Gravitational Potential Perturbations Research Articles

ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534

The lensing power spectra for gravitational potential, astrometric shift, and convergence perturbations are powerful probes to investigate dark matter structures on small scales. We report the first lower and upper bounds of these lensing power spectra on angular scale ∼1″ toward the anomalous quadruply lensed quasar MG J0414+0534 at a redshift z = 2.639. To obtain the spectra, we conducted observations of MG J0414+0534 using the Atacama Large Millimeter/submillimeter Array with high angular resolution (0.″02–0.″05). We developed a new partially nonparametric method in which Fourier coefficients of potential perturbation are adjusted to minimize the difference between linear combinations of weighted mean de-lensed images. Using positions of radio-jet components, extended dust emission on scales >1 kpc, and mid-infrared flux ratios, the range of measured convergence, astrometric shift, and potential powers at an angular scale of ∼1.″1 (corresponding to an angular wavenumber of l = 1.2 × 106 or ∼9 kpc in the primary lens plane) within 1σ are Δ κ = 0.021–0.028, Δ α = 7–9 mas, and Δ ψ = 1.2–1.6 mas2, respectively. Our result is consistent with the predicted abundance of halos in the line of sight and subhalos in cold dark matter models. Our partially nonparametric lens models suggest the presence of a clump in the vicinity of object Y, a possible dusty dwarf galaxy, and some small clumps in the vicinity of other lensed quadruple images. Although much fainter than the previous report, we detected weak continuum emission possibly from object Y with a peak flux of ∼100 μJy beam−1 at the ∼4σ level.

On the Dynamical Heating of Dwarf Galaxies in a Fuzzy Dark Matter Halo

Fuzzy dark matter (FDM), consisting of ultralight bosons, is an intriguing alternative to cold dark matter. Numerical simulations solving the Schrödinger–Poisson (SP) equation, which governs FDM dynamics, show that FDM halos consist of a central solitonic core (representing the ground state of the SP equation), surrounded by a large envelope of excited states. Wave interference gives rise to density fluctuations of order unity throughout the envelope and causes the soliton to undergo density oscillations and execute a confined random walk in the central region of the halo. The resulting gravitational potential perturbations are an efficient source of dynamical heating. Using high-resolution numerical simulations of a 6.6 × 109 M ⊙ FDM halo with boson mass m b = 8 × 10−23 eV, we investigate the impact of this dynamical heating on the structure and kinematics of spheroidal dwarf galaxies of a fixed mass but different initial sizes and ellipticities. The galaxies are set up in equilibrium in the time-and-azimuthally averaged halo potential and evolved for 10 Gyr in the live FDM halo. We find that they continuously increase their sizes and central velocity dispersions. In addition, their kinematic structures become strongly radially anisotropic, especially in the outskirts. Dynamical heating also causes initially ellipsoidal galaxies to become more spherical over time from the inside out and gives rise to distorted, nonconcentric isodensity contours. These telltale characteristics of dynamical heating of dwarf galaxies in FDM halos can potentially be used to constrain the boson mass.

Can ultralight dark matter explain the age–velocity dispersion relation of the Milky Way disc: A revised and improved treatment

ABSTRACT Ultralight axion-like particles ma ∼ 10−22 eV, or Fuzzy Dark Matter (FDM), behave comparably to cold dark matter (CDM) on cosmological scales and exhibit a kpc-size de Broglie wavelength capable of alleviating established (sub-)galactic-scale problems of CDM. Substructures inside an FDM halo incur gravitational potential perturbations, resulting in stellar heating sufficient to account for the Galactic disc thickening over a Hubble time, as first demonstrated by Church et al. We present a more sophisticated treatment that incorporates the full baryon and dark matter distributions of the Milky Way and adopts stellar disc kinematics inferred from recent Gaia, APOGEE, and LAMOST surveys. Ubiquitous density granulation and subhalo passages, respectively, drive inner disc thickening and flaring of the outer disc, resulting in an observationally consistent ‘U-shaped’ disc vertical velocity dispersion profile with the global minimum located near the solar radius. The observed age–velocity dispersion relation in the solar vicinity can be explained by the FDM-substructure-induced heating and places an exclusion bound ma ≳ 0.4 × 10−22 eV. We assess non-trivial uncertainties in the empirical core–halo relation, FDM subhalo mass function and tidal stripping, and stellar heating estimate. The mass range ma ≃ 0.5–0.7 × 10−22 eV favoured by the observed thick disc kinematics is in tension with several exclusion bounds inferred from dwarf density profiles, stellar streams, and Milky Way satellite populations, which could be significantly relaxed due to the aforesaid uncertainties. Additionally, strongly anisotropic heating could help explain the formation of ultra-thin disc galaxies.

The Strength of the Dynamical Spiral Perturbation in the Galactic Disk

Abstract The mean Galactocentric radial velocities of luminous red giant stars within the midplane of the Milky Way reveal a spiral signature, which could plausibly reflect the response to a nonaxisymmetric perturbation of the gravitational potential in the Galactic disk. We apply a simple steady-state toy model of a logarithmic spiral to interpret these observations, and find a good qualitative and quantitative match. Presuming that the amplitude of the gravitational potential perturbation is proportionate to that in the disk’s surface mass density, we estimate the surface mass density amplitude to be at the solar radius when choosing a fixed pattern speed of . Combined with the local disk density, this implies a surface mass density contrast between the arm and inter-arm regions of approximately ±10% at the solar radius, with an increase toward larger radii. Our model constrains the pitch angle of the dynamical spiral arms to be approximately 12°.

Tilting Styx and Nix but not Uranus with a Spin-Precession-Mean-motion resonance.

A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about a star. We expand the planet-planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet's obliquity to near 90 or 180 degrees depending upon whether the spin resonance is first or zero-th order in inclination. Past capture of Uranus into such a spin resonance could give an alternative non-collisional scenario accounting for Uranus's high obliquity. However we find that the time spent in spin resonance must be so long that this scenario cannot be responsible for Uranus's high obliquity. Our model can be used to study spin resonance in satellite systems. Our Hamiltonian model explains how Styx and Nix can be tilted to high obliquity via outward migration of Charon, a phenomenon previously seen in numerical simulations.

Scalar and vector perturbations in a universe with discrete and continuous matter sources

We study a universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies and their groups and clusters) and two sets of perfect fluids with linear and nonlinear equations of state, respectively. The background spacetime geometry is defined by the FLRW metric. In the weak gravitational field limit, we develop the first-order scalar and vector cosmological perturbation theory. Our approach works at all cosmological scales (i.e. sub-horizon and super-horizon ones) and incorporates linear and nonlinear effects with respect to energy density fluctuations. We demonstrate that the scalar perturbation (i.e. the gravitational potential) as well as the vector perturbation can be split into individual contributions from each matter source. Each of these contributions satisfies its own equation. The velocity-independent parts of the individual gravitational potentials are characterized by a finite time-dependent Yukawa interaction range being the same for each individual contribution. We also obtain the exact form of the gravitational potential and vector perturbation related to the discrete matter sources. The self-consistency of our approach is thoroughly checked. The derived equations can form the theoretical basis for numerical simulations for a wide class of cosmological models.

Non-radial oscillations in rotating giant planets with solid cores: Application to Saturn and its rings

Recent observations have revealed evidence for the global acoustic oscillations of Jupiter and Saturn. Such oscillations can potentially provide a new window into the interior structure of giant planets. Motivated by these observations, we study the non-radial oscillation modes of giant planets containing a solid core. Our calculations include the elastic response of the core and consider a wide range of possible values of the core shear modulus. While the elasticity of the core only slightly changes the frequencies of acoustic modes (including the f-modes), which reside mostly in the fluid envelope, it adds two new classes of shear modes that are largely confined to the core. We also calculate the effects of the Coriolis force on the planetary oscillation modes. In addition to changing the mode frequencies, the Coriolis force can cause the shear modes to mix with the f-modes. Such mixing occurs when the frequencies of the shear mode and the f-mode are close to each other, and results in “mixed modes” that have similarly large surface displacements and gravitational potential perturbations, but are slightly split in frequency. We discuss our results in light of the recent work by Hedman and Nicholson (Hedman, M., Nicholson, P. [2013]. arXiv:1304.3735), which revealed the presence of density waves in Saturn’s C-ring that appear to be excited by the gravitational perturbations associated with the f-mode oscillations within Saturn. We find that the fine splitting in wave frequencies observed in the rings can in principle be explained by the rotation-induced mixing between core shear modes and f-modes, possibly indicating the presence of a solid core within Saturn. However, in our current calculations, which assume rigid-body rotation and include only first-order rotational effects, significant fine-tuning in the planetary model parameters is needed in order to achieve these mode mixings and to explain the observed fine frequency splitting. We briefly discuss other effects that may modify the f-modes and facilitate mode mixing.

A new model for gravitational potential perturbations in disks of spiral galaxies. An application to our Galaxy

We propose a new, more realistic, description of the perturbed gravitational potential of spiral galaxies, with spiral arms having Gaussian-shaped groove profiles. We investigate the stable stellar orbits in galactic disks, using the new perturbed potential. The influence of the bulge mass on the stellar orbits in the inner regions of a disk is also investigated. The new description offers the advantage of easy control of the parameters of the Gaussian profile of its potential. We find a range of values for the perturbation amplitude from 400 to 800 km^2 s^{-2} kpc^{-1} which implies a maximum ratio of the tangential force to the axisymmetric force between 3% and 6%, approximately. Good self-consistency of arm shapes is obtained between the Inner Lindblad resonance (ILR) and the 4:1 resonance. Near the 4:1 resonance the response density starts to deviate from the imposed logarithmic spiral form. This creates bifurcations that appear as short arms. Therefore the deviation from a perfect logarithmic spiral in galaxies can be understood as a natural effect of the 4:1 resonance. Beyond the 4:1 resonance we find closed orbits which have similarities with the arms observed in our Galaxy. In regions near the center, in the presence of a massive bulge, elongated stellar orbits appear naturally, without imposing any bar-shaped potential, but only extending the spiral perturbation a little inward of the ILR. This suggests that a bar is formed with a half-size around 3 kpc by a mechanism similar to that of the spiral arms. The potential energy perturbation that we adopted represents an important step in the direction of self-consistency, compared to previous sine function descriptions of the potential. Our model produces a realistic description of the spiral structure, able to explain several details that were not yet understood.

Symplectic integration of space debris motion considering several Earth’s shadowing models

In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones. Indeed, it has already been demonstrated that such objects could stay there for hundreds of years. Our model takes into account the Earth’s gravitational potential, luni-solar and planetary gravitational perturbations and direct solar radiation pressure. Based on the analysis of the energy conservation and on a comparison with a high order non-symplectic integrator, we show that our algorithm allows us to use large time steps and keep accurate results. We also propose an innovative method to model Earth’s shadow crossings by means of a smooth shadow function. In the particular framework of symplectic integration, such a function needs to be included analytically in the equations of motion in order to prevent numerical drifts of the energy. For the sake of completeness, both cylindrical shadows and penumbra transitions models are considered. We show that both models are not equivalent and that big discrepancies actually appear between associated orbits, especially for high area-to-mass ratios.

Hydrodynamics of rapidly rotating superfluid neutron stars with mutual friction

We study time evolutions of superfluid neutron stars, focussing on the nature of the oscillation spectrum, the effect of mutual friction force on the oscillations and the hydrodynamical spin-up phase of pulsar glitches. We linearise the dynamical equations of a Newtonian two-fluid model for rapidly rotating backgrounds. In the axisymmetric equilibrium configurations, the two fluid components corotate and are in beta-equilibrium. We use analytical equations of state that generate stratified and non-stratified stellar models, which enable us to study the coupling between the dynamical degrees of freedom of the system. By means of time evolutions of the linearised dynamical equations, we determine the spectrum of axisymmetric and non-axisymmetric oscillation modes, accounting for the contribution of the gravitational potential perturbations, i.e. without adopting the Cowling approximation. We study the mutual friction damping of the superfluid oscillations and consider the effects of the non-dissipative part of the mutual friction force on the mode frequencies. We also provide technical details and relevant tests for the hydrodynamical model of pulsar glitches discussed by Sidery, Passamonti and Andersson (2010). In particular, we describe the method used to generate the initial data that mimic the pre-glitch state, and derive the equations that are used to extract the gravitational-wave signal.

Time evolution of rapidly rotating stratified neutron stars

We study the time evolution of non-axisymmetric oscillations of rapidly rotating neutron stars. The rotation is assumed uniform and the stellar models have composition gradients that generate gravity restored oscillation modes. We work in linear Newtonian perturbation theory and in Cowling approximation, i.e. we neglect the gravitational potential perturbations. We study for the first time the behaviour of the inertia-gravity modes in fast spinning stars, and carry out a detailed comparison of non-stratified and stratified models. In particular, we show that each g-mode becomes rotation-dominated, i.e. approaches a particular inertial mode, as the rotation rate of the star is increased.

Statistics of gravitational potential perturbations: A novel approach to deriving the X-ray temperature function

<i>Context. <i/>While the halo mass function is theoretically a very sensitive measure of cosmological models, masses of dark-matter halos are poorly defined, global, and unobservable quantities.<i>Aims. <i/>We argue that local, observable quantities such as the X-ray temperatures of galaxy clusters can be directly compared to theoretical predictions without invoking masses. We derive the X-ray temperature function directly from the statistics of Gaussian random fluctuations in the gravitational potential.<i>Methods. <i/>We derive the abundance of potential minima constrained by the requirement that they belong to linearly collapsed structures. We then use the spherical-collapse model to relate linear to non-linear perturbations, and the virial theorem to convert potential depths to temperatures. No reference is made to mass or other global quantities in the derivation.<i>Results. <i/>Applying a proper high-pass filter that removes large enough modes from the gravitational potential, we derive an X-ray temperature function that agrees very well with the classical Press-Schechter approach on relevant temperature scales, but avoids the necessity of measuring masses.<i>Conclusions. <i/>This first study shows that and how an X-ray temperature function of galaxy clusters can be analytically derived, avoiding the introduction of poorly defined global quantities such as halo masses. This approach will be useful for reducing scatter in observed cluster distributions and thus in cosmological conclusions drawn from them.

Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of ${\ensuremath{\varphi}}_{v}$ order higher than the second-order terms where ${\ensuremath{\varphi}}_{v}$ is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have $\ensuremath{\delta}\ensuremath{\Phi}\ensuremath{\sim}\frac{3}{5}{\ensuremath{\varphi}}_{v}$ to the linear order. Therefore, the pure general relativistic effects are of ${\ensuremath{\varphi}}_{v}$ order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have $\frac{\ensuremath{\delta}T}{T}\ensuremath{\sim}\frac{1}{3}\ensuremath{\delta}\ensuremath{\Phi}\ensuremath{\sim}\frac{1}{5}{\ensuremath{\varphi}}_{v}\ensuremath{\sim}{10}^{\ensuremath{-}5}$. Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon.

Surface gravitational field and topography changes induced by the Earth?s fluid core motions

Using a Love number formalism, the elastic deformations of the mantle and the mass redistribution gravitational potential within the Earth induced by the fluid pressure acting at the core–mantle boundary (CMB) are computed. This pressure field changes at a decadal time scale and may be estimated from observations of the surface magnetic field and its secular variation. First, using a spherical harmonic expansion, the poloidal and toroidal part of the fluid velocity field at the CMB for the last 40 years is computed, under the hypothesis of tangential geostrophy. Then the associated geostrophic pressure, whose order of magnitude is about 1000 Pa, is computed. The surface topography induced by this pressure field is computed using Love numbers, and is a few millimetres. The mass redistribution gravitational potential induced by these deformations and, in particular, the zonal components of the related surface gravitational potential perturbation (ΔJ2, ΔJ3 and ΔJ4 coefficients), are calculated. Overall perturbations for the J2 coefficient of about 10−10, for J3 of about 10−11 and for J4 are found of about 0.3×10−11. Finally, these theoretical results are compared with recent observations of the decadal variation of J2 from satellite laser ranging. Results concerning ΔJ2 can be described as follows: first, they are one order of magnitude too small to explain the observed decadal variation of J2 and, second, they show a significant linear trend over the last 40 years, whose rate of decrease amounts to 7% of the observed value.

Deformation Response of a Snrei Earth to Surface Loads and Tidal Forces

AbstractBased on the preliminary reference Earth model (PREM), we use the deformation theory for a spherically stratified and non‐rotating Earth with perfectly elastic and isotropic structural relation (SNREI Earth) to investigate the deformation characteristics under different forces exerting on the Earth. The 4th order Runge‐Kutta numerical integration technique is utilized to solve the motion equations of the Earth's displacement field. The numerical solutions for the deformation and gravitational potential perturbation within the Earth interior and on the surface under the surface loads and luni‐solar tidal force, as well as the Love numbers for surface loads and body tides are obtained. The results indicate that deformation within the solid inner core is very small. The variation of displacement at low spherical harmonic degrees (n &lt; 10) with radius is relatively complicated within the liquid outer core. While the loading degree is larger than 10, the deformation and the gravitational potential perturbation in the core, including both the inner and outer core, are significantly little. As a result, the Earth's response is mainly expressed as the radial displacement in the elastic mantle and decreases rapidly with increasing depth. The higher the loading degree is, the more rapidly this response decreases. The frequency‐dependence of Love numbers for the surface loads and body tides is very weak for a SNREI Earth. In the computation of Love numbers for the body tides, the motion equations for a SNREI Earth are also adopted. Meanwhile, the additional pressure on the core mantle boundary (CMB) is taken into account due to the Earth's rotation and ellipticity. The final results, obtained with this approximate procedure, are in good agreement with the tidal gravity observations on the Earth surface.

Effects of nonlinear rheology on degree 2 harmonic deformation in a spherical self‐gravitating earth

The effect of non‐linear rheology on surface displacements, gravitational potential perturbation and ∂tJ2 (or J2‐dot) for a self‐gravitating spherical earth is studied using a finite element code coupled to Poisson's equation. Four earth models investigated are: a model with uniform linear rheology throughout the mantle and three others containing nonlinear rheology in the whole mantle, upper mantle and lower mantle respectively. The effect of self‐gravitation is shown to be non‐negligible. The effects of nonlinear rheology in different parts of the mantle on surface displacements and potential have also been shown to be large. ∂tJ2 due to cyclic glaciation of the Laurentian, Fennoscandian, Barents Sea and Antarctic ice sheets over realistic oceans is also computed for all four rheology models. The model with nonlinear lower mantle cannot be ruled out by the observed data.

Super–Large‐Scale Structure and Large‐Scale Bias

We examine the in—uence of large-scale perturbations of gravitational potential on the spatial distribu- tion of galaxies and dark matter (DM). For appropriate parameters of the power spectrum, the cosmo- logical model, and the mass of dark matter particles, such perturbations can produce the wall-like superlarge-scale structure. Dynamics and parameters of the walls found in observations and simulations are related to the moments of the power spectrum. The wall-like elements are identi—ed with the Zeldo- vich pancakes (caustics) that form as a result of galaxy infall into the largest and deepest gravitational potential wells. Their properties are sensitive to the power spectrum and the background cosmological model, and they can be used to test and discriminate between diUerent models. When reheating of the baryonic component at redshifts and is allowed, the same perturbations produce sig- z z h 5 z h 10 ni—cant large-scale modulation of the spatial galaxy distribution relative to the more homogeneous DM distribution (large-scale bias). Subject headings: cosmology: theorygalaxies: clusters: generallarge-scale structure of universe

Normal Modes of Oscillation for Rotating Stars. V. A New Numerical Method for Computing Nonradial Eigenfunctions

This paper is a progress report on my efforts to develop a robust numerical scheme for computing eigenmodes of arbitrary order at arbitrary rotation rates. The slowly pulsating B stars and the line-profile variables on the upper main sequence provide the main impetus for the work. Consequently, the focus here is on the gravity modes responsible for these variables rather than on pressure modes. Unfortunately, the g-modes are harder to compute in general because their oscillation periods can be longer than the rotation periods of high-mass stars, which makes them more sensitive to the effects of inertial forces. The standard technique for calculating the nonradial modes of spherical stellar models is generalized to two dimensions. The four dependent variables are the radial and latitudinal components of the Lagrangian displacement together with the Eulerian pressure and gravitational potential perturbations, all evaluated on level surfaces and normalized to have nonzero values on the boundaries. The integration in polar angle is replaced by numerical differentiation which is performed by various techniques involving Fourier, Legendre, or Chebyshev transforms. For the radial integrations, two numerical schemes are explored. One involves explicit Runge-Kutta integration inward and outward with fitting at an intermediate level surface. The other is an implicit, finite-difference method that does not require an initial trial solution. Each has advantages and disadvantages, but both ultimately fail for the same reason—small numerical errors in the θ-derivatives of eigenfunctions that are being distorted by growing high-order spherical harmonic components that are mixed in by rotation. Lack of convergence appears when the ratio Ω/σ of angular velocity and mode frequency exceeds about 0.5. This makes high-order g-modes (n > 15) in the presence of large rotation inaccessible with the methods proposed here. Nevertheless, it is possible to conclude that rapid rotation and large radial order suppress the pressure perturbations but enhance the horizontal motions especially near the surface and the equatorial plane. In fact, this trend is sufficiently clear and persistent that it should be possible to model the line profiles of the observationally relevant modes without actually computing them exactly.

Cosmic Microwave Background Anisotropies from the Rees-Sciama Effect in Omega 0 &lt;=1 Universes

We investigate the imprint of nonlinear matter condensations on the Cosmic Microwave Background (CMB) in $\Omega_{0}<1$ cold dark matter (CDM) model universes. We consider simulation domains ranging from $120h^{-1}$ Mpc to $360h^{-1}$ Mpc in size. We concentrate on the secondary temperature anisotropies induced by time varying gravitational potentials occurring after decoupling. Specifically, we investigate the importance of the Rees-Sciama effect due to: (1) intrinsic changes in the gravitational potential of forming, nonlinear structures, (2) proper motion of nonlinear structures, and (3) late time decay of gravitational potential perturbations in open universes. CMB temperature anisotropies are obtained by numerically evolving matter inhomogeneities and CMB photons from an early, linear epoch ($z=100$) to the present, nonlinear epoch $(z=0)$. We test the dependence and relative importance of these secondary temperature anisotropies as a function of the scale of the underlying matter (voids, superclusters) and as a function of $\Omega_{0}$. The results of the $\Omega_{0}<1$ models are compared to a similarly executed $\Omega_{0}=1.0$ simulation. We find that in low density models all three sources of anisotropy could be relevant and reach levels of $\Delta T/T \sim 10^{-6}$. In particular, we find that for $\Omega_{0}<1$ at large scales, secondary temperature anisotropies are dominated by the decaying potential.

Looking for a cosmological constant with the Rees-Sciama effect.

In models with a cosmological constant a significant component of the cosmic microwave background (CMB) anisotropy is produced at rather low redshifts $z\ensuremath{\lesssim}1$. In these models, the gravitational potential perturbations begin to evolve at late times, shifting the frequencies of photons passing though them. Since the potential reflects the matter density, the latter should be correlated with the CMB anisotropy. We examine this correlation and discuss the prospects for using an x-ray/COBE comparison to detect a cosmological constant.