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 the super-void has a radius rv = 190 Mpc this. Figure 1 shows that the HSW profile can -1 h , with the central density contrast�� δc describe the void compensation well. . �� =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�

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( ) ( , ) 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. 휓 푏⁄푟� 푟� 푧 ≃ 푆 푟� 푧 휓� 푏⁄푟� where the impact parameter b = Ddθ, Dd is the angular diameter distance to the lens plane, Measure the CS One Dimensional Temperature ( ) is the scale-invariant lensing potential, Profile and ( , ) is the lensing potential scaling The Planck SMICA 2015 data has � 휓factor.푥 � been used in this research. We obtain the 푆 푟 푧 1-dimensional CS temperature profile by ( ) = exp( ) × (1.0 + ) , (13) finding the average temperature fluctuations �� within a ring, where each ring has a thickness � � � w휓here푥 휓 Γ 푥 푥 of 1o. For example, the average temperature at 2 -2 = 9.06 × 10 Mpc h , 1.5o ( ( = 1.5°)) is = 1.29, �� 휓�= 2.86, � 휃 ( = ∆1.푇5°)휃= ( ) (15) 훾 = 1.72, and � � 훾 = 0.31. �°��° � ∆푇 휃 � ∑ ∆푇 휃 훾 − where is the number of pixels inside the ring � Γ − ( ) ( ) o ( , ) = , with an inner radius of 1 and an outer radius ( / � ) (14) �� o 푁 � �� of 2 and we sum over all pixels inside the ring. � � �� 푆 푟 푧 � Ω 휌 �� The uncertainty of the CS profile at data point where Ωm is the density parameter of matter and is the critical density. i ( ) is calculated by random generation of 1000 CMB maps and calculating the standard � 휌�� deviation휎 inside the rings over the 1000 maps. Result and Discussion Cold Spot Fitting Data 2 ISW and CMB Weak Lensing Comparison In order to test the model, the χ reduced method As mentioned earlier, the ISW effect is a is used to find a goodness of fit. We describe large-scale effect. In contrast, the weak only a summary of this method; for more gravitational lensing, which only changes the details the readers can follow Press et al. appearance of the CMB map, is a small-scale (2007). Let be the observed temperature effect. For example, if we consider a typical at the data point�� ith, be the ISW � Δ푇 �� ∆푇�

Figure 2. A comparison between the ISW and CMB weak lensing effects for a void of radius -1 rv = 30 Mpc h ; it is obvious that the ISW is dominant

SuranareeSuranaree J. J. Sci. Sci. Technol. Technol. Vol.Vol. 23 No. 44;; October –- DecemberDecember 2016 89439 temperature at data point ith, and be the the negative while the region near the edge of uncertainty of observational data at data point the CS (r ≈ 15o) has the positive fluctuations. � ith, then the χ2 will be 휎 Figure 4 shows the χ2 contour plot between parameters. From the plot, we can see that there are correlations between those sets of � = �� (16) parameters. In fact, Hamaus et al. (2014) �∆�� shows that δc tends to be -0.5 for a void with a � � 휒 ∑ � -1 2 2 radius greater than 70 Mpc h and rs/rv = 0.91 The χ reduced is just χ divided by the number of degrees of freedom, which is the for an effective value. If we follow this number of data points subtracted by the assumption, the best fit parameters are now number of free parameters. δc = −0.5, -1 = (17) rV = 190 [Mpc h ], � � � rs/rv = 0.91,�� 2 휒 In this research the number of data points χ reduced = 0.99. is 30 (we have 30 positions) and 4 parameters ( , z, and / ). Hence, the Comparing to the other void profiles such number of degrees of 휃freedom is 26. The as Finelli et al. (2015), we found that the HSW 훿� 푟� 푟� 푟� 2 parameter set that gives us the minimum χ is void also provides a void of radius greater than the best-fit parameter set. We also report the 150 Mpc h-1 to fit the CS. For the positive 2 2 χ reduced calculated from the minimum χ using fluctuation region, which is at the edge of the 2 CS, the fluctuation is much lower than inside Equation (17). The χ reduced can be used to indicate the goodness of fit of the model. If it the CS. We may assume that this is the ISW is close to 1, then the model is considered to be effect due to galaxy clusters (the over-dense a good fit. For χ2 that is much greater than region, the opposite of the void) or it may be reduced just the normal CMB fluctuation (30 μK is less 1, it indicates that the model is not good than 3 of the CMB temperature fluctuations). enough, while a value much lower than 1 Note that, from Hamaus et al. (2014), the HSW means that the measured uncertainty could be profile휎 is only well approximated up to rV 60 over-estimated. Mpc h-1. In this work, we extrapolate the Figure 3 shows the ISW effect from the profile to a larger size. ≤ best-fit parameter set fit to the CS temperature In addition, we not only calculate the profile. The void parameters are z = 0.45, δ = c ISW effect of the HSW void. We also find that -1 2 0.5, rv = 190 Mpc h , rs/rv = 0.91, and χ reduced the probability of a void with a radius greater = 0.99 (with degrees of freedom 26). We can than 150 Mpc h-1 would exist by considering see that the ISW effect approaches zero from the void abundance (Pisani et al., 2015),

Figure 3. The best-fit parameter set of HSW void ISW to the CS 1-dimensional temperature profile

44090 HSW Void asas thethe OriginOrigin ofof ColdCold SpotSpot multiverse cosmology, which predicts that our ( , ) Universe is just the local Universe and that = ( ) , (18) �� there would be at least 1017 Universes to ensure

� � 휈푓 휈 � that the super-void exists. where M is the void mass, the background density, and n(M, z) the number density of voids of a given mass and휌̅ redshift. The fraction ( ) of mass that has evolved into Conclusions voids can be approximated as: 푓 휈 In this work, we aim to investigate the origin of the CS as the secondary anisotropy CMB ( ) exp ( 2), (19) � fluctuations due to a super-void. Our void 휈푓 휈 ≈ �� −휈⁄ model is the HSW void profile, which is where = / ( ) is the critical under- claimed to be the universal void profile by density of void� formation� and ( ) is the Hamaus et al. (2014). The calculation of the � � variance휈 of훿 linear휎 푀density fluctuations� on a ISW and the weak lensing effect had shown / 휎� 푀 that the ISW effect is the dominant effect on a scale = . The indication from Pisani �� large scale. The best-fit parameters of the et al. (2015)� �is� that the appropriate value of δν HSW void are = -0.5 (specific value), rV = 푅 � � -1 . 190 Mpc h , = 0.91, = 0.45 . , is -0.45. By applying Equation (19), we can � find the probability that a void of a radius and �the�� goodness훿 of fit = 0.99 with�� 26 �� greater than 150 Mpc h-1, is ≈ 10-17. This can degrees of freedom푟 ⁄.푟 The� size 푧of the void is �� be interpreted that the origin of the CS may not extrapolated from typical휒 voids (15 be the ISW effect due to a super-void or that 70 Mpc ) to a super-void ( 120 � the large-scale structure formation theory is Mpc )�. �This indicates that the HSW≤ profile푟 ≤ � incomplete or that the ΛCDM is missing could be��ℎ used to describe large voids.푟 The≥ CS something. Another interpretation is the data showsℎ that there is a hot region near the

Figure 4. χ2 contour plot between parameters

SuranareeSuranaree J.J. Sci.Sci. Technol.Technol. Vol. 23 No. 4;4; October -– DecemberDecember 20162016 44191 edge of the CS, which may be the ISW due to Cruz, M., Martínez-González, E., Vielva, P., and Cayón, a galaxy cluster or just a normal fluctuation. L. (2005). Detection of a non-Gaussian spot in WMAP. Mon. Not. R. Astron. Soc., 356:29-40. The probability of a super-void of a size Cruz, M., Turok, N., Vielva, P., Martínez-González, E., -1 greater than 150 Mpc h is extremely low and Hobson, M. (2007). A cosmic microwave (10-17) which means the origin of the CS is background feature consistent with a cosmic probably not the ISW effect due to a super- texture. Science, 318:1,612-1,614. Finelli, F., Garcia-Bellido, J., Kovacs, A., Paci, F., and void. Szapudi, I. (2015). Supervoids in the WISE- 2MASS catalogue imprinting cold spots in the cosmic microwave background. Mon. Not. R. Acknowledgements Astron. Soc., 455:1,246-1,256. Hamaus, N., Sutter, P.M., and Wandelt, B.D. (2014). Universal density profile for cosmic voids. Phys. This work could not have been done if the Rev. Lett., 112(25):251302. following did not provide support both in Inoue, K.T. (2012). On the origin of the cold spot. Mon. terms of funding and facilities: Suranaree Not. R. Astron. Soc., 421:2,731-2,736. Pisani, A., Sutter, P.M., Hamaus, N., Alizadeh, E., Biswas, University of Technology (SUT), SUT R., Wandelt, B.D., and Hirata, C.M. (2015). scholarships for outstanding students, the Counting voids to probe dark energy. Phys. Rev. D, Thailand Research Fund (TRF) under Grant 92(8):083531. Number IRG57800010, and Naresuan Planck Collaboration: Ade, P.A.R., Aghanim, N., Alves, M.I.R., Armitage-Caplan, C., Arnaud, M., University provided the funds and opportunity Ashdown, M., Atrio-Barandela, F., Aumont, J., for us to work together; the National Aussel, H., et al. (2014). Planck 2013 results. I. Astronomical Research Institute of Thailand Overview of products and scientific results. Astron. provided both funding and allowed us to use its Astrophys., 571A1:1-48. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and High Performance Computing (HPC) cluster. Flannery, B.P. (2007). Numerical Recipes: The Art of Scientific Computing. 3rd ed. Cambridge University Press, New York, NY, USA, 1,235p. References Sachs, R.K. and Wolfe, A.M. (1967). Perturbations of a cosmological model and angular variations of the microwave background. Astrophys. J., 147:73-90. Chantavat, T., Sawangwit, U., Sutter, P.M., and Wandelt, B.D. (2016). Cosmological parameter constraints from CMB lensing with cosmic voids. Phys. Rev. D, 93(4):043523.