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Hsw Void As the Origin of Cold Spot

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Hsw Void As the Origin of Cold Spot Suranaree J. Sci. Technol. Vol. 23 No. 4; October – December 2016 85 Suranaree J. Sci. Technol. Vol. 23 No. 4; October - December 2016 435 HSW VOID AS THE ORIGIN OF COLD SPOT Anut Sangka1,2 , Utane Sawangwit2, Nuanwan Sanguansak1, and 3 Teeraparb Chantavat∗ Received: September 09, 2016; Revised: November 28, 2016; Accepted: December 01, 2016 Abstract The cosmic microwave background (CMB) cold spot (CS) anomaly is one of the most important unresolved issues in CMB observations. The CS has an angular radius in the o sky greater than 5 and a temperature at the centre of about 160 μK which is lower than the average (8.3 times the root mean square of CMB fluctuations). This research is aimed at investigating the origin of the CS as the secondary anisotropy CMB fluctuations, specifically the integrated Sachs-Wolfe (ISW) effect by cosmic voids. The Hamaus, Sutter, and Wendelt void profile is used in the ISW calculation. The calculation shows that the radius of void rv, the central density contrast δc, and the redshift z are needed to be −1 . Mpc h , −0.5 (specific value), and . , respectively. The void profile can fit the data�ퟑퟎ quite well except for the positive fluctuation�ퟎ ퟔퟎ region in the CS and the probability �ퟐퟎ �ퟎ ퟏퟑ ofퟏퟗퟎ finding such a void is only 10−17. ퟎ ퟒퟓ Keywords: CMB, cosmic voids, ISW effect Introduction The cosmic microwave background (CMB) with very small Gaussian fluctuations. The radiation is the earliest electromagnetic signal root mean square (RMS) of the fluctuations is of the Universe that can be observed. In hot about 18 μK (Planck Collaboration, 2014). The Big Bang cosmology, the CMB is an CMB measurement by Planck has shown that electromagnetic wave that freely traversed the its results almost agree with the standard Universe after the epoch of recombination. cosmological model’s Lambda cold dark The CMB has a black-body spectrum with the matter (ΛCDM) predictions except for some current average temperature of 2.725 K. strange imprinted parts in the CMB map such Theoretically, the primordial CMB map is as the CS. In 2005, Cruz et al. analysed the 5- almost smooth everywhere across the Universe year data of the Wilkinson Microwave 1 School of Physics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand. Tel. 0-4422-4319; Fax. 0-4422-4651; E-mail: [email protected] 2 National Astronomical Research Institute of Thailand, Chiang Mai, 50200, Thailand. 3 The Institute for Fundamental Study, Naresuan University, Phitsanulok, 65000, Thailand. * Corresponding author SuranareeSuranaree J. Sci.J. Sci. Technol. Technol. 23(4):435-441 23(4):xxx-xxx 43686 HSW Void asas thethe OriginOrigin ofof ColdCold SpotSpot Anisotropy Probe (WMAP) mission and found (2014). The HSW profile was obtained from the CS. This large CS is located in the Southern N-body simulations. This profile can fit the Galactic Cap, l 209o, b −57o. It has an observational data very well, especially for the -1 angular radius about 10o in the sky. The voids of a radius 10 < rv < 60 Mpc h (Hamaus et al., 2014). For the voids with a radius greater temperature of the centre of the CS is 160 μK -1 lower than the average CMB temperature (8.9 than 60 Mpc h the profile is not well times the RMS). Since, both the temperature examined due to the lack of data in the and size of the CS deviate from the theoretical simulations. In this work, we try to extrapolate prediction significantly, the origin of the CS is the HSW profile to a high radius and try to fit not expected to be the primordial CMB the ISW effect of the HSW profile to the CS. anisotropy temperature fluctuations. Other studies such as Finelli et al. (2015) and Inoue (2012) point out that the origin of the CS could Theoretical Background be the ISW effect due to a super-void. The other explanations are the parallel Universe HSW Void Profile and the cosmic texture, a remnant of a phase The HSW void density profile has 3 transition in the early Universe (Cruz et al., parameters, the central density contrast δc, the 2007). The ISW effect (Sachs and Wolfe, radius rv, and the scale radius rs at which the 1967), is the effect that the photon changes density contrast is zero. the temperature when it travels though the dynamical gravitational field. In a flat ( ) ( ) = 1 = , (1) ( / )� Friedmann-Lemaître-Robertson-Walker (FLRW) �� �� �⁄�� � universe, the ISW effect occurs if, and only if, 훿 푟 � − 훿� �� � �� the Universe expands; however, it is very where and are the density of the void and mean cosmic density, respectively. α and β sensitive to dark energy. This makes the ISW � effect an excellent probe for the dark energy. have an휌 approximately휌̅ linear relation with When a photon travels through dense regions rs/rv by the following equations: (galaxy clusters), it gains energy and when it comes out it loses energy. But due to the α(rs/rv) ≃ −2(rs/rv − 2), (2) accelerated expansion of the Universe, the galaxy cluster loses its density; the amount of 17.5 6.5 for < 0.91 energy that the photon loses when it comes out 9.8 + 18.6 for 0.91 (3) �⁄ � �⁄ � is less than the amount of energy that is gains 푟 푟 − 푟 푟 훽 ≃ � � � � � when it goes in and, consequently, the We− can푟 ⁄ 푟write Equation푟 ⁄ (1)푟 ≥ as a function temperature of the photon will be increased. of x = r/rv, On the other hand, when a photon travels through the under-dense regions (voids) it ( ) ( ) = 1 = , (4) ( �) will be colder. For a decelerated universe the �� ���� � results of the ISW effect will be inverse. There � � ��� 훿 푟 − -α 훿 are many void profiles, which were proposed where λ = (rs/rv) . The plot between the profile to solve the origin of the CS. Most of those of Equation (1) and observational data is models prefer the radius of the void (rv) to be illustrated in Figure 1. One of the special greater than 150 Mpc h-1. For example, Finelli features of the HSW profile is that it includes et al. (2015) uses the Λ-Lemaître-Tolman- a positive density contrast region (a so-called Bondi (LTB) geometry to find the density void compensation) (Hamaus et al., 2014), perturbation of a void. This work states that while other void density profiles do not include v 190 this. Figure 1 shows that the HSW profile can the super-void has a radius r = Mpc -1 ��� describe the void compensation well. h , with the central density contrast δc . ��� =0.37 . That void should be located at . redshift�� �� = 0.15 . In 2014, Hamaus, ISW Effect Calculation �� �� . Sutter, and Wendelt�� �� (HSW) proposed the The ISW temperature fluctuation ( ) � universal푧 void density�� �� profile in Hamaus et al. at the direction can be calculated by ∆푇��� 푛� 푛� SuranareeSuranaree J.J. Sci.Sci. Technol.Technol. Vol. 23 No. 4;4; October -– DecemberDecember 20162016 43787 ( ) ( , ) CMB Weak Gravitational Lensing = (5) ◦ ∆���� �� � ��� �� � �� On a small scale (<1 ) the weak � � � gravitational lensing effect can change the where the� integration− � ∫ is performed�� 푑푧 from the redshift z = 0 to the last scattering surface appearance of the CMB map by deflecting the z ≈ 1000. The Newtonian potential Φ relates photon’s trajectory with the deflection angle LS . Regarding the lensed CMB temperature to the density contrast δ by the Poisson anisotropy in the direction in the sky, ( ) equation, 훼is� equivalent to an unlensed anisotropy ( + ). Because the deflection푛� angle is 푇�very푛� = 4 ( ) ( = 0), (6) small, we can use Taylor’s expansion푇 푛 � to � � � approximate훼� ( ) as 훼� where∇ Φ G휋퐺 is푎 the휌̅퐷 Newton푧 훿 푧 universal gravitation constant, a is scale factor (a = 1/(1+z)), and 푇� 푛� 1 ( ) = ( ) + ( ) + ( ) + ( ). D (z) is the linear growth factor. 2 + � � � � Equation (5) can be discretised to the 푇 � 푛� 푇 푛� 훼�휕 푇 푛� 훼�훼�휕 휕 푇 푛� 풪(9)훼 summation form by, The deflection angle for a typical void ( , ) −1 ≃ { ( , ) ( , )}. (7) (15 rV 30 Mpc h and rs/rV 0.91) can be ��� �� � �� 훼� � ��� ��� calculated by finding the gradient of lensing ∫ � �� 푑푧 → ∑ Φ 푧 푛� − Φ 푧 푛� With linear perturbation density, the summation potential≤ ≤ ( ), can be described by ( ) = 휓 휃( ) (10) { ( , ) ( , )} = ( ){ ( ( ), ) ( ( ), )}, (8) � ∑� Φ 푧��� 푛� − Φ 푧��� 푛� ∑� 퐷� 푧� Φ� 퐷� 푧��� 푛� − The훼� 휃 lensing∇ 휓potential휃 is defined by Φ � 퐷� 푧��� 푛� ( ( ), ) where is the non-redshift ( ) = ( , ) (11) evolution Newtonian potential at the angular � � � Φ 퐷 푧 푛� � diameter distance ( ) in the direction . 휓 휃 − � ∫ Φ 휒 푛� 푑휒 퐷� 푧 푛� Figure 1. Stacked density profiles of voids at redshift zero in 8 sets of the voids’ radii. The shaded regions represent the standard deviation σ of each stacks (scaled down by 20 forvisibility), while the error bars come from standard errors on the mean profile where is the number of voids. The solid lines are the best fit solutions from the density profile of Equation (1). The picture is captured from Hamaus et al., (2014) 흈⁄�푵푽 푵푽 43888 HSW Void as the Origin of Cold Spot -1 where we integrate along the line of sight χ. void of size 10 < rv < 45 Mpc h and find the For the HSW void profile with rs/rv = 0.91, ISW effect and CMB weak lensing of such Chantavat et al. (2016) show that the lensing a void, we will see that the contribution of potential can be described by the ISW effect is dominant (Figure 2). Consequently, the contribution from the weak ( , , ) ( , ) × ( ), (12) lensing effect can be ignored for the CS temperature.
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