Gravitational Redshift Effect Research Articles

A quantitative explanation of the cyclotron-line variation in accreting magnetic neutron stars of super-critical luminosity

Context. Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Cyclotron lines are believed to be generated in the radiative shock in the accretion column. High-luminosity NSs show a smooth anti-correlation between the cyclotron-line centroid (ECRSF) and X-ray luminosity (LX). Aims. It has been pointed out that the observed ECRSF − LX smooth anti-correlation in high-luminosity NSs is in tension with the theoretically predicted one, if the radiative shock is the site of cyclotron-line formation. The shock height increases approximately linearly with luminosity, while the dipolar magnetic field drops as the cubic power of distance, thereby implying that the cyclotron-line energy ought to decrease significantly when the luminosity increases by, say, an order of magnitude, which is contrary to observations. Since there is no other candidate site for the cyclotron-line formation, we re-examine the predicted rate of change of the cyclotron-line energy with luminosity at the radiative shock, taking a closer look at the Physics involved. Methods. We developed a purely analytical model describing the overall dependence of the observed cyclotron energy centroid on the shock front’s height, including both the relativistic boosting and the gravitational redshift effects in our considerations. The relativistic boosting effect is due to the mildly relativistic motion of the accreting plasma upstream with respect to the shock’s reference frame. Reults. We find that the cyclotron-line energy varies with (a) the shock height due to the dipolar magnetic field, (b) the Doppler boosting between the shock and bulk-motion frames, and (c) the gravitational redshift. We show that the relativistic effects noticeably weaken the predicted ECRSF − LX anti-correlation. We use our model to fit the data of the X-ray source V0332+53 that exhibits a weak negative correlation and demonstrate that the model fits the data impressively well, thereby alleviating the tension between observations and theory. Conclusions. The reported weak anti-correlation between cyclotron-line centroid and X-ray luminosity in the supercritical accretion regime may be explained by the combination of the variation of the magnetic-field strength along the accretion column, the effect of Doppler boosting, and the gravitational redshift. As a result of these effects, the actual magnetic field on the surface of the neutron star may be a factor of ∼2 larger than the naively inferred value from the observed CRSF.

Dynamical traceback age of the Octans young stellar association

Context. Octans is one of the most distant (d ∼ 150 pc) young stellar associations of the solar neighbourhood, and it has not yet been sufficiently explored. Its age is still poorly constrained in the literature and requires further investigation. Aims. We take advantage of the state-of-the-art astrometry delivered by the third data release of the Gaia space mission combined with radial velocity measurements obtained from high-resolution spectroscopy to compute the 3D positions and 3D spatial velocities of the stars and derive the dynamical traceback age of the association. Methods. We created a clean sample of cluster members by removing potential outliers from our initial list of candidate members. We then performed an extensive traceback analysis using different subsamples of stars, different metrics to define the size of the association, and different models for the Galactic potential to integrate the stellar orbits in the past. Results. We derive a dynamical age of $ 34^{+2}_{-2} $ Myr that is independent from stellar models and represents the most precise age estimate currently available for the Octans association. After correcting the radial velocity of the stars for the effect of gravitational redshift, we obtain a dynamical age of $ 33^{+3}_{-1} $ Myr, which is in very good agreement with our first solution. This shows that the effect of gravitational redshift is small for such a distant young stellar association. Our result is also consistent with the less accurate age estimates obtained in previous studies from lithium depletion (30–40 Myr) and isochrones (20–30 Myr). By integrating the stellar orbits in time, we show that the members of Octans and Octans-Near had different locations in the past, which indicates that the two associations are unrelated despite the close proximity in the sky. Conclusions. This is the first reliable and precise dynamical age result for the Octans young stellar association. Our results confirm that it is possible to derive precise dynamical ages via the traceback method for ∼30 Myr old stellar clusters at about ∼150 pc with the same precision level that has been achieved in other studies for young stellar groups within 50 pc of the Sun. This represents one more step towards constructing a self-consistent age scale based on the 3D space motion of the stars in the young stellar clusters of the solar neighbourhood.

Accretion/Ejection Phenomena and Emission-Line Profile (A)symmetries in Type-1 Active Galactic Nuclei

The distinct behaviors of blue- and redshifted broad emission-line shifts, emitted by ionic species with varying ionization potentials in active galactic nuclei (AGN), can be elucidated by considering the balance between radiation and gravitational forces along the quasar main sequence. Blueshifts are attributed to outflowing motions of the line-emitting gas toward the observer, and they are most pronounced in AGN with high Eddington ratios (Population A) and high luminosities. Conversely, redshifts in the broad-line wings are observed in Balmer emission lines of sources radiating at low Eddington ratios (Population B), though the origin of these redshifts remains a subject of ongoing debate. A correlation linking the redward asymmetry as measured by the centroid shift of the Hβ line profile to the black hole mass lends support to the notion that these shifts arise from gravitational and transverse redshift effects, particularly for black hole masses MBH≳108.7 M⊙.

Cosmological test of local position invariance from the asymmetric galaxy clustering

ABSTRACT The local position invariance (LPI) is one of the three major pillars of Einstein equivalence principle, ensuring the space–time independence on the outcomes of local experiments. The LPI has been tested by measuring the gravitational redshift effect in various depths of gravitational potentials. We propose a new cosmological test of the LPI by observing the asymmetry in the cross-correlation function between different types of galaxies, which predominantly arises from the gravitational redshift effect induced by the gravitational potential of haloes at which the galaxies reside. We show that the ongoing/upcoming galaxy surveys give a fruitful constraint on the LPI-violating parameter, α, in the distant universe (redshift z ∼ 0.1–1.8) over the cosmological scales (separation s ∼ 5–$10\, {\rm \mathit{ h}^{ -1}\,Mpc}$) that have not yet been explored, finding that the expected upper limit on α can reach 0.03.

Testing general relativity: New measurements of gravitational redshift in galaxy clusters

Context. The peculiar velocity distribution of cluster member galaxies provides a powerful tool to directly investigate the gravitational potentials within galaxy clusters and to test the gravity theory on megaparsec scales. Aims. We exploit spectroscopic galaxy and galaxy cluster samples extracted from the latest releases of the Sloan Digital Sky Survey (SDSS) to derive new constraints on the gravity theory. Methods. We considered a spectroscopic sample of 3058 galaxy clusters, with a maximum redshift of 0.5 and masses between 1014 − 1015 M⊙. We analysed the velocity distribution of the cluster member galaxies to make new measurements of the gravitational redshift effect inside galaxy clusters. We accurately estimated the cluster centres, computing them as the average of angular positions and redshifts of the closest galaxies to the brightest cluster galaxies. We find that this centre definition provides a better estimation of the centre of the cluster gravitational potential wells, relative to simply assuming the brightest cluster galaxies as the cluster centres, as done in past literature works. We compared our measurements with the theoretical predictions of three different gravity theories: general relativity (GR), the f(R) model, and the Dvali–Gabadadze–Porrati (DGP) model. A new statistical procedure was used to fit the measured gravitational redshift signal, and thus to discriminate among the considered gravity theories. Finally, we investigated the systematic uncertainties that possibly affect the analysis. Results. We clearly detect the gravitational redshift effect in the exploited cluster member catalogue. We recover an integrated gravitational redshift signal of −11.4 ± 3.3 km s−1, which is in agreement, within the errors, with past literature works. Conclusions. Overall, our results are consistent with both GR and DGP predictions, while they are in marginal disagreement with the predictions of the considered f(R) strong field model.

Relativistic distortions in galaxy density–ellipticity correlations: gravitational redshift and peculiar velocity effects

ABSTRACT We study relativistic effects, arising from the light propagation in an inhomogeneous universe. We particularly investigate the effects imprinted in a cross-correlation function between galaxy positions and intrinsic galaxy shapes (GI correlation). Considering the Doppler and gravitational redshift effects as major relativistic effects, we present an analytical model of the GI correlation function, from which we find that the relativistic effects induce non-vanishing odd multipole anisotropies. Focusing particularly on the dipole anisotropy, we show that the Doppler effect dominates at large scales, while the gravitational redshift effect originated from the halo potential dominates at the scales below 10–$30\, {\rm Mpc}\, h^{-1}$, with the amplitude of the dipole GI correlation being positive over all the scales. Also, we newly derive the covariance matrix for the modelled GI dipole. Taking into account the full covariance, we estimate the signal-to-noise ratio and show that the GI dipole induced by the relativistic effects is detectable in future large-volume galaxy surveys. We discuss how the measurement of dipole GI correlation could be helpful to detect relativistic effects in combination with the conventional galaxy–galaxy cross-correlation.

Performance Evaluation and Requirement Analysis for Chronometric Leveling with High-Accuracy Optical Clocks

The high-precision unification of global height datum has long been a hot issue in the field of geodesy. The chronometric leveling method originates from the gravitational redshift effect of general relativity, which may provide a new solution for the unification of global height datum. The height difference between the two locations could be measured via the frequency comparison of high-precision optical clocks. We build the error model for chronometric leveling, mainly including the measurement systematic error of two optical clocks, frequency statistical error of two optical clocks, and transmission path error of optical fiber when using optical fiber as carrier. Then, we put forward the schemes to achieve chronometric leveling. The performance of the height measurement using different schemes is evaluated. Additionally, considering the requirements of geodesy, four typical height measurement accuracy factors for chronometric leveling are proposed. Meanwhile, the corresponding accuracy requirements for optical clocks and frequency transmission techniques are also given. It has important guiding significance for the unification of the global height datum and related geoscience fields using high-accuracy chronometric leveling in the future.

Electromagnetism in Curved Space–Time: Coupling Doppler shifts and gravitational redshifts

We present the basic prerequisites of electromagnetism in flat spacetime and provide the description of electromagnetism in terms of the Faraday tensor. We generalise electromagnetic theory to a general relativistic setting, introducing the Einstein field equations to describe the propagation of electromagnetic radiation in curved space-time. We investigate gravitational redshift and derive formulae for the combined effect of gravitational redshift and the Doppler shift in curved spacetime.

Detection of Gravitational Redshift in Open Cluster Nondegenerate Stars

Abstract A key observational prediction of Einstein’s Equivalence Principle is that light undergoes redshift when it escapes from a gravitational field. Although astrophysics provides a wide variety of physical conditions in which this redshift should be significant, until very recently the observational evidence for this gravitational effect was limited to the light emitted by the Sun and white dwarfs. Gaia-DR2 astrometric and kinematic data, in combination with other spectroscopic observations, provides a test bench to validate such predictions in statistical terms. The aim of this paper is to analyze several thousand main-sequence and giant stars in open clusters (OCs) in order to measure the gravitational redshift effect. Observationally, a spectral shift will depend on the stellar mass-to-radius ratio as expected from the theoretical estimation of relativity. After the analysis, the obtained correlation coefficient between theoretical predictions and observations for 28 (51) OCs is a = 0.977 ± 0.218 (0.899 ± 0.137). The result has proven to be statistically robust and with little dependence on the details of the methodology or sample selection criteria. This study represents one of the more extensive validations of a fundamental prediction of gravity theories.

Detectability of the gravitational redshift effect from the asymmetric galaxy clustering

ABSTRACT It has been recently recognized that the observational relativistic effects, mainly arising from the light propagation in an inhomogeneous universe, induce the dipole asymmetry in the cross-correlation function of galaxies. In particular, the dipole asymmetry at small scales is shown to be dominated by the gravitational redshift effects. In this paper, we exploit a simple analytical description for the dipole asymmetry in the cross-correlation function valid at quasi-linear regime. In contrast to the previous model, a new prescription involves only 1D integrals, providing a faster way to reproduce the results obtained by Saga et al. Using the analytical model, we discuss the detectability of the dipole signal induced by the gravitational redshift effect from upcoming galaxy surveys. The gravitational redshift effect at small scales enhances the signal-to-noise ratio (S/N) of the dipole, and in most of the cases considered, the S/N is found to reach a maximum at z ≈ 0.5. We show that current and future surveys such as DESI and SKA provide an idealistic data set, giving a large S/N of 10–20. Two potential systematics arising from off-centred galaxies are also discussed (transverse Doppler effect and diminution of the gravitational redshift effect), and their impacts are found to be mitigated by a partial cancellation between two competitive effects. Thus, the detection of the dipole signal at small scales is directly linked to the gravitational redshift effect, and should provide an alternative route to test gravity.

An improved approach for testing gravitational redshift via satellite-based three frequency links combination

We propose a novel approach for testing the gravitational redshift based on frequency signals transmitted between a spacecraft and a ground station. The main idea is integrating one uplink signal from ground to spacecraft and two downlink signals from spacecraft to ground. Based on the integration and certain correction models, the gravitational shift of the signals between spacecraft and ground station can be detected at high precision level. The gravitational redshift effect can be used to validate the Einstein equivalence principle (EEP), which can be tested at about 10 - 6 ∼ 10 - 8 levels in different cases for a short period (less than a month) if the stability of on-board atomic clock reach 10 - 17 /day. Compared to the scheme of Gravity Probe-A (GP-A) experiment conducted in 1976, in the new approach, any on-board signal transponders is not required, and the frequency values of the three links can be arbitrary. Since the hardware requirement is decreased, a number of spacecrafts can be candidates for a gravitational redshift experiment provided that they are able to emit two different frequency signals and receive a frequency signal from the ground.

Spin effects on neutron star fundamental-mode dynamical tides: Phenomenology and comparison to numerical simulations

Gravitational waves from neutron star binary inspirals contain information on strongly-interacting matter in unexplored, extreme regimes. Extracting this requires robust theoretical models of the signatures of matter in the gravitational-wave signals due to spin and tidal effects. In fact, spins can have a significant impact on the tidal excitation of the quasi-normal modes of a neutron star, which is not included in current state-of-the-art waveform models. We develop a simple approximate description that accounts for the Coriolis effect of spin on the tidal excitation of the neutron star's quadrupolar and octupolar fundamental quasi-normal modes and incorporate it in the SEOBNRv4T waveform model. We show that the Coriolis effect introduces only one new interaction term in an effective action in the co-rotating frame of the star, and fix the coefficient by considering the spin-induced shift in the resonance frequencies that has been computed numerically for the mode frequencies of rotating neutron stars in the literature. We investigate the impact of relativistic corrections due to the gravitational redshift and frame-dragging effects, and identify important directions where more detailed theoretical developments are needed in the future. Comparisons of our new model to numerical relativity simulations of double neutron star and neutron star-black hole binaries show improved consistency in the agreement compared to current models used in data analysis

Gravitational redshift of the Sun

Gravitation General relativity predicts that light emitted from a massive body is redshifted by its gravitational field. This gravitational redshift effect has previously been verified using white dwarfs and terrestrial experiments. Measuring it for the Sun is complicated by the motions of plasma on the surface, which Doppler-shift spectral lines by amounts similar to that of the predicted signal. Gonzalez Hernandez et al. analyzed a high-resolution spectrum of sunlight reflected off the Moon, thereby averaging over the solar disc, calibrated using a laser frequency comb. After compensating for plasma motions, they measured a gravitational redshift that is consistent with general relativity, within the uncertainty of 1 to 2%. Astron. Astrophys. 643 , A146 (2020).

Modelling the asymmetry of the halo cross-correlation function with relativistic effects at quasi-linear scales

ABSTRACT The observed galaxy distribution via galaxy redshift surveys appears distorted due to redshift-space distortions (RSD). While one dominant contribution to RSD comes from the Doppler effect induced by the peculiar velocity of galaxies, the relativistic effects, including the gravitational redshift effect, are recently recognized to give small but important contributions. Such contributions lead to an asymmetric galaxy clustering along the line of sight, and produce non-vanishing odd multipoles when cross-correlating between different biased objects. However, non-zero odd multipoles are also generated by the Doppler effect beyond the distant-observer approximation, known as the wide-angle effect, and at quasi-linear scales, the interplay between wide-angle and relativistic effects becomes significant. In this paper, based on the formalism developed by Taruya et al., we present a quasi-linear model of the cross-correlation function taking a proper account of both the wide-angle and gravitational redshift effects, as one of the major relativistic effects. Our quasi-linear predictions of the dipole agree well with simulations even at the scales below $20\, h^{-1}\,$Mpc, where non-perturbative contributions from the halo potential play an important role, flipping the sign of the dipole amplitude. When increasing the bias difference and redshift, the scale where the sign flip happens is shifted to a larger scale. We derive a simple approximate formula to quantitatively account for the behaviours of the sign flip.

A Gravitational Redshift Measurement of the White Dwarf Mass–Radius Relation

Abstract The mass–radius relation of white dwarfs is largely determined by the equation of state of degenerate electrons, which causes the stellar radius to decrease as mass increases. Here we observationally measure this relation using the gravitational redshift effect, a prediction of general relativity that depends on the ratio between stellar mass and radius. Using observations of over 3000 white dwarfs from the Sloan Digital Sky Survey and the Gaia space observatory, we derive apparent radial velocities from absorption lines, stellar radii from photometry and parallaxes, and surface gravities by fitting atmospheric models to spectra. By averaging the apparent radial velocities of white dwarfs with similar radii and, independently, surface gravities, we cancel out random Doppler shifts and measure the underlying gravitational redshift. Using these results, we empirically measure the white dwarf mass–radius relation across a wide range of stellar masses. Our results are consistent with leading theoretical models, and our methods could be used with future observations to empirically constrain white dwarf core composition and evolution.

Resonant instability of axionic dark matter clumps

Axion is a popular candidate for dark matter particles. Axionic dark matter may form Bose-Einstein condensate and may be gravitationally bound to form axion clumps. Under the presence of electromagnetic waves with frequency ω= ma/ 2, where ma is the axion mass, a resonant enhancement may occur, causing an instability of the axion clumps. With analytical and numerical approaches, we study the resonant instability of axionic dark matter clumps with infinite homogeneous mass distribution, as well as distribution with a finite boundary. After taking realistic astrophysical environments into consideration, including gravitational redshift and plasma effects, we obtain an instability region in the axion density—clump size parameter space with given mass and coupling of axions. In particular, we show that, for axion clumps formed by the QCD axions in equilibrium, no resonant instability will occur.

Modeling relativistic contributions to the halo power spectrum dipole

We study the power spectrum dipole of an N-body simulation which includes relativistic effects through ray-tracing and covers the low redshift Universe up to zmax = 0.465 (RayGalGroup simulation). We model relativistic corrections as well as wide-angle, evolution, window and lightcone effects. Our model includes all relativistic corrections up to third-order including third-order bias expansion. We consider all terms which depend linearly on H/k (weak field approximation). We also study the impact of 1-loop corrections to the matter power spectrum for the gravitational redshift and transverse Doppler effect. We found wide-angle and window function effects to significantly contribute to the dipole signal. When accounting for all contributions, our dipole model can accurately capture the gravitational redshift and Doppler terms up to the smallest scales included in our comparison (k=0.48 h Mpc−1), while our model for the transverse Doppler term is less accurate. We find the Doppler term to be the dominant signal for this low redshift sample. We use Fisher matrix forecasts to study the potential for the future Dark Energy Spectroscopic Instrument (DESI) to detect relativistic contributions to the power spectrum dipole. A conservative estimate suggests that the DESI-BGS sample should be able to have a detection of at least 4.4σ, while more optimistic estimates find detections of up to 10σ. Detecting these effects in the galaxy distribution allows new tests of gravity on the largest scales, providing an interesting additional science case for galaxy survey experiments.

Electrostatic time dilation and redshift

We first present the salient features of the gravitational time dilation and redshift effects in two ways; by considering the oscillation frequencies/rates of clocks at different heights/potentials and by considering the photons emitted by these clocks such as atoms/nuclei. We then point out to the extension of these gravitational effects to static electricity along with two experiments performed in the '30s with null results of the electrostatic redshift. We show that the absence of this redshift is a consequence of the conservation of electric charge. We discuss the electrical time dilation and redshift effects in detail and argue that the electrostatic time dilation in an electric field must be a fact of Nature. We then present a general relativistic scheme that explains this effect. We also introduce an electrical equivalence principle analogous to the gravitational one and demonstrate how to obtain the electrostatic time dilation by this principle. We emphasize the importance of ionic atomic clocks to measure this effect whose confirmation would support the general relativistic scheme presented. We finally go over an attempt in the literature to explain the impossibility of the experimental observation of the electrostatic redshift due to its smallness by employing the Reissner - Nordström metric in general relativity. We argue that the Q2 - term in this metric is due to the minuscule contribution of the energy of the electric field of the central body to its gravitational field. Thus being gravitational, this metric cannot be used to calculate the amount of the alleged electrostatic redshift.

Forecasting cosmological bias due to local gravitational redshift

When photons from distant galaxies and stars pass through our neighboring environment, the wavelengths of the photons would be shifted by our local gravitational potential. This local gravitational redshift effect can potentially have an impact on the measurement of cosmological distance–redshift relation. Using available supernovae data, Wojtak, Davis and Wiis [J. Cosmol. Astropart. Phys. 2015 (2015) 025] found seemingly large biases of cosmological parameters for some extended models (nonflat [Formula: see text]CDM, [Formula: see text]CDM, etc.). Huang [Phys. Rev. D 91 (2015) 121301] pointed out that, however, the biases can be reduced to a negligible level if cosmic microwave background (CMB) data are added to break the strong degeneracy between parameters in the extended models. In this paper, we forecast the cosmological bias due to local gravitational redshifts for a future WFIRST-like supernovae survey. We find that the local gravitational redshift effect remains negligible, provided that CMB data or some future redshift survey data are added to break the degeneracy between parameters.

Gravitational redshift in the Galactic Center

Gravitation General relativity predicts that light emitted by an object in a strong gravitational field—for example, close to a black hole—should be shifted to longer wavelengths. This gravitational redshift does not exist in the Newtonian theory of gravity. Do et al. monitored the position and spectrum of the star S0-2 as it passed Sagittarius A*, the supermassive black hole at the center of the Milky Way. Around the closest part of S0-2's 16-year orbit, they detected the effect of gravitational redshift on its spectrum. These results are more consistent with general relativity than Newtonian gravity at the 5σ level. Science , this issue p. [664][1] [1]: /lookup/doi/10.1126/science.aav8137