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The eclipsing X-ray binary system Centaurus X-3.

Introduction

A binary stellar system is simply one in which two stars orbit around a common center of mass, that is they are gravitationally bound to each other. Almost 50 percent of the stars in the sky are part of a binary or multiple stellar systems.

A sub-class of binary systems are X-ray binaries, the systems in which a compact object (a white dwarf, neutron star or a black hole formed after collapse of an ordinary star) and a stellar companion, orbit each other at a distance small enough to enable mass transfer from the companion star to the compact object. The transferred matter spirals towards the compact object and forms an "accretion disk" around it.

The accreted gaseous matter is heated to very high temperatures (106-108 K), releasing the energy it acquired through gravitational infill in the form of X-ray radiation.

In case of a neutron star or a white dwarf the emission originates from both the accretion disk and the surface of the compact star while in black hole binaries the only source of X-rays is the accretion disk. Figure 1 shows a sketch of an X-ray binary system as it would be seen by a nearby observer.

X-ray binary stars are usually subdivided into two categories:

* High Mass X-ray Binaries (HMXB) where the companion's mass is greater than several solar masses, which enable it to eject matter through the stellar wind

* Low Mass X-ray Binaries (LMXB) where the companion's mass is around one solar mass and it provides matter through the inner Lagrangian point-the point where gravitational forces of the two stars and centrifugal force cancel

The first X-ray source (Sco X-1) was discovered in 1962 during a rocket flight by a group led by Riccardo Giacconi et al. (1964) Giacconi and Gursky (1974) who won the Nobel Prize for Physics in 2002 for his pioneering studies in X-ray astronomy.

[FIGURE 1 OMITTED]

The actual study of the X-ray binary stars began in the 1970s with the use of satellites equipped with X-ray detectors. The first one, UHURU, was launched in 1970 (Giacconi et al., 1972). It mapped the X-ray sky in the energy range 2-6 keV. The Einstein observatory was launched in November 1978, It provided high-resolution images and accurate locations for thousands of X-ray sources (Harris et al., 1993). The European X-Ray Observatory Satellite (EXOSAT) operated from May 1983 to April 1986 allowed to perform continuous observations of X-ray sources lasting several days without the interference of Earth occultation's. These and later missions (Chandra, XMM-Newton, Rossi XTE, BeppoSAX, INTEGRAL and others) observed X-ray radiation from different sources.

As a result of this development by a number of scientists to the set of results shown in table (1), which represents the previous studies of this system Centaurus X-3.

Ground-based observations with optical telescopes have demonstrated that X-ray sources are often members of binary systems. A fraction of these sources are eclipsing systems that show periodic light variations with time, known as the light curves.

Many contributions have been made to study and analyze the light curves of the X-ray eclipsing binaries, such as (Hutchings, 1978; Avni, 1978a; Antokhina and Cherpashchuk, 1987; Antokhina and Cherpashchuk 1994; Al-Wardat et al., 1998; Sabat et al., 1998). The present study focuses on the analysis of one such binary, Centaurus X-3, in a step to derive more reliable physical and geometrical elements.

Specifications of the system Centaurus X-3 (Krzemenski's star):

The eclipsing X-ray binary system Krzemenski's star (Centaurus X-3) is known as a high-mass X-ray binary system consists of 18 [M.sub.o] O6.5V-III giant optical star and a 1.2 M0 neutron star (Bahcall, 1978).

The X-ray star Cen X-3 was discovered from the UHURU observation by Giacconi et al, (1971) where it has been distinguished as 4.84 Second X-ray pulsar with a 2.087 day eclipse period. Krzemenski (1974) declared that the X-ray star Cen X-3 is a component of an eclipsing binary system consists of the star Cen X-3 and a giant optical star of the spectral type B0, with optical magnitude 13.4 mag at a distance of 10 kpc.

There are other issued values of the spectral type of the star, these are:O6.5II-Ve (Van den Heuvel, 1981), O6.5V-III (Hoffmeister et al., 1985) and O6f (Hutchings, 1978)

The light curve of this system characterized by two maximums at phases (0.25and 0.75) because the observer faces the maximum area of the system and two minimums at phases (0.0 and 0.5), one results from the eclipse of the compact object to the optical star and the other the deeper results from the cold hemisphere of the optical star.

Materials and Methods

Our method of determining the elements of eclipsing X-ray binaries depends on iterated attempts of getting the best fitting between the optical observational light curve and a synthetic one. The standard model of X-ray binaries was used in synthesizing light-curves of the system. The synthetic light curves were built in accordance to Roche model and taking into account the X-ray reflection and heating of the opposite side of the optical companion. We followed Sabat et al. (1998) in their solution to the Roche Model's basic equation, where they used Newton-Raphson method to solve it, after changing it into an eighth-degree polynomial equation, which proved to be more preciseand yet, more efficient than the series solutions developed by Kopal (1959).

We considered the input elements of the best fit as the elements of the system. These elements are; mass ratio of the system q, fractional radius of the optical component r, limb darkening coefficient u, gravity darkening coefficient [t.sub.o], efficiency of absorption and re-emission h, optical X-ray luminosity ratio [L.sub.opt]/[L.sub.x] and the effective temperature of the optical star [T.sub.eff].

Many attempts were performed to get the best fit. As an observational reference and guide, we used the observational light curves of Petro (1975) and (Kelley et al. 1983).

Results and discussion

The best fit was achieved using a synthetic light curve represented by the new physical and geometrical elements listed in Table 2.

The achieved best between different observation light curve and our synthetic one are represented by Fig. 2 and 3. Where Fig. 2 shows our synthetic light curve against the observations of Petro (1975), Fig. 3 shows it against the observations of Kelley et al. (1983).

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Conclusion

New physical and geometrical elements of the X-ray eclipsing binary system Centaurus X-3 (Krzemenski's star) were found. The procedure depended on getting the best fit between the observational photometric light curves, which measured using ground based telescopes and a synthetic light curve built up in accordance to the Roche model.

In building the synthetic light curves, we assumed that the optical component of the system is filling to Roche lobe, the system is rotationally synchronized and we neglecting the effect of the magnetic fields of both components.

References

Al-Wardat, M.A., H.M. AL-Naimiy, I.A. Barghouthi and H.A. Sabat., 1998. New elements for three eclipsing X-Ray binary systems: HZ Herculis, Centaurus X-3 and VELA X-1. Astrophysics Space Sci., 260: 335-345.

Antokhina, E.A. and A.M. Cherepashchuk, 1994. Synthesizing of radial velocity curves of close binary systems. Astronomicheskij Zhurnal, 71(30): 420-430.

Antokhina, E.A. and A.M. Cherpashchuk, 1987. SS 433-The parameters of the eclipsing system with a processing thick accretion disk. Astronomicheskii Zhurnal, 64: 562-585.

Avni, Y. and J.N. Bahcall, 1975. Ellipsoidal light variations and masses of X-ray binaries. Astrophysical J., 197: 675-688.

Avni, Y., 1978. Mass Estimates from Optical Light Curves for Binary X-Ray Sources. In: Physics and Astrophysics of Neutron Stars and Black. Holes Giacconi, R. and R. Ruffini (Eds.). North-Holland Publishing Company, Amsterdam, pp: 43-62.

Avni. Y., 1978. On the contribution of active galactic nuclei to the diffuse X-ray background. Astronomy Astrophysics, 63: 13-16.

Bagot, P., 1996. Boost of the orbital motion in high mass X-ray binaries. Astronomy Astrophysics, 314: 576-584.

Bahcall, J.N., 1978.Optical Properties of Binary X-Ray Sources. In: Physics and Astrophysics of Neutron Stars and Black Holes. Giacconi, R. and R. Ruffini (Eds.). North-Holland Publishing Company, Amsterdam, pp: 63-110.

Giacconi, R., H. Gursky and E. Kellogg, E. Schreier and H. Tananbaum, 1971. Discovery of Periodic X-Ray Pulsations in Centaurus X-3 from HURU. Astrophysical, J., 167: 67-73.

Giacconi, R. and H. Gursky, 1974. X-ray astronomy. In: X-ray Astronomy. Giacconi R. and H. Gursky(Eds.). Dordrecht, D. Reidel Publishing Co. (Astrophysics and Space Science Library., 43: 461.

Giacconi, R. and R. Ruffini, 1978. Physics and astrophysics of neutron stars and black holes. In: Physics and Astrophysics of Neutron Stars and Black Holes. Giacconi R., and R.Ruffini, Bologna, Societa Italiana di Fisica; Amsterdam, North Holland Publishing Co., (p.907) In Italian and English (For individual items see A79-19102 to A79-19134). Giacconi, R., H. Gursky, J. Waters, R. Clark, G and B. Rossi, 1964. Two Sources of Cosmic X-rays in Scorpius and Sagittarius, Nature, 204(4962) 981-982.

Giacconi, R., S. Murray, H. Gursky, E. Kellogg, E. Schreier and H. Tananbaum, 1972. The Uhuru catalog of X-ray sources. Astrophysical, J., 178: 281-308.

Harris, M.J. and G.H. Share and M.D. Leising and J. E. Grove, 1993. SMM observations of gamma-ray transients. I. A search for variable emission at mev energies from five galactic and extragalactic sources. Astrophysical J., 416: 601-619.

Hoffmeister, C., Richter, G. and W. Wenzel, 1985. Variable Stars. Translated by S. Dunlop, Berlin), Springer Verlag., pp: 122-131.

Hutchings, J.B, A.P. Cowely, D. Crampton, J. Van Paradijs and N.E. White, 1979. Centaurus X-3. Astrophysical J., 229: 1079-1084.

Hutchings, J.B., 1974. The synthesis of close-binary light curves. VI. X-ray and collapse binaries. Astrophysical J., 188: 341-348.

Hutchings, J.B., 1978. Optical Observations of X-Ray Sources. In: Physics and Astrophysics of Neutron Stars and Black Hole. Giacconi, R. and R. Ruffini (Eds.). (A79-19101 06-90) Bologna, Societa Italiana di Fisica; Amsterdam, North Holland Publishing Co., pp: 202-215.

Kelley, R.L., S. Rappaport, G.W. Clark and L.D. Petro, 1983. Orbital period changes in Centaurus X-3. Astrophysical J., 268: 790-799.

Kopal. Z., 1959. Close Binary Systems. In: The International Astrophysics Series. Chapman and Hall LTD. London, 5: 498.

Krzemenski, W., 1974. The identification and UBV photometry of the visible component of the Centaurus X-3 binary system. Astrophysical J., 192: L135-L138.

Petro, L., 1975. Photoelectric observations of Krzeminski's star, the companion of Centaurus X-3. Astrophysical J., 195: 709-713.

Sabat, H.A. and H.M. Al-Naimiy and I.A. Barghouthi, and M. A. Al-Wardat, 1998. Synthetic Light-Curves of Some Eclipsing X-Ray Binary Systems. Astrophysics Space Sci., 260: 347-357.

Schreier, E. and R. Levinson and H. Gursky and E. Kellogg and H.Tananbaum and R. Giacconi, 1972. Evidence for the Binary Nature of Centaurus X-3 from UHURU X-Ray Observations. Astrophysical J., 172: L79-L89.

Van den Heuvel, E.P., 1981. X-Ray Binaries and Stellar Evolution. In: X-Ray Astronomy,Space Science Reviews. Anderson, R.D. (Ed.). D Reidel Publishing Company, Dordrecht, pp: 309-309.

Van den Heuvel, E.P.J., 1978. Evolution of close binaries, with possible applications to massive X-ray binaries. In: Physics and astrophysics of neutron stars and black holes. Giacconi, R. and R. Ruffini (Eds.). Bologna, Societa Italiana di Fisica; Amsterdam, North Holland Publishing Co., pp: 828-871.

Omar Al-Banawi

Department of Physics, Al-Hussein Bin Talal University, P.O. Box 20, 71111, Ma'an, Jordan

Corresponding Author: Omar Al-Banawi, Department of Physics, Al-Hussein Bin Talal University, P.O. Box 20, 71111, Ma'an, Jordan

E-mail: OMAR BAI" <oabph@yahoo.com
Table 1: Lists of the physical and geometrical elements of
the system as given by earlier studies

Parameter                                         Reference

Mass of The Optical    Mopt = (17 [+ or -] 2) Mo  (Bahcall, 1978;
Star                        = (18.25 [+ or -]     Hutchings et al.,
                              1.75) Mo            1979) (Bahcall,
                                                  1978) (Hutchings et
                                                  al., 1979)

Mass of The Neutron    Mn = (1.2 [+ or -]         (Avni and Bahcall,
Star                        0.6) Mo               1975; Krzemenski,
                          = (1 [+ or -] 0.3) Mo   1974)
                          = (0.85 [+ or -]
                             0.25) Mo
Eccentricity of The       e < 0.002               (Hutchings, 1974)
Orbit

Inclination of The       i = 90o                  (Giacconi and
System                                            Ruffini, 1978)

Orbital Period         Porb  = 2.087d             (Schreier et al,
                           = 2.08712d             1972) (Bagot, 1996)

Orbital Period         [P.sub.orb]/[P.sub.orb]    (Van den Heuvel,
Change                 = -1.6C10-6 s/yr           1978)

X-Ray Luminosity       L ~ 7.7C1037 erg/s         (Bahcall, 1978)

Optical to X-Ray       Lopt/Lx = 100              (Schreier et al.,
Luminosity Ratio                                  1972)

Pulsation Period       Pp =4.84s                  (Bahcall, 1978)

Distance From Earth    5 to 10 kpc                (Bahcall, 1978)

Visual Magnitude       mv = 13.4 mag              (Krzemenski, 1974)
                                                  (Hutchings, 1974)
                                                  (Avni, 1978b)

Duration of X-Ray      [theta]e =                 Dm = 0.7 mag Dm =
Eclipse                39 [+ or -] 2o             0.8mag (Al-Wardat et
                                                  al., 1998)

Mass Ratio of The      q = 0.06 [+ or -] 0.002    (Al-Wardat et al,
System                                            1998)

Radius of The          r = 0.625 [+ or -] 0.003   (Al-Wardat et al,
Optical Component                                 1998)

[+ or -] 0.02 Limb     u = 0.8                    (Al-Wardat et al,
Darkening                                         1998)
Coefficient

Gravity Darkening      to = 0.4 [+ or -] 0.02     (Al-Wardat et al,
Coefficient                                       1998)

Efficiency of          h = 0.1 [+ or -] 0.05      (Al-Wardat et al,
Absorption and                                    1998)
Re-emission

Optical to X-Ray       Lopt/Lx = 100 [+ or -] 5   (Al-Wardat et al,
Luminosity Ratio                                  1998)

Effective              Teff = 38000               (Al-Wardat et al,
Temperature of The     K [+ or -] 1000            1998)
Optical Star

Table 2: New elements of Centaurus X-3

Mass Ratio of The System             q = 0.062 [+ or -] 0.001

Radius of The Optical Component      r = 0.63 [+ or -] 0.002
Limb Darkening Coefficient           u = 0.82 [+ or -] 0.02
Gravity Darkening Coefficient        t = 0.42 [+ or -] 0.01
Efficiency of Absorption
  and Re-emission                    h = 0.12 [+ or -] 0.04
Optical to X-Ray Luminosity Ratio    Lopt/Lx = 103 [+ or -] 4
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Title Annotation:Original Article
Author:Banawi, Omar Al-
Publication:Advances in Natural and Applied Sciences
Article Type:Report
Geographic Code:7JORD
Date:May 1, 2010
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