Cosmic-ray antimatter: A primary origin hypothesis

We examine the possibility that the observed cosmic-ray protons are of primary extragalactic origin. The present \(\bar p\) data are consistent with a primary extragalactic component having \(\bar p\) /p?3.2±0.7 x 10^-4 independent of energy. Following the suggestion that most extragalactic cosmic rays are from active galaxies, we propose that most of the observed \(\bar p\) 's are alos from the same sites. This would imply the possibility of destroying the corresponding \(\bar \alpha \) 'sat the source, thus leading to a flux ratio \(\bar \alpha \) /α< \(\bar p\) /p. We further predict an estimate for \(\bar \alpha \) α～10^-5, within the range of future cosmic-ray detectors. the cosmological implications of this proposal are discussed.     

Forecasting the intensity of solar proton events from the time characteristics of solar microwave bursts

A survey of the main characteristics of solar microwave bursts in relation to their usefulness for indicating the intensity of associated solar proton emissions suggests that time parameters give much better results than intensity or spectrum parameters. In particular, best results are obtained by using the effective, or mean, burst duration defined by $$T_M = 1/P_{max} \int_0^T {P(t)dt} $$ where T is the overall burst duration, P is the power density at time T, and P _max is the maximum power density. For proton energies > 10 MeV the proton flux N _p is given approximately by N _p = 0.034 T _M ³ particles ster^?1 cm^?2 s^?1, where T _m is in minutes, with a correlation factor of 0.8. Corresponding coefficients have been derived for a number of energy ranges. Using this parameter solar proton warnings and intensity estimates can be made with observations at only one frequency, preferably in the range 5–20 GHz.     

Variability of Fe ii in Two NLS1s, PG 1700+815 and NGC 4051

We analyze the spectral variability for two narrow line Seyfert 1 galaxies, PG 1700+518 and NGC 4051 using the spectral decomposition method. We focus on their optical Fe ii variability to investigate the origin of Fe ii in AGNs. For PG 1700+518, we find that the Fe ii size is about 200 light-days, which is consistent with the Hβ size derived from the empirical R–L relation. For NGC 4051, the [O iii] 5007 Å flux is strongly correlated with continuum flux, suggesting that we should recalibrate the spectral flux on a scale defined by [O iii] flux. The corrected light curves of Fe ii, Hβ, He ii, f _λ (5100 Å) are given here. A detailed analysis will be given in the near future.     

Ultraviolet solar identifications based on extended absorption series observed in the laboratory spectrum of Sii

The absorption spectrum of Sii in the wavelength region 1500–1900 Å has been photographed at high resolution. The silicon vapour was produced in a 122 cm long King furnace at 1800–2300°C. Forty-two Rydberg series have been observed from the ground state terms 3p ^{2 3} P and¹ D to terms associated with the 3pns and 3pnd configurations. All of the series from these configurations withJ<4 have been extended with the 3pnd ³ D ₃ ^o levels reachingn=56. Numerous perturbations have been observed. This laboratory work has provided the basis for extending the identification of silicon lines in the solar spectrum. Nearly all lines found in the laboratory spectrum are also found in rocket spectrograms of the solar chromosphere. More than 300 lines have been attributed to Sii. The excellent correlation between laboratory and solar Sii lines will be illustrated.     

Sur un modele explicitant les differents types morphologiques des galaxies

In the now classical Lindblad-Lin density-wave theory, the linearization of the collisionless Boltzmann equation is made by assuming the potential functionU expressed in the formU=U ₀ + \(\tilde U\) +... WhereU ₀ is the background axisymmetric potential and \(\tilde U<< U_0 \) . Then the corresponding density distribution is \(\rho = \rho _0 + \tilde \rho (\tilde \rho<< \rho _0 )\) and the linearized equation connecting \(\tilde U\) and the component \(\tilde f\) of the distribution function is given by $$\frac{{\partial \tilde f}}{{\partial t}} + \upsilon \frac{{\partial \tilde f}}{{\partial x}} - \frac{{\partial U_0 }}{{\partial x}} \cdot \frac{{\partial \tilde f}}{{\partial \upsilon }} = \frac{{\partial \tilde U}}{{\partial x}}\frac{{\partial f_0 }}{{\partial \upsilon }}.$$ One looks for spiral self-consistent solutions which also satisfy Poisson's equation $$\nabla ^2 \tilde U = 4\pi G\tilde \rho = 4\pi G\int {\tilde f d\upsilon .} $$ Lin and Shu (1964) have shown that such solutions exist in special cases. In the present work, we adopt anopposite proceeding. Poisson's equation contains two unknown quantities \(\tilde U\) and \(\tilde \rho \) . It could be completelysolved if a second independent equation connecting \(\tilde U\) and \(\tilde \rho \) was known. Such an equation is hopelesslyobtained by direct observational means; the only way is to postulate it in a mathematical form. In a previouswork, Louise (1981) has shown that Poisson's equation accounted for distances of planets in the solar system(following to the Titius-Bode's law revised by Balsano and Hughes (1979)) if the following relation wasassumed $$\rho ^2 = k\frac{{\tilde U}}{{r^2 }} (k = cte).$$ We now postulate again this relation in order to solve Poisson's equation. Then, $$\nabla ^2 \tilde U - \frac{{\alpha ^2 }}{{r^2 }}\tilde U = 0, (\alpha ^2 = 4\pi Gk).$$ The solution is found in a classical way to be of the form $$\tilde U = cte J_v (pr)e^{ - pz} e^{jn\theta } $$ wheren = integer,p =cte andJ _v (pr) = Bessel function with indexv (v ² =n ² + α²). By use of the Hankel function instead ofJ _v (pr) for large values ofr, the spiral structure is found to be given by $$\tilde U = cte e^{ - pz} e^{j[\Phi _v (r) + n\theta ]} , \Phi _v (r) = pr - \pi /2(v + \tfrac{1}{2}).$$ For small values ofr, \(\tilde U\) = 0: the center of a galaxy is not affected by the density wave which is onlyresponsible of the spiral structure. For various values ofp,n andv, other forms of galaxies can be taken into account: Ring, barred and spiral-barred shapes etc. In order to generalize previous calculations, we further postulateρ ₀ =kU ₀/r ², leading to Poisson'sequation which accounts for the disc population $$\nabla ^2 U_0 - \frac{{\alpha ^2 }}{{r^2 }}U_0 = 0.$$ AsU ₀ is assumed axisymmetrical, the obvious solution is of the form $$U_0 = \frac{{cte}}{{r^v }}e^{ - pz} , \rho _0 = \frac{{cte}}{{r^{2 + v} }}e^{ - pz} .$$ Finally, Poisson's equation is completely solvable under the assumptionρ =k(U/r ². The general solution,valid for both disc and spiral arm populations, becomes $$U = cte e^{ - pz} \left\{ {r^{ - v} + } \right.\left. {cte e^{j[\Phi _v (r) + n\theta ]} } \right\},$$ The density distribution along the O _z axis is supported by Burstein's (1979) observations.     

Energy changes of cosmic rays in the interplanetary region

A clarification and discussion of the energy changes experienced by cosmic rays in the interplanetary region is presented. It is shown that the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system is 〈p〉 =p V·G/3 (p=momentum,V is the solar wind velocity andG=cosmic-ray density gradient). This result is obtained in three ways:

1. by a rearrangement and reinterpretation of the cosmic-ray continuity equation;
2. by using a scattering analysis based on that of Gleeson and Axford (1967);
3. by using a special scattering model in which cosmic-rays are trapped in ‘magnetic boxes’ moving with the solar wind.

The third method also gives the rate of change of momentum of particles within a moving ‘magnetic box’ as 〈p〉_ad = ?p ?·V/3, which is the adiabatic deceleration rate of Parker (1965). We conclude that ‘turnaround’ energy change effects previously considered separately are already included in the equation of transport for cosmic rays.     

The coronal hole at the 7 March 1970 solar eclipse

Coronal interferograms in the lines of Fe xiv 5303 Å, He i 5876 Å and Fe x 6374 Å were obtained during the total solar eclipse of 10 July, 1972 (see Figure 2). He i emission was found in the chromosphere only. The upper limit of the D₃ equivalent width in terms of the coronal continuous background is 0.013 Å in the inner corona (r=1.15 R⊙). The λ6374 negative was taken with low contrast. The half width of 16374 is 1.0–1.08 Å for a limited area of the corona (P=88?104°, r=1.30?1.44 R⊙). A detailed photometry of the 5303 Å line was carried out and the behaviour of the half widths and equivalent widths were studied in different regions of the corona. The half width of λ5303 increases with distance from the Sun's center in almost all the studied regions (1.2 R⊙ ? r ? 1.7 R⊙). This increase corresponds to an increase of the non-thermal velocities with a gradient of 1–2 km s^-1 per 0.1 R⊙. The equivalent widths, expressed in the coronal continuous background intensity remain constant on the average.     

The Chandra X-ray galaxy clusters at z<1.4: constraints on the evolution of L X −T−M g relations

We analyzed the luminosity-temperature-mass of gas (L _X ?T?M _g ) relations for a sample of 21 Chandra galaxy clusters. We used the standard approach (β?model) to evaluate these relations for our sample that differs from other catalogues since it considers galaxy clusters at higher redshifts (0.4<z<1.4). We assumed power-law relations in the form $L_{X} \sim(1 +z)^{A_{L_{X}T}} T^{\beta_{L_{X}T}}$ , $M_{g} \sim(1 + z)^{A_{M_{g}T}} T^{\beta_{M_{g}T}}$ , and $M_{g} \sim(1 + z)^{A_{M_{g}L_{X}}} L^{\beta_{M_{g}L_{X}}}$ . We obtained the following fitting parameters with 68 % confidence level: $A_{L_{X}T} = 1.50 \pm0.23$ , $\beta_{L_{X}T} = 2.55 \pm0.07$ ; $A_{M_{g}T} = -0.58 \pm0.13$ and $\beta_{M_{g}T} = 1.77 \pm0.16$ ; $A_{M_{g}L_{X}} \approx-1.86 \pm0.34$ and $\beta_{M_{g}L_{X}} = 0.73 \pm0.15$ , respectively. We found that the evolution of the M _g ?T relation is small, while the M _g ?L _X relation is strong for the cosmological parameters Ω _m =0.27 and Ω _Λ =0.73. In overall, the clusters at high-z have stronger dependencies between L _X ?T?M _g correlations, than those for clusters at low-z. For most of galaxy clusters (first of all, from MACS and RCS surveys) these results are obtained for the first time.     

Fourier analysis of light curves of eclipsing variable stars

The photometric perturbationsB _h ^(l) arising from both tidal and rotational distortion of a close eclipsing binary have been given in two previous papers (Livaniou, 1977; Rovithis-Livaniou, 1977). The aim of the present paper will be to find the eclipse perturbationsB _2m =B _{2m, tid} +B _{2m, rot} of a close binary exhibiting partial eclipses. This will be done giving the suitable combinations of theB _h ^(l) 's and will make easier the application to real stars. After a very brief introduction, Section 2 gives both theB _{2m, tid} andB _{2m, rot} for uniformly bright discs; while in Sections 3 and 4 they are given for linear and quadratic limb-darkening, respectively. Finally, Section 5 gives a brief discussion of the results.     

Etude variationnelle des decalages spectraux

In a static gravitational field the paths of light are curved, as noticed by H. Weyl. This property can bea priori stated for aV ₃ Riemannian manifold: through any two points ofV ₃ it is possible to draw two families of curves, the straight lines of Euclidean geometry and the photon trajectoriesz. We can perform a fibration of the Galilean space-time in an original way, by taking thez-trajectories of the photons as the base, the isochronic surfaces as fibres, and ‘the equal length time on az trajectory to reach a given point’ as the equivalence relation. The straight lines of Euclidean geometry can then carry the classical mechanics timet, and thez trajectories can carry the optics time t. These times are related by dt=F(x,t) dt. If we class the Universe as a pseudo-Riemannian manifold of normal hyperbolic typeC ^∞, the time t determined above can be taken as the time coordinate inV ₄. Under these conditions we have \(d\overline s ^2 \) =F ² \(d\overline s ^2 \) , where \(d\overline s ^2 \) is the metric of the Riemannian manifold, conforming to the metric ds ² and allowing t as the cosmic time. We can then use the results previously achieved by the author (Peton, 1979) and write: 1 +Z _G =F(A _s,t _s,)/F(Ao_s,t _o) wherez _G denotes the shift of the spectral lines due to the metric. In the case of relative motion betweenO andS, we have $${\text{1 + z' = (1 + }}z_{\text{G}} {\text{)(1 + }}\beta _{\text{r}} {\text{)(1 }} - {\text{ }}\beta ^2 {\text{)}}^{ - 1/2} $$ The Doppler-Fizeau effect therefore appears as a result of the application of the Fermat principle.     

Normality condition in the ideal resonance problem

The Ideal Resonance Problem, defined by the Hamiltonian $$F = B(y) + 2\mu ^2 A(y)\sin ^2 x,\mu \ll 1,$$ has been solved in Garfinkelet al. (1971). As a perturbed simple pendulum, this solution furnishes a convenient and accurate reference orbit for the study of resonance. In order to preserve the penduloid character of the motion, the solution is subject to thenormality condition, which boundsAB" andB' away from zero indeep and inshallow resonance, respectively. For a first-order solution, the paper derives the normality condition in the form $$pi \leqslant max(|\alpha /\alpha _1 |,|\alpha /\alpha _1 |^{2i} ),i = 1,2.$$ Herep _i are known functions of the constant ‘mean element’y', α is the resonance parameter defined by $$\alpha \equiv - {\rm B}'/|4AB\prime \prime |^{1/2} \mu ,$$ and $$\alpha _1 \equiv \mu ^{ - 1/2}$$ defines the conventionaldemarcation point separating the deep and the shallow resonance regions. The results are applied to the problem of the critical inclination of a satellite of an oblate planet. There the normality condition takes the form $$\Lambda _1 (\lambda ) \leqslant e \leqslant \Lambda _2 (\lambda )if|i - tan^{ - 1} 2| \leqslant \lambda e/2(1 + e)$$ withΛ ₁, andΛ ₂ known functions of λ, defined by $$\begin{gathered} \lambda \equiv |\tfrac{1}{5}(J_2 + J_4 /J_2 )|^{1/4} /q, \hfill \\ q \equiv a(1 - e). \hfill \\ \end{gathered}$$      

Observational constraints on G-corrected holographic dark energy using a Markov chain Monte Carlo method

We constrain holographic dark energy (HDE) with time varying gravitational coupling constant in the framework of the modified Friedmann equations using cosmological data from type Ia supernovae, baryon acoustic oscillations, cosmic microwave background radiation and X-ray gas mass fraction. Applying a Markov Chain Monte Carlo (MCMC) simulation, we obtain the best fit values of the model and cosmological parameters within 1σ confidence level (CL) in a flat universe as: $\varOmega_{b}h^{2}=0.0222^{+0.0018}_{-0.0013}$ , $\varOmega_{c}h^{2}=0.1121^{+0.0110}_{-0.0079}$ , $\alpha_{G}\equiv \dot{G}/(HG) =0.1647^{+0.3547}_{-0.2971}$ and the HDE constant $c=0.9322^{+0.4569}_{-0.5447}$ . Using the best fit values, the equation of state of the dark component at the present time w _d0 at 1σ CL can cross the phantom boundary w=?1.     

Solar activity and the 11-year modulation of cosmic rays

The cosmic-ray intensity during the 18th and 19th solar cycles is examined in the light of Gnevyshev's suggestion of the presence of two maxima in each solar cycle. The 18th solar cycle (1944–54) has two prominent and widely separated cosmic-ray minima corresponding in phase with the two maxima in Bartel's A_p index. For the 19th solar cycle the existence of two minima is less prominent than for the 18th solar cycle. The maximum at higher solar latitudes is more effective in reducing cosmic-ray intensity than the maximum at the lower latitudes. A_p, however, has a larger maximum during the lower latitude solar maximum. A relation between A_p and cosmic-ray intensity is obtained. This relationship is shown to be consistent with Parker's solar-wind theory of the modulation of cosmic rays.     

A photometric study of the star V1016 Ori

New photoelectric UBVRI observations of the eclipsing variable V 1016 Ori have been obtained with the AZT-11 telescope at Crimean Astrophysical Observatory and with the Zeiss-600 telescope at Mount Maidanak Observatory. Light curves are constructed from the new observations and from published and archival data. We use a total of 340, 348, 386, 185, and 62 magnitude estimates in the bands from U to I, respectively. An analysis of these data has yielded the following results. The photometric elements were refined; their new values are $Min I = JDH 2441966.820 + 65\mathop .\limits^d 4331E$ . The UBVRI magnitudes outside eclipse were found to be $5\mathop .\limits^m 95$ , $6\mathop .\limits^m 77$ , $6\mathop .\limits^m 75$ , $6\mathop .\limits^m 68$ , and $6\mathop .\limits^m 16$ , respectively. No phase effect was detected. We obtained two light-curve solutions: (1) assuming that the giant star was in front of the small one during eclipse, we determined the stellar radii, r _s=0.0141 and r _g=0.0228 (in fractions of the semimajor axis of the orbit); and (2) assuming that the small star was in front of the giant one, we derived r _g=0.0186 and r _s=0.0180 for the V band. The brightness of the primary star in the bands from U to I is L ₁=0.96, 0.92, 0.90, 0.89, and 0.88, the orbital inclination is $i = 87^\circ .1$ , and the maximum eclipse phase is α₀= 0.66. In both cases, we accepted the U hypothesis, assumed the orbit to be elliptical, and took into account the flux from the star Θ¹ Ori E that fell within the photometer aperture. The first solution leads to a discrepancy between the primary radius determined by solving the light curve and the radial-velocity curve and its value estimated from the luminosity and temperature. This discrepancy is eliminated in the second solution, and it turns out that, by all parameters, the primary corresponds to a normal zero-age main-sequence star.     

Long-Term Modulation of Cosmic-Ray Intensity and Correlation Analysis Using Solar and Heliospheric Parameters

Based on the monthly sunspot numbers (SSNs), the solar-flare index (SFI), grouped solar flares (GSFs), the tilt angle of heliospheric current sheet (HCS), and cosmic-ray intensity (CRI) for Solar Cycles 21?–?24, a detailed correlation study has been performed using the cycle-wise average correlation (with and without time lag) method as well as by the “running cross-correlation” method. It is found that the slope of regression lines between SSN and SFI, as well as between SSN and GSF, is continuously decreasing from Solar Cycle 21 to 24. The length of regression lines has significantly decreased during Cycles 23 and 24 in comparison to Cycles 21 and 22. The cross-correlation coefficient (without time lag) between SSN–CRI, SFI–CRI, and GSF–CRI has been found to be almost the same during Cycles 21 and 22, while during Cycles 23 and 24 it is significantly higher between SSN–CRI and HCS–CRI than for SFI–CRI and GSF–CRI. Considering time lags of 1 to 20 months, the maximum correlation coefficient (negative) amongst all of the sets of solar parameters is observed with almost the same time lags during Cycles 21?–?23, whereas exceptional behaviour of the time lag has been observed during Cycle 24, as the correlation coefficient attains its maximum value with two time lags (four and ten months) in the case of the SSN–CRI relationship. A remarkably large time lag (22 months) between HCS and CRI has been observed during the odd-numbered Cycle 21, whereas during another odd cycle, Cycle 23, the lag is small (nine months) in comparison to that for other solar/flare parameters (13?–?15 months). On the other hand, the time lag between SSN–CRI and HCS–CRI has been found to be almost the same during even-numbered Solar Cycles 22 and 24. A similar analysis has been performed between SFI and CRI, and it is found that the correlation coefficient is maximum at zero time lag during the present solar cycle. The GSFs have shown better maximum correlation with CRI as compared to SFI during Cycles 21 to 23, indicating that GSF could also be used as a significant solar parameter to study the cosmic-ray modulation. Furthermore, the running cross-correlation coefficient between SSN–CRI and HCS–CRI, as well as between solar-flare activity parameters (SFI and GSF) and CRI is observed to be strong during the ascending and descending phases of solar cycles. The level of cosmic-ray modulation during the period of investigation shows the appropriateness of different parameters in different cycles, and even during the different phases of a particular solar cycle. We have also studied the galactic cosmic-ray modulation in relation to combined solar and heliospheric parameters using the empirical model suggested by Paouris et al. (Solar Phys.280, 255, 2012). The proposed model for the calculation of the modulated cosmic-ray intensity obtained from the combination of solar and heliospheric parameter gives a very satisfactory value of standard deviation as well as \(R^{2}\) (the coefficient of determination) for Solar Cycles 21?–?24.     

Theoretical emission line strengths for Ov compared to EUV solar observations

RecentR-matrix calculations of electron impact excitation rates in Ov are used to derive the emission line intensity ratios (in energy units) $$\begin{gathered} R_1 = I(2s2p^{ 3} P - 2p^{2 3} P)/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(761.1\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ ), \hfill \\ R_2 = I(2s^{2 1} S_0 - 2s2p^{ 3} P_1 )/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(1218.4\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ ), \hfill \\ \end{gathered} $$ and $$R_3 = I(2s2p^{ 1} P_1 - 2p^{2 1} S_0 )/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(774.5\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ )$$ as a function of electron temperature (T _e) and density (N _e). These results are presented as plots ofR ₁ vsR ₂, andR ₁ vsR ₃, which should allowboth N _e andT _e to be deduced for the Ov line emitting region of a plasma. Electron densities derived from the (R ₁,R ₂) and (R ₁,R ₃) diagrams in conjunction with observational data for several solar features obtained with the Harvard S-055 spectrometer on boardSkylab are found to be compatible, and in good agreement with values ofN _e estimated from line ratios in species formed at similar electron temperatures to Ov. In addition, values ofT _e determined from (R ₁,R ₂) and (R ₁,R ₃) are generally close to that expected theoretically. These results provide experimental support for the accuracy of the diagnostic calculations presented in this paper, and hence the atomic data used in their derivation.     

Continuum spectrum of the star Θ1 Ori C

Published photoelectric measurements over a wide wavelength range (0.36–18 µm) are used to study the continuum spectrum of the star Θ¹ Ori C. The model that assumes the following three radiation sources is consistent with observations: (1) a zero-age main-sequence O7 star (object 1) of mass M ₁=20M _⊙, radius R ₁=7.4R _⊙, effective temperature T ₂=37 000 K, and absolute bolometric magnitude $M\mathop {bol}\limits^1 = - 7\mathop .\limits^m 7$ ; (2) object 2 with M ₂=15M _⊙, R ₂=16.2R _⊙, T ₂=4000 K, and $M\mathop {bol}\limits^2 = - 5\mathop .\limits^m 1$ ; and (3) object 3 with R ₃10 700 R _⊙, T ₃=190 K, and $M\mathop {bol}\limits^3 = - 0\mathop .\limits^m 6$ . The visual absorption toward the system is $A_V = 0\mathop .\limits^m 95$ and obeys a normal law. The nature of objects 2 and 3 has not been elucidated. It can only be assumed that object 2 is a companion of the primary star, its spectral type is K7, and it is in the stage of gravitational contraction. Object 3 can be a cocoon star and a member of the system, but can also be a dust envelope surrounding the system as a whole.     

On the connection between the Nekhoroshev theorem and Arnold diffusion

The analytical techniques of the Nekhoroshev theorem are used to provide estimates on the coefficient of Arnold diffusion along a particular resonance in the Hamiltonian model of Froeschlé et al. (Science 289:2108–2110, 2000). A resonant normal form is constructed by a computer program and the size of its remainder ||R _opt || at the optimal order of normalization is calculated as a function of the small parameter ${\epsilon}$ . We find that the diffusion coefficient scales as ${D \propto ||R_{opt}||^3}$ , while the size of the optimal remainder scales as ${||R_{opt}|| \propto {\rm exp}(1/\epsilon^{0.21})}$ in the range ${10^{-4} \leq \epsilon \leq 10^{-2}}$ . A comparison is made with the numerical results of Lega et al. (Physica D 182:179–187, 2003) in the same model.     

On the mass-luminosity relation

The results of a least-squares study of the mass-luminosity relation for eclipsing and visual binary stars consisting of main sequence components are presented. Two methods are discussed. In Part A, the values of the coefficientsA andB in the relation logM=A+BM _Bol are determined. Part B presents a technique which permits the determination of α and β in the relationM=αL ^β, when only the sum of the masses, and not the individual masses of each component, is known. The results and a comparison of the two methods are discussed. It is found that the following massluminosity relation represents the observational data satisfactorily: $$log M = 0.504 - 0.103M_{BOL,} {\text{ }} - \leqslant M_{BOL} \leqslant + 10.5$$ . A discussion of the data and of the possibility that separate mass-luminosity relations may exist for visual and eclipsing binaries is given. The possiblity that more than one mass-luminosity relation is required in the range ?8≤M _Bol ≤+13 is also discussed.