Research Paper Simplified : Galactic Archaeology with Gaia: Alis J. Deasona , Vasily Belokurov

Exploring the Milky Way's evolution has become more exciting thanks to the Gaia mission. Let’s break down what this revolutionary mission reveals about our Galaxy's past!

Summary of the Blog:

The Gaia mission has transformed our understanding of the Milky Way’s evolution by mapping over a billion stars. It reveals the galaxy’s hidden history, particularly through the discovery of the Gaia-Sausage-Enceladus (GSE) merger, which occurred 8–11 billion years ago and significantly shaped the inner stellar halo. Gaia's precise measurements provide insights into stellar orbits and chemical compositions, allowing scientists to distinguish between stars formed within the Milky Way and those from GSE. This mission enhances our knowledge of the Milky Way's structure and evolution, offering a clearer picture of the cosmic events that have shaped our galaxy over billions of years.


In this blog, we will explore several key topics related to the Milky Way’s evolution. First, we’ll examine the stellar halo and its role as a fossil record of past mergers. Then, we will discuss the Gaia-Sausage-Enceladus (GSE) merger, highlighting the evidence for its significance in shaping the Milky Way’s structure. Next, we’ll analyze the chemical signatures of different stellar populations, which reveal their origins and formation histories. Finally, we’ll showcase how Gaia's innovative data techniques have revolutionized galactic archaeology, enhancing our understanding of the Milky Way’s formation and broader galaxy development. Join us as we uncover this fascinating narrative!

Introduction: The Hidden History of the Milky Way

Figure 1: Artistic Representation of Milky Way

The Milky Way, like a cosmic archaeologist, carries the remnants of its formation and evolution (Fig.1). Over billions of years, it has consumed smaller galaxies, leaving behind debris in the form of stars and dark matter. This "stellar halo" acts like a fossil record, telling the story of these galactic mergers and the Milky Way’s dynamic history. Stars act as fossil records of the past, preserving information about their origins, motions, and chemical compositions.

Figure 2: Gaia Observers Milky Way

In this image, milky way can be seen as a brownish band in the background with Gaia Satellite in the foreground.

Image Source : Wikimedia Commons

The Gaia Mission, launched by the European Space Agency, has transformed how we study these remnants (Figure 2). By providing highly detailed maps of the positions, motions, and chemical compositions of over a billion stars, Gaia gives scientists an unprecedented view of our Galaxy Milky way.

Key Questions for Discussion:

• How has the Milky Way grown over billions of years?
• What role do mergers, like Gaia-Sausage-Enceladus (GSE), play in this process?
• How does the Gaia mission allow us to reconstruct the Galaxy’s history?
• Key Discoveries in Galactic Archaeology

1. The Stellar Halo: A Galactic Fossil Record

The stellar halo is a diffuse, spherical region of stars surrounding the Milky Way. It holds clues about the galaxies our Galaxy devoured over time.

Pre-Gaia Observations:

Earlier studies provided hints of a stellar halo, but the data was sparse and incomplete. Astronomers used models to guess the properties of these stars, often based on limited samples from telescopes like SDSS. Also, the most studies relied on indirect methods to infer the orbits and origins of stars.

The Gaia Revolution 

 The Gaia mission provides precise astrometric data, including positions, proper motions, parallaxes, and radial velocities for over 1 billion stars, enabling detailed reconstructions of their orbits and origins.

Post-Gaia Era:

With Gaia’s precise data, astronomers discovered that most of the inner stellar halo (within 20 kpc of the Galactic center) is dominated by debris from a single massive dwarf galaxy, referred to as Gaia-Sausage-Enceladus (GSE).

2. The Discovery of Gaia-Sausage-Enceladus (GSE)

Figure 3. A visualization of the moment of impact between the MW’s progenitor and the Gaia Sausage (or Gaia-Enceladus) (credit: Instituto de Astrofísica de Canarias).

The GSE is one of the Milky Way’s largest mergers, occurring about 8–11 billion years ago (Figure 3). Its debris dominates the Milky Way’s inner stellar halo (r < 20 kpc). Here’s why it’s important:

Key Evidence for GSE:

1. Radial Orbits of Stars: 

GSE stars exhibit highly eccentric orbits, with elongated paths that repeatedly bring them close to the Galactic center. The radial velocity distribution of GSE stars shows two prominent "lobes," indicating their highly eccentric motion. The symmetry of these lobes supports the idea of a single progenitor contributing to the inner halo.

2. Chemical Fingerprints:

Figure3. X-axis represents Fe/H and Y-axis represents [α/Fe] in upper panel and number of stars in the lower panel. Black Dots represent the milky way stars that formed in-situ while the blue stars are associated with GSE. Solid (dotted) lines show the distribution of [Fe/H] when high-α stars are excluded (included). Image Credits: arXiv:2402.12443

Chemical composition plays a vital role in identifying stellar populations. Stars from the Milky Way and accreted galaxies differ in their ratios of heavy elements, such as alpha-elements (like magnesium) and iron.

Stars with higher [Fe/H] are more metal-rich, meaning they formed later in a galaxy’s history when there was more iron available from previous generations of supernovae. [α/Fe] is the ratio of alpha elements (α) to iron (Fe). Alpha elements include magnesium, silicon, calcium, and oxygen, which are primarily produced by massive stars in Type II supernovae. Higher [α/Fe] Indicates rapid star formation because massive stars dominate in enriching the environment before Type Ia supernovae contribute significant iron.

Figure 3 shows the metallicity distribution with [Fe/H] vs. [α/Fe]. 

The distribution of stars in chemical space ([Fe/H] vs. [α/Fe] shows distinct groups. This allows astronomers to separate in-situ stars (formed in the Milky Way) from accreted stars like those from GSE. Milky Way stars have higher [Fe/H], varying [α/Fe] from GSE stars with lower [Fe/H], higher [α/Fe] This chemical distinction helps identify which stars belong to the Milky Way and which came from GSE.

3. Apocenter Pile-Up:

Figure4. The figure represents the variation of density with distance. Apocenter distributions (Fig. 8) confirm that GSE debris dominates within ~20 kpc.Image Credits: arXiv:2402.12443

 

In a galaxy, the apocenter pile-up is a phenomenon that can lead to distinctive features in the stellar halo. This occurs when stars build up at the apocenter of a common dwarf progenitor, resulting in a broken density profile. The stellar debris deposited during this event has similar apocenters, which is responsible for the stellar halo break. The apocenters of GSE stars cluster around ~20 kpc, aligning with the break in the stellar halo’s density profile. Figure 4 in the paper shows the apocenters of GSE stars overlap with the observed density break, reinforcing the idea that GSE debris dominates the inner halo.

3. Globular Clusters (GCs) and GSE

GCs are dense star clusters often associated with their host galaxies. In the Milky Way, they provide additional clues about past mergers. Several GCs on highly eccentric orbits are linked to GSE.

These clusters share orbital characteristics with GSE stars, confirming their common origin.

Figure 7 in the paper shows the peri- and apocenter distances of GSE’s GCs overlap with those of GSE stars, indicating a shared history.

4. Implications of GSE for Galactic Evolution

• GSE was the last major merger, significantly shaping the Milky Way’s inner halo.
• Its debris dominates the inner halo (r < 20 kpc).
• The GSE merger influenced the Milky Way’s dark matter halo, contributing to its current structure.
• GSE brought globular clusters (GCs) into the Milky Way.Figure Reference (Fig. 7 in paper): Many GSE globular clusters have highly eccentric orbits, consistent with GSE stars.

5. How Gaia Revolutionized Galactic Archaeology

• Before Gaia, astronomers relied on indirect methods and limited data to study the Galaxy’s structure. Now, Gaia provides:
• 6D Maps: Positions, velocities, and chemical compositions of stars.
• High Precision: Data that allows scientists to track the orbits of stars and identify their origins.
• Complementary Surveys: Combining Gaia data with spectroscopic surveys like APOGEE and SDSS reveals even more details about star chemistry and motion.

Why This Matters

• Understanding the Milky Way’s formation gives us a glimpse into the broader universe:
• The Milky Way’s mergers are part of a universal process of galaxy formation.
• Stellar motions reveal the distribution of invisible dark matter in the Galaxy.
•  The chemical fingerprints of stars teach us about the life cycles of galaxies.

The Gaia mission has opened a new chapter in studying the Milky Way’s history. By combining stellar motion, chemistry, and models, scientists can reconstruct the story of our Galaxy’s growth and evolution.

References :

[1] Galactic Archaeology with Gaia, Jul 2024, Alis J. Deason , Vasily Belokurov

arXiv:2402.12443 [astro-ph.GA]

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ASTRONOMERS DISCOVERED THE BRIGHTEST OBJECT IN THE UNIVERSE ! A QUASAR 500 TRILLION TIMES BRIGHTER THAN OUR SUN!

Imagine a cosmic light source so powerful it could bathe the entire observable universe in its glow, its brilliance reaching us after billions of years of travel through the inky blackness of space. Believe it or not, astronomers haven't just dreamed this up – they've actually found it! This celestial object is a quasar named J0529-4351, boasting a luminosity that's a mind-boggling 500 trillion times greater than our very own Sun!

                                                            Source : NASA Images

Cracking the Quasar Code

Quasars, short for quasi-stellar objects, are the energetic powerhouses at the cores of distant galaxies (see Fig.1). These powerhouses are fueled by supermassive black holes, millions to billions of times more massive than our Sun. As these gravitational giants eat up surrounding gas and dust, a swirling disk of superheated material forms around them. The intense friction within this disk releases tremendous amounts of energy across the entire electromagnetic spectrum, making quasars some of the brightest objects in the cosmos.

J0529-4351: A Feeding Frenzy on a Cosmic Scale

The newly discovered J0529-4351 exemplifies this phenomenon on a scale unlike anything ever witnessed before. Situated 12 billion light-years away (remember, a light-year is a whopping 5.8 trillion miles!), the light we see from J0529-4351 has been traveling for an incomprehensible amount of time before reaching our telescopes.

The Black Hole Behind the Brilliance

The secret behind J0529-4351's extraordinary light show lies in its central supermassive black hole. According to a study published in the prestigious journal Nature Astronomy, this black hole devours a sun's worth of material every single day! This phenomenal rate of growth fuels the quasar's immense light output, making it the fastest-growing black hole ever observed.

A Hidden Colossus Emerges

Source : Eso.org

The discovery of J0529-4351 is particularly intriguing because it remained undetected for so long. It was first spotted back in 1980 by the European Southern Observatory's Very Large Telescope (VLT) during a sky survey, but it was mistakenly classified as just another star ! It wasn't until recent observations led by an Australian National University team using a 2.3-meter telescope and subsequent confirmation by ESO's VLT that J0529-4351's true nature as a quasar was revealed
. This hidden giant, despite being one of the brightest objects in the sky, managed to evade our detection for decades!

A Cosmic Time Capsule

Studying quasars is like peering back in time. Since their light takes billions of years to reach Earth, these objects offer a glimpse into the early universe, a time when galaxies were just starting to take shape. J0529-4351 acts as a unique time capsule, allowing us to witness the processes that led to the birth and evolution of supermassive black holes and galaxies.

Pushing the Boundaries of Knowledge

This record-breaking quasar presents a fascinating puzzle for astronomers. Its extreme luminosity and environment push the very limits of our current understanding of black hole physics and galaxy formation. Studying J0529-4351 might unlock secrets about these extreme environments, leading to breakthroughs in our comprehension of the universe's most powerful objects.

The discovery of J0529-4351 serves as a reminder of the universe's hidden wonders and our ongoing quest to unravel its mysteries. With advancements in technology and our insatiable curiosity, who knows what other incredible cosmic behemoths await to be unearthed in the vast expanse of space? This discovery is a stepping stone on the path to a deeper understanding of the universe's grand story.

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Stellar Structure And Evolution: Part 2: Basic Assumptions and Accuracy of Assumptions

In the previous blog I explained why do we need a theory of Stellar Structure and Evolution when we can get information about stars by just observing them. In this blog I will cover-

1. The basic assumptions of theory of Stellar Structure and Evolution

2. Accuracy of Assumptions of theory of Stellar Structure and Evolution

To understand above mentioned aims more clearly, let's first understand( answer these questions - that I generally don't see many writers stress about:

What are the assumptions for a theory ?

Assumptions are basically the foundation stones for a theory. These are taken as the postulates that are generally assumed to be true throughout the explanation.

 

Now, What is the need for assumptions to a theory?

-First of all, because they are reasonable - they offer observational or at least mathematical verification.

-- Secondly, Making assumptions simplify our work in terms of crucial/critical understanding and mathematics.

- Lastly, although it is harsh but true: We only have limited information about things. Thus, as long as these are not true in general, we choose not to include them (esp while teaching) instead of including it with ad-hoc suppositions that lack any observational verification.

Now that we know what are assumptions and why do we need them for building a theory let's see what are the basic assumptions for the theory of Stellar Structure and Evolution

1. Stars are isolated in space - This is a fairly reasonable assumption for most of the single stars in galaxies as this condition is satisfied to a high degree - compare the distance of sun to its nearest star Proxima Centauri. We are ignoring binary stars and stars in dense clusters.

2.Stars are formed with a homogeneous composition- it is again reasonable as the clouds from which stars are formed are well - mixed.

3.Stars have no magnetic field - This is fully reasonable as for most of the stars magnetism plays a notable role only in phenomena related to surface of stars but in overall life cycle they don't play any significant role.

Stellar evolution is fully determined by internal physical processes which take deep inside the star near it's core.

4. Stars are rotating slowly- This one is a lot harder to justify as most of the stars rotate at a considerable fraction of their critical velocity(*1). Since we do not have a theory that shows how Stellar interior rotates at the birth of the star and making this assumption causes a huge mathematical simplification we are going to hold it.

5. Stars are in mechanical equilibrium(*2) : Majority of stars are in such long lived phases of their evolution that no structural changes are observed for them for most period of times. This implies that there is no noticeable acceleration and all the forces balance each other perfectly.

For an isolated, slowly rotating, homogeneous composition star with no magnetic field these forces are gravity and pressure. Thus, all the stars are in hydrostatic equilibrium.

All of the above mentioned assumptions can be tested just by testing for accuracy of hydrostatic and spherical symmetry assumptions.

Accuracy of Hydrostatic Assumption -

Let's first understand the equation of Hydrostatic support using simplest Newtonian dynamics

Balance between gravity and pressure is called hydrostatic equilibrium.

For a given time t, let's consider a spherical mass shell with infinitesimal thickness δr at a distance r from the centre. 

 

Mass of the element δm at this distance is δm= ρ(r)δs δr

ρ(r) = density at radius r

Outward force = pressure exerted by stellar material on lower surface

P(r)δs

Inward force on mass element= Pressure exerted by stellar material on upper surface and gravitational attraction of all stellar material lying within r

P(r+δr)δs+ GM(r)δm/r² = P(r+δr)δs+ GM(r)ρ(r)δs δr/r²

For hydrostatic equilibrium, inward force= outward force

P(r)δs=P(r+δr)δs+ GM(r)ρ(r)δs δr/r²

so, P(r+δr)-P(r)= GM(r)ρ(r)δr/r²

 For infinitesimal element:

P(r+δr)-P(r)/δr = dP(r)/dr

Thus, dP(r)/dr=-GM(r)ρ(r)/r²

which is the equation of Hydrostatic support.

Accuracy of hydrostatic assumption

To answer how valid is that assumption let's consider a situation where inward force and outward force aren't equal which gives rise to acceleration a.

P(r+δr)δs+GM(r)ρ(r)δs δr/r² -P(r)δs = ρ(r) δs δr a

»dP(r)/dr +GM(r)ρ(r)= ρ(r) a

 

this is the generalized form of equation of hydrostatic support.

Now consider there is a resultant force on element with the sum being a small fraction of gravitational term(β)

Inward acceleration a = β.g

Spatial displacement from rest after time t = d= 0.5.a.t² =0.5.β.g.t²

If if allow star to collapse or expand, by setting d=r we obtain

t=(2.r³/G.M.β)^1/2

Assuming beta =1 we obtain

t=(2.r³/G.M)^1/2

This is the dynamical time scale of the star.

Of course each mass shell will be accelerated at different rate so this should be taken as an average value for star to collapse at radius R.

Since average density is we can also write this t to be

½.(G.ρ)^1/2

For sun we obtain a value of 1600 sec or about half an hour. Thus, any significant departure from hydrostatic equilibrium should lead very quickly to an observable phenomenon (sudden collapse or explosion of the star ) . But age of sun is already

This is much smaller than the age of sun - 10^17 secs - by 14 orders of magnitude. Thus if this assumption have been wrong we would have noticed a significant collapse or explosion of sun much earlier.

This assumption is very much accurate.

Accuracy of spherical symmetry assumption

Let's see if average rotation rate of stars is causing significant departure from spherical symmetry.

Consider a star of mass M and radius R with an element of mass δm near the surface of the star.

star of mass M and radius R with an element of mass δm near the surface rotating at angular speed w

Gravity supplies the extra centripetal force to make the object move around in a circular path.

Thus, for mass δm, centripetal force = gravitational force

There will be a departure from spherical symmetry if there will be any difference between gravitational and centripetal force i.e.

(δmω²r)/(GMδm/r²) <<1

or ω²<<GM/r³

note RHS of last equation is similar to t

>> ω²<<2/t² (ω=2π/T) where T =rotation period

 for spherical symmetry to be valid T>>t

for example, for sun t~2000 sec and T~21 month

Thus, for majority of stars, departures from spherical symmetry can be ignored.

With this we complete the basic assumptions of theory of Stellar Structure and Evolution and see that these assumptions are qualified to build a theory of Stellar Structure and Evolution.

 

 

*1.Definition of Critical velocity : Stars have a maximum speed at which they can spin. If stars exceed the critical rotation, the outward force caused by their spinning will overcome the inward gravitational force that keeps the star together.

If stars get to that limit, they will begin to fly apart.

*2. Mechanical equilibrium : A state of rest or unaccelerated motion in which sum of all the forces acting on a particle is 0. In case of stars, this state is reached when pressure forces are balanced by gravity. In astronomy, this is called hydrostatic equilibrium.

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Stellar Structure and Evolution Part : 1

Aim of this Blog is to explain why we need a theory of Stellar Structure and Evolution- A war for need of theory over observation.

Before coming to the central question let us look at the answers to some simple looking but very crucial questions:

Q1. What is meant by Stellar Structure and Evolution?

 To understand structure and evolution of stars using laws of physics.

Q2. What are stars ? 

A star is an object that - 

1. Radiates energy from an internal source 

2. It is bound by its own gravity 

3. Star should evolve ? But why ? 

Stars are born within the clouds of dust scattered throughout most galaxies. 

Evolution is the change in properties of star with time. In stars it occurs due to burning of fuel to balance the forces of gas and pressure.  This evolution is highly dependent on mass of stars - On average, Greater the mass shorter it's life

Now coming to the central question -

What is the need for theory for stellar evolution when we can have so much information by just observation of Stars ?

To answer this let's understand what all we can gather by the known observational techniques that we use to study stars -

1. Photometric measurements (Photometry, in astronomy, the measurement of the brightness of stars and other celestial objects) yield the apparent brightness of a star, i.e. the energy flux ( f )  received on Earth, in different wavelength bands.

(I have covered more of the terminologies here ) 

2. Distances to nearby stars can be measured with the help of parallax. As Hipparcos satellite has measured parallaxes with 1 milliarcsec accuracy of more than 105 stars.

                                         

3. Spectroscopy (Spectroscopy is the study of the interaction between matter and electromagnetic radiation as a function of the wavelength or frequency of the radiation.) at sufficiently high resolution gives detailed information about the physical conditions in the atmosphere. With detailed spectral-line analysis using stellar atmosphere models one can determine the photospheric properties of a star ( like effective temperature, surface gravity , rotation velocity etc.)

 

4.Mass of stars -one of its most fundamental properties can 'only' be measured indirectly by using binary stars (spectroscopic binaries)

Spectroscopic binaries

As you might have noticed, all of these( Mass, Temperature , Rotation Velocity, Distance etc.)  are only surface properties. Thus, we need to build a theory of Stellar Evolution to derive internal properties of stars as observational techniques seem to fail in that !?

Well Game isn't over yet ! Observation always provides astronomers  a window to interior of stars like -

1. Neutrinos: which escape from interior of stars without any interaction. But neutrinos interact little with matter regardless of energy. Moreover, beyond certain temperature, there is a decrease in relative flux of neutrinos

2. Oscillations: Yes, I am talking about Seismology here. Stars are musical instruments. You can refer  my blogpost on Helioseismology  to know more. Here is a brief -  The surfaces of stars oscillate with a particular time period and this can give us valuable information about size, age and mass of stars

Why we need a theory for stellar structure and evolution when we can just decode information from observation? 

It is true that Astronomical observations can yield information about important stellar parameters. But these are like snapshots of the life of star as timespan of these observations is much smaller than the age of stars. Thus, any of these observations cannot give us a complete picture of Stellar Evolution. 

Moreover, a theory is also need to explain some of the most important results of Astronomy such as  mass - luminosity relationship and mass - radius relationship that we get from HR Diagram of stars. (I am going to cover HR Diagram in my future Blogs so don't worry about that :) 

Thus overall, we see that the observational techniques we use cannot provide us with 'all' of the necessary information about stars.

Thus a theory is needed to explain Stellar evolution and results of Stellar Observation.

In the next blog I will cover -

The basic assumptions of theory of Stellar Structure and Evolution

Accuracy of Assumptions of theory of Stellar Structure and Evolution

stellar evolution

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How to destroy a Cluster of Stars/ Globular Cluster

 This blog includes - 

1.1 What are Globular clusters ?

1.2 What are Binary Stars ?

1.3 What is escape velocity ?

1.4 How to Destroy a Globular Cluster ?

1.5 Summary of Topic 

In this blog we will destroy a Cluster of Stars called Globular Cluster!

The main focus of this Blog is to make you understand how you can destroy a Globular cluster for which we will run from 1.1 to 1.3 to gather all the material to understand the topic. If you know about all of this already you can directly skip to section 1.4 to know the real tea 🍵

1.1) What are Globular clusters ? 

The name is derived by Latin word - Globulus - which means a small sphere (they are really big though- approximate size of a Globular cluster is - 300 light years) 

Globular clusters are a group of stars all formed at approximately same time and held together by gravity. ( Fig 1) They are called 'museums of stars' as they have held the stars intact since they were formed and thus help astronomers in studying age and properties of various stars( Bonus : As the stars in clusters are all formed at same time, the globular clusters help in comparing the properties of different mass stars formed at approximately same time, which is an excellent opportunity for astronomers ! ) 

fig 1

GLOBULAR CLUSTER

Although they look dense, collisions between stars in globular clusters are very rare as distances between individual stars are greater than approximate distance between stars. Moreover,  velocities of stars at any point inside the cluster are fairly random, in direction as well as size. The stars form what is called a 'collision less gas'.

Soon we will see how to boil away or destroy these museums of stars 😈

1.2) What are Binary Stars ? 

A binary system consists of two stars orbiting each other around a common centre of mass.

BINARY STARS

Given the stars in a binary system are themselves spherical, both of their orbits will be ellipses, just as for planets in the Solar System ( Bonus : for a spherical star system, the gravitational field is as such as if all of the mass is concentrated in center, when this is not the case - like when stars come close to each other tidal forces might deform the shape and resultant orbits will be complex then )

Escape velocity from a binary system : 

Let's consider a binary system of two stars orbiting around a common center of mass as shown below

Two binary stars (in purple) in orbit around a common center of mass

For simplicity, let's consider orbits to be circular and masses of both stars to be equal = M

Radius of circle = R 

In order for one of star to escape from gravitational field of other star, the kinetic energy of star should become equal the gravitational potential of the other star.

(1/2)*m*v^2 = (G*M*M)/(2*R)  (Kinetic energy = potential energy)

So, v= sqrt(GM/R)

Therefore, energy of 1 star when it has this speed

is 1/2 * m *v^2 = (G*M*M)/(2*R)   ------------ (1) 

We need to learn only this much about binary stars to understand today's topic :)

1.3) What is escape velocity ? 

The minimum velocity which is needed by a non- propelled body to escape from gravitational field of another object is called it's escape velocity. 

Formula - sqrt( 2*GM/ R ) where,  ----------(2)

G - Gravitational Constant = 6.674 x10−11 m3⋅kg−1⋅s−2

M = Mass of object which is to be escaped 

R = Radius of object which is to be escaped

Now that we are equipped with all the necessary tools to destroy a Globular cluster let's dive into it ! 

1.4) How to destroy a Globular cluster?

Let's understand what is meant by destruction of a Globular cluster. It means kicking out every star from the cluster so that it no longer remains a Globular cluster. 

Here's is the recipe, let's do it together 

Step 1. Let's calculate how much energy is needed to kick out stars from a Globular cluster?

 To do this let's take a sample cluster. 

* Mass of cluster Mcl      = Mass of 10^(6) stars, where avg. mass of 1 star = 1 Mo ( 1 solar mass ) 

* Radius of Cluster Rcl   = 50 parsecs ( pc),where 1 parsec = 3.086e+13 km 

* Escape velocity for a single star =  v_escape = sqrt( 2*G*Mcl/ Rcl ) ~ 13 km/s  ----from(2)

* Escape energy for a single star, 

   E_escape = 0.5*mass of 1 star * (v_escape)^2

                   = 2*(10^38) Joules

* Escape or destruction energy for whole cluster! 

   E_escapecluster = 

   Escape energy for a single star × total number of stars =2 × 10^38 × 10^6 

                                                                                          = 2 × 10^44 Joules

To destroy whole cluster, we need to provide 2 × 10^44 Joules energy to it. But how can we do it ?

Answer: Step 2: By forming binary pairs of stars!

Formation of a binary pair releases energy, as the two stars become bound. The energy required to form a binary pair is the same that is required to split it again. 

Thus, From (1) we know that energy released when a binary pair is formed is - (G*M*M)/(2*R)

 Suppose the stars each have one solar mass and are separated by 

the radius of a white dwarf, about 5 × 10^6 m.  Formation of such a system releases energy equivalent to 3 × 10^43 Joules.( using (1) )

Wow! only 10% of the binding energy of the cluster is provided by only one binary system. The formation of a handful of such systems could easily provide enough energy to expand the cluster or even disrupt it!!!

The energy released in this way goes to the third star by Newton's third law ( Newton's Third Law: every action has equal and opposite reaction)  and the third star now has so much energy that it simply shoots straight out of the cluster. ( This is not out of some magic, when two stars form a binary pair energy is released in a same way it is released when a particle is falling onto the star. If third star were not present, they couldn't form a binary pair ) - see the last section of this Blog ( * )to understand more accurately how the energy is actually transferred :)

Finally! We have successfully destroyed the Globular Cluster

Summary of Topic 

Globular clusters are a group of stars all formed at approximately same time and held together by gravity.

Destruction of cluster is possible by formation of a handful of binary pairs. The energy released in this way goes to the third star by Newton's third law and the third star now has so much energy that it simply shoots straight out of the cluster.

Thus one by one, shooting the stars out we can completely destroy the Globular Cluster !

___________________________________________________

                                     ( *)

(Let's take 3 stars in a Globular cluster with masses say 1, 2 and 3 solar mass. We arrange them in mercury - sun distance and give them some small initial velocity so that no star has energy to escape the three - body system. After some time, two stars become bound and the third one is expelled. 

Now how does that happen? 

The answer is in gravitational energy.When two stars become more tightly bound, they release energy, just as a particle falling onto a star releases energy . This energy goes into the motion of the third star by Newton’s third law which says that every action has equal and opposite reaction. By this law, the force exerted on the pair by the third star is exerted back on the third star by the pair: which results in binding the pair more tightly and expelling the third. If the third star were not present, the first two could not form a tight binary pair: they would fall towards one another and then recede to the same distance. )

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Dark Matter Slowing Down Milky Way

Topics of this Blog include- 

1.1- A brief about Milky Way Spiral Galaxy and Dark Matter 

1.2- Details about Topic -Dark Matter Slowing down Milky Way

1.3 - Conclusion and Learnings from this discovery 

1.4 - Summary of Topic

1.1) A brief about Milky Way galaxy and Dark Matter

       Milky Way Galaxy  

Milky way ( or Akashganga ) is our home galaxy. Approximately two-thirds of all spiral galaxies contain a bar, so does our galaxy - It is a barred spiral galaxy which means that it has a central bar with spiral body structure ( Fig. 1and 2) 

Fig 1

Fig 2

                                                                      

This bar-shaped core region is surrounded by disk of gas, dust and stars

       Dark matter 

- To know more about dark matter you can refer to this link : Dark matter 

Dark matter constitutes 27 % of content of whole universe. It is made up of 'something' that cannot be detected by electromagnetic force ( basically by touch or sight ). It's gravitational effects are responsible for flattening of velocity vs radius curves in the outer regions of galaxies.  According to theories It forms a spherical halo around the galaxy. 

1.2) Details about Topic - How dark matter is slowing down Milky Way

"Astrophysicists have long suspected that the spinning bar at the center of our galaxy is slowing down, but we have found the first evidence of this happening," study co-author Ralph Schoenrich, in a statement.

Galaxy models have long predicted that galactic bars slow down by losing angular momentum to their postulated dark haloes.

Hercules stream is a group of stars currently rotating away from center of Milky Way. This stream is in resonance with the central bar - i.e. it is gravitationally trapped by the central bar and thus, revolves around at the same rate as bar's spin ( like Jupiter's Trojan ) 

If the bar's rotation slows, the stars in the stream move outward to have orbit in sync with rotation of bar. Researchers investigated the chemical composition of stars in Hercules stream and found them to be rich in heavier elements which is possible only when they have been formed close to the center of Galaxy.

Thus they have been sweeping out of the center of galaxy which implies that galactic rotation has been slowing down and has slowed down by 24%.

 The one possible and seemingly correct explanation is that dark matter has been slowing down the spin by dynamical friction. Loss of the bar's angular momentum has been attributed to dark matter.

This possible explanation, although seeming the most correct till now has run into rivals.  Schoenrich said "Our finding also poses a major problem for alternative gravity theories — as they lack dark matter in the halo, they predict no, or significantly too little slowing of the bar ". There are also alternating theories of gravity which propose tweaks in Einstein's relativity and disregard dark matter possibility. But Einstein's theory has passed all of the tests till now ( Our GPS works on basis of that, the famous black hole picture that we have obtained is also consistent with his theory ) 

1.3) Conclusion and Learnings from this discovery 

• This model supports the presence of Dark Matter, while physical detection is yet to be done.

•It again put a shade on alternating theory of gravity and dark matter. ( Like MOND )

• We have got new constraints on galactic history and the unique opportunity to differentiate between different dark matter models.

• Due to position of  Sun’s position far from the center we currently see only the outer region of the resonance of spin of bar and Hercules stream . By performing the analysis at a spatial coordinate closer to the Lagrange points, we could probe deeper into the inner region of the resonance, where we may find traces of events that happened in the early epoch of bar formation and also determine the size of the initial core of the resonance which stems from the formation of the bar. However author mentions that this will be possible in the future with extended data covering the full range of resonance and a proper chemo-dynamical model predicting the age-dependent effects. 

1.4) Summary of Topic 

Analysing data from Gaia, a European Space Agency Mission to map position of stars in milky way, researchers at University College London (UCL) and the University of Oxford have shown that the spin of the Milky Way's galactic bar has slowed by about 24 % or a quarter since its formation. Most plausible explanation is Dark matter acts as a counterweight slowing the spin. 

Also Check :

Milky way : https://en.m.wikipedia.org/wiki/Milky_Way

Dark matter: https://en.wikipedia.org/wiki/Dark_matter

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HOW FAR AWAY ARE STARS?

"...Looking at the stars always makes me dream , as simply as i dream over the black dots representing towns and villages on map. Why, i asked myself shouldn't the shiny dots of sky be as accessible as black dots on the map of France"

-Vincent Van Gogh

Study of heavens is older than study of navigation, agriculture and even language itself. It is one of the oldest sciences ever studied . From the dawn of civilisation , humans have wondered about twinkling dots above their heads , far far away from the reach. Study of these twinkling dots has laid down the most important building blocks in arousing the curiosity of mankind into knowing - who we are ?

Stars are all born in nebuli , the cloud of dust. With the gravity working is magic , dust and gas start to collapse. As the temperature rises further stellar evolution continues ; thermonuclear fusion begins, forming helium and we get heat and light .

How far away are stars?

It seems impossible to understand stars, unless one has an understanding of tackling distances between them. Taking the understandings of Greeks in measuring the distance of moon forward , we reached the stars . 

Let's first understand the term parallax - Its the apparent shift in position of an object when it is viewed along different positions. Eg.  hold a pencil in your  hand and extend your arm. Notice the shift in position of pencil as you view it through your one eye keeping the other closed at a time. Your eyes have a certain distance between them that causes this parallax . Similar shift in the position of star occurs when it is viewed from different locations of earth and the astronomers didn't spare this and made it one of the most powerful tools of astronomy !

Let me show you how -

As seasons change, the location of stars in the sky changes - this apparent change in the position of the star when viewed from different points on earth is called - Parallax. 

We take the benefit of this observation and by measuring the position of the star in the sky 6 months apart , by simple mathematics , we get the distance to stars .

we already knew the distance from sun to earth( 1 AU ) 

we measured the angle' alpha 'from earth and putting all in formula - 

alpha= (1 AU)/d  , we get the distance to the star.

But the process is not as straight forward as it looks , twinkling of stars - though soothing to eyes are a major trouble for astronomers because it limits the accuracy to which the position of star is known .

One way to solve this problem is to have thousand of observations to get the accurate position of star and the other is to position our telescopes outside the atmosphere of earth to avoid turbulence due to atmosphere and get the measurement of accurate position. That's why we have most of the telescopes placed higher up in atmosphere.

Everytime we need to measure the position of a star , it's tedious to take thousands of observations . This parallax method surely has limitations . Is there a better way?( yes obviously , else why would i be having this question here ) . It lies in measuring the brightness of star.

How bright are stars and how to measure the brightness?

Let's first talk about brightness in daily life. You go to market and purchase 1000 W bulb. This bulb gives off 1000 Joules of energy in one second. Physicists call this term luminosity.

The other term is apparent brightness. It describes how a star gets dimmer and dimmer as it gets far away. We use this relationship between distance and brightness to a great extent in astronomy.

 How Astronomers measure the brightness?

Stars radiate enormous amount of energy so thy don't use units like Watts cuz that will be very inconvenient. 

The apparent luminosity of of a star is descirbed as

 apparent magnitude (m) and

                                                 

 total luminosity is described as absolute magnitude (M)-magnitude of an object placed 10 pc     away.

                                                 

 Where parsec(pc) is the distance which a star has to travel for it's parallax to be 3.26 light year(light year is equal to the distance light travels in one year = speed of light(m/s) * no. of seconds in an year)

The construction of magnitude scales was done on the basis of the most fundamental logic-

Our eyes are more sensitive to geometric than arithmetic progression.

This fact can be understood very easily as you will be able to distinguish more clearly in between two bulbs if brightness of one bulb is greater than that of other by a factor 5 i.e b1=5*b2

 than if the brightness of one bulb is 5 + greater than the other , i.e b1=b2+5.

There are two things which we need to note about these magnitudes here -

The scale runs on logarithmic scale ( magnitude of one star is dimmer than other by same factor)and backwards( higher the magnitude , dimmer the star )

Here is the mathematical expression for apparent magnitude- 

m1 - m2 = -2.5 * log( B1/B2) where m1 , m2  and B1 , B2 are magnitudes and brightness of objects respectively. 

and here is mathematical expression for absolute magnitude- m-M = 2.5 log (d/10)^2

 If the object is at a distance d pc, then (10/d)^2 is the ratio of its apparent brightness and the brightness it would have if it were at a distance of 10pc. 

Starlight deciphering the mysteries of cosmos

Stars send us message encoded in the starlight. We decode this message by studying the spectrum of stars, we can encode many things, like what is the star made up of , the age of star .

 

Suppose two stars have same spectrum, one is near and one is very far away . If spectra of two stars is identical then experience has shown astronomers that the two stars will also be very similar in their other properties, such as their mass, radius, and total luminosity. If it turns out that the second star has apparent luminosity that is only one ninth that of  1st one , then it is likely that this is because the star is thrice as far away, so that its light is spread over a sphere whose area is nine times as large as that of the first one. Noticed how cleverly we figured out distance here ? This is what astronomers use to take account of very large distances.  

well..this is not the end to the story still , we got a lot of information from a single twinkling speck on the sky , that realisation is awesome in itself. I wonder , what it would be like decoding every single bit of information that is given to us ! Our ancestors were definitely excellent at it ; we owe our understanding to all those curious , passionate and brave minds who decoded the biggest mysteries without any basic tools. There is still a long long way to go .. Every piece of the sky tells a story , just be curious enough to decipher one.

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