Gravitational redshift

Fig. 12.10. Comparison of the observed spectrum of the gravitationally lensed LBG MS 1512-cB58 (bold), with a redshift of 2.7, with synthetic spectra calculated with Starburst 99 together with the theoretical spectral library WM-basic for various metallicities (faint). The left panels show the region of the A. 1425 complex (a blend of Si, C and Fe photospheric lines), while the right panels show photospheric features of Fe hi between 1900 and 2000 A. After Rix etal. (2004).

Cottam, J., Paerels, F., Mendez, M. (2002), Gravitationally redshifted absorption lines in the X-ray burst spectra of a neutron star , Nature 420, 51. 

Other constraints come from recent observations from X-ray satellites. Most robust seem the data from the low mass X-ray binary EXO 0478-676 obtained by Cottam et al. [37], From the redshifted absorption lines from ionized Fe and O a gravitational redshift z = 0.23 was deduced this gives rise to a mass-to-radius relation... 

Decisive informations on the mass-to-radius ratio can be provided by measuring the gravitational redshift of lines in the spectrum emitted from the compact star atmosphere. Very recently, redshifted spectral lines features have been reported for two different X-ray sources (Cottam et al. 2002 Sanwal et al. 2002). The first of these sources is the compact star in the low mass X-ray binary EXO 0748-676. Studying the spectra of 28 type-I X-ray bursts in... 

EXO 0748-676, Cottam et al. (2002) have found absorption spectral line features, which they identify as signatures of Fe XXVI (25-time ionized hydrogenlike Fe) and Fe XXV from the n = 2 —> 3 atomic transition, and of O VIII (n = 1 —> 2 transition). All of these lines are redshifted, with a unique value of the redshift z = 0.35. Interpreting the measured redshift as due to the strong gravitational field at the surface of the compact star (thus neglecting general relativistic effects due to stellar rotation on the spectral lines (Oezel Psaltis 2003)), one obtains a relation for the stellar mass-to-radius ratio ... 

The second source for which it has been claimed the detection of redshifted spectral lines is IE 1207.4-5209, a radio-quite compact star located in the center of the supernova remnant PSK 1209-51/52. IE 1207.4-5209 has been observed by the Chandra X-ray observatory. Two absorption features have been detected in the source spectrum and have been interpreted (Sanwal et al. 2002) as spectral lines associated with atomic transitions of once-ionized helium in the atmosphere of a strong magnetized (B 1.5 x 1014 G) compact star. This interpretation gives for the gravitational redshift at the star surface z = 0.12 -0.23 (Sanwal et al. 2002), which is reported in Fig. 3 and by the two dashed lines labeled z = 0.12 and z = 0.23. 

For most astronomers, the solution to these cosmological problems resides in a combination of various methods. The luminosity-redshift test must be combined with independent techniques, such as anisotropies in the cosmic background radiation and statistical study of gravitational lenses. 

As hinted in the Introduction, the present viewpoint combines the microscopic and the macroscopic domain. Hence, we need to incorporate a satisfactory treatment also of the theory of general relativity. Simultaneously the problem associated with micro-macro correlates, discussed initially, and the universality of the superposition principle, briefly mentioned above and to be discussed in more detail below, aims at the idea of decoherence in regard to classical reality. Since the issues brought up are interrelated, we will illustrate the problem of decoherence by examples drawn from general relativity, i.e., the law of light deflection, the gravitational redshift, and the time delay. 

Note that Eq. (116) is compatible with the gravitational redshift and the gravitational time delay... 

Because cosmic shear surveys probe the dark matter distribution up to significant redshift, it is a probe of the details of the gravitational dynamics. With large scale surveys it then becomes possible to test the details of large-scale structure growth with unprecedented accuracy. 

Let us use (12) to compute the gravitational redshift, the reduction in the frequency of waves as they climb out of a gravitational potential well. Recall that we obtained (12) by assuming gag is time independent. Imagine an oscillator (decaying atom, radar device) produces a wave train of sharp frequency u at a point xi. This means that N = u Ari is the number of cycles of the wave in an interval At of the (proper) time ticked by a clock at rest at xi. But by (12) we have the relation At = (c2 + 24w(xi))1/2At with the interval of t time spanned by the train. Thus the number of cycles can be written N = (c2 + 2(I> fxi))1 /2 At. Now the metric is not changing,... 

How big can the gravitational redshift get A neutron star of 1.5M has a radius of 10 km giving a formal surface Newtonian potential 0.22c2. This already calls for nonlinear corrections. A BH, being totally collapsed, is more extreme. We observe from (14) that z/2 — 0 for any vi when /v(xi) —> —c2/2. We are obviously pushing our formulae too far because they were obtained from nonrelativistic arguments, and when (I>/v is of order unity, motion is relativistic. Nevertheless the prediction that the formal Newtonian potential... 

The deflection of light by gravitating bodies is another famous phenomenon. Unlike the gravitational redshift, it does depend on gt/l and gtJ. The reason is that photons move at speed c, so the terms in Eq. (9) involving Vt] and I n]k are no longer small compared to that with Y t, which was the only one implicated in nonrelativistic motion. I jj and I l]k both involve spatial derivatives of gij, so gij must be known to calculate light deflection. Newtonian arguments cannot help us here. 

Schwarzschild s metric describes the exterior of any spherical mass-energy distribution as well as the simplest BH. Obviously the gu of this metric is the same as for the approximate metric (12). Hence the discussion about gravitational redshift of a source at rest goes as before, and we again have... 

Again, radiation reaching a distant observer from an emitter at rest there has its frequency gravitationally redshifted to zero. 

Any astronomically measured frequency shift consists of several components, including the chemical shift, described here. Other contributions include relativistic gravitational redshifting, a distance-dependent redshift caused by the topological curvature of space-time, and a Doppler shift where the source is in relative motion. 

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