Light curve

Figure 5.5. Profile of dimensionless concentration of A versus dimensionless time for n = 2 and n = 1 (light curve). Here Cao = 15.

Figure 5.175. Changing K] from 0.25 (dark curve) to 10.0 (light curve) resulted in faster attainment of equilibrium.

Figure A2. ( Ra/ °Th) and f °Th/ U) calculated from the analytical solution (solid light curves), approximate analytical solution (dotted light curves) and full numerical solution (solid dark curves). Horizontal curves represent constant maximum porosity ( x), while vertical curves represent constant upwelling rates (W ) in cm/yr. Selected contours are labeled. Contours range from 1-100 cm/a and 0.1-10% for upwelling velocity and maximum porosity, respectively. See text for explanation.

Figure 8 An example of the decreasing heat requirement during primary drying at a chamber pressure of 0.15 torr. 5% mannitol maintained at -20°C during primary drying. Results obtained by computer simulation of freeze drying (see Ref. 3). Heavy curve Shelf Fluid. Light curve Shelf surface. Lightweight dashed curve Product Bottom. Heavy dashed curve Sublimation.

The 27-cm telescope is equipped with four CCD detectors and measures the light curves of bright stars in the wavelength range 370-950 nm. The scientific goals of the mission are ... 

The emission of light from Cepheid stars has a characteristic light curve seen in Figure 4.14 for a Cepheid in the constellation of Perseus. The sawtooth pattern is characteristic of the class and enables the period of variation to be determined. The observation, however, that the luminosity and period are related has powerful consequences. The Cepheid variables fall into two classes type I classical Cepheids have periods of 5-10 days and type II have periods of 12-20 days. The two types of Cepheids initially caused problems when determining the luminosity-period relation but the relation has now been determined. Type I Cepheids follow the expression... 

Figure 4.14 Light curve for the star SX Persei. (Reproduced by permission of David L. Dupuy, Virginia Military Institute)...

Fig. 6.3. Product aN of abundance and neutron capture cross-section for s-only nuclides in the Solar System. The main and weak s-process components are shown by the heavy and light curves respectively. Units are mb per 106 Si atoms. After Kappeler, Beer and Wisshak (1989). Copyright by IOP Publishing Ltd. Courtesy Franz Kappeler.

If one of the stars in the binary is not a neutron star, then the tests become less precise. Suppose that one observes the optical light from the companion to a neutron star. In addition to the spectral information that allows measurement of P and i i, one also has photometric information (e.g., the total optical flux from the companion). The companion is distorted into a pear shape by the gravity of the neutron star, with the point towards the neutron star. Therefore, from the side there is more projected area and hence greater flux than from either end. If the orbit is edge-on (i = 90°) then the flux varies maximally if the orbit is face-on (i = 0°) then there is no variation. Therefore, by modeling the system one can estimate the inclination from the flux variations. This is called the method of ellipsoidal light curves (Avni Bahcall 1975). 

However, one must be careful because in an LMXB the optical emission from the accretion disk (whether in the outer, cool regions or as reprocessed X-ray emission) can outshine the companion by a large factor. This makes spectral lines difficult to measure and also complicates the ellipsoidal light curve technique. The ideal systems to study are therefore transient systems, which undergo periods of active mass transfer (often for a few weeks to a few months) before lapsing into quiescence, where there is little to no mass transfer. During quiescence, the companion is still distorted by the gravity of the neutron star, hence the flux variations still occur, but without any contamination by the accretion disk. There is a relatively new approach similar to this that... 

In just the last year, several observations have allowed new constraints on neutron star structure (1) a mass of M > 1.6 M (at >95% confidence) has been measured for a neutron star (Nice et al. 2003) (2) the first surface redshift, 2 = 0.35, has been detected from a neutron star (Cottam et al. 2002), and (3) the first non-sinusoidal light curve has been measured from an accreting millisecond neutron star (Strohmayer et al 2003). These observations, along with many previously available data, hold out good hope for strong constraints on high-density matter in the next few years. 

Hoflich P, Wheeler JC, Thielemann FK (1998) Type la supemovae influence of the initial composition on the nucleosynthesis, light curve, and spectra and consequences for the determination of 2 and A. Astrophys 1495 617-629... 

When it became possible to obtain the spectrum of one of these objects in 1937, it was obvious that they looked like nothing yet known. All supernovas discovered in subsequent years displayed a remarkable uniformity, both in intensity and in behaviour. This observation led Zwicky to suggest that they might be used as standard candles to calibrate distance across the cosmos. But then, in 1940, a supernova with a completely different spectrum was discovered. It soon became clear that there were at least two classes of supernova, distinguished by their spectral features. It was the presence or absence of the Balmer lines of hydrogen near the maximum of the light curve that provided this classification. 

I would like to mention Richard Schaeffer of the Theoretical Physics Department at the CEA in Orme des Merisiers, France, and Robert Mochkovitch of die Institute of Astrophysics in Paris, widi whom I calculated die light curve of an undressed star that looked so like the precursor of SN 1987A. 

Apart from these three facts, nuclear astrophysicists take pains to point out that the rate at which the luminosities of SNla events decline, once beyond the maximum, is commensurable with the decay of radioactive cobalt-56, son of nickel-56, atomic nucleus of noble lineage as we know. This is a common factor with gravitational collapse supernovas. SNla light curves are explained through the hypothesis that half a solar mass of nickel-56 is produced when one of these white dwarfs explodes. 

SN 1997ef is a very unusual supernova, to judge by its light curve and spec-tram. Hydrogen is striking by its absence. Oxygen and iron absorption lines are abnormally broad. 

At first glance, the spectral properties, absolute magnitudes (intrinsic luminosities) and shapes of the light curves of the majority of type la supernovas (SNIa) are remarkably similar. Only a few rather subtle photometric and spectrometric differences can be discerned from one object to another. 

Hydrogen shines by its absence and the optical spectra of SNIa events feature spectral lines of neutral and once ionised elements (Ca, Mg+, S+ and 0+) at the minimum of the light curve. This indicates that the outer layers are composed of intermediate mass elements. SNIa events reach their maximum luminosity after about 20 days. This luminous peak is followed by a sharp drop amounting to three magnitudes per month. Later the light curve falls exponentially at the rate of one magnitude per month. 

Fig. A2.1. Light curves for various SNIa events. The figure shows empirical families of light curves. The brightest shine longer, at the peak of their glory. (From Riess et al. 1998.)...

The important datum for cosmology is precisely the luminosity at the peak of the light curve. It is crucial to be able to establish this maximum value in order to use the SNIa event as a distance indicator. Correctly cahbrated and reproducible hght curves from type la supernovas have become a major tool for determining the local expansion rate and geometrical structure of the Universe (Fig. A2.1). A great deal of effort has been put into producing adequate models of these events over the past few years. 

Many connections have been found between the luminosity peak, the shape of the light curve, evolution in the colour, spectral appearance, and membership of a galaxy of given morphology. However, after the first 150 days, uniformity takes over and all these objects fade in the same way and with the same spectrum. 

Furthermore, the fact that iron is s5mthesised in the form of a nickel isotope has important implications from an observational standpoint. Indeed, it provides a check on the foundations of the whole theory of explosive nucleosynthesis. These implications are twofold, as we have seen. They concern supernova light curves and gamma emission from these objects. 

The dividing line between core and envelope determines the amount of nickel-56 ejected. At the end of the day, this is what fixes the brightness of the supernova. We therefore have a handle on this parameter and for the time being may content ourselves by fitting it in such a way as to account for observations of supernova light curves. 

Ricard M. Thuan T.X. (2000) L Infini dans la paume de la main (Fayard, Paris). Riess A.G. et al. (1998) Light curves for 22 type la supernovae. CERN Document Server astro-ph/9810291. 

Figure 7.11 Transformation of Raman spectra in amorphous Sbg osSeg 97, subjected to exposure of linearly polarized light curve 1, reference Raman spectrum of amorphous state curves 2-A, after exposure to = 3, 5, and 6kJ/cm, respectively. The inducing intensity was I = 1.25W/cml...

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