# UAST: Unicode Aware Saṃskṛta Transliteration

Aneri Dalwadi  0000-0002-1771-1576 Dhruvil Dave  0000-0003-0616-7277

###### Abstract

Devanāgarī is the writing system that is adapted by various languages like
Saṃskṛta. International Alphabet of Sanskrit Transliteration (IAST) is a
transliteration scheme for romanisation of Sanskrit language. IAST makes use
of diacritics to represent various characters. On a computer, these are
represented using Unicode standard which differs from how the Sanskrit
language behaves at a very fundamental level. This results in an issue that is
encountered while designing typesetting software for devanāgarī and IAST. We
hereby discuss the problems and provide a solution that solves the issue of
incompatibilities between various transliteration and encoding schemes.
Implementation available at https://github.com/aneri0x4f/uast-cli and
https://github.com/dhruvildave/uast .

###### Keywords:

Human-Computer Interaction Interaction Techniques Text input

##  1 Handling Unicode Characters in IAST

###  1.1 Pros and Cons of IAST

#####

International Alphabet of Sanskrit Transliteration (IAST) is a popular
transliteration scheme used by Saṃskṛta language for the romanisation of
Devanāgarī script that has seen adaptation amongst scholars.

#####

IAST has many benefits:

  * •

Closely follows the original scripts.

  * •

Unambiguous.

  * •

Intuitive.

  * •

Case-insensitive.

#####

IAST uses various diacritics with letters. When it comes to typesetting
Saṃskṛta with IAST, we have to use non-ASCII Unicode characters which creates
a problem of having to use non-standard key bindings and/or packages to input
those characters. Figuring out those key bindings and setting up IAST input
has been a pain point for scholars and students alike. For example, depending
on the operating system, package, or editor one might be using, ā can be
entered via Ctrl + a, Alt + a, or any other key binding in that case. This
hugely hinders portability.

###  1.2 UAST-IO syntax for handling Unicode

#####

We suggest a new syntax, UAST-IO, for representing the characters that use
diacritics that are used in IAST:

  * •

Any non-ASCII character should be entered between /x/ as per Table 1 where x
should be replaced with ASCII replacement for the corresponding Unicode
character. We use SOLIDUS (U+002F), also known as forward slash.

  * •

All other ASCII characters should be entered as-is.

Table 1: Unicode diacritic to ASCII mapping Unicode Name | Code Point | ASCII replacement
---|---|---
LATIN SMALL LETTER A WITH MACRON | 0101 | a
LATIN SMALL LETTER A WITH TILDE | 00E3 | au
LATIN SMALL LETTER I WITH MACRON | 012B | i
LATIN SMALL LETTER U WITH MACRON | 016B | u
LATIN SMALL LETTER R WITH DOT BELOW | 1E5B | r
LATIN SMALL LETTER R WITH DOT BELOW AND MACRON | 1E5D | ru
LATIN SMALL LETTER L WITH DOT BELOW | 1E37 | l
LATIN SMALL LETTER L WITH DOT BELOW AND MACRON | 1E39 | lu
LATIN SMALL LETTER L WITH LINE BELOW | 1E3B | ll
LATIN SMALL LETTER T WITH DOT BELOW | 1E6D | t
LATIN SMALL LETTER D WITH DOT BELOW | 1E0D | d
LATIN SMALL LETTER N WITH TILDE | 00F1 | n
LATIN SMALL LETTER N WITH DOT ABOVE | 1E45 | nu
LATIN SMALL LETTER N WITH DOT BELOW | 1E47 | nl
LATIN SMALL LETTER S WITH ACUTE | 015B | su
LATIN SMALL LETTER S WITH DOT BELOW | 1E63 | sl
LATIN SMALL LETTER M WITH DOT BELOW | 1E43 | m
LATIN SMALL LETTER H WITH DOT BELOW | 1E25 | h

Table 1 values have been derived as follows:

  * •

If a diacritic appears above of a character, the character is appended with a
u where u stands for "upper". If a diacritic appears below of a character, the
character is appended with a l where l stands for "lower".

    * –

LATIN SMALL LETTER S WITH ACUTE becomes su.

    * –

LATIN SMALL LETTER N WITH DOT ABOVE becomes nu.

    * –

LATIN SMALL LETTER S WITH DOT BELOW becomes sl.

    * –

LATIN SMALL LETTER N WITH DOT BELOW becomes nl.

  * •

For characters that only have a single diacritic, we mention the character
directly as it is unambiguous by default.

    * –

LATIN SMALL LETTER I WITH MACRON becomes i.

    * –

LATIN SMALL LETTER U WITH MACRON becomes u.

    * –

LATIN SMALL LETTER D WITH DOT BELOW becomes d.

    * –

LATIN SMALL LETTER T WITH DOT BELOW t.

    * –

LATIN SMALL LETTER M WITH DOT BELOW m.

    * –

LATIN SMALL LETTER H WITH DOT BELOW becomes h.

  * •

For diacritics with a clash, frequency of usage guides selection of
replacement. The higher the frequency, the lower the length of replacement.

    * –

LATIN SMALL LETTER A WITH MACRON becomes a and LATIN SMALL LETTER A WITH TILDE
becomes au.

    * –

LATIN SMALL LETTER R WITH DOT BELOW becomes r and LATIN SMALL LETTER R WITH
DOT BELOW AND MACRON becomes ru.

    * –

LATIN SMALL LETTER L WITH DOT BELOW becomes l, LATIN SMALL LETTER L WITH DOT
BELOW AND MACRON becomes lu, and LATIN SMALL LETTER L WITH LINE BELOW becomes
ll.

  * •

Remaining diacritics are mapped to simplest possible representations that are
closest to its IAST counterparts.

    * –

LATIN SMALL LETTER N WITH TILDE becomes n.

#####

This mapping is intended for replacement of non-ASCII characters only. Thus,
ḍha should be written as /d/ha and not /dh/a as only the former would be a
correct mapping while latter would be an invalid case as there is no mapping
defined for dh but only d.

#####

The benefits that arise from doing this is that now we have a standard way of
representing unicode glyphs without having to worry about keyboard layouts and
key bindings.

#####

There are two main reasons why we use a new syntax, as inspired by LaTeX, and
not resort to other techniques that are adopted by other schemes and
encodings.

  * •

Using a mix of lowercase and uppercase would make the scripting and
typesetting case-sensitive which tends to be error-prone, harm readability,
and involve lot of extra invisible key-pressing in form of Shift or Caps Lock.
Our system makes typing those extra characters completely explicit and remove
the problem of case-sensitivity altogether.

  * •

The only new character which gets introduced is SOLIDUS (U+002F) which would
explicitly demark the character boundary. Adding other non-alphanumeric
characters like AMPERSAND (U+0027) or FULL STOP (U+002E). A suitable
competitor to forward slash would be LOW LINE (U+005F) but it would involve
pressing Shift key. We could equivalently use HYPHEN-MINUS (U+002D) but we
reserve it for a special purpose that we present in the next section.

#####

Here are a few examples to exemplify the above principles:

Table 2: Bhagavadgītā 15.15 (UAST-IO) IAST | UAST-IO
---|---
sarvasya cāhaṃ hṛdi saṃniviṣṭo | sarvasya c/a/ha/m/ h/r/di sa/m/nivi/sl//t/o
mattaḥ smṛtirjñānamapohanaṃ ca | matta/h/ sm/r/tirj/n//a/namapohana/m/ ca
vedaiśca sarvairaham eva vedyo | vedai/su/ca sarvairaham eva vedyo
vedāntakṛdvedavideva cāham | ved/a/ntak/r/dvedavideva c/a/ham
Table 3: A comparison of various transliteration schemes or encodings for Saṃskṛta. IAST | rāmaḥ | kṛṣṇaḥ | prajñā
---|---|---|---
Harvard-Kyoto | rAmaH | kRSNaH | prajJA
SLP1 | rAmaH | kfzRaH | prajYA
Velthuis | raama.h | k.r.s.na.h | praj$\sim$naa
ITRANS | rAmaH | kRRiShNaH | praj$\sim$nA
UAST-IO | r/a/ma/h/ | k/r//sl//nl/a/h/ | praj/n//a/

##  2 Devanāgarī and Unicode

###  2.1 Problems with existing systems

#####

The previous section handled the problem of handling input of Unicode
characters when using IAST. The situation doesn’t improve when we move from
IAST to devanāgarī. We have the same problems mentioned earlier.

#####

We already have many systems that make use of ASCII characters to input
devanāgarī script. A very popular system is Harvard-Kyoto convention. It uses
a mix of lowercase and uppercase ASCII characters. In this case, rāma in IAST
would become rAma in Harvard-Kyoto.

#####

The comparison of various systems is best done by formalising the requirements
for a good typesetting system:

  * •

Case-insensitive.

  * •

Uses only ASCII characters.

  * •

Does not involve invisible key-pressing like Shift or Caps Lock.

  * •

Follow IAST.

  * •

The character entered should be intuitive and follow the language
pronunciation.

#####

All the other encodings fall short in atleast one of the criterias. But the
problems amplify.

###  2.2 Unicode Aware Saṃskṛta Transliteration

#####

We can use the UAST-IO (Section 1.2) syntax and extend it further. We suggest
the following system for typesetting devanāgarī:

  * •

The typesetting should follow IAST.

  * •

Any unicode diacritics to be entered in IAST should follow the system
presented in Section 1.2 and all ASCII characters should simply be entered as-
is.

  * •

Put an explicit HYPHEN-MINUS (U+002D) to represent a halanta (U+094D). Thus,
unlike IAST, k would become k- to signify a lack of inherent vowel.

  * •

a after a consonant is redundant but supported. So, kamala and kml would both
mean the same.

  * •

To place an explicit vowel instead of a vowel sign, follow it with a REVERSE
SOLIDUS (U+005C). It is also used to explicitly mark character boundary. dh
would be parsed as dha. To treat them individually, place a like dah which
would be parsed as daha.

  * •

The typesetting should be case-insensitive. Thus, both p and P should be
treated in the same way.

#####

We call this the Unicode Aware Saṃskṛta Transliteration (UAST) system. Any
system which implements UAST will be able to unambiguously transpile it to
IAST and devanāgarī using an algorithm with linear space and time complexity.
The primary purpose of UAST is to bridge the gap between how typesetting of
IAST and devanāgarī is done.

#####

The following benefits arise from using UAST:

  * •

It is case-insensitive.

  * •

All the key-presses are explicit. There are no use of keys like Shift or Caps
Lock.

  * •

The only non-alphanumeric characters are SOLIDUS, REVERSE SOLIDUS, and FULL
STOP.

  * •

It is highly intuitive as it does not deviate from IAST and follows character
sounds.

###  2.3 Design Decisions

There are a few decisions that were involved and inspired the design of UAST.

####  2.3.1 Following IAST

The main problem with certain encodings and keyboard-layouts is that they map
many devanāgarī characters to key-bindings that are non-intuitive. They
distance themselves from IAST. IAST is widely used for many reasons:

  * •

Its mapping is unambiguous and exact.

  * •

Related sounds have related mappings. This makes IAST a very logical and
intuitive mapping to use. As a result, IAST bridges the gap between Saṃskṛta
and English phonetics.

  * •

Follows original script as-is.

#####

This makes it arguably the most popular transliteration scheme used by
scholars and students alike. Since IAST so closely follows the language, it
would make sense that the devanāgarī typesetting also follow IAST to prevent
confusion and remove ambiguity. We believe that a person trying to learn or
use a language and interact with it via a typesetting system should be more
concerned with "what to write" rather than "how to write".

#####

The more an encoding or transliteration system distances itself from IAST, the
less intuitive it becomes. Other systems work well in isolation but only add
to more confusion when it comes to dealing with them alongside IAST.

####  2.3.2 Avoiding mix of lowercase and uppercase characters

There are major disadvantages involved with the use of both lowercase and
uppercase characters. The first is slowing down of reading and writing speeds
([1]). Consider the following example. pitā in IAST would be written as pitA
in Harvard-Kyoto and pit/a/ in UAST. The first three characters stay the same
in both. The difference occurs at the end. Ignoring any user-specific or
system-specific changes, there are two possible sequences to enter A after t:

  * •

Shift + a

  * •

Caps Lock, a, Caps Lock

The former involves two key-presses while the latter does three. Thus, to
write pitA, we would have to do 5 or 6 key-presses. For writing pit/a/, there
is no uppercase involved. Thus it would be completed in 6 key-presses. So at
the cost of additional key-presses, we end up with two major benefits:

  * •

All the key-presses are now explicit. Infact, since we are now using all
lowercase characters on a standard ASCII keyboard, number of key-presses =
length of string. So a user writes what a user sees. The errors arising due to
that are no longer a problem.

  * •

The problem of case-sensitivity is completely eliminated. In conventions like
Harvard-Kyoto, change a character to lowercase even by mistake would incur
significant penalty on accuracy and precision of transliteration.

####  2.3.3 Avoiding use of non-ASCII Unicode diacritics

The main problem involved with IAST is entering non-ASCII Unicode diacritics.
There are a lot of problems as discussed in Section 1.1 involved with entering
non-ASCII Unicode diacritics as used in IAST. It might involve finding a
specific package or even manually setting up key-bindings. This brings up a
problem of portability. There is no standard syntax for devanāgarī or even
IAST in case of absence of unicode diacritics on keyboard. In UAST, we address
that problem by the solutions suggested in Section 1.1.

###  2.4 Explicit halanta and Choice of character set

#####

Saṃskṛta language and computers have a difference that is very fundamental to
the entire problem of encoding, transliteration, and typesetting.

#####

saṃskṛta language is written using IAST or devanāgarī script. Computers use
Unicode encoding. In saṃskṛta, the consonants are inherently without a vowel
and vowels including a are added later on. But this is not the case in
Unicode. There is a very subtle but very important distinction. In Unicode
Standards, consonants are inherently with an a and halanta is added later on
to signify the absence of any vowel. Refer Fig. 1

Figure 1: Comparing pūrvī for language vs computer.

#####

This means that Unicode [2] is fundamentally incompatible with how the
language and IAST function. There is no explicit representation of the halanta
in IAST as it is not needed after all. But then parsing IAST and converting it
to devanāgarī means we have to look for those additional and missing a. For
example, on pressing k, IAST assumes that IAST equivalent of k is entered but
Unicode assumes that IAST equivalent of ka is entered. Now a person using IAST
will press an a. At this point, for the user, IAST equivalent of ka should
have been entered. But what one really ends up with is IAST equivalent of kaa.
This occurs frequently with every consonant that IAST has to fight with
Unicode for removal of that extra a to make things work as per standards. This
addition and removal of characters makes it completely unintuitive to use IAST
directly while typesetting devanāgarī. This is a problem because at this
point, we are directly working with unicode glyphs of devanāgarī rather than a
romanised representation. It won’t be a problem if IAST or even devanāgarī
were to function in isolation. Things get more confusing when going to both of
IAST and devanāgarī as various encodings add new characters that aren’t a part
of IAST which leads to unintuitive key-bindings in devanāgarī.

#####

To resolve this issue, UAST prefers the use of an explicit halanta to bridge
this very gap between devanāgarī/IAST and Unicode. Since IAST is already the
standard to work with, the entire character set of UAST is same as that of
IAST with added - for a halanta as it very much resembles a dash. So under
UAST, when k is entered, IAST equivalent of ka will be entered to take Unicode
into consideration more closely and be in center of the spectrum between the
two. This makes a redundant. This little detail can be very easily parsed and
it now comes with an added benefit that since the inherent vowel is now
explicit, we can easily use UAST to directly parse it into devanāgarī directly
and to IAST with very little to no modification. UAST uses no diacritics and
hence there is no problem of either of missing characters, non-standard key-
bindings, or case-sensitivity.

#####

This makes UAST the single typesetting system and solving multiple encoding
problems for representing Sanskrit in computers by mixing the good parts of
both IAST and Unicode while being intuitive, fast, and easy to learn, use, and
remember at the same time.

## References

  * [1] Babayigit, Özgür. 2019. "The Reading Speed of Elementary School Students on the All Text Written with Capital and Lowercase Letters." Universal Journal of Educational Research 7 (2): 371-80.
  * [2] Unicode Consortium. 2021. "Unicode - The World Standard for Text and Emoji." Unicode. https://home.unicode.org/.


# Deliquescence probability map of Mars and key limiting factors using GCM
model calculations

Bernadett D. Pál  Research Centre for Astronomy and Earth Sciences, Konkoly
Thege Miklos Astronomical Institute, ELKH, Budapest, Hungary  Eötvös Loránd
University, Budapest, Hungary<EMAIL_ADDRESS>Ákos Kereszturi

###### Abstract

There may be a chance of small-scale ephemeral liquid water formation on
present day Mars, even though the current climate does not support the
existence of larger bodies of water. Through a process called deliquescence,
hygroscopic salts can enter solution by absorbing water vapor directly from
the atmosphere. Due to the absence of in-situ deliquescence experiments so
far, the most reliable way to forecast deliquescence is through atmospherical
modeling, however, the locations and times when salty liquid water could
emerge are not yet well known. In this paper we present our results of likely
brine formation on Mars, their proposed locations and seasons, as well as the
possible limiting factors. For our calculations we used the data of
Laboratoire de Météorologie Dynamique Mars General Circulation Model version
5. The results show that from Ls 35∘ \- Ls 160∘, between 9 PM and 11 PM there
is a good chance for calcium perchlorate deliquescence above 30∘ N, while in
this zone the ideal regions are concentrated mostly to Acidalia Planitia and
Utopia Planitia between 1 AM and 3 AM. We found that in the Southern
Hemisphere, between Ls 195∘ and Ls 320∘, there is a noticeable, but weaker
band in the vicinity of 60∘ S, and both Argyre Planitia and Hellas Planitia
show some chance for brine formation. According to our statistics the key
limiting factor of deliquescence could be relative humidity in most cases. Our
results suggest that during summer – early fall seasons, there could be
deliquescence in both hemispheres in specific areas from the late evening
until the early morning hours. There are only few studies detailing the
geological and temporal distribution of brine formation through deliquescence,
thus this work could be used as a good guide for future landing site analysis
or in choosing a specific location for further research.

###### keywords:

deliquescence , Mars , near-surface relative humidity , general circulation
model , liquid water

††journal: Icarus

##  1 Introduction

Liquid water is one of the key elements in the search for extraterrestrial
life. In the last decades Mars has been a primary target in finding signs of
extant or ancient life. As we set our eyes on future crewed Mars explorations,
the pursuit of liquid water is ever growing. However, the present martian
conditions are not favourable for large scale pure liquid water formation on
its surface (Haberle et al., 2001); most of the studies favor the ephemeral
emergence (e.g. Brass, 1980, Knauth and Burt, 2002, Mellon et al., 2000,
Kereszturi et al., 2009, Kossacki and Markiewicz, 2004, McEwen et al., 2014,
Szynkiewicz et al., 2009), but there are theoretical works suggesting a longer
presence (e.g. Clow, 1987, Hecht, 2002). The transient formation of salty
brines is a likely candidate for water formation, as perchlorate salts have
been identified by multiple martian rovers (Hecht et al., 2009b, Navarro-
González et al., 2010, A. et al., 2013, Ming et al., 2014). Perchlorates are
hygroscopic, meaning that they are able to form an aqueous solution if the
temperature and relative humidity is appropriate through a process called
deliquescence (Gough et al., 2011, 2014, Fischer et al., 2014, Nuding et al.,
2014, Zorzano et al., 2009). This process will be tested in-situ on board the
ExoMars Rosalind Franklin rover (BOTTLE experiment (Martín-Torres et al.,
2020)). One of the major topics investigated in this field is the habitability
of brines, in which the most recent findings suggest a reason for optimism
(E.G. et al., 2020, Hallsworth, 2020).

Perchlorates, including calcium perchlorate (Ca(ClO4)2) are abundant in the
Martian top regolith (Hanley et al., 2012), and might be a widespread
component of the Martian soil, with 0.5-1% concentration (Hecht et al.,
2009a). This was identified by the Wet Chemistry Laboratory instrument onboard
Phoenix mission Toner et al. (2015), and later detected by the SAM instrument
onboard Curiosity rover (Navarro-Gonzalez et al., 2013, Glavin et al., 2013).
In the 1970’s, it is proposed to have been detected by the Viking landers as
well, and might be relevant to the field of astrobiology (Wadsworth and
Cockell, 2017). Based on Earth based simulations and calculations, calcium
perchlorate could contribute to daily hydration cycles and thus being
influenced by the deliquescence process (Gough et al., 2019).

Regarding the occurrence of calcium and magnesium perchlorate (Mg(ClO4)2) on
Mars, the recent detections in the loose top regolith suggests a global
occurrence, that is expected by wind mixing. Evaluating the formation
conditions, calcium perchlorate might be produced by UV irradiance under
Martian conditions with olivine minerals (Escamilla-Roa et al., 2020), while
atmospheric origin is also proposed (Catling et al., 2010) – both models
favour nearly global formation. If this salt have been produced by
evaporation, it might show specific surface occurrence, however since there
are no such observations the best current estimation is to consider a globally
homogeneous presence with moderately small concentration (below 1%). As a
result our global spatial and temporal maps based distribution is a realistic
approach using the present knowledge.

Our research focuses on the possibility of global-scale calcium perchlorate
and magnesium perchlorate deliquescence. To our knowledge, there is only one
study that attempted to study this phenomenon at this extent, published
recently (E.G. et al., 2020), using a different martian climate model.
Therefore our proposing of another calculation method is beneficial to get a
more complete picture of global deliquescence. The ultimate goal is to produce
a map of possible thin liquid briny layer formation, that can be used as a
guide in finding interesting locations, daily and seasonal periods for
deliquescence studies, or in planning future Mars missions targeting liquid
water.

To tackle this problem, we used an accomplished martian circulation model to
simulate the annual variations of deliquescence likelihood on present Mars. We
calculated the necessary environmental factors (relative humidity,
temperature) for salt deliquescence and analyzed the global and annual
characteristics. To demonstrate our results and find tendencies in brine
emergence, we created zonally averaged and annual average global maps, as well
as animations to show the day-to-day variations in detail (included as online
supporting material). This paper summarizes our findings regarding magnesium
perchlorate and calcium perchlorate deliquescence during the martian year 29.

##  2 Methods

We calculated the relative humidity using surface temperature, atmospheric
pressure and water vapor volume mixing ratio data from the model Laboratoire
de Météorologie Dynamique Mars General Circulation Model (LMDZ GCM) version 5.
This Mars climate model is detailed in Hourdin et al. (2006), the second
generation of the model described in the works of Sadourny and Laval (1984)
and Forget et al. (1999). The grid values were $64\times 48\times 49$ in
longitude, latitude, altitude respectively. For Mars, this $64\times 48$
horizontal grid corresponds to grid boxes of the order of $330\times 220$
kilometers near the equator. The first layer of the altitude describes the
first few meters above the ground. The data were simulated for the Mars year
29, which was a year without a global dust storm. For the simulation of this
year, the model was set to the ,,climatology" dust scenario, which is built by
averaging the krigged MY24-MY31 dust scenarios (excluding data from MY25 and
MY28 global dust storms). For further details of the input files, please reach
out to the authors. To derive the relative humidity with respect to ice and
with respect to liquid, we calculated the saturation water vapor volume mixing
ratio with an equation (used in the Martian Climate Database) based on the
Goff-Gratch equation (Goff and Gratch, 1946, List, 1984). For the detailed
calculations please refer to the methods section of Pál and Ákos Kereszturi
(2020).

As the main local times of interest, we chose the late afternoon – morning
hours, from 5 PM to 7 AM, because during the day, with the rising surface
temperatures, the relative humidity decreases to an almost zero level. Based
on our earlier results (Pál and Kereszturi, 2017) we chose to focus on the
local times with a possible chance for deliquescence, and excluded those from
this manuscript, that showed little to no chance in our selected time range.
Finding ideal times is a difficult task, because relative humidity levels tend
to increase during the night, when the temperatures are usually too low for
deliquescence, and decrease during the day, when the temperatures are high
enough Pál and Kereszturi (2017). In the late night and early morning hours,
we see ideal time windows ranging from tens of minutes to a few hours at a
time, thus these seem to be the best times to search for the emergence of
liquid water.

We have analysed the chance for liquefaction of calcium perchlorate (Toner et
al., 2014) and magnesium perchlorate (Möhlmann and Thomsen, 2011) by
estimating the possibility of deliquescence on a binary scale (0 = no chance,
1 = definite chance). According to the research of Rivera-Valentín et al.
(2018) if the relative humidity with respect to ice greatly exceeds 1,
nucleation is favored rather than brine formation. Thus a certain time and
place was determined ideal if both the temperature and the relative humidity
with respect to liquid were above the necessary values, while at the same time
the relative humidity with respect to ice stayed below 150%.

Salt | Eutectic temperature | Water activity
---|---|---
Ca(ClO4)2 | 199 K | 0.51
Mg(ClO4)2 | 212 K | 0.53
Table 1: Parameters of the examined hygroscopic salts and water activity of
the eutectic solution.

We calculated the relative humidity from GCM data and determined whether the
necessary circumstances for deliquescence (see Table 1.) were present at a
certain time and location. Since the model output is for 2 hour intervals, we
calculated for every 2 hours between 5 PM – 7 AM. We converted the results to
NetCDF files, and used Panoply to visualize the data creating georeferenced
maps at different local times and martian sols. For easier interpretation of
our results we show zonal (Subsection 3.1) and annual averages (Subsection
3.3), as well as animations in the online supporting materials.

##  3 Results

The zonally averaged region with the greatest extent and highest average
deliquescence probability, thus suggesting the best chance for deliquescence
in the northern hemisphere, appears to be around 11 PM; while the best chance
in the southern hemisphere is suggested to be around 1 AM. To determine the
ideal time periods and locations, we used the GCM to model the Mars year 29
and calculated the probabilities on the binary scale described in Section 2.
We show latitudinal zonal averages in Subsection 3.1. to highlight seasonal
trends, while to illustrate the typical regions we show binary snapshots in
Subsection 3.3. To support the interpretation of the results, we investigate
the annual climate of the polar regions in Subsection 3.2, and highlight two
of the most interesting seasons of the year, Ls 90

∘

and Ls 270

∘

(Ls being the solar longitude) with global meteorological maps in Subsection
3.4. From the statistics of our results we focus on the likely limiting
factors of deliquescence in 3.5. Animations and figures excluded from this
manuscript are included in the online version as supporting materials.

###  3.1 Ideal seasons in a year - zonal averages

In this subsection we show the most typical zonal average maps (average of
given latitudinal bands) of deliquescence probability. During daytime the
relative humidity is usually too low for deliquescence, resulting in scarce
areas of possible liquid layer formation. The main point of the zonal averaged
maps is to highlight how the martian seasons affect the chance for
deliquescence, in different latitudes, throughout a year at a given local
nighttime daily period. For the detailed, day-to-day latitude-longitude
results we refer the reader to the animations in the online supporting
materials. These longitudinally averaged maps highlight the seasons and
latitudes, when there could be a chance for deliquescence, and do not depict
specific geological locations. The notable moments are displayed on the maps:
spring equinox (SE), summer solstice (SS), autumn equinox (AE) and winter
solstice (WS), all with regards to the northern hemisphere.

Figure 1: Zonal averages of calcium-perchlorate deliquescence probability at
11 PM local time during Mars year 29. Calculations are from LMDZ GCM, where 1
means definite chance and 0 means no chance.

The Northern mid and higher latitudes (20∘ and up) show a good chance of
deliquescence during the northern late spring and summer to early autumn (Ls
$\approx$ 80 - 140

∘

). In Figure 1. we can see the zonal averages of binary deliquescence
possibilities during the Martian year 29 at 11 PM local time. The prominent
area in the northern hemisphere is the “teardrop" shaped zone between
approximately sol 40 - 360. The saturation above 75∘N is most likely
influenced by the perennial H2O icecap layer. The upper arch of the northern
area starting from sol 67 is in agreement with the seasonal sublimation of the
CO2 ice cap, exposing the H2O ice underneath during the retreat of seasonal
CO2 ice cap. The higher temperatures and higher local atmospheric water vapor
lead to a good chance for deliquescence, according to the model. As the year
progresses, from sol 200, we see a steady expansion towards the southern
hemisphere. The thin “line" remains the sole feature from sol 360 until the
end of the year, steadily shifting towards south until sol 600. At the end of
the year, the candidate latitudes for deliquescence seem to shift back towards
the equator.

Figure 2: Zonal averages of calcium-perchlorate deliquescence probability at 1
AM local time during Mars year 29. Calculations are from LMDZ GCM, where 1
means definite chance and 0 means no chance.

The chance for deliquescence in the southern hemisphere peaks at 1 AM (Figure
2., compared to all the other local times shown in the online supporting
materials), though the areal extent is still significantly smaller than in the
northern counterpart. There is a rather thin line starting from around sol
400, branching out into an intrigue shape as the year progresses. Just as in
the northern case, the edge of the potentially ideal region is in good
agreement with the receding polar CO2 ice cap. As the CO2 ice sublimes, the
now exposed H2O ice heats up and sublimes quickly, opening a very brief window
of warm temperatures and higher local water vapor levels.

Figure 3: Zonal averages of magnesium-perchlorate deliquescence probability at
1 AM local time during Mars year 29. Calculations are from LMDZ GCM, where 1
means definite chance and 0 means no chance.

The magnesium perchlorate shows little chance for deliquescence throughout the
Martian year 29 compared with calcium perchlorate. The visible area in Figure
3 is limited between sol 135 - 270 and is confined to the polar regions, where
the perennial water ice may be influencing the calculations. There is a barely
visible scatter between sol 490 - 540 near the southern polar region, however
the rest of the latitudes remain empty. This 1 AM data is the best chance we
have seen in our magnesium perchlorate results.

Figure 4: Zonal averages of water vapor volume mixing ratio and surface
temperature at 11 PM local time during Mars year 29.

The annual "wave-like" tendency seen in the zonally averaged deliquescence
maps (Figure 1, 2.) is clearly observable in the atmospheric water vapor and
surface temperature figures (Figure 4) too. The regions with higher water
vapor and higher temperatures are the ones that show up potentially ideal in
the deliquescence maps, as expected.

###  3.2 Annual climate at the Polar regions

We have seen in the previous results, that the edges of the zonally averaged,
potentially ideal regions follow the receding CO2 ice caps in both
hemispheres. However, while in the north, the likely ideal periods span right
up to the poles, in the south, the shape stops around 75∘S. To better
understand this, we examine the annual climate of the higher polar regions
below.

Figure 5: Annual variation of the surface temperatures (left) and the water
vapor volume mixing ratio (right) at the northern (blue) and southern (red)
polar regions during the martian year 29.

First we examine the annual temperature and water vapor variability, to figure
out, why the northern polar region shows a chance for deliquescence, while the
southern does not. In Figure 5. we see the annual surface temperature curves
at 85∘ S and 85∘ N with red and blue colors respectively. The length of the
northern and southern summers do not differ as much as to explain the
difference in deliquescence. In the northern polar region the maximum
temperatures reach up to 223 K, while these remain lower, around 210 K in the
southern hemisphere; however, both go above the minimum eutectic temperature
of calcium perchlorate.

The average annual water vapor volume mixing ratio maximum is lower in the
southern hemisphere, reaching only about 33% of the average northern maximum.
From this graph it seems, that during the local summer, the northern polar cap
evaporates stronger, thus the amount of water vapor in the near-surface
atmosphere is also higher. This combined with the high enough temperatures
could lead to better chances for deliquescence in the northern polar region.

Another main difference between the northern and southern seasonal ice caps is
their composition. The measurements of the OMEGA imaging spectrometer
confirmed that during the recession state, the southern seasonal polar ice cap
is mainly composed of CO2 ice (Langevin et al., 2007). There are only a few
specific locations, where surface H2O ice is present between around 220

∘

and 250

∘

Ls. In agreement with this, the occasional deliquescence chance close to the
southern pole is visible in the animations, but not enough to show up in the
averaged maps. The seasonal northern polar cap however contains both CO2 and
H2O ices (Schmitt et al., 2006). During the local summer and the recession of
the polar caps it is thus expected, that the northern polar regions would show
a higher chance of deliquescence.

###  3.3 Ideal geological regions - annual probability

In this subsection we show global annual averages of the deliquescence
probabilities for Mars year 29 to highlight the potentially interesting
geological regions. The maps shown in this section are not averaged
longitudinally anymore, instead we averaged the results of the whole martian
year 29. Please note, that the average chance for deliquescence ranges from 0
to 0.3 instead of 0 to 1 for better visibility. For the detailed day-to-day
data before averaging, as well as for other local times, we refer the reader
to supplementary animations and figures in the online version.

Figure 6: Annual averages of calcium-perchlorate deliquescence at 9 PM (left)
and 1 AM (right). Data is from LMDZ GCM for Mars year 29. On the scale 0 means
no chance and 1 would mean definite chance.

At 9 PM the latitudes above 30∘ N present the overall best chance for
deliquescence throughout the Martian year 29, as seen in Figure 6. (left).
Here we chose to include the 9 PM local time map instead of the 11 PM (online
supporting material), because the contrast between 9 PM and 1 AM is more
apparent. In Acidalia Planitia, around 15∘ W there is a region with elevated
chance of deliquescence, which stretches down nearly to the equator. Utopia
Planitia also strikes out as a good place for deliquescence at this time. We
can see fainter regions southeast of Isidis Basin, at the equator between 105
- 135∘ E and in Hellas Planitia. Around 1 AM the northern upper latitudes show
much concentrated possible deliquescence regions in Acidalia Planitia and
Utopia Planitia. The somewhat continuous band between 45∘ \- 75∘ N is barely
visible, however, the southern band around 60∘ S is brighter. Hellas Planitia
and Argyre Planitia both show a slight chance of deliquescence (this is a bit
hard to see, we advise the reader to see the online supporting animations).

Figure 7: Annual average of magnesium perchlorate deliquescence at 11 PM. Data
is from LMDZ GCM for Mars year 29. On the scale 0 means no chance and 1 would
mean definite chance. Please note, that the scale is different from the rest
to better visualize the small chance of deliquescence.

There is very little chance for magnesium-perchlorate deliquescence according
to our calculations. If we look at Figure 7. we can see, that there are barely
any regions visible outside of the vicinity of the northern polar cap, above
75∘ N. Please note, that unlike the previous figures, the scale here ranges
only from 0 to 0.1 in order to make the area between 75∘ W to 30∘ W, 60∘ N -
75∘ N visible. That zone in the northern parts of Acidalia Planitia show the
only possible chance for deliquescence throughout the year. We chose 11 PM to
show as the annual average, because this showed the overall best chance in our
results. There are some spots below 60∘ S, but they form no continuous band,
nor do they show a significant possibility.

###  3.4 Global climate modelling results

Looking at the zonally averaged maps Ls 90∘ and Ls 270∘, 1 AM local time seem
to be two of the best times for deliquescence in the northern and southern
hemispheres respectively. In Section 3.3. we have shown the annual averaged
maps, detailing the global regions with the best chance for deliquescence. In
this subsection we included global meteorological maps for Ls 90∘ and Ls 270∘,
to aid the interpretation of our deliquescence probability results.

Figure 8: The global water vapor volume mixing ratio (left) and surface
temperature (right) at Ls 90∘ ($\approx$ sol 195) 1 AM local time for Mars
year 29.

With regard to seasons, in Figure 2. Ls 90∘ ($\approx$ sol 195) is an
interesting point with the deliquescence chance reaching down almost to the
equator, while the polar regions are not yet saturated. With regard to
location, in the 1 AM annual average figures (Fig. 6., right) Acidalia
Planitia, Utopia Planitia and the region around Isidis Basin strike out as the
regions with the highest average deliquescence chance. At Ls 90∘ both the
water vapor ratio and the surface temperature is high enough at these regions
(Fig. 8.). In the left figure we can see, that the water vapor content is
similarly high around 60∘ N, however if we take the surface temperature (right
side) into consideration, the regions with higher deliquescence chance have
approximately 15-20 K higher temperatures at 1 AM.

Figure 9: The global water vapor volume mixing ratio (left) and surface
temperature (right) at Ls 270∘ ($\approx$ sol 515) 1 AM local time for Mars
year 29.

The case of Ls 270∘ ($\approx$ sol 515) is similar to Ls 90∘. In the zonal
average maps (Fig. 2.) this season shows the best chance for deliquescence in
the southern hemisphere. In the annual average maps (Fig. 6.) the southern
hemisphere seems to show a significantly lower chance overall, than the
northern hemisphere. Still, three regions strike out as possibly ideal
locations: Argyre Basin, Hellas Basin, and the somewhat continuous band around
60∘ S. In the Ls 270∘ snapshots, shown in Figure 9., we can see that almost
the entire southern hemisphere shows elevated water vapor levels. Please note,
that the water vapor range is smaller, than in the northern hemisphere to be
able to visualize finer details. The atmosphere above Argyre Basin shows
higher water vapor content, than the northern parts of Hellas Basin. Both of
these regions have elevated temperatures, compared with their surroundings.
While the water vapor content is similar, the temperatures differ in the 60∘ S
band; but still seem to stay just above the eutectic temperature threshold of
calcium perchlorate.

###  3.5 Main limiting factors of deliquescence

In this subsection we consider the cases, when all the necessary circumstances
for deliquescence were met except for one. Summing these instances up and
taking a look at the statistics, we can get a clearer picture of the limiting
circumstances according to local time and location (Fig. 10 and 11). We
calculated the percentages with respect to every single location between 80∘N
- 80∘S and local time (the polar regions were cut due to frequent saturation
in the model). An example calculation would be: 35 % of dry scenarios mean
that compared to all instances (43 latitude gridpoints, 65 longitude
gridpoints and 669 sols totaling 1 869 855 cases at each local time between 9
PM and 5 AM), 35 % of them (approximately 654 449) fell into the dry scenario.

If we examine the Mars year 29 and separate the data by hemispheres and by
seasons, the data suggests that relative humidity is the primary limiting
factor most of the time. Albeit the temperature is above the necessary
eutectic temperature, the relative humidity remains too low (dry scenario).
This is a substantially more frequent case, than when either the relative
humidity with respect to liquid is high enough with too low temperatures (cold
scenario), or the relative humidity with respect to ice is too high, favoring
nucleation instead of deliquescence (nucleation scenario).

Figure 10: Distribution of different non-ideal and ideal cases of calcium
perchlorate deliquescence in the northern hemisphere of Mars, between 0∘ \-
80∘ N. Dry: relative humidity with respect to liquid too low. Cold: surface
temperature too low. Nucleation: relative humidity with respect to ice too
high. Ideal: possible chance for deliquescence. Figure 11: Distribution of
different non-ideal and ideal cases of calcium perchlorate deliquescence in
the southern hemisphere of Mars, between 0∘ \- 80∘ S. Dry: relative humidity
with respect to liquid too low. Cold: surface temperature too low. Nucleation:
relative humidity with respect to ice too high. Ideal: possible chance for
deliquescence.

Separating by seasons, the local spring and summer show higher percentages of
being too dry with sufficient temperatures. Besides, the local spring and
summer in the northern hemisphere display the highest chance for deliquescence
(ideal scenario) between 9 PM and 3 AM. There is a similar trend in the
southern hemisphere, but with overall lower percentages and mostly between 11
PM and 3 AM. In the southern hemisphere from 1 AM to 5 AM the ratio for too
cold scenarios also increase, resulting in a 8-15 % chance. There is one
particularly interesting point, which is 1 AM in the southern hemisphere,
during the local autumn. At this time the ratio for too cold scenarios is 74.6
%, an obvious outlier compared to all the other cold cases. If we take a look
at a close-up between sol 1 and sol 194 at the southern hemisphere at 60∘S, 1
AM local time, the relative humidity is elevated between sol 1 and sol 80, the
beginning of the local autumn (Fig. 13). This elevation is visible at all
latitudes, 60∘S was selected as an illustration. Comparing the 1 AM data with
11 PM and 3 AM data, in the latter cases the relative humidity is still
elevated at the beginning of the year, but not enough to stay above the
necessary minimum level for calcium perchlorate. At the same time, the surface
temperature remains strictly below the eutectic temperature (Fig. 12), thus we
arrive at the 74.6 % of cold scenarios.

Figure 12: Surface temperature in the southern hemisphere during the local
autumn.  Figure 13: Relative humiditiy with respect to liquid (blue) and with
respect to ice (red) in the southern hemisphere during the local autumn.

Overall the data suggests that relative humidity could be the main limiting
factor to deliquescence during local spring and summer in both hemispheres.
The ratios, where surface temperature was high enough with relative humidity
with respect to ice still low enough is considerably higher, than the other
scenarios (too cold or nucleation). The northern hemisphere seems more
favourable between 9 PM and 3 AM, while in the southern hemisphere between 1
AM and 3 AM are suggested as more ideal local times. From the hemispherically
and seasonally averaged data we can conclude, that the overall chance for
ideal periods is still rather low, but usually not zero. Reviewing local “hot
spots for deliquescence” might be a good follow up to these results.

##  4 Discussion and conclusions

As the search for extraterrestrial habitability (past or present) and even
future manned mission plans (requiring in-situ water production) are gaining
popularity, the importance of searching and predicting liquid water formation
and the stability of solutions on the surface of Mars is increasing.
Deliquescence is a way for liquid water to form, even in present conditions,
that shows good potential, but is not yet widely researched in Martian
conditions. The investigation of annual, global distribution of potential
briny liquids is a substantial objective, that guides the selection of future
landing sites with the aim of finding or producing/acquiring liquid water from
local sources.

We used meteorological modelling to find seasonal and annual characteristics
of calcium perchlorate and magnesium perchlorate salt deliquescence on Mars.
We followed the criteria for liquefaction detailed in the work of Rivera-
Valentín et al. (2018), and used an equation based on the Goff-Gratch equation
to calculate relative humidities (with respect to ice and with respect to
liquid) as previously described in Pál and Ákos Kereszturi (2020). In general,
the late night hours, from 9 PM to 3 AM, showed a significant global chance
for deliquescence during the local late spring and early summer (Ls 90

∘

– 130

∘

) in the northern hemisphere. Acidalia Planitia and Utopia Planitia show the
best chance for Ca(ClO4)2 deliquescence in the northern hemisphere, while
there is chance for deliquescence scattered across the northern upper
latitudes (as can be seen in the animations included in the online version).
While there is no significant difference in the daily maximum temperatures
between these two regions and the rest of the northern hemisphere below 60∘,
the minimum temperatures are 30-50 K higher. The overall higher amounts of
water vapor combined with higher night time temperatures could be the reason
why these two larger regions show up in the annual average figures. The lower
thermal inertia regions, that showed elevated relative humidity values
throughout the year, seem to be less ideal for the deliquescence process (Pál
et al., 2019).

In the southern hemisphere the best season was also local spring (Ls 230

∘

– 300

∘

) with smaller chance than in the northern, produced by the increased
atmospheric water vapor through exposed water ice from below the receding
seasonal carbon-dioxide polar cap. At the southern hemisphere Hellas Planitia
and Argyre Planitia both show some chance for deliquescence, with 3 AM being
the overall best period during the year. They both have higher daily minimum
temperatures compared with their vicinity, with no significant variation in
relative humidity levels (Pál et al., 2019).

Patterns visible in annual zonal average deliquescence probability figures
largely follow the annual cycle of water vapor (Smith, 2002). The northern
upper arch starting around sol 67 is in agreement with the seasonal
sublimation of the CO2 ice cap, releasing water vapor from below. In both
hemispheres the amount of atmospheric water vapor reaches maximum during the
local summertime, however, after the decay of this maximum their behaviour
differs completely. In the northern hemisphere, between mid-summer and mid-
autumn, the area of relatively high water vapor extends increasingly towards
the equator - crossing over to the southern hemisphere eventually. This
extension towards the equator is visible in the zonal average maps at all
local times. In comparison, there is no significant transport from the
southern hemisphere to the northern hemisphere. The amplitude of the water
vapor maxima differs as well, with approximately 85% of the total atmospheric
water vapor in the northern hemisphere at maximum, and only about 65% in the
southern hemisphere at maximum. Possible deliquescence area is substantially
larger in the northern hemisphere, that could be the result of the overall
higher amounts of water vapor in the atmosphere.

The outer edges of the zonally averaged ideal regions are in strong agreement
with the seasonal recession of the polar ice caps (see James et al. (1990),
Schmidt et al. (2009) for the southern, and James and Cantor (2001), Calvin et
al. (2015) for the northern ice caps). As the ice caps sublimate in warmer
seasons, releasing water vapor back into the atmosphere, the relative humidity
levels reach the necessary minimum for deliquescence. In the northern
hemisphere there is a chance at almost all latitudes around 9 PM and 11 PM,
the ideal regions narrowing down to Acidalia Planitia and parts of Utopia
Planitia by the early morning hours. However, comparing the two hemispheres,
the potentially ideal regions are substantially smaller in the southern
hemisphere. The narrow ideal “curved band-like” feature in the southern
hemisphere is essentially showing the recession and refreezing of the southern
polar cap. As the CO2 ice sublimates, the albedo of the surface decreases,
thus the daily surface temperatures get higher (Wagstaff et al., 2008, Appéré
et al., 2011). Due to the difference of the freezing point of H2O and CO2, the
H2O is the first to freeze to the surface, followed by the CO2. During the
southern spring the CO2 ice starts to sublime, exposing the frozen H2O layer.
Above this layer, the atmospheric water vapor might be locally higher, thus
creating the potentially ideal circumstances for deliquescence for a short
time. Taking the temperature, available water vapor and overall meteorological
differences into account, the deliquescence chance variations could be
anticipated.

If there is a modelling based theoretical possibility for deliquescence, it
does not mean it happens in reality. However such modelling based calculations
are useful, partly as there are no better methods available for the estimation
of deliquescence yet, and partly because these calculations fine tune the
temporal and spatial characteristics where instruments on next missions should
focus; like the HABIT (Martin-Torres and Zorzano, 2018, Martín-Torres et al.,
2020, Nazarious et al., 2019) onboard the ExoMars rover mission (Vago et al.,
2017, 2019). In this work we presented the meteorological conditions based
evaluation of deliquescence, which requires the presence and hydration state
of calcium perchlorate on the surface. Depending on the hydration state of
calcium perchlorate, the threshold limit of deliquescence might also change.
Based on the work of Nuding et al. (2014), higher hydration states deliquesce
at a higher relative humidty than the lower hydration states.

Taking the thermal inertia (TI) values into consideration, the ideal regions
have overall higher values, in the range of 170 - 250 Jm-2K-1s-1/2 (indicating
fine grained particles as the surface layer), with the coarser material
bearing (> 400 Jm-2K-1s-1/2) upper regions of Acidalia Planitia and Utopia
Planitia showing the best chance during the late night hours. In the southern
hemisphere, parts of Argyre Basin and Hellas Basin are covered with slightly
higher TI materials, but the contrast with surrounding regions is
significantly less, than in the northern hemisphere. As a result the low TI
and the fine material causing it, this zone is unfavourable because it leads
to too low nighttime temperatures. Considering the band around 60∘ S, the TI
values “shift” here from the 170 - 250 Jm-2K-1s-1/2 range to the low 65 - 165
Jm-2K-1s-1/2 range indicating a dusty, very fine layer. This band corresponds
most likely to the H2O “ring” around the receding seasonal southern polar ice
cap.

There is limited amount of research regarding deliquescence mapping, but a map
showing the distribution of (meta)stable brines was published recently, thanks
to the work of E.G. et al. (2020). Comparing our results to their work, the
potential regions are a good match both in the case of Ca(ClO4)2 and
Mg(ClO4)2. The almost continuous band above 30∘ N (most visible at 9 PM in our
results) is also present in both studies, as well as the southern band around
60∘ S (most visible at 1 AM in our results). One difference to highlight is
Argyre Planitia, which showed a small chance of deliquescence in our results,
but is an area, where such brines cannot form in the work of E.G. et al.
(2020). Thus, Argyre Planitia would be an interesting place for further
research to see, what may cause the differences in results.

The driving force of the enigmatic Recurring Slope Lineae (RSL) is another
highly debated question in the topic of possible signs of martian liquid
water. Perchlorates were detected near some RSL sites (Ojha et al., 2015),
thus the hypothesis of brine flow produced RSLs (Gough et al., 2016) gained
new momentum. Mitchell and Christensen (2016) tested this theory, and
concluded that deliquescence of water from the atmosphere is an unlikely
mechanism for RSL formation due to the atmospheric water vapor not reaching
high enough quantities. The distribution of chlorides and confirmed RSL sites
showed in their work range from approximately 45∘ S to the equator. If we
compare this to our maps we can see, that our results reinforce, that even
with confirmed sources of chlorides, the region is not likely to be an ideal
place for deliquescence. Munaretto et al. (2020) presented the first CaSSIS
(Color and Surface Science Imaging System on board ESA’s ExoMars Trace Gas
Orbiter) observation of RSL at Hale crater during the early morning hours, and
their results also support dry granular flow dynamics (C.M. et al., 2017,
Vincendon et al., 2019, Schaefer et al., 2019). Although Argyre Basin shows a
chance for deliquescence in our results, Hale crater, located just north, does
not appear to be ideal, thus aligning with the conclusion of Munaretto et al.
(2020). In contrast, in the recent work of Horne (2018) the dry flow
mechanisms seemed inadequate to explain the leeved fissures and gutters in
Meridinai Planum. These fissures and gutters could provide geomorphological
evidence of recent transient processes, for example deliquescence of calcium
perchlorate. In our results, the equatorial region shows limited chance for
deliquescence, however, Meridiani Planum does seem to show a small chance
throughout the year.

The results we presented in this work were calculated using the LMDZ GCM, and
as such has certain limitations. The saturation of the northern polar region
could be an artifact related to the seasonal evaporation of the polar ice,
rather than a definite chance for deliquescence. In our work we assume the
water vapor volume mixing ratio to be well mixed between approximately 4
meters altitude and at the surface. This is due to the complexity of near-
surface processes, resulting in uncertain water vapor data under 4 meters (the
first altitude level in the atmospheric model). This approach gives us
reasonable results and is currently the best way to estimate the relative
humidity this close to the surface from the GCM. Analysing temporal humidity
changes might help to improve this, from the data of future missions.

We have calculated for the Mars year 29 in this work, and comparing our
results with different years would be a beneficial direction for a follow-up
study. Analyzing the differences and similarities between multiple martian
years would be a great way to distinguish year specific results. Another
compelling question to pursue could be a detailed study of the chance for
deliquescence in the Argyre and Hellas Planitia regions. Taking hygroscopic
salts with different eutectic temperature - relative humidity pairs into
consideration would be another good path to better understand the balance of
temperature and relative humidity in global deliquescence probabilities.

Our results suggest that there is a good chance for calcium perchlorate
deliquescence at larger regions on Mars, and the possibly ideal times are
spread throughout several hours. From the statistics of our calculations,
relative humidity might be the main limiting factor of deliquescence. Our
deliquescence probability maps could be used as a good starting point in
finding interesting locations for local ephemeral brine studies, or as a
preliminary guide in planning future, liquid brine related in-situ missions.

##  5 Acknowledgement

This work was supported by the EXODRILTECH project of ESA and the Excellence
of Strategic R&D centres (GINOP-2.3.2-15-2016-00003) project of NKFIH and the
related H2020 fund, the COOP-NN-116927 project of NKFIH and the TD1308 Origins
and evolution of life on Earth and in the Universe COST actions number 39045
and 39078. The NetCDF files were visualized with the NASA GISS Panoply viewer
developed by Dr. Robert B. Schmunk at the NASA Goddard Institute for Space
Studies.

##  Appendix A Limiting factors of deliquescence

Local time | Lat | Sol | Cold | Nucleation | Dry | Ideal
---|---|---|---|---|---|---
09:00 PM | 0 ∘ \- 80 ∘ | 1 – 194 | 4.332% | 1.076% | 35.264% | 4.065%
|  | 194 – 372 | 2.648% | 4.599% | 42.418% | 8.821%
|  | 372 – 514 | 5.454% | 0.000% | 15.678% | 0.011%
|  | 514 – 669 | 3.926% | 0.000% | 11.248% | 0.004%
09:00 PM | -80 ∘ \- 0 ∘ | 1 – 194 | 7.190% | 0.004% | 4.492% | 0.018%
|  | 194 – 372 | 5.848% | 0.002% | 9.186% | 0.089%
|  | 372 – 514 | 2.034% | 0.014% | 68.404% | 0.090%
|  | 514 – 669 | 3.120% | 0.005% | 71.592% | 0.116%
11:00 PM | 0 ∘ \- 80 ∘ | 1 – 194 | 7.122% | 3.842% | 10.630% | 4.744%
|  | 194 – 372 | 3.762% | 8.581% | 17.741% | 8.642%
|  | 372 – 514 | 5.861% | 0.000% | 11.077% | 0.002%
|  | 514 – 669 | 5.059% | 0.000% | 4.669% | 0.000%
11:00 PM | -80 ∘ \- 0 ∘ | 1 – 194 | 6.704% | 0.001% | 0.750% | 0.004%
|  | 194 – 372 | 6.332% | 0.000% | 3.101% | 0.016%
|  | 372 – 514 | 4.205% | 0.140% | 55.897% | 0.479%
|  | 514 – 669 | 6.616% | 0.033% | 52.027% | 0.662%
01:00 AM | 0 ∘ \- 80 ∘ | 1 – 194 | 7.120% | 1.966% | 3.635% | 3.091%
|  | 194 – 372 | 5.663% | 4.694% | 7.038% | 6.885%
|  | 372 – 514 | 6.477% | 0.000% | 6.025% | 0.000%
|  | 514 – 669 | 6.680% | 0.000% | 1.724% | 0.000%
01:00 AM | -80 ∘ \- 0 ∘ | 1 – 194 | 74.661% | 0.000% | 0.063% | 0.000%
|  | 194 – 372 | 6.601% | 0.000% | 0.861% | 0.005%
|  | 372 – 514 | 8.046% | 0.465% | 39.016% | 1.662%
|  | 514 – 669 | 12.765% | 0.137% | 30.434% | 2.237%
03:00 AM | 0 ∘ \- 80 ∘ | 1 – 194 | 6.419% | 0.528% | 3.072% | 2.419%
|  | 194 – 372 | 8.776% | 1.171% | 4.913% | 5.698%
|  | 372 – 514 | 8.720% | 0.000% | 2.956% | 0.000%
|  | 514 – 669 | 6.795% | 0.000% | 0.337% | 0.000%
03:00 AM | -80 ∘ \- 0 ∘ | 1 – 194 | 4.303% | 0.000% | 0.001% | 0.0004%
|  | 194 – 372 | 5.865% | 0.000% | 0.250% | 0.0004%
|  | 372 – 514 | 11.445% | 0.030% | 29.070% | 1.242%
|  | 514 – 669 | 18.917% | 0.001% | 20.519% | 0.850%
05:00 AM | 0 ∘ \- 80 ∘ | 1 – 194 | 9.896% | 0.006% | 11.341% | 0.526%
|  | 194 – 372 | 14.222% | 0.036% | 17.930% | 1.898%
|  | 372 – 514 | 10.278% | 0.000% | 1.465% | 0.000%
|  | 514 – 669 | 6.579% | 0.000% | 0.003% | 0.000%
05:00 AM | -80 ∘ \- 0 ∘ | 1 – 194 | 4.001% | 0.000% | 0.000% | 0.000%
|  | 194 – 372 | 5.294% | 0.000% | 0.039% | 0.000%
|  | 372 – 514 | 10.403% | 0.000% | 29.802% | 0.043%
|  | 514 – 669 | 15.130% | 0.005% | 27.884% | 0.014%
Table 2: Statistics of the limiting factor in deliquescence, detailed in
Section 3.5.

## References

  * A. et al. (2013) A., L.L., R., M.P., R., W.C., M., C., P., C., Conrad, P.G., Archer, P.D., Atreya, S.K., Brunner, A.E., Buch, A., Eigenbrode, J.L., Flesch, G.J., Franz, H.B., Freissinet, C., Glavin, D.P., McAdam, A.C., Miller, K.E., Ming, D.W., Morris, R.V., Navarro-González, R., Niles, P.B., Owen, T., Pepin, R.O., Squyres, S., Steele, A., Stern, J.C., Summons, R.E., Sumner, D.Y., Sutter, B., Szopa, C., Teinturier, S., Trainer, M.G., Wray, J.J., Grotzinger, J.P., 2013.  Volatile, isotope, and organic analysis of martian fines with the mars curiosity rover.  Science 341.  URL: https://science.sciencemag.org/content/341/6153/1238937, doi:10.1126/science.1238937, arXiv:https://science.sciencemag.org/content/341/6153/1238937.full.pdf.
  * Appéré et al. (2011) Appéré, T., Schmitt, B., Langevin, Y., Douté, S., Pommerol, A., Forget, F., Spiga, A., Gondet, B., Bibring, J.P., 2011.  Winter and spring evolution of northern seasonal deposits on Mars from OMEGA on Mars Express.  Journal of Geophysical Research (Planets) 116, E05001.  doi:10.1029/2010JE003762.
  * Brass (1980) Brass, G.W., 1980.  Stability of brines on Mars.  Icarus 42, 20–28.  doi:10.1016/0019-1035(80)90237-7.
  * Calvin et al. (2015) Calvin, W., James, P., Cantor, B., Dixon, E., 2015\.  Interannual and seasonal changes in the north polar ice deposits of mars: Observations from my 29–31 using marci.  Icarus 251, 181 – 190.  URL: http://www.sciencedirect.com/science/article/pii/S0019103514004424, doi:https://doi.org/10.1016/j.icarus.2014.08.026. dynamic Mars.
  * Catling et al. (2010) Catling, D.C., Claire, M.W., Zahnle, K.J., Quinn, R.C., Clark, B.C., Hecht, M.H., Kounaves, S., 2010.  Atmospheric origins of perchlorate on Mars and in the Atacama.  Journal of Geophysical Research (Planets) 115, E00E11.  doi:10.1029/2009JE003425.
  * Clow (1987) Clow, G.D., 1987.  Generation of liquid water on Mars through the melting of a dusty snowpack.  Icarus 72, 95–127.  doi:10.1016/0019-1035(87)90123-0.
  * C.M. et al. (2017) C.M., D., A.S., M., M., C., et al., 2017.  Granular flows at recurring slope lineae on mars indicate a limited role for liquid water.  Nature Geosci 10, 903–907.  doi:https://doi.org/10.1038/s41561-017-0012-5.
  * E.G. et al. (2020) E.G., R.V., V.F., C., Soto, A., et al., 2020.  Distribution and habitability of (meta)stable brines on present-day mars.  Nat Astron 4, 756–761.  doi:https://doi.org/10.1038/s41550-020-1080-9.
  * Escamilla-Roa et al. (2020) Escamilla-Roa, E., Zorzano, M.P., Martin-Torres, J., Hernández-Laguna, A., Ignacio Sainz-Díaz, C., 2020.  DFT study of the reduction reaction of calcium perchlorate on olivine surface: Implications to formation of Martian’s regolith.  Applied Surface Science 512, 145634\.  doi:10.1016/j.apsusc.2020.145634.
  * Fischer et al. (2014) Fischer, E., Martínez, G.M., Elliott, H.M., Rennó, N.O., 2014\.  Experimental evidence for the formation of liquid saline water on mars.  Geophysical Research Letters 41, 4456–4462.  URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2014GL060302, doi:10.1002/2014GL060302, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2014GL060302.
  * Forget et al. (1999) Forget, F., Hourdin, F., Fournier, R., Hourdin, C., Talagrand, O., Collins, M., Lewis, S.R., Read, P.L., Huot, J.P., 1999.  Improved general circulation models of the Martian atmosphere from the surface to above 80 km.  J. Geophys. Res. 104, 24155–24176.  doi:10.1029/1999JE001025.
  * Glavin et al. (2013) Glavin, D.P., Freissinet, C., Miller, K.E., Eigenbrode, J.L., Brunner, A.E., Buch, A., Sutter, B., Archer, P.D., Atreya, S.K., Brinckerhoff, W.B., Cabane, M., Coll, P., Conrad, P.G., Coscia, D., Dworkin, J.P., Franz, H.B., Grotzinger, J.P., Leshin, L.A., Martin, M.G., McKay, C., Ming, D.W., Navarro-González, R., Pavlov, A., Steele, A., Summons, R.E., Szopa, C., Teinturier, S., Mahaffy, P.R., 2013\.  Evidence for perchlorates and the origin of chlorinated hydrocarbons detected by SAM at the Rocknest aeolian deposit in Gale Crater.  Journal of Geophysical Research (Planets) 118, 1955–1973.  doi:10.1002/jgre.20144.
  * Goff and Gratch (1946) Goff, J.A., Gratch, S., 1946\.  Low pressure properties of water from -160 to 212 F.  Trans. Amer. Soc. Heat. Vent. Eng. 52, 95.
  * Gough et al. (2016) Gough, R., Chevrier, V., Tolbert, M., 2016.  Formation of liquid water at low temperatures via the deliquescence of calcium chloride: Implications for antarctica and mars.  Planetary and Space Science 131, 79 – 87.  URL: http://www.sciencedirect.com/science/article/pii/S0032063315301720, doi:https://doi.org/10.1016/j.pss.2016.07.006.
  * Gough et al. (2011) Gough, R.V., Chevrier, V.F., Baustian, K.J., Wise, M.E., Tolbert, M.A., 2011.  Laboratory studies of perchlorate phase transitions: Support for metastable aqueous perchlorate solutions on Mars.  Earth and Planetary Science Letters 312, 371–377.  doi:10.1016/j.epsl.2011.10.026.
  * Gough et al. (2014) Gough, R.V., Chevrier, V.F., Tolbert, M.A., 2014.  Formation of aqueous solutions on Mars via deliquescence of chloride-perchlorate binary mixtures.  Earth and Planetary Science Letters 393, 73–82.  doi:10.1016/j.epsl.2014.02.002.
  * Gough et al. (2019) Gough, R.V., Primm, K.M., Rivera-Valentín, E.G., Martínez, G.M., Tolbert, M.A., 2019\.  Solid-solid hydration and dehydration of Mars-relevant chlorine salts: Implications for Gale Crater and RSL locations.  Icarus 321, 1–13.  doi:10.1016/j.icarus.2018.10.034.
  * Haberle et al. (2001) Haberle, R.M., McKay, C.P., Schaeffer, J., Cabrol, N.A., Grin, E.A., Zent, A.P., Quinn, R., 2001.  On the possibility of liquid water on present-day Mars.  J. Geophys. Res. 106, 23317–23326.  doi:10.1029/2000JE001360.
  * Hallsworth (2020) Hallsworth, J., 2020.  Salt deliquescence can support extraterrestrial life.  Nat Astron 4, 739–740.  doi:hhttps://doi.org/10.1038/s41550-020-1081-8.
  * Hanley et al. (2012) Hanley, J., Chevrier, V.F., Berget, D.J., Adams, R.D., 2012\.  Chlorate salts and solutions on Mars.  Geophysical Research Letters 39, L08201.  doi:10.1029/2012GL051239.
  * Hecht (2002) Hecht, M.H., 2002.  Metastability of Liquid Water on Mars.  Icarus 156, 373–386.  doi:10.1006/icar.2001.6794.
  * Hecht et al. (2009a) Hecht, M.H., Catling, D.C., Clark, B.C., Deflores, L., Gospodinova, K., Kapit, J., Kounaves, S.P., Ming, D.W., Quinn, R.C., West, S.J., Young, S.M.M., 2009a.  Perchlorate in Martian Soil: Evidence and Implications, in: Lunar and Planetary Science Conference, p. 2420.
  * Hecht et al. (2009b) Hecht, M.H., Kounaves, S.P., Quinn, R.C., West, S.J., Young, S.M.M., Ming, D.W., Catling, D.C., Clark, B.C., Boynton, W.V., Hoffman, J., DeFlores, L.P., Gospodinova, K., Kapit, J., Smith, P.H., 2009b.  Detection of Perchlorate and the Soluble Chemistry of Martian Soil at the Phoenix Lander Site.  Science 325, 64\.  doi:10.1126/science.1172466.
  * Horne (2018) Horne, D.J., 2018.  Young, small-scale surface features in meridiani planum, mars: A possible signature of recent transient liquid and gas emissions.  Planetary and Space Science 157, 10 – 21.  URL: http://www.sciencedirect.com/science/article/pii/S0032063317302714, doi:https://doi.org/10.1016/j.pss.2018.04.012.
  * Hourdin et al. (2006) Hourdin, F., Musat, I., Bony, S., Braconnot, P., Codron, F., Dufresne, J.L., Fairhead, L., Filiberti, M.A., Friedlingstein, P., Grandpeix, J.Y., Krinner, G., Levan, P., Li, Z.X., Lott, F., 2006\.  The LMDZ4 general circulation model: climate performance and sensitivity to parametrized physics with emphasis on tropical convection.  Climate Dynamics 27, 787–813.  doi:10.1007/s00382-006-0158-0.
  * James and Cantor (2001) James, P.B., Cantor, B.A., 2001\.  Martian north polar cap recession: 2000 mars orbiter camera observations.  Icarus 154, 131 – 144.  URL: http://www.sciencedirect.com/science/article/pii/S0019103501966539, doi:https://doi.org/10.1006/icar.2001.6653.
  * James et al. (1990) James, P.B., Martin, L.J., Henson, J.R., Birch, P.V., 1990\.  Seasonal recession of mars’ south polar cap in 1986.  Journal of Geophysical Research: Solid Earth 95, 1337–1341.  URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB095iB02p01337, doi:https://doi.org/10.1029/JB095iB02p01337, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/JB095iB02p01337.
  * Kereszturi et al. (2009) Kereszturi, A., Möhlmann, D., Berczi, S., Ganti, T., Kuti, A., Sik, A., Horvath, A., 2009.  Recent rheologic processes on dark polar dunes of Mars: Driven by interfacial water?  Icarus 201, 492–503.  doi:10.1016/j.icarus.2009.01.014.
  * Knauth and Burt (2002) Knauth, L.P., Burt, D.M., 2002\.  Eutectic Brines on Mars: Origin and Possible Relation to Young Seepage Features.  Icarus 158, 267–271.  doi:10.1006/icar.2002.6866.
  * Kossacki and Markiewicz (2004) Kossacki, K.J., Markiewicz, W.J., 2004\.  Seasonal melting of surface water ice condensing in martian gullies.  Icarus 171, 272–283.  doi:10.1016/j.icarus.2004.05.018.
  * Langevin et al. (2007) Langevin, Y., Bibring, J.P., Montmessin, F., Forget, F., Vincendon, M., Douté, S., Poulet, F., Gondet, B., 2007\.  Observations of the south seasonal cap of Mars during recession in 2004-2006 by the OMEGA visible/near-infrared imaging spectrometer on board Mars Express.  Journal of Geophysical Research (Planets) 112, E08S12.  doi:10.1029/2006JE002841.
  * List (1984) List, R.J., 1984.  Smithsonian Meteorological Tables.  6th ed. Smithsonian Institution Press , 347–350.
  * Martin-Torres and Zorzano (2018) Martin-Torres, J., Zorzano, M.P., 2018\.  The instrument HABIT (HabitAbility, Brine Irradiation and Temperature) on the ExoMars platform, in: 42nd COSPAR Scientific Assembly, pp. F3.3–6–18.
  * Martín-Torres et al. (2020) Martín-Torres, J., Zorzano, M.P., Soria-Salinas, Á., Nazarious, M.I., Konatham, S., Mathanlal, T., Ramachandran, A.V., Ramírez-Luque, J.A., Mantas-Nakhai, R., 2020.  The HABIT (HabitAbility: Brine Irradiation and Temperature) environmental instrument for the ExoMars 2022 Surface Platform.  Planet. Space Sci. 190, 104968\.  doi:10.1016/j.pss.2020.104968.
  * Martín-Torres et al. (2020) Martín-Torres, J., Zorzano, M.P., Álvaro Soria-Salinas, Nazarious, M.I., Konatham, S., Mathanlal, T., Ramachandran, A.V., Ramírez-Luque, J.A., Mantas-Nakhai, R., 2020.  The habit (habitability: Brine irradiation and temperature) environmental instrument for the exomars 2022 surface platform.  Planetary and Space Science 190, 104968\.  doi:https://doi.org/10.1016/j.pss.2020.104968.
  * McEwen et al. (2014) McEwen, A., Dundas, C., Mattson, S., Toigo, A., Ojha, L., Wray, J., Chojnacki, M., Byrne, S., Murchie, S., Thomas, N., 2014\.  Recurring slope lineae in equatorial regions of mars.  Nature Geoscience 7, 53–58.  doi:10.1038/ngeo2014.
  * Mellon et al. (2000) Mellon, M.T., Jakosky, B.M., Kieffer, H.H., Christensen, P.R., 2000\.  High-Resolution Thermal Inertia Mapping from the Mars Global Surveyor Thermal Emission Spectrometer.  Icarus 148, 437–455.  doi:10.1006/icar.2000.6503.
  * Ming et al. (2014) Ming, D.W., Archer, P.D., Glavin, D.P., Eigenbrode, J.L., Franz, H.B., Sutter, B., Brunner, A.E., Stern, J.C., Freissinet, C., McAdam, A.C., Mahaffy, P.R., Cabane, M., Coll, P., Campbell, J.L., Atreya, S.K., Niles, P.B., Bell, J.F., Bish, D.L., Brinckerhoff, W.B., Buch, A., Conrad, P.G., Des Marais, D.J., Ehlmann, B.L., Fairén, A.G., Farley, K., Flesch, G.J., Francois, P., Gellert, R., Grant, J.A., Grotzinger, J.P., Gupta, S., Herkenhoff, K.E., Hurowitz, J.A., Leshin, L.A., Lewis, K.W., McLennan, S.M., Miller, K.E., Moersch, J., Morris, R.V., Navarro-González, R., Pavlov, A.A., Perrett, G.M., Pradler, I., Squyres, S.W., Summons, R.E., Steele, A., Stolper, E.M., Sumner, D.Y., Szopa, C., Teinturier, S., Trainer, M.G., Treiman, A.H., Vaniman, D.T., Vasavada, A.R., Webster, C.R., Wray, J.J., Yingst, R.A., 2014.  Volatile and organic compositions of sedimentary rocks in yellowknife bay, gale crater, mars.  Science 343.  URL: https://science.sciencemag.org/content/343/6169/1245267, doi:10.1126/science.1245267, arXiv:https://science.sciencemag.org/content/343/6169/1245267.full.pdf.
  * Mitchell and Christensen (2016) Mitchell, J.L., Christensen, P.R., 2016\.  Recurring slope lineae and chlorides on the surface of mars.  Journal of Geophysical Research: Planets 121, 1411–1428.  URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2016JE005012, doi:10.1002/2016JE005012, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016JE005012.
  * Möhlmann and Thomsen (2011) Möhlmann, D., Thomsen, K., 2011\.  Properties of cryobrines on Mars.  Icarus 212, 123–130.  doi:10.1016/j.icarus.2010.11.025.
  * Munaretto et al. (2020) Munaretto, G., Pajola, M., Cremonese, G., Re, C., Lucchetti, A., Simioni, E., McEwen, A., Pommerol, A., Becerra, P., Conway, S., Thomas, N., Massironi, M., 2020\.  Implications for the origin and evolution of martian recurring slope lineae at hale crater from cassis observations.  Planetary and Space Science 187, 104947\.  URL: http://www.sciencedirect.com/science/article/pii/S0032063320300660, doi:https://doi.org/10.1016/j.pss.2020.104947.
  * Navarro-Gonzalez et al. (2013) Navarro-Gonzalez, R., Sutter, B., Archer, D., Ming, D., Eigenbrode, J., Franz, H., Glavin, D., McAdam, A., Stern, J., McKay, C., Coll, P., Cabane, M., Conrad, P., Mahaffy, P., Martín-Torres, F., Zorzano-Mier, M., Grotzinger, J., MSL Science Team, 2013.  Possible detection of perchlorates by the Sample Analysis at Mars (SAM) Instrument: Comparison with previous missions, in: EGU General Assembly Conference Abstracts, pp. EGU2013–6529.
  * Navarro-González et al. (2010) Navarro-González, R., Vargas, E., de la Rosa, J., Raga, A.C., McKay, C.P., 2010.  Reanalysis of the viking results suggests perchlorate and organics at midlatitudes on mars.  Journal of Geophysical Research: Planets 115\.  URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2010JE003599, doi:10.1029/2010JE003599, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2010JE003599.
  * Nazarious et al. (2019) Nazarious, M.I., Ramachandran, A.V., Zorzano, M.P., Martin-Torres, J., 2019\.  Calibration and preliminary tests of the Brine Observation Transition To Liquid Experiment on HABIT/ExoMars 2020 for demonstration of liquid water stability on Mars.  Acta Astronautica 162, 497–510.  doi:10.1016/j.actaastro.2019.06.026.
  * Nuding et al. (2014) Nuding, D., Rivera-Valentin, E., Davis, R., Gough, R., Chevrier, V., Tolbert, M., 2014\.  Deliquescence and efflorescence of calcium perchlorate: An investigation of stable aqueous solutions relevant to mars.  Icarus 243, 420 – 428.  URL: http://www.sciencedirect.com/science/article/pii/S0019103514004527, doi:https://doi.org/10.1016/j.icarus.2014.08.036.
  * Ojha et al. (2015) Ojha, L., Wilhelm, M.B., Murchie, S.L., McEwen, A.S., Wray, J.J., Hanley, J., Massé, M., Chojnacki, M., 2015\.  Spectral evidence for hydrated salts in recurring slope lineae on Mars.  Nature Geoscience 8, 829–832.  doi:10.1038/ngeo2546.
  * Pál and Kereszturi (2017) Pál, B., Kereszturi, Á., 2017\.  Possibility of microscopic liquid water formation at landing sites on Mars and their observational potential.  Icarus 282, 84–92.  doi:10.1016/j.icarus.2016.09.006, arXiv:1609.07976.
  * Pál and Ákos Kereszturi (2020) Pál, B., Ákos Kereszturi, 2020\.  Annual and daily ideal periods for deliquescence at the landing site of insight based on gcm model calculations.  Icarus 340, 113639\.  doi:https://doi.org/10.1016/j.icarus.2020.113639.
  * Pál et al. (2019) Pál, B., Ákos Kereszturi, Forget, F., Smith, M.D., 2019\.  Global seasonal variations of the near-surface relative humidity levels on present-day mars.  Icarus 333, 481 – 495.  URL: http://www.sciencedirect.com/science/article/pii/S0019103518305529, doi:https://doi.org/10.1016/j.icarus.2019.07.007.
  * Rivera-Valentín et al. (2018) Rivera-Valentín, E.G., Gough, R.V., Chevrier, V.F., Primm, K.M., Martínez, G.M., Tolbert, M., 2018\.  Constraining the potential liquid water environment at gale crater, mars.  Journal of Geophysical Research: Planets 123, 1156–1167.  doi:10.1002/2018JE005558.
  * Sadourny and Laval (1984) Sadourny, R., Laval, K., 1984\.  January and july performance of the lmd general circulation model.  Berger A., Nicolis C. (eds) New perspectives in climate modeling. Elsevier, Amsterdam , 173197.
  * Schaefer et al. (2019) Schaefer, E., McEwen, A., Sutton, S., 2019.  A case study of recurring slope lineae (rsl) at tivat crater: Implications for rsl origins.  Icarus 317, 621 – 648.  URL: http://www.sciencedirect.com/science/article/pii/S0019103518300137, doi:https://doi.org/10.1016/j.icarus.2018.07.014.
  * Schmidt et al. (2009) Schmidt, F., Douté, S., Schmitt, B., Vincendon, M., Bibring, J.P., Langevin, Y., 2009\.  Albedo control of seasonal south polar cap recession on mars.  Icarus 200, 374 – 394.  URL: http://www.sciencedirect.com/science/article/pii/S0019103508004351, doi:https://doi.org/10.1016/j.icarus.2008.12.014.
  * Schmitt et al. (2006) Schmitt, B., Schmidt, F., Douté, S., Langevin, Y., Forget, F., Bibring, J.P., Gondet, B., OMEGA Team, 2006\.  Recession of the Northern Seasonal Condensates on Mars by OMEGA/Mars Express, in: Fourth International Conference on Mars Polar Science and Exploration, p. 8050.
  * Smith (2002) Smith, M.D., 2002.  The annual cycle of water vapor on Mars as observed by the Thermal Emission Spectrometer.  Journal of Geophysical Research (Planets) 107, 5115.  doi:10.1029/2001JE001522.
  * Szynkiewicz et al. (2009) Szynkiewicz, A., Ewing, R.C., Fishbaugh, K.E., Bourke, M.C., Bustos, D., Pratt, L.M., 2009\.  Geomorphological Evidence of Plausible Water Activity and Evaporatic Deposition in Interdune Areas of the Gypsum-rich Olympia Undae Dune Field, in: Lunar and Planetary Science Conference, p. 2038.
  * Toner et al. (2014) Toner, J.D., Catling, D.C., Light, B., 2014.  The formation of supercooled brines, viscous liquids, and low-temperature perchlorate glasses in aqueous solutions relevant to Mars.  Icarus 233, 36–47.  doi:10.1016/j.icarus.2014.01.018.
  * Toner et al. (2015) Toner, J.D., Catling, D.C., Light, B., 2015.  Modeling salt precipitation from brines on Mars: Evaporation versus freezing origin for soil salts.  Icarus 250, 451–461.  doi:10.1016/j.icarus.2014.12.013.
  * Vago et al. (2019) Vago, J.L., Rodionov, D.S., Svedhem, H., Sefton-Nash, E., Baglioni, P., Haldemann, A., Rover Science Ops Working Group, ExoMars Science Working Team, ExoMars Project Team, 2019.  ExoMars 2020 Progress.  LPI Contributions 2089, 6011\.
  * Vago et al. (2017) Vago, J.L., Westall, F., Pasteur Instrument Team, Pasteur Landing Team, Coates, A.J., Jaumann, R., Korablev, O., Ciarletti, V., Mitrofanov, I., Josset, J.L., De Sanctis, M.C., Bibring, J.P., Rull, F., Goesmann, F., Steininger, H., Goetz, W., Brinckerhoff, W., Szopa, C., Raulin, F., Westall, F., Edwards, H.G.M., Whyte, L.G., Fairén, A.G., Bibring, J.P., Bridges, J., Hauber, E., Ori, G.G., Werner, S., Loizeau, D., Kuzmin, R.O., Williams, R.M.E., Flahaut, J., Forget, F., Vago, J.L., Rodionov, D., Korablev, O., Svedhem, H., Sefton-Nash, E., Kminek, G., Lorenzoni, L., Joudrier, L., Mikhailov, V., Zashchirinskiy, A., Alexashkin, S., Calantropio, F., Merlo, A., Poulakis, P., Witasse, O., Bayle, O., Bayón, S., Meierhenrich, U., Carter, J., García-Ruiz, J.M., Baglioni, P., Haldemann, A., Ball, A.J., Debus, A., Lindner, R., Haessig, F., Monteiro, D., Trautner, R., Voland, C., Rebeyre, P., Goulty, D., Didot, F., Durrant, S., Zekri, E., Koschny, D., Toni, A., Visentin, G., Zwick, M., van Winnendael, M., Azkarate, M., Carreau, C., ExoMars Project Team, 2017.  Habitability on Early Mars and the Search for Biosignatures with the ExoMars Rover.  Astrobiology 17, 471–510.  doi:10.1089/ast.2016.1533.
  * Vincendon et al. (2019) Vincendon, M., Pilorget, C., Carter, J., Stcherbinine, A., 2019\.  Observational evidence for a dry dust-wind origin of mars seasonal dark flows.  Icarus 325, 115 – 127.  URL: http://www.sciencedirect.com/science/article/pii/S0019103518305712, doi:https://doi.org/10.1016/j.icarus.2019.02.024.
  * Wadsworth and Cockell (2017) Wadsworth, J., Cockell, C.S., 2017\.  Perchlorates on Mars enhance the bacteriocidal effects of UV light.  Scientific Reports 7, 4662\.  doi:10.1038/s41598-017-04910-3.
  * Wagstaff et al. (2008) Wagstaff, K.L., Titus, T.N., Ivanov, A.B., Castaño, R., Bandfield, J.L., 2008.  Observations of the north polar water ice annulus on Mars using THEMIS and TES.  Planetary and Space Science 56, 256–265.  doi:10.1016/j.pss.2007.08.008.
  * Zorzano et al. (2009) Zorzano, M.P., Mateo-Martí, E., Prieto-Ballesteros, O., Osuna, S., Renno, N., 2009.  Stability of liquid saline water on present day Mars.  Geophysical Research Letters 36, L20201.  doi:10.1029/2009GL040315.


# Realizing late-time cosmology in the context of Dynamical Stability Approach

Anirban Chatterjee  Saddam Hussain  Department of Physics, Indian Institute of
Technology Kanpur, Kanpur 208016, India  Kaushik Bhattacharya  Department of
Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India

###### Abstract

We examine the scenario of non-minimally coupled relativistic fluid and
$k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker
universe. By adding a non-minimal coupling term in the Lagrangian level, we
study the variation of Lagrangian with respect to independent variables, which
produces modified scalar field and Friedmann equations. Using dynamical
stability approach in different types of interaction models with two types of
scalar field potential, we explore this coupled framework. Implementing
detailed analysis, we can conclude our models can able to produce stable late-
time cosmic acceleration.

##  1 Introduction

Standard model of cosmology ($\Lambda$-CDM model) [1], mainly suffers from two
drawbacks, first one is the fine-tuning problem and second one is a cosmic-
coincidence problem. In this standard model of cosmology, $\Lambda$ represents
the cosmological constant and CDM denotes the cold-dark matter. Another
important downside of the $\Lambda$-CDM model from the observational
perspective is the discrepancy between the local measurement of present
observed value of Hubble’s constant and the value predicted from the Planck
experiment using $\Lambda$-CDM model [2]. These fundamental discrepancies
motivate us to study different kinds of cosmological models found in the non-
minimally coupled field-fluid sectors [3],[4],[5]. Based on these above
considerations, we build a theoretical framework for a coupled field-fluid
sector, where field sector is made of a non-canonical scalar field
($k$-essence sector [6],[7]) and the fluid sector is composed of pressure-less
dust. The non-minimal coupling term is introduced at the Lagrangian level. We
employ the variational approach [8] with respect to independent variables that
produce modified $k$-essence scalar field equations and the Friedmann
equations. Then we analyze this coupled field-fluid framework explicitly using
the dynamical system technique [9], considering two forms of the scalar field
potential, viz. inverse power-law type [3] and constant type [4]. After
examining these scenarios, both models can produce accelerating attractor
solutions and satisfy adiabatic sound speed conditions.

##  2 Theoretical Framework

Total action for this non-minimally coupled field-fluid sector [3] can be
written as,

$\displaystyle S$ $\displaystyle=$
$\displaystyle\int_{\Omega}d^{4}x\left[\sqrt{-g}\frac{R}{2\kappa^{2}}-\sqrt{-g}\rho(n,s)+J^{\mu}(\varphi_{,\mu}+s\theta_{,\mu}+\beta_{A}\alpha^{A}_{,\mu})-\sqrt{-g}{\mathcal{L}}(\phi,X)\right.$
$\displaystyle\left.-\sqrt{-g}f(n,s,\phi,X)\right],\quad\quad\mbox{(Here,
$\kappa^{2}=8\pi G$)}$

The first term corresponds to the action’s gravitational part, and the second
and third terms represent the action related to the relativistic fluid sector.
Fourth term implies the action for the $k$-essence scalar field. Finally, the
last term describes the action for the non-minimal coupling. Non-minimal
coupling term ($n,s,\phi,X$) depends on the functions of both sectors of field
($\phi,X$) and fluid ($n,s$). Varying the grand action respect to
$g_{\mu\nu}$, we get the total energy-momentum tensor for this coupled system
$T_{\mu\nu}^{\rm tot.}=T_{\mu\nu}^{(\phi)}+T_{\mu\nu}^{(M)}+T_{\mu\nu}^{({\rm
int})}$. Total energy-momentum tensor has been conserved, but the individual
components have not been conserved. Variation of above action with respect to
the independent variables produce the modified field equation as,
${\mathcal{L}}_{,\phi}+\nabla_{\mu}({\mathcal{L}}_{,X}\nabla^{\mu}\phi)+f_{,\phi}+\nabla_{\mu}(f_{,X}\nabla^{\mu}\phi)=0$.
In the context of a flat-FLRW metric ($ds^{2}=-dt^{2}+a(t)^{2}d{\bf x}^{2}$),
the above equation can be redundant for both potential and kinetic terms
dependent scalar field case [3] as,
$\left[\mathcal{L}_{,\phi}+f_{,\phi}\right]-3H\dot{\phi}\left[\mathcal{L}_{,X}+f_{,X}\right]+\dfrac{\partial{}}{\partial{}X}(P_{\rm
int}+f)(3H\dot{\phi})\,-\ddot{\phi}\left[(\mathcal{L}_{,X}+f_{,X})+2X(\mathcal{L}_{,XX}+f_{,XX})\right]-\dot{\phi}^{2}(\mathcal{L}_{,\phi
X}+f_{,\phi X})=0$. And for purely kinetic dependent scalar field [4] as,
$-3H\dot{\phi}\left[\mathcal{L}_{,X}+f_{,X}\right]+\dfrac{\partial{}}{\partial{}X}(P_{\rm
int}+f)(3H\dot{\phi})\,-\ddot{\phi}\left[(\mathcal{L}_{,X}+f_{,X})+2X(\mathcal{L}_{,XX}+f_{,XX})\right]=0$.

##  3 Results & Discussion

Utilizing some dimensionless variables, we recast field, fluid, and
interaction sectors in terms of them. Friedmann equations are also modified in
terms of these variables and acted like constraint equations of the dynamical
system. Depending on the total number of used independent variables dimension
of the phase space has been decided. Depending on the dimension of the phase
space, we have divided our analysis into two cases.

  * •

I. Algebraic Coupling with arbitrary scalar field potential: To study this
case, we can choose the form of interaction [3],
$f=\rho\alpha\left(\dfrac{\phi}{\kappa}\right)^{m}\beta X^{n}$
($\alpha,\beta,m,n$ are constant). Using linear stability approach, we get a
total of eight critical points from the phase space analysis, in which two
sets are stable and other two sets are showing saddle type nature. From
Evolutionary dynamics of this coupled system suggest that a late-time stable
accelerating phase can be achieved through this non-minimal coupling. Transfer
of energy from field-to-fluid and finally fluid-to-field can also be observed.
Total EOS parameter of this coupled sector saturates near $-1$ at late-time
era. At present epoch energy density of dark matter and dark energy are in
same order of magnitude, also observed from here.

(a) Phase space plot for $n=1,m=3,\delta=10$

(b) Evolution plot for the model parameters $n=1,m=3,\delta=10$

Figure 1: Phase space and evolution plots for Case-I (For details see [3])

  * •

II.Algebraic Coupling with constant scalar field potential: The form of
interaction for this case [4] has been chosen
$f=gV_{0}\rho^{q}X^{\beta}M^{-4q}$ (where, $q=-1,g,V_{0},\beta$ are constant).
Due to the absence of the potential term the dimension of the phase space is
reduced into 2-D. Utilizing the phase space analysis of dynamical system, we
have also found one stable critical for this type of system. Phase space is
constrained by the modified Friedmann equation, accelerating universe, and
sound speed condition. Evolution plot suggests that late-time stable
accelerating phase can be achieved and an energy transfer between field to
fluid sector has also been observed through this framework of non-minimal
coupling. Total EOS parameter of this coupled sector saturates near $-1$ at
late-time era.

(a) Phase space plot for
$A=1/2,B=1/3,q=-1,\alpha=1,g=1/2,\beta=1/3,\mathcal{M}=1$

(b) Evolution plot for the model parameters
$A=1/2,B=1/3,q=-1,\alpha=1,g=1/2,\beta=1/3,\mathcal{M}=1$

Figure 2: Phase space and evolution plots for Case-II (For details see[4])

## References

  * [1] Sean M. Carroll, William H. Press and Edwin L. Turner  In _Annual Review of Astronomy and Astrophysics_ 30, 1992, pp. 499–542  DOI: 10.1146/annurev.aa.30.090192.002435
  * [2] Eleonora Di Valentino et al.  In _Class. Quant. Grav._ 38.15, 2021, pp. 153001  DOI: 10.1088/1361-6382/ac086d
  * [3] Anirban Chatterjee, Saddam Hussain and Kaushik Bhattacharya  In _Phys. Rev. D_ 104.10, 2021, pp. 103505  DOI: 10.1103/PhysRevD.104.103505
  * [4] Saddam Hussain, Anirban Chatterjee and Kaushik Bhattacharya  In _Universe_ 9.2, 2023, pp. 65  DOI: 10.3390/universe9020065
  * [5] Kaushik Bhattacharya, Anirban Chatterjee and Saddam Hussain  In _Eur. Phys. J. C_ 83.6, 2023, pp. 488  DOI: 10.1140/epjc/s10052-023-11666-w
  * [6] C. Armendariz-Picon, T. Damour and Viatcheslav F. Mukhanov  In _Phys. Lett. B_ 458, 1999, pp. 209–218  DOI: 10.1016/S0370-2693(99)00603-6
  * [7] C. Armendariz-Picon, Viatcheslav F. Mukhanov and Paul J. Steinhardt  In _Phys. Rev. D_ 63, 2001, pp. 103510  DOI: 10.1103/PhysRevD.63.103510
  * [8] J. David Brown  In _Class. Quant. Grav._ 10, 1993, pp. 1579–1606  DOI: 10.1088/0264-9381/10/8/017
  * [9] Sebastian Bahamonde et al.  In _Phys. Rept._ 775-777, 2018, pp. 1–122  DOI: 10.1016/j.physrep.2018.09.001