self-focusing” in the gaseous disk of the Galaxy

We consider perturbations in interstellar gas excited by the gravitational field of the spiral-density wave that is responsible for the Galactic arms, taking into account thermal effects. Under the conditions of fairly efficient cooling, the reaction of the gas to the perturbing field is non-trivial: the thickness of the gaseous layer is reduced in the region of the Galactic disk where the density of the gas is enhanced. We call this effect “self-focusing,” and explain it using observational results for the Galactic radio emission in the 21 cm line. Under our assumptions, we find the control parameter (δ) governing the relationship between perturbations of the thickness of the gaseous disk and the gas density in the vicinity of the Galactic equator, i.e., this parameter shows whether the correlation between these quantities is positive or negative, and provides important additional information on the thermal properties of the medium. It can be used as a diagnostic in joint studies of Galactic structure and large-scale features of the interstellar gas. Estimates for the typical Galactic parameters show that the effect of self-focusing should be clearly manifest in the Galaxy.     

Characteristics of the pulsed emission of the peculiar pulsar B1822-09 at low radio frequencies

The pulse structure of the pulsar B1822-09 has been studied at 112, 62, and 42 MHz. The observations were conducted in 2010 on the Large Scanning Antenna and the DKR-1000 radio telescope of the Pushchino Radio Astronomy Observatory. The shape of the main pulse and interpulse undergo considerable changes at low radio frequencies. In the main pulse, the precursor disappears and is replaced by a new component that trails 50 ms behind the main component. At 62 MHz, the interpulse acquires a pronounced two-peaked shape. At 62 and 112 MHz, as well as at higher frequencies, the brighter second component of the interpulse follows the main pulse at 185° and has a relative amplitude of about 5%. The main pulse width changes with frequency according to the power law W _0.5 ∼ ν ^−0.15 in the frequency range 42–4750-MHz. The interpulse width follows this law only in the range 325–4750 MHz; at 112, 102, and 62 MHz, the interpulse is almost a factor of three broader than themain pulse. The parameters of the pulse’s scattering on interstellar plasma inhomogeneities and the initial pulse width before it enters the scattering medium have been measured at 62 and 42 MHz. The frequency dependence of the characteristic scale for scattering of the pulses of B1822-09 corresponds to a Kolmogorov spectrum for the electron-density fluctuations in the interstellar medium in the direction toward this pulsar.     

The space velocities of radio pulsars

Known models proposed to explain the high space velocities of pulsars based on asymmetry of the transport coefficients of different sorts of neutrinos or electromagnetic radiation can be efficient only in the presence of high magnetic fields (to 10¹⁶ G) or short rotation periods for the neutron stars (of the order of 1 ms). This current study shows that the observed velocities are not correlated with either the pulsar periods or their surface magnetic fields. The initial rotation periods are estimated in a model for the magnetedipolar deceleration of their spin, aßsuming that the pulsar ages are equal to their kinematic ages. The initial period distribution is bimodal, with peaks at 5 ms and 0.5 s, and similar to the current distribution of periods. It is shown that asymmetry of the pulsar electromagnetic radiation is insufficient to give rise to additional acceleration of pulsars during their evolution after the supernova explosion that gave birth to them. The observations testify to deceleration of the motion, most likely due to the influence of the interstellar medium and interactions with nearby objects. The time scale for the exponential decrease in the magnetic field τ_D and in the angle between the rotation axis and magnetic moment τ_ß are estimated, yielding τ_β = 1.4 million years. The derived dependence of the transverse velocity of a pulsar on the angle between the line of sight and the rotation axis of the neutron star corresponds to the expected dependence for acceleration mechanisms associated with asymmetry of the radiation emitted by the two poles of the star.     

Formation of galactic shocks and the vertical structure of the gaseous disk of the galaxy in a “turbulent” interstellar medium

The effects on the formation of Galactic shocks and the vertical structure of the Galactic disk due to thermal processes in a cloudy interstellar medium as it flows through a spiral density wave in the plane of the Galactic disk are considered. The evolution of the gas is fundamentally different, depending on the thermal properties of the medium. For example, if it is compressed in the horizontal direction (parallel to the Galactic plane) by the gravitational forces of the spiral density waves responsible for the formation of spiral arms, an isothermal and adiabatic medium is swept out in the vertical direction. However, on the contrary, a medium whose volume loss function increases fairly rapidly with density and temperature is further compressed under the action of the overall gravitational field of the galaxy. This effect is referred to as “self-focusing,” and may serve as an additional mechanism to explain the recently discovered anticorrelation between the width of the atomic hydrogen layer in the Galaxy and the gas density. The difference in the vertical behavior of media with different thermal properties can be used as an indicator of the thermal properties of a particular component of the interstellar gas (atomic or molecular). Attention is drawn to the fact that Galactic shocks themselves represent a mechanism that can heat the ensemble of clouds, i.e., increase the dispersion of cloud velocities. The vertical structure of a Galactic shock front is constructed, which is in qualitative agreement with the “bow shock” inferred from radio data.     

Monitoring of the radio emission of the Crab Nebula pulsar at low frequencies

Results of long-term (2002–2010) monitoring of giant radio pulses of the pulsar PSR B0531+21 in the Crab Nebula at ν = 44, 63, and 111 MHz are reported. The observations were conducted on the LPA and DKR-1000 radio telescopes of the Lebedev Physical Institute. The giant pulses were analyzed using specialized software for calculating the magnitude of the scattering τ _sc , signal-to-noise ratio, and other required parameters by modeling the propagation of a pulse in the scattering interstellar medium. Three pronounced sharp increases in the scattering were recorded in 2002–2010. Analysis of the dependence between the variations of the scattering and dispersion measure (data of Jodrell Bank Observatory) shows a strong correlation at all frequencies, ≈0.9. During periods of anomalous increase in scattering and the dispersion measure, the index γ in the frequency dependence of the scattering in the Crab Nebula, τ _sc (ν) ∝ ν ^−γ , was smaller than the generally accepted values γ = 4.0 for a Gaussian and γ = 4.4 for a Kolmogorov distribution. This difference in combination with the piece-wise power-law spectrum may be due to the presence of a dense plasma structure with developed Langmuir turbulence in the nebula, along the pulsar’s line of sight. The magnetic field in the Crab Nebula estimated from measurements of the rotation measure toward the pulsar is 100 μG.     

Distribution of interstellar plasma in the direction of PSR B0525+21 from data obtained on a ground–space interferometer

Observations on the RadioAstron ground–space interferometer with the participation of the Green Bank and Arecibo ground telescopes at 1668 MHz have enabled studies of the characteristics of the interstellar plasma in the direction of the pulsar PSR B0525+21. The maximum projected baseline for the ground–space interferometer was 233 600 km. The scintillations in these observations were strong, and the spectrum of inhomogeneties in the interstellar plasma was a power law with index n = 3.74, corresponding to a Kolmogorov spectrum. A new method for estimating the size of the scattering disk was applied to estimate the scattering angle (scattering disk radius) in the direction toward PSR B0525+21, θ _scat = 0.028 ± 0.002 milliarcsecond. The scattering in this direction occurs in a plasma layer located at a distance of 0.1Z from the pulsar, where Z is the distance from the pulsar to the observer. For the adopted distance Z = 1.6 kpc, the screen is located at a distance of 1.44 kpc from the observer.     

Compact radio sources and interstellar scattering near the galactic center

Using literature data on approximately 400 compact radio sources detected with the Very Large Array and located in the direction of the Galactic center within 2° of the compact source Sgr A*, 69 sources whose angular sizes are determined by scattering on electron density inhomogeneities were distinguished. Fifty-five of these are extragalactic, two are supercompact HII regions, ten are sources of maser emission, and two are variable Galactic sources. The excess of the apparent angular sizes of maser sources within 2° of the Galactic center above the mean size of objects of this class in other parts of the Galaxy found in many studies cannot be explained purely by the effect of scattering of their radio emission on interstellar plasma inhomogeneities. The angular sizes of these objects are increased due to scattering only within Galactic longitudes of about 0.4° and Galactic latitudes less than 0.1°. The turbulent medium responsible for scattering of radio emission of compact sources in the immediate vicinity of the Galactic center is strongly concentrated toward the compact source Sgr A* at the Galactic center. No extragalactic sources are observed within 0.4° in longitude and 0.2° in latitude of the Galactic center, because of their low brightness due to the superstrong scattering in this region. Data on scatter broadening can be used to study the distribution of turbulent plasma near the Galactic center.     

Evolution of the first supernovae in protogalaxies: Dynamics of mixing of heavy elements

The paper considers the evolution of the supernova envelopes produced by Population III stars with masses ofM _* ?? 25?C200M _?? located in non-rotating protogalaxies with masses of M ?? 10⁷ M _?? at redshifts z = 12, with dark-matter density profiles in the form of modified isothermal spheres. The supernova explosion occurs in the ionization zone formed by a single parent star. The properties of the distribution of heavy elements (metals) produced by the parent star are investigated, as well as the efficiency with which they are mixed with the primordial gas in the supernova envelope. In supernovae with high energies (E ? 5 × 10⁵² erg), an appreciable fraction of the gas can be ejected from the protogalaxy, but nearly all the heavy elements remain in the protogalaxy. In explosions with lower energies (E ? 3 × 10⁵² erg), essentially no gas and heavy elements are lost from the protogalaxy: during the first one to threemillion years, the gas and heavy elements are actively carried from the central region of the protogalaxy (r ?? 0.1r _v , where r _v is the virial radius of the protogalaxy), but an appreciable fraction of the mass of metals subsequently returns when the hot cavity cools and the envelope collapses. Supernovae with high energies (E ? 5 × 10⁵² erg) are characterized by a very low efficiency of mixing of metals; their heavy elements are located in the small volume occupied by the disrupted envelope (in a volume comparable with that of the entire envelope), with most of the metals remaining inside the hot, rarified cavity of the envelope. At the same time, the efficiency of mixing of heavy elements in less energetic supernovae (E ? 3 × 10⁵² erg) is appreciably higher. This comes about due to the disruption of the hot cavity during the collapse of the supernova envelope. However, even in this case, a clear spatial separation of regions enriched and not enriched in metals is visible. During the collapse of the supernova envelope, the metallicity of the gas is appreciably higher in the central region ([Z] ?? ?1 to 0) than at the periphery ([Z] ?? ?2 to ?4) of the protogalaxy; most of the enriched gas has metallicities [Z] ?? ?3.5 to ?2.5. The masses of enriched fragments of the supernova envelope remain appreciably lower than the Jeans mass, except in regions at the center of the protogalaxy upon which the surrounding enriched gas is efficiently accreted. Consequently, the birth of stars with metallicities close to those characteristic of present-day Galactic stars is very probable in the central region of the protogalaxy.