New Measurements of the Solar Spectrum verify Einstein's theory of GR

New measurements of the solar spectrum verify Einstein's theory of General Relativity
by Instituto de Astrofísica de Canarias

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Artistic representation of the Sun, the Earth and the Moon (not to scale) with the space-time curvature of Einstein's General Relativity over the spectrum of sunlight reflected from the Moon (in colors from blue to red). The spectrum is taken with the HARPS instrument and calibrated with the LFC. Credit: Gabriel Pérez Díaz, SMM (IAC).
An international team of researchers led by the Instituto de Astrofísica de Canarias (IAC) has measured, with unprecedented accuracy, the gravitational redshift of the Sun, a change in frequency of the lines in the solar spectrum which is produced when the light escapes from the gravitational field of the Sun on its way to Earth. This work, which verifies one of the predictions of Einstein's General Relativity, is to be published in the journal Astronomy & Astrophysics.

The General Theory of Relativity, published by Albert Einstein between 1911 and 1916, introduced a new concept of space and time, by showing that massive objects cause a distortion in space-time which is felt as gravity. In this way, Einstein's theory predicts, for example, that light travels in curved paths near massive objects, and one consequence is the observation of the Einstein Cross, four different images of a distant galaxy which lies behind a nearer massive object, and whose light is distorted by it.

Other well known effects of General Relativity are the observed gradual change in Mercury's orbit due to space-time curvature around the "massive" Sun, or the gravitational redshift, the displacement to the red of lines in the spectrum of the Sun due to its gravitational field.

The gravitational redshift is an important effect for satellite navigation systems such as GPS, which would not work if General Relativity was not put into the equations. This effect depends on the mass and the radius of an astronomical object, so that even though it is bigger for the Sun than for the Earth, it is still difficult to measure in the solar spectrum.

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the paper:

https://arxiv.org/pdf/2009.10558.pdf

The solar gravitational redshift from HARPS-LFC Moon spectra

A test of the general theory of relativity:

ABSTRACT:
Context. The general theory of relativity predicts the redshift of spectral lines in the solar photosphere as a consequence of the gravitational potential of the Sun. This effect can be measured from a solar disk-integrated flux spectrum of the Sun’s reflected light on Solar System bodies. Aims. The laser frequency comb (LFC) calibration system attached to the HARPS spectrograph offers the possibility of performing an accurate measurement of the solar gravitational redshift (GRS) by observing the Moon or other Solar System bodies. Here, we analyse the line shift observed in Fe absorption lines from five high-quality HARPS-LFC spectra of the Moon. Methods. We selected an initial sample of 326 photospheric Fe lines in the spectral range between 476–585 nm and measured their line positions and equivalent widths (EWs). Accurate line shifts were derived from the wavelength position of the core of the lines compared with the laboratory wavelengths of Fe lines. We also used a CO5BOLD 3D hydrodynamical model atmosphere of the Sun to compute 3D synthetic line profiles of a subsample of about 200 spectral Fe lines centred at their laboratory wavelengths. We fit the observed relatively weak spectral Fe lines (with EW< 180 mÅ) with the 3D synthetic profiles. Results. Convective motions in the solar photosphere do not affect the line cores of Fe lines stronger than about ∼ 150 mÅ. In our sample, only 15 Fe i lines have EWs in the range 150 < EW(mÅ) < 550, providing a measurement of the solar GRS at 639±14 m s−1 , which is consistent with the expected theoretical value on Earth of ∼ 633.1 m s−1 . A final sample of about 97 weak Fe lines with EW < 180 mÅ allows us to derive a mean global line shift of 638 ± 6 m s−1 , which is in agreement with the theoretical solar GRS. Conclusions. These are the most accurate measurements of the solar GRS obtained thus far. Ultrastable spectrographs calibrated with the LFC over a larger spectral range, such as HARPS or ESPRESSO, together with a further improvement on the laboratory wavelengths, could provide a more robust measurement of the solar GRS and further testing of 3D hydrodynamical models.


7. Discussion and Conclusions:
The analysis of high-quality HARPS spectra of the Moon calibrated with the laser frequency comb allows us to obtain an observational measurement of the solar GRS. We performed the analysis on an automated basis, using data reduction, wavelength calibration, continuum normalisation, and identification of lines and measurement of equivalent widths, line core shifts and global line shifts. There are uncertainties hidden in these process that certainly introduce some scatter in the measurements at the level of several tens of m s−1 . We note the pixel size is ∼ 800 m s−1 in the HARPS blue and red detectors. We are able to show a rather clear boundary in the equivalent widths of the lines, at 165 ± 15 mÅ, where lines with larger equivalent widths do not show any sign of convective shift. The 15 Fe lines with EWs larger than 150 mÅ, are distributed around the theoretical value of solar GRS with a dispersion of 56 m s−1 . The mean uncertainty on line core shift of these 15 lines is 23 m s−1 , which is almost half of the dispersion of the measurements. This may be explained by the uncertainty on laboratory wavelengths at the level of 16 − 75 m s−1 (Nave et al. 1994). The mean uncertainty on EW for these 15 Fe lines is 2.4 mÅ. For the total number of 188 Fe lines, the mean uncertainty on line core shift is 19.2 m s−1 , whereas mean uncertainty on EW is only 1.2 mÅ.

The velocity field in the 3D model atmosphere of the Sun seems to reproduce quite well the observed behaviour of line core shifts, at least qualitatively, and quantitatively for weak lines with EW < 60 mÅ. On the other hand, the global line shift from the 3D profiles matching the observed profiles behaves better although there remains a dispersion in the measurements around the mean of about 73 m s−1 for the sub-sample of 102 Fe lines, and goes down to 55 m s−1 if we discard the five outliers by applying a σ clipping procedure, leaving 97 Fe lines depicted in Fig. 7. The mean uncertainty on the global line shift that comes from the automated fitting procedure and computed as the standard deviation from the measurements of the five HARPS-LFC spectra is much smaller at 6 m s−1 . However, the statistical uncertainty on the wavelength position of the average 3D profiles is a bit larger at about 30 m s−1 . This may indicate that the dispersion around the theoretical value of solar GRS of 55 m s−1 may be indeed related to the uncertainty on the laboratory wavelengths. The recalibrated wavelengths, λnist, do provide a slightly different result than the original laboratory wavelengths, λlab, in Nave et al. (1994), shifting the result by +20 m s−1 . Similarly, although the uncertainties on the recalibrated Ritz wavelengths estimated from the energy levels, λritz, are smaller than those of the original wavelengths, using the λritz moves the result by +35 m s−1 and provides a larger dispersion. New laboratory experiments to improve the accuracy and revise the laboratory wavelengths of Fe i and other element species abundant in the visible solar spectrum appears necessary. Assuming the recalibrated wavelengths, λnist, as a laboratory reference, we have been able to achieve an observational measurements of the solar GRS of vGRS,3D = 638 ± 6 m s−1 from the mean of observed global line shifts of 97 Fe lines with 10 < EWs[mÅ] < 180, and vGRS,obs = 639 ± 14 m s−1 from the mean line core shift of 15 strong Fe lines with EW > 150 mÅ. Both measurements are in perfect agreement with the theoretical value of the solar gravitational redshift, vGRS,theo = 633.1 m s−1 , representing an observational test of the general theory of relativity (Einstein 1911, 1916). At the same time, our observations point out the high quality, along with some limitations, in the current 3D modelling of the solar lines. New, high-quality spectra of the Moon taken with HARPS (Mayor et al. 2003), or at an even higher resolution with ESPRESSO (Pepe et al. 2014; González Hernández et al. 2018) and calibrated with the laser frequency comb in a wider spectral range, could provide a larger number of Fe lines that can be used to measure accurate line shifts (and, in fact, line bisectors) as diagnostics for understanding the structure and dynamics of the solar photosphere and for validating and improving 3D model atmospheres, in addition to serving as a tool for definitively probing solar gravitational redshift.