Trouble understanding speed-dispersion in (elliptical) galaxies

Trouble understanding speed-dispersion in (elliptical) galaxies

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I'm learning about LOSVDs (Line Of Sight Velocity Distributions) and I'm having a bit of trouble understanding the used terms.

As I understand, the LOSVD of a given (elliptical) galaxy is the density distribution of the LOS-velocities. The full LOSVD is difficult to find and it's easier to find 2 parameters of the distribution: $ar v_{_{LOS}}$ and $sigma_{_{LOS}}$ by fitting a (Gaussian) model to the spectrum of the galaxy.

I have a limited understanding of statistics, so I'm having trouble intuitively understanding what these 2 parameters mean later on.

I think that $ar v_{_{LOS}}$ is simply the average value of the LOS-velocity for the whole galaxy while $sigma_{_{LOS}}$ is the equivalent of a standard deviation.

Now later on in my coursebook, there's an explanation of how to get a LOSVDs for every point (/pixel) in the (projection onto the celestial sphere of the) galaxy by using 3D spectrography.
From this we can get a 3D dynamic model from our 2D kinematic model. In this newly found 3D distribution there's also 3 Sigmas, one for every dimension.

But here comes the part I don't understand:
The book is looking at the movement of stars in a spiral galaxy, the Milky way in particular.

We're trying to find a correlation between the age of MS-stars and their dispersion and so there's a dataset of a few stars in the neighbourhood of the sun with their dispersion in every dimension.

What is the meaning of dispersion in this context? How can a single object have a dispersion if it's a parameter of a density distribution?

The total light of a galaxy is the sum of perhaps billions of stars, each with their own line of sight velocity. You can characterise this distribution with a mean and a standard deviation (dispersion), and this will be reflected in the absorption line profiles of that galaxy.

Equally you might choose to measure this distribution as a function of position in a galaxy, if you are able to spatially resolve different regions. For instance one could put a spectrograph slit across a galaxy and get the velocity dispersion as a function of position along the slit.

When you are talking about nearby stars, you can measure the 3D velocities individually, providing you can measure the radial velocity, proper motion and distance of each star. You can then find the mean and standard deviation for this group of measurements in each velocity coordinate.

Answer Desk

You won't find a good book that presents the 'weaknesses' of the theory of evolution, and for good reason. There has to date been no convincing challenge to the theory, whilst it has been supported by experimental and circumstantial evidence as well as clear logic over and over and over again, as well as actually being observed taking place numerous times. The closest to what looking for is a book which presents our best understanding of how evolution works, or which discusses competing ideas about how evolution works - there's no question about whether it works.

The Selfish Gene by Richard Dawkins, whilst it contains some errors, has some very clear thinking about evolution in it, and in particular explains why group selection is a misguided idea.

The Logic of Chance: The Nature and Origin of Biological Evolution by Eugene Koonin is a more up-to-date coverage of our current understanding of evolution, in particular with insights from modern genomics.

There are plenty of terrible books about the weaknesses of evolution, but they are deeply flawed. Pick one and I'll be happy to debunk it for you.

Galaxy - Trouble understanding speed-dispersion in (elliptical) galaxies

I'm learning about LOSVDs (Line Of Sight Velocity Distributions) and I'm having a bit of trouble understanding the used terms.

As I understand, the LOSVD of a given (elliptical) galaxy is the density distribution of the LOS-velocities. The full LOSVD is difficult to find and it's easier to find 2 parameters of the distribution: $bar v_<_>$ and $sigma_<_>$ by fitting a (Gaussian) model to the spectrum of the galaxy.

I have a limited understanding of statistics, so I'm having trouble intuitively understanding what these 2 parameters mean later on.

I think that $bar v_<_>$ is simply the average value of the LOS-velocity for the whole galaxy while $sigma_<_>$ is the equivalent of a standard deviation.

Now later on in my coursebook, there's an explanation of how to get a LOSVDs for every point (/pixel) in the (projection onto the celestial sphere of the) galaxy by using 3D spectrography.
From this we can get a 3D dynamic model from our 2D kinematic model. In this newly found 3D distribution there's also 3 Sigmas, one for every dimension.

But here comes the part I don't understand:
The book is looking at the movement of stars in a spiral galaxy, the Milky way in particular.

We're trying to find a correlation between the age of MS-stars and their dispersion and so there's a dataset of a few stars in the neighbourhood of the sun with their dispersion in every dimension.

What is the meaning of dispersion in this context? How can a single object have a dispersion if it's a parameter of a density distribution?

A Long Time Ago in a Galaxy Far, Far Away

What has become the widely accepted model of galaxy formation is largely gleaned from simulations of cosmic evolution that reproduce our observations of the local universe&mdashthe stuff we can see near the Milky Way.

After the big bang, the cosmos expanded and stretched out fairly evenly in all directions. But, Neeleman says, you get &ldquotiny density variations in the fabric of the universe.&rdquo These variations are home to clumps of dark matter, a substance that emits little, if any, electromagnetic radiation. As such, dark matter has yet to be directly detected, but observations of galaxies indicate that this invisible mass produces its own gravitational pull. That means that these dark matter clumps attract &ldquoordinary&rdquo matter (the stuff we humans can detect and interact with), most of which is gas. The gas tumbles into these gravity wells and squashes together to trigger star formation. More matter continues to tumble into these ever expanding wells&mdashcalled dark matter &ldquohalos&rdquo by astronomers&mdashgradually forming bigger and bigger structures over the 13.8-billion-year lifetime of the universe. This process should more or less create the distribution of galaxies we see today, says Paolo Saracco, an astronomer at Italy&rsquos National Institute for Astrophysics and the lead author of a study reporting the recent observations of C1-23152.

That is why ancient massive galaxies are problematic. &ldquoFor our current understanding of galaxy formation, we sort of built on the galaxies we knew at the time,&rdquo says Coral Wheeler, an astronomer at California State Polytechnic University, Pomona, who was not involved with the new study. These galaxies did not include the very old, small or big ones. Looking further back in time with increasingly powerful telescopes began to reveal these apparent outliers. And as the tally of anomalous entities rose, astronomers started wondering if their models needed to expand to make room for them or if those models would buckle and break under the strain.

As reported in the Astrophysical Journal in December 2020, Saracco&rsquos team managed to extract some juicy details out of C1-23152. Light from far-distant cosmic regions is stretched by the expanding universe as it travels to Earth. The more it is stretched, the greater its shift towards the longer-wavelength &ldquoredder&rdquo section of the electromagnetic spectrum. This &ldquoredshift&rdquo of C1-23152&rsquos starlight indicates that it appeared 12 billion years ago, way back in the universe's youth. The fact that this galaxy is both ancient and massive alone is problematic enough for traditional slowly-but-surely models of galaxy formation. But it did not just appear fully formed. Saracco and his team&rsquos real breakthrough was to trace C1-23152&rsquos history of star formation from across the universe.

The key to that breakthrough was seeing the giant galaxy&rsquos spectrum&mdasha rainbowlike measurement of the various wavelengths, or colors, that an object emits or absorbs. Particular color combinations distinguish specific elements, which means this spectral symphony can be used to determine the composition of a galaxy&rsquos stars. Using that power, Saracco says, &ldquofor the first time, we derived, with very good accuracy, the mean age of the stellar population inside [C1-23152] and the time necessary to form those stars.&rdquo

The number of elements in C1-23152 that were found to be heavier than hydrogen and helium&mdashwhich astronomers collectively refer to as &ldquometals&rdquo&mdashhinted at its strangeness. Metals are produced by star formation, which jettisons them into a galaxy&rsquos interstellar medium through supernovae&mdashmaking them available for next-generation stars to use. More metals equal more cycles of star formation, and it took present-day massive galaxies many billions of years to become metal-rich. C1-23152&rsquos spectrum revealed the galaxy to be a veritable metal bonanza back in its early days, which means it made a lot of stars very rapidly not long after it first formed.

How rapidly? The spectral features of stars can answer that question, too, because they reveal which ones have elements typical of younger or older stars. The youngest stars in C1-23152 are roughly 150 million years old. The most ancient are about 600 million years old. That means the galaxy made some 200 billion solar masses in just a half-billion years&mdasha rate of 450 stars per year, more than one per day. The figure is almost 300 times greater than estimates of the Milky Way&rsquos current output. If most galaxies are slow-burning log fires, with new flames popping up every so often, C1-23152 is a gasoline-soaked bonfire.

C1-23152 and its similar cousins present astronomers with a potentially model-breaking conundrum: How can massive galaxies be assembled and set alight so quickly so early on? For now the answer, in short, is that they can&rsquot.

“Disturbing” –The Existence of Gargantuan Galaxies at Dawn of the Universe

The anatomy of an enigma: a team of astronomers using the Large Binocular Telescope Observatory (LBT) atop Mount Graham in southeastern Arizona collected 17 hours’ worth of light from the abnormally massive elliptical galaxy dubbed C1-23152 (image above). The young galaxy is 12 billion light years away and defies conventional models of its origins as it must have accumulated its enormous mass within 1.8 billion years after the big bang, less than 13% of the present age of the universe. Most elliptical galaxies, such as C1-23152 at the center of a galaxy cluster, take many billions of years to reach their massive sizes. Hence the enduring mystery of how and why these monster objects exist in the early universe.

The Enigma of C1-23152

The most massive galaxies that we observe in the universe reach masses of several hundred billion times that of our Sun. Although they comprise only one third of all galaxies, they contain more than 70% of the stars in the Universe. The current model of galaxy formation – the so-called hierarchical model – predicts that smaller galaxies formed earlier, while more massive systems formed later, through subsequent mergers of the pre-existing smaller galaxies. Hence the enigma of C1-23152 — how these galaxies formed so rapidly is among the most debated questions of modern astrophysics.

“The data show that the formation time of C1-23152, that is the time elapsed between the formation of the first stars from the pre-existing gas to the moment when the star formation has almost completely ceased, is less than 500 million of years” says Paolo Saracco, researcher at INAF in Milan and first author of the article published in The Astrophysical Journal. “Also, from the data collected with LBT we were able to establish that in this short time, corresponding to less than 4 hundredths of the age of the Universe, the galaxy formed a mass equal to about 200 billion stars like the Sun, that is about 450 suns per year.” or more than one per day, a star formation rate almost 300 times higher than the current rate in our galaxy, the Milky Way.”

“The Milky Way, now forms no more than two a year”, adds Danilo Marchesini , full professor at Tufts University and second author of the article. The large amount of information collected allowed the team to quantify for the first time in a galaxy so distant the abundance of chemical elements heavier than helium (the so-called metallicity). The stars of this ancient galaxy have a higher metallicity than that of our much younger Sun, similar to that observed in the most massive galaxies in the universe today.

Massive Galaxies in the Universe Can Occur Extremely Quickly

“These observations showed that the formation of the most massive galaxies in the universe can occur extremely quickly, through an extremely intense star formation process in the early Universe, as for C1-23152″, underscores Francesco La Barbera , researcher at INAF in Naples, in the team that conducted the study.

“Understanding whether the scenario that describes the formation of C1-23152 is a particular case or whether, on the contrary, it is what happens for most of the most massive galaxies in the universe is of fundamental importance since this would require a profound revision of the galaxy formation models”, adds Adriana Gargiulo , also a researcher at INAF in Milan and co-author of the study.

The image at the top of the page shows galaxy C1-23152 at a redshift when the Universe was 1.8 billion years old. The image is the sum of images at different wavelengths taken with the Hubble Space Telescope. Its light profile matches exactly those of typical elliptical galaxies in the local Universe but with a mass of about 200 billions sun-like stars that formed in less than 500 million years.

The image below from the LBT Observatory illustrates the formation scenario of massive elliptical galaxies like C1-23152. Massive primordial gas clouds, falling in the same region under the effect of gravitational force, collide triggering violent and massive star formation processes. The starburst phase is expected to last a few hundred million years during which hundreds to thousands of stars per year are formed, as for C1-23152. The resulting massive elliptical galaxy will then evolve with time, possibly experiencing different evolutionary phenomena.

The formation of stellar masses as high as for C1-23152 requires both high masses of gas to convert into stars and particular physical conditions, reports the LBT. A possible scenario hypothesized by the researchers is that massive primordial gas clouds, falling under the effect of gravitational force in the same region, collide, triggering violent and massive star formation processes. From the observational point of view, the precursors of the most massive galaxies could therefore be remote galaxies with a very high rate of star formation.

This image shows an example of starburst galaxies forming about a thousand stars per year at the time of observation. This phase is most likely the formation phase of massive galaxies in the early Universe, like C1-23152.

Galaxy Dark-Matter Halos 40 Million Years After Big Bang

Scientists have found clues elsewhere that may account for these ancient mega galaxies, reports Robin George Andrews for Scientific American : “ Anastasia Fialkov , a cosmologist at the University of Cambridge, who was not involved with the latest work, says that, unlike full-blown simulations, analytic physics calculations can “take into account the whole volume of the universe.” And they suggest that a small number of dark matter halos capable of initiating star formation show up just 40 million years after the big bang.”

“To test our hypotheses, the observations that the next generation of instrumentations will allow us to carry out will be decisive, in particular the James Webb Space Telescope (JWST) which will be launched in orbit at the end of 2021, and the Extremely Large Telescope (ELT) the largest ground-based telescope ever built, with a main mirror of 39 meters in diameter, which will be operational in 2026”, concludes Saracco.

The Daily Galaxy, with Maxwell Moe , NASA Einstein Fellow , University of Arizona , via LBT , INAF , and Scientific American


Computer simulations of merging galaxies are amusing to watch -- they compress hundreds of millions of years into a few seconds of screen time. The Space Telescope Science Institute has both Mpeg and QuickTime videos of a computer simulation of the merger of the ``Mice''.

(2) Galaxy collisions often trigger bursts of star formation.

Although stars don't collide when two galaxies merge, the much larger gas clouds do. The clouds in the two galaxies slam into each other violently. Shock waves from the collision run through the clouds and trigger the collapse of dark nebulae to form stars. Thus, if the two colliding galaxies are rich in gas, their merger will be accompanied by a burst of star formation.

  • Infrared radiation from protostars embedded within dusty clouds. The galaxy named M82 is the galaxy with the greatest apparent brightness in the infrared. Why? Because it is undergoing star formation after a recent collision with its neighbor M83.
  • Blue light emitted by luminous but short-lived O and B stars. The two galaxies shown below are known as the ``Antennae'' galaxies. They are in the process of merging with each other note how tidal forces have warped them into asymmetric shapes. The blue areas within the galaxies are regions where star formation is being triggered.

(3) The merger of spiral galaxies produces elliptical galaxies.

Spiral galaxies are ordered systems. All the stars in the spiral's disk go around the center on circular orbits, in the same direction.
Elliptical galaxies, by contrast, are very disordered systems. The stars in the elliptical galaxy are on orbits of all eccentricities, oriented randomly. Elliptical galaxies, in sort, are not tidy.

Galaxy mergers are like car crashes. When you collide two neat, orderly sports cars, you don't get a neat, orderly SUV. Instead you get a disordered, chaotic tangle of metal. Similarly, when you collide two neat, orderly spiral galaxies, you don't get a neat, orderly bigger spiral. Instead you get a disordered, chaotic elliptical galaxy.

Elliptical galaxies are found most frequently in rich clusters because rich clusters are crowded with many galaxies, and collisions are frequent.
Spiral galaxies are found most frequently in poor clusters because poor clusters contain few galaxies, spaced relatively far apart, and collisions are less frequent.

The giant elliptical galaxies found near the center of rich clusters are huge, containing about a trillion stars apiece. They have gradually grown to this immense size by ``cannibalizing'' smaller galaxies. In many cases, you can see the partially ``digested'' smaller galaxies as luminous spots within the giant galaxy that has engulfed it.

Collisions do occur from time to time within poor clusters. For instance, within the Local Group itself, our galaxy and the Andromeda Galaxy are falling toward each other at a speed of 300 kilometers/sec. About 3 billion years from now, they will be close enough together to distort each other tidally, producing long tails. About 4 or 5 billion years from now, they will have merged into a single (badly mis-shapen) galaxy. About 6 billion years from now, all the stars from the two galaxies, as well as the stars that formed when they merged, will have settled down into a single giant elliptical galaxy.

Thursday, May 12, 2011

Sanders Final Post

Final Exam Paper for Astronomy 561

My Subject for this paper is Possibility of Settlement between Modification of Newtonian Mechanics versus Dark Matter and Dark Energy. While I wish to produce a scholarly paper, I would also like my high school students to read this article and begin to understand what the nature of science and the nature of scientist are all about. Even when experienced scientist and engineers are on the trail of understanding, they sometimes forget that for every question they answer two new questions seem to appear. It seems the more we learn, the less we know. Also no student or professional should forget the pursuit of knowledge can be fun and exciting, not boring.

Before we have an argument between MOND versus Dark Matter and Dark Energy, maybe we should observe the disagreements between MOND believers. When I read any single paper, I am lead by reason to believe a solution is at hand. However, the next paper always points out some problem with the new adjustment to Newton’s modified law. In this paper I have quoted:

Astronomy Abstract Service and provide the
Bibliographic Code: 2010MNRAS.407.1128S
for that particular Abstract

The idea is to allow each reader to make a judgment about several modified theories and the weakness of each. My judgment is that each adjustment seems reasonable but with thirteen adjustments we have one monster formula not ready for use in our own homes.

Title: The Universal Faber-Jackson relation by Sanders, R. H. #1
Bibliographic Code: 2010MNRAS.407.1128S

In the context of modified Newtonian dynamics, the Fundamental Plane, as the observational signature of the Newtonian viral theorem, is defined by high-surface-brightness objects that deviate from being purely isothermal: the line-of-sight velocity dispersion should slowly decline with radius as observed in luminous elliptical galaxies. All high-surface-brightness objects (e.g. globular clusters, ultra-compact dwarfs) will lie, more or less, on the Fundamental Plane defined by elliptical galaxies, but low-surface-brightness objects (dwarf spheroidals) would be expected to deviate from this relation. This is borne out by observations. With Milgrom's modified Newtonian dynamics (MOND), the Faber-Jackson relation (L

σ4), ranging from globular clusters to clusters of galaxies and including both high- and low-surface-brightness objects, is the more fundamental and universal scaling relation in spite of its larger scatter. The Faber-Jackson relation reflects the presence of an additional dimensional constant (the MOND acceleration a0) in the structure equation.

Title: Exact Solutions and Approximations of Mond Fields of Disk Galaxies #2
Author: Brada, R and Milgrom, M
Bibliographic Code:

We consider models of thin disks (with and without bulges) in the Bekenstein-Milgrom formulation of MOND as a modification of Newtonian gravity. Analytic solutions are found for the full gravitational fields of Kuzmin disks, and of disk-plus-bulge generalizations of them. For all these models a simple algebraic relation between the MOND potential field and the Newtonian potential holds everywhere outside the disk. We give exact expressions for the rotation curves for these models. We also find that the algebraic relation is a very good approximation for exponential disks. The algebraic relation outside the disk is then extended into the disk to derive an improved approximation for the MOND rotation curve of disk galaxies that requires only knowledge of the Newtonian curve and the surface density.

Title: MOND in the early universe #3
Author: McGaugh, Stacy
Bibliographic Code: 1999AIPC..470󈼠M

I explore some consequences of Milgrom's modified dynamics for cosmology. There appear to be two promising tests for distinguishing MOND from CDM: (1) the rate of growth of structure and (2) the baryon fraction. These should be testable with observations of clusters at high redshift and the microwave background, respectively.

Title: Modified Newtonian dynamics and its implications #4
Author: Sanders, R. H.
Bibliographic Code:

Milgrom has proposed that the appearance of discrepancies between the Newtonian dynamical mass and the directly observable mass in astronomical systems could be due to a breakdown of Newtonian dynamics in the limit of low accelerations rather than the presence of unseen matter. Milgrom's hypothesis, modified Newtonian dynamics or MOND, has been remarkably successful in explaining systematic properties of spiral and elliptical galaxies and predicting in detail the observed rotation curves of spiral galaxies with only one additional parameter-- a critical acceleration which is on the order of the cosmologically interesting value of $cH_o$. Here I review the empirical successes of this idea and discuss its possible extension to cosmology and structure formation.

Title: Modified Newtonian dynamics and its implications #5
Author: Sanders, R. H. McGaugh, Stacy S.
Bibliographic Code: 2002ARA&A..40..263S

Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below ao

cHo/6 the effective gravitational attraction approaches √(gnao), where gn is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and a mass-rotation velocity relation of the form M ∝ V4 that forms the basis for the observed luminosity-rotation velocity relation-the Tully-Fisher law. We review the phenomenological success of MOND on scales ranging from dwarf spheroidal galaxies to super clusters and demonstrate that the evidence for dark matter can be equally well interpreted as evidence for MOND. We discuss the possible physical basis for an acceleration-based modification of Newtonian dynamics as well as the extension of MOND to cosmology and structure formation.

Title: General Relativity and Quantum Cosmology, Astrophysics #6
Origin: ARXIV
Bibliographic Code: 2006gr.qc…..4047F

Empirical implications of a teleparallel displacement of momentum between initial and final quantum states, using conformally flat quantum coordinates are investigated. An exact formulation is possible in an FRW cosmology in which cosmological redshift is given by 1+z=a_0^2/a^2(t). This is consistent with current observation for a universe expanding at half the rate and twice as old as indicated by a linear law, and, in consequence, requiring a quarter of the critical density for closure. A no CDM teleconnection model resolves inconsistencies between galactic profiles found from lensing data, rotation curves and analytic models of galaxy evolution. The teleconnection model favors a closed no Lambda cosmology. After rescaling Omega so that Omega=1 is critical density, for 225 supernovae, the best fit teleconnection no Lambda model with Omega=1.89 is marginally preferred to the best fit standard flat space Lambda model with Omega=0.284. It will require many observations of supernovae at z>1.5 to eliminate either the standard or teleconnection magnitude-redshift relation. In quantum coordinates the anomalous Pioneer blueshift and the flattening of galaxies' rotation curves appear as optical effects, not as modifications to classical motions. An exact form of Milgrom's phenomenological law (MOND) is shown.

Title: Are Dark Matter and Dark Energy the Residue of the Expansion-Reaction to the Big Bang? #7
Author: Ringermacher, Harry I.Mead, Lawrence R.
Bibliographic Code: 2006gr.qc….10083R

We derive the phenomenological Milgrom square-law acceleration, describing the apparent behavior of dark matter, as the reaction to the Big Bang from a model based on the Lorentz-Dirac equation of motion traditionally describing radiation reaction in electromagnetism but proven applicable to expansion reaction in cosmology. The model is applied within the Robertson-Walker hypersphere, and suggests that the Hubble expansion exactly cancels the classical reaction imparted to matter following the Big Bang, leaving behind a residue proportional to the square of the acceleration. The model further suggests that the energy density associated with the reaction acceleration is precisely the critical density for flattening the universe thus providing a potential explanation of dark energy as well. A test of this model is proposed.

Title: Modified Gravity Without Dark Matter #8
Author: Sanders, Robert
Bibliographic Code: 2007LNP�..375S

On an empirical level, the most successful alternative to dark matter in bound gravitational systems is the modified Newtonian dynamics, or MOND, proposed by Milgrom. Here I discuss the attempts to formulate MOND as a modification of General Relativity. I begin with a summary of the phenomenological successes of MOND and then discuss the various covariant theories that have been proposed as a basis for the idea. I show why these proposals have led inevitably to a multi-field theory. I describe in some detail TeVeS, the tensor-vector-scalar theory proposed by Bekenstein, and discuss its successes and shortcomings. This lecture is primarily pedagogical and directed to those with some, but not a deep, background in General Relativity.

Title: Modified gravity and the phantom of dark matter #9
Author: Brownstein, Joel Richard
Bibliographic Code: 2009PhDT….�B

Astrophysical data analysis of the weak-field predictions support the claim that modified gravity (MOG) theories provide a self-consistent, scale-invariant, universal description of galaxy rotation curves, without the need of non-baryonic dark matter. Comparison to the predictions of Milgrom's modified dynamics (MOND) provides a best-fit and experimentally determined universal value of the MOND acceleration parameter. The predictions of the modified gravity theories are compared to the predictions of cold non-baryonic dark matter (CDM), including a constant density core-modified fitting formula, which produces excellent fits to galaxy rotation curves including the low surface brightness and dwarf galaxies. Upon analyzing the mass profiles of clusters of galaxies inferred from X-ray luminosity measurements, from the smallest nearby clusters to the largest of the clusters of galaxies, it is shown that while MOG provides consistent fits, MOND does not fit the observed shape of cluster mass profiles for any value of the MOND acceleration parameter. Comparison to the predictions of CDM confirm that whereas the Navarro-Frenk-White (NFW) fitting formula does not fit the observed shape of galaxy cluster mass profiles, the core-modified dark matter fitting formula provides excellent best-fits, supporting the hypothesis that baryons are dynamically important in the distribution of dark matter halos.
Origin: WILEY

MNRAS Keywords: galaxies: kinematics and dynamics, cosmology: theory, dark matter
DOI: 10.1111/j.1365-2966.2009.16184.x

The above link should access all the Bibliographic Code.
A new formulation of modified Newtonian dynamics (MOND) as a modified-potential theory of gravity is propounded. In effect, the theory dictates that the MOND potential φ produced by a mass distribution ρ is a solution of the Poisson equation for the modified source density, where g = ν(|gN|/a0)gN, and gN is the Newtonian acceleration field of ρ. This makes φ simply the scalar potential of the algebraic acceleration field g. The theory thus involves solving only linear-differential equations, with one non-linear, algebraic step. It is derivable from an action, satisfies all the usual conservation laws, and gives the correct centre-of-mass acceleration to composite bodies. The theory is akin in some respects to the non-linear Poisson formulation of Bekenstein and Milgrom, but it is different from it, and is obviously easier to apply. The two theories are shown to emerge as natural modifications of a Palatini-type formulation of Newtonian gravity, and are members in a larger class of bi-potential theories.

I hope these articles of scholarly research give readers some idea of the many views of fellow scientists who agree in their pursuit of MOND theory. I know as a trained scientist and engineer, I have tried to make astute observations.

I have attempted, with earnest effort, to avert all feelings from my youth while I lived across the street from a Pentecostal Church. This period of time was before TV. On Saturday night neighbors from far and near would arrive at my parent’s front porch to watch the “Holy Rollers” in action!! At times when I review some of this “Science Debate,” that “Old Time Feeling” returns. I may be watching “Scientist Holy Rollers” in a MOND versus Dark Matter debate.

If You Could See Neutrinos.

. how far back into the universe could you see?

For the case of photons we look at the cosmic microwave background (CMB) and use it to construct an image of the so called 'surface of last scattering', which represents the moment when photons decoupled from and were able to escape the cosmic plasma. This corresponds to a t=380,000 years (with t=0 being the very beginning) in the current theory.

For the case of neutrinos we would look to the cosmic neutrino background (CNB) and try to use that to construct a surface of last scattering for the neutrinos. At what time did neutrinos decouple from the cosmic plasma? Current theories predict that this decoupling time occurred when the universe was less then a second old.

It would stand to reason then that one should be able to use neutrinos to 'look further back' into the universe. In other words, one would expect the last scattering surface for neutrinos to be further back than the last scattering surface for photons.

However, at least one paper finds the opposite to be true:

Somewhat counter-intuitively, the CNB last scattering surface turns out to be much closer and much thicker than the CMB surface--the paper suggests it has to do with the fact that neutrinos are able to have different velocities from each other.

So perhaps the neutrino's LSS is inside the CMB's, but where might the dark matter LSS be?

Mass-to-Light Ratio

A useful way of characterizing a galaxy is by noting the ratio of its mass (in units of the Sun’s mass) to its light output (in units of the Sun’s luminosity). This single number tells us roughly what kind of stars make up most of the luminous population of the galaxy, and it also tells us whether a lot of dark matter is present. For stars like the Sun, the mass-to-light ratio is 1 by our definition.

Galaxies are not, of course, composed entirely of stars that are identical to the Sun. The overwhelming majority of stars are less massive and less luminous than the Sun, and usually these stars contribute most of the mass of a system without accounting for very much light. The mass-to-light ratio for low-mass stars is greater than 1 (you can verify this using the data in [link]). Therefore, a galaxy’s mass-to-light ratio is also generally greater than 1, with the exact value depending on the ratio of high-mass stars to low-mass stars.

Galaxies in which star formation is still occurring have many massive stars, and their mass-to-light ratios are usually in the range of 1 to 10. Galaxies consisting mostly of an older stellar population, such as ellipticals, in which the massive stars have already completed their evolution and have ceased to shine, have mass-to-light ratios of 10 to 20.

But these figures refer only to the inner, conspicuous parts of galaxies ([link]). In The Milky Way Galaxy and above, we discussed the evidence for dark matter in the outer regions of our own Galaxy, extending much farther from the galactic center than do the bright stars and gas. Recent measurements of the rotation speeds of the outer parts of nearby galaxies, such as the Andromeda galaxy we discussed earlier, suggest that they too have extended distributions of dark matter around the visible disk of stars and dust. This largely invisible matter adds to the mass of the galaxy while contributing nothing to its luminosity, thus increasing the mass-to-light ratio. If dark invisible matter is present in a galaxy, its mass-to-light ratio can be as high as 100. The two different mass-to-light ratios measured for various types of galaxies are given in [link].

Figure 1. This galaxy is a face-on spiral at a distance of 21 million light-years. M101 is almost twice the diameter of the Milky Way, and it contains at least 1 trillion stars. (credit: NASA, ESA, K. Kuntz (Johns Hopkins University), F. Bresolin (University of Hawaii), J. Trauger (Jet Propulsion Lab), J. Mould (NOAO), Y.-H. Chu (University of Illinois, Urbana), and STScI)

These measurements of other galaxies support the conclusion already reached from studies of the rotation of our own Galaxy—namely, that most of the material in the universe cannot at present be observed directly in any part of the electromagnetic spectrum. An understanding of the properties and distribution of this invisible matter is crucial to our understanding of galaxies. It’s becoming clearer and clearer that, through the gravitational force it exerts, dark matter plays a dominant role in galaxy formation and early evolution. There is an interesting parallel here between our time and the time during which Edwin Hubble was receiving his training in astronomy. By 1920, many scientists were aware that astronomy stood on the brink of important breakthroughs—if only the nature and behavior of the nebulae could be settled with better observations. In the same way, many astronomers today feel we may be closing in on a far more sophisticated understanding of the large-scale structure of the universe—if only we can learn more about the nature and properties of dark matter. If you follow astronomy articles in the news (as we hope you will), you should be hearing more about dark matter in the years to come.

Answers and Replies

That has nothing to do with local and distant galaxies. It's referring to our Milky Way galaxy

Many thanks for the help folks.

I thought this thread had died stillborn.

The recent discovery of the galaxy SPT0418-47 has piqued my interest.

It's my current understanding that galaxies at this red shift are expected to display very different characteristics (star formation rates, rotation, metallicity, size, etc.) to the mature and highly-evolved galaxies in the local universe. But, it appears that certain characteristics of SPT0418-47 seem to buck this expectation.

It occurs to me that I need to discover more about how galaxies are characterised. Then, knowing this I could look at the characteristics of local galaxies and compare them to those distant ones with a better understanding.

So, this prompts me to ask the following questions.

Is finding out about how galaxies are characterised a good first step in understanding the differences between distant, early galaxies and nearby, evolved ones in the local universe?

If so, could I please be directed to some Basic Level resources (links, websites, blogs, etc.) that will help me achieve this?

If not, could I please be guided to a better option?

1) is correct, but the link offered for 2) is not a very good one, yet I don´ t know a better one.

The classification of nearby galaxies is basically into "elliptical" and "spiral" galaxies, with intermediate group of "lenticular". plus "irregular" galaxies.
Irregular galaxies are common even in local universe - just look up for the Magellanic Clouds. Yet the link only briefly mentions irregular galaxies, and discusses elliptical and spiral galaxies at length.

The problem with SPT0418-47 refers to a guess that young world should have had only irregular galaxies, and no elliptic or spiral galaxies.

Trouble understanding speed-dispersion in (elliptical) galaxies - Astronomy

Elliptical galaxies are the second largest class of galaxies by number, comprising roughly 30% of all observed galaxies, and a larger fraction of galaxies in dense environments such as galaxy clusters. Compared with spiral galaxies, elliptical galaxies are very regular and smooth in appearance, and contain very little gas, dust, or young stars.

Until 1975, most astronomers viewed elliptical galaxies as oblate spheroids flattened by rotation. In this model, elliptical galaxies were thought to be similar to spiral galaxies in their dynamics and formation history, the principal difference being the efficiency of star formation during collapse of the protogalactic cloud (low efficiency in spirals, high in ellipticals). However, that year saw the publication of the first accurate measurements of the rotation velocities of elliptical galaxies, derived from absorption-line spectra of the stars. These studies, and a large body of observational work since that time, have indicated that the majority of bright elliptical galaxies rotate much too slowly for their shapes to be determined by rotation. It is now believed that the motions of the stars in most elliptical galaxies are essentially random the shapes of these galaxies are determined by the large-scale anisotropy of the stellar motions, that is, the degree to which random velocities are different in different directions. Since rotation is not very important in these galaxies, there is no compelling reason to assume that they are oblate, and it is now generally believed that elliptical galaxies are triaxial, that is, that their figures are ellipsoids (possibly slowly rotating) with three unequal axes. Since 1975, theoretical and observational work on the dynamics of elliptical galaxies has focused on the following problems: determining their three-dimensional shapes, understanding the character of stellar orbits in triaxial potential wells, constructing self-consistent triaxial models, searching for correlations between the kinematical and morphological parameters of elliptical galaxies, deriving their masses and mass distributions, and resolving the structure of their cores.


To first order, the appearance of an elliptical galaxy on the sky can be described in terms of its surface brightness profile and its apparent shape. Most elliptical galaxies are well described by an empirical surface brightness law first proposed by Gerard de Vaucouleurs:

where Re is the effective radius and corresponds to the radius that encloses half of the total integrated luminosity of the galaxy, and e is the surface brightness at Re. Deviations from this law are often correlated with a galaxy's environment. For instance, dwarf companions to larger galaxies often show surface brightness profiles that fall off more rapidly than de Vaucouleurs's law, an effect that may be attributable to tidal truncation of the envelopes of these galaxies. The brightest elliptical galaxies, called cD galaxies, have more extensive envelopes than predicted by de Vaucouleurs's law. These galaxies are always located at the centers of galaxy clusters, and their envelopes are thought to consist of tidal debris from other cluster galaxies.

The isophotal contours of most elliptical galaxies are usually elliptical to a high degree of accuracy. However, the elongation and orientation of these isophotal ellipses often varies with position. In contrast to surface brightness, ellipticity shows no characteristic dependence on radius: Flattening sometimes increases, sometimes decreases, and sometimes remains roughly constant with radius. The same is true with regard to the orientation of the isophotal major axis as a function of position. The origin and significance of these isophotal twists is not well understood. One possibility is that they result simply from the galaxy's triaxial form, because a set of nested, triaxial ellipsoids with differing ellipticities will show twisted isophotes if viewed from a direction that does not lie along one of the symmetry axes. Alternatively, the twists may be intrinsic, resulting from tidal interactions with neighboring galaxies.


Galaxies are "collisionless" systems: Each star moves along its orbit under the influence of the smooth gravitational potential of the whole galaxy, and hardly ever comes close enough to another star for its motion to be significantly perturbed by the encounter. The basic time scale that governs the dynamical evolution of a collisionless system is just the time for a typical star to cross it in its orbit, called the "dynamical" or "crossing" time it is given roughly by

where Mgal and Rgal are the galaxy's mass and radius, M is the mass of the Sun, and G is the gravitational constant. A typical large elliptical galaxy has a dynamical time near the center of about 10 8 yr. Because this value is much shorter than the age of the universe (

10 10 yr), elliptical galaxies are thought to be well "relaxed" that is, the spatial distribution of stars in these galaxies should long since have reached a smooth unchanging state, and the potential well through which each star moves should be nearly fixed in time.

Computer modeling has shown that most of the stellar orbits in nonrotating triaxial potentials fill volumes with one of two characteristic shapes. "Box" orbits densely fill regions similar to rectangular parallelepipeds the basic character of the motion is up and down along the long axis of the galaxy. "Tube" orbits fill roughly doughnut-shaped regions these orbits circulate around the short or the long axis of the galaxy and avoid the center. Tube orbits are the only orbits present in axisymmetric (oblate or prolate) potentials it is the box orbits that are uniquely associated with triaxial potentials, and that permit self-consistent triaxial galaxies to exist. Box orbits have the important additional property that a star on such an orbit eventually passes arbitrarily close to the center of the galaxy. This could be important if - as recent observations suggest-some elliptical galaxies contain massive objects (such as black holes) in their cores, since the massive objects will perturb the orbits and induce slow changes in the galaxy's shape.

In addition to the box and tube orbits, which are called "regular," some fraction of the orbits in most triaxial potentials are found to be "irregular," or "stochastic." Stochastic orbits have no well-defined shape instead they traverse first one, then another, volume, with the transition occurring nearly randomly. It is at present uncertain whether the slow diffusion of these stochastic orbits implies a slow evolution of the structure of elliptical galaxies, on a time scale longer than the dynamical time but shorter than the age of the universe.

Important as orbital studies are for understanding the internal structure of elliptical galaxies, the interpretation of observational data generally involves considerably less-detailed models than the sort described above. This is because the dynamical information available observationally - the rotation velocity and the velocity dispersion of the stars, projected along lines of sight through the galaxy - is not nearly sufficient to constrain a unique orbital model, even if the three-dimensional shape of the galaxy were known. Fortunately, many interesting questions about the dynamics of elliptical galaxies can be answered, at least in part, with the types of observational data currently available. One such question, mentioned above, concerns the degree to which elliptical galaxies are supported by rotation as opposed to velocity anisotropies. Simple calculations based on an isotropic model, in which the random component of the stellar motion is the same in all directions at a given point, indicate that the rotation velocity of an elliptical galaxy with an axis ratio of 1:2 should be roughly comparable to its velocity dispersion along the line of sight. In the early 1970s, advances in photon-detection systems and digital data processing permitted the first accurate determinations of these quantities in a number of elliptical galaxies. The results showed clearly that the majority of bright ellipticals were rotating too slowly, by a factor of about 2, for their flattenings to be explained by rotation thus the velocity distributions in these galaxies had to be strongly anisotropic. In general, the degree of rotational support is observed to increase as galaxy luminosity decreases, with the least-luminous elliptical galaxies having rotation velocities consistent with that expected for isotropic oblate rotators. More recent work has uncovered significant rotation around the apparent long axis of several elliptical galaxies, a result that is easiest to understand if these galaxies are strongly triaxial or prolate.

Much observational work has concentrated on measuring the dependence of stellar velocity dispersion on radius in a large sample of galaxies. These data can be used in one of two ways. If one assumes that the variation of mass density with radius is known for a galaxy - for instance, by equating the mass density to some fixed multiple (the mass-to-light ratio) of the luminosity density, which is easily measured - then one can use the velocity dispersion profile to understand how the basic character of the stellar motion varies with radius. For instance, if the stellar orbits are predominantly radial (i.e., boxes), then the component of their motion along the line of sight falls off more rapidly with radius than if the orbits are mostly circular (i.e., tubes). Alternatively, if one makes an assumption about the orbital character - for instance, that the stellar motions are approximately isotropic - then the variation of velocity dispersion with radius constrains the distribution of mass in the galaxy, since the typical orbital velocity at every radius depends on the amount of matter producing the gravitational acceleration. Unfortunately, it is impossible to determine both the orbital character and the mass distribution given only the observed velocity dispersions, and this fact has greatly hampered the interpretation of dynamical data. Fortunately, other techniques can sometimes be used to place independent constraints on the mass-to-light ratio these include measurement of the rotation velocity of the gaseous disks that appear in a small fraction of elliptical galaxies, and observations at x-ray wavelengths of the hot gas that is sometimes present in galactic potential wells. At present, however, there is no elliptical galaxy for which the mass distribution or the character of the stellar orbits has been well determined. It is not yet certain, for instance, whether elliptical galaxies are typically surrounded by the massive dark matter halos that are known to be prevalent around spiral galaxies, although the x-ray data strongly suggest the existence of such halos around a few elliptical galaxies.


Observations of the very centers of elliptical galaxies are hampered by distortions induced by motions in the earth's atmosphere, which limit angular resolution to about one second of arc, regardless of the size of the telescope. It was not until about 1985 that careful observations verified the existence of cores in most elliptical galaxies, that is, regions near the center where the surface brightness levels off to a nearly constant value. (Note that de Vaucouleurs's law predicts an ever-rising central brightness.) Typical core radii, that is, radii at which the surface brightness equals half its central value, range from about 1 kpc for the brightest elliptical galaxies to less than 100 Pc for the fainter ones. Many elliptical galaxies are also observed to have unresolved, pointlike nuclei, with much smaller radii and much higher surface brightnesses. The first elliptical galaxy for which useful dynamical information about its core was obtained was M87, the brightest member of the Virgo galaxy cluster. Because M87 is relatively nearby and very large, its core is easily resolved. Early observations of the core of M87 revealed stellar random velocities that rose steeply toward the center, an effect that was initially attributed to the gravitational influence of a massive central object, perhaps a black hole. It was later pointed out that other models were equally consistent with the data, including models in which the stellar velocities are very anisotropic, or the core is elongated along the line of sight. However, recent studies of several other nearby elliptical galaxies make a much stronger case for massive central objects. For instance, stars within a few parsecs of the center of M32, a dwarf elliptical galaxy in the Local Group, are observed to rotate about the center with a velocity of about 100 km s -1 . The mass required to produce such large rotational velocities can be derived from the classical equation relating centripetal acceleration to force:

V 2 / R = GM / R 2 ,

where V is the velocity of a star in orbit around a point mass M. The implied mass for the central object in M32 is of order 10 7 solar masses because of the high rotation, this estimate is not strongly dependent on the unknown anisotropies. A number of other nearby galaxies (including our own) appear to have dark massive objects in their nuclei, with masses ranging from 10 6 to 10 9 solar masses. The nature and origin of the central mass concentrations in elliptical galaxies is still obscure. One possibility is that many elliptical galaxies were once quasars, and that the massive objects are the black holes that once powered their phenomenal radio and optical emission. Alternatively, the nuclei of these galaxies may contain dense clusters of stellar remnants such as neutron stars.

On a somewhat larger scale, the presence of significant rotation in the cores of elliptical galaxies is now believed to be a common phenomenon. Observations of nearby elliptical galaxies show that the cores of 1/4 to 1/2 of these galaxies exhibit strong rotation, often around a different axis than that of the rest of the galaxy. These rapidly rotating cores are thought to be the remains of dwarf galaxies that have spiraled to the center of the larger galaxies, remaining substantially intact during the descent their large rotation velocities are all that remains of the original orbital velocity of the dwarf.


In spite of their complexity, elliptical galaxies appear to obey certain laws relating their kinematical and morphological properties. The existence of these laws is important, because they suggest that the process of galaxy formation - which is still very poorly understood - somehow imposes constraints on the present-day form of galaxies, preferring certain final configurations over others. One such correlation, mentioned above, is between the luminosity and rotation velocity of elliptical galaxies: Luminous elliptical galaxies exhibit less rotation, measured in terms of the amount required for rotational support, than faint elliptical galaxies. The dependence is not very tight, however. A much tighter correlation is seen between the total luminosity L and the central velocity dispersion of elliptical galaxies:

called the Faber-Jackson relation (after Sandra M. Faber and Robert E. Jackson). This relation is important because it allows one to estimate the intrinsic luminosity of a galaxy from its observed velocity dispersion, and hence to calculate the galaxy's approximate distance. The Faber-Jackson relation, combined with Fish's law (after Robert Fish), which states that the average surface brightness of elliptical galaxies is roughly constant, implies that all elliptical galaxies have roughly the same mass-to-light ratio. Additional correlations are observed between the parameters that characterize the cores of elliptical galaxies. For instance, the core radius rc depends on total luminosity through the approximate relation

These relations suggest that elliptical galaxies, in spite of their individual complexity, constitute a basically one-parameter family, the single parameter being the total luminosity or the total mass.

Binney, J. and Tremaine, S.(1987). Galactic Dynamics. Princeton University Press, Princeton.

de Zeeuw, T., ed.(1987). Structure and Dynamics of Elliptical Galaxies. proceedings of IAO Symposium 127. Reidel, Dordrecht.

Martinet, L. and Mayor, M., eds.(1982). Morphology and Dynamics of Galaxies. Geneva Observatory, Geneva.

Merritt, D., ed.(1989). Dynamics of Dense Stellar Systems. Cambridge University Press, Cambridge.

Mihalas, D. and Binney, J.(1981). Galactic Astronomy. W.H. Freeman, San Francisco.

Adapted from The Astronomy and Astophysics Encyclopedia, ed. Stephen P. Maran

We've mapped a million previously undiscovered galaxies beyond the Milky Way. Take the virtual tour here.

Credit: CSIRO, Author provided

Astronomers have mapped about a million previously undiscovered galaxies beyond the Milky Way, in the most detailed survey of the southern sky ever carried out using radio waves.

The Rapid ASKAP Continuum Survey (or RACS) has placed the CSIRO's Australian SKA Pathfinder radio telescope (ASKAP) firmly on the international astronomy map.

While past surveys have taken years to complete, ASKAP's RACS survey was conducted in less than two weeks—smashing previous records for speed. Data gathered have produced images five times more sensitive and twice as detailed as previous ones.

What is radio astronomy?

Modern astronomy is a multi-wavelength enterprise. What do we mean by this?

Well, most objects in the universe (including humans) emit radiation over a broad spectrum, called the electromagnetic spectrum. This includes both visible and invisible light such as X-rays, ultraviolet light, infrared light and radio waves.

To understand the universe, we need to observe the entire electromagnetic spectrum as each wavelength carries different information.

Radio waves have the longest wavelength of all forms of light. They allow us to study some of the most extreme environments in the universe, from cold clouds of gas to supermassive black holes.

Long wavelengths pass through clouds, dust and the atmosphere with ease, but need to be received with large antennas. Australia's wide open (but relatively low-altitude) spaces are the perfect place to build large radio telescopes.

We have some of the most spectacular views of the center of the Milky Way from our position in the Southern Hemisphere. Indigenous astronomers have appreciated this benefit for millennia.

A stellar breakthrough

Radio astronomy is a relatively new field of research, dating back to the 1930s.

The first detailed 30cm radio map of the southern sky—which includes everything a telescope can see from its location in the Southern Hemisphere—was Sydney University's Molonglo Sky Survey. Completed in 2006, this survey took almost a decade to observe 25% of the entire sky and produce final data products.

Our team at CSIRO's Astronomy and Space Science division has smashed this record by surveying 83% of the sky in just ten days.

With the RACS survey we produced 903 images, each requiring 15 minutes of exposure time. We then combined these into one map covering the entire area.

The giant Centaurus A galaxy was one elliptical galaxy captured in the RACS survey. Although more than ten million light years away, it’s one of the closest radio galaxies to Earth. You can see its ‘intensity’ represented by different colours. Credit: CSIRO, Author provided

The resulting panorama of the radio sky will look surprisingly familiar to anyone who has looked up at the night sky themselves. In our photos, however, nearly all the bright points are entire galaxies, rather than individual stars.

Astronomers working on the catalog have identified about three million galaxies—considerably more than the 260,000 galaxies identified during the Molonglo Sky Survey.

Why do we need to map the universe?

We know how important maps are on Earth. They provide crucial navigational assistance and offer information about terrain which is useful for land management.

Similarly, maps of the sky provide astronomers with important context for research and statistical power. They can tell us how certain galaxies behave, such as whether they exist in clusters of companions or drift through space on their own.

Being able to conduct an all-sky survey in less than two weeks opens numerous opportunities for research.

For example, little is known about how the radio sky changes over timescales of days to months. We can now regularly revisit each of the three million galaxies identified in the RACS catalog to track any differences.

Also, some of the largest unanswered questions in astronomy relate to how galaxies became the elliptical, spiral, or irregular shapes we see. A popular theory suggests large galaxies grow via the merger of many smaller ones.

But the details of this process are elusive and difficult to reconcile with simulations. Understanding the 13 billion or so years of our universe's cosmic history requires a telescope that can see across vast distances and accurately map everything it finds.

High technology putting new goals within reach

The CSIRO's RACS survey is an amazing advance made possible by huge leaps in space tech. The ASKAP radio telescope, which became fully operational in February last year, was designed for speed.

CSIRO's engineers developed innovative radio receivers called "phased array feeds" and high-speed digital signal processors specifically for ASKAP. It's these technologies that provide ASKAP's wide field of view and rapid surveying capability.

Over the next few years, ASKAP is expected to conduct even more sensitive surveys in different wavelength bands.

In the meantime, the RACS survey catalog is greatly improving our knowledge of the radio sky. It'll continue to be a key resource for researchers around the world.

Full resolution images can be downloaded from the ASKAP data archive.

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Watch the video: Διαδικτυακά Μαθήματα Αστρονομίας. Μάθημα 21ο: ΟΙ ΓΑΛΑΞΙΕΣ (November 2022).