Microwave background anisotropies and non-linear structures — II. Numerical computations

Dabrowski, Y.; Hobson, M. P.; Lasenby, A.; Doran, C.

doi:10.1046/j.1365-8711.1999.02164.x

Cited by 12 publications

(28 citation statements)

References 35 publications

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“…The perturbation is of finite extent, and we therefore need to fix initial conditions so that standard cosmology is satisfied outside a given radius R i . Here we will use a family of simple four‐parameter models based on polynomial perturbations in the density and velocity fields, as described in detail in Lasenby et al (1999) and Dabrowski et al (1999). The parameters controlling the velocity perturbation are: (i) the width of the perturbation R i ; (ii) the velocity gradient at the origin H ( t i , 0); (iii) the degree of the polynomial describing the perturbation, so that at r R i , the velocity and its first m derivatives match the external values; and (iv) the external velocity gradient ( t i ), equal to the Hubble constant at the time t i .…”

Section: Cluster Formation Modelmentioning

confidence: 99%

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Microwave background anisotropies arising from non-linear structures in open and Λ universes

Dabrowski¹,

Hall²,

Sawicki³

et al. 2000

Monthly Notices of the Royal Astronomical Society

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A new method arising from a gauge-theoretic approach to general relativity is applied to the formation of clusters in an expanding universe. The three cosmological models (Ω 0 =1, Ω Λ =0), (Ω 0 =0.3, Ω Λ =0.7), (Ω 0 =0.3, Ω Λ =0) are considered, which extends our previous application . A simple initial velocity and density perturbation of finite extent is imposed at the epoch z = 1000 and we investigate the subsequent evolution of the density and velocity fields for clusters observed at redshifts z = 1, z = 2 and z = 3. Photon geodesics and redshifts are also calculated so that the Cosmic Microwave Background (CMB) anisotropies due to collapsing clusters can be estimated. We find that the central CMB temperature decrement is slightly stronger and extends to larger angular scales in the non-zero Ω Λ case. This effect is strongly enhanced in the open case. Gravitational lensing effects are also considered and we apply our model to the reported microwave decrement observed towards the quasar pair PC 1643+4631 A&B.Key words: Gravitation -cosmology: theory -cosmology: gravitational lensingcosmic microwave background -quasars: individual: PC1643+4631 A&B -galaxies: clustering SECONDARY GRAVITATIONAL EFFECTRees and Sciama (1968) suggested that the presence of an evolving structure on the line of sight of a Cosmic Microwave Background (CMB) photon could significantly affect its observed temperature. This secondary gravitational effect is often described in terms of the potential well experienced by the CMB photon. For example, the potential well of a collapsing cluster becomes deeper over time so that the CMB photon has to climb out of a well deeper than that into which it fell, suffering a net loss of energy. As suggested in Rees and Sciama (1968) there is however a competing effect due to the extra time delay encountered by the photon. The overall effect can therefore be of either sign. The photon accumulates a redshift along its geodesic, resulting in a net temperature perturbation. In the weak-field approximation we have (see Martínez-González, Sanz & Silk 1990) where Φ is the gravitational potential of the perturbation and t is the cosmic time. A rough estimate of an upper limit to this effect can be estimated by assuming that the potential well varies from Φ = 0 to Φ = Φc during the time ⋆ Email: youri@mrao.cam.ac.uk that the photon traverses it, where Φc is the gravitational potential of a rich Abell cluster. In this case, we haveThe potential of the cluster can be related to the velocity dispersion σ through σ 2 = GM/R = Φc, where M and R are the mass and radius of the cluster. Assuming σ = 1000 km s −1 givesIn most cases, this anisotropy should therefore be small compared with other secondary anisotropies caused by the interaction of CMB photons with non-linear structures, such as the thermal Sunyaev-Zel'dovich (SZ) effect. However, equation (1) is only valid in the linear regime and a fully relativistic treatment in the non-linear regime is necessary to estimate accurately the Rees-Sciama effect. Seve...

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Section: Cluster Formation Modelmentioning

confidence: 99%

“…Although parameters (ii) and (iii) are somewhat arbitrary, we believe that they establish a simple way to obtain a continuous and smooth velocity perturbation with only two parameters. As a typical value, we assume in this paper m =3 (see Dabrowski et al 1999).…”

Section: Cluster Formation Modelmentioning

confidence: 99%

Microwave background anisotropies arising from non-linear structures in open and Λ universes

Dabrowski¹,

Hall²,

Sawicki³

et al. 2000

Monthly Notices of the Royal Astronomical Society

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“…For example, the microwave decrements associated with quasar pairs reported by Jones et al (1997) and Richards et al (1997) may be due to combined Sunyaev‐‐Zel'dovich and gravitational effects from high‐redshift clusters. This is discussed further in an accompanying paper (Dabrowski et al 1999, hereafter Paper II), where the theoretical model for the gravitational effect described here is implemented numerically. Some results of this analysis are briefly discussed in the concluding section.…”

Section: Introductionmentioning

confidence: 99%

Microwave background anisotropies and non-linear structures — I. Improved theoretical models

Lasenby¹,

Doran²,

Hobson³

et al. 1999

Monthly Notices of the Royal Astronomical Society

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A new method is proposed for modelling spherically symmetric inhomogeneities in the Universe. The inhomogeneities have finite size and are compensated, so they do not exert any measurable gravitational force beyond their boundary. The region exterior to the perturbation is represented by a Friedmann‐‐Robertson‐‐Walker (FRW) universe, which we use to study the anisotropy in the cosmic microwave background (CMB) induced by the cluster. All calculations are performed in a single, global coordinate system, with non‐linear gravitational effects fully incorporated. An advantage of the gauge choices employed here is that the resultant equations are essentially Newtonian in form. Examination of the problem of specifying initial data shows that the new model presented here has many advantages over `Swiss cheese' and other models. Numerical implementation of the equations derived here is described in a subsequent paper.

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“…Martínez‐Gonzalez & Sanz 1990; Puchades et al 2006). With such angular scales and amplitudes, this effect is not likely to have a significant contribution to decrement H. However, Dabrowski et al (1999) studied the physical properties a galaxy cluster may have to produce a combined SZ and RS signal which could account for the CMB decrement detected by Jones et al (1997) in the direction of the quasar pair PC 1643+4631 A&B without X‐ray emission and found a more significant RS signal. According to their calculations, a galaxy cluster at z = 1 with T e ∼ 1.3 keV and enclosing a total mass of ∼10 16 M ⊙ would produce SZ and RS effects, respectively, of the order of ∼500 and ∼250 μK without a significant X‐ray emission.…”

Section: Origin Of the Decrementmentioning

confidence: 99%

Observations of the Corona Borealis supercluster with the superextended Very Small Array: further constraints on the nature of the non-Gaussian cosmic microwave background cold spot

Génova-Santos¹,

Rubiño-Martín²,

Rebolo³

et al. 2008

Monthly Notices of the Royal Astronomical Society

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We present interferometric imaging at 33 GHz, with the new superextended configuration of the Very Small Array (VSA), of a very deep decrement in the cosmic microwave background (CMB) temperature. This decrement is located in the direction of the Corona Borealis supercluster, at a position with no known galaxy clusters, and was discovered by a previous VSA survey. A total area of 3 deg2 has now been imaged, with an angular resolution of 7 arcmin and a flux sensitivity of 5 mJy beam−1. These observations confirm the presence of this strong and resolved negative spot at −37 ± 5 mJy beam−1(−229 ± 32 μK). This structure is also present in the Wilkinson Microwave Anisotropy Probe 5‐year data. The temperature of the W‐band (94 GHz) data at the position of the decrement agrees within 0.3σn with that observed by the VSA at 33 GHz and within 0.2σn with the Sunyaev–Zel'dovich (SZ) spectrum. Our analyses show that it is a non‐Gaussian feature in the CMB at a level of 4.4σ, where sigma accounts for primordial CMB fluctuations, thermal noise and residual radio source contributions. The probability of finding such a deviation or larger in simulations including Gaussian CMB is only 0.63 per cent. Therefore, an explanation other than primordial Gaussian CMB is required. We have considered the possibility of an SZ effect generated in a diffuse, extended warm/hot gas distribution. This hypothesis is especially relevant, as the presence of such structures, if confirmed, could provide the location for a significant fraction of the missing baryons in the Local Universe. However, from the absence of X‐ray emission in this region we conclude that the whole decrement cannot be generated solely via the SZ effect in such structure. Therefore, the most plausible scenario is a combination between a negative CMB feature and a SZ effect, probably generated by a warm/hot gas distribution.

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Microwave background anisotropies and non-linear structures — II. Numerical computations

Cited by 12 publications

References 35 publications

Microwave background anisotropies arising from non-linear structures in open and Λ universes

Microwave background anisotropies arising from non-linear structures in open and Λ universes

Microwave background anisotropies and non-linear structures — I. Improved theoretical models

Observations of the Corona Borealis supercluster with the superextended Very Small Array: further constraints on the nature of the non-Gaussian cosmic microwave background cold spot

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