The ubiquity of black holes in modern physics

Jorge V. Rocha

Departamento de Matemática, ISCTE – Instituto Universitário de Lisboa,

Avenida das Forças Armadas, 1649-026 Lisboa, Portugal

and

CENTRA, Instituto Superior Técnico – IST, Universidade de Lisboa – UL,

Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal

<EMAIL_ADDRESS>
This is a translation of an article written originally in Portuguese for the
journal Gazeta de Física, in a special edition celebrating the 2020 Nobel
prize in physics. The text targets a broad audience and focuses on the key
ideas and developments in an entirely non-technical fashion, requiring from
the reader only a keen interest in theoretical physics. The aim is to explain
in an accessible way —employing only basic and intuitive concepts— the huge
influence black holes have had in modern theoretical physics. Among the
various topics covered, string theory and the AdS/CFT correspondence, extra
dimensions, the quark-gluon plasma and holographic superconductors are
highlighted.

###### Contents

  1. 1 The irresistible attraction of black holes Introduction
  2. 2 Gravitating strings  String theory and general relativity
  3. 3 Strings wear black  Black holes in string theory
    1. 3.1 A curse becomes a blessing Extra dimensions
    2. 3.2 More dimensions makes for more storage Black holes with extra dimensions
    3. 3.3 Radiation from where it was least expected Black hole thermodynamics
  4. 4 The rise of holography The AdS/CFT correspondence
    1. 4.1 Deconfining with black holes Black holes and the quark-gluon plasma
    2. 4.2 Black holes offer no resistance Superconductivity from holography
  5. 5 In search of new horizons Conclusion

O sonho é ver as formas invisíveis
Da distância imprecisa, e, com sensíveis
Movimentos da esp’rança e da vontade,
Buscar na linha fria do horizonte
A árvore, a praia, a flor, a ave, a fonte –
Os beijos merecidos da Verdade.

Fernando Pessoa, from the poem “Horizonte” in “Mensagem”

##  1 The irresistible attraction of black holes
Introduction

The most recent Nobel prize in physics was awarded in October of 2020 jointly
to Roger Penrose, for the theoretical discovery of the inevitability of black
holes, and to Reinhard Genzel and Andrea Ghez, for the observational
confirmation of a supermassive black hole located at the center of our own
galaxy [1].

Putting events in perspective, it should be noted that this recognition was
bestowed more than one hundred years after the discovery of the first
nontrivial solution of general relativity, corresponding to a static black
hole in isolation. It also arrived more than 50 years after Penrose published
the results that earned him the Nobel prize! Even the genesis of the term
“black hole” dates back to that golden era of general relativity [2]. However,
in the last two decades black holes have shined under the spotlight.

Several factors contributed to this phenomenon. Among them, one must first
highlight the long-awaited detection of gravitational waves by the LIGO and
Virgo collaborations in 2015 [3], which brought along with it another type of
waves —those of excitement!—, and which was also awarded the Nobel prize in
2017. Secondly, the obtention of the first image of a black hole [4] also
stands out as a milestone. Both of these occasions had an enormous impact in
the media, which reflects its importance —much like the confirmation of the
supermassive black hole at the center of the Milky Way.

Black holes are extreme deformations of space and time, so drastic that they
cause the appearance of what is called an event horizon. This horizon is an
imaginary surface that encloses a region of spacetime from within which
nothing can escape, not even light.

Having in mind the definition above, the astrophysical relevance of black
holes in the cosmos is quite obvious. A lot more can be said about that topic,
but it is not the main focus of this article. Much harder to understand is the
importance of black holes for other subjects in physics, such as high energy
physics or condensed matter. Yet, these intriguing objects play a central role
in recent theoretical developments in multiple fields of modern physics. One
might rightfully say that the black hole’s irresistible attraction congregated
around it many branches of physics that are apparently unrelated.

The rest of this article aims at giving a flavor of the fascinating
connections between the science of black holes and other areas of physics.
Namely, we will touch upon topics like extra dimensions, the quark-gluon
plasma, or superconductivity, and their respective relations with black holes.
All these elements find a place in the context of string theory, albeit the
links between them are often far from being obvious. What allowed us to
realize such connections exist? The main advancement that should be held
accountable for this progress was a theoretical development of the end of the
twentieth century, which was equally predominant in the recent ascent of black
holes, known under the name of “AdS/CFT correspondence”, or more simply
“holography”, in academic jargon. This field of scientific knowledge has grown
tremendously, and it has become an independent and prominent subject of study.
Nevertheless, it has its origins also in the context of string theory, to
which we turn to next.

Before engaging with the subject, a brief note about the bibliography is in
order. Since this article is not intended as a comprehensive review, the
reference list is far from being complete, and many relevant works have been
undeservingly left out. We direct the interested reader to the books [5, 6]
and to the review articles [10, 12, 18, 25, 26] for further details.

##  2 Gravitating strings
String theory and general relativity

String theory had its origins in the end of the ’60s. Curiously, it was
initially proposed as a potential candidate to describe the strong
interaction, which appeared at the time as the greatest mystery in particle
physics [5]. Meanwhile, as years passed by, it became clear that quantum
chromodynamics, based on a quantum field theory framework —and in that respect
similar to the theory of electroweak interactions, already understood by that
time—, could describe correctly the strong interactions. But string theory was
not immediately abandoned, since it showed other virtues…

String theory is built over the simple and appealing idea that elementary
particles and the forces that mediate them are nothing but different
vibrational modes of sub-microscopic unidimensional objects [5, 6]. In
essence, the same happens with a violin string, which can produce several
notes depending on how the string is allowed to vibrate, although the
characteristic scales are completely distinct: the fundamental objects of
string theory typically have sizes of the order of the Planck length, which is
the scale at which gravitational, quantum and relativistic effects all
contribute with equal relevance. To have an idea of the enormous disparity of
scales, the proportion is roughly the same as the size of a proton relative to
the extent of the Milky Way!

What, then, has string theory to offer that quantum chromodynamics hadn’t
solved yet? Besides its built-in ability to generate a multitude of particles
from a single fundamental constituent, there is (at least) one other excellent
reason to take such a theory seriously: it automatically incorporates the
unification of all known forces of nature.

Let us contrast these attributes with those of the standard model of particle
physics, formulated in the language of quantum field theories. The standard
model is the upshot of more than 100 years of studies and offers a deep
understanding of the behavior of elementary particles and their quantum
interactions mediated by the electromagnetic, weak or strong forces.
Nevertheless, this formalism embarrassingly leaves out the only remaining
known force in nature: gravitation.

Just like photons (“particles of light”) can be understood as the mediators of
the electromagnetic field, the gravitational field also has its own mediators:
the gravitons. However, the methods used to “quantize” the electromagnetic,
weak and strong interactions hopelessly fail when applied to the gravitational
field. This is where string theory comes to the rescue. It turns out that the
vibrational modes of fundamental strings reproduce not only the properties of
the particles already included in the standard model, but also feature a
particle with the correct behavior to play the role of the graviton. Moreover,
the Einstein equations —which govern all of general relativity— magically
emerge from string theory!

Hence, string theory accomplishes the long sought-after unification of
fundamental forces. This feat is so much more incredible because, in the
process, it provides a formalism to consistently tackle the gravitational
interaction under the rules of quantum mechanics. String theory is therefore a
theory of quantum gravity, something that Albert Einstein himself searched for
for decades, unfortunately and uncharacteristically, without being successful.

##  3 Strings wear black
Black holes in string theory

Since gravitation is encompassed by string theory, it is not surprising that
black holes also make an appearance in its realm.

Astrophysical black holes are formed when a massive body is crushed —under the
action of gravity, and even opposing other forces— into a sufficiently small
region. Let us imagine that we take a ball and start compressing it in all
directions equally. The critical value of the ball’s radius for which a
horizon appears is directly proportional to the mass of the sphere. For a ball
with the mass of the Sun, this critical value, known as the Schwarzschild
radius, is about 3 km. In other words, if the Sun were reduced to slightly
less than the size of the Halley comet, it would become a black hole.

What is then the situation with strings? The mass of a string grows (linearly)
with its length, in such a way that each additional vibrational mode increases
the associated mass. A simple calculation based on “random walks” shows that a
sufficiently excited string typically has a smaller size than its own
Schwarzschild radius. Such a configuration should naturally originate a black
hole.111This argument ignores interactions between strings. Nevertheless, this
effect tends to further compress the structure, so it does not invalidate the
reasoning. This is the key idea that was expressed in the correspondence
principle between black holes and strings, during the ’90 [7, 8].

Formally, a black hole in string theory can be considered as a solution of the
equations that govern the several fields involved, while featuring a horizon.
We stress the word “several”, since string theory accommodates many other
fields that frequently interact, in addition to the gravitational field. As a
consequence, a black hole is not exclusively determined by the corresponding
gravitational field — it might have multiple associated charges. A simple
example is helpful to support this claim: in the context of Einstein-Maxwell
theory an electrically charged (and static) black hole is more compact than a
neutral black hole with the same mass.

The previous paragraph suggests that there is a wide variety of black hole
solutions in string theory. Yet, the framework has a structural characteristic
that raises this multiplicity to a whole new level: basic consistency of the
formalism demands spacetime to be ten dimensional. This allows an even greater
multitude of black holes in string theory, as we will see in the next section.
For now, we shall content ourselves with noting a common trace shared by black
holes in string theory: they can be infinitely extended in some directions
[9]. In such cases, they go under the name of black branes222The term “brane”
stems from the word “membrane.”.

###  3.1 A curse becomes a blessing
Extra dimensions

At first sight, the extra dimensions required by string theory seem to be
inconvenient. To make contact with reality, all the additional dimensions have
to be somehow hidden from our perception. The ways to achieve this can be
classified into two big categories: compactification models and braneworld
models. Each of these methods deserves a whole dedicated article and we will
not delve much into none of them. Nevertheless, it is worth mentioning the key
ideas on which they are based.

In compactification models the extra dimensions are curled up in sub-
microscopic spaces. An illustrative analogy can be made with the help of an
ant moving along the exterior surface of a hose: the insect can choose to move
in any of the infinite possible directions, including preserving the alignment
with the overall direction of the tube, or transversally (in which case it
will not make much progress); but if we observe the hose from far away, we
loose the notion of its thickness and it will be perceived as a one-
dimensional object that can only be traversed in one direction. The existence
of many possible viable ways to compactify space is a hallmark of these
methods.

Figure 1: A tube with its bidimensional surface (left) looks like a zero-
thickness string when observed from sufficiently far away (right).

The idea behind brane-world models is completely different. In those setups
the constraints on the size of the extra dimensions are not so tight, but our
physical reality is restricted to just three of the available spacial
dimensions. The possibility that the dynamics of the brane-world in which we
live could be related to the cosmological evolution of our universe is one of
the most appealing aspects of these models.

In any case, extra dimensions have an interesting virtue: they greatly enlarge
the configuration space. And this gives rise to an associated increase in the
space of solutions, as we discuss next.

###  3.2 More dimensions makes for more storage
Black holes with extra dimensions

In spite of being fascinating, black holes in general relativity are, with its
presumed four dimensions, the simplest objects in the universe. In the absence
of substancial matter in its vicinity or of perturbations caused, for
instance, by other nearby black holes —as was the case of the first detections
from the LIGO-Virgo collaboration— they are completely characterized by just
two numbers: their mass and angular momentum. This claim is backed by certain
uniqueness theorems [10], and therefore it is an inevitable conclusion… Unless
the hypotheses of these theorems are evaded.

One such hypothesis concerns the number of spacetime dimensions. Namely, four
dimensions are assumed. But, as we saw, string theory requires extra
dimensions and this offers more possibilities, including the already mentioned
existence of several black brane solutions. Yet, if we (theoretically) look
for black holes localized in space, what do we find?

Curiously, the uniqueness theorems are not applicable in more than four
spacetime dimensions. This was explicitly demonstrated when, in 2001, the
first black ring solution of Einstein’s gravity theory in five dimensions was
presented [11]. Since then many other solutions —illustrated in figure 2— have
been discovered in 5D or higher dimensions [12].

Figure 2: Some of the known black holes in five dimensions, displaying
distinct topologies of the event horizon. One of the four spatial dimensions
is suppressed for illustration purposes. The color coding was chosen so that
disconnected horizons can be easily distinguished, and has no particular
meaning.

###  3.3 Radiation from where it was least expected
Black hole thermodynamics

An important aspect of black holes is that they have an associated
temperature, which is a surprising statement. It is surprising because it
implies that it must radiate but, according to the classical definition of a
black hole, nothing —not even light— can escape from inside a black hole.

The apparent contradiction in the previous paragraph can only be clarified
within the framework of quantum gravity. Perhaps the most intuitive way to
understand this phenomenon is to recall that quantum fluctuations can
momentarily cause particle-antiparticle pairs to randomly pop up. When this
occurs close to a black hole, it might happen that one of the particles falls
through the event horizon, while the other escapes to infinity (see figure 3).
In order to conserve the total amount of energy in the system, the absorbed
particle must carry with it some negative energy. The net result is that the
black hole emits radiation and looses mass in the process.

Figure 3: Heuristic illustration of the Hawking effect. Every so often,
quantum fluctuations spontaneously create a particle-antiparticle pair. When
this occurs in a black hole neighborhood it can happen that one of the
particles (carrying negative energy) falls through the horizon, while the
other one escapes to infinity. In the process, the mass of the black hole is
reduced.

This heuristic explanation for a black hole’s quantum emissivity is firmly
supported by a rigorous semiclassical calculation performed by Stephen Hawking
in 1975 [13]. That analysis also revealed that the radiation emitted by a
black hole —the Hawking radiation— has a characteristic blackbody spectrum,
with a well defined temperature. This temperature is related with the mass of
the black hole, with this relation usually being an inverse
proportionality333Further ahead we will consider black holes living in other
kinds of spaces, for which this relation is modified..

Historically, the path leading to this discovery was a bit less
straightforward. In the first half of the ’70s it became apparent that
suggestive similarities exist between the laws that govern global properties
of black holes and the laws of thermodynamics [14]. This analogy can be
promoted to a quantitative agreement if we are willing to assign the Hawking
temperature to black holes, in addition to a corresponding entropy, which was
identified by Jacob Bekenstein [15]. The correct entropy is proportional to
the area of the event horizon. This is another curious feature of black holes
(actually, of gravitational systems) —usually the entropy grows with the
volume of the object, instead of its surface area.

The assignment of an entropy to black holes raises an obvious question. In
statistical mechanics, entropy provides a measure of the uncertainty about the
macroscopic state of a system, simply because there exist several possible
microstates compatible with the same course-grained description. Then, what
are the microstates of a black hole, accounting for its entropy? General
relativity does not seem to offer any answer to this question. But a
resolution can be found in the context of string theory. In fact, we saw in
section 3 that, within this framework, a black hole can be described as a
collection of highly-excited strings. What we did not mention before —but is
equally important for portraying a black brane— is that there are other
extended objects in string theory. This refers to the colloquially known
D-branes [16], which, among other aspects, are entities on which the endpoints
of fundamental strings can terminate. The possibility of interpreting a black
hole as a multitude of D-brane configurations connected by strings manifestly
offers many more degrees of freedom than a bare spacetime geometry, which is
the only viable description in general relativity. The correct identification
of the entropy of black holes through the counting of such microstates444The
microstate counting that reproduces the entropy of a black hole has been
achieved only for certain classes of black holes with special properties that
make the calculation feasible. remains until today as one of the greatest
successes of string theory [17].

##  4 The rise of holography
The AdS/CFT correspondence

It is impossible to talk about the successes of string theory without
mentioning its most impactful offspring, which is certainly one of its
pinnacles: the AdS/CFT correspondence.555Many excellent references devoted to
the AdS/CFT correspondence can be found in the literature. The review article
[18] offers a very concise, clear and non-technical exposition.

The AdS/CFT correspondence was a remarkable development in the realm of string
theory in the late ’90s, and it all began with an incredible —but well-
supported— proposal by Juan Maldacena [19]. This surprising correspondence
postulates the full equivalence between two apparently unrelated theories! In
such a case, the two theories are said to be dual to each other. One of the
protagonists is a quantum gravity theory —one that can also be simplified to a
classical theory of gravity in a certain limit— performing in a very peculiar
stage: anti-de Sitter space, or AdS for short, about which we will have more
to say later. The other actor is a quantum field theory (similar to quantum
chromodynamics) in which gravitation is simply absent —it was not even invited
to the party! In the original studies this theory came equipped with a high
degree of symmetry. In technical jargon, it is called a conformal field
theory, from which the acronym CFT is derived. Nevertheless, nowadays we know
that there are means of breaking this conformal symmetry in such a way as to
obtain quantum field theories better adapted to describe nature.

Initially, the amazing duality put forward by Maldacena had a somewhat
abstract character. But in a matter of a few months the correspondence was
formulated in a precise fashion [20, 21], giving it the status of an extremely
useful theoretical tool, with enormous computational potential. Despite all
this, the AdS/CFT correspondence still remains a conjecture: a rigorous proof
of its veracity has proved hard to accomplish, but one should keep in mind
that the evidence in its favor is overwhelming, both in quality as in
quantity.

It is not the aim of this article to explain the many reasons behind our firm
belief in the validity of this duality. To that end, several first-rate
reviews on the subject already exist. Instead, we will content ourselves in
highlighting some of its main properties and virtues for the remainder of the
paper.

Let us start by tackling the most pressing question: “How is it possible that
two such different theories can be equivalent to each other?” One of the most
striking aspects about AdS/CFT that contributes to, at least, not reject this
proposal immediately is that the two theories are not formulated in the same
physical space; they do not even live in spaces with the same number of
dimensions! The gravitational theory possesses more dimensions, and one of
them is associated with the energy scale in the dual theory. The conformal
symmetry of the field theory translates into the requirement that the ambient
geometry for the gravitational theory is also highly symmetrical, but with one
particularity: the curvature is negative (and constant throughout spacetime).

The feature just mentioned defines AdS space.666An example of an object whose
surface has negative curvature, and approximately constant, is a saddle. This
should be contrasted with a spherical surface, which also has constant
curvature (but in that case it is positive). This geometry has a bizarre
characteristic: although it is an unlimited space, light rays propagate out to
infinity (and back) in a finite time. For all practical purposes, AdS behaves
like a finite box. In a certain sense, the CFT can be thought of as living on
the boundary of AdS. If we accept that the two theories are indeed equivalent,
then every process occurring in the gravitational side must have a dual
description in a space with one less dimension. Therefore, this is a
holographic duality, one which explicitly implements the holographic principle
enunciated by Gerard ’t Hooft a few years before [22]. Holography, which had
been experimentally discovered more than 50 years earlier, thus became the
center of the attention for hoards of theoretical physicists.

As we have alluded to above, the AdS/CFT conjecture posits the existence of an
exact dictionary relating concepts and quantities on both sides of the
equivalence. A significant amount of the efforts conducted in this area has
been devoted precisely to putting together such a dictionary. One of the main
items in this mapping has to do with coupling constants, which generically
determine the strength of the interactions between the fundamental elements of
each theory. It turns out that, in AdS/CFT, the coupling constants are
inversely proportional to each other. This implies that when one of the sides
is strongly coupled, the dual theory is weakly coupled, and vice versa. Hence,
AdS/CFT is also an example of a strong-weak correspondence. This aspect is
probably the greatest obstacle standing in the way of a mathematical proof of
the equivalence. However, it is also its greatest virtue: if we face a
difficult problem in a strongly coupled regime in one side of the duality, we
can map it into an equivalent problem in a weakly coupled context, for which
simple perturbative methods can be employed to make progress.

###  4.1 Deconfining with black holes
Black holes and the quark-gluon plasma

777This title may, or may not, be inspired by the covid-19 pandemics.

In the vast conceptual scenario of the AdS/CFT correspondence, black holes
play a crucial role, and they fit quite naturally in the gravitational side of
the duality. We certainly can consider black holes in AdS and we know how to
describe them. What is, then, the holographic representation of a black hole?

To answer this question it is helpful to recall one of the lessons from
section 3.3: black holes have an associated temperature. For the relevant AdS
black holes, this temperature increases as their mass grows. Typically —but
not always— we do not have the option of populating the dual field theory with
black holes. Nevertheless, it includes another kind of states with a well-
defined temperature: a gas formed out of elementary particles in thermal
equilibrium. The relation we seek can now be uncovered. A black hole in AdS
with a given Hawking temperature is the holographic dual of such a gas at
exactly the same temperature. We thus conclude that by inserting a black hole
in AdS space we are effectively warming up the dual theory, and the bigger the
black hole is, the hotter the corresponding state will be (see figure
4).888Incidentally, the fact that the ambient space containing the black hole
behaves asymptotically like AdS is crucial for the agreement between the
entropies computed from the field theory side and from the gravitational dual.

Figure 4: Representation of AdS space as a finite box (and highly symmetric).
The dual field theory may be considered, in a certain sense, to live on the
boundary of this box. In the absence of any matter or black holes, the
holographic dual to which it is associated is in a cold state (left).
Inserting a black hole in AdS increases the temperature of the thermal state
to which it corresponds (right).

One of the most impressive checks on the validity of the AdS/CFT
correspondence concerns the identification between phase transitions in the
two dual theories. In fact, an isolated black hole in AdS is not in thermal
equilibrium, since it emits Hawking radiation (thereby shrinking ever so
slightly). Naturally, what occurs is that the full system evolves until the
black hole and the gas of surrounding particles remain at the same
temperature, in a steady state. Naively, one might think that such a
configuration at any desired temperature could exist. However, this is not the
case. Below a certain temperature (related to the curvature of AdS) the
thermodynamically preferred state simply does not include a black hole, only a
gas of particles at that temperature.This Hawking-Page transition, as it
became known, is yet another surprise that AdS space had in store for us, one
that had been discovered back in the ’80s [23].

How is this phase transition reproduced in the dual quantum field theory? In
that framework, the only thing we have at our disposal are the fundamental
constituents of the theory. It is helpful to borrow some intuition from
quantum chromodynamics, where the elementary particles are identified as
quarks and gluons. However, those degrees of freedom become apparent only at
high temperatures, giving rise to the quark-gluon plasma. At low temperatures
the elementary particles are confined, without ever making a solo appearance.
The different possible combinations produce composites which we call hadrons,
such as protons and neutrons. Hence, we also find a phase transition in this
context —one that has been dubbed the confinement-deconfinement transition.
The fact that such a phase transition actually occurs in the holographic dual
to AdS, and in such a way that the entropies computed from both sides of the
correspondence agree, was uncovered by Edward Witten in a seminal article that
kickstarted AdS/CFT [24].

There exists an intuitive argument that provides a graphical interpretation of
this identification between the Hawking-Page transition and the confinement-
deconfinement transition. It is based on the holographic description of the
interaction between quark-antiquark pairs —forming the so-called mesons—,
which can be thought of as the endpoints of strings that “hang” from the AdS
boundary. The fact that the strings have an intrinsic tension explains why the
quarks are mutually attracted, and the restitutive force grows with the
distance between the quarks. This description is appropriate when the system
is at low temperatures. According to what was discussed previously, this
occurs when there is no black hole in the interior of AdS, corresponding to
the left panel in figure 5.999In fact, for technical reasons the space that
must be considered is not simply empty AdS, but instead a certain modification
of it. The relevant aspect is that this altered space has exactly the same
asymptotic behavior as AdS with a black hole, but without featuring any event
horizon [25]. As we increase the temperature by inserting a black hole in AdS,
as illustrated in the right panel of figure 5, the string that connects the
quark-antiquark pair falls through the event horizon if it becomes too long.
Consequently, the string snaps and the quarks become free.

Figure 5: The confinement-deconfinement transition from the holographic point
of view, focusing on quark-antiquark interactions. The quarks, constrained to
move on the boundary of AdS, are connected by strings that fall into the
interior of the dual space. In the absence of a horizon, the restitutive force
that attracts the pair of quarks grows as the particles move apart and the
string stretches. This low-temperature phase is illustrated in the left panel.
In a high temperature phase, corresponding to the presence of a black hole in
AdS, the strings can break up as shown in the right-hand panel. As a
consequence, the quarks can then move freely, i.e., they cease to be confined.

###  4.2 Black holes offer no resistance
Superconductivity from holography

Another application of AdS/CFT in which black holes play a central role is
concerned with the so-called holographic superconductors. An important phase
transition also occurs in this setting —one that can be understood in much the
same way as what was described in section 4.1.

In order to somehow capture the essence of superconductors, we must introduce
electric fields. What kind of modifications does figure 5 suffer when we
consider AdS black holes that are electrically charged? Keeping this purpose
in mind, adding charge to the black hole has a significant effect only if
there exists some other field (or its quantum description in terms of
particles) to interact with, through their combined electrodynamics. In this
context, the simplest possible additional element is provided by an
electrically charged scalar field.

A detailed discussion about holographic superconductors is a somewhat
technical subject, but the key idea can be understood with minimal use of
advanced physics [26]. The electric field of the black hole can spontaneously
create pairs of particles with opposite charges, by virtue of the well-known
Schwinger effect. The frequency of occurrence of this quantum phenomenon
increases with the intensity of the electric field, so it is predominant near
the horizon. But the effect is also more relevant when the black hole’s
temperature is lower. The reason behind this is also connected with the
strength of the electric field: colder black holes are smaller, and in that
case the horizon sits closer to the origin of the electric field. In any case,
since the Schwinger particles have opposite charges, one of them is attracted
to the black hole while the other is repelled. Given that AdS behaves like a
finite box, the repelled particle cannot move away indefinitely. Instead, it
will wander until it finds a stable position. The repetition of this sequence
causes the accumulation of a cloud of charged scalar particles in the black
hole’s neighborhood (see left panel in figure 6).

The condensation of a scalar cloud around a black hole happens only when the
latter is sufficiently cold. At higher temperatures the event horizon covers a
larger volume and the situation changes. On the one hand, the intensity of the
electric field at the surface of the black hole is decreased. On the other
hand, there is less room left in the black hole exterior and at a certain
point the characteristic Compton wavelength of the scalar field no longer fits
there, in contrast with what happened at lower temperatures (see right hand
panel of figure 6).

The charged scalar cloud that forms at lower temperatures is the holographic
representation of the condensate of electron pairs with opposite spins, which
are responsible for the phenomenon of superconductivity —the Cooper pairs.
Their presence indicates that the conductivity in such a phase is amplified
and this prediction is indeed backed up by computations performed in the
gravitational dual theory. In the context of AdS/CFT, both the expectation
value of the condensate and the conductivity can be extracted explicitly as a
function of the temperature of the system. The upshot is that below a certain
critical temperature, the condensate acquires a non-vanishing expectation
value, with a qualitative behavior similar to that experimentally observed in
real world superconductors. This comes hand-in-hand with a formally infinite
conductivity. Above the critical temperature the condensate disappears and the
holographic system displays the usual electric resistivity.

Figure 6: Dual description of the phase transition occurring in holographic
superconductors. At low temperatures (left) the event horizon of an
electrically charged black hole sits far away from the boundary of AdS. This
allows the formation of a cloud of charged scalar field, which is the dual
representation of the condensate responsible for superconductivity. At high
temperatures (right) there is less room between the horizon and the AdS
boundary, and the scalar cloud does not fit in that region. Without the
presence of a condensate, the conductivity drops abruptly.

So far, holographic models like the one just described can reproduce the
behavior of real world superconductors only in a qualitatively correct manner.
Nonetheless, the ability to explain superconducting phase transitions using
black hole physics is remarkable. Even more so, if it is taken into account
that other more conventional methods are not applicable to superconductors
with high critical temperatures, usually. Such materials typically form in a
strongly coupled regime and, as discussed in the end of section 4, AdS/CFT is
a particularly well adapted tool to employ under those conditions.

##  5 In search of new horizons
Conclusion

The ubiquity of black holes in modern physics is unquestionable. The advent of
the AdS/CFT correspondence largely contributed to this state of affairs, as we
have tried to demonstrate.

It is not at all surprising that black holes play a central role in
theoretical physics. Being objects where essentially quantum mechanical
phenomena can compete with purely classical gravitational effects, they form
the ideal theoretical laboratory to unravel the mysteries of quantum gravity —
the current chimera in physics.

On the other hand, the influence that black holes have had on fields so
loosely related, such as plasma physics or condensed matter, was, at least,
unexpected.

Many other interesting and relevant subjects were not covered in this article,
and the topics discussed represent just a sample of the extent to which the
study of black holes contributed to broaden the horizons of scientific
knowledge.

Thus, we owe much of the recent advances in theoretical physics to black
holes. But who could have guessed that precisely these intriguing objects
—from where not even light can escape— would enlighten this endeavor of human
civilization?

### Acknowledgements

I am grateful to Antonia Frassino, Carlos Herdeiro and Roberto Emparan for
helpful comments on the manuscript. I also thank Carlos Herdeiro and José
Lemos, as editors of Gazeta de Física, for the kind invitation to write up the
article that served as the basis for this translation. The author acknowledges
financial support from Fundação para a Ciência e a Tecnologia (FCT) through
projects CERN/FIS-PAR/0023/2019 and UIDB/00099/2020.

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# UVIT view of NGC 5291: Ongoing star formation in tidal dwarf galaxies at
$\sim$ 0.35 kpc resolution

Rakhi R 1, Geethika Santhosh 1, Prajwel Joseph 2,3, Koshy George 4, Smitha
Subramanian 2, Indulekha Kavila 5, J. Postma 6, Pierre-Alain Duc 7, Patrick
Côté 8, Luca Cortese 9, S. K. Ghosh 10, Annapurni Subramaniam 2, Shyam Tandon
11, John Hutchings 8, P Samuel Wesley 3, Aditya Bharadwaj 3, Neeran Niroula 3

1 Department of Physics, NSS College, Pandalam, Kerala 689 501, India
2 Indian Institute of Astrophysics, Bangalore 560034, India
3 Department of Physics and Electronics, CHRIST (Deemed to be University),
Bangalore 560029, India
4 Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679,
Munich, Germany
5 School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam,
Kerala 686560 India
6 University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada
7 Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR
7550, F-67000 Strasbourg, France
8 Herzberg Astronomy and Astrophysics Research Centre, National Research
Council of Canada, 5071 W. Saanich Road, Victoria, BC, V9E 2E7, Canada
9 International Centre for Radio Astronomy Research (ICRAR), University of
Western Australia, Crawley, WA 6009, Australia
10 Tata Institute of Fundamental Research, Colaba, Mumbai 400005, India
11 Inter-University Centre for Astronomy and Astrophysics, PostBag 4,
Ganeshkhind, Pune-411007, India
E-mail<EMAIL_ADDRESS>
###### Abstract

NGC 5291, an early-type galaxy surrounded by a giant HI ring, is believed to
be formed from collision with another galaxy. Several star forming complexes
and tidal dwarf galaxies are distributed along the collisional ring which are
sites of star formation in environments where extreme dynamical effects are
involved. Dynamical effects can affect the star formation properties and the
spatial distribution of star forming complexes along the tidal features. To
study and quantify the star formation activity in the main body and in the
ring structure of the NGC 5291 system, we use high spatial resolution FUV and
NUV imaging observations from the Ultraviolet Imaging Telescope onboard
AstroSat. A total of 57 star-forming knots are identified to be part of this
interacting system out of which 12 are new detections (star forming complexes
that lie inside the HI contour) compared to the previous measurements from
lower resolution UV imaging. We estimate the attenuation in UV for each of the
resolved star-forming knots using the UV spectral slope $\beta$, derived from
the $FUV-NUV$ colour. Using the extinction corrected UV fluxes, we derive the
star formation rate of the resolved star forming complexes. The extinction
corrected total star formation rate of this system is estimated as 1.75 $\pm$
0.04 $M_{\odot}/yr$. The comparison with dwarf galaxy populations (BCD, Sm and
dIm galaxies) in the nearby Universe shows that many of the knots in the NGC
5291 system have SFR values comparable to the SFR of BCD galaxies.

###### keywords:

galaxies: star formation – galaxies: interactions – galaxies: dwarf –
galaxies: formation – ultraviolet: galaxies-stars: formation

††pubyear: 2021††pagerange: UVIT view of NGC 5291: Ongoing star formation in
tidal dwarf galaxies at $\sim$ 0.35 kpc resolution–LABEL:lastpage

##  1 Introduction

Study of galaxy mergers and interactions are of great importance in advancing
our current understanding of galaxy formation and evolution (Conselice et al.,
2003; Pearson et al., 2019). In the hierarchical $\Lambda$ Cold Dark Matter
($\Lambda$CDM) clustering paradigm, large massive halos form and grow by the
merging or clustering of low mass halos. The hierarchical clustering model
predicts that massive galaxies must have undergone several merging activities
in the past. This leads to the possibility of dwarf galaxies being the primary
ingredients in the formation of the large galaxies we see in the nearby
universe (White & Rees, 1978; White & Frenk, 1991).

The local Universe is observed to have several interacting or merging galaxy
systems characterized by dust and gas-rich tidal tails, collisional rings and
tidal bridges (Buta & Crocker, 1993; Higdon, 1995; Sotnikova & Reshetnikov,
1998). Tidal dwarf galaxies (TDGs) are gravitationally bound systems of gas
and stars formed during interaction of galaxies and are kinematically
decoupled from the surrounding tidal debris. During close encounters between
gas-rich galaxies, neutral hydrogen gas (HI), stars and dust from the disks of
the galaxies can get pulled out by tidal forces/gravitational torques
(Bournaud, 2010) forming rings, tidal tails, bridges and plumes. star
formation takes place in the gas thrown out of the galaxies during tidal
interactions. Star forming knots or clumps are observed along the tidal
features (Struck, 1999) and the massive clumps are potential young TDG
candidates (Mirabel et al., 1992; Elmegreen et al., 1993; Alonso-Herrero et
al., 2000; Duc et al., 2004; Hancock et al., 2009; Duc, 2012). The most
massive TDGs in an interacting system may evolve to become self-bound dwarf
galaxies that may detach from the host system (Duc & Mirabel, 1999). Once
separated from their progenitors, they will closely resemble the independent
dwarf galaxy populations. Being pre-enriched these TDGs are more metal rich
than isolated dwarf galaxies of the same luminosity. This property of TDGs can
be used to identify these recycled dwarf galaxies and to investigate the
origin of their building material in the disk of their progenitors (Hunter et
al., 2000).

TDGs comprise of young stars, which are formed from the recent collapse of
ejected HI clouds as well as the older stellar population coming from the disk
of their parent galaxies. Duc & Mirabel (1999) studied the relative proportion
of both these populations using multi-wavelength observations of several
interacting systems in the nearby Universe. They proposed that TDGs are
divided into two categories. Category 1 consists of extremely young objects,
forming their first generation of stars (e.g. dwarfs around NGC 5291). These
have high star formation rates (SFR) similar to that of blue compact dwarf
(BCD) galaxies. Category 2 corresponds to galaxies dominated by the older
stellar population coming from the disk of their progenitors and these
galaxies resemble dwarf irregulars (e.g. NGC 2992) (Duc et al., 2000;
Bournaud, 2010).

Young, hot, massive and luminous O, B, A stars on the main sequence give out
immense amount of ultraviolet (UV) radiation and therefore regions of ongoing
star formation could appear bright in ultraviolet images. The ultraviolet
continuum is thus a direct tracer of recent star formation in galaxies ($\sim$
200 Myr) (Kennicutt & Evans, 2012). With the advent of UV missions capable of
providing deep and high resolution UV images of extragalactic systems, a
quantitative analysis of the star formation activity in star forming knots in
terms of the SFR is possible. Tidal dwarf galaxy formation is connected to
merging or interacting galaxies in the universe (Okazaki & Taniguchi, 2000).
TDGs with ongoing star formation are important structures to study the process
of star formation in the smallest mass systems (dwarf galaxies) also. NGC 5291
is an interacting galaxy system that lies in the western outskirts of the
cluster Abell 3574. The system comprises of an early-type galaxy NGC 5291
(morphological type: SA.0+ ) and a companion galaxy called "the Seashell"
(morphology: distorted edge-on spiral) interacting with it (Longmore et al.,
1979).

The system has extensions or tails, defined by knots, emerging from the
galaxy. Deep optical and spectroscopic studies of NGC 5291 pointed out that
the optical knots that extend to the north and south of the system may be
sites of recent star formation (Pedersen et al., 1978; Longmore et al., 1979).
21 cm radio observations, using the Very Large Array (VLA), revealed a giant
collisional HI ring structure connected to the NGC 5291 system which indicated
that the knots observed are indeed star forming complexes that may even be
young tidal dwarf galaxies (Malphrus et al., 1997; Bournaud et al., 2007). The
fragmented HI ring structure, which hosts numerous intergalactic HII regions
of the NGC 5291 system, is exceptional in itself because of its moderately
high metallicity $\left(8.4\leq 12+log(O/H)\leq 8.6\right)$ and the absence of
an old stellar population. This suggests that the dwarf galaxies observed in
the system are in fact young tidal dwarf galaxies formed from the pre-enriched
gas in the collisional/tidal debris (Duc & Mirabel, 1998).

Many studies of the NGC 5291 system in the ultraviolet have come up over the
past few decades consequent to observations using the Far Ultraviolet Space
Telescope (FAUST) (Bixler et al., 1984), the Hubble Space Telescope (HST) and
the Galaxy Evolution Explorer (GALEX) (Deharveng et al., 1994; Boquien et al.,
2007; Boquien et al., 2009; Fensch et al., 2019; Elmegreen et al., 2020).
Among these, GALEX is fully dedicated to observations in the ultraviolet
regime and is capable of providing wide field (1.2°) far ultraviolet (FUV) and
near ultraviolet (NUV) images with a spatial resolution of
4.2$\arcsec$/5.3$\arcsec$ (FUV/NUV) (Morrissey et al., 2007). Boquien et al.
(2007) presented a polychromatic view of NGC 5291 based on GALEX observations
together with archival H$\alpha$, 8 $\mu$m and HI data. They identified 29
star forming regions along the ring structure and determined their SFR. More
recently, Fensch et al. (2019), using HST data, studied massive star cluster
formation in the three TDGs (NGC 5291N, NGC 5291S and NGC 5291 SW) associated
with the NGC 5291 system.

Figure 1: colour composite image of the NGC 5291 system made using FUV (blue),
NUV (green) and DECaLS z band image (red). The dashed rectangle shows the
region of interest. (Field of View: 21.8 $\arcmin$ $\times$ 11.6 $\arcmin$)

In this paper, we present high resolution ultraviolet imaging observations (in
Far and Near UV bands, FUV: 1.4$\arcsec$ and NUV: 1.2$\arcsec$) of the NGC
5291 system using data from the Ultraviolet Imaging Telescope (UVIT) on board
AstroSat. The main aim of the paper is to identify and characterize the star
forming knots in the tidal tails and determine the star formation rates in
these knots at the best possible resolution, taking into account dust
attenuation of the ultraviolet spectrum. This paper is outlined as follows.
Section 2 of the paper describes data acquisition, data reduction, source
extraction and identification in detail. The results are discussed in Section
3 and conclusions are presented in Section 4.

Throughout the paper, magnitudes are computed in AB system (Oke & Gunn, 1983).
The value of the Hubble parameter $H_{0}$ used is 72 km s-1 Mpc-1, assuming
flat $\Lambda$CDM cosmology. For this value of $H_{0}$, the distance (D) to
NGC 5291 is 62 Mpc (Boquien et al., 2007) and 1" in the sky corresponds to
0.296 kpc at system rest frame.

##  2 Data & Analysis

Table 1:  NGC 5291 UVIT observations Channel | Filter Name |  $\lambda$mean (Å) |  $\Delta\lambda$ (Å) |  Integration time (s)
---|---|---|---|---
FUV | F148W | 1481 | 500 | 8242
NUV | N242W | 2418 | 785 | 8079

NGC 5291 (RA:206.852,Dec:-30.407)111https://ned.ipac.caltech.edu/ has been
observed (PI: K. George, proposal ID: G07_003) with Ultraviolet Imaging
Telescope (UVIT) on board AstroSat (Kumar et al., 2012). UVIT performs imaging
simultaneously in three channels: visible (320-550 nm), the near-ultraviolet
(NUV: 200-300 nm) and the far-ultraviolet (FUV : 130-180 nm). UVIT has a set
of filters mounted on a wheel to facilitate imaging in the NUV and FUV in
different narrow and broad wavelength bands. The field of view of UVIT is
28$\arcmin$ in diameter. UVIT has a resolution of $\sim$1.4$\arcsec$ in FUV
and $\sim$ 1.2$\arcsec$ in NUV. This implies that UVIT can resolve star
forming knots in NGC 5291 down to approximately 0.35 kpc at NUV and 0.41 kpc
at FUV.

###  2.1 Data

We use Level 1 (L1) UVIT data of NGC 5291. For the multiple orbit observations
of the target field NGC 5291, the filters used are NUV: N242W and FUV: F148W.
Details on the UVIT filter combinations and the performance parameters for the
individual filters are given in Tandon et al. (2017). We have reported the
filter details and the integration time of the UVIT observations of NGC 5291
in Table 1. A HI map of the galaxy, obtained with the VLA (Bournaud et al.,
2007) is used for identifying the relevant star-forming knots. To check
whether the detections are bonafide knots, we use the observations from the
Dark Energy Camera Legacy Survey (DECaLS) DR10 imaging data in three optical
filters (g, r, z) (Dey et al., 2019) 222https://www.legacysurvey. org/viewer.

###  2.2 Data Reduction

L1 data of NGC 5291 is reduced to Level 2 (L2) scientific images using CCDLAB
(Postma & Leahy, 2017, 2021). Using CCDLAB, UVIT data is corrected for fixed
pattern noise, distortion and drift, and flat fielded. The orbit-wise images
are aligned to a common frame before merging the data. The PSF of master NUV
and FUV images are optimized. Finally, the images are aligned with respect to
the sky coordinates using the automated WCS solver in CCDLAB (Postma & Leahy,
2020). The NUV and FUV images have 4096 $\times$ 4096 pixel array size where
one pixel corresponds to 0.416$\arcsec$.

The NUV and FUV images thus created are used for further analysis. Flux
calibration is done for NUV and FUV images using the zero point and unit
conversion factors given in Tandon et al. (2017) and updated in Tandon et al.
(2020).

##  3 NGC 5291 UV imaging

Fig. 1 shows the false-colour combined image of the NGC 5291 system created
from the UVIT FUV and NUV images (North is up and East is towards the left of
the image) overlaid with Legacy survey z band image . Here, FUV is given in
blue, NUV in green and DECaLS z band image is given in red. The interacting
galaxies NGC 5291 and the Seashell are located towards the center of the
image. As seen in Fig. 1, several UV bright knots extend towards the north,
south and south-west directions following the fragmented ring structure seen
in HI imaging data.

###  3.1 Source extraction

The sources from the FUV and NUV images are extracted using the photometry
package ProFound (Robotham et al., 2018). ProFound is capable of both source
identification and photometric extraction. It detects sources in noisy images,
then generates segmentation maps by identifying the pixels belonging to each
source, and measures statistics including flux, size, and ellipticity.
ProFound first detects pixels from the intensity map that are above a
threshold value and these pixels are allowed to grow or dilate freely until a
certain intensity limit is reached based on the set threshold. The dynamic
dilation will ensure close to total magnitudes regardless of the differing
PSFs. ProFound uses watershed algorithm for de-blending pixels that are above
the threshold value. The deblended collection of pixels that are above a
threshold is called a segment. This method of segmentation is unique as it
does not assume a fixed aperture for an object and the segment corresponding
to a source agrees with the underlying morphology of the source. After
segmentation, ProFound extracts the image data flux from each of the pixels
that are part of the segments.

ProFound was run on the slightly lower resolution FUV image. Along with the
FUV image, the sky and sky RMS values were given as inputs to the ProFound
function and it extracted 206 sources along with their flux, magnitude and
area for sources from the entire UVIT field of view. For NUV source
extraction, we provided the dilated FUV segmentation map created by ProFound
as an additional input to the function to make sure that the same source
position is used for both NUV and FUV.

The segmentation map obtained from ProFound, overlaid by HI contour, showing
the extend of each UV source is given in Fig. 2. ProFound assigns a unique
number called the segID for each segment of the map. Different colors in Fig.
2 corresponds to different segIDs. The circled regions correspond to the
galaxies, NGC 5291 and Seashell.

Figure 2: Segmentation map from ProFound overlaid by HI contour. The circled
regions correspond to the galaxies, NGC 5291 and Seashell.

###  3.2 Identification of star-forming knots

In order to identify the star-forming knots that are part of the NGC 5291
interacting system, we analysed the FUV-NUV colour distribution of all the
sources in the UVIT field of view with a signal to noise ratio (SNR) greater
than 5. The Gaussian fitted histogram of the UV colour (FUV-NUV) of these
sources is shown in Fig. 3. The mean ($\mu$), standard deviation ($\sigma$),
and FWHM of the best fit are 0.26 mag, 0.39 mag, and 0.93 mag respectively.

Figure 3: Distribution of FUV-NUV colour of all the sources above 5$\sigma$
detection threshold in both FUV and NUV

From this, we consider those 109 sources that lie within a 1$\sigma$ colour
range, for further analysis. Due to the lack of redshift information for the
knots, the sources that are part of the system are identified based on
location within the HI contour.

####  3.2.1 Sources lying within the HI contour

All the knots that fall within the HI contour are identified with the help of
SAOImageDS9 (Joye & Mandel, 2003). Out of the 109 sources that lie within
1$\sigma$ colour range, 64 sources lie inside the HI column density contour
and 45 sources lie outside (Fig. 2).

Figure 4: Distribution of areas (in kpc2) of the resolved knots: (a)
Uncontaminated regions (b) Possibly contaminated regions

####  3.2.2 Sources lying outside the HI contour

Among the 45 sources that lie outside the HI contour, some lie far away from
the NGC 5291 interacting system. Hence we consider only those knots which are
lying nearer to the HI contour for further analysis. For this, we consider the
sources that are lying within a circle, which is centered at the NGC
5291-central galaxy and has a radius roughly half the diameter of the
projected HI ring. We find that a total of 10 sources out of 45 lie within
this region.

In order to confirm that the selected sources (both inside as well as outside
the HI contour) are star-forming regions and to check for any possible
contamination, we make a comparison of these knots with DECaLS image of the
system. The star-forming knots appear blue in the DECaLS image and other knots
seem to be contaminated by foreground/background sources. Thus we further
eliminate a total of 17 sources (10 inside the HI contour and 7 outside the HI
contour) which are possibly foreground/background sources We finally have a
total of 57 star-forming (SF) knots (54 inside the HI contour and 3 outside
the HI contour) for the present study.

Fig. 4 depicts the distribution of UV clump sizes for the resolved knots. The
selected star forming knots of the NGC 5291 system (using FUV) are shown Fig.
5.

Figure 5: Selected star forming knots of the NGC 5291 system marked on FUV
image. The individual knots are labeled using numbers, and the sizes of these
labels represent the relative sizes of the knots. Annotated regions 1 to 57
are the knots.

##  4 Results

###  4.1 Comparison with previous UV observations

We first compare our high resolution UV image with the results from the
earlier UV mission GALEX, which has a resolution $\sim$ 4-5 arcsec. The 54
star forming regions of the NGC 5291 system that lie inside the HI contour
obtained with UVIT have been compared against GALEX. The study of the NGC 5291
system using GALEX reported 29 knots within the same region (Boquien et al.,
2007; Boquien et al., 2009). A comparison of the selected knots in the present
study to the knots in the GALEX study is shown in Fig. 6. We note that 12 of
the 54 UVIT knots selected within the HI contour are unreported in the GALEX-
based study. It is further observed that several of the knots which appeared
as a single entity in the GALEX images are well resolved by UVIT into two or
more knots (see Fig. 7).

Figure 6: Knots in the GALEX study (Boquien et al., 2007; Boquien et al.,
2009) overlaid on the scatter plot of selected knots in the present study. The
sizes of the markers for the knots represent their relative sizes.

Fig. 8 shows the distributions of fluxes (uncorrected for extinction) for the
knots in UVIT and GALEX (Boquien et al., 2009).

(a) UVIT

(b) GALEX

Figure 7: Comparison of NUV images for NGC 5291 taken with UVIT (top) and
GALEX (bottom). North is up and east is to the left. Figure 8: Comparison of
the flux values for the knots measured from UVIT and GALEX FUV imaging data.
(Boquien et al., 2009)

It is seen that the flux distribution for the knots in UVIT has moved to the
low flux values as compared to GALEX. This can be attributed to the improved
spatial resolution of UVIT in comparison with GALEX which enabled better
deblending of structures.

###  4.2 Slope of the UV continuum $\beta$ and extinction $A_{FUV}$

The interstellar medium within the star forming knots can contain significant
amount of dust. The UV radiation emitted by young massive O,B,A stars can get
attenuated by dust. Dust grains can scatter and absorb UV radiation and this
can greatly complicate the interpretation of the detected UV emission.
Determining the level of dust attenuation is crucial in accurately deriving
intrinsic UV luminosity and hence star formation rates. The slope of
ultraviolet continuum has been proposed as a powerful diagnostic of dust
attenuation in star-forming galaxies (Boquien et al., 2012; Overzier et al.,
2011). The UV continuum spectrum of star forming galaxies is characterised by
the spectral index $\beta$ where $f_{\lambda}\propto\lambda^{\beta}$ (Calzetti
et al., 1994) for $\lambda>1200$ Å, $f_{\lambda}$ (erg cm-2 s-1 Å-1) is the
flux density of the source. For the case of UVIT FUV and NUV passbands,

$\hskip 42.67912pt\beta_{UVIT}=1.88(m_{FUV}-m_{NUV})-2.0$ (1)

where $m_{FUV}$ and $m_{NUV}$ are the magnitudes in FUV and NUV respectively.

Meurer et al. (1999) (hereafter, M99) established a relationship between the
UV spectral slope $\beta$ and the ratio of far infrared (FIR) and UV fluxes
for a sample of starburst galaxies. This method relates the FIR and UV
radiation emitted from galaxies. It is considered to be a powerful tool in
recovering the UV radiation lost due to the dust, regardless of the geometry
of the dust.

We use the M99 relation for the starburst case to determine dust attenuation
from $\beta$ which is given as,

$\hskip 42.67912ptA_{FUV}=4.43+1.99\;\beta$ (2)

where $\beta$ is given by Eq. 1 for our case.

A histogram showing the slope of UV continuum $\beta$ for the selected knots
in the NGC 5291 system is presented in Fig. 9. The numerical value of $\beta$
ranges from -2.18 to -1.73.

Figure 9: Histogram of the values of the slope of the UV continuum $\beta$

Fig. 10 gives the spatial distribution of $A_{FUV}$ for the selected knots and
the value of $A_{FUV}$ ranges from 0.05 to 0.99.

Figure 10: Spatial distribution of dust attenuation $A_{FUV}$ of the selected
knots in the NGC 5291 system

###  4.3 Star formation rates of the knots

The measured FUV flux of the knots are corrected for extinction using the
$A_{FUV}$ values computed for each knot. Ultraviolet flux is a direct tracer
of ongoing star formation and the star formation rate (SFR) can be calculated
from the extinction corrected UV luminosity (Kennicutt & Evans, 2012).

For the computation of the SFR, the following form of the relation is used
which assumes a constant rate of star formation over a timescale of $10^{8}$
years, with a Salpeter initial mass function (IMF) (Salpeter, 1955) from 0.1
to 100 M⊙ as described in Iglesias-Páramo et al. (2006) and in Cortese et al.
(2008)

$SFR_{FUV}[M_{\odot}/yr]=\frac{L_{FUV}[erg/sec]}{3.83\times 10^{33}}\times
10^{-9.51}$ (3)

where, $L_{FUV}$ is the extinction corrected FUV luminosity.

The total extinction corrected star formation rate, derived from the FUV flux,
for the SF knots lying within the HI contour (excluding that of NGC 5291 and
the Seashell galaxies) amounts to 1.72 $\pm$ 0.04 M⊙ yr-1 and the same for the
knots that lie outside HI contour is 0.026 $\pm$ 0.004 M⊙ yr-1. The SFR of the
galaxies, NGC 5291 and the Seashell is 1.93$\pm$ 0.21 M⊙ yr-1 and 1.16 $\pm$
0.16 M⊙ yr-1 respectively.

##  5 Discussion

There exists many observational studies on the star formation and TDG
formation in interacting systems in the UV using GALEX data (Hibbard et al.,
2005; Neff et al., 2005; Hancock et al., 2009; Sheen et al., 2009; Boquien et
al., 2009). Boquien et al. (2009) made a detailed multi-wavelength (UV,
infrared and H$\alpha$) analysis of six interacting systems with star forming
regions. The interacting systems considered by them include NGC 5291, Arp 105,
Arp 245, NGC 7252, Stephan’s Quintet (SQ) and VCC 2062. George et al. (2018)
performed a detailed study using UVIT on star formation in TDGs along the
tails of the post-merger system NGC 7252.

Figure 11: Spatial distribution of star formation rate SFRFUV of the selected
knots in the NGC 5291 system

The main concern in the estimation of SFRs using UV flux is the effect of dust
attenuation. Dust plays a significant role in the attenuation of UV flux in
galaxies. A common technique for measuring the extinction towards stars in our
Galaxy is to use the colour excess. If a star’s spectral type (and therefore
its intrinsic colour) is known, the extinction towards it can be determined.
However, this technique cannot be applied to galaxy systems, as the relative
extinction at different wavelengths is sensitive to the unknown relative
geometry of stars and dust, and differs for different optical depths
(Trewhella, 1998).

The $L_{IR}/L_{UV}$ ratio has been identified as one of the powerful
estimators of dust attenuation in star-forming galaxies e.g. (Gordon et al.,
2000; Buat et al., 2005). From UV and FIR (Spitzer / Herschel) data available
for NGC 5291, one could directly measure the dust attenuation from FIR/UV, but
not at the spatial resolution of UVIT. The relation established by Meurer et
al. (1999) between the slope of the rest frame UV continuum $\beta$ and dust
attenuation deduced from their $L_{IR}/L_{UV}-\beta$ relation for local
starburst galaxies is hence used to determine the extinction towards the
knots.

In this paper, we have analysed the extinction in the star forming regions
associated with the NGC 5291 interacting system using high resolution UVIT
data. The SFR for the knots of the selected knots of the NGC 5291 system has
been computed from corrected UV luminosities. The spatial distribution of
extinction corrected FUV star formation rate (SFRFUV) of the selected knots in
NGC 5291 interacting system is presented in Fig. 11. The extinction corrected
SFR (log SFR) of the knots ranges from -2.80 to -0.53. The M99 relation
provides us with accurate estimates of the attenuation for starburst galaxies
(Boquien et al., 2012; Overzier et al., 2011). Considering the ongoing star
formation in the NGC 5291 system to be more like a starburst, the M99 relation
is used here for the estimation of extinction. This is the first time such an
analysis is performed on the NGC 5291 system. UVIT has resolved the star
forming regions in comparison to the previous UV mission GALEX. Several of the
knots that appeared as a single entity in the GALEX images have been resolved
into two or more knots in the UVIT images. This enabled the estimation of the
extinction to the smallest scales that have been ever possible for NGC 5291.
The UVIT based extinction corrected SFRs for the selected knots in the current
study is compared with that of the previously measured SFR values given in
Boquien et al. (2007) and shown in Fig. 12.

Figure 12: Histograms of SFRs (corrected for extinction) of the knots in the
current study and SFRs of knots given in Boquien et al. (2007) for the NGC
5291 interacting system

In order to check whether the recently formed TDGs exhibit SFR values
comparable to other dwarf galaxies of similar stellar masses in the local
universe, we compared the extinction corrected SFR values of the selected
knots in the NGC 5291 system with the SFR values of dwarf galaxies (eg. BCD),
Sm and dIm galaxies in the local universe as determined using GALEX FUV data
by Hunter et al. (2010) as well as with the uncorrected SFR of knots in NGC
7252 system as given in George et al. (2018). Histograms for the SFR values of
the aforementioned systems are shown in Fig. 13. We note that the values are
very similar to the uncorrected SFR of star forming knots detected in NGC 7252
from UVIT imaging.

Figure 13: Histograms showing the SFR values of the selected knots of the NGC
5291 system as per current study, SFRs of BCD (8 samples), Sm (7 samples) and
dIm (29 samples) galaxies in the nearby universe from Hunter et al. (2010) and
uncorrected SFR of knots of the NGC 7252 system given in George et al. (2018).

From the histogram, it is further noted that log SFRs of the selected knots in
the NGC 5291 system is greater than -3. The distribution of SFRs in the knots
is similar to those of dIm galaxies for log SFR greater than -3. The maximum
value of log SFR is similar for the knots in the NGC 5291 system, dIm and BCD
galaxies. It is also seen that many of the knots associated with the NGC 5291
system have high SFRs similar to BCD galaxies; this is characteristic of
Category 1 TDGs. The three known tidal dwarf galaxies in the system, located
to the north - NGC 5291N, south - NGC 5291S (Duc & Mirabel, 1998, 1999; Higdon
et al., 2006) and south-west - NGC 5291SW have SFR values of 0.30 M⊙ yr-1,
0.30 M⊙ yr-1 and 0.22 M⊙ yr-1 respectively. They are located far from the
center of the system and are located at peaks in the HI column density map.
The highest log SFR values reported by Hunter et al. (2010) for dIm, BCD and
Sm galaxies in their samples are -0.62, -0.62 and -0.94 respectively, while
the log SFR of the three known TDGs in the NGC 5291 system are -0.52 (NGC
5291N), -0.52 (NGC 5291S) and -0.66 (NGC 5291SW).

##  6 SUMMARY

The star forming knots in the NGC 5291 interacting system, which includes
three bonafide TDGs and several TDG candidates was investigated using high-
resolution FUV and NUV data from AstroSat’s UVIT. The star-formation activity
in the selected star-forming knots was further studied by determining their
extinction-corrected SFR values. The results are summarized as below:

  * -

A total of 57 star-forming knots have been identified as being part of the NGC
5291 interacting system.

  * -

The resolved star-forming knots range in size from 1.4 kpc to 11.4 kpc.

  * -

In comparison to the previous UV imaging at lower resolution, we have 12 new
detections. The higher resolution of UVIT has allowed for better de-blending
of the structures. Several of the knots in the NGC 5291 system which appeared
as single star forming regions in GALEX images are well resolved into smaller
star forming knots in the UVIT images.

  * -

The extinction towards each of the resolved star-forming knots and the main
body of the NGC 5291 interacting system was computed using the slope of the UV
continuum and hence the extinction-corrected SFR was determined. The total
extinction-corrected SFR of the knots (inside and outside HI contour),
excluding NGC 5291 and Seashell galaxies, is estimated as 1.75 $\pm$ 0.04 M⊙
yr-1.

  * -

Comparison of the NGC 5291 system with NGC 7252 using UVIT data showed that
the SFR for both the systems are similar. Also the comparison with independent
dwarf galaxy populations (BCD, Sm and dIm galaxies) in the nearby Universe
showed that many of the knots in the NGC 5291 system have SFR values
comparable to the SFR of BCD galaxies.

## Acknowledgements

The authors RR and GS acknowledge the financial support of ISRO under AstroSat
archival Data utilization program (No. DS_2B-13013(2)/9/2020-Sec.2). This
publication uses data from the AstroSat mission of the Indian Space Research
Organisation (ISRO), archived at the Indian Space Science Data Centre (ISSDC).
RR acknowledges visiting associateship of IUCAA, Pune. KG and LC acknowledge
support from the Australia-India Council/Department of Foreign Affairs and
Trade (via grant AIC2018-067). We thank Aaron Robotham for help with ProFound.
SS acknowledges support from the Science and Engineering Research Board of
India through Ramanujan Fellowship and POWER grant (SPG/2021/002672). LC
acknowledges support from the Australian Research Council Discovery Project
and Future Fellowship funding schemes (DP210100337, FT180100066). This work
used Astropy, Matplotlib and Reproject software packages (Astropy
Collaboration et al., 2013, 2018, 2022; Hunter, 2007; Robitaille, 2018).

## Data Availability

The Astrosat UVIT imaging data underlying this article are available in ISSDC
Astrobrowse archive
(https://astrobrowse.issdc.gov.in/astro_archive/archive/Home.jsp) and can be
accessed with proposal ID: G07_003.

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