Luminosity distance

A distance measure d] known as the luminosity distance is relevant here. In a spatially flat space-time, it is given by the formula... 

As compared to a cosmological constant, quintessence modifies the late time evolution of the expansion rate of the universe. It can therefore affect the luminosity distance of supernovae as well as the angular distance of CMB patterns. However the most dramatic difference between a quintessence models and the now standard ACDM scenario comes when one considers structure formation. 

Cosmology with supernovae has developed over the second half of the last century. Their extreme luminosities always made them attractive candidates to measure large distances. Various methods were devised to use supernovae to measure cosmological parameters ranging from simple standard candle paradigms to physical explanations of the supernova explosions and subsequent derivation of distances. Essentially, supernovae have been used to determine luminosity distances, i.e. the comparison of the observed flux to the total emitted radiation. The trick is to find a reliable way to measure the absolute luminosity of the objects. 

Type la supernovae measure luminosity distances to objects out to about a redshift of 1. These distances are the most accurate currently available to astronomers for cosmological purposes, i.e. beyond the Coma cluster distance. Since the luminosity distances depend on the evolution of the Hubble parameter and this in turn depends on the energy content of the universe through the Einstein equation (e.g. Carroll et al. 1993) one can derive the energy... 

In the past decade several projects contributed to the luminosity distance measurements and by now (i.e., as of 2009) the list includes over 200 events. Specifically with the help of the Hubble telescope 13 new Sn la were found with spectroscopically confirmed redshifts exceeding z = 1 and at present the full sample contains already 23 z > 1 objects (Riess et al. 2007). Such objects most strongly influence the value of the deceleration parameter. A combined analysis of all Sn la data yields a deceleration parameter value of —0.7 0.1 (Kowalski et al. 2008). Its negative value signals an accelerating expansion rate at distance scales comparable to the size of the Universe. 

Scl is a close companion of the Milky Way, at a distance of 72 5 kpc [7], with a low total (dynamical) mass, (1.4 0.6) x 107Mq [8], and modest luminosity, My = —10.7 0.5, and central surface brightness, Soy = 23.5 0.5 mag/arcsec2 [9] with no HI gas [10]. CMD analysis, including the oldest Main Sequence turnoffs, has determined that this galaxy is predominantly old and that the entire star formation history can have lasted only a few Gyr [11]. 

The chemical analysis has revealed that rather low C/O ratios are found in metal-poor extragalactic carbon stars, as found for galactic carbon stars of the solar vicinity. Furthermore, the three analyzed stars show similar s-elements enhancements [ls/Fe]=0.8-1.3 and [hs/Fe]=l.l-1.7. This leads to new constraints for evolutionary models. For instance, the derived C/O and 13C/12C ratios are lower than model predictions at low metallicity. On the contrary, theoretical predictions of neutrons exposures for the production of the s-elements are compatible with observations (see Fig. 1). Finally, from their known distances, we have estimated the luminosities and masses of the three stars. It results that SMC-B30 and Sgr-C3 are most probably intrinsic carbon stars while Sgr-Cl could be extrinsic. 

The calculation for flux arriving at the Earth requires the Sun s luminosity and the distance from the Sun. The total solar flux (FSun x total area of the Sun) gives solar luminosity LSun = 3.8 x 1026 W and the flux at the Earth, /, is given by ... 

The B/V intensity ratio is an excellent relative measure of magnitude and it is possible to derive a B/V magnitude and, using Equation 2.7, derive a calibration curve for the temperature of a star (Figure 2.4) so that the temperature of the star can be measured directly by telescopes. Now, with a measure of the luminosity of a star the radius can be determined, but there is a problem the luminosity of a star as measured on Earth depends on how far away the star is - the Inverse Square Law - so the distance to the star must also be known to understand the absolute luminosity of the star. 

Figure 2.4 The B/V luminosity calibration curve Distance to the stars...

Consider the amount of radiation arriving on the surface of the Earth at a distance of 1 AU or 1.5 x 1011 m. The total flux of the Sun is distributed evenly over a sphere of radius at the distance of the planet, d. From the luminosity calculation of the Sun, F, the solar flux at the surface of Earth, FEarth, is F/47t(1.5 x 1011)2 = 1370 Wm-2 from the least-square law of radiation discussed in Example 2.4 (Equation 2.4). Substituting this into Equation 7.6 with the estimate of the albedo listed in Table 7.2 gives a surface temperature for Earth of 256 K. 

Calculate the distance spanned by the habitable zone around the Sun at its current luminosity of 3.8 x 1026 W. Using Equation 7.5 for the flux at a distance corresponding to 273 K, the freezing point of water is given by ... 

Cepheid variable Stars that have a periodic variation in their luminosity with a direct relation between the luminosity and the period. These stars are important distance markers. 

The most metal-deficient stars comprise field stars in the solar neighbourhood (where in some cases distances and luminosities can be found from parallaxes) and stars in globular clusters where the morphology of the HR diagram can be studied (Fig. 4.8). Such stars are of particular interest because their content of heavy elements (synthesized in still earlier generations of stars) is so low that they can... 

FIGURE 8.15 Typical temperature profiles along the centerline of laminar hydrocarbon fuel jets diluted with N2 to the point of no luminosity when burning in overventilated air streams. H is the height of the flame Zis the distance from jet exit along the centerline. 

Multiplying the apparent luminosity of a heavenly body by the square of its distance, the astronomer calculates its true brightness. The stars can then be sorted, separating out remote bright stars from nearby faint ones which might otherwise appear to be on a par. Colour, on the other hand, does not depend on distance, once corrections have been made for reddening due to interstellar dust. 

There are many obstacles to extragalactic astronomy. The main difficulty is that the very great distances involved imply extremely limited sizes and apparent luminosities. In addition, large distances mean spectral shifts from the interesting spectral region (blue) into the near infrared, which is difficult to detect. 

Fig. 5.2. Internal structure of the Sun. The top four graphs show the density, temperature, chemical composition and luminosity as a function of distance from the centre. Such profiles can be buUt up for each stage of the star s evolution. The figure shows the general regions of radiative transfer and convection in the bulk of the Sun. The bottom graph shows the gradual increase in radius, temperature and luminosity from birth.

Following one of the biggest inquiries ever held in modern astronomy, it transpires that their apparent luminosity is slightly less than would be found if space were Euclidean and expansion were merely slowed down by the gravitational effects of matter. In fact, the expansion is more vivacious than was previously thought. This means that distances to remote objects are slightly distended, so that the supernovas appear less luminous than expected. 

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. 

Today, a certain level of diversity has been discovered in SNIa events. Before they can be used as cosmological distance standards, it must be checked that their maximal luminosity has an appropriate value. Otherwise ad hoc corrections must be brought to bear to... 

When large spherical AP particles dg = 3 mm) are added, large flamelets are formed in the dark zone.Pl Close inspection of the AP particles at the burning surface reveals that a transparent bluish flame of low luminosity is formed above each AP particle. These are ammonia/perchloric acid flames, the products of which are oxidizer-rich, as are also observed for AP composite propellants at low pressures, as shown in Fig. 7.5. The bluish flame is generated a short distance from the AP particle and has a temperature of up to 1300 K. Surrounding the bluish flame, a yellowish luminous flame stream is formed. This yellowish flame is produced by in-terdiffusion of the gaseous decomposition products of the AP and the double-base matrix. Since the decomposition gas of the base matrix is fuel-rich and the temperature in the dark zone is about 1500 K, the interdiffusion of the products of the AP and the matrix shifts the relative amounts towards the stoichiometric ratio, resulting in increased reaction rate and flame temperature. The flame structure of an AP-CMDB propellant is illustrated in Fig. 8.1. 

In TNT pellets the initial Type II low-order detonation does not lead immediately to the final high order but to an intermediate level, of almost normal rate but of very low shock luminosity. A luminous strip due to the collision of the shock waves of two low-ordet detonations in TNT is observed in the simple dark space in some still photographs. Initiation at slightly below the limit, in all of the expls studied, produces low-order detons that fade after traversing-a short distance and the wave fronts show a strong shock effect. In TNT pellets the intermediate-order may also fade... 

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