# The SKA as a prebiotic molecule detector

Izaskun Jiménez-Serra 1,∗, Jesús Martín-Pintado 1, Aran Insausti2,3, Elena R.
Alonso2,3, Emilio J. Cocinero 2,3 and Tyler L. Bourke4

###### Abstract

One of the theories for the origin of life proposes that a significant
fraction of prebiotic material could have arrived to Earth from outer space
between 4.1 and 3.8 billion years ago. This suggests that those prebiotic
compounds could have originated in interstellar space, to be later on
incorporated to small Solar-system bodies and planetesimals. The recent
discovery of prebiotic molecules such as hydroxylamine and ethanolamine in the
interstellar medium, strongly supports this hypothesis. However, some species
such as sugars, key for the synthesis of ribonucleotides and for metabolic
processes, remain to be discovered in space. The unmatched sensitivity of the
Square Kilometer Array (SKA) at centimeter wavelengths will be able to detect
even more complex and heavier prebiotic molecules than existing
instrumentation. In this contribution, we illustrate the potential of the SKA
to detect simple sugars with three and four carbon atoms, using a moderate
investment of observing time.

##  1 Keywords:

Square Kilometer Array (SKA), complex organic molecules, prebiotic chemistry,
interstellar medium, astrochemistry

##  2 Introduction

The question of the origin of life has attracted the interest of researchers
for centuries. Two main lines of thought have been proposed: i) Life may have
emerged endogenously so that the building blocks of life could have formed
$"$in situ$"$ on Earth; or ii) Life could have originated somewhere else in
the Universe and been transported to Earth in small Solar-system bodies.
Alternatively, an intermediate theory contemplates the possibility that a
fraction of the prebiotic material essential for the origin of life could have
originated exogenously and been transferred to a young Earth via planetesimal
impact on its surface (Anders, 1989; Chyba and Sagan, 1992). Prebiotic
molecules such as amino acids, nucleobases and sugars have indeed been
detected in meteorites (Cooper et al., 2001; Pizzarello et al., 2006; Glavin
et al., 2020; Callahan et al., 2011; Furukawa et al., 2019) and in comets
(Altwegg et al., 2016), which supports the latter hypothesis.

In the past decade, it has become clear that the interstellar medium (ISM) is
an extraordinary chemical factory. About 250 molecules, including ringed-
molecules (see e.g. Cernicharo et al., 2021; McGuire et al., 2021), have so
far been reported in the ISM. In addition, the pace at which new molecules are
detected not only seems steady but accelerating (McGuire, 2021). In
particular, the so-called complex organic molecules (or COMs)111COMs are
defined as carbon-based molecules with $\geq$6 atoms in their structure (see
e.g. methanol or CH3OH; Herbst and van Dishoeck, 2009). have attracted great
interest in recent years since a subset of them could have been involved in
the first biochemical reactions leading to the origin of life. This sub-set of
COMs are typically called prebiotic. Some examples of prebiotic COMs include
urea and hydroxylamine (Belloche et al., 2019; Jiménez-Serra et al., 2020;
Rivilla et al., 2020) since they are possible precursors of ribonucleotides
(see e.g. Becker et al., 2019; Menor Salvan et al., 2020); ethanolamine and
n-propanol because they could have triggered the formation of phospholipids
(Rivilla et al., 2021; Jimenez-Serra et al., 2021); or amino acetonitrile,
vinyl amine and ethyl amine since they are considered precursors of amino
acids (Belloche et al., 2008; Zeng et al., 2021).

One of the most extended theories about the origin of life is the primordial
RNA world. In this scenario, early forms of life relied solely on RNA to store
genetic information and to catalyze chemical reactions. The basic units of RNA
are ribonucleotides, which are composed of a phosphate group, a nitrogenous
base, and a ribose sugar (a C5 sugar with five carbon atoms). Interestingly,
only small precursors of sugars such as glycolonitrile (HOCH2CN; see Patel et
al., 2015) or the simplest C2 sugar molecule, glycolaldehyde (CH2OHCHO), have
been reported in the ISM (Hollis et al., 2000; Beltrán et al., 2009; Jørgensen
et al., 2012; Zeng et al., 2019). Indeed, searches of C3 sugars such as
glyceraldehyde (CHOCHOHCH2OH) or dihydroxyacetone (DHA, with the chemical
formula CH2OHCOCH2OH), have not yielded any robust detection (Hollis et al.,
2004; Widicus Weaver and Blake, 2005; Apponi et al., 2006; Jiménez-Serra et
al., 2020). In contrast, larger sugar-like species such as C3 sugars and
ribose have been found in meteorites (de Marcellus et al., 2015; Furukawa et
al., 2019), which opens the possibility that these species form in
interstellar space.

The search of sugars in the ISM has partly been hindered by the lack of
spectroscopic rotational data since these species are thermolabile and
hygroscopic. This has triggered the development of new sample preparation
techniques as well as the use of ultrafast laser vaporization sources to avoid
their decomposition (Cocinero et al., 2012; Calabrese et al., 2020). Recently,
the rotational spectroscopy of C4 and C5 sugars such as erythrulose and ribose
has been obtained in the laboratory (Cocinero et al., 2012; Insausti et al.,
2021), which enables their search in interstellar space.

##  3 Searching for sugars in sources with low excitation temperatures (Tex)

The first searches in the ISM of glyceraldehyde and dihydroxyacetone (DHA)
targeted the massive star-forming region SgrB2 N-LMH. While an upper limit to
the abundance of glyceraldehyde of $\leq$2.4-5.7$\times$10-11 was obtained by
Hollis et al. (2004), Widicus Weaver and Blake (2005) reported a tentative
detection of DHA toward this source with an abundance of 1.2$\times$10-9. The
latter detection, however, was never confirmed (Apponi et al., 2006). For low-
mass star-forming regions, Jiménez-Serra et al. (2020) also reported upper
limits to the abundance of both species in the range $\leq$0.6-4$\times$10-10
toward the low-mass hot corino IRAS16293-2422 B.

Massive hot cores and low-mass hot corinos are among the most chemically rich
sources in the Galaxy and, traditionally, they have been the selected targets
for searches of new prebiotic COMs in the ISM (see e.g. Jørgensen et al.,
2012; Belloche et al., 2014; Jørgensen et al., 2016; Belloche et al., 2019).
Their disadvantage, however, lies in the fact that their observed rotational
spectra present hundreds (even thousands) of different molecular rotational
transitions as a result of the high excitation temperatures (of Tex=100-300
K). These high temperatures populate a wide number of energy levels of a COM
since its partition function is large. In addition, at temperatures of 100-300
K COM rotational spectra present their peak emission shifted towards
millimeter and sub-millimeter wavelengths, which are heavily contaminated by
the emission from smaller and lighter species such as CO. Consequently, the
COM spectra observed in massive hot cores and low-mass hot corinos not only
largely suffer from line blending and line confusion but also present weak
lines due to the large partition functions expected at high excitation
temperatures.

Alternatively, sources where COMs show low excitation temperatures (Tex)
represent better targets for the search and discovery of new large prebiotic
species in the ISM (Jimenez-Serra et al., 2014)222In massive hot cores and hot
corinos, Tex$\sim$Tkin because of the high H2 gas densities ($\geq$106 cm-3)
found in these star-forming regions.. As a result of the low Tex, the emission
peak of the COM observed spectra is shifted towards lower frequencies, which
are cleaner from the contribution from lighter molecules. In addition, the
line intensities increase since only the lowest energy levels of the COMs can
be populated at such low Tex and so, the number of rotational transitions
present in the measured spectra is significantly smaller than in hotter
sources. The frequency span for the transitions between the lowest energy
levels is also much larger than for those between the higher energy levels,
which helps reducing significantly line blending and line confusion in the
observed spectra (Jimenez-Serra et al., 2014).

Giant Molecular Clouds (GMCs) located in the Galactic Center such as the
molecular cloud G+0.693-0.027 (hereafter G+0.693) have proven to be not only
efficient chemical factories for the formation of complex organics (Requena-
Torres et al., 2006, 2008; Zeng et al., 2018), but also excellent targets for
the discovery of new prebiotic species (see e.g. Jiménez-Serra et al., 2020;
Rivilla et al., 2020, 2021; Zeng et al., 2021). These clouds show low H2 gas
densities of $\sim$104 cm-3 and their gas and dust temperatures are decoupled
(while Tdust$\leq$20 K, Tgas$\sim$70-150 K; see Rodríguez-Fernández et al.,
2000; Zeng et al., 2018). The low H2 gas densities also imply that for high-
dipole moment molecules (such as COMs), and despite the high gas kinetic
temperatures and broad linewidths of their emission (of $\sim$20 km s-1),
their Tex is low (between 5 and 20 K) and thus their observed spectra will be
less affected by line blending and line confusion. Recent searches of
prebiotic molecules toward the Galactic Center molecular cloud G+0.693 have
yielded the discovery of several of these species for the first time in the
ISM such as hydroxylamine (NH2OH; Rivilla et al., 2020), ethanolamine
(NH2CH2CH2OH; Rivilla et al., 2021), thioformic acid (HC(O)SH; Rodríguez-
Almeida et al., 2021) or $n$-propanol (n-C3H7OH; Jimenez-Serra et al., 2021).
As a result, Galactic Center GMCs are prime targets for the search and
discovery of large C3 and C4 sugars in the ISM.

##  4 The potential of the SKA to detect new prebiotic species in the ISM: The
case of sugars

The Square Kilometre Array (SKA) will be the largest radio telescope in the
world operating at centimeter and meter wavelengths. The Phase 1 of this
observatory will consist of two radio interferometers located at two different
sites: SKA1 LOW in Western Australia and SKA1 MID in South Africa (Braun et
al., 2019). SKA1 LOW will have 512 stations of 256 log periodic dipole
antennas each operating within the frequency range between 50 and 350 MHz,
while SKA1 MID will have a total of 197 antennas (that include the 64 antennas
of the MeerKAT array) operating at frequencies between 350 MHz and 15 GHz
(Braun et al., 2019). Given the frequency coverage and how dramatically the
strength of the rotational transitions of high-dipole molecules drops for
frequencies $\leq$5 GHz, SKA1 MID, and in particular its Band 5 receivers
covering the frequency range between 4.8 and 15.3 GHz, are well suited for
searches of prebiotic molecules in the ISM. On top of the advantages of
observing at centimeter wavelengths noted in Section 3, it is important to
stress that radio interferometers such as the SKA1 filter out any extended
emission in the line of sight of the targeted source, significantly decreasing
the linewidths of the observed molecular line emission and reducing the level
of line blending and line confusion. In Section 4.1, we evaluate the
feasibility of detecting large sugar-like species such as glyceraldehyde,
dihydroxyacetone and erythrulose in the ISM using the Band 5 receivers of SKA1
MID.

###  4.1 SKA1 simulations for C3 and C4 sugars in Galactic Center GMCs:
glyceraldehyde, dihydroxyacetone and erythrulose

The emission from COMs in the Galactic Center GMCs is known to be extended
(Martín-Pintado et al., 2001; Li et al., 2017, 2020). This is particularly
interesting for absorption studies in which COMs can be searched for against a
bright continuum background source. This technique may allow the detection of
low-abundance COMs whose emission spectra is expected to be very weak. Indeed,
in the presence of a bright background continuum source, the predicted
absorption line intensity (TL) is given by (see e.g. Martín et al., 2019):

$T_{L}=(T_{ex}-T_{c}-T_{bg})\times[1-exp(-\tau_{\nu})]$ (1)

where Tc is the temperature of a continuum source and Tbg is the temperature
of the comic microwave background radiation (Tbg=2.73 K). If Tc$>>$Tex, this
will largely enhance the observed absorption line intensity over the emission
for the Tex expected to be close to Tbg.

Therefore, we simulate the case of absorption spectra of glyceraldehyde,
dihydroxyacetone and erythrulose (C4H8O4) using the SLIM tool within the
MADCUBA software package333MADCUBA, or MAdrid Data CUBe Analysis, is a
software developed at the Center of Astrobiology in Madrid: https://cab.inta-
csic.es/madcuba/index.html. (see Martín et al., 2019). We focus our
simulations on C3 and C4 sugars because, as discussed in Section 4.2, C5
sugars such as ribose are not expected to be abundant enough to be detected
with SKA1 in a reasonable amount of observing time. We assume the physical
conditions of the G+0.693 molecular cloud with a typical Tex of $\leq$10 K,
linewidths of $\Delta_{v}$=20 km s-1 and extended morphology across the SKA1
beam for the COMs emission (Zeng et al., 2020). As background source, we
consider the L source located in the SgrB2 N complex, which is a bright HII
region found nearby the emission peak of G+0.693, and whose measured flux at
23 GHz is $\sim$300 mJy within a beam of $\sim$1$"$ (de Pree et al., 1995). We
have assumed that the emission from the HII region is optically thin and thus,
that it shows an almost flat spectral energy distribution between 23 GHz and
10 GHz. The simulations have been obtained considering a beam of 1$"$, which
will easily be reached by the SKA1 at the frequencies of the Band 5 receivers
of SKA1 MID (see Braun et al., 2019). The spectroscopic data for
glyceraldehyde have been extracted from the CDMS catalogue (entry 090501;
Endres et al., 2016), while the data for dihydroxyacetone is available in the
JPL molecular catalogue (entry 90002; Pickett et al., 1998). The spectroscopic
information for erythrulose can be found in Insausti et al. (2021).

As column densities, we have assumed that glyceraldehyde and dihydroxyacetone
have column densities of 1013 cm-2 and 6.8$\times$1012 cm-2, respectively.
These column densities correspond to the upper limits obtained toward G+0.693
in previous spectral surveys (see Table 2 in Jiménez-Serra et al., 2020). For
erythrulose, we consider that this C4 sugar is a factor of 10 less abundant
than the C3 sugar glyceraldehyde, with an assumed column density of 1012 cm-2
for erythrulose. We note that this decrease by one order of magnitude in the
column density of molecules from the same family when one carbon atom is added
to the molecular structure, has been reported for alcohols (Jimenez-Serra et
al., 2021) and thiols (Rodríguez-Almeida et al., 2021). The assumed spectral
resolution considered in our simulations is 79.3 kHz (equivalent to a velocity
resolution between $\sim$1.6 and 5.0 km s-1) across the full Band 5 frequency
coverage.

Figure 1 presents the predicted absorption spectra of glyceraldehyde,
dihydroxyacetone and erythrulose obtained for the extended GMC G+0.693 against
the background source L. Depending on the structure of the molecule, the
transitions that show the larger absorption depths lie in the range between
4.8-7.0 GHz for glyceraldehyde and erythrulose, and 8-14 GHz for
dihydroxyacetone. The maximum bandwidth that will be covered simultaneously by
the Band 5 receivers of SKA1 MID in its Phase 1 is 4 GHz at frequencies
between 4.6 and 8.5 GHz, and 5 GHz for frequencies between 8.3 and 15.3 GHz.
Given that the deepest absorption lines appear clustered within frequency
ranges of $\leq$4-5 GHz-width, future detection experiments of these lines
with SKA1 MID could be carried out in just two observing runs: one to
simultaneously cover all the deepest features of glyceraldehyde and
erythrulose, and a second one to simultaneously cover all the transitions of
dihydroxyacetone. We stress that Figure 1 includes all possible transitions of
these C3 and C4 sugars available within the frequency range covered by the
Band 5 receivers of SKA1 MID. The intensities of the deepest absorption
features in our simulated spectra reach values of $-$0.47 mJy for
glyceraldehyde, of $-$0.17 mJy for dihydroxyacetone, and $-$0.01 mJy for
erythrulose. Table 1 lists the spectroscopic information of the deepest
features found in our predicted spectra for each molecule. In Section 4.2, we
evaluate the observing time required to perform these detection experiments
with SKA1 MID during its Phase 1 of operations, which will have only 133
antennas equipped with Band 5 receivers.

Table 1: List of transitions of glyceraldehyde, dihydroxyacetone and
erythrulose that present the deepest features in the simulated spectra

Molecule | Formula | Frequency | Transition | log [Int(300K)] | El | Idepth
---|---|---|---|---|---|---
|  | (MHz) |  |  | (cm-1) | (mJy)
Glyceraldehyde | CHOCHOHCH2OH | 4955.4998 | 62,5$\rightarrow$61,5 | -7.7002 | 3.8458 |  $-$0.488
|  | 5907.2556 | 52,4$\rightarrow$51,4 | -7.6715 | 2.7805 |  $-$0.360
|  | 6762.4103 | 42,3$\rightarrow$41,3 | -7.6931 | 1.8888 |  $-$0.260
|  | 4835.6480 | 123,10$\rightarrow$122,10 | -7.4495 | 14.2538 |  $-$0.223
|  | 6240.1302 | 113,9$\rightarrow$112,9 | -7.3127 | 12.1285 |  $-$0.186
Dihydroxyacetone | CH2OHCOCH2OH | 9605.9342 | 41,3$\rightarrow$40,4 | -7.6869 | 1.2584 |  $-$0.172
|  | 10540.6391 | 51,4$\rightarrow$50,5 | -7.5446 | 1.8837 |  $-$0.166
|  | 8898.3733 | 31,2$\rightarrow$30,3 | -7.8427 | 0.7563 |  $-$0.161
|  | 11731.7585 | 61,5$\rightarrow$60,6 | -7.4104 | 2.6308 |  $-$0.147
|  | 8391.9655 | 21,1$\rightarrow$20,2 | -8.0253 | 0.3786 |  $-$0.132
Erythrulose | C4H8O4 | 4609.6719 | 103,8$\rightarrow$102,8 | -8.3205 | 5.1592 |  $-$0.010
|  | 5583.4870 | 93,7$\rightarrow$92,7 | -8.2442 | 4.2624 |  $-$0.0075
|  | 5131.3265 | 22,1$\rightarrow$21,1 | -9.0513 | 0.3329 |  $-$0.0071a
|  | 5131.4115 | 20,2$\rightarrow$10,1 | -8.8061 | 0.0861 |  $-$0.0071a
|  | 6508.3240 | 83,6$\rightarrow$82,6 | -8.199 | 3.4522 |  $-$0.0061

a Intensity of the feature resulting from the blending of the two indicated
transitions.

###  4.2 Time estimates and Key Science Projects

As seen from Table 1, the predicted intensities for the deepest absorption
features lie in the range between $-$0.19 and $-$0.5 mJy for glyceraldehyde,
$-$0.13 and $-$0.2 mJy for dihydroxyacetone, and $-$0.006 and $-$0.01 mJy for
erythrulose. According to Braun et al. (2019), a line sensitivity of 90
$\mu$Jy will be achieved in one hour of observing time with the Band 5
receivers of SKA1 MID at frequencies of 4.6-8.5 GHz, and of 85 $\mu$Jy at
frequencies of 8.5-15.3 GHz, for a velocity resolution of $\sim$30 km s-1.

Taking these numbers into account, the deepest absorption line of
glyceraldehyde at 4955 MHz could be detected with a S/N$\geq$5 in just 8.5 hrs
assuming a velocity resolution of 3 km s-1. The weakest transitions of
glyceraldehyde at 4835 MHz and at 6240 MHz, however, would require about 50
hrs of observing time for a similar velocity resolution and S/N. This is also
the case of dihydroxyacetone, for which a total of $\geq$100 hrs of
integration time on-source would be needed to detect its weakest transitions
at 8391 MHz and 11731 MHz with a S/N$\geq$5 and a velocity resolution of 3 km
s-1. A more time-consuming experiment would have to be performed for the
discovery of the deepest absorption features of erythrulose. In order to
detect the erythrulose transition at 4609 MHz with a S/N$\geq$3, and
considering a velocity resolution of 20 km s-1 (i.e. the linewidth of the
molecular emission in G+0.693; see Zeng et al., 2018), a total of $\geq$1100
hrs of observing time on-source would be required.

The time estimates to perform the detection experiments of glyceraldehyde,
dihydroxyacetone and erythrulose proposed above, may seem excessive. However,
we note that these long integration times are contemplated within the future
Key Science Projects (KSPs) scheme that will be carried out by the SKA1. The
KSPs are major surveys targeting ground-breaking transformational science in
Astrophysics and Astrobiology that require considerable amount of time.
Therefore, the expected integration time requests for these projects are
typically of a few thousands of hours, which guarantees the detection of at
least C3 sugars such as glyceraldehyde and dihydroxyacetone, if present in the
ISM. As discussed in Section 5, the discovery of C4 sugars such as erythrulose
may require the development of future instrumentation for SKA1 MID such as the
high-frequency Band 6 receivers.

We note that, when performing deep integrations as proposed here, it is
expected that the level of line confusion increases even at the low
frequencies covered by the SKA1 as a consequence of weak features of low-
abundance molecules becoming bright in the spectra. However, this potential
problem is likely not an issue for the discovery of intermediate-sized species
such as C3 and C4 sugars. As recently found by Jimenez-Serra et al. (2021) and
by Rodríguez-Almeida et al. (2021), the addition of a $-$CH2 group to the
structure of alcohols, thiols, isocyanates, and carboxylic acids implies a
decrease in their abundance by at least one order of magnitude (see also
Section 4.1). This decrease in the abundance would imply an increase in the
required SKA1 observing time by a factor of 100 and thus, for a reasonable
integration time within the context of SKA1 Key Science Projects, the only
sugars for which absorption features could be detected with SKA1 are the C3
and the C4 sugars together with their lowest-energy conformers. Indeed, for
the case of $n$-propanol, only the $Ga$ and $Aa$ conformers with relative
energies of E=0 K and E=40 K, have been found toward G+0.693 (the rest of
conformers with energies $>$50 K do not show any detected features; see
Jimenez-Serra et al., 2021). Therefore, although the conformers of C3 and C4
sugars as well as even larger sugars may be present in Galactic Center Giant
Molecular Clouds such as G+0.693, these species likely do not confuse much the
observed SKA1 spectrum because either their abundance is too low (as for C5
sugars such as ribose) or their low-energy levels are not populated at the low
excitation temperatures measured in these clouds (as for high-energy
conformers).

##  5 Future expansion of the SKA: the Band 6 receivers

From Section 4.2, it is clear that, while relatively small molecules such as
glyceraldehyde or dihydroxyacetone could be detected with a moderate
investment of SKA1 MID observing time, larger prebiotic COMs such as
erythrulose would still be well below the limit of what the SKA1 will be able
to detect in its Phase 1. For this reason, one possible future expansion of
SKA1 MID contemplates the development of higher-frequency receiver(s), the
Band 6 receivers, which will increase the frequency coverage of SKA1 MID to
higher frequencies from 15.3 up to 50 GHz. As reported in Memo 20-01 of SKA1
titled $"$SKA1 Beyond 15GHz: The Science case for Band 6$"$ (see Conway et
al., 2021), high-dipole moment molecules such as COMs present rotational
transitions at frequencies $\geq$20 GHz that can be factors $\geq$10 brighter
than those found at frequencies $\leq$15 GHz (see Section 3.3.1 in this Memo).
This is due to the fact that the Einstein Aul coefficients increase as
$\nu^{3}$ with $\nu$ being the frequency, making them one order of magnitude
higher at 36 GHz than at 12 GHz. This implies that observing times about
$\sim$100 times shorter would be needed to detect the C4 sugar erythrulose in
the ISM, reducing the total observing time needed for the discovery of this
species from $\geq$1100 hrs to a few tens of hours (or at most, to a few
hundreds of hours). Therefore, if these receivers were finally included in the
development program of the SKA1, they would make this observatory an
unbeateable machine for the discovery of large prebiotic compounds in space.

##  6 Conclusions

In this contribution, we evaluate the feasibility of detecting small sugars in
the ISM using the Band 5 receivers of SKA1 in its Phase 1. Our simulations
show that Galactic Center Giant Molecular Clouds such as G+0.693 represent
prime targets for future searches of these key prebiotic species in space. As
shown in Section 4.1, the detection of small sugars could be achieved by
carrying out broad spectroscopic surveys between 5 and 14GHz in absorption
against a bright continuum background source. By taking as template the L HII
region source located in the SgrB2 N molecular complex, we estimate that the
detection of C3 sugars could be achieved in a few hundreds of hours. Larger C4
sugars such as erythrulose would require thousands of hours of observing time.
Future developments of the SKA such as the Band 6 receivers (which will
increase the frequency coverage of SKA1 MID up to, at least, 24 GHz), will
enable the search of these large sugars and other prebiotic COMs in just a few
hundreds of hours.

##  7 Figures

Figure 1: Predicted absorption spectra of the C3 and C4 sugars glyceraldehyde,
dihydroxyacetone and erythrulose obtained with the SLIM tool of the MADCUBA
package considering the physical conditions of the G+0.693 molecular cloud
(Tex=10 K, linewidths of $\Delta_{v}$=20 km s-1 and extended emission across
the beam) and a background source similar to the L source in the SgrB2 N
molecular complex (measurex flux of $\sim$300 mJy within a beam of 1$"$ at 10
GHz). The assumed column densities for glyceraldehyde and dihydroxyacetone are
1013 cm-2 and 6.8$\times$1012 cm-2, respectively, while for erythrulose we
assume a column density one order of magnitude lower than that of
glyceraldehyde (of 1012 cm-2; see Section 4.1).

## Author Contributions

I.J.-S. has written the first version of the manuscript. I.J.-S. and J.M.-P.
have produced the MADCUBA-SLIM simulations of the spectra of glyceraldehyde,
dihydroxyacetone and erythrulose reported in Section 4.1. All authors have
contributed to the discussion of the results and have provided comments on the
text.

## Funding

I.J.-S. and J.M.-P. acknowledge partial support from the Spanish State
Research Agency (AEI) through project numbers PID2019-105552RB-C41 and
MDM-2017-0737 Unidad de Excelencia María de Maeztu–Centro de Astrobiología
(CSIC-INTA). E.J.C. thanks the support received from the MINECO
(PID2020-117892RB-I00), the Basque Government (IT1162-19 and PIBA 2018-11),
the UPV/EHU (PPG17/10, GIU18/207), and CSIC (PIC2018, LINKA20249).
Computational resources and laser facilities of the UPV/EHU (SGIker) and CESGA
were used in this work.

## Acknowledgments

We would like to thank an anonymous referee for his/her positive and
constructive comments on an earlier version of the manuscript.

## References

  * Altwegg et al. (2016) Altwegg, K., Balsiger, H., Bar-Nun, A., Berthelier, J. J., Bieler, A., Bochsler, P., et al. (2016).  Prebiotic chemicals–amino acid and phosphorus–in the coma of comet 67P/Churyumov-Gerasimenko.  _Science Advances_ 2, e1600285–e1600285.  10.1126/sciadv.1600285
  * Anders (1989) Anders, E. (1989).  Pre-biotic organic matter from comets and asteroids.  _Nature_ 342, 255–257.  10.1038/342255a0
  * Apponi et al. (2006) Apponi, A. J., Halfen, D. T., Ziurys, L. M., Hollis, J. M., Remijan, A. J., and Lovas, F. J. (2006).  Investigating the Limits of Chemical Complexity in Sagittarius B2(N): A Rigorous Attempt to Confirm 1,3-Dihydroxyacetone.  _The Astrophysical Journal Letters_ 643, L29–L32.  10.1086/504979
  * Becker et al. (2019) Becker, S., Feldmann, J., Wiedemann, S., Okamura, H., Schneider, C., Iwan, K., et al. (2019).  Unified prebiotically plausible synthesis of pyrimidine and purine rna ribonucleotides.  _Science_ 366, 76–82.  10.1126/science.aax2747
  * Belloche et al. (2014) Belloche, A., Garrod, R. T., Müller, H. S. P., and Menten, K. M. (2014).  Detection of a branched alkyl molecule in the interstellar medium: iso-propyl cyanide.  _Science_ 345, 1584–1587.  10.1126/science.1256678
  * Belloche et al. (2019) Belloche, A., Garrod, R. T., Müller, H. S. P., Menten, K. M., Medvedev, I., Thomas, J., et al. (2019).  Re-exploring Molecular Complexity with ALMA (ReMoCA): interstellar detection of urea.  _Astronomy & Astrophysics_ 628, A10.  10.1051/0004-6361/201935428
  * Belloche et al. (2008) Belloche, A., Menten, K. M., Comito, C., Müller, H. S. P., Schilke, P., Ott, J., et al. (2008).  Detection of amino acetonitrile in Sgr B2(N).  _Astronomy & Astrophysics_ 482, 179–196.  10.1051/0004-6361:20079203
  * Beltrán et al. (2009) Beltrán, M. T., Codella, C., Viti, S., Neri, R., and Cesaroni, R. (2009).  First Detection of Glycolaldehyde Outside the Galactic Center.  _The Astrophysical Journal Letters_ 690, L93–L96.  10.1088/0004-637X/690/2/L93
  * Braun et al. (2019) Braun, R., Bonaldi, A., Bourke, T., Keane, E., and Wagg, J. (2019).  Anticipated Performance of the Square Kilometre Array – Phase 1 (SKA1).  _arXiv e-prints_ , arXiv:1912.12699
  * Calabrese et al. (2020) Calabrese, C., Uriarte, I., Insausti, A., Vallejo-López, M., Basterretxea, F. J., Cochrane, S. A., et al. (2020).  Observation of the unbiased conformers of putative dna-scaffold ribosugars.  _ACS Central Science_ 6, 293–303.  10.1021/acscentsci.9b01277.  PMID: 32123748
  * Callahan et al. (2011) Callahan, M. P., Smith, K. E., Cleaves, H. J., Ruzicka, J., Stern, J. C., Glavin, D. P., et al. (2011).  Carbonaceous meteorites contain a wide range of extraterrestrial nucleobases.  _Proceedings of the National Academy of Science_ 108, 13995–13998.  10.1073/pnas.1106493108
  * Cernicharo et al. (2021) Cernicharo, J., Agúndez, M., Cabezas, C., Tercero, B., Marcelino, N., Pardo, J. R., et al. (2021).  Pure hydrocarbon cycles in TMC-1: Discovery of ethynyl cyclopropenylidene, cyclopentadiene, and indene.  _Astronomy & Astrophysics_ 649, L15.  10.1051/0004-6361/202141156
  * Chyba and Sagan (1992) Chyba, C. and Sagan, C. (1992).  Endogenous production, exogenous delivery and impact-shock synthesis of organic molecules: an inventory for the origins of life.  _Nature_ 355, 125–132.  10.1038/355125a0
  * Cocinero et al. (2012) Cocinero, E. J., Lesarri, A., Écija, P., Basterretxea, F. J., Grabow, J.-U., Fernández, J. A., et al. (2012).  Ribose found in the gas phase.  _Angewandte Chemie International Edition_ 51, 3119–3124.  https://doi.org/10.1002/anie.201107973
  * Conway et al. (2021) Conway, J., Beswick, R., Bourke, T., Coriat, M., Ferrari, C., Jimenez-Serra, I., et al. (2021).  _Memo 20-01, SKA1 Beyond 15GHz: The Science case for Band 6_ (Square Kilometre Array)
  * Cooper et al. (2001) Cooper, G., Kimmich, N., Belisle, W., Sarinana, J., Brabham, K., and Garrel, L. (2001).  Carbonaceous meteorites as a source of sugar-related organic compounds for the early Earth.  _Nature_ , 879–883https://doi.org/10.1038/414879a
  * de Marcellus et al. (2015) de Marcellus, P., Meinert, C., Myrgorodska, I., Nahon, L., Buhse, T., d’Hendecourt, L. L. S., et al. (2015).  Aldehydes and sugars from evolved precometary ice analogs: Importance of ices in astrochemical and prebiotic evolution.  _Proceedings of the National Academy of Science_ 112, 965–970.  10.1073/pnas.1418602112
  * de Pree et al. (1995) de Pree, C. G., Gaume, R. A., Goss, W. M., and Claussen, M. J. (1995).  The Sagittarius B2 Star-forming Region. II. High-Resolution H66 alpha Observations of Sagittarius B2 North.  _The Astrophysical Journal_ 451, 284.  10.1086/176218
  * Endres et al. (2016) Endres, C. P., Schlemmer, S., Schilke, P., Stutzki, J., and Müller, H. S. P. (2016).  The Cologne Database for Molecular Spectroscopy, CDMS, in the Virtual Atomic and Molecular Data Centre, VAMDC.  _Journal of Molecular Spectroscopy_ 327, 95–104.  10.1016/j.jms.2016.03.005
  * Furukawa et al. (2019) Furukawa, Y., Chikaraishi, Y., Ohkouchi, N., Ogawa, N. O., Glavin, D. P., Dworkin, J. P., et al. (2019).  Extraterrestrial ribose and other sugars in primitive meteorites.  _Proceedings of the National Academy of Science_ 116, 24440–24445.  10.1073/pnas.1907169116
  * Glavin et al. (2020) Glavin, D. P., McLain, H. L., Dworkin, J. P., Parker, E. T., Elsila, J. E., Aponte, J. C., et al. (2020).  Abundant extraterrestrial amino acids in the primitive cm carbonaceous chondrite asuka 12236.  _Meteoritics & Planetary Science_ 55, 1979–2006.  https://doi.org/10.1111/maps.13560
  * Herbst and van Dishoeck (2009) Herbst, E. and van Dishoeck, E. F. (2009).  Complex Organic Interstellar Molecules.  _Annual Review of Astronomy & Astrophysics_ 47, 427–480.  10.1146/annurev-astro-082708-101654
  * Hollis et al. (2004) Hollis, J. M., Jewell, P. R., Lovas, F. J., and Remijan, A. (2004).  Green Bank Telescope Observations of Interstellar Glycolaldehyde: Low-Temperature Sugar.  _The Astrophysical Journal Letters_ 613, L45–L48.  10.1086/424927
  * Hollis et al. (2000) Hollis, J. M., Lovas, F. J., and Jewell, P. R. (2000).  Interstellar glycolaldehyde: The first sugar.  _The Astrophysical Journal_ 540, L107–L110.  10.1086/312881
  * Insausti et al. (2021) Insausti, A., Alonso, E. R., Tercero, B., Santos, J. I., Calabrese, C., Vogt, N., et al. (2021).  Laboratory Observation of, Astrochemical Search for, and Structure of Elusive Erythrulose in the Interstellar Medium.  _The Journal of Physical Chemistry Letters_ 12, 1352–1359.  10.1021/acs.jpclett.0c03050
  * Jiménez-Serra et al. (2020) Jiménez-Serra, I., Martín-Pintado, J., Rivilla, V. M., Rodríguez-Almeida, L., Alonso Alonso, E. R., Zeng, S., et al. (2020).  Toward the RNA-World in the Interstellar Medium—Detection of Urea and Search of 2-Amino-oxazole and Simple Sugars.  _Astrobiology_ 20, 1048–1066.  10.1089/ast.2019.2125
  * Jimenez-Serra et al. (2021) Jimenez-Serra, I., Rodríguez-Almeida, L. F., Martín-Pintado, J., Rivilla, V. M., Melosso, M., Zeng, S., et al. (2021).  Precursors of fatty alcohols in the ISM: Discovery of n-propanol.  _Astronomy & Astrophysics_
  * Jimenez-Serra et al. (2014) Jimenez-Serra, I., Testi, L., Caselli, P., and Viti, S. (2014).  Detectability of Glycine in Solar-type System Precursors.  _The Astrophysical Journal Letters_ 787, L33.  10.1088/2041-8205/787/2/L33
  * Jørgensen et al. (2012) Jørgensen, J. K., Favre, C., Bisschop, S. E., Bourke, T. L., van Dishoeck, E. F., and Schmalzl, M. (2012).  Detection of the Simplest Sugar, Glycolaldehyde, in a Solar-type Protostar with ALMA.  _The Astrophysical Journal Letters_ 757, L4.  10.1088/2041-8205/757/1/L4
  * Jørgensen et al. (2016) Jørgensen, J. K., van der Wiel, M. H. D., Coutens, A., Lykke, J. M., Müller, H. S. P., van Dishoeck, E. F., et al. (2016).  The ALMA Protostellar Interferometric Line Survey (PILS). First results from an unbiased submillimeter wavelength line survey of the Class 0 protostellar binary IRAS 16293-2422 with ALMA.  _Astronomy & Astrophysics_ 595, A117.  10.1051/0004-6361/201628648
  * Li et al. (2017) Li, J., Shen, Z., Wang, J., Chen, X., Li, D., Wu, Y., et al. (2017).  Widespread Presence of Glycolaldehyde and Ethylene Glycol around Sagittarius B2.  _The Astrophysical Journal Letters_ 849, 115.  10.3847/1538-4357/aa9069
  * Li et al. (2020) Li, J., Wang, J., Qiao, H., Quan, D., Fang, M., Du, F., et al. (2020).  Mapping observations of complex organic molecules around Sagittarius B2 with the ARO 12 m telescope.  _Monthly Notices of the Royal Astronomical Society_ 492, 556–565.  10.1093/mnras/stz3337
  * Martín et al. (2019) Martín, S., Martín-Pintado, J., Blanco-Sánchez, C., Rivilla, V. M., Rodríguez-Franco, A., and Rico-Villas, F. (2019).  Spectral Line Identification and Modelling (SLIM) in the MAdrid Data CUBe Analysis (MADCUBA) package. Interactive software for data cube analysis.  _Astronomy & Astrophysics_ 631, A159.  10.1051/0004-6361/201936144
  * Martín-Pintado et al. (2001) Martín-Pintado, J., Rizzo, J. R., de Vicente, P., Rodríguez-Fernández, N. J., and Fuente, A. (2001).  Large-Scale Grain Mantle Disruption in the Galactic Center.  _The Astrophysical Journal Letters_ 548, L65–L68.  10.1086/318937
  * McGuire (2021) McGuire, B. A. (2021).  2021 Census of Interstellar, Circumstellar, Extragalactic, Protoplanetary Disk, and Exoplanetary Molecules.  _arXiv e-prints_ , arXiv:2109.13848
  * McGuire et al. (2021) McGuire, B. A., Loomis, R. A., Burkhardt, A. M., Lee, K. L. K., Shingledecker, C. N., Charnley, S. B., et al. (2021).  Detection of two interstellar polycyclic aromatic hydrocarbons via spectral matched filtering.  _Science_ 371, 1265–1269.  10.1126/science.abb7535
  * Menor Salvan et al. (2020) Menor Salvan, C., Bouza, M., Fialho, D. M., Burcar, B. T., Fernández, F. M., and Hud, N. V. (2020).  Prebiotic origin of pre-rna building blocks in a urea “warm little pond” scenario.  _ChemBioChem_ 21, 3504–3510.  https://doi.org/10.1002/cbic.202000510
  * Patel et al. (2015) Patel, B. H., Percivalle, C., Ritson, D. J., Duffy, C. D., and Sutherland, J. D. (2015).  Common origins of RNA, protein and lipid precursors in a cyanosulfidic protometabolism.  _Nature Chemistry_ , 301–307https://doi.org/10.1038/nchem.2202
  * Pickett et al. (1998) Pickett, H. M., Poynter, R. L., Cohen, E. A., Delitsky, M. L., Pearson, J. C., and Müller, H. S. P. (1998).  Submillimeter, millimeter and microwave spectral line catalog.  _Journal of Quantitative Spectroscopy and Radiative Transfer_ 60, 883–890.  10.1016/S0022-4073(98)00091-0
  * Pizzarello et al. (2006) Pizzarello, S., Cooper, G. W., and Flynn, G. J. (2006).  The Nature and Distribution of the Organic Material in Carbonaceous Chondrites and Interplanetary Dust Particles.  In _Meteorites and the Early Solar System II_ , eds. D. S. Lauretta and H. Y. McSween. 625
  * Requena-Torres et al. (2008) Requena-Torres, M. A., Martín-Pintado, J., Martín, S., and Morris, M. R. (2008).  The Galactic Center: The Largest Oxygen-bearing Organic Molecule Repository.  _The Astrophysical Journal_ 672, 352–360.  10.1086/523627
  * Requena-Torres et al. (2006) Requena-Torres, M. A., Martín-Pintado, J., Rodríguez-Franco, A., Martín, S., Rodríguez-Fernández, N. J., and de Vicente, P. (2006).  Organic molecules in the Galactic center. Hot core chemistry without hot cores.  _Astronomy & Astrophysics_ 455, 971–985.  10.1051/0004-6361:20065190
  * Rivilla et al. (2021) Rivilla, V. M., Jiménez-Serra, I., Martín-Pintado, J., Briones, C., Rodríguez-Almeida, L. F., Rico-Villas, F., et al. (2021).  Discovery in space of ethanolamine, the simplest phospholipid head group.  _Proceedings of the National Academy of Science_ 118, 2101314118\.  10.1073/pnas.2101314118
  * Rivilla et al. (2020) Rivilla, V. M., Martín-Pintado, J., Jiménez-Serra, I., Martín, S., Rodríguez-Almeida, L. F., Requena-Torres, M. A., et al. (2020).  Prebiotic Precursors of the Primordial RNA World in Space: Detection of NH2OH.  _The Astrophysical Journal Letters_ 899, L28.  10.3847/2041-8213/abac55
  * Rodríguez-Almeida et al. (2021) Rodríguez-Almeida, L. F., Jiménez-Serra, I., Rivilla, V. M., Martín-Pintado, J., Zeng, S., Tercero, B., et al. (2021).  Thiols in the Interstellar Medium: First Detection of HC(O)SH and Confirmation of C2H5SH.  _The Astrophysical Journal Letters_ 912, L11.  10.3847/2041-8213/abf7cb
  * Rodríguez-Fernández et al. (2000) Rodríguez-Fernández, N. J., Martín-Pintado, J., de Vicente, P., Fuente, A., Hüttemeister, S., Wilson, T. L., et al. (2000).  Non-equilibrium H_2 ortho-to-para ratio in two molecular clouds of the Galactic Center.  _Astronomy & Astrophysics_ 356, 695–704
  * Widicus Weaver and Blake (2005) Widicus Weaver, S. L. and Blake, G. A. (2005).  1,3-Dihydroxyacetone in Sagittarius B2(N-LMH): The First Interstellar Ketose.  _The Astrophysical Journal Letters_ 624, L33–L36.  10.1086/430407
  * Zeng et al. (2018) Zeng, S., Jiménez-Serra, I., Rivilla, V. M., Martín, S., Martín-Pintado, J., Requena-Torres, M. A., et al. (2018).  Complex organic molecules in the Galactic Centre: the N-bearing family.  _Monthly Notices of the Royal Astronomical Society_ 478, 2962–2975.  10.1093/mnras/sty1174
  * Zeng et al. (2021) Zeng, S., Jiménez-Serra, I., Rivilla, V. M., Martín-Pintado, J., Rodríguez-Almeida, L. F., Tercero, B., et al. (2021).  Probing the Chemical Complexity of Amines in the ISM: Detection of Vinylamine (C2H3NH2) and Tentative Detection of Ethylamine (C2H5NH2).  _The Astrophysical Journal Letters_ 920, L27.  10.3847/2041-8213/ac2c7e
  * Zeng et al. (2019) Zeng, S., Quénard, D., Jiménez-Serra, I., Martín-Pintado, J., Rivilla, V. M., Testi, L., et al. (2019).  First detection of the pre-biotic molecule glycolonitrile (HOCH2CN) in the interstellar medium.  _Monthly Notices of the Royal Astronomical Society_ 484, L43–L48.  10.1093/mnrasl/slz002
  * Zeng et al. (2020) Zeng, S., Zhang, Q., Jiménez-Serra, I., Tercero, B., Lu, X., Martín-Pintado, J., et al. (2020).  Cloud-cloud collision as drivers of the chemical complexity in Galactic Centre molecular clouds.  _Monthly Notices of the Royal Astronomical Society_ 497, 4896–4909.  10.1093/mnras/staa2187


# The El Gordo Galaxy Cluster Challenges $\Lambda$CDM for Any Plausible
Collision Velocity

Elena Asencio Helmholtz-Institut für Strahlen und Kernphysik (HISKP),
University of Bonn, Nussallee 14$-$16, D-53115 Bonn, Germany  Indranil Banik
Scottish Universities Physics Alliance, University of Saint Andrews, North
Haugh, Saint Andrews, Fife, KY16 9SS, UK  Pavel Kroupa Helmholtz-Institut für
Strahlen und Kernphysik (HISKP), University of Bonn, Nussallee 14$-$16,
D-53115 Bonn, Germany  Astronomical Institute, Faculty of Mathematics and
Physics, Charles University, V Holešovičkách 2, CZ-180 00 Praha 8, Czech
Republic Elena Asencio<EMAIL_ADDRESS>
###### Abstract

El Gordo (ACT-CL J0102-4915) is an extraordinarily large and bright galaxy
cluster collision. In a previous study, we found that El Gordo is in
$6.2\sigma$ tension with the $\Lambda$ cold dark matter ($\Lambda$CDM)
standard model when assuming the nominal mass and infall velocity values from
the hydrodynamical simulations of Zhang et al. ($M_{200}=3.2\times
10^{15}M_{\odot}$ and $V_{\textrm{infall}}=2500~{}\textrm{km~{}s}^{-1}$,
respectively). The recent weak-lensing study of Kim et al. showed that the
mass of El Gordo is actually $2.13^{+0.25}_{-0.23}\times 10^{15}M_{\odot}$.
Here we explore the level of tension between El Gordo and $\Lambda$CDM for the
new mass estimate, assuming several $V_{\textrm{infall}}$ values. We find that
in order to reduce the tension below the $5\sigma$ level, the El Gordo
subclusters should have $V_{\textrm{infall}}<2300~{}\textrm{km~{}s}^{-1}$
($V_{\textrm{infall}}<1800~{}\textrm{km~{}s}^{-1}$ when considering the
combined tension with the Bullet Cluster). To the best of our knowledge, the
El Gordo hydrodynamical simulations conducted so far require
$V_{\textrm{infall}}\geq 2500~{}\textrm{km~{}s}^{-1}$ to simultaneously
reproduce its morphology and its high X-ray luminosity and temperature. We
therefore conclude that El Gordo still poses a significant challenge to
$\Lambda$CDM cosmology. Whether the properties of El Gordo can be reconciled
with a lower $V_{\textrm{infall}}$ should be tested with new hydrodynamical
simulations that explore different configurations of the interaction.

galaxies: clusters: individual (El Gordo) – galaxies: clusters: individual
(Bullet Cluster) – large-scale structure of universe – gravitation – dark
matter – methods: statistical

hyperrefOption hyperrefToken pdftex(dest) ApJ

##  1 Introduction

El Gordo (ACT-CL J0102-4915) is a supermassive interacting galaxy cluster
composed of two infalling subclusters observed at redshift $z=0.87$. It was
found by the Atacama Cosmology Telescope (ACT) collaboration in a 455 deg2
survey (Menanteau et al., 2010; Marriage et al., 2011). El Gordo is well known
for its extreme properties of mass, redshift, and infall velocity, which are
remarkably rare in the context of the $\Lambda$ cold dark matter
($\Lambda$CDM) standard model of cosmology (Menanteau et al., 2012; Katz et
al., 2013; Jee et al., 2014).

The properties of El Gordo were constrained for the first time by Menanteau et
al. (2012) from the analysis of additional multi-wavelength observations.
Those authors described El Gordo as the most massive, hottest, most X-ray
luminous, and brightest Sunyaev-Zel’dovich (SZ) effect cluster known at
redshift $z>0.6$. They also noted the presence of a wake formed in the X-ray
surface brightness caused by the passage of one subcluster through the other.
Their estimated values for the redshift, mass, and relative velocity between
the two subclusters at the time of observation are: $z=0.87$,
$M_{200a}=2.16\pm 0.32\times 10^{15}h^{-1}_{70}M_{\odot}$, and
$V_{\textrm{obs}}=1200-2300~{}\textrm{km~{}s}^{-1}$, respectively, where
$h_{70}$ is the Hubble constant $H_{0}$ in units of 70 km s-1 Mpc-1 and
$M_{200a}$ is the mass within the radius such that the average enclosed
density is $200\times$ the cosmic average, which at that epoch was slightly
below the critical density. The estimated range of $V_{\textrm{obs}}$ was
obtained from the line-of-sight peculiar velocity difference between the two
subclusters ($\Delta V_{\textrm{pec}}=586\pm 96~{}\textrm{km~{}s}^{-1}$) and
from assuming that the collision is likely taking place close to the plane of
the sky (inclination angle $\theta=15^{\circ}-30^{\circ}$), leading to
$V_{\textrm{obs}}=\Delta V_{\textrm{pec}}/\sin\theta$. Menanteau et al. (2012)
justified the low adopted $\theta$ by noting that we can only see the El Gordo
morphological features so prominently if the interaction is nearly in the
plane of the sky. The low $\theta$ assumption is also supported by the high
degree of polarization in the radio relics of El Gordo (Lindner et al., 2014).
Menanteau et al. (2012) assumed that the infall velocity of the two
subclusters ($V_{\textrm{infall}}$) should be about the same as
$V_{\textrm{obs}}$. However, the present velocity is not necessarily a good
guide to the pre-merger velocity due to dynamical friction and gas drag, among
other processes. $N$-body/hydrodynamical simulations are needed to get a
better constraint on $V_{\textrm{infall}}$.

Ng et al. (2015) performed a series of $N$-body simulations of El Gordo that
focused on estimating its particular dynamical and kinematic features. They
aimed to constrain $\theta$, $V_{\textrm{obs}}$, and the pericenter velocity
$V_{\textrm{peri}}$, among other parameters. Their estimated $\Delta
V_{\textrm{pec}}=476\pm 242~{}\textrm{km~{}s}^{-1}$ is lower than that
observed by Menanteau et al. (2012) but consistent within uncertainties. From
the polarization fraction of El Gordo’s synchrotron radiation (Lindner et al.,
2014), Ng et al. (2015) obtained an upper limit to the inclination angle of
$\theta\leq 35^{\circ}$. Taking as inputs a mass of $M_{200}=2.06\times
10^{15}$ $M_{\odot}$, a mass ratio of 1.71, a projected separation of
$0.740\pm 0.007$ Mpc between the subclusters, and their estimated value for
$\Delta V_{\textrm{pec}}$, their best-fit model obtained with the Markov Chain
Monte Carlo (MCMC) method yields $\theta=21^{\circ}\pm^{9}_{11}$,
$V_{\textrm{obs}}=940^{+860}_{-580}~{}\textrm{km~{}s}^{-1}$, and
$V_{\textrm{peri}}=2400_{-200}^{+400}~{}\textrm{km~{}s}^{-1}$. In their model,
the value of $V_{\textrm{infall}}$ at a subcluster separation equal to the sum
of the two virial radii roughly corresponds to $50\%$ of the
$V_{\textrm{peri}}$ value (see section 5.1 of Ng et al., 2015), which means
that they would have obtained $V_{\textrm{infall}}\approx
1200~{}\textrm{km~{}s}^{-1}$ for their best-fit $V_{\textrm{peri}}$ value. It
is worth noting that in their MCMC analysis, they exclude all realizations
that would result in $V_{\textrm{peri}}$ higher than the escape velocity.
Unlike other studies of El Gordo, Ng et al. (2015) found that the best-fitting
configuration is that in which the two subclusters already had a pericenter
passage and are returning toward a second passage.

Hydrodynamical simulations of El Gordo aim to understand the detailed gas
dynamics required to reproduce the SZ and X-ray observables of this cluster,
including its twin-tailed morphology. The first hydrodynamical simulation of
El Gordo was carried out by Donnert (2014). Using the results of Menanteau et
al. (2012), they chose as initial parameters: total mass $M_{200}=2.71\times
10^{15}M_{\odot}$, mass ratio of 2.35, main cluster radius $R_{200,1}=2.550$
Mpc, secondary cluster radius $R_{200,2}=1.925$ Mpc,
$V_{\textrm{infall}}=2600~{}\textrm{km~{}s}^{-1}$ at a distance of 5.23 Mpc,
and a small impact parameter of $b=20$ kpc. Though they were not able to
reproduce the X-ray wake in their simulation, they managed to match the
observed X-ray luminosity of $L_{X}=2.19\pm 0.11\times 10^{45}~{}h^{-2}_{70}$
erg s-1 (Menanteau et al., 2012) very accurately when the observed dark matter
core separation is $d_{\textrm{core}}=690$ kpc, similar to the observed
separation of $\approx 700$ kpc (Jee et al., 2014).

The hydrodynamical simulations of Molnar & Broadhurst (2015) used a total mass
of $M_{200}=2.15\times 10^{15}$ $M_{\odot}$ with mass ratio 1.87 and radii of
$R_{200,1}=2.304$ Mpc and $R_{200,2}=1.944$ Mpc for the individual
subclusters. Those authors ran several simulations for different
$V_{\textrm{infall}}$ (at a distance of 4.25 Mpc) and $b$ in order to find the
best match to observations of El Gordo. They found that for
$V_{\textrm{infall}}=2250\pm 250~{}\textrm{km~{}s}^{-1}$ and
$b=300^{+50}_{-100}$ kpc, they could reproduce the twin-tailed morphology of
El Gordo, its relative radial velocity, and the relative positions of its
X-ray, SZ, and weak-lensing peaks. However, they could not match the high
observed X-ray luminosity and temperature of El Gordo (Zhang et al., 2015).
Moreover, their best-fit model assumes an inclination angle of
$\theta=45^{\circ}$, which is well above the maximum value of
$\theta=35^{\circ}$ as constrained by Ng et al. (2015) from the polarization
fraction. However, they obtained
$V_{\textrm{obs}}=1009~{}\textrm{km~{}s}^{-1}$ for this model, very consistent
with the value obtained by Ng et al. (2015). With this, Molnar & Broadhurst
(2015) also showed that the $V_{\textrm{infall}}\approx V_{\textrm{obs}}$
assumption made by Menanteau et al. (2012) clearly underestimates the value of
$V_{\textrm{infall}}$: according to their simulations,
$V_{\textrm{infall}}\approx 1.5\,V_{\textrm{obs}}$.

The latest and most complete exploration of the parameter space using
hydrodynamical simulations of El Gordo was done by Zhang et al. (2015). These
are also the simulations that better manage to reproduce the observed
properties of El Gordo as they simultaneously reproduce its morphology,
luminosity, temperature, and relative radial velocity. Zhang et al. (2015)
test two different scenarios for the interaction. The first scenario (referred
to as Model A by the authors) assumes that the interaction is a very energetic
head-on collision between the two subclusters. Donnert (2014) and Molnar &
Broadhurst (2015) also assume this scenario in their simulations. The best-fit
parameters found by Zhang et al. (2015) in their Model A are:
$M_{200}=1.95\times 10^{15}M_{\odot}$, mass ratio of 2, $R_{200,1}=1.66$ Mpc,
$R_{200,2}=1.32$ Mpc, $V_{\textrm{infall}}=3000~{}\textrm{km~{}s}^{-1}$ (at
5.84 Mpc), and $b=300$ kpc, viewed at an inclination angle
$\theta=75^{\circ}$. With these parameters, they could generate X-ray surface
brightness and mass density distributions that match the observations. But the
twin-tailed X-ray morphology that they obtained is smaller and more asymmetric
than observed and only appears when the projected distance between the
clusters is $\approx 600$ kpc. Also, the luminosity for this model
($L_{X}=2.48\pm 0.03\times 10^{45}~{}h^{-2}_{70}$ erg s-1) is a bit higher
than observed, while the inclination angle surpasses significantly the maximum
estimated value (Ng et al., 2015).

In their second scenario (Model B), Zhang et al. (2015) assume that the
interaction took place as a less violent, off-centered collision. The best-fit
parameters in this Model B case are: $M_{200}=3.19\times 10^{15}M_{\odot}$,
mass ratio of 3.6, $R_{200,1}=2.06$ Mpc, $R_{200,2}=1.35$ Mpc,
$V_{\textrm{infall}}=2500~{}\textrm{km~{}s}^{-1}$ (at 6.72 Mpc), and $b=800$
kpc, viewed at an inclination angle of $\theta=30^{\circ}$. With these
parameters, the model reproduces the temperature and X-ray luminosity of El
Gordo and a two-tailed X-ray morphology bearing closer resemblance to the
observed morphology, especially concerning the size and symmetry of the tails
and the projected separation of the clusters ($\approx 780$ kpc). Since this
model performs better than fiducial Model A at reproducing the morphological
properties of El Gordo, Zhang et al. (2015) chose this set of parameters as
their preferred model.

In our previous work (Asencio, Banik, & Kroupa, 2021), we calculated the
probability of finding a pair of clusters in $\Lambda$CDM cosmology at $z=1$
with the mass, mass ratio, and infall velocity given by the best-fit pre-
merger parameters of Model B (Zhang et al., 2015) in the survey region in
which the El Gordo properties were first constrained (sky area of 755 deg2;
Menanteau et al., 2012). We found that the probability of such a pre-merger
configuration arising in $\Lambda$CDM is only $7.51\times 10^{-10}$, which
corresponds to a $6.16\sigma$ failure for a 1D Gaussian. In other words,
according to our statistical analysis, only one El Gordo analog is expected in
a volume of $\approx 5.6\times 10^{8}~{}\textrm{cGpc}^{3}$. This is $\approx
10^{9}\times$ larger than the effective (from $z=1$ to $z=1.06$) survey volume
of El Gordo, and $\approx 5\times 10^{7}\times$ larger than the effective
full-sky volume. The probability is even lower if we take into account that El
Gordo is not the only object whose properties pose a problem for the
$\Lambda$CDM model. The Bullet Cluster is another interacting galaxy cluster
known for its very high infall velocity ($\approx
3000~{}\textrm{km~{}s}^{-1}$; Lage & Farrar, 2014). From Kraljic & Sarkar
(2015), we inferred that the probability of observing the Bullet Cluster in
the survey region where it was discovered is $5.4\times 10^{-3}$
($2.78\sigma$). Combining the probability of observing both El Gordo and the
Bullet Cluster in their respective survey regions, we obtained a total
probability of $1.24\times 10^{-10}$ ($6.43\sigma$). We also discussed the
impact that the different uncertainties in the analysis assumptions could have
had on our nominal result. These caused the final result to differ somewhat
from the nominal $6.43\sigma$ value. But for the most plausible assumptions,
we always obtained a tension $>5\sigma$. From these results, we concluded that
the $\Lambda$CDM model is falsified at high significance ($>5\sigma$) $-$
assuming the best-fit parameters of Zhang et al. (2015) $-$ whether we
consider El Gordo alone or together with other problematic clusters.

However, a very recent and detailed weak-lensing study of El Gordo (Kim et
al., 2021) obtained a lower estimate for its mass and mass ratio. In Section
2, we obtain the tension between El Gordo and $\Lambda$CDM for the new mass
and mass ratio values, assuming several different infall velocities. In
Section 3, we discuss our results and their implications for $\Lambda$CDM in
light of the $V_{\textrm{infall}}$ values obtained in prior numerical and
hydrodynamical simulations of El Gordo. We conclude in Section 4.

##  2 Analysis and results

The weak-lensing study of Kim et al. (2021) found that El Gordo has a mass of
$M_{200}=2.13^{+0.25}_{-0.23}\times 10^{15}\,M_{\odot}$ and a mass ratio of
1.52. The mass estimate of $M_{200}\approx 2\times 10^{15}\,M_{\odot}$ is
supported by recent strong-lensing analyses (Caminha et al., 2023; Diego et
al., 2023). Kim et al. (2021) claim that using the new mass estimate and
assuming $V_{\textrm{infall}}\approx 450~{}\textrm{km~{}s}^{-1}$ at a
separation of 5.5 Mpc, the tension with the $\Lambda$CDM model disappears.
This is technically true since repeating the analysis performed in Asencio et
al. (2021) for the nominal values of mass, mass ratio, and infall velocity
assumed in Kim et al. (2021) increases the probability of finding an El Gordo-
like object in $\Lambda$CDM to $6.26\times 10^{-3}$ (2.73$\sigma$).

However, the significant decrease of the tension with respect to our previous
study (Asencio et al., 2021) is mainly caused by the lower infall velocity
assumption and not by the lower mass estimate. Kim et al. (2021) obtained this
$V_{\textrm{infall}}$ by performing a similar analysis to that of Ng et al.
(2015), but also accounting for some of the inaccuracies present in this
analysis. The main problems that they identified in Ng et al. (2015) were the
assumption that dynamical friction is negligible in the El Gordo case, an
incorrect sampling of the angle $\theta$ in their MCMC analysis, and the fact
that they allow for merger scenarios in which the two subclusters start to
free-fall at a distance similar to the present subcluster separation. In their
corrected version of the analysis, they found that the scenario in which El
Gordo’s subclusters are returning for a second pericenter passage is no longer
favored. As in Ng et al. (2015), they also impose an upper limit to their MCMC
analysis that rules out all models with collision velocities higher than their
escape velocity ($\approx 3600~{}\textrm{km~{}s}^{-1}$ at the current
subcluster separation of 0.7 Mpc for the parameters found by Kim et al.,
2021)111This corresponds to an escape velocity of $\approx
1200~{}\textrm{km~{}s}^{-1}$ at $6.06$ Mpc, the distance at which we obtain
$V_{\textrm{infall}}$ in our analysis, which is the main reason they obtain
such a low $V_{\textrm{infall}}$. This constraint is motivated by the fact
that previous studies from cosmological simulations had already shown that it
is highly unlikely that the pairwise velocity of massive merging clusters
($M\gtrsim 10^{15}\,M_{\odot}$) exceeds 3000 km s-1 in a $\Lambda$CDM
cosmology (Lee & Komatsu, 2010; Thompson & Nagamine, 2012; Ng et al., 2015).
Since the analysis of Kim et al. (2021) imposes as a prior that we should not
consider any $V_{\textrm{infall}}$ value which is unlikely to arise in
$\Lambda$CDM, the $V_{\textrm{infall}}$ value they obtain cannot be used to
estimate the likelihood of observing El Gordo in $\Lambda$CDM.

As it is not possible to infer the actual infall velocity needed to reproduce
the observed morphology of El Gordo for the new mass estimate without
performing a more detailed study using $N$-body or hydrodynamical simulations,
we obtain the level of tension between $\Lambda$CDM and El Gordo assuming
$M_{200}=2.13^{+0.25}_{-0.23}\times 10^{15}\,M_{\odot}$, a mass ratio of 1.52,
and several different values of $V_{\textrm{infall}}$ at a distance of 6.06
Mpc using the nominal ‘lightcone tomography’ technique we presented in Asencio
et al. (2021). The method can be briefly summarized as follows: the
probability of observing an El Gordo-like object in the survey region
according to $\Lambda$CDM is determined by looking for pre-merger El Gordo
analogs in a large $N$-body cosmological simulation. The conditions required
for a cluster pair to be a candidate are: (i) mass ratio below that of El
Gordo (1.52 for the model that we test in this study); and (ii) infall
velocity/escape velocity ratio above that of El Gordo at twice the sum of its
virial radii. This lets us obtain
$\log_{10}N\left(\geq\log_{10}M/M_{\odot}\right)$, the number of candidate
pairs above a certain mass (in logarithmic scale). This function is very well
fitted by a parabola. From this fit, the frequency of very high-mass
candidates $-$ for which there are no analogs in the simulation box $-$ can be
extrapolated. This process is repeated at three different redshifts. This
allows us to infer the relation between the redshift and the number of analogs
$N$ above a certain minimum mass. From this, one can obtain the number of El
Gordo analogs in any mass and redshift range. We estimate that the pre-merger
configuration took place at $z=1$ and take $M_{200}=2.13\times
10^{15}\,M_{\odot}$ for the El Gordo mass. The number of analogs then has to
be scaled to account for the fact that the survey volume in which El Gordo was
found is smaller than the simulation box volume. The number $N$ of analogs
which have $M$ and cosmic scale factor $a\equiv 1/\left(1+z\right)$ in a less
likely region of parameter space than El Gordo is then converted into a
probability using Poisson statistics: $P=1-\exp\left(-N\right)$. This
probability is related to the equivalent number of standard deviations for a
normal distribution by the Gaussian equation:
$1-\frac{1}{\sqrt{2\mathrm{\pi}}}\int_{-\chi}^{\chi}\exp\left(-x^{2}/2\right)dx\equiv
P$.

The results are shown in Figure 1, where we have also plotted the level of
tension for El Gordo and the Bullet Cluster combined. This can be
approximately done by adding the square of the El Gordo $\chi$ value
($\chi_{EG}$) to $\chi_{BC}^{2}$, where $\chi_{BC}=2.78$ is based on scaling
the result of Kraljic & Sarkar (2015) to the sky area in which the Bullet
Cluster was discovered (see section 3.4 of Asencio et al., 2021).

Figure 1: The equivalent number of standard deviations for a Gaussian ($\chi$)
against the assumed El Gordo $V_{\textrm{infall}}$ at twice the sum of the
virial radii for the El Gordo survey region (solid red line). For reference,
the logarithmic probability $\log_{10}\left(P\right)$ corresponding to each
$\chi$ is also shown on the right axis. The solid black line shows $\chi$
considering both El Gordo and the Bullet Cluster in their respective survey
regions (with $\chi_{BC}=2.78$). The error bars account for the uncertainty in
the El Gordo mass (Kim et al., 2021). The dotted lines in the same colors
represent more conservative estimates assuming the respective survey regions
cover the whole sky, in which case $\chi_{BC}=1.65$ (Kraljic & Sarkar, 2015).

##  3 Discussion

Figure 1 shows that the infall velocity required to get below $5\sigma$ in the
El Gordo case is $\approx 2300~{}\textrm{km~{}s}^{-1}$. This falls to $\approx
1800~{}\textrm{km~{}s}^{-1}$ when considering both El Gordo and the Bullet
Cluster. In the following, we discuss the implications of these results given
the $V_{\textrm{infall}}$ values obtained in previous studies of El Gordo.

As mentioned in Section 2, the $V_{\textrm{infall}}\approx
450~{}\textrm{km~{}s}^{-1}$ value (Kim et al., 2021) is obtained for those
models in which the collision velocity does not exceed the escape velocity.
When testing for possible scenarios of the El Gordo interaction, there is no
observational reason to assume that the two subclusters are gravitationally
bound, as far as we are concerned. The argument that Kim et al. (2021) provide
to impose a limit to $V_{\textrm{infall}}$ is the “timing argument” (also
invoked by Ng et al., 2015), the idea that structures in the Universe owe
their peculiar velocities to interactions with other structures. Due to
dynamical friction, when massive structures interact with less massive
structures, kinetic energy in bulk motion is transformed into random motions.
The maximum velocity that massive structures are expected to have can be
inferred from cosmological simulations. These show that objects with
$M>10^{15}\,M_{\odot}$ and relative velocity $>3000~{}\textrm{km~{}s}^{-1}$
are very unlikely to arise in the $\Lambda$CDM cosmology (Lee & Komatsu, 2010;
Thompson & Nagamine, 2012). Kim et al. (2021) and Ng et al. (2015) imposed
this upper limit to $V_{\textrm{infall}}$ since the escape velocity of El
Gordo is of the same order as the maximum pairwise velocity found in
$\Lambda$CDM cosmological simulations. This constitutes a circular argument,
so we consider all studies that imposed this condition to be unsuitable for
assessing the likelihood of observing El Gordo in the $\Lambda$CDM cosmology.

A collision velocity larger than the escape velocity can arise if the two
subclusters are infalling on hyperbolic orbits and dynamical friction from the
dark matter halos does not operate to slow down the relative velocity of the
subclusters. It is also possible that the standard description of galaxy
clusters as systems governed by Newtonian gravity and surrounded by a cold
dark matter halo might be incorrect (see section 4.3 of Asencio et al., 2021).
In that case, the infall velocity required to achieve a certain morphology
could be different than in the standard model. Moreover, if the collisionless
component surrounding the clusters was formed by sterile neutrinos (or some
form of hot dark matter), the effect of dynamical friction would be less
significant due to their higher velocity dispersion. Thus, if the $\Lambda$CDM
description of galaxy clusters is incorrect, this could manifest as a
particularly large $V_{\textrm{infall}}$ in $\Lambda$CDM models. Therefore, it
is necessary to account for all $V_{\textrm{infall}}$ values in order to
objectively assess the validity of $\Lambda$CDM with regards to the properties
of the El Gordo cluster.

Moreover, $V_{\textrm{infall}}\approx 450~{}\textrm{km~{}s}^{-1}$ seems rather
unlikely since all the El Gordo studies that used hydrodynamical simulations
have shown that $V_{\textrm{infall}}\gtrsim 2000~{}\textrm{km~{}s}^{-1}$ is
required to reproduce its morphology and/or its strong X-ray emission
(Donnert, 2014; Molnar & Broadhurst, 2015; Zhang et al., 2015). The X-ray
emission in galaxy clusters is generally understood to be caused by thermal
bremsstrahlung from hot gas (Sarazin, 1986). In the case of El Gordo, the fact
that the X-ray morphology presents one single peak (with two faint tails)
strongly suggests that the gas heating was caused by the energetic collision
of the two subclusters and that the passage of one of the subclusters through
the other led to the formation of an X-ray wake (Menanteau et al., 2012). The
hot intracluster medium of each individual subcluster could also have
generated some X-ray emission, but the hydrodynamic simulations show that the
X-ray morphology and luminosity require a strong collision. The fact that the
bolometric X-ray luminosity of El Gordo seems to be correlated with radio
relics $-$ which have no obvious connection with the individual galaxy
clusters $-$ further supports the hypothesis that the X-ray emission of El
Gordo is mainly generated from the interaction of its two subclusters (section
4.4 of Menanteau et al., 2012).

Very low $V_{\textrm{infall}}$ values are also not supported by the observed
peculiar velocity ($\Delta V_{\textrm{pec}}=476\pm
242~{}\textrm{km~{}s}^{-1}$) and inclination angle ($\theta\leq 35^{\circ}$;
Ng et al., 2015) as these imply $V_{\textrm{obs}}=(234/\sin
35^{\circ})~{}\textrm{km~{}s}^{-1}=408~{}\textrm{km~{}s}^{-1}$ in the most
conservative scenario. This means that $V_{\textrm{obs}}$ would already be of
the same order as $V_{\textrm{infall}}\approx 450~{}\textrm{km~{}s}^{-1}$ in
the Kim et al. (2021) model, which is in contradiction with the results of
hydrodynamical simulations as these imply $V_{\textrm{infall}}\approx
1.5\,V_{\textrm{obs}}$ (Molnar & Broadhurst, 2015).

The results of Ng et al. (2015) do not give a clear estimate of
$V_{\textrm{infall}}$ as they consider $V_{\textrm{peri}}$ more relevant for
their study. Still, $V_{\textrm{infall}}\approx 1200~{}\textrm{km~{}s}^{-1}$
can be inferred by comparison with other studies. For this
$V_{\textrm{infall}}$ value, El Gordo would be in $\approx 3.5\sigma$ tension
with $\Lambda$CDM (see Figure 1). However, Kim et al. (2021) identified
several problems with their MCMC analysis, so their nominal results might not
be very reliable. More importantly, Ng et al. (2015) also excluded all models
in which the collision velocity exceeds the escape velocity of El Gordo, which
makes their velocity estimates unsuitable to test $\Lambda$CDM as they
implicitly assume its validity.

The first hydrodynamical simulations of El Gordo (Donnert, 2014) found that
with $V_{\textrm{infall}}=2600~{}\textrm{km~{}s}^{-1}$, the total X-ray
luminosity of El Gordo can be reproduced, but not its two-tailed morphology.
According to our analysis, this infall velocity is incompatible with
$\Lambda$CDM at $>5\sigma$ confidence. Donnert (2014) assumed a mass ratio and
initial distance quite similar to those adopted in our analysis, but they
assumed a somewhat higher mass ($M_{200}=2.71\times 10^{15}\,M_{\odot}$).
Their $V_{\textrm{infall}}$ value is quite consistent with the best-fit
$V_{\textrm{infall}}=2500~{}\textrm{km~{}s}^{-1}$ obtained in the more
detailed simulations of Zhang et al. (2015) for a similar mass
($M_{200}\approx 3\times 10^{15}\,M_{\odot}$). Given that in the Zhang et al.
(2015) simulations the higher-mass Model B ($M_{200}\approx 3\times
10^{15}\,M_{\odot}$) requires a lower infall velocity than the lower-mass
Model A ($M_{200}\approx 2\times 10^{15}\,M_{\odot}$), we find it unlikely
that assuming a higher mass had caused Donnert (2014) to overestimate
$V_{\textrm{infall}}$.

Molnar & Broadhurst (2015) explored a wider parameter space in their
hydrodynamical simulations of El Gordo. They found that for
$V_{\textrm{infall}}=2250~{}\textrm{km~{}s}^{-1}$, they could fairly
accurately reproduce the X-ray morphology, the positions of the X-ray peak and
mass peaks, and the observed relative radial velocity. Still, the mean
temperature and total X-ray luminosity obtained with this model are lower than
observed (Zhang et al., 2015). Molnar & Broadhurst (2015) used a similar mass
and mass ratio to the ones used in our analysis, but they chose a lower
initial separation (4.25 Mpc). At our initial distance (6.06 Mpc) $-$ and
under the assumption of energy conservation $-$ their $V_{\textrm{infall}}$
corresponds to

$\displaystyle V_{\textrm{infall}}~{}$ $\displaystyle=$
$\displaystyle~{}\biggl{[}\left(2250~{}\textrm{km~{}s}^{-1}\right)^{2}$
$\displaystyle+$
$\displaystyle~{}2\,GM\left(\frac{1}{4.25~{}\textrm{Mpc}}-\frac{1}{6.06~{}\textrm{Mpc}}\right)\biggr{]}^{1/2}$
$\displaystyle=$ $\displaystyle~{}2522.29~{}\textrm{km~{}s}^{-1}\,,$ (1)

where $G$ is the gravitational constant and $M=2.15\times 10^{15}\,M_{\odot}$
is the total mass (Molnar & Broadhurst, 2015). This value corresponds to an
$\approx 5.1\sigma$ tension with the $\Lambda$CDM model in our analysis
($\approx 5.5\sigma$ with the Bullet Cluster). This tension is slightly
reduced by considering their other valid models with
$V_{\textrm{infall}}=2000~{}\textrm{km~{}s}^{-1}$ at 4.25 Mpc (2302.05 km s-1
at 6.06 Mpc), but with this velocity it is not possible to reproduce the X-ray
brightness profile of El Gordo as accurately as with
$V_{\textrm{infall}}=2250~{}\textrm{km~{}s}^{-1}$.

Zhang et al. (2015) presented two models of the El Gordo interaction in their
hydrodynamical simulations. We focus on their Model A since this is the one
that most closely resembles the latest observations and the assumptions made
in our analysis. It has an infall velocity of
$V_{\textrm{infall}}=3000~{}\textrm{km~{}s}^{-1}$, which our analysis shows to
be in more than $5\sigma$ tension with $\Lambda$CDM. Even though it still has
some deficiencies (e.g. more asymmetric tidal tail, inclination angle is too
large), this model is the only one so far that manages to reach the high
temperature and luminosity of El Gordo, reproduce its surface brightness
profile and mass density distribution and, to some extent, generate the two-
tailed X-ray morphology, all while assuming a total mass of $\approx 2\times
10^{15}\,M_{\odot}$ and a mass ratio of $\approx 2$, consistent with the
latest weak-lensing results (Kim et al., 2021).

The previous estimates of the El Gordo (or the joint El Gordo $+$ Bullet
Cluster) tension with the $\Lambda$CDM cosmology were obtained accounting for
the area of the survey regions in which El Gordo and the Bullet Cluster were
found. Our more conservative estimates (dotted lines in Figure 1) assume these
survey regions covered the full sky, which would imply that El Gordo (and the
Bullet Cluster) are the only problematic objects for $\Lambda$CDM that have
been observed so far. However, other interacting galaxy clusters with extreme
properties have already been found, including A1758 at $z=0.279$ with two
subclusters of total mass $M_{200}=3.3^{+0.4}_{-0.6}\times 10^{15}\,M_{\odot}$
(Schellenberger et al., 2019) and MACS J1149.5+2223 at $z=0.544$ with three
subclusters of total mass $M_{500}=(1.04\pm 0.05)\times 10^{15}\,M_{\odot}$
(Bruno et al., 2021), Moreover, full-sky surveys such as the Planck survey
have already identified several other clusters with very high masses at
$z>0.3$, including PLCK G214.6+37.0 (composed of three subclusters at
$z\approx 0.47$ with total mass $M_{200}\approx 1.17\times
10^{15}\,M_{\odot}$; Planck Collaboration VIII, 2011) and PLCK G287.0+32.9 (a
quadruple system of clusters at $z=0.39$ with total mass
$M_{200}=2.04^{+0.20}_{-0.21}\times 10^{15}\,M_{\odot}$; Planck Collaboration
VI, 2013).222Note that at $z\approx 0.5$ and $z\approx 0.3$ structures with
$M_{178}\gtrsim 1.7\times 10^{15}\,M_{\odot}$ and $M_{178}\gtrsim 2.1\times
10^{15}\,M_{\odot}$, respectively, are expected to be extremely rare in a
$\Lambda$CDM cosmology (Watson et al., 2014). We therefore consider it
reasonable to scale the number of candidate pairs to the survey volume in our
nominal analysis.

However, we cannot be certain about whether there were any selection effects
involved in the discovery of El Gordo and the Bullet Cluster. An important
issue is whether wider less sensitive surveys had been used to get hints that
extreme galaxy cluster collisions would be found in certain regions of the
sky. If this were the case, the tension obtained in our nominal analysis might
have been overestimated. The maximum impact that this could have on our
results is given by our conservative scenario (dotted lines in Figure 1),
where we obtained the tension at each $V_{\textrm{infall}}$ for the case in
which El Gordo (and the Bullet Cluster) are assumed to be the only objects in
the sky contributing to the tension with $\Lambda$CDM. These results show that
even in this extremely conservative scenario, the tension with $\Lambda$CDM is
still $\approx 4.5\sigma$ for $V_{\textrm{infall}}\approx
2500~{}\textrm{km~{}s}^{-1}$ (Molnar & Broadhurst, 2015; Zhang et al., 2015,
Model B). This increases to $\approx 4.9\sigma$ for
$V_{\textrm{infall}}=3000~{}\textrm{km~{}s}^{-1}$, the infall velocity of
Model A (Zhang et al., 2015).

##  4 Conclusions

For the new weak-lensing mass estimate of El Gordo (Kim et al., 2021) and for
all infall velocities consistent with the hydrodynamical simulations described
in Section 1, El Gordo still falsifies $\Lambda$CDM at close to $5\sigma$.
According to the nominal model of Molnar & Broadhurst (2015), infall
velocities of $\approx 2500~{}\textrm{km~{}s}^{-1}$ are required to reproduce
the morphological properties of El Gordo ($\approx 5.1\sigma$ tension).
$V_{\textrm{infall}}$ needs to be higher in order to reproduce El Gordo’s high
temperature and luminosity: $V_{\textrm{infall}}\approx
2600~{}\textrm{km~{}s}^{-1}$ according to Donnert (2014), which corresponds to
$\approx 5.2\sigma$ tension. The only nominal models that manage to
simultaneously reproduce both its morphology and its high luminosity and
temperature are fiducial Model A and fiducial Model B from Zhang et al.
(2015), with $V_{\textrm{infall}}=3000~{}\textrm{km~{}s}^{-1}$ and
$V_{\textrm{infall}}=2500~{}\textrm{km~{}s}^{-1}$, respectively. Out of these
two models, only Model A has a mass and mass ratio similar to the observed
ones. Its $V_{\textrm{infall}}$ value corresponds to $\approx 5.4\sigma$
tension. The tension with $\Lambda$CDM is even higher ($\approx 5.7\sigma$)
when we take into account the Bullet Cluster as another problematic object for
$\Lambda$CDM. El Gordo and the Bullet Cluster are not the only observed galaxy
clusters whose properties are highly unusual in a $\Lambda$CDM context.
Because of this, we took into consideration the sky area in which El Gordo and
the Bullet Cluster were found when obtaining our previous results. However, it
is possible that the surveys might have already been targeting these
particular objects based on previous wider surveys, which could have enabled
their identification in a smaller survey region. To estimate the maximum
extent to which this could have caused us to overestimate the tension with
$\Lambda$CDM, we obtained the tension assuming the discovery surveys covered
the full sky. We found that even in this very conservative scenario, the
tension between these galaxy cluster collisions and $\Lambda$CDM amounts to
$4.5\sigma-4.9\sigma$. We therefore conclude that El Gordo and the Bullet
Cluster would still pose a significant challenge to $\Lambda$CDM even if
selection effects had an influence on the survey areas in which they were
discovered.

Given the recent more accurate results on El Gordo’s mass and other
properties, we expect that our results will encourage the scientific community
to revisit the hydrodynamical simulations of El Gordo. This will clarify if a
lower $V_{\textrm{infall}}$ compatible with $\Lambda$CDM can be consistent
with the observed properties of El Gordo, or if this massive early collision
does indeed point to a failure of the $\Lambda$CDM model.

## Data availability

The data underlying this article are available in the article.

E.A. is supported by a stipend from the Stellar Populations and Dynamics
Research Group at the University of Bonn. I.B. is supported by Science and
Technology Facilities Council grant ST/V000861/1. P.K. acknowledges support
through the Deutscher Akademischer Austauschdienst-Eastern European Exchange
Programme. The authors would like to thank the referee for comments and
suggestions that have helped to improve this manuscript.

## References

  * Asencio et al. (2021) Asencio, E., Banik, I., & Kroupa, P. 2021, MNRAS, 500, 5249, doi: 10.1093/mnras/staa3441
  * Bruno et al. (2021) Bruno, L., Rajpurohit, K., Brunetti, G., et al. 2021, A&A, 650, A44, doi: 10.1051/0004-6361/202039877
  * Caminha et al. (2023) Caminha, G. B., Grillo, C., Rosati, P., et al. 2023, A&A, in press, arXiv:2209.02718, doi: 10.1051/0004-6361/202244897
  * Diego et al. (2023) Diego, J. M., Meena, A. K., Adams, N. J., et al. 2023, A&A, 672, A3, doi: 10.1051/0004-6361/202245238
  * Donnert (2014) Donnert, J. M. F. 2014, MNRAS, 438, 1971, doi: 10.1093/mnras/stt2291
  * Jee et al. (2014) Jee, M. J., Hughes, J. P., Menanteau, F., et al. 2014, ApJ, 785, 20, doi: 10.1088/0004-637X/785/1/20
  * Katz et al. (2013) Katz, H., McGaugh, S., Teuben, P., & Angus, G. W. 2013, ApJ, 772, 10, doi: 10.1088/0004-637x/772/1/10
  * Kim et al. (2021) Kim, J., Jee, M. J., Hughes, J. P., et al. 2021, ApJ, 923, 101, doi: 10.3847/1538-4357/ac294f
  * Kraljic & Sarkar (2015) Kraljic, D., & Sarkar, S. 2015, JCAP, 2015, 050, doi: 10.1088/1475-7516/2015/04/050
  * Lage & Farrar (2014) Lage, C., & Farrar, G. 2014, ApJ, 787, 144, doi: 10.1088/0004-637X/787/2/144
  * Lee & Komatsu (2010) Lee, J., & Komatsu, E. 2010, ApJ, 718, 60, doi: 10.1088/0004-637X/718/1/60
  * Lindner et al. (2014) Lindner, R. R., Baker, A. J., Hughes, J. P., et al. 2014, ApJ, 786, 49, doi: 10.1088/0004-637X/786/1/49
  * Marriage et al. (2011) Marriage, T. A., Acquaviva, V., Ade, P. A. R., et al. 2011, ApJ, 737, 61, doi: 10.1088/0004-637X/737/2/61
  * Menanteau et al. (2010) Menanteau, F., González, J., Juin, J., et al. 2010, ApJ, 723, 1523, doi: 10.1088/0004-637x/723/2/1523
  * Menanteau et al. (2012) Menanteau, F., Hughes, J. P., Sifón, C., et al. 2012, ApJ, 748, 7, doi: 10.1088/0004-637x/748/1/7
  * Molnar & Broadhurst (2015) Molnar, S. M., & Broadhurst, T. 2015, ApJ, 800, 37, doi: 10.1088/0004-637x/800/1/37
  * Ng et al. (2015) Ng, K. Y., Dawson, W. A., Wittman, D., et al. 2015, MNRAS, 453, 1531, doi: 10.1093/mnras/stv1713
  * Planck Collaboration VI (2013) Planck Collaboration VI. 2013, A&A, 550, A132, doi: 10.1051/0004-6361/201220039
  * Planck Collaboration VIII (2011) Planck Collaboration VIII. 2011, A&A, 536, A8, doi: 10.1051/0004-6361/201116459
  * Sarazin (1986) Sarazin, C. L. 1986, Reviews of Modern Physics, 58, 1, doi: 10.1103/RevModPhys.58.1
  * Schellenberger et al. (2019) Schellenberger, G., David, L., O’Sullivan, E., Vrtilek, J. M., & Haines, C. P. 2019, ApJ, 882, 59, doi: 10.3847/1538-4357/ab35e4
  * Thompson & Nagamine (2012) Thompson, R., & Nagamine, K. 2012, MNRAS, 419, 3560, doi: 10.1111/j.1365-2966.2011.20000.x
  * Watson et al. (2014) Watson, W. A., Iliev, I. T., Diego, J. M., et al. 2014, MNRAS, 437, 3776, doi: 10.1093/mnras/stt2173
  * Zhang et al. (2015) Zhang, C., Yu, Q., & Lu, Y. 2015, ApJ, 813, 129, doi: 10.1088/0004-637x/813/2/129