Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Resolution of the apparent discrepancy between the number of massive subhaloes in Abell 2744 and ΛCDM

Resolution of the apparent discrepancy between the number of massive subhaloes in Abell 2744 and... MNRAS 478, L34–L38 (2018) doi:10.1093/mnrasl/sly069 Advance Access publication 2018 April 24 Resolution of the apparent discrepancy between the number of massive subhaloes in Abell 2744 and CDM 1,2 1 3 1 1,2 1 Tian-Xiang Mao, Jie Wang, Carlos S. Frenk, Liang Gao, Ran Li, Qiao Wang, 1,2 1 Xiaoyue Cao and Ming Li Key Laboratory for Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China Department of Physics, Institute for computational cosmology, University of Durham, South Road, Durham DH1 3LE, UK Accepted 2018 April 17. Received 2017 August 04; in original form 2018 April 16 ABSTRACT Schwinn et al. have recently compared the abundance and distribution of massive substructures identified in a gravitational lensing analysis of Abell 2744 by Jauzac et al. and N-body simulation, and found no cluster in Lambda cold dark matter (CDM) simulation that is similar to Abell 2744. Schwinn et al. identified the measured projected aperture masses with the actual masses associated with subhaloes in the Millenium XXL N-body simulation. We have used the high-resolution Phoenix cluster simulations to show that such an identification is incorrect: the aperture mass is dominated by mass in the body of the cluster that happens to be projected along the line of sight to the subhalo. This enhancement varies from factors of a few to factors of more than 100, particularly for subhaloes projected near the centre of the cluster. We calculate aperture masses for subhaloes in our simulation and compare them to the measurements for Abell 2744. We find that the data for Abell 2744 are in excellent agreement with the matched predictions from CDM. We provide further predictions for aperture mass functions of subhaloes in idealized surveys with varying mass detection thresholds. Key words: dark matter – gravitational lensing: strong – galaxies: clusters: individual: Abell be used to measure the mass function on larger mass scales. Using 1 INTRODUCTION this approach Jauzac et al. (2015, 2016) have reconstructed the total The existence of a very large number of dark matter haloes and projected mass distribution of Abell 2744, one of the most massive subhaloes is a fundamental prediction of the Lambda cold dark galaxy clusters known (which lies at z = 0.308). Their technique is matter (CDM) cosmology. The halo and subhalo mass functions particularly sensitive to density variations in the outer parts of the can be accurately calculated from N-body simulations (e.g. Frenk cluster and thus is ideal for identifying subhaloes in these regions et al. 1988; Jenkins et al. 2001; Gao et al. 2004, 2011, 2012; Springel and estimating their mass quite accurately. et al. 2008). These functions are characteristic of CDM and can Jauzac et al. (2016) identified seven massive subhaloes (or eight differ in models with different types of dark matter such as warm if the main core is included) within a radius of 1 Mpc around the or self-interacting dark matter (Vogelsberger, Zavala & Loeb 2012; centre of Abell 2744; and they estimated their enclosed mass within Bose et al. 2016; Hellwing et al. 2016). an aperture of R = 150 kpc to be greater than 5 × 10 M in all The abundance of haloes and subhaloes, their mass, and their cases. Schwinn et al. (2017) claimed that this result is inconsis- spatial distribution can, in principle, be measured from their weak tent with the abundance and distribution of cluster subhaloes in the gravitational lensing effects (e.g. Yang et al. 2006; Limousin et al. Millennium XXL simulation (MXXL; Angulo et al. 2012)and that 2007; Natarajan, De Lucia & Springel 2007; Natarajan et al. 2009; a more careful comparison should be performed. They considered Li et al. 2013, 2016a,b; Okabe et al. 2014). Strong lensing may be subhaloes previously identified in a sample of clusters in the simu- used to measure the small mass end of the mass function (Vegetti & lation and, assuming that they have NFW density profiles (Navarro, Koopmans 2009) and this provides a promising test to differentiate Frenk & White 1996), they estimated their mass by integrating the between, for example, cold and warm dark matter (e.g. Li et al. density profile within a cylindrical volume of radius R = 150 kpc 2016b, 2017). The combination of strong and weak lensing may and length l = 30 Mpc, finding a maximum of three subhaloes with mass M (R < 150 kpc) > 5 × 10 M located within 1 Mpc of the centre. They attempted to account for possible effects, such as projection along the line of sight or changes in the assumed subhalo Email: [email protected] 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 Massive subhaloes in clusters L35 density profiles induced by baryons but found these to be unimpor- tant, and concluded that the number of observed massive subhaloes in Abell 2744 is in conflict with the predictions of CDM. To try and explain the discrepancy, Lee (2017) hypothesized that Abell 2744 may be embedded within a filamentary supercluster aligned with the line of sight. Natarajan et al. (2017) compared the subhalo mass function of galaxy members in Abell 2744 with the results for clusters in a hydrodynamical simulation (Vogelsberger et al. 2014), finding no discrepancy between observations and the simulation. The discrepancy, however, does not appear to be exclu- sive to Abell 2744. Chiriv`ıetal. (2017) found a similar mismatch with N-body simulations in the MACS J0416.1−2403 cluster and, like Schwinn et al. (2017), found that projection effects cannot account for the discrepancy. In this paper we show that the discrepancy between Abell 2744 and the CDM simulation reported by Schwinn et al. (2017)is simply due to an inconsistency in their comparison with the MXXL Figure 1. The relation between the projected aperture mass of a halo, M , 1.3 calculated within a projected cylinder of radius r = 1.3 Mpc and depth simulation, specifically an inconsistency between the masses they 30 Mpc, and its virial mass, M . Each point shows a projection of a cluster infer for the subhaloes and the masses assigned to subhaloes in in the Indra simulations, with red, green, and blue indicating three orthogonal the simulation. We mimic the procedure of deriving an aperture projects. The upper and lower error bars show 60 and 10 Mpcprojection mass that was applied to the lensing data in the high-resolution depths, respectively. The black error bar shows the entire range of M in 1.3 Phoenix (Gao et al. 2012) and Indra (Falck et al., in preparation) 200 random projections of Ph-I-4. The 3σ mass range in M for Abell 1.3 N-body simulations and find that the discrepancy with Abell 2744 2744 is marked by the two solid horizontal lines. is removed. In Section 2 we describe the Phoenix simulations; the comparison 3 RESULTS with Abell 2744 is presented in Section 3. Finally, we discuss our results and draw conclusions in Section 4. 3.1 The aperture mass of Abell 2744 Since the subhalo mass function depends on the host halo mass (e.g. Gao et al. 2011), it is important to select simulated clusters of mass similar to that of Abell 2744. There are different ways to define the mass of a halo in a simulation, but in lensing analyses the 2 SIMULATIONS mass of the lens is usually estimated as the projected mass within The N-body simulations used in this study are the Indra suite of a certain circular aperture. For Abell 2744, the aperture has radius large cosmological simulations (Falck et al., in preparation) and the R = 1.3 Mpc. Phoenix set of very high resolution simulations of individual rich We select all haloes of mass, M > 2.5 × 10 M from 128 clusters (Gao et al. 2012). realizations of the Indra simulation suite (a volume equivalent to a 3 −3 3 Indra consists of 512 N-body simulations, each with 1024 dark cube of side 128 h Gpc )at z = 0.32. For each halo, we compute −1 matter particles in a periodic cube 1 h Gpc on a side. The cos- an ‘aperture mass’, analogous to that Abell 2744, by projecting the mological parameters are taken to be:  = 0.272,  = 0.728, particle distribution along the x-, y-, and z-axis of the simulation, = 0.045, h = 0.704, σ = 0.81, and n = 0.967. Indra includes keeping all dark matter particles within 1.3 Mpc of the centre of b 8 s a very large volume and thus produces a large sample of clusters each cluster. The depth of projection was chosen to be 10, 30, and 10 −1 like Abell 2744, but the resolution, m = 7.03 × 10 h M ,is 60 Mpc. We refer to all these masses collectively as M . In Fig. 1 p 1.3 too low to resolve subhaloes like those in Abell 2744. We use these we plot M against aperture mass, M , for the clusters in our 200 1.3 simulations to compare aperture against total masses for clusters sample. Different colours represent the three different projections; analogous to Abell 2744. the error bars indicate the scatter in aperture mass due to different Phoenix consists of very high resolution resimulations of nine projection depths. The projection depth has a negligible effect on clusters and their surroundings selected from the Millennium sim- the aperture mass except in a few cases where there is contamination by a massive structure along the line of sight. The aperture mass is ulation (Springel et al. 2005). The Millennium simulation assumes thus essentially insensitive to the assumed projection depth. cosmological parameters consistent with the first year WMAP data, The observed 3σ range of M for Abell 2744 is marked by the = 0.25,  = 0.75, σ = 0.9, n = 1, and h = 0.7. These m  8 s 1.3 values deviate from the latest Planck results but this small off- two solid horizon lines in Fig. 1. To fall in the allowed region of set is of no consequence for the topic of this study. The most M for Abell 2744, a cluster should have M > 3 × 10 M . 1.3 200 massive of the nine Phoenix clusters, ‘Ph-I’, has a virial mass of Only one of the nine Phoenix clusters, Ph-I, has such a large mass; 15 −1 M = 2.427 × 10 h M , close to that of Abell 2744 (see Sec- the range of values of M for that cluster from 200 random pro- 200  1.3 tion 3), and we choose this halo at z = 0.32 for detailed comparison jections is indicated with a black error bar. Only 10 per cent of with Abell 2744. We identify subhaloes in Ph-I using the SUBFIND these projections fall within the 3σ allowed region of M for Abell 1.3 algorithm of Springel et al. (2001). To test numerical convergence, 2744. However, since the amplitude of the subhalo mass function the Phoenix clusters were re-simulated at various resolutions. In this study we have analysed the ‘level-4’ resolution for which the 8 −1 particle mass is m = 4.559 × 10 h M ; at this resolution all p M is defined as the mass contained with the radius, r , at which the 200 200 massive subhaloes are well resolved. mean interior density is equal to 200 times the critical density. MNRASL 478, L34–L38 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 L36 T.-X. Mao et al. Figure 3. The relation between the aperture mass of subhaloes, M ,and 3D their mass ‘boost’ factor, M /M , in our 24 Abell 2744 analogues. Here, 3D M is the mass enclosed within a sphere of radius 150 kpc of the subhalo Figure 2. A2 Mpc × 2 Mpc projected mass map of Ph-I-4 viewed along 150 3D centre. The points are colour coded according to the value of M .Adashed a random direction. The black stars, surrounded by circles of radius R 150 vertical line marks the limit M = 5 × 10 M . = 150 kpc, mark substructures with aperture mass, M > 5 × 10 M . The mass map is in a logarithmic scale. scales approximately linearly with halo mass (Wang et al. 2012), our conclusions from comparing this simulated cluster (the only one available with the required resolution) with Abell 2744 are conservative. 3.2 Projected massive subhaloes in clusters We project the particle distribution of Ph-I-4 along 200 random projections, each of depth 30 Mpc. The resulting mass maps are not sensitive to the projection depth as long as it is greater than the diameter of the cluster. In 24 of these projections the Ph-I cluster has aperture mass, M , within the 3σ allowed range for Abell 2744. 1.3 Hereafter, we refer to these as our Abell 2744 analogues, which use to compare the simulation with the observational data. In lensing observations, subhalo candidates are identified in the reconstructed mass map. In this paper, we will assume that all sub- Figure 4. The number of massive substructures, M > 5 × 10 M ,as haloes of mass larger than a threshold, M , are detected in the 150 th a function of the aperture mass for all 200 projections of Ph-I-4. Each point lensing analysis. For each massive subhalo in the simulation we corresponds to one projection. The 3σ allowed range of M for Abell 2744 1.3 calculate an aperture mass, M , analogous to the aperture masses is shown by the dashed vertical lines. The horizontal line corresponds to the measured in observational analyses (e.g. Jauzac et al. 2016)bymea- eight subhaloes with M > 5 × 10 M found in Abell 2744. suring the mass that falls within a projected radius, R = 150 kpc. Since close subhalo pairs cannot be distinguished in lensing obser- vations, we merge the density peaks of subhalo pairs of separation tified with SUBFIND. Clearly, the aperture mass, of a subhalo can be 3D less than 200 kpc, which is approximately the shortest pair separa- very different from its real mass, M . This is because aperture tion among the massive subhaloes in Abell 2744. masses can be greatly boosted by mass in the body of the halo In Fig. 2, we show the mass map of the particular projec- which happens to fall within the projection. This can increase the tion that has the most abundant substructures among the 200 projected mass by factors varying from a few to about 100. Thus, projections of Ph-I-4. Setting a subhalo mass detection limit of even intrinsically small subhaloes can appear to be very massive M = 4.6 × 10 M , we find nine subhaloes (shown as black as judged by their aperture mass, particularly if they happen to be th stars) whose aperture masses are comparable to the aperture masses projected close to the host halo centre. of the subhaloes in Abell 2744. It is clear that some of these appar- In Fig. 4 we show the number of projected subhaloes of aperture ently massive subhaloes in projections are actually associated with mass, M > 5 × 10 M , in our 200 projections of Ph-I-4, rather puny subhaloes such as one of the pair in the bottom left of assuming a projected mass detection limit of M = 4.6 × 10 M . th the image or the one slightly above that on the right. Clearly, the number correlates strongly with the projected aperture In Fig. 3 we show the relation between the aperture mass, M , mass. This is expected because, as we have just seen, the subhalo measured from different directions, and the mass ‘boost factor’, aperture mass is dominated by mass in the body of the cluster that is 3D 3D M /M ,where M is the true mass of the subhalo contained projected along the line of sight. Among 24 projections, four have 150 150 within a sphere of radius 150 kpc around the subhalo centre iden- at least eight subhaloes with M > 5 × 10 M , as indicated by MNRASL 478, L34–L38 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 Massive subhaloes in clusters L37 are over 100 times larger than the actual mass associated with the subhalo. Although our procedure captures the main effect of measuring aperture masses, our comparison with the observations of Abell 2744 is only approximate. In practice, the detectability of subhaloes in gravitational lensing analyses depends not only on their mass but also on the mass reconstruction method. For example, Merten et al. (2011) also performed a strong and weak lensing analysis of Abell 2744, using imaging data from HST and Subaru; they were only able to find four of the Jauzac et al. (2016) subhaloes. A more realistic comparison with the results of Jauzac et al. (2016) would require a ray-tracing calculation allowing for limitations and complications of the observational data such as resolution, completeness, etc. Such a calculation is beyond the scope of this paper. However, our main result – that projected aperture masses of subhaloes in observed rich clusters can be significant overestimates of the true masses of the subhaloes – is general and sufficient to conclude that the number of substructures detected in Abell 2744 by Jauzac et al. (2016) does Figure 5. The predicted aperture mass function of subhaloes. The solid lines show the mean values, and the shadow areas the 1σ range, obtained from not pose a crisis for CDM. We have presented simple predictions our 24 analogues of Abell 2744. Different colours correspond to threshold for the aperture mass function of subhaloes in rich clusters. More values of 2.3, 4.6, 9.1, and 13.7 × 10 M , respectively, as shown in the detailed theoretical calculations of the kind we have sketched above, legend. The black star symbols show the cumulative mass function of the tailored to specific lensing surveys, could provide a useful test of eight massive substructures in Abell 2744. CDM. the horizontal line. We conclude that when the simulations and the ACKNOWLEDGEMENTS data are analysed in a consistent way, the detection of eight massive We thank Dandan Xu, Guoliang Li, and Simon White for useful dis- subhaloes in Abell 2744 is perfectly consistent with the predictions cussions. We acknowledges the 973 program grant 2015CB857005, of CDM. 2017YFB0203300, and NSFC grant nos. 11373029, 11390372, Lowering the detection mass threshold, M , rapidly increases th and 11851301. We acknowledge support from NSFC grant (nos. the number of massive projected subhaloes. In Fig. 5 we show the 11573030, 11133003, 11425312, and 1303033). RL acknowledges predicted aperture mass functions of subhaloes in our 24 Abell 2744 NSFC grant (nos. 11511130054 and 11333001), support from analogues for different values of the threshold. Red, green, blue, and the Youth Innovation Promotion Association of CAS and Neb- yellow lines correspond to threshold values, M of 2.3, 4.6, 9.1, and th 11 11 ula Talent Program of NAOC and Newton Mobility award. This 13.7 × 10 M , respectively. For the value, M = 2.3 × 10 M , th work was supported by the Science and Technology Facilities that we have assumed for the lensing analysis of Abell 2744 carried out by Jauzac et al. (2016), the measured aperture mass function Council ST/L00075X/1. It used the DiRAC Data Centric sys- (shown as star symbols in the figure) agrees remarkably well with tem at Durham University, operated by the Institute for Compu- the simulations. tational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, STFC DiRAC Operations grant 4 DISCUSSION AND CONCLUSIONS ST/K003267/1, and Durham University. DiRAC is part of the Na- We have made use of cosmological N-body simulations to test tional E-Infrastructure. whether the identification of eight massive subhaloes by Jauzac et al. (2016) in a gravitational lensing mass reconstruction of Abell REFERENCES 2744 is in conflict with predictions from the CDM cosmologi- cal paradigm. Gravitational lensing is sensitive to projected mass; Angulo R. E., Springel V., White S. D. M., Jenkins A., Baugh C. M., Frenk projected masses associated with subhaloes are normally mea- C. S., 2012, MNRAS, 426, 2046 sured within a specified aperture. First, using a large-volume, low- Bose S., Hellwing W. A., Frenk C. S., Jenkins A., Lovell M. R., Helly J. C., resolution suite of simulations, we established that the projected Li B., 2016, MNRAS, 455, 318 aperture mass of Abell 2744 itself corresponds to a minimum true ` Chirivı G., Suyu S. H., Grillo C., Halkola A., Balestra I., Caminha G. B., mass of about 3 × 10 M . One of the clusters from the much Mercurio A., Rosati P., 2017, preprint (arXiv:1706.07815) Frenk C. S., White S. D. M., Davis M., Efstathiou G., 1988, ApJ, 327, 507 higher resolution Phoenix cluster N-body re-simulation project sat- Gao L., White S. D. M., Jenkins A., Stoehr F., Springel V., 2004, MNRAS, isfies this mass constraint; we used it to construct a sample of 24 355, 819 analogues of Abell 2744 by viewing it from different directions. Gao L., Frenk C. S., Boylan-Kolchin M., Jenkins A., Springel V., White S. Projected masses for subhaloes in Abell 2744 are measured D. M., 2011, MNRAS, 410, 2309 within 150 kpc apertures. We calculated equivalent masses for the Gao L., Navarro J. F., Frenk C. S., Jenkins A., Springel V., White S. D. M., subhaloes in the simulation by integrating the mass within a cylinder 2012, MNRAS, 425, 2169 of radius 150 kpc along the line of sight to each subhalo. Our main Hellwing W. A., Frenk C. S., Cautun M., Bose S., Helly J., Jenkins A., finding is that the measured aperture mass of a subhalo is dominated Sawala T., Cytowski M., 2016, MNRAS, 457, 3492 by mass in the body of the host halo that happens to be projected Jauzac M. et al., 2015, MNRAS, 446, 4132 on to the aperture. This can lead to measured aperture masses that Jauzac M. et al., 2016, MNRAS, 463, 3876 MNRASL 478, L34–L38 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 L38 T.-X. Mao et al. Jenkins A., Frenk C. S., White S. D. M., Colberg J. M., Cole S., Evrard A. Schwinn J., Jauzac M., Baugh C. M., Bartelmann M., Eckert D., Harvey D., E., Couchman H. M. P., Yoshida N., 2001, MNRAS, 321, 372 Natarajan P., Massey R., 2017, MNRAS, 467, 2913 Lee J., 2017, preprint (arXiv:1701.04220) Springel V., White S. D. M., Tormen G., Kauffmann G., 2001, MNRAS, Li R., Mo H. J., Fan Z., Yang X., Bosch F. C. v. d., 2013, MNRAS, 430, 328, 726 3359 Springel V. et al., 2005, Nature, 435, 629 Li R. et al., 2016a, MNRAS, 458, 2573 Springel V. et al., 2008, MNRAS, 391, 1685 Li R., Frenk C. S., Cole S., Gao L., Bose S., Hellwing W. A., 2016b, Vegetti S., Koopmans L. V. E., 2009, MNRAS, 392, 945 MNRAS, 460, 363 Vogelsberger M., Zavala J., Loeb A., 2012, MNRAS, 423, 3740 Li R., Frenk C. S., Cole S., Wang Q., Gao L., 2017, MNRAS, 468, 1426 Vogelsberger M. et al., 2014, MNRAS, 444, 1518 Limousin M., Kneib J. P., Bardeau S., Natarajan P., Czoske O., Smail I., Wang J., Frenk C. S., Navarro J. F., Gao L., Sawala T., 2012, MNRAS, 424, Ebeling H., Smith G. P., 2007, A&A, 461, 881 2715 Merten J. et al., 2011, MNRAS, 417, 333 Yang X., Mo H. J., van den Bosch F. C., Jing Y. P., Weinmann S. M., Natarajan P., De Lucia G., Springel V., 2007, MNRAS, 376, 180 Meneghetti M., 2006, MNRAS, 373, 1159 Natarajan P., Kneib J.-P., Smail I., Treu T., Ellis R., Moran S., Limousin M., Czoske O., 2009, ApJ, 693, 970 Natarajan P. et al., 2017, MNRAS, 468, 1962 This paper has been typeset from a T X/LT X file prepared by the author. E E Navarro J. F., Frenk C. S., White S. D. M., 1996, ApJ, 462, 563 Okabe N., Futamase T., Kajisawa M., Kuroshima R., 2014, ApJ, 784, 90 MNRASL 478, L34–L38 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Notices of the Royal Astronomical Society Letters Oxford University Press

Resolution of the apparent discrepancy between the number of massive subhaloes in Abell 2744 and ΛCDM

Loading next page...
 
/lp/ou_press/resolution-of-the-apparent-discrepancy-between-the-number-of-massive-vXqyQrCkwt

References (31)

Publisher
Oxford University Press
Copyright
© 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society
ISSN
1745-3925
eISSN
1745-3933
DOI
10.1093/mnrasl/sly069
Publisher site
See Article on Publisher Site

Abstract

MNRAS 478, L34–L38 (2018) doi:10.1093/mnrasl/sly069 Advance Access publication 2018 April 24 Resolution of the apparent discrepancy between the number of massive subhaloes in Abell 2744 and CDM 1,2 1 3 1 1,2 1 Tian-Xiang Mao, Jie Wang, Carlos S. Frenk, Liang Gao, Ran Li, Qiao Wang, 1,2 1 Xiaoyue Cao and Ming Li Key Laboratory for Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China Department of Physics, Institute for computational cosmology, University of Durham, South Road, Durham DH1 3LE, UK Accepted 2018 April 17. Received 2017 August 04; in original form 2018 April 16 ABSTRACT Schwinn et al. have recently compared the abundance and distribution of massive substructures identified in a gravitational lensing analysis of Abell 2744 by Jauzac et al. and N-body simulation, and found no cluster in Lambda cold dark matter (CDM) simulation that is similar to Abell 2744. Schwinn et al. identified the measured projected aperture masses with the actual masses associated with subhaloes in the Millenium XXL N-body simulation. We have used the high-resolution Phoenix cluster simulations to show that such an identification is incorrect: the aperture mass is dominated by mass in the body of the cluster that happens to be projected along the line of sight to the subhalo. This enhancement varies from factors of a few to factors of more than 100, particularly for subhaloes projected near the centre of the cluster. We calculate aperture masses for subhaloes in our simulation and compare them to the measurements for Abell 2744. We find that the data for Abell 2744 are in excellent agreement with the matched predictions from CDM. We provide further predictions for aperture mass functions of subhaloes in idealized surveys with varying mass detection thresholds. Key words: dark matter – gravitational lensing: strong – galaxies: clusters: individual: Abell be used to measure the mass function on larger mass scales. Using 1 INTRODUCTION this approach Jauzac et al. (2015, 2016) have reconstructed the total The existence of a very large number of dark matter haloes and projected mass distribution of Abell 2744, one of the most massive subhaloes is a fundamental prediction of the Lambda cold dark galaxy clusters known (which lies at z = 0.308). Their technique is matter (CDM) cosmology. The halo and subhalo mass functions particularly sensitive to density variations in the outer parts of the can be accurately calculated from N-body simulations (e.g. Frenk cluster and thus is ideal for identifying subhaloes in these regions et al. 1988; Jenkins et al. 2001; Gao et al. 2004, 2011, 2012; Springel and estimating their mass quite accurately. et al. 2008). These functions are characteristic of CDM and can Jauzac et al. (2016) identified seven massive subhaloes (or eight differ in models with different types of dark matter such as warm if the main core is included) within a radius of 1 Mpc around the or self-interacting dark matter (Vogelsberger, Zavala & Loeb 2012; centre of Abell 2744; and they estimated their enclosed mass within Bose et al. 2016; Hellwing et al. 2016). an aperture of R = 150 kpc to be greater than 5 × 10 M in all The abundance of haloes and subhaloes, their mass, and their cases. Schwinn et al. (2017) claimed that this result is inconsis- spatial distribution can, in principle, be measured from their weak tent with the abundance and distribution of cluster subhaloes in the gravitational lensing effects (e.g. Yang et al. 2006; Limousin et al. Millennium XXL simulation (MXXL; Angulo et al. 2012)and that 2007; Natarajan, De Lucia & Springel 2007; Natarajan et al. 2009; a more careful comparison should be performed. They considered Li et al. 2013, 2016a,b; Okabe et al. 2014). Strong lensing may be subhaloes previously identified in a sample of clusters in the simu- used to measure the small mass end of the mass function (Vegetti & lation and, assuming that they have NFW density profiles (Navarro, Koopmans 2009) and this provides a promising test to differentiate Frenk & White 1996), they estimated their mass by integrating the between, for example, cold and warm dark matter (e.g. Li et al. density profile within a cylindrical volume of radius R = 150 kpc 2016b, 2017). The combination of strong and weak lensing may and length l = 30 Mpc, finding a maximum of three subhaloes with mass M (R < 150 kpc) > 5 × 10 M located within 1 Mpc of the centre. They attempted to account for possible effects, such as projection along the line of sight or changes in the assumed subhalo Email: [email protected] 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 Massive subhaloes in clusters L35 density profiles induced by baryons but found these to be unimpor- tant, and concluded that the number of observed massive subhaloes in Abell 2744 is in conflict with the predictions of CDM. To try and explain the discrepancy, Lee (2017) hypothesized that Abell 2744 may be embedded within a filamentary supercluster aligned with the line of sight. Natarajan et al. (2017) compared the subhalo mass function of galaxy members in Abell 2744 with the results for clusters in a hydrodynamical simulation (Vogelsberger et al. 2014), finding no discrepancy between observations and the simulation. The discrepancy, however, does not appear to be exclu- sive to Abell 2744. Chiriv`ıetal. (2017) found a similar mismatch with N-body simulations in the MACS J0416.1−2403 cluster and, like Schwinn et al. (2017), found that projection effects cannot account for the discrepancy. In this paper we show that the discrepancy between Abell 2744 and the CDM simulation reported by Schwinn et al. (2017)is simply due to an inconsistency in their comparison with the MXXL Figure 1. The relation between the projected aperture mass of a halo, M , 1.3 calculated within a projected cylinder of radius r = 1.3 Mpc and depth simulation, specifically an inconsistency between the masses they 30 Mpc, and its virial mass, M . Each point shows a projection of a cluster infer for the subhaloes and the masses assigned to subhaloes in in the Indra simulations, with red, green, and blue indicating three orthogonal the simulation. We mimic the procedure of deriving an aperture projects. The upper and lower error bars show 60 and 10 Mpcprojection mass that was applied to the lensing data in the high-resolution depths, respectively. The black error bar shows the entire range of M in 1.3 Phoenix (Gao et al. 2012) and Indra (Falck et al., in preparation) 200 random projections of Ph-I-4. The 3σ mass range in M for Abell 1.3 N-body simulations and find that the discrepancy with Abell 2744 2744 is marked by the two solid horizontal lines. is removed. In Section 2 we describe the Phoenix simulations; the comparison 3 RESULTS with Abell 2744 is presented in Section 3. Finally, we discuss our results and draw conclusions in Section 4. 3.1 The aperture mass of Abell 2744 Since the subhalo mass function depends on the host halo mass (e.g. Gao et al. 2011), it is important to select simulated clusters of mass similar to that of Abell 2744. There are different ways to define the mass of a halo in a simulation, but in lensing analyses the 2 SIMULATIONS mass of the lens is usually estimated as the projected mass within The N-body simulations used in this study are the Indra suite of a certain circular aperture. For Abell 2744, the aperture has radius large cosmological simulations (Falck et al., in preparation) and the R = 1.3 Mpc. Phoenix set of very high resolution simulations of individual rich We select all haloes of mass, M > 2.5 × 10 M from 128 clusters (Gao et al. 2012). realizations of the Indra simulation suite (a volume equivalent to a 3 −3 3 Indra consists of 512 N-body simulations, each with 1024 dark cube of side 128 h Gpc )at z = 0.32. For each halo, we compute −1 matter particles in a periodic cube 1 h Gpc on a side. The cos- an ‘aperture mass’, analogous to that Abell 2744, by projecting the mological parameters are taken to be:  = 0.272,  = 0.728, particle distribution along the x-, y-, and z-axis of the simulation, = 0.045, h = 0.704, σ = 0.81, and n = 0.967. Indra includes keeping all dark matter particles within 1.3 Mpc of the centre of b 8 s a very large volume and thus produces a large sample of clusters each cluster. The depth of projection was chosen to be 10, 30, and 10 −1 like Abell 2744, but the resolution, m = 7.03 × 10 h M ,is 60 Mpc. We refer to all these masses collectively as M . In Fig. 1 p 1.3 too low to resolve subhaloes like those in Abell 2744. We use these we plot M against aperture mass, M , for the clusters in our 200 1.3 simulations to compare aperture against total masses for clusters sample. Different colours represent the three different projections; analogous to Abell 2744. the error bars indicate the scatter in aperture mass due to different Phoenix consists of very high resolution resimulations of nine projection depths. The projection depth has a negligible effect on clusters and their surroundings selected from the Millennium sim- the aperture mass except in a few cases where there is contamination by a massive structure along the line of sight. The aperture mass is ulation (Springel et al. 2005). The Millennium simulation assumes thus essentially insensitive to the assumed projection depth. cosmological parameters consistent with the first year WMAP data, The observed 3σ range of M for Abell 2744 is marked by the = 0.25,  = 0.75, σ = 0.9, n = 1, and h = 0.7. These m  8 s 1.3 values deviate from the latest Planck results but this small off- two solid horizon lines in Fig. 1. To fall in the allowed region of set is of no consequence for the topic of this study. The most M for Abell 2744, a cluster should have M > 3 × 10 M . 1.3 200 massive of the nine Phoenix clusters, ‘Ph-I’, has a virial mass of Only one of the nine Phoenix clusters, Ph-I, has such a large mass; 15 −1 M = 2.427 × 10 h M , close to that of Abell 2744 (see Sec- the range of values of M for that cluster from 200 random pro- 200  1.3 tion 3), and we choose this halo at z = 0.32 for detailed comparison jections is indicated with a black error bar. Only 10 per cent of with Abell 2744. We identify subhaloes in Ph-I using the SUBFIND these projections fall within the 3σ allowed region of M for Abell 1.3 algorithm of Springel et al. (2001). To test numerical convergence, 2744. However, since the amplitude of the subhalo mass function the Phoenix clusters were re-simulated at various resolutions. In this study we have analysed the ‘level-4’ resolution for which the 8 −1 particle mass is m = 4.559 × 10 h M ; at this resolution all p M is defined as the mass contained with the radius, r , at which the 200 200 massive subhaloes are well resolved. mean interior density is equal to 200 times the critical density. MNRASL 478, L34–L38 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 L36 T.-X. Mao et al. Figure 3. The relation between the aperture mass of subhaloes, M ,and 3D their mass ‘boost’ factor, M /M , in our 24 Abell 2744 analogues. Here, 3D M is the mass enclosed within a sphere of radius 150 kpc of the subhalo Figure 2. A2 Mpc × 2 Mpc projected mass map of Ph-I-4 viewed along 150 3D centre. The points are colour coded according to the value of M .Adashed a random direction. The black stars, surrounded by circles of radius R 150 vertical line marks the limit M = 5 × 10 M . = 150 kpc, mark substructures with aperture mass, M > 5 × 10 M . The mass map is in a logarithmic scale. scales approximately linearly with halo mass (Wang et al. 2012), our conclusions from comparing this simulated cluster (the only one available with the required resolution) with Abell 2744 are conservative. 3.2 Projected massive subhaloes in clusters We project the particle distribution of Ph-I-4 along 200 random projections, each of depth 30 Mpc. The resulting mass maps are not sensitive to the projection depth as long as it is greater than the diameter of the cluster. In 24 of these projections the Ph-I cluster has aperture mass, M , within the 3σ allowed range for Abell 2744. 1.3 Hereafter, we refer to these as our Abell 2744 analogues, which use to compare the simulation with the observational data. In lensing observations, subhalo candidates are identified in the reconstructed mass map. In this paper, we will assume that all sub- Figure 4. The number of massive substructures, M > 5 × 10 M ,as haloes of mass larger than a threshold, M , are detected in the 150 th a function of the aperture mass for all 200 projections of Ph-I-4. Each point lensing analysis. For each massive subhalo in the simulation we corresponds to one projection. The 3σ allowed range of M for Abell 2744 1.3 calculate an aperture mass, M , analogous to the aperture masses is shown by the dashed vertical lines. The horizontal line corresponds to the measured in observational analyses (e.g. Jauzac et al. 2016)bymea- eight subhaloes with M > 5 × 10 M found in Abell 2744. suring the mass that falls within a projected radius, R = 150 kpc. Since close subhalo pairs cannot be distinguished in lensing obser- vations, we merge the density peaks of subhalo pairs of separation tified with SUBFIND. Clearly, the aperture mass, of a subhalo can be 3D less than 200 kpc, which is approximately the shortest pair separa- very different from its real mass, M . This is because aperture tion among the massive subhaloes in Abell 2744. masses can be greatly boosted by mass in the body of the halo In Fig. 2, we show the mass map of the particular projec- which happens to fall within the projection. This can increase the tion that has the most abundant substructures among the 200 projected mass by factors varying from a few to about 100. Thus, projections of Ph-I-4. Setting a subhalo mass detection limit of even intrinsically small subhaloes can appear to be very massive M = 4.6 × 10 M , we find nine subhaloes (shown as black as judged by their aperture mass, particularly if they happen to be th stars) whose aperture masses are comparable to the aperture masses projected close to the host halo centre. of the subhaloes in Abell 2744. It is clear that some of these appar- In Fig. 4 we show the number of projected subhaloes of aperture ently massive subhaloes in projections are actually associated with mass, M > 5 × 10 M , in our 200 projections of Ph-I-4, rather puny subhaloes such as one of the pair in the bottom left of assuming a projected mass detection limit of M = 4.6 × 10 M . th the image or the one slightly above that on the right. Clearly, the number correlates strongly with the projected aperture In Fig. 3 we show the relation between the aperture mass, M , mass. This is expected because, as we have just seen, the subhalo measured from different directions, and the mass ‘boost factor’, aperture mass is dominated by mass in the body of the cluster that is 3D 3D M /M ,where M is the true mass of the subhalo contained projected along the line of sight. Among 24 projections, four have 150 150 within a sphere of radius 150 kpc around the subhalo centre iden- at least eight subhaloes with M > 5 × 10 M , as indicated by MNRASL 478, L34–L38 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 Massive subhaloes in clusters L37 are over 100 times larger than the actual mass associated with the subhalo. Although our procedure captures the main effect of measuring aperture masses, our comparison with the observations of Abell 2744 is only approximate. In practice, the detectability of subhaloes in gravitational lensing analyses depends not only on their mass but also on the mass reconstruction method. For example, Merten et al. (2011) also performed a strong and weak lensing analysis of Abell 2744, using imaging data from HST and Subaru; they were only able to find four of the Jauzac et al. (2016) subhaloes. A more realistic comparison with the results of Jauzac et al. (2016) would require a ray-tracing calculation allowing for limitations and complications of the observational data such as resolution, completeness, etc. Such a calculation is beyond the scope of this paper. However, our main result – that projected aperture masses of subhaloes in observed rich clusters can be significant overestimates of the true masses of the subhaloes – is general and sufficient to conclude that the number of substructures detected in Abell 2744 by Jauzac et al. (2016) does Figure 5. The predicted aperture mass function of subhaloes. The solid lines show the mean values, and the shadow areas the 1σ range, obtained from not pose a crisis for CDM. We have presented simple predictions our 24 analogues of Abell 2744. Different colours correspond to threshold for the aperture mass function of subhaloes in rich clusters. More values of 2.3, 4.6, 9.1, and 13.7 × 10 M , respectively, as shown in the detailed theoretical calculations of the kind we have sketched above, legend. The black star symbols show the cumulative mass function of the tailored to specific lensing surveys, could provide a useful test of eight massive substructures in Abell 2744. CDM. the horizontal line. We conclude that when the simulations and the ACKNOWLEDGEMENTS data are analysed in a consistent way, the detection of eight massive We thank Dandan Xu, Guoliang Li, and Simon White for useful dis- subhaloes in Abell 2744 is perfectly consistent with the predictions cussions. We acknowledges the 973 program grant 2015CB857005, of CDM. 2017YFB0203300, and NSFC grant nos. 11373029, 11390372, Lowering the detection mass threshold, M , rapidly increases th and 11851301. We acknowledge support from NSFC grant (nos. the number of massive projected subhaloes. In Fig. 5 we show the 11573030, 11133003, 11425312, and 1303033). RL acknowledges predicted aperture mass functions of subhaloes in our 24 Abell 2744 NSFC grant (nos. 11511130054 and 11333001), support from analogues for different values of the threshold. Red, green, blue, and the Youth Innovation Promotion Association of CAS and Neb- yellow lines correspond to threshold values, M of 2.3, 4.6, 9.1, and th 11 11 ula Talent Program of NAOC and Newton Mobility award. This 13.7 × 10 M , respectively. For the value, M = 2.3 × 10 M , th work was supported by the Science and Technology Facilities that we have assumed for the lensing analysis of Abell 2744 carried out by Jauzac et al. (2016), the measured aperture mass function Council ST/L00075X/1. It used the DiRAC Data Centric sys- (shown as star symbols in the figure) agrees remarkably well with tem at Durham University, operated by the Institute for Compu- the simulations. tational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, STFC DiRAC Operations grant 4 DISCUSSION AND CONCLUSIONS ST/K003267/1, and Durham University. DiRAC is part of the Na- We have made use of cosmological N-body simulations to test tional E-Infrastructure. whether the identification of eight massive subhaloes by Jauzac et al. (2016) in a gravitational lensing mass reconstruction of Abell REFERENCES 2744 is in conflict with predictions from the CDM cosmologi- cal paradigm. Gravitational lensing is sensitive to projected mass; Angulo R. E., Springel V., White S. D. M., Jenkins A., Baugh C. M., Frenk projected masses associated with subhaloes are normally mea- C. S., 2012, MNRAS, 426, 2046 sured within a specified aperture. First, using a large-volume, low- Bose S., Hellwing W. A., Frenk C. S., Jenkins A., Lovell M. R., Helly J. C., resolution suite of simulations, we established that the projected Li B., 2016, MNRAS, 455, 318 aperture mass of Abell 2744 itself corresponds to a minimum true ` Chirivı G., Suyu S. H., Grillo C., Halkola A., Balestra I., Caminha G. B., mass of about 3 × 10 M . One of the clusters from the much Mercurio A., Rosati P., 2017, preprint (arXiv:1706.07815) Frenk C. S., White S. D. M., Davis M., Efstathiou G., 1988, ApJ, 327, 507 higher resolution Phoenix cluster N-body re-simulation project sat- Gao L., White S. D. M., Jenkins A., Stoehr F., Springel V., 2004, MNRAS, isfies this mass constraint; we used it to construct a sample of 24 355, 819 analogues of Abell 2744 by viewing it from different directions. Gao L., Frenk C. S., Boylan-Kolchin M., Jenkins A., Springel V., White S. Projected masses for subhaloes in Abell 2744 are measured D. M., 2011, MNRAS, 410, 2309 within 150 kpc apertures. We calculated equivalent masses for the Gao L., Navarro J. F., Frenk C. S., Jenkins A., Springel V., White S. D. M., subhaloes in the simulation by integrating the mass within a cylinder 2012, MNRAS, 425, 2169 of radius 150 kpc along the line of sight to each subhalo. Our main Hellwing W. A., Frenk C. S., Cautun M., Bose S., Helly J., Jenkins A., finding is that the measured aperture mass of a subhalo is dominated Sawala T., Cytowski M., 2016, MNRAS, 457, 3492 by mass in the body of the host halo that happens to be projected Jauzac M. et al., 2015, MNRAS, 446, 4132 on to the aperture. This can lead to measured aperture masses that Jauzac M. et al., 2016, MNRAS, 463, 3876 MNRASL 478, L34–L38 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018 L38 T.-X. Mao et al. Jenkins A., Frenk C. S., White S. D. M., Colberg J. M., Cole S., Evrard A. Schwinn J., Jauzac M., Baugh C. M., Bartelmann M., Eckert D., Harvey D., E., Couchman H. M. P., Yoshida N., 2001, MNRAS, 321, 372 Natarajan P., Massey R., 2017, MNRAS, 467, 2913 Lee J., 2017, preprint (arXiv:1701.04220) Springel V., White S. D. M., Tormen G., Kauffmann G., 2001, MNRAS, Li R., Mo H. J., Fan Z., Yang X., Bosch F. C. v. d., 2013, MNRAS, 430, 328, 726 3359 Springel V. et al., 2005, Nature, 435, 629 Li R. et al., 2016a, MNRAS, 458, 2573 Springel V. et al., 2008, MNRAS, 391, 1685 Li R., Frenk C. S., Cole S., Gao L., Bose S., Hellwing W. A., 2016b, Vegetti S., Koopmans L. V. E., 2009, MNRAS, 392, 945 MNRAS, 460, 363 Vogelsberger M., Zavala J., Loeb A., 2012, MNRAS, 423, 3740 Li R., Frenk C. S., Cole S., Wang Q., Gao L., 2017, MNRAS, 468, 1426 Vogelsberger M. et al., 2014, MNRAS, 444, 1518 Limousin M., Kneib J. P., Bardeau S., Natarajan P., Czoske O., Smail I., Wang J., Frenk C. S., Navarro J. F., Gao L., Sawala T., 2012, MNRAS, 424, Ebeling H., Smith G. P., 2007, A&A, 461, 881 2715 Merten J. et al., 2011, MNRAS, 417, 333 Yang X., Mo H. J., van den Bosch F. C., Jing Y. P., Weinmann S. M., Natarajan P., De Lucia G., Springel V., 2007, MNRAS, 376, 180 Meneghetti M., 2006, MNRAS, 373, 1159 Natarajan P., Kneib J.-P., Smail I., Treu T., Ellis R., Moran S., Limousin M., Czoske O., 2009, ApJ, 693, 970 Natarajan P. et al., 2017, MNRAS, 468, 1962 This paper has been typeset from a T X/LT X file prepared by the author. E E Navarro J. F., Frenk C. S., White S. D. M., 1996, ApJ, 462, 563 Okabe N., Futamase T., Kajisawa M., Kuroshima R., 2014, ApJ, 784, 90 MNRASL 478, L34–L38 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/478/1/L34/4983127 by Ed 'DeepDyve' Gillespie user on 21 June 2018

Journal

Monthly Notices of the Royal Astronomical Society LettersOxford University Press

Published: Apr 24, 2018

Keywords: dark matter; gravitational lensing: strong; galaxies: clusters: individual: Abell 2744

There are no references for this article.