The Quark-Hadron Transition in Cosmology and Dark Energy
Neşever BALTACI1
1 Umraniye Anatolia I.H.High School –Istanbul –Turkiye
e-mail : nesever@yahoo.com
Dark sides and golden ages Astronomers first started talking about a "golden age" of astrophysics and cosmology in the late 1990s. • Ironically, the outstanding questions in the golden age concern the dark side of the universe - what are the "dark matter" and the "dark energy" that cannot be seen but which make themselves known through their gravitational influence? •
But dark matter and dark energy are just two puzzles, albeit two extremely difficult and important ones, in a galaxy of questions that still new evidence has confirmed that the expansion of the universe is accelerating under the influence of a gravitationally repulsive form of energy that makes up two-thirds of the cosmos.
It is an irony of nature that the most abundant form of energy in the universe is also the most mysterious. Since the breakthrough discovery that the cosmic expansion is accelerating, a consistent picture has emerged indicating that two-thirds of the cosmos is made of "dark energy" - some sort of gravitationally repulsive material.
But is the evidence strong enough to justify exotic new laws of nature? Or could there be a simpler, astrophysical explanation for the results? The dark-energy story begins in 1998, when two independent teams of astronomers were searching for distant supernovae, hoping to measure the rate at which the expansion of the universe was slowing down. They were in for a shock: the observations showed that the expansion was speeding up
In fact, the universe started to accelerate long ago, some time in the last 10 billion years. Like detectives, cosmologists around the world have built up a description of the culprit responsible for the acceleration: it accounts for two-thirds of the cosmic energy density; it is gravitationally repulsive; it does not appear to cluster in galaxies; it was last seen stretching space–time apart; and it goes by the assumed name of "dark energy".
Many theorists already had a suspect in mind: the cosmological constant. It certainly fits the accelerating-expansion scenario. But is the case for dark energy airtight? The existence of gravitationally repulsive dark energy would have dramatic consequences for fundamental physics.
The most conservative suggestions are that the universe is filled with a uniform sea of quantum zero-point energy, or
a condensate of new particles that have a mass that is 10-39 times smaller than that of the electron.
Some researchers have also suggested changes to Einstein's general theory of relativity, such as a new long-range force that moderates the strength of gravity.
But there are shortcomings with even the leading conservative proposals. For instance, the zero-point energy density would have to be precisely tuned to a value that is an unbelievable factor of 10120 below the theoretical prediction. Until recently the supernova data were the only direct evidence for the cosmic acceleration, and the only compelling reason to accept dark energy. Precision measurements of the cosmic microwave background (CMB), including data from the Wilkinson Microwave Anisotropy Probe (WMAP), have recently provided circumstantial evidence for dark energy. The same is true of data from two extensive projects charting the large-scale distribution of galaxies - the Two-Degree Field (2DF) and Sloan Digital Sky Survey (SDSS)now a second witness has testified.
By combining data from WMAP, SDSS and other sources, four independent groups of researchers have reported evidence for a phenomenon known as the integrated Sachs-Wolfe effect. The case for the existence of dark energy has suddenly become a lot more convincing. One of the prime methods for measuring extragalactic distances is to use "standard candles" such as Cepheid variable stars , the total amount of matter in universe - including all the dark matter - accounts for just one-third of the total energy. This has been confirmed by surveys such as the 2DF and SDSS projects, which have mapped the positions and motions of millions of galaxies. But general relativity predicts that there is a precise connection between the expansion and the energy content of the universe. We therefore know that the collective energy density of all the photons, atoms, dark matter and everything else ought to add up to a certain critical value determined by the Hubble constant: ρcritical = 3H02/8π G, where G is the gravitational constant. The snag is that they do not. Mass, energy and the curvature of space-time are intimately related in relativity.
One explanation is therefore that the gap between the critical density and the actual matter density is filled by the equivalent energy density of a large-scale warping of space that is discernable only on scales approaching c/H0 (about 4000 Mpc).
In a universe where the full critical energy density comes from atoms and dark matter only, the weak gravitational potentials on very long length scales - which correspond to gentle waves in the matter density - evolve too slowly to leave a noticeable imprint on the CMB photons., gravitational collapse is slowed by the repulsive dark energy.
Consequently, gravitational potentials grow shallower and photons gain energy as they pass by. Similarly, photons lose energy passing through underdense regions. Negative pressure; to examine this strange property of dark energy it is helpful to introduce a quantity w = pdark/ρdark, where pdark is the mean pressure and ρdark is the density of dark energy in the universe. The rate of change in the cosmic expansion is proportional to -(ρtotal + 3ptotal), where ρtotal is the density of all the matter and energy in the universe and ptotal is the corresponding pressure. To account for the accelerated expansion, however, this quantity must be positive. Since ρtotal is a positive quantity, and the mean pressure due to both ordinary and dark matter is negligible because it is cold or non-relativistic, we arrive at the requirement that 3w x ρdark + ρtotal < 0 for an accelerating expansion. Since ρdark ~ 2/3ρtotal, we find that
w≥-1/2, so the pressure of the dark energy is not just a little negative but a lot negative!
Cartan torsion (The non-Riemannian geometry of macroscopic spin distributions in thermodynamics and ferromagnetism is obtained from the respective partition functions. An expression for the Cartan torsion in terms of the chemical potential is obtained. Analogies with the Einstein-Cartan theory of gravitation are discussed. From the partition function of ferromagnetism a spin-torsion relation analogous to the one obtained in Einstein-Cartan theory is given where piezomagnetic effects are taken into account) contribution to Sachs-Wolfe effect in the inflationary phase of the Universe is discussed. From the COBE data of the microwave anisotropy is possible to compute the spin-density in the Universe as 10^{16} mks units.The spin-density fluctuations at the hadron era (the Big Bang era when the Universe was matter-dominated, containing many hadrons in equilibrium with the radiation field and when kT ≈ mπ. The hadron era ended when the characteristic photon energy fell below the rest mass of a pion or π-meson (270 electron masses), and very few hadrons remained (about one hadron for every 108 photons).) is shown to coincide with the anisotropy temperature fluctuations
A transition from normal hadronic matter (such as protons and neutrons) to quark-gluon matter is expected at both high temperatures and densities. In physical situations, this transition may occur in heavy ion collisions, the early universe, and in the cores of neutron stars. Astrophysics and cosmology can be greatly affected by such a phase transition. With regard to the early universe, big bang nucleosynthesis, the theory describing the primordial origin of the light elements, can be affected by inhomogeneities produced during the transition. A transition to quark matter in the interior by neutron stars further enhances our uncertainties regarding the equation of state of dense nuclear matter and neutron star properties such as the maximum mass and rotation frequencies. Difficulties : higher energy scales
Planck era : ~ 10*77 GeV*4 GUT : ~ 10*64 GeV*4 Electroweak : ~ 10*8 GeV*4 QCD : ~ 10*-4 GeV*4
Puzzle Why rDE is so small ???
Quark-hadron phase transition The standard picture of cosmology assumes that a phase transition (associated with chiral symmetry breaking following the electroweak transition) occurred at approximately after the Big Bang to convert a plasma of free quarks and gluons into hadrons. Although this transition can be of significant cosmological importance, it is not known with certainty whether it is of first order or higher, and what the astrophysical consequences might be on the subsequent state of the Universe. For example, the transition may play a potentially observable role in the generation of primordial magnetic fields. The QCD transition may also give rise to important baryon number inhomogeneities which can affect the distribution of light element abundances from primordial Big Bang nucleosynthesis. The distribution of baryons may be influenced hydrodynamically by the competing effects of phase mixing and phase separation, which arise from any inherent instability of the interface surfaces separating regions of different phase. Unstable modes, if they exist, will distort phase boundaries and induce mixing and diffusive homogenization through hydrodynamic turbulence
In an effort to support and expand theoretical studies, a number of one-dimensional numerical simulations have been carried out to explore the behavior of growing hadron bubbles and decaying quark droplets in simplified and isolated geometries. For example, Rezolla et al. considered a first order phase transition and the nucleation of hadronic bubbles in a supercooled quark-gluon plasma, solving the relativistic Lagrangian equations for disconnected and evaporating quark regions during the final stages of the phase transition. They investigated numerically a single isolated quark drop with an initial radius large enough so that surface effects can be neglected. The droplet evolves as a self-similar solution until it evaporates to a sufficiently small radius that surface effects break the similarity solution and increase the evaporation rate. Their simulations indicate that, in neglecting long-range energy and momentum transfer (by electromagnetically interacting particles) and assuming that baryon number is transported with the hydrodynamical flux, the baryon number concentration is similar to what predicted by chemical equilibrium calculations.
Kurki-Suonio and Laine studied the growth of bubbles and the decay of droplets using a one-dimensional spherically symmetric code that accounts for a phenomenological model of the microscopic entropy generated at the phase transition surface. Incorporating the small scale effects of finite wall width and surface tension, but neglecting entropy and baryon flow through the droplet wall, they simulate the process by which nucleating bubbles grow and evolve to a similarity solution. They also compute the evaporation of quark droplets as they deviate from similarity solutions at late times due to surface tension and wall effects. Ignatius et al. carried out parameter studies of bubble growth for both the QCD and electroweak transitions in planar symmetry, demonstrating that hadron bubbles reach a stationary similarity state after a short time when bubbles grow at constant velocity. They investigated the stationary state using numerical and analytic methods, accounting also for preheating caused by shock fronts.
Figure 1:
Image sequence of the scalar field from a 2D calculation showing the interaction of two deflagration systems (one planar wall propagating from the right side, and one spherical bubble nucleating from the center). The physical size of the grid is set to and resolved by zones. The run time of the simulation is about two sound crossing times, where the sound speed is , so the shock fronts leading the condensing phase fronts travel across the grid twice. The hot quark (cold hadron) phases have smaller (larger) scalar field values and are represented by black (color) in the colormap.
Figure 2:
Image sequence of the scalar field from a 2D calculation showing the interaction of two detonation systems (one planar wall propagating from the right side, and one spherical bubble nucleating from the center). The physical size of the grid is set to and resolved by zones. The run time of the simulation is about two sound crossing times.
Figure 3:
Image sequence of the scalar field from a 2D calculation showing the interaction of shock and rarefaction waves with a deflagration wall (initiated at the left side) and a detonation wall (starting from the right). A shock and rarefaction wave travel to the right and left, respectively, from the temperature discontinuity located initially at the grid center (the right half of the grid is at a higher temperature). The physical size of the domain is set to and resolved by zones. The run time of the simulation is about two sound crossing times.
Fragile and Anninos performed two-dimensional simulations of first order QCD transitions to explore the nature of interface boundaries beyond linear stability analysis, and determine if they are stable when the full nonlinearities of the relativistic scalar field and hydrodynamic system of equations are accounted for. They used results from linear perturbation theory to define initial fluctuations on either side of the phase fronts and evolved the data numerically in time for both deflagration and detonation configurations. No evidence of mixing instabilities or hydrodynamic turbulence was found in any of the cases they considered, despite the fact that they investigated the parameter space predicted to be potentially unstable according to linear analysis. They also investigated whether phase mixing can occur through a turbulence-type mechanism triggered by shock proximity or disruption of phase fronts. They considered three basic cases (see image sequences in Figures 1, 2, and 3 above): interactions between planar and spherical deflagration bubbles, collisions between planar and spherical detonation bubbles, and a third case simulating the interaction between both deflagration and detonation systems initially at two different thermal states. Their results are consistent with the standard picture of cosmological phase transitions in which hadron bubbles expand as spherical condensation fronts, undergoing regular (non-turbulent) coalescence, and eventually leading to collapsing spherical quark droplets in a medium of hadrons. This is generally true even in the detonation cases which are complicated by greater entropy heating from shock interactions contributing to the irregular destruction of hadrons and the creation of quark nuggets.
However, Fragile and Anninos also note a deflagration ‘instability’ or acceleration mechanism evident in their third case for which they assume an initial thermal discontinuity in space separating different regions of nucleating hadron bubbles. The passage of a rarefaction wave (generated at the thermal discontinuity) through a slowly propagating deflagration can significantly accelerate the condensation process, suggesting that the dominant modes of condensation in an early Universe which super-cools at different rates within causally connected domains may be through supersonic detonations or fast moving (nearly sonic) deflagrations. A similar speculation was made by Kamionkowski and Freese who suggested that deflagrations become unstable to perturbations and are converted to detonations by turbulent surface distortion effects. However, in the simulations, deflagrations are accelerated not from turbulent mixing and surface distortion, but from enhanced super-cooling by rarefaction waves. In multi-dimensions, the acceleration mechanism can be exaggerated further by upwind phase mergers due to transverse flow, surface distortion, and mode dissipation effects, a combination that may result in supersonic front propagation speeds, even if the nucleation process began as a slowly propagating deflagration.
The Higgs is Different! All the matter particles are spin-1/2 fermions. All the force carriers are spin-1 bosons.
Higgs particles are spin-0 bosons. The Higgs is neither matter nor force; The Higgs is just different.
This would be the first fundamental scalar ever discovered. The Higgs field is thought to fill the entire universe.
Could give some handle of dark energy(scalar field)? Many modern theories predict other scalar particles like the Higgs.
Why, after all, should the Higgs be the only one of its kind? LHC and ILC can search for new scalars with precision.
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References,
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23 Şubat 2009 Pazartesi
RX1856-3754 NEUTRON STAR
represented by: Ayşe Banu BİRLİK Uludağ University Physics Departmant ; researching Jan, 2001-preparing May,2005
Supervisors; Neşever BALTACI-2001-2005 and M.Ali ALPAR 2001
Title:: AN ISOLATED and PROPELLER NEUTRON STAR RX J1856-3754
ABSTRACT
Comparing on RX J185635-3754 Neutron Star on optical and X-ray for 1° view with other rays taken from satallites and researching on where it borns calculating excess flux of RX J1856 optical flux (49eV) to x-ray blacbody flux (57eV) discussing AXPs ,SGRs, DNTs and RQNSs models for propeller neutron star.Comparing on datas which are taken from the satalites RASS-Cnt Broad,PSPC 2.0 Deg-Inten, Digitized Sky Survey, 1420 MHz (Bonn), GB6 (4850 Mhz), Old PSPC (2 deg), COBE DIRBE, IRAS 12 micron and 100 micron.Where the target (neutron star) was born?Why is the neutron star’s closest to earth and lack of a companion so important to astronomers?Explaning the models for the target in AXP and SGR.Calculation about the difference flux of the target to the x-ray blackbody flux.This is a main question for us; Is this target a magnetar or a propeller neutron star?
INTRODUCTION
DATAS FROM SATALLITES:*RASS-Cnt Broad, PSPC 2.0 Deg-Inten, Old PSPC (2 deg), COBE DIRBE, IRAS 12 micron, IRAS 100 micron,1420 Mhz (Bonn) and GB6 (4850 MHz) are taken at 1° view. RASS-Cnt Broad: X-rays datas from ROSAT satallite. PSPC 2.0 Deg-Inten: X-ray data from ROSAT satallite but the spectrum is diffErent.Old PSPC (2 Deg): X-rays data but Old PSPC’s spectrum is bigger than PSPC 2.0 Digitized Sky Survey: Optical view.COBE DIRBE: Infrared rays.IRAS 12 micron: Toward infrared rays of region which IRAS 100 micron ray parted in 12 and 100 view.420 MHz (BONN): Radio waves.GB6 (4850 MHz): Radio waves but the frequency is different. *RASS-Cnt Broad, PSPC 2.0 Deg-Inten, Old PSPC (2 deg), COBE DIRBE, IRAS 12 micron, IRAS 100 micron,1420 Mhz (Bonn) and GB6 (4850 MHz) are taken at 1° view. *Where does it come from?*(preprint Walter 2000);X J185635-3754 is confirmed to be an isolated neutron star. At a of 61+9 pc, with a heliocentric space velocity of 108+16 km s-1. ıt appears to have left the upper Sco OB association between 0,9 and 1,0 million years ago. It may have been the binary companion of the runaway O star z Oph, which left Upper Sco at the same time. If so, the neutron star suffered a kick velocity of about 200 km s-1 amplitude at birth.Rexamination of the space motions of z Oph and Sco-Cen OB association casts some doubt on van Rensenbergen et al.’s conclusion that z Oph orginated in the Upper-Cen-Lup association. It is not clear how to reconcile their binary evolutionary scenarios with these geometric constaints.The existence of an old, isolated neutron star of known age permits one to place another point on the cooling curve, a point not contaminated by possible non-thermal emission. The exact temperature depends on the choice of atmospheric model, but in any event the luminosity lies near the FP (Friedman & Pandharipande 1981) cooling curve at an age near 1 Myr.The infarred radius of the neutron star depends on the angular diameter, which is model-dependent. The smallest angular diameter for a given temperature is given by a black body. For a temperature kT=49 eV the lower bound on the radius R¥ is 6,0+1,2 km, and preliminary atmospheric models yield R¥ =11.2+3,4 kmRX J185635-3754 will make its closest approach to the Earth in about 280,000 years, at a distance of 52+9 pc, in the constellation Grus Resalba:AXPs sources of pulsed X-ray emission with persitent luminodities Lx ~ 1035-1036 erg/s ans soft spectra.Periods lie a very narrow range,between 6 and 12s.Their charecteristic ages of order 103-105 yr.Corpared to binary X-ray pulsars,AXPs have lower luminosities and exhisits narrow distiribution of periods.Unlike young radio pulsars ,AXPs have rather long periods and appear to be radio quiet.To understanding there differences is to try and identfy the energy source that powers the x-ray emmision. It is quite clear that this energy can’t be provided by rotation (as it is in radio pulsars)For values P* and P that are charecteristics of AXPs the rate of lots of rotational energy is E= 4p2IP/P3 » 1032,5 erg s-1 orders of magnitude smaller than the observed X-ray luminosities.
Researching on its condition ,excess flux ,either it has a companion or not , its age and comparing with
AXPs and SGRs Models of the target - RX J1856-3754
.First One AXPs Models (X-ray emmision)Isolated ultramagnetized with field strengths in the range 1014-105 G.Lose rotational energy similar radio pulsars field strengths consistend for soft gamma repeaters. Magnetars: X-ray luminosities could be powered by magnetic field.Residual thermal energy (if it is correct the envolope of the star must consist light elements such as hyrdogen and helium).The emission is powered by magnetic field deray then a value of B ³ 1016 G is requried unlies nonstandart deray processes are invoked.Second One AXPs Model:X-ray emission is powered by accetion, high values of the magnetic field are not required.Accetion can occur from binary companions of very low mass OR from the interstellar medium.If the emission is powered by accetion from a disrupted binary companion, it is not clear why AXPs should be associated with young supernovea remnats.X-ray luminosity can be explained by cooling without requiring that this neutron star be old and have experienced magnetic field decay.Another accetion model, in which neutron stars accerete from disks that formed from fallback material after a supernovae explossion (by Alpar 1999 and Marsolen at al 1999). The possibility that material might fall back onto a neutron star following a supernovae explosion and settle in a disk is not now (e.g Woosley 1998) suggested that this process might account for the presence of planets around some radio pulsars.Subsequent accretion can occur only under specific circumstencesDepending on relative locations of the magnetospheric radius.The light cylinder radius. Corotation radius related there conditions to physical parametres ,Mitial mass of the disk (Md) İntial period of the neutron star (Po)The strength of the magnetic field B. As to SGR Models: (soft gamma Repetars) The neutron stars are accepted as a magnetar. They are formed like the other neutron stars remain of the explosion of giant stars becoming supernovae.Magnetar stars are special in their high velocities. Their rotating speed is too more, after the explosion the conductive liquid matter inside the star causes 1*1012 Gauss Magnetic Field that makes the star like a dynamo
Rotating Dynamos’s Kınetic Energy:KE=1/2*I*W2(dipolradiation)I*W*W=2/3*B2*R6/c3W4(erg/s) W(rad/s2)=(2/3*R2/c3*I)B2*W3 Rotating dynoma’s energy speed.As to magnetar model; the high magnetic field damages iron crust so in high velocity elemantar particles produces high energy luminosity.On of the SGR identicially observation on a neutron star; while the rotating of the star it gets slow in velocity as 1/1000 ratio in a few years.“Magnetic Breaking” causes the star to be rotating in slowly with producing 8*1011 Gauss in Magnetic Field. As to that model there is a star quake on the extraordinary strength of magnetic field.As to AXP Model (Anomalous X-ray Pulsars):Their brightness of the neutron star is because of the observation of the gass around in gravitational force.That means; while mass is transferring disk around of the star it gets heating and that produces energy.They are alone; have no companion so the disk around of the star is the gass remnant of the supernovae explosion.There is an other AXP model in last years; that is the existance of the rotating heated gass of the mass transffering disk is not necessary for brightness.The getting slow in rotating that is ; slow rotating energy produces lumonisity.For the angular momentum of the small neutron star; it is not enough effective equal mass but big radius stars it can be.Both of the SGR abd AXP common properties:They are the remain of a supernovae.They are alone, they have no companion for transfferring mass.Their rotating period is 5-12 second.Their rotating speed is getting slowly apperantly.They are approximately 20 km. in diameter with dense center after supernovae explosion.As to Duncan; the stars are in different two phase of the same process in AXP and SGR observations.The Age of The Neutron Star In AXP and In SGR:Magnetars can be 104 year in age. At the end of that age temperature decrease the level where the mecanism produces extraordinary magnetic energy. So there is no quake on the crust and no soft gamma ray explosion. After 105 year the star cares the magnetic field that produces regularly X-ray radiation. The end of that age magnetic field gets weak and the star can not be observed.In Milkyway, every 1000 year a magnetar can be observed. So now in Milkyway there must be 107 died magnetar travelling in space.The age of the magnetar is @ W/2W Rotating dynoma energy speed W(rad/s2) = (2/3* R2/c3*I)B2*W3 For radio pulsar which is only known magnetic filed B ~ 1012 Gauss (W,W) B ~ 1012 Gauss There are approximately 1000 radio pulsars. W»10-13 W»10-100 rad/s 1012 Gauss For RX J1856 neutron star W=? W= 2p/P = 2p/8,4 second @ 1 W=? Not known ( age t @ W/2W) can be found(W , t) , B (magnetic field) ,rotation, age,speed dP= dP/dt P~10-15 s.s-1 P=2p/W P= dP/dt = -2p/W2*WSlow W and high W (breaking) B ~ 1015 gauss (magnetic field) Slow W and young age t B ~ 1015 gauss
CALCULATIONS;In mathematically operations by using engtral we can calculate the areas under graphics.The upper line (observed) in between l1-l2 wavelength bands shows total flux from the target (erg/cm2s).= ò A/l4*dl = A/3* (1/l3) = A/3* (1/l3 – 1/l3)The upper line (X-rays for black body line continues) in between l1-l2 wavelength bands shows total flux from a black body. = ò B/l4*dl = B/3* (1/l3 – 1/l3) The difference flux=(observed flux) – (x-rays for black body line continues)The difference flux = (1/l3 – 1/l3)* (A/3 – B/3) = 1/3* (1/l3 – 1/l3)*(l4f1 - l4f1) The difference flux = erg/cm2 s cm Using logaritmic rules for graphics;Excess flux of optical spectral energy distribution flux to x-ray for blackbody energy distribution flux (57eV) [Between F303 HSTU and F606 HSTV] Excess flux= åflux(upper) - åflux(lower)
-15 -15 -15 2 -15 2
Excess flux= 1,56*10 – 0,67*10 Excess flux= 0,89*10 erg/cm.s.cm Excess flux= 0,9*10 erg/cm.scm
CONCLUSIONS: Keywords; equilibrium periods magnetic fields and mass age.Properties of (DNTs) (dim isolated thermal neutron stars)Common mechanism with an asymptotic spindown phase extending through the propeller and early accretion stage.They are interpreted as sources in the propeller stage.Their luminosities arise from frictional heating in the neutron star. Rotation period is close to its rotational equilibrium period. Propeller torque indicates a magnetic field in the 1012 Gauss range . The mass inflow rate onto the propeller is of the order of the accretion rates of the AXPs (by Chatterkee,Hernquist&Narayan 1999)The limited range of rotation periods. Taken to be close to equilibrium periods, and conventional magnetic fields in the range 5*1011 – 5*1012 Gauss.Range of mass inflow rates3,2*1014 g/s < M < 4,2*1017 g/s.Those neutron stars do not become radio pulsars.Highest mass inflow rates the propeller action may support enough circumstellar material so that the optical thickness to electron scattering destroys the X-ray beaming, and the rotation period is not observable. These are radio quiet neutron stars (RQNSs) at the centers of supernovae remnants. RQNSs are at the highest mass inflow rate, these are propellers whose pulse periods are not observable because of accumulated circumstellar material that is optically thick to electron scattering.DNTs fits to balckbody with tempeature 57eV and 79eV and luminosities in the Lx ~1031-32 erg/s range and similiar blackbody tempeatures flux values and limits on the radio of x-ray flux to optical flux and ages ~106 years are or longer.Thermal luminosity which takes over at ~105~106 years after the intial cooling and losts longer than the cooling luminosity. There will be energy dissipation (frictional heating) in a neutron star being spun down by some external torque. The rate of energy dissiptaion is given by (Alpar at al.1984, Alpar, Nandkumar&Pines 1985)Ediss will supply the termal luminosity of a non-accreting nutron star at ages greater than ~106 years.Between DNTs,AXPs and SGRs, AXP spindown takes actually sugsut that the DTN spindown rate may be closer to W~W-12 rad/sn-2. are there spindown mechanisms that will give high spindown rates, larger than 10-12 rad s-2with 1012 G magnetic fields typical of the canonical radio pulsars and of the accreting neutron stars wth observed cyclotron lines? Propeller spindown with high spindown rates larger than 10-12 rad/s2 can indeed be expected for neutron stars eith conventinal 1012 Gauss fields under the typical spindown torques for certain phases of accreting sources Propeller torques depend on the magnetic moment of the neutron star and on the rate of mass in flow
SOURCES: 1)Alpar Ali.M, preprint astro-ph/0005211“The lives of the neutron stars2)Ögalman H. ed. Alpar Ali.M, Kızıloğlu Ü. and Paradijs Van.J. Publishing House: Kluwer 1995Page: 101”3).Neuhäuser R. preprint astroa-ph/0102004 1 Feb. 2000 4).Perna R. , Hemquist L. and Narayan R. Review name: astrophysical JournelBinding: 541:344-350 Pages: 344-501 October 2000 5)Walter Frederich M. preprint astroa-ph/0009031“The proper motion, parallax and origin of the isolated neutron star RX J1856-3754” 6). Web Adress;Legacy.gsfc.nasa.gov Astroa.physics.metu.edu.tr.html Copernic 2000 (search RX J1856-3754). 7)Sabancı University in Istanbul. Alpar Ali.M.–2001 8)Yerli Sinan.K.- Middle East Technical University 9)Supervisor Physics Teacher, Baltacı Neşever-2001-2005
Supervisors; Neşever BALTACI-2001-2005 and M.Ali ALPAR 2001
Title:: AN ISOLATED and PROPELLER NEUTRON STAR RX J1856-3754
ABSTRACT
Comparing on RX J185635-3754 Neutron Star on optical and X-ray for 1° view with other rays taken from satallites and researching on where it borns calculating excess flux of RX J1856 optical flux (49eV) to x-ray blacbody flux (57eV) discussing AXPs ,SGRs, DNTs and RQNSs models for propeller neutron star.Comparing on datas which are taken from the satalites RASS-Cnt Broad,PSPC 2.0 Deg-Inten, Digitized Sky Survey, 1420 MHz (Bonn), GB6 (4850 Mhz), Old PSPC (2 deg), COBE DIRBE, IRAS 12 micron and 100 micron.Where the target (neutron star) was born?Why is the neutron star’s closest to earth and lack of a companion so important to astronomers?Explaning the models for the target in AXP and SGR.Calculation about the difference flux of the target to the x-ray blackbody flux.This is a main question for us; Is this target a magnetar or a propeller neutron star?
INTRODUCTION
DATAS FROM SATALLITES:*RASS-Cnt Broad, PSPC 2.0 Deg-Inten, Old PSPC (2 deg), COBE DIRBE, IRAS 12 micron, IRAS 100 micron,1420 Mhz (Bonn) and GB6 (4850 MHz) are taken at 1° view. RASS-Cnt Broad: X-rays datas from ROSAT satallite. PSPC 2.0 Deg-Inten: X-ray data from ROSAT satallite but the spectrum is diffErent.Old PSPC (2 Deg): X-rays data but Old PSPC’s spectrum is bigger than PSPC 2.0 Digitized Sky Survey: Optical view.COBE DIRBE: Infrared rays.IRAS 12 micron: Toward infrared rays of region which IRAS 100 micron ray parted in 12 and 100 view.420 MHz (BONN): Radio waves.GB6 (4850 MHz): Radio waves but the frequency is different. *RASS-Cnt Broad, PSPC 2.0 Deg-Inten, Old PSPC (2 deg), COBE DIRBE, IRAS 12 micron, IRAS 100 micron,1420 Mhz (Bonn) and GB6 (4850 MHz) are taken at 1° view. *Where does it come from?*(preprint Walter 2000);X J185635-3754 is confirmed to be an isolated neutron star. At a of 61+9 pc, with a heliocentric space velocity of 108+16 km s-1. ıt appears to have left the upper Sco OB association between 0,9 and 1,0 million years ago. It may have been the binary companion of the runaway O star z Oph, which left Upper Sco at the same time. If so, the neutron star suffered a kick velocity of about 200 km s-1 amplitude at birth.Rexamination of the space motions of z Oph and Sco-Cen OB association casts some doubt on van Rensenbergen et al.’s conclusion that z Oph orginated in the Upper-Cen-Lup association. It is not clear how to reconcile their binary evolutionary scenarios with these geometric constaints.The existence of an old, isolated neutron star of known age permits one to place another point on the cooling curve, a point not contaminated by possible non-thermal emission. The exact temperature depends on the choice of atmospheric model, but in any event the luminosity lies near the FP (Friedman & Pandharipande 1981) cooling curve at an age near 1 Myr.The infarred radius of the neutron star depends on the angular diameter, which is model-dependent. The smallest angular diameter for a given temperature is given by a black body. For a temperature kT=49 eV the lower bound on the radius R¥ is 6,0+1,2 km, and preliminary atmospheric models yield R¥ =11.2+3,4 kmRX J185635-3754 will make its closest approach to the Earth in about 280,000 years, at a distance of 52+9 pc, in the constellation Grus Resalba:AXPs sources of pulsed X-ray emission with persitent luminodities Lx ~ 1035-1036 erg/s ans soft spectra.Periods lie a very narrow range,between 6 and 12s.Their charecteristic ages of order 103-105 yr.Corpared to binary X-ray pulsars,AXPs have lower luminosities and exhisits narrow distiribution of periods.Unlike young radio pulsars ,AXPs have rather long periods and appear to be radio quiet.To understanding there differences is to try and identfy the energy source that powers the x-ray emmision. It is quite clear that this energy can’t be provided by rotation (as it is in radio pulsars)For values P* and P that are charecteristics of AXPs the rate of lots of rotational energy is E= 4p2IP/P3 » 1032,5 erg s-1 orders of magnitude smaller than the observed X-ray luminosities.
Researching on its condition ,excess flux ,either it has a companion or not , its age and comparing with
AXPs and SGRs Models of the target - RX J1856-3754
.First One AXPs Models (X-ray emmision)Isolated ultramagnetized with field strengths in the range 1014-105 G.Lose rotational energy similar radio pulsars field strengths consistend for soft gamma repeaters. Magnetars: X-ray luminosities could be powered by magnetic field.Residual thermal energy (if it is correct the envolope of the star must consist light elements such as hyrdogen and helium).The emission is powered by magnetic field deray then a value of B ³ 1016 G is requried unlies nonstandart deray processes are invoked.Second One AXPs Model:X-ray emission is powered by accetion, high values of the magnetic field are not required.Accetion can occur from binary companions of very low mass OR from the interstellar medium.If the emission is powered by accetion from a disrupted binary companion, it is not clear why AXPs should be associated with young supernovea remnats.X-ray luminosity can be explained by cooling without requiring that this neutron star be old and have experienced magnetic field decay.Another accetion model, in which neutron stars accerete from disks that formed from fallback material after a supernovae explossion (by Alpar 1999 and Marsolen at al 1999). The possibility that material might fall back onto a neutron star following a supernovae explosion and settle in a disk is not now (e.g Woosley 1998) suggested that this process might account for the presence of planets around some radio pulsars.Subsequent accretion can occur only under specific circumstencesDepending on relative locations of the magnetospheric radius.The light cylinder radius. Corotation radius related there conditions to physical parametres ,Mitial mass of the disk (Md) İntial period of the neutron star (Po)The strength of the magnetic field B. As to SGR Models: (soft gamma Repetars) The neutron stars are accepted as a magnetar. They are formed like the other neutron stars remain of the explosion of giant stars becoming supernovae.Magnetar stars are special in their high velocities. Their rotating speed is too more, after the explosion the conductive liquid matter inside the star causes 1*1012 Gauss Magnetic Field that makes the star like a dynamo
Rotating Dynamos’s Kınetic Energy:KE=1/2*I*W2(dipolradiation)I*W*W=2/3*B2*R6/c3W4(erg/s) W(rad/s2)=(2/3*R2/c3*I)B2*W3 Rotating dynoma’s energy speed.As to magnetar model; the high magnetic field damages iron crust so in high velocity elemantar particles produces high energy luminosity.On of the SGR identicially observation on a neutron star; while the rotating of the star it gets slow in velocity as 1/1000 ratio in a few years.“Magnetic Breaking” causes the star to be rotating in slowly with producing 8*1011 Gauss in Magnetic Field. As to that model there is a star quake on the extraordinary strength of magnetic field.As to AXP Model (Anomalous X-ray Pulsars):Their brightness of the neutron star is because of the observation of the gass around in gravitational force.That means; while mass is transferring disk around of the star it gets heating and that produces energy.They are alone; have no companion so the disk around of the star is the gass remnant of the supernovae explosion.There is an other AXP model in last years; that is the existance of the rotating heated gass of the mass transffering disk is not necessary for brightness.The getting slow in rotating that is ; slow rotating energy produces lumonisity.For the angular momentum of the small neutron star; it is not enough effective equal mass but big radius stars it can be.Both of the SGR abd AXP common properties:They are the remain of a supernovae.They are alone, they have no companion for transfferring mass.Their rotating period is 5-12 second.Their rotating speed is getting slowly apperantly.They are approximately 20 km. in diameter with dense center after supernovae explosion.As to Duncan; the stars are in different two phase of the same process in AXP and SGR observations.The Age of The Neutron Star In AXP and In SGR:Magnetars can be 104 year in age. At the end of that age temperature decrease the level where the mecanism produces extraordinary magnetic energy. So there is no quake on the crust and no soft gamma ray explosion. After 105 year the star cares the magnetic field that produces regularly X-ray radiation. The end of that age magnetic field gets weak and the star can not be observed.In Milkyway, every 1000 year a magnetar can be observed. So now in Milkyway there must be 107 died magnetar travelling in space.The age of the magnetar is @ W/2W Rotating dynoma energy speed W(rad/s2) = (2/3* R2/c3*I)B2*W3 For radio pulsar which is only known magnetic filed B ~ 1012 Gauss (W,W) B ~ 1012 Gauss There are approximately 1000 radio pulsars. W»10-13 W»10-100 rad/s 1012 Gauss For RX J1856 neutron star W=? W= 2p/P = 2p/8,4 second @ 1 W=? Not known ( age t @ W/2W) can be found(W , t) , B (magnetic field) ,rotation, age,speed dP= dP/dt P~10-15 s.s-1 P=2p/W P= dP/dt = -2p/W2*WSlow W and high W (breaking) B ~ 1015 gauss (magnetic field) Slow W and young age t B ~ 1015 gauss
CALCULATIONS;In mathematically operations by using engtral we can calculate the areas under graphics.The upper line (observed) in between l1-l2 wavelength bands shows total flux from the target (erg/cm2s).= ò A/l4*dl = A/3* (1/l3) = A/3* (1/l3 – 1/l3)The upper line (X-rays for black body line continues) in between l1-l2 wavelength bands shows total flux from a black body. = ò B/l4*dl = B/3* (1/l3 – 1/l3) The difference flux=(observed flux) – (x-rays for black body line continues)The difference flux = (1/l3 – 1/l3)* (A/3 – B/3) = 1/3* (1/l3 – 1/l3)*(l4f1 - l4f1) The difference flux = erg/cm2 s cm Using logaritmic rules for graphics;Excess flux of optical spectral energy distribution flux to x-ray for blackbody energy distribution flux (57eV) [Between F303 HSTU and F606 HSTV] Excess flux= åflux(upper) - åflux(lower)
-15 -15 -15 2 -15 2
Excess flux= 1,56*10 – 0,67*10 Excess flux= 0,89*10 erg/cm.s.cm Excess flux= 0,9*10 erg/cm.scm
CONCLUSIONS: Keywords; equilibrium periods magnetic fields and mass age.Properties of (DNTs) (dim isolated thermal neutron stars)Common mechanism with an asymptotic spindown phase extending through the propeller and early accretion stage.They are interpreted as sources in the propeller stage.Their luminosities arise from frictional heating in the neutron star. Rotation period is close to its rotational equilibrium period. Propeller torque indicates a magnetic field in the 1012 Gauss range . The mass inflow rate onto the propeller is of the order of the accretion rates of the AXPs (by Chatterkee,Hernquist&Narayan 1999)The limited range of rotation periods. Taken to be close to equilibrium periods, and conventional magnetic fields in the range 5*1011 – 5*1012 Gauss.Range of mass inflow rates3,2*1014 g/s < M < 4,2*1017 g/s.Those neutron stars do not become radio pulsars.Highest mass inflow rates the propeller action may support enough circumstellar material so that the optical thickness to electron scattering destroys the X-ray beaming, and the rotation period is not observable. These are radio quiet neutron stars (RQNSs) at the centers of supernovae remnants. RQNSs are at the highest mass inflow rate, these are propellers whose pulse periods are not observable because of accumulated circumstellar material that is optically thick to electron scattering.DNTs fits to balckbody with tempeature 57eV and 79eV and luminosities in the Lx ~1031-32 erg/s range and similiar blackbody tempeatures flux values and limits on the radio of x-ray flux to optical flux and ages ~106 years are or longer.Thermal luminosity which takes over at ~105~106 years after the intial cooling and losts longer than the cooling luminosity. There will be energy dissipation (frictional heating) in a neutron star being spun down by some external torque. The rate of energy dissiptaion is given by (Alpar at al.1984, Alpar, Nandkumar&Pines 1985)Ediss will supply the termal luminosity of a non-accreting nutron star at ages greater than ~106 years.Between DNTs,AXPs and SGRs, AXP spindown takes actually sugsut that the DTN spindown rate may be closer to W~W-12 rad/sn-2. are there spindown mechanisms that will give high spindown rates, larger than 10-12 rad s-2with 1012 G magnetic fields typical of the canonical radio pulsars and of the accreting neutron stars wth observed cyclotron lines? Propeller spindown with high spindown rates larger than 10-12 rad/s2 can indeed be expected for neutron stars eith conventinal 1012 Gauss fields under the typical spindown torques for certain phases of accreting sources Propeller torques depend on the magnetic moment of the neutron star and on the rate of mass in flow
SOURCES: 1)Alpar Ali.M, preprint astro-ph/0005211“The lives of the neutron stars2)Ögalman H. ed. Alpar Ali.M, Kızıloğlu Ü. and Paradijs Van.J. Publishing House: Kluwer 1995Page: 101”3).Neuhäuser R. preprint astroa-ph/0102004 1 Feb. 2000 4).Perna R. , Hemquist L. and Narayan R. Review name: astrophysical JournelBinding: 541:344-350 Pages: 344-501 October 2000 5)Walter Frederich M. preprint astroa-ph/0009031“The proper motion, parallax and origin of the isolated neutron star RX J1856-3754” 6). Web Adress;Legacy.gsfc.nasa.gov Astroa.physics.metu.edu.tr.html Copernic 2000 (search RX J1856-3754). 7)Sabancı University in Istanbul. Alpar Ali.M.–2001 8)Yerli Sinan.K.- Middle East Technical University 9)Supervisor Physics Teacher, Baltacı Neşever-2001-2005
Saros cycle and eclipces
SAROS CYCLE AND ECLIPCES
Neşever BALTACI1
1 Ümraniye Anadolu İ.H.ve İ.H.Lisesi-İstanbul, e-posta: nesever@yahoo.com
SUMMARYMonth (new Synodic moon to new moon) 29.53059 days = 29d 12h 44mDraconic Month (node to node) 27.21222 days = 27d 05h 06mAnomalistic Month (perigee to perigee) 27.55455 days = 27d 13h 19m
One saros is equal to 223 synodic months. However, 242 draconic months and 239 anomalistic months are also equal to this same period (to within a couple hours)!
Any two eclipses separated by one saros cycle share very similar geometries. They occur at the same node with the Moon at nearly the same distance from Earth and at the same time of year. Because the saros period is not equal to a whole number of days, its biggest drawback is that subsequent eclipses are visible from different parts of the globe. The extra 1/3 day displacement means that Earth must rotate an additional ~8 hours or ~120º with each cycle. For solar eclipses, this results in the shifting of each successive eclipse path by ~120º westward. Thus, a saros series returns to about the same geographic region every 3 saroses (54 years and 34 days).
A saros series doesn't last indefinitely because the three lunar months are not perfectly commensurate with one another. In particular, the Moon's node shifts eastward by about 0.5º with each cycle. A typical saros series for a solar eclipse begins when new Moon occurs ~18° east of a node. If the first eclipse occurs at the Moon's descending node, the Moon's umbral shadow will pass ~3500 km below Earth and a partial eclipse will be visible from the south polar region. On the following return, the umbra will pass ~300 km closer to Earth and a partial eclipse of slightly larger magnitude will result. After ten or eleven saros cycles (about 200 years), the first central eclipse will occur near the south pole of Earth. Over the course of the next 950 years, a central eclipse occurs every 18.031 years (= saros) but will be displaced northward by an average of ~300 km. Halfway through this period, eclipses of long duration will occur near the equator. The last central eclipse of the series occurs near the north pole. The next approximately ten eclipses will be partial with successively smaller magnitudes. Finally, the saros series will end a dozen or more centuries after it began at the opposite pole. Due to the ellipticity of the orbits of the Earth and Moon, the exact duration and number of eclipses in a complete saros is not constant. A series may last 1226 to 1550 years and is comprised of 69 to 87 eclipses, of which about 40 to 60 are central (i.e. - total or annular). Since there are two to five solar eclipses every year, there are approximately forty different saros series in progress at any one time. For instance, during the later half of the twentieth century, there are 41 individual series and 26 of them are producing central eclipses. As old series terminate, new ones are beginning and take their places.To illustrate, the ten central solar eclipses of 1891, 1909, 1927, 1945, 1963, 1981, 1999, 2017, 2035 and 2053 are all members of Saros 145. The series began with a partial eclipse near the north pole in 1639. The first central eclipse of the series was an annular eclipse in 1891. It was followed by another annular in 1909. The next event was the first total eclipse in 1927. The total solar eclipse of 1999 August 11 is number 21 of 77 eclipses in Saros 145, and it is the 5th of 41 total eclipses in the series. Each of the subsequent total eclipses shifts southwards. The last total eclipse occurs in 2648 near the south pole. The last eclipse of the series takes place in 3009. Table of Saros 145 gives details for every eclipse in the series
Solar eclipses that take place near the Moon's ascending node have odd saros numbers. Each succeeding eclipse in a series shifts progressively southward with respect to the center of the Earth. On the other hand, solar eclipses occurring near the Moon's descending node have even saros numbers. Each succeeding eclipse in a series shifts progressively northward with respect to the center of the Earth. The numbering system used for the saros series was introduced by the Dutch Astronomer G. van den Bergh in his book Periodicity and Variation of Solar (and Lunar) Eclipses (Tjeenk Willink, Haarlem, Netherlands, 1955). He assigned the number 1 to a pair of solar and lunar eclipse series that were in progress during the second millennium BC.
Neşever BALTACI1
1 Ümraniye Anadolu İ.H.ve İ.H.Lisesi-İstanbul, e-posta: nesever@yahoo.com
SUMMARYMonth (new Synodic moon to new moon) 29.53059 days = 29d 12h 44mDraconic Month (node to node) 27.21222 days = 27d 05h 06mAnomalistic Month (perigee to perigee) 27.55455 days = 27d 13h 19m
One saros is equal to 223 synodic months. However, 242 draconic months and 239 anomalistic months are also equal to this same period (to within a couple hours)!
Any two eclipses separated by one saros cycle share very similar geometries. They occur at the same node with the Moon at nearly the same distance from Earth and at the same time of year. Because the saros period is not equal to a whole number of days, its biggest drawback is that subsequent eclipses are visible from different parts of the globe. The extra 1/3 day displacement means that Earth must rotate an additional ~8 hours or ~120º with each cycle. For solar eclipses, this results in the shifting of each successive eclipse path by ~120º westward. Thus, a saros series returns to about the same geographic region every 3 saroses (54 years and 34 days).
A saros series doesn't last indefinitely because the three lunar months are not perfectly commensurate with one another. In particular, the Moon's node shifts eastward by about 0.5º with each cycle. A typical saros series for a solar eclipse begins when new Moon occurs ~18° east of a node. If the first eclipse occurs at the Moon's descending node, the Moon's umbral shadow will pass ~3500 km below Earth and a partial eclipse will be visible from the south polar region. On the following return, the umbra will pass ~300 km closer to Earth and a partial eclipse of slightly larger magnitude will result. After ten or eleven saros cycles (about 200 years), the first central eclipse will occur near the south pole of Earth. Over the course of the next 950 years, a central eclipse occurs every 18.031 years (= saros) but will be displaced northward by an average of ~300 km. Halfway through this period, eclipses of long duration will occur near the equator. The last central eclipse of the series occurs near the north pole. The next approximately ten eclipses will be partial with successively smaller magnitudes. Finally, the saros series will end a dozen or more centuries after it began at the opposite pole. Due to the ellipticity of the orbits of the Earth and Moon, the exact duration and number of eclipses in a complete saros is not constant. A series may last 1226 to 1550 years and is comprised of 69 to 87 eclipses, of which about 40 to 60 are central (i.e. - total or annular). Since there are two to five solar eclipses every year, there are approximately forty different saros series in progress at any one time. For instance, during the later half of the twentieth century, there are 41 individual series and 26 of them are producing central eclipses. As old series terminate, new ones are beginning and take their places.To illustrate, the ten central solar eclipses of 1891, 1909, 1927, 1945, 1963, 1981, 1999, 2017, 2035 and 2053 are all members of Saros 145. The series began with a partial eclipse near the north pole in 1639. The first central eclipse of the series was an annular eclipse in 1891. It was followed by another annular in 1909. The next event was the first total eclipse in 1927. The total solar eclipse of 1999 August 11 is number 21 of 77 eclipses in Saros 145, and it is the 5th of 41 total eclipses in the series. Each of the subsequent total eclipses shifts southwards. The last total eclipse occurs in 2648 near the south pole. The last eclipse of the series takes place in 3009. Table of Saros 145 gives details for every eclipse in the series
Solar eclipses that take place near the Moon's ascending node have odd saros numbers. Each succeeding eclipse in a series shifts progressively southward with respect to the center of the Earth. On the other hand, solar eclipses occurring near the Moon's descending node have even saros numbers. Each succeeding eclipse in a series shifts progressively northward with respect to the center of the Earth. The numbering system used for the saros series was introduced by the Dutch Astronomer G. van den Bergh in his book Periodicity and Variation of Solar (and Lunar) Eclipses (Tjeenk Willink, Haarlem, Netherlands, 1955). He assigned the number 1 to a pair of solar and lunar eclipse series that were in progress during the second millennium BC.
calculating distance of SN 1987A
CALCULATING DISTANCE of SN1987A
Neşever BALTACI
Ozel Kultur Science High School,Astronomy and Physics Supervisor Teacher-
Physics Teacher in Umraniye Anatolia I.H.High School-Istanbul/Turkiye
nesever@yahoo.com
SUMMARY
Views which are taken by Hubble telescop, ESA – ESO at Feb, 1994 for SN 1987A are used for calculating the distance(D) of SN1987A to Earth .Calculations are done for appear diameter ,inclination angle and period from the light curves on milimetric papers by using mathematical toolkit inversions.It’s found outside of the ringD = 57,63 kpc inside of the ring D = 68,59 kpc average of distances:D= 63,11 kpc
A ) Calculating from outer part of the ring
1.Step by using mm graphic paper on the image
distance ( mm ) distance( arcs ) ratio ( arcs / mm ) avarage ratio ( arcs / mm)
2. star to 1. star 89 3,0 0,03371
3. star to 1. star 50 1,4 0,02800 0,03111
3. star to 2. star 136 4,3 0,003162
2.Step
Appear diameter (a)= 51 mm
a = ( 51 mm ) . ( 0,03111 arcs / mm ) . ( 4,848 . 10-6 rad / arcs )
a = 4,848 . 10-6 rad / arcs
a = 7,6915 . 10-6 rad
3.Step cos i = near side / hypothenous so;
cos i = small axis/ big axis
cos i = 37 mm / 51 mm
= 0,7591 rad = >
i= 43,49 degree
4.Step by using light –time graph that is given
the day that first light is taken: t1=85,36 days
the day that max light is taken : t2 =451,21 day t= t2 – t1
t1 = 85,36 days t2= 451,21 t= 451,21 – 85,36 = >
t = 365,85 days
5.Step
sin i = dp / d => d = dp / ( sin i )
c = light speed( 2,977 . 10 8 m/s )
t = day ( 365,85 . 24 . 60 . 60 ) = 31609440 seconds
dp = c.t d = dp / (sin i ) = ( c.t ) / ( sin i )
d=( 2,977 . 108) . ( 365,85 . 24 . 60 . 60 ) / sin ( 43,49 )
d = ( 2977 . 105) . ( 31609440 ) / ( sin 42,63 )
d = 9,41013028815 / 0,68822 . 10-1 =>
(in meters) d = 13,673143 . 1016
6.Step
D = d / a
D = 13,673143 . 1016 / 7,6915 . 10-6
D = 1,7776 . 1022 m = 1,7776 . 1019 km
D = 1,7776 . 1019 / 3,084 . 1013
D = 57,63 kpc
B) Calculating from inner part of the ring
1.Step
distance ( mm ) distance( arcs ) ratio ( arcs / mm ) average ratio( arcs / mm)
2. star to 1.star 83 3,0 0,0361
3. star to 1.star 47 1,4 0,0297 0,0331
3. star to 2. star 128 4,3 0,0335
2.Step
Appear diameter:(a) = 42 mm a = (42 mm ) . ( 0,0331 arcs / mm ) . ( 4,848 . 10-6 rad / arcs )
(in radian) a = 6,7396 . 10-6
3.Step cos i = near side / hypothenous so;
cos i = small axis / big axis
cos i = 31 mm / 43 mm
= 0,0809 rad
i = 41,30 degree
4.Step
the first days that light is taken: 85,36 days
the days that max. light is taken : 451,21 days
t=t2 – t1 t t1 = 85,36 days t2 = 451,21 days
t= 451,21 – 85,36
t = 365,85 days
5 .Step c = speed of light ( 2,977 . 10 8 m/s )
t = day ( 365,85 . 24 . 60 . 60 ) = 31609440seconds
sin i = dp / d => d = dp / ( sin i )
dp = c.t
d = dp / (sin i ) = ( c.t ) / ( sin i )
d = ( 2,977 . 108) . ( 365,85 . 24 . 60 . 60 ) / sin ( 41,30 )
d = ( 2977 . 105) . ( 31609440 ) / ( sin 41,30 )
d = 9,41013028815 / 0,660001
d = 14,25775756 . 1017 m
6.Step D = d / a
D = 14,25775756 . 1017 / 6,7396 . 10-6
D = 21,1551 . 1024 m = 21,1551 . 1021 km
D= 21,1551 . 1021 / 3,084 . 1013
D = 68,59 kpc
CONCULATION:
Distance of SN 1987A to Earth is calculated as 68,59kpc and 57,63 kpc
so the average of two results is taken DISTANCE=63,11 kpc
SOURCES:
• Fransson, C.; Cassatella, A.; Gilmozzi, R.; Kirshner, R. P.; Panagia, N.; Sonneborn, G.; Wamsteker, W.., 1989, Ap.J., 336, 429-441: Narrow ultraviolet emission lines from SN 1987A - Evidence for CNO processing in the progenitor - PDF FILE (ADS - 2.1 MB) - PDF FILE (LOCAL - 2.1 MB).
• Gould, A., 1994, Ap.J., 425, 51-56: The ring around supernova 1987A revisited. 1: Ellipticity of the ring - PDF FILE (ADS - 1.0MB) - PDF FILE (LOCAL - 1.0 MB).
• Panagia, N., Gilmozzi, R., Macchetto, F., Adorf, H.M., Kirshner, R.P. 1991, Ap.J., 380, L23-L26: Properties of the SN 1987A circumstellar ring and the distance to the Large Magellanic Cloud - PDF FILE (ADS - 0.8 MB) - PDF FILE (LOCAL - 0.8MB).
• Jakobsen, P., Albrecht, R., Barbieri, C., Blades, J. C., Boksenberg, A., Crane, P., Deharveng, J. M.,Disney, M. J., Kamperman, T. M., King, I. R., Macchetto, F., Mackay, C. D., Paresce, F., Weigelt, G., Baxter, D., Greenfield, P., Jedrzejewski, R., Nota, A., Sparks, W. B., Kirshner, R. P., Panagia, N., 1991, ApJ, 369, L63-L66: First results from the Faint Object Camera - SN 1987A - PDF FILE (ADS - 1.0MB) - PDF FILE (LOCAL - 1.0 MB).
Neşever BALTACI
Ozel Kultur Science High School,Astronomy and Physics Supervisor Teacher-
Physics Teacher in Umraniye Anatolia I.H.High School-Istanbul/Turkiye
nesever@yahoo.com
SUMMARY
Views which are taken by Hubble telescop, ESA – ESO at Feb, 1994 for SN 1987A are used for calculating the distance(D) of SN1987A to Earth .Calculations are done for appear diameter ,inclination angle and period from the light curves on milimetric papers by using mathematical toolkit inversions.It’s found outside of the ringD = 57,63 kpc inside of the ring D = 68,59 kpc average of distances:D= 63,11 kpc
A ) Calculating from outer part of the ring
1.Step by using mm graphic paper on the image
distance ( mm ) distance( arcs ) ratio ( arcs / mm ) avarage ratio ( arcs / mm)
2. star to 1. star 89 3,0 0,03371
3. star to 1. star 50 1,4 0,02800 0,03111
3. star to 2. star 136 4,3 0,003162
2.Step
Appear diameter (a)= 51 mm
a = ( 51 mm ) . ( 0,03111 arcs / mm ) . ( 4,848 . 10-6 rad / arcs )
a = 4,848 . 10-6 rad / arcs
a = 7,6915 . 10-6 rad
3.Step cos i = near side / hypothenous so;
cos i = small axis/ big axis
cos i = 37 mm / 51 mm
= 0,7591 rad = >
i= 43,49 degree
4.Step by using light –time graph that is given
the day that first light is taken: t1=85,36 days
the day that max light is taken : t2 =451,21 day t= t2 – t1
t1 = 85,36 days t2= 451,21 t= 451,21 – 85,36 = >
t = 365,85 days
5.Step
sin i = dp / d => d = dp / ( sin i )
c = light speed( 2,977 . 10 8 m/s )
t = day ( 365,85 . 24 . 60 . 60 ) = 31609440 seconds
dp = c.t d = dp / (sin i ) = ( c.t ) / ( sin i )
d=( 2,977 . 108) . ( 365,85 . 24 . 60 . 60 ) / sin ( 43,49 )
d = ( 2977 . 105) . ( 31609440 ) / ( sin 42,63 )
d = 9,41013028815 / 0,68822 . 10-1 =>
(in meters) d = 13,673143 . 1016
6.Step
D = d / a
D = 13,673143 . 1016 / 7,6915 . 10-6
D = 1,7776 . 1022 m = 1,7776 . 1019 km
D = 1,7776 . 1019 / 3,084 . 1013
D = 57,63 kpc
B) Calculating from inner part of the ring
1.Step
distance ( mm ) distance( arcs ) ratio ( arcs / mm ) average ratio( arcs / mm)
2. star to 1.star 83 3,0 0,0361
3. star to 1.star 47 1,4 0,0297 0,0331
3. star to 2. star 128 4,3 0,0335
2.Step
Appear diameter:(a) = 42 mm a = (42 mm ) . ( 0,0331 arcs / mm ) . ( 4,848 . 10-6 rad / arcs )
(in radian) a = 6,7396 . 10-6
3.Step cos i = near side / hypothenous so;
cos i = small axis / big axis
cos i = 31 mm / 43 mm
= 0,0809 rad
i = 41,30 degree
4.Step
the first days that light is taken: 85,36 days
the days that max. light is taken : 451,21 days
t=t2 – t1 t t1 = 85,36 days t2 = 451,21 days
t= 451,21 – 85,36
t = 365,85 days
5 .Step c = speed of light ( 2,977 . 10 8 m/s )
t = day ( 365,85 . 24 . 60 . 60 ) = 31609440seconds
sin i = dp / d => d = dp / ( sin i )
dp = c.t
d = dp / (sin i ) = ( c.t ) / ( sin i )
d = ( 2,977 . 108) . ( 365,85 . 24 . 60 . 60 ) / sin ( 41,30 )
d = ( 2977 . 105) . ( 31609440 ) / ( sin 41,30 )
d = 9,41013028815 / 0,660001
d = 14,25775756 . 1017 m
6.Step D = d / a
D = 14,25775756 . 1017 / 6,7396 . 10-6
D = 21,1551 . 1024 m = 21,1551 . 1021 km
D= 21,1551 . 1021 / 3,084 . 1013
D = 68,59 kpc
CONCULATION:
Distance of SN 1987A to Earth is calculated as 68,59kpc and 57,63 kpc
so the average of two results is taken DISTANCE=63,11 kpc
SOURCES:
• Fransson, C.; Cassatella, A.; Gilmozzi, R.; Kirshner, R. P.; Panagia, N.; Sonneborn, G.; Wamsteker, W.., 1989, Ap.J., 336, 429-441: Narrow ultraviolet emission lines from SN 1987A - Evidence for CNO processing in the progenitor - PDF FILE (ADS - 2.1 MB) - PDF FILE (LOCAL - 2.1 MB).
• Gould, A., 1994, Ap.J., 425, 51-56: The ring around supernova 1987A revisited. 1: Ellipticity of the ring - PDF FILE (ADS - 1.0MB) - PDF FILE (LOCAL - 1.0 MB).
• Panagia, N., Gilmozzi, R., Macchetto, F., Adorf, H.M., Kirshner, R.P. 1991, Ap.J., 380, L23-L26: Properties of the SN 1987A circumstellar ring and the distance to the Large Magellanic Cloud - PDF FILE (ADS - 0.8 MB) - PDF FILE (LOCAL - 0.8MB).
• Jakobsen, P., Albrecht, R., Barbieri, C., Blades, J. C., Boksenberg, A., Crane, P., Deharveng, J. M.,Disney, M. J., Kamperman, T. M., King, I. R., Macchetto, F., Mackay, C. D., Paresce, F., Weigelt, G., Baxter, D., Greenfield, P., Jedrzejewski, R., Nota, A., Sparks, W. B., Kirshner, R. P., Panagia, N., 1991, ApJ, 369, L63-L66: First results from the Faint Object Camera - SN 1987A - PDF FILE (ADS - 1.0MB) - PDF FILE (LOCAL - 1.0 MB).
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