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September 26, 2023

Dark Stars in the Early Universe

By darkmatterdarkenergy
Image Credit: Bill Saxton, ALMA (ESO/NAOJ/NRAO), NRAO/AUI/NSF In this image, from the Atacama Large Millimeter Array in Chile, we are seeing three stars forming from a dusty disk within our own Milky Way. The two objects in the center are separated by 61 astronomical units (Earth-Sun distance is one AU, astronomical unit). One sees evidence of the disk fragmenting to form additional protostars.

Dark Stars is the name given to hypothetical stars in the early universe that were overwhelmingly composed of ordinary matter (baryons [protons and neutrons] and electrons) but that also were ‘salted’ with a little bit of dark matter.

And stars in this category have not evolved to the point of achieving stellar nucleosynthesis in their cores, instead they are, again hypothetically, heated by the dark matter within.

Professor Katherine Freese of the University of Texas physics department (previously at U. Michigan) and others have been suggesting the possibility of dark stars for well over a decade, see “The Effect of Dark Matter on the First Stars: A New Phase of Stellar Evolution”.

In a paper from last year “Dark stars powered by self-interacting dark matter” authors Wu, Baum, Freese, Visinelli, and Yu propose a type of self-interacting dark matter (SIDM). The authors start with the consideration of overdense regions known as ‘halos’ at the epoch of 200 million years for the universe’s age, corresponding to redshift z ~ 20. These are expected due to gravitational instability of slightly overdense regions that we see in the cosmic microwave background maps, from an epoch of only 0.38 million years.

One starts out with these dark matter dominated halos, but the ordinary matter within is much more efficient at collapse since it can radiate energy away electromagnetically. Dark matter, by definition, does not interact electromagnetically, that is why we don’t see it except through its  gravitational effects or if it were to decay into normal matter. That also minimizes its ability to cool and collapse, other than through decay processes.

As the normal matter radiates, cools, and collapses further it concentrates into the center, away from the dark matter halo overall, but would include some modest amount of dark matter. A dark star might be fueled by only 0.1% dark vs. ordinary matter.

New Particles χ, φ

This SIDM scenario requires two new particles that the authors refer to as χ and φ. The χ dark matter particle (a fermion) could have a mass of order 100 GeV, similar to that of the Higgs particle (but that is a boson, not a fermion), and some 100 times that of a proton or neutron.

The φ particle (a scalar field) is a low-mass mediator in the dark sector with a mass closer to that of an electron or muon (heavy electron), in the range of 1 to 100 MeV. This particle would mediate between the χ and ordinary matter, baryons and electrons.

The main mechanism for heating is the decay of the charged χ and its anti-particle into pairs of (neutral) φ particles that can then go on to decay to electron / positron pairs. These easily thermalize within the ionized hydrogen and helium gas cloud as the electrons and positrons annihilate to gamma rays when they meet their corresponding anti-particle.

The decay mean free path for the φ would need to be of order 1 AU or less (an astronomical unit, the Earth-Sun distance); in this way, the decays would deposit heat into the protostellar cloud. The clouds can heat up to thousands of degrees Kelvin such that they are very efficient radiators. And since they can be large, larger than 1 AU their luminosity can also be very large.

A Model Dark Star

In their paper, Wu and co-authors model a 10 solar mass dark star with a photosphere of 3.2 AU radius. Such a dark star if placed at the Sun’s location would have its photosphere beyond the orbits of Earth and Mars and reaching to the outer edge of the asteroid belt. 

The temperature of their model star is 4300 Kelvin, or 3/4 that of the Sun. Despite the lower temperature, because of the large size, the total luminosity in this case is 150,000 times that of our Sun. It would be reddish in color at the source, but highly redshifted into the infrared light would reach us. This luminosity is 100 times more luminous than the most luminous red supergiant star, but not much brighter intrinsically than the (much hotter) blue supergiant Rigel.

Because such a star would be a first stellar generation, it would have no spectral lines from any elements other than hydrogen or helium. Only hydrogen and helium and a trace amount of lithium are formed in the Big Bang.

Black holes as a result?

Other dark stars might have temperatures of 10,000 Kelvin, and possibly accrete matter from the aforementioned halo until they reach luminosities as large as 10 million times that of the Sun. These might be visible with the James Webb Space Telescope (JWST).

Dark stars might last as long as half a billion years, or the annihilation might shut down sooner due to the collapse of ordinary matter in the protostellar envelope. Once the dark star phase ends, there could be a rapid collapse to high mass nucleosynthesis-powered stars that would end their short lives as black holes, or one could even have direct collapse to black holes of high masses. These would be interesting candidates as the seeds of the supermassive black holes of millions and billions of solar masses that we observe today in the centers of galaxies, both nearby and at high redshifts. 

The James Webb Space Telescope is finding more early galaxies than expected within the first 500 million years of the universe. It is able to peer back that far because of its instruments’ sensitivity in the infrared portion of the spectrum. The light from such early galaxies is heavily shifted from optical to infrared frequencies, by order a factor of 10, due to the universe’s expansion over the past 13 billion plus years. Perhaps seeing more early-onset galaxies is in part because of the role that dark stars play in hastening the evolution of the stellar population.

We look forward to JWST detecting the earliest stars, that might be dark stars, or providing constraints on their visibility or viability.

– Stephen Perrenod, Ph.D., September 2023

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March 10, 2020

Hexaquark Dark Matter: Bosons, but not WIMPy at all

By darkmatterdarkenergy

Dibaryons

Imagine you smash a proton and neutron together. What do you get? Typically you get a deuteron which is the nucleus of deuterium, heavy hydrogen. Deuterium has one electron in its neutral atomic state. And it has two baryons, the proton and neutron, so it is known as a dibaryon.

Now as you have heard, protons and neutrons are really quark triplets, held together by gluons in bound configurations. A proton has two up quarks (electric charge +2/3) and a down quark (charge -1/3) for a net charge of +1 and a neutron has two down quarks and an up quark for a net charge of 0.

These are the two lightest quarks and protons and neutrons are by far the dominant components in the ordinary matter in the universe, mostly as hydrogen and helium.

Quarks, protons, and neutrons are all fermions, particles with half-integer spins (1/2, 3/2, -1/2, etc.).

The other main class of particles is called bosons, and that class includes photons, gluons, the W and Z of the weak interaction, and the never directly observed graviton. They all have integer spins (typically 1, but 0 for the Higgs boson, and 2 for the graviton).

752px-Standard_Model_of_Elementary_Particles.svg

Figure 1: The Standard Model major particles: quarks (purple), leptons (green), force carrier bosons (orange), Higgs boson (yellow) with mass, charge, spin indicated.

Six quarks in a Bag

Suppose you collided a proton and neutron together, each with three quarks, and you ended up with a single six quark particle that was stable. It would be a more exotic type of dibaryon. It would have three up quarks, three down quarks, and it would not be a fermion. It would be a boson, with integer spin, spin 0 or 1, in this case. It would be six quarks in a bag, a bound state held together by gluons.

sixquarksinabag

Figure 2. Six quarks in a bag, a hexaquark

Hexaquark2380

Figure 3. The d* resonance at 2.38 GeV, observed at the Cooler Synchrotron in Julich, Germany

Such a particle has been discovered in the past decade, and is named the d* hexaquark. It is seen as the resonance in Figure 3 above, found in proton-neutron collisions, and has a mass of 2.38 GeV (for reference the proton mass is 0.935 GeV and the neutron mass is 0.938 GeV). It decays to a deuteron and two pions, either neutral as shown in the figure, or charged pions.

It is also possible to produce a d* by irradiating a deuteron with a gamma ray.

The d* was already predicted by the famed mathematician and physicist Freeman Dyson in 1964, working with his collaborator Xuong. Their mass estimate was quite close at 2.35 GeV, using a simple quark model.

Dyson just passed away recently; you may have heard of his Dyson sphere concept. The idea is that an advanced civilization would build a sphere of solid material surrounding its star in order to hold an extremely large population and absorb virtually all of the star’s energy. Larry Niven modified this to a ring in his 1970 sci-fi novel Ringworld.

Hexaquark dark matter

Azizi, Ageav, and Sundu have recently suggested a hexaquark of the form uuddss, that is, two up, two down, and two strange quarks. Their mass estimate is around 1.2 GeV, half that of the d* composed of only up and down quarks. It is expected to be stable with long lifetime.

And also recently, Bashkanov and Watts at the University of York have made a nice proposal that d* could be the dark matter particle. The d* particle is itself unstable, but they propose that stable condensates with many d* particles could form. Their paper,  “A New Possibility for Light-Quark Dark Matter” is here:

https://iopscience.iop.org/article/10.1088/1361-6471/ab67e8/pdf

The d* has one great advantage over the other proposed particles, it has actually been discovered! The d* has a good sized mass for a dark matter candidate, at about 2.5 times the mass of the proton.

The authors find that the d* could form lengthy chains or spherical condensates with thousands to millions of d* particles. Unlike individual d* particles, the condensates could be stable ‘super atoms’ lasting for billions of years.

However to make this work the binding energy would have to exceed the difference between the 2.38 GeV d* mass and the deuteron mass of 2.014mGeV, thus would have to be greater than about 0.4 GeV.

The d* would be produced thermally when the universe was at temperatures in the range from 1 to 3 trillion Kelvins. The condensates would need to form quickly before individual d* particles of short lifetimes decayed away.

The favored candidates for dark matter have been WIMPs, supersymmetric particles. But no supersymmetric particle has ever been detected at the Large Hadron Collider or elsewhere, which is incredibly disappointing for many particle physicists. The other main candidates have been the axion and sterile neutrino, both quite low in mass. These have never been directly detected either; they remain hypothetical.

The d* particle is a boson, and the authors’ theoretical approach is that in the early universe as it cooled, both baryons and dibaryonic matter froze out. The baryons ended up, after the cosmic nucleosynthesis phase as protons, deuterium dibaryons, and helium nuclei (alpha particles, that are composed essentially of two deuterons), the main constituents of ordinary matter.

What would happen to d* under the early conditions of the Big Bang? Bosons like to clump together, into something called Bose-Einstein condensates. Yes, that Einstein. And that Boson. Bose-Einstein statistics were developed in the 1920s and govern the statistics of bosons (integer spin particles), and differ from that of fermions.

To confirm this model would require astronomical observations or cosmic ray observations. Decays of d* particles could result in gamma ray production with energies up to 0.5 GeV. Their decay products might also be seen as upward moving cosmic rays, in Earth-bound cosmic ray experiments. These would be seen coming up through the Earth, unlike normal cosmic rays that cannot penetrate so much ordinary matter, and the decay events would result in gamma rays, nucleons and deuterons, as well as pions as the decay products.

 

Additional reference: http://www.sci-news.com/physics/dark-matter-particle-d-star-hexaquark-08188.html

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November 11, 2019

Dark Catastrophe, a few Trillion Years away?

By darkmatterdarkenergy

The Equation of State for Dark Energy

The canonical cosmological model, known as ΛCDM, has all matter including CDM (cold dark matter), at approximately 30% of critical density. And it has dark energy, denoted by Λ, at 70%. While the cosmological constant form of dark energy, first included in the equations of general relativity by Einstein himself, has a positive energy, its pressure is negative.

The negative pressure associated with dark energy, not the positive dark energy density itself, is what causes the universe’s expansion to accelerate.

The form of dark energy introduced by Einstein does not vary as the universe expands, and the pressure, although of opposite sign, is directly proportional to the dark energy density. The two are related by the formula

P = – ρ c²

where P is the pressure and ρ the energy density, while c is the speed of light.

More generally one can relate the pressure to the energy density as an equation of state with the parameter w:

P = – w ρ c²

And in the cosmological constant form, w = -1 and is unvarying over the billions of years of cosmological time.

Does Dark Energy vary over long timescales?

String theory (also known as membrane theory) indicates that dark energy should evolve over time.

The present day dark energy may be the same field that was originally much much stronger and drove a very brief period of inflation, before decaying to the current low value of about 6 GeV (proton rest masses) per cubic meter.

There are searches for variation in the equation of state parameter w; they are currently inconclusive.

How much variance could there be?

In string theory, the dark energy potential gradient with respect to the field strength yields a parameter c of order unity. For differing values of c, the equation of state parameter w varies with the age of the universe, more so as c is larger.

When we talk about cosmological timescales, it is convenient to speak in terms of the cosmological redshift, where z = 0 is the present and z > 0 is looking back with a larger z indicating a larger lookback time. If the parameter c were zero then the value of w would be -1 at all redshifts (z = 0 is the current epoch and z = 1 is when the universe only about 6 billion years old, almost 8 billion years ago).

WvsC

This Figure 3 from an article referenced below by Cumrun Vafa of Harvard shows the expected variance with redshift z for the equation of state parameter w. The observationally allowed region is shaded gray. The colored lines represent different values of the parameter c from string theory (not the speed of light). APS/Alan Stonebraker

Observational evidence constraining w is gathered from the cosmic microwave background, from supernovae of Type Ia, and from the large scale galaxy distribution. That evidence from all three methods in combination restricts one to the lower part of the diagram, shaded gray, thus w could be -1 or somewhat less. There are four colored curves, labelled by their value of the string theory parameter c, and it appears that c > 0.65 could be ruled out by observations.

Hubble Constant tension: String theory explaining?

It’s not the constant tension of the Hubble constant. Rather it is the tension, or disagreement between the cosmic microwave background observational value of the Hubble constant, at around 67 kilometers/sec/Megaparsec and the value from supernovae observations, which yield 73 kilometers/sec. And the respective error bars on each measurement are small enough that the difference may be real.

The cosmic microwave background observations imply a universe about a billion years older, and also better fit with the ages of the oldest stars.

It turns out a varying dark energy with redshift as described above could help to explain much of the discrepancy although perhaps not all of it.

Better observations of the early universe’s imprint on the large scale distribution of galaxies from ground-based optical telescope surveys and from the Euclid satellite’s high redshift gravitational lensing and spectroscopic redshift measurements in the next decade will help determine whether dark energy is constant or not. This could help to disprove string theory or enhance the likelihood that string theory has explanatory power in physics.

Tests of string theory have been very elusive since we cannot reach the extremely high energies required with our Earth-based particle accelerators. Cosmological tests may be our best hope, small effects from string theory might be detectable as they build up over large distances.

And this could help us to understand if the “swampland conjecture” of string theory is likely, predicting an end to the universe within the next few trillion years as the dark energy field tunnels to an even lower energy state or all matter converts into a “tower of light states” meaning much less massive particles than the protons and neutrons of which we are composed.

Reference

“Cosmic Predictions from the String Swampland”, Cumrun Vafa, 2019. Physics 12, 115, physics.aps.org

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April 3, 2019

Modified Gravity

By darkmatterdarkenergy

We don’t Need no Stinkin’ Dark Matter

Extra Acceleration

You’ve heard of dark matter, right? Some sort of exotic particle that lurks in the outskirts of galaxies.

Maybe you know the story of elusive dark matter. The first apparent home for dark matter was in clusters of galaxies, as Fritz Zwicky postulated for the Coma Cluster in the 1930s, due to the excessive galaxy random motions that he measured.

There have been eight decades of discovery and measurement of the gravitational anomalies that dark matter is said to cause, and eight decades of notable failure to directly find any very faint ordinary matter, black holes, or exotic particle matter in sufficient quantities to explain the magnitude of the observed anomalies.

If dark matter is actually real and composed of particles or primordial black holes then there is five times as much mass per unit volume on average in that form as there is in the form of ordinary matter. Ordinary matter is principally in the form of protons and neutrons, primarily as hydrogen and helium atoms and ions. 

Why do we call it dark? It gives off no light. Ordinary matter gives off light, it radiates. What else gives off no light? A gravitational field stronger than predicted by existing laws.

Gravitational anomalies are seen in the outer regions of galaxies by examining galaxy rotation curves, which flatten out unexpectedly with distance from the galactic center.  They are seen in galaxy groups and clusters from measuring galaxy velocity dispersions, from X-ray observations of intracluster gas, and from gravitational lensing measurements. A dark matter component is also deduced at the cosmic scale from the power spectrum of the cosmic microwave background spatial variations.

The excessive velocities due to extra acceleration are either caused by dark matter or by some departure of gravity over and above the predictions of general relativity. 

Actually at high accelerations general relativity is the required model but at low accelerations Newtonian dynamics is an accurate approximation. The discrepancies arise only at very low accelerations. These excess velocities, X-ray emission, and lensing are observed only at very low accelerations, so we are basically talking about an alternative of extra gravity which is over and above the 1/r² law for Newtonian dynamics.

Alternatives to General Relativity and Newtonian Dynamics

There are multiple proposed laws for modifying gravity at very low accelerations. To match observations the effect should start to kick in for accelerations less than c * H, where H is the Hubble expansion parameter and its inverse is nearly equal to the present age of the universe. 

That is only around 1 part in 14 million expressed in units of centimeters per second per second. This is not something typically measurable in Earth-bound laboratories; scientists have trouble pinning down the value of the gravitational constant G to within 1 part in 10,000. 

This is a rather profound coincidence, suggesting that there is something fundamental at play in the nature of gravity itself, not necessarily a rather arbitrary creation of exotic dark matter particle in the very early universe. It suggests instead that there is an additional component of gravity tied in some way to the age and state of our universe.

Do you think of general relativity as the last word on gravity? From an Occam’s razor point of view it is actually simpler to think about modifying the laws of gravity in very low acceleration environments, than to postulate an exotic never-seen-in-the-lab dark matter particle. And we already know that general relativity is incomplete, since it is not a quantum theory.

The emergent gravity concept neatly solves the quantum issue by saying gravity is not fundamental in the way that electromagnetism and the nuclear forces are. Rather it is described as an emergent property of a system due to quantum entanglement of fields and particles. In this view, the fabric of space also arises from this entanglement. Gravity is a statistical property of the system, the entropy (in thermodynamic terms) of entanglement at each point.

Dark Energy

Now we have a necessary aside on dark energy. Do you know that dark energy is on firmer standing now than dark matter? And do you know that dark energy is just described by additional energy and pressure components in the stress-energy tensor, fully described within general relativity?

We know that dark energy dominates over dark matter in the canonical cosmological model (Lambda-Cold Dark Matter) for the universe. The canonical model has about 2/3 dark energy and the solution for the universe’s expansion approximates a de Sitter model in general relativity with an exponential ‘runaway’ expansion.

Dark Gravity

As we discuss this no dark matter alternative, we refer to it as dark gravity, or dark acceleration. Regardless of the nature of dark matter and dark gravity, the combination of ordinary gravity and dark gravity is still insufficient to halt the expansion of the universe. In this view, the dark gravity is due to ordinary matter, there is just more of it (gravity) than we expect, again only for the very low c * H or lower acceleration environments.

Some of the proposed laws for modified gravity are:

  1. MOND – Modified Newtonian Dynamics, from Milgrom
  2. Emergent gravity, from Verlinde
  3. Metric skew tensor gravity (MSTG), from Moffat (and also the more recent variant scalar-tensor-vector gravity (STVG), sometimes called MOG (Modified gravity)

Think of the dark gravity as an additional term in the equations, beyond the gravity we are familiar with. Each of the models adds an additional term to Newtonian gravity, that only becomes significant for accelerations less than c*H. The details vary between the proposed alternatives. All do a good job of matching galaxy rotation curves for spiral galaxies and the Tully-Fisher relation that can be used for analyzing elliptical galaxies.

Things are trickier in clusters of galaxies, which are observed for galaxy velocity dispersions, X-ray emission of intracluster gas, and gravitational lensing. The MOND model appears to come up short by a factor of about two in explaining the total dark gravity implied.

Emergent gravity and modified gravity theories including MSTG claim to be able to match the observations in clusters.

Clusters of Galaxies

Most galaxies are found in groups and clusters.

Clusters and groups form from the collapse of overdense regions of hydrogen and helium gas in the early universe. Collapsing under its own gravity, such a region will heat up via frictional processes and cooler sub-regions will collapse further to form galaxies within the cluster.

Rich clusters have hundreds, even thousands of galaxies, and their gravitational potential is so high that the gas is heated to millions of degrees via friction and shock waves and gives off X-rays. The X-ray emission from clusters has been actively studied since the 1970s, via satellite experiments.

What is found is that most matter is in the form of intracluster gas, not galaxies. Some of this is left over primordial gas that never formed galaxies and some is gas that was once in a galaxy but expelled via energetic processes, especially supernovae.

Observations indicate that around 90% of (ordinary) matter is in the form of intracluster gas, and only around 10% within the galaxies in the form of stars or interstellar gas and dust. Thus modeling the mass profile of a cluster is best done by looking at how the X-ray emission falls off as one moves away from the center of a cluster.

In their 2005 paper, Brownstein and Moffat compiled X-ray emission profiles and fit gas mass profiles with radius and temperature profiles for 106 galaxy clusters. They aggregated data from a sample of 106 clusters and find that an MSTG model can reproduce the X-ray emission with a mass profile that does not require dark matter.

The figure below shows the average profile of cumulative mass interior to a given radius. The mass is in units of solar masses and runs into the hundreds of trillions. The average radius extends to over 1000 Kiloparsecs or over 1 Megaparsec (a parsec is 3.26 light-years).

The bottom line is that emergent gravity and MSTG both claim to have explanatory power without any dark matter for observations of galaxy rotation curves, gravitation lensing in clusters (Brower et al. 2016), and cluster mass profiles deduced from the X-ray emission from hot gas.

galaxyclustermasseswodm.fig2

Figure 2 from J.R. Brownstein⋆ and J.W. Moffat (2005), “Galaxy Cluster Masses without Non-Baryonic Dark Matter”. Shown is cumulative mass required as a function of radius. The red curve is the average of X-ray observations from a sample of 106 clusters. The black curve is the authors’ model assuming MSTG, a good match. The cyan curve is the MOND model, the blue curve is a Newtonian model, and both require dark matter. The point is that the authors can match observations with much less matter and there is no need to postulate additional exotic dark matter.

What we would very much like to see is a better explanation of the cosmic microwave background density perturbation spectrum for the cosmic scale, for either of these dark gravity models. The STVG variant of MSTG claims to address those observations as well, without the need for dark matter.

In future posts we may look at that issue and also the so called ‘silver bullet’ that dark matter proponents often promote, the Bullet Cluster, that consists of two galaxy clusters colliding and a claimed separation of dark matter and gas.

References

Brower, M. et al. 2016, “First test of Verlinde’s theory of Emergent Gravity using Weak Gravitational Lensing Measurements” https://arxiv.org/abs/1612.03034v2

Brownstein, J. and Moffat, J. 2005, “Galaxy Cluster Masses without Non-baryonic Dark Matter”, https://arxiv.org/abs/astro-ph/0507222

Perrenod, S. 1977 “The Evolution of Cluster X-ray Sources” http://adsabs.harvard.edu/abs/1978ApJ…226..566P, thesis.

https://darkmatterdarkenergy.com/2018/09/19/matter-and-energy-tell-spacetime-how-to-be-dark-gravity/

https://darkmatterdarkenergy.com/2016/12/30/emergent-gravity-verlindes-proposal/

https://darkmatterdarkenergy.com/2016/12/09/modified-newtonian-dynamics-is-there-something-to-it/

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January 27, 2019

Mini Black Holes as Dark Matter?

By darkmatterdarkenergy

Ancient Voyager Satellite Says No for the Smallest Possible

Hawking Radiation

Black holes can come in all sizes from about a billion tons up to billions of solar masses.

Because isolated black holes are difficult to detect, especially smaller mass ones, they have long been considered as candidates for dark matter, invoked to explain the extra gravitational accelerations measured at the outskirts of galaxies.

Stephen Hawking showed that black holes radiate low energy particles very slowly due to quantum thermodynamic effects. So the very lowest mass black holes evaporate away due to Hawking radiation during the life of the universe.

Voyager Satellites

The Voyager satellites were launched in 1977 and NASA has determined that Voyager 1 crossed the heliopause in 2012. This is the boundary for the solar wind, which holds back a large portion of galactic cosmic rays. Voyager 2 crossed the heliopause last year.

Forty-two years after launch, and having toured Jupiter, Saturn, Uranus, and Neptune, these remarkable satellites are still returning valuable data about the outer reaches of the Solar System.

What is the connection between black holes, dark matter, and Voyager 1?

In the early universe, large numbers of so-called primordial black holes (PBHs) of various sizes may have formed. The question arises, could these be the primary component of dark matter?

Primordial Black Holes as Dark Matter Candidates

The detection of gravitational waves from half a dozen mergers of black holes of intermediate mass has given new energy to this idea. Also, there is the continued failure to detect exotic particle candidates for dark matter in Earth-bound laboratory experiments.

A team of Japanese astronomers, searching for microlensing effects with stars in the Andromeda galaxy, have ruled out small black holes in the range of 10^{20} grams up to about 3 times the Earth’s mass. https://darkmatterdarkenergy.com/2017/12/07/primordial-black-holes-and-dark-matter has more detail.

Constraints from other lensing experiments (MACHO, EROS) and the cosmic microwave background appear to rule out more massive primordial black holes as the explanation for most dark matter.

What about the tiniest allowable black holes, from about 4 \cdot 10^{14} gm (smaller ones have evaporated already) up to 10^{20} gm?

Voyager 1 Constraints

With a recent analysis researchers at the Laboratoire de Physique Theorique et Hautes Energies (LPTHE) show that the Voyager 1 satellite now rules out primordial black holes with masses below 10^{17} gm as well, as the source of most dark matter. And it is because of the Hawking radiation that we do not detect.

Although Hawking radiation has never been detected, it is on very firm theoretical grounds that it should exist. Everything, including strange objects like black holes, has a quantum nature.

Smaller black holes radiate at higher temperatures and have shorter lifetimes. The Hawking radiation temperature is

T = 1.1  GeV / (m/10^{13} gm)

Thus for an m = 10^{16} gm black hole the Hawking temperature is about 1 MeV. (GeV or giga electron-Volt is a billion eV and around the rest mass energy of a proton, and an MeV or mega electron-Volt is a million eV and about twice the rest mass energy of an electron.)

Since these temperatures are in the MeV range, only very light particles such as neutrinos, electrons, and positrons would be emitted by the PBHs.

Figure 1 from the Boudaud and Cirelli paper shows the observed combined electron and positron cosmic ray flux from Voyager 1 in the energy range from 3 MeV to 50 MeV. It also shows results in the 1 to 10 GeV range from the Alpha Magnetic Spectrometer 2 experiment on the International Space Station (located well inside the heliopause). Two different models of how the energetic particles propagate through the galaxy are used.

Smallest possible Black Holes ruled out

PBHs with 10^{15} or 10^{16} grams are clearly ruled out; they would inject far too many energetic electron and positron cosmic rays into the interstellar medium that Voyager 1 has entered.

The authors state that no more than 0.1% of dark matter can be due to PBHs of mass less than 10^{16} grams (10 billion tons).

In Figure 1, a monotonic mass distribution was assumed (PBHs all have the same mass). They also consider various log-normal mass distributions and similar constraints on the allowable PBH mass were found.

What about at 10^{17} grams and above? Most mass regions are ruled out.

The mass region above 5 \cdot 10^{17} grams and up to about 10^{20} grams has been excluded as a primary source of dark matter from PBHs by a 2012* result from Barnacka, Glicenstein, and Moderski. They searched for gravitational lensing effects upon gamma ray burst sources due to intervening black holes.

So vast ranges of possible PBH masses are ruled out. However the mass region from 3 \cdot 10^{16} up to 5 \cdot 10^{17} grams remains a possibility as a dark matter hideout for PBHs.

*The same year that Voyager 1 crossed the heliopause, coincidentally

References

Boudaud, M. And Cirelli, M. 2019 “Voyager 1 electrons and positrons further constrain primordial black holes as dark matter” https://arxiv.org/abs/1807.03075

https://darkmatterdarkenergy.com/2017/12/07/primordial-black-holes-and-dark-matter/

Barnacka, A., Glicenstein, J.-F., Moderski, R. 2012 “New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts” http://arxiv.org/abs/1204.2056

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June 2, 2017

Yet Another Intermediate Black Hole Merger

By darkmatterdarkenergy

Another merger of two intermediate mass black holes has been observed by the LIGO gravitational wave observatories.

There are now three confirmed black hole pair mergers, along with a previously known fourth possible, that lacks sufficient statistical confidence.

These three mergers have all been detected in the past two years and are the only observations ever made of gravitational waves.

They are extremely powerful events. The lastest event is known as GW170104 (gravitational wave discovery of January 4, 2017).

It all happened in the wink of an eye. In a fifth of a second, a black hole of 30 solar masses approximately merged with a black hole of about 20 solar masses. It is estimated that the two orbited around one another six times (!) during that 0.2 seconds of their final existence as independent objects.

The gravitational wave generation was so great that an entire solar mass of gravitational energy was liberated in the form of gravitational waves.

This works out to something like 2 \cdot 10^{47} Joules of energy, released in 0.2 seconds, or an average of 10^{48} Watts during that interval. You know, a Tera Tera Tera Terawatt.

Researchers have now discovered a whole new class of black holes with masses ranging from about 10 solar masses (unmerged) to 60 solar masses (merged). If they keep finding these we might have to give serious consideration to intermediate mass black holes as contributors to dark matter.  See this prior blog for a discussion of primordial black holes as a possible dark matter contributor:

https://darkmatterdarkenergy.com/2016/06/17/primordial-black-holes-as-dark-matter/

IMG_0462

Image credit: LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet)

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April 25, 2017

No Dark Energy?

By darkmatterdarkenergy

Dark Energy is the dominant constituent of the universe, accounting for 2/3 of the mass-energy balance at present.

At least that is the canonical concordance cosmology, known as the ΛCDM or Lambda – Cold Dark Matter model. Here Λ is the symbol for the cosmological constant, the simplest, and apparently correct (according to most cosmologists), model for dark energy.

Models of galaxy formation and clustering use N-body simulations run on supercomputers to model the growth of structure (galaxy groups and clusters) in the universe. The cosmological parameters in these models are varied and then the models are compared to observed galaxy catalogs at various redshifts, representing different ages of the universe.

It all works pretty well except that the models assume a fully homogeneous universe on the large scale. While the universe is quite homogeneous for scales above a billion light-years, there is a great deal of filamentary web-like structure at scales above clusters, including superclusters and voids, as you can easily see in this map of our galactic neighborhood.

399px-2MASS_LSS_chart-NEW_Nasa

Galaxies and clusters in our neighborhood. IPAC/Caltech, by Thomas Jarrett – “Large Scale Structure in the Local Universe: The 2MASS Galaxy Catalog”, Jarrett, T.H. 2004, PASA, 21, 396

Well why not take that structure into account when doing the modeling? It has long been known that more local inhomogeneities such as those seen here might influence the observational parameters such as the Hubble expansion rate. Thus even at the same epoch, the Hubble parameter could vary from location to location.

Now a team from Hungary and Hawaii have modeled exactly that, in a paper entitled “Concordance cosmology without dark energy” https://arxiv.org/pdf/1607.08797.pdf . They simulate structure growth while estimating the local values of expansion parameter in many regions as their model evolves.

Starting with a completely matter dominated (Einstein – de Sitter) cosmology they find that they can reasonably reproduce the average expansion history of the universe — the scale factor and the Hubble parameter — and do that somewhat better than the Planck -derived canonical cosmology.

Furthermore, they claim that they can explain the tension between the Type Ia supernovae value of the Hubble parameter (around 73 kilometers per second per Megaparsec) and that determined from the Planck satellite observations of the cosmic microwave background radiation (67 km/s/Mpc).

Future surveys of higher resolution should be able to distinguish between their model and ΛCDM, and they also acknowledge that their model needs more work to fully confirm consistency with the cosmic microwave background observations.

Meanwhile I’m not ready to give up on dark energy and the cosmological constant since supernova observations, cosmic microwave background observations and the large scale galactic distribution (labeled BAO in the figure below) collectively give a consistent result of about 70% dark energy and 30% matter. But their work is important, something that has been a nagging issue for quite a while and one looks forward to further developments.

 

Measurements of Dark Energy and Matter content of Universe

Dark Energy and Matter content of Universe

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March 29, 2017

Distant Galaxy Rotation Curves Appear Newtonian

By darkmatterdarkenergy

One of the main ways in which dark matter was postulated, primarily in the 1970s, by Vera Rubin (recently deceased) and others, was by looking at the rotation curves for spiral galaxies in their outer regions. Although that was not the first apparent dark matter discovery, which was by Fritz Zwicky from observations of galaxy motion in the Coma cluster of galaxies during the 1930s.

Most investigations of spiral galaxies and star-forming galaxies have been relatively nearby, at low redshift, because of the difficulty in measuring these accurately at high redshift. For what is now a very large sample of hundreds of nearby galaxies, there is a consistent pattern. Galaxy rotation curves flatten out.

M64

M64, image credit: NASA, ESA, and the Hubble Heritage Team (AURA/STScI)

If there were only ordinary matter one would expect the velocities to drop off as one observes the curve far from a galaxy’s center. This is virtually never seen at low redshifts, the rotation curves consistently flatten out. There are only two possible explanations: dark matter, or modification to the law of gravity at very low accelerations (dark gravity).

Dark matter, unseen matter, would case rotational velocities to be higher than otherwise expected. Dark, or modified gravity, additional gravity beyond Newtonian (or general relativity) would do the same.

Now a team of astronomers (Genzel et al. 2017) have measured the rotation curves of six individual galaxies at moderately high redshifts ranging from about 0.9 to 2.4.

Furthermore, as presented in a companion paper, they have stacked a sample of 97 galaxies with redshifts from 0.6 to 2.6  to derive an average high-redshift rotation curve (P. Lang et al. 2017). While individually they cannot produce sufficiently high quality rotation curves, they are able to produce a mean normalized curve for the sample as a whole with sufficiently good statistics.

In both cases the results show rotation curves that fall off with increasing distance from the galaxy center, and in a manner consistent with little or no dark matter contribution (Keplerian or Newtonian style behavior).

In the paper with rotation curves of 6 galaxies they go on to explain their falling rotation curves as due to “first, a large fraction of the massive high-redshift galaxy population was strongly baryon-dominated, with dark matter playing a smaller part than in the local Universe; and second, the large velocity dispersion in high-redshift disks introduces a substantial pressure term that leads to a decrease in rotation velocity with increasing radius.” 

So in essence they are saying that the central regions of galaxies were relatively more dominated in the past by baryons (ordinary matter), and that since they are measuring Hydrogen alpha emission from gas clouds in this study that they must also take into account the turbulent gas cloud behavior, and this is generally seen to be larger at higher redshifts.

Stacy McGaugh, a Modified Newtonian Dynamics (MOND) proponent, criticizes their work saying that their rotation curves just don’t go far enough out from the galaxy centers to be meaningful. But his criticism of their submission of their first paper to Nature (sometimes considered ‘lightweight’ for astronomy research results) is unfounded since the second paper with the sample of 97 galaxies has been sent to the Astrophysical Journal and is highly detailed in its observational analysis.

The father of MOND, Mordehai Milgrom, takes a more pragmatic view in his commentary. Milgrom calculates that the observed accelerations at the edge of these galaxies are several times higher than the value at which rotation curves should flatten. In addition to this criticism he notes that half of the galaxies have low inclinations, which make the observations less certain, and that the velocity dispersion of gas in galaxies that provides pressure support and allows for lower rotational velocities, is difficult to correct for.

As in MOND, in Erik Verlinde’s emergent gravity there is an extra acceleration (only apparent when the ordinary Newtonian acceleration is very low) of order. This spoofs the behavior of dark matter, but there is no dark matter. The extra ‘dark gravity’ is given by:

g _D = sqrt  {(a_0 \cdot g_B / 6 )}

In this equation a0 = c*H, where H is the Hubble parameter and gB is the usual Newtonian acceleration from the ordinary matter (baryons). Fundamentally, though, Verlinde derives this as the interaction between dark energy, which is an elastic, unequilibrated medium, and baryonic matter.

One could consider that this dark gravity effect might be weaker at high redshifts. One possibility is that density of dark energy evolves with time, although at present no such evolution is observed.

Verlinde assumes a dark energy dominated de Sitter model universe for which the cosmological constant is much larger than the matter contribution and approaches unity, Λ = 1 in units of the critical density. Our universe does not yet fully meet that criteria, but has Λ about 0.68, so it is a reasonable approximation.

At redshifts around z = 1 and 2 this approximation would be much less appropriate. We do not yet have a Verlindean cosmology, so it is not clear how to compute the expected dark gravity in such a case, but it may be less than today, or greater than today. Verlinde’s extra acceleration goes as the square root of the Hubble parameter. That was greater in the past and would imply more dark gravity. But  in reality the effect is due to dark energy, so it may go with the one-fourth power  of an unvarying cosmological constant and not change with time (there is a relationship that goes as H² ∝ Λ in the de Sitter model) or change very slowly.

At very large redshifts matter would completely dominate over the dark energy and the dark gravity effect might be of no consequence, unlike today. As usual we await more observations, both at higher redshifts, and further out from the galaxy centers at moderate redshifts.

References:

R. Genzel et al. 2017, “Strongly baryon-dominated disk galaxies at the peak of galaxy formation ten billion years ago”, Nature 543, 397–401, http://www.nature.com/nature/journal/v543/n7645/full/nature21685.html

P. Lang et al. 2017, “Falling outer rotation curves of star-forming galaxies at 0.6 < z < 2.6 probed with KMOS^3D and SINS/ZC-SINF” https://arxiv.org/abs/1703.05491

Stacy McGaugh 2017, https://tritonstation.wordpress.com/2017/03/19/declining-rotation-curves-at-high-redshift/

Mordehai Milgrom 2017, “High redshift rotation curves and MOND” https://arxiv.org/abs/1703.06110v2

Erik Verlinde 2016, “Emergent Gravity and the Dark Universe” https;//arXiv.org/abs/1611.02269v1

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March 12, 2017

Emergent Gravity in the Solar System

By darkmatterdarkenergy

In a prior post I outlined Erik Verlinde’s recent proposal for Emergent Gravity that may obviate the need for dark matter.

Emergent gravity is a statistical, thermodynamic phenomenon that emerges from the underlying quantum entanglement of micro states found in dark energy and in ordinary matter. Most of the entropy is in the dark energy, but the presence of ordinary baryonic matter can displace entropy in its neighborhood and the dark energy exerts a restoring force that is an additional contribution to gravity.

Emergent gravity yields both an area entropy term that reproduces general relativity (and Newtonian dynamics) and a volume entropy term that provides extra gravity. The interesting point is that this is coupled to the cosmological parameters, basically the dark energy term which now dominates our de Sitter-like universe and which acts like a cosmological constant Λ.

In a paper that appeared in arxiv.org last month, a trio of astronomers Hees, Famaey and Bertone claim that emergent gravity fails by seven orders of magnitude in the solar system. They look at the advance of the perihelion for six planets out through Saturn and claim that Verlinde’s formula predicts perihelion advances seven orders of magnitude larger than should be seen.

hst_saturn_nicmos

No emergent gravity needed here. Image credit: NASA GSFC

But his formula does not apply in the solar system.

“..the authors claiming that they have ruled out the model by seven orders of magnitude using solar system data. But they seem not to have taken into account that the equation they are using does not apply on solar system scales. Their conclusion, therefore, is invalid.” – Sabine Hossenfelder, theoretical physicist (quantum gravity) Forbes blog 

Why is this the case? Verlinde makes 3 main assumptions: (1) a spherically symmetric, isolated system, (2) a system that is quasi-static, and (3) a de Sitter spacetime. Well, check for (1) and check for (2) in the case of the Solar System. However, the Solar System is manifestly not a dark energy-dominated de Sitter space.

It is overwhelmingly dominated by ordinary matter. In our Milky Way galaxy the average density of ordinary matter is some 45,000 times larger than the dark energy density (which corresponds to only about 4 protons per cubic meter). And in our Solar System it is concentrated in the Sun, but on average out to the orbit of Saturn is a whopping 3.7 \cdot 10^{17} times the dark energy density.

The whole derivation of the Verlinde formula comes from looking at the incremental entropy (contained in the dark energy) that is displaced by ordinary matter. Well with over 17 orders of magnitude more energy density, one can be assured that all of the dark energy entropy was long ago displaced within the Solar System, and one is well outside of the domain of Verlinde’s formula, which only becomes relevant when acceleration drops near to or below  c * H. The Verlinde acceleration parameter takes the value of 1.1 \cdot 10^{-8}  centimeters/second/second for the observed value of the Hubble parameter. The Newtonian acceleration at Saturn is .006 centimeters/second/second or 50,000 times larger.

The conditions where dark energy is being displaced only occur when the gravity has dropped to much smaller values; his approximation is not simply a second order term that can be applied in a domain where dark energy is of no consequence.

There is no entropy left to displace, and thus the Verlinde formula is irrelevant at the orbit of Saturn, or at the orbit of Pluto, for that matter. The authors have not disproven Verlinde’s proposal for emergent gravity.

 

 

 

 

 

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February 5, 2017

Leo II Dwarf Orbits Milky Way: Dark Matter or Emerging Gravity

By darkmatterdarkenergy

In a prior blog, “The Curiously Tangential Dwarf Galaxies”, I reported on results from Cautun and Frenk that indicate that a set of 10 dwarf satellite galaxies near the Milky Way with measured proper motions have much more tangential velocity than expected by random. Formally, there is a 5 standard deviation negative velocity anisotropy with over 80% of the kinetic energy in tangential motion.

While in no way definitive, this result appears inconsistent with the canonical cold dark matter assumptions. So one speculation is that the tangential motions are reflective of the theory of emergent gravity, for which dark matter is not required, but for which the gravitational force changes (strengthens) at very low accelerations, of order c \cdot H, where H is the Hubble parameter, and the value at which the force begins to strengthen works out to be accelerations of only less than about 2 centimeters per second per year.

One of the 10 dwarf galaxies in the sample is Leo II. The study of its proper motion has been reported by Piatek, Pryor, and Olszewski. They find that the galactocentric radial and tangential velocity components are 22 and 127 kilometers per second, respectively. While there is a rather large uncertainty in the tangential component, for their measured values some 97% of the kinetic energy is in the tangential motion.

local_group_and_nearest_galaxies

Artist’s rendering of the Local Group of galaxies. This representation is centered on the Milky Way, you can see a large number of dwarf galaxies near the Milky Way and many near the Andromeda Galaxy as well. Leo II is in the swarm around our Milky Way. Image credit: Antonio Ciccolella. This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

So let’s look at the implications for this dwarf galaxy, assuming that it is in a low-eccentricity, nearly circular orbit about the Milky Way, which seems possible. We can compare calculations for Newtonian gravity with the implications from Verlinde’s emergent gravity framework.

Under the assumption of a near circular orbit, either there is a lot of dark matter in the Milky Way explaining the high tangential orbital velocity of Leo II, or there is excess gravity. So what do the two alternatives look like?

Let’s look at the dark matter case first. The ordinary matter mass of the Milky Way is measured to be 60 billion solar masses, mostly in stars, but considering gas as well. The distance to the Leo II dwarf galaxy is 236 kiloparsecs (770,000 light-years), well beyond the Milky Way’s outer radius.

So to first order, for a roughly spherical Milky Way, including a dark matter halo, we can evaluate what the total mass including dark matter would be required to hold Leo II in a circular orbit. This is determined by equating the centripetal acceleration v²/R to the gravitational acceleration inward GM/R². So the gravitational mass under Newtonian physics required for velocity v at distance R for a circular orbit is M = R v² / G. Using the tangential velocity and the distance measures above yields a required mass of 870 billion solar masses.

This is 14 times larger than the Milky way’s known ordinary matter mass from stars and gas. Now there are some other dwarf galaxies such as the Magellanic Clouds within the sphere of influence, but they are very much smaller, so this estimate of the total mass required is reasonable to first order. The assumption of circularity is a larger uncertainty. But what this says is something like 13 times as much dark matter as ordinary matter would be required.

Now let’s look at the emergent gravity situation. In this case there is no dark matter, but there is extra acceleration over and above the acceleration due to Newtonian gravity.  To be clear, emergent gravity predicts both general relativity and an extra acceleration term. When the acceleration is modest general relativity reduces to Newtonian dynamics. And when it is very low the total acceleration in the emergent gravity model includes both a Newtonian term and an extra term related to the volume entropy contribution.

In other words, gT = gN + gE is the total acceleration, with gN = GM/R² the Newtonian term and gE the extra term in the emergent gravity formulation. The gN term is calculated using the ordinary mass of 60 billion solar masses, and one gets a tiny acceleration of gN = 1.5 \cdot 10^{-11} centimeters / second / second (cm/s/s).

The extra, or emergent gravity, acceleration is given by the formula gE = sqrt (gN \cdot c \cdot H / 6 ), where H is the Hubble parameter (here we use 70 kilometers/second/Megaparsec). The value of c \cdot H / 6 turns out to be 1.1 \cdot 10^{-8} cm/s/s. This is just a third of a centimeter per second per year.

The extra emergent gravity term from Verlinde’s paper is the square root of the product of 1.1 \cdot 10^{-8} and the Newtonian term amounting to 1.5 \cdot 10^{-11} . Thus the extra gravity is 4.1 \cdot 10^{-10} cm/s/s, which is 27 times larger than the Newtonian acceleration. The total gravity is about 28 times that or 4.3 \cdot 10^{-10} cm/s/s. Now a 28 times larger gravitational acceleration leads to tangential orbital velocities over 5 times greater than expected in the Newtonian case.

Setting v²/R = 4.3 \cdot 10^{-10} cm/s/s and using the distance to Leo II results in an orbital velocity of 177 kilometers/second. With the Newtonian gravity and ordinary matter mass of the Milky Way, one would expect only 33 km/s, a velocity over 5 times lower.

Now the observed tangential velocity is 127 km/s, so the calculated number with emergent gravity is a bit high, but there is no guarantee of a circular orbit. Also, Verlinde’s model assumes quasi-static conditions, and this assumption may break down for a dynamically young system. The time to traverse the distance to Leo II using its radial velocity is of order 10 billion years, so the system may not have settled down sufficiently. There could also be tidal effects from neighbors, or possibly from Andromeda.

This is not a clear argument demonstrating that the Leo II dwarf galaxy’s observed tangential velocity is explained by emergent gravity. But it is a plausible alternative explanation, and made here to show how the calculations work out in this sample case.

So the main alternatives are a Milky Way dominated by dark matter and with a mass close to a trillion solar masses, or a Milky Way of ordinary matter only amounting to 60 billion solar masses. But in that latter case, the Milky Way exerts an extra gravitational force due to emergent gravity that only becomes apparent at very small accelerations less than about 10^{-8} cm/s/s.

Future work with the Hubble and future telescopes is expected to determine many more proper motions in the Local Group so that a fuller dynamical picture of the system can be developed. This will help to discriminate between the emergent gravity and dark matter alternatives.

 

 

 

 

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