Spiral Galaxies, no dark matter

Spiral Galaxies

Galactic rotation curves without dark matter.

A new paradigm for the universe.

https://msp.warwick.ac.uk/~cpr/paradigm

ISBN: 9781973129868

I keep dipping into this book.

Each time with new understanding. Each time with a new perspective.

It is a wonderful work, with compelling arguments.

Chapter 2, Sciama’s principle finishes with:

Sciama’s initiative, to base a dynamical theory on Mach’s principle as formulated in Sciama’s principle, has never been followed up and this approach to dynamics remains dormant. One of the aims of this book is to reawaken this approach.

One of the aims of this project is to help understanding of such theories.

In particular, help my own understanding with computer simulations and visualisations of astrophysical data.

This project will explore the mathematics of the book, aiming to make it accessible to a wider audience.

The mathematics of the book is accessible to anyone with a good understanding of high school calculus. This project aims to extend that group, to include myself.

The project will require astropy, matpotlib, scipy and of course numpy.

Create a Sciama Principle version of the galactic gravitational potential.

Simulations of gravitational wave from a new galactic arrival.

2021 update

The Geometry of the Universe

Colin Rourke

https://www.worldscientific.com/worldscibooks/10.1142/12195

ISBN: 978-981-123-386-9 (hardcover)

A new book, with a bold claim. A stunning story, a revival of some old ideas and new brilliance too.

Spiral

Spiral galaxies? Why spirals?

The problem noted by observational scientist Vera Rubin was that stars in the outer reaches of spiral galaxies are moving far too fast.

This observation is what lead to the dark matter assumption: there must be some matter we can’t see that is dragging the stars along.

Colin Rourke, says nonesense, there must be a giant rotating mass at the centre, dragging things along.

More specifically, as we have learnt from the Pulsar Timing Array and the LIGO/Virgo/Kagra (LVK) detections of gravitational waves is that space time is itself oscillating.

It’s a medium through which waves propagate. Much of the time these oscillations can be ignored, but sometimes they matter.

It’s like boats on the water. A cruise ship can ignore the waves from a passing dingy, but the wake from a cruise ship is very noticable in the dingy.

Now General Relativity captures the curvature that is generated by the high frequency oscillations of matter such as protons and electrons.

Second order effects such as the rotations of bodies can largely be ignored.

Indeed, under General Relativity, the Kerr metric provides the unique solution, assuming space is not a vacuum. That metric has the induced rotation on the surrounding space time proportional to 1/r**3, at distance r from the rotating body. Provided r is large, it can be ignored.

The catch is that Kerr just gives the locally induced rotation of space time. This rotation of space-time will then propagate at the speed of light, according to the Sciama Principle.

Now in the case of a mature galaxy, a central black hole with mass 10s or 100s of billions of solar masses is required.

There is growing evidence that galaxies do indeed harbour such supermassive black holes.

The detection of nanohertz gravitational waves is going to be taken as evidence of a period in the early universe when galaxies were merging, hence seeing the gravitational wave background that we are seeing.

My estimate is that the Pulsar Timing Array will see larger and larger amplitude waves, leading to belief in larger and larger mergers, earlier and earlier in the universe.

Further, it will be assumed that this is the period in which dark matter was created.

And the theory is >almost< correct, if we take dark matter as the wobbles of space time, not some mysterious particle waiting to be detected.

And if we also recognise that the waves are coming from all the matter in our visible universe and have been pretty much the same for a very long time. The Perfect Copernican Principle.

They are not coming from an un-seen phase of the Big Bang theory, but rather from all the matter that we can see.

Rourke points out an important point about the magnitude of the gravitational wave background. There is a thing called the Rees-Sciama effect. Imagine a photon crossing the universe. It experiences the wobbles of space time.

If the trough of a wave is deeper than the peak, the photon will lose energy, if it is the reverse, it will gain energy.

So the temperature of the Cosmic Microwave Background should be in balance with the background waves.

In turn, the magnitude of these waves impacts how far a photon can travel before being thoroughly diverted from its original course.

This is important, since it in turn has an impact on the temperature of the Cosmic Microwave Background, the intensity of gamma-ray bursts and the strength of gravitational waves detected by LVK.

These waves reduce the intensity of gamma-ray bursts since there is a limit to how long a wave can travel through space before being thoroughly diverted from its original direction.

Einstein’s general relativity withstands double pulsar’s Scrutiny

https://physics.aps.org/articles/v14/173

Strong-Field Gravity Tests with the Double Pulsar

13. Kramer et al.

Phys. Rev. X 11, 041050 (2021)

Published December 13, 2021

Binary pulsars provide strong tests of general relativity. The idea is that there are two, rapidly rotating, neutron stars in a close orbit around each other.

The Hulse-Taylor binary system has long been the best observed system and the strongest test.

A new system PSR J0737-3039A/B has now taken that crown as the best observed system. Lets call it Jumb0 737, from the J designate, or Jumbo for short.

The rotations of the Jumbo are incredibly stable, at the level of an atomic clock, allowing very precise measurements of the time delays of the pulses of energy as the system makes each rotation.

In addition, Jumbo is nearer than the Hulse-Taylor system and there is much less uncertainty in our estimate of its distance from earth.

It all gets complicated, since although the system is in our own galaxy, the intervening spacetime modulates the signal we receive.

The new paper explains the precise measurements that can now be made and how variations on general relativity, can, in some cases, be tested.

In particular, the paper now mentions that rotation of the faster rotating body now has to be taken into account in the equations of state of the entire system. The other body is rotating around one hundred times slower so the effect can largely be ignored.

The aproach that is taken is to assume the Lense-Thiring effect.

This is discussed in some detail in chapter 3 of the book, the biggest blunder…. Particular attention should be paid to the discussion around page 60.

There are some quite technical arguments. The Lense Thiring effect is intuitively compelling. General relativity tells us that if space-time is a vacuum, then the Kerr metric is the only solution that fits Einstein’s equations.

This is problematic for the book’s arguments as the Kerr metric falls off as 1/(r**3) whereas the book argues it should fall off as 1/r.

Rourke makes the assumption that linear motion has no inertial effect and notes that you can change angular momentum by adding a linear motion, whereas angular velocity cannot be changed in this way.

Is space time a vacuum?

The impasse is resolved if we assume that space is not in fact a vacuum.

For starters, there is an awful lot of microwave radiation buzzing around: the cosmic microwave background.

The nature of this background depends critically on our assumptions about the geometry of the universe: big bang, or static universe?

What would a static universe look like given the effects of special relativity, simplifying a universe to the set of galaxies above a certain size?

This model will instead show how by assuming this 1/r relation for the effect of a masses rotation on its surroundings, produces galactic rotation curves very much in line with observations.

What about Jumbo?

So the cool news is that we now get estimates of the angular velocity of each body and it’s moment of inertia.

The latter adds some uncertainty to model fit as there is uncertainty of the exact distribution of the matter within each neutron star, which is important to know, as the model being used assumed it is angular momentum that drives the rotational frame dragging.

As noted above, Rourke argues that it is angular velocity, rather than angular momentum that matters in the calculation, in short the matter distribution within the black hole is not required for his model.

Further, that the Lense-Thiring effect drops off as 1/r, not the 1/r**3 that is presumably being used by the new paper. The question is at what point does the Sciama effect become large enough to offset the Kerr metric, which induces a reduction of the angular momentum of the system, leading to a belief in black hole inspirals as a source of gravitational waves.

This may mean that a fit using Rourke’s model reduces the uncertainty in all the parameters that the fitting process estimates, since the uncertainty in the matter distribution no longer comes into play, just the uncertainty in angular velocity.

Another project would be to fit the model to the latest Hulse-Taylor data and see what changes. Calculations show that the objects are currently too far apart for the Sciama effects to matter. It should also be noted that the objects have strong magnetic fields.

Calculations also show the potential merger time of some systems is of the order of a handful of millions, or tens of millions of years. As this is short on cosmological timescales it raises questions of why there are so many systems that have not already merged?

I believe the explanation for binary pulsars is that the neutron stars are the result of supernova explosions and hence the system has periodically kicked itself apart.

I am also curious how Rourke’s model affects the long term evolution of these systems. My hunch (actually I think I read something along these lines in the book) is that the feedback from the rotation keeps these binary systems stable and that it is highly improbable that they will in-spiral and coalesce.

Which raises the interesting question of what is the source of the waves that our gravitational wave detectors are seeing?

Which reminds me, I need to work on the grb module.

What about the spiral module?

The idea is to create a visualisation of the formation of spiral galaxies with a omega m / r model.

It would be good to also be able to model binary systems while we are at it.

2024 July Update

This module has now hit 2000 lines and has evolved into a joint exploration of the Sciama Principle and de Sitter Space.

There are simulations of the gravitational wave background from distant galaxies and a collection of pieces of code that I have written to help my own understanding of de Sitter Space.

The full de Sitter Space is a space-time with the Perfect Copernican Principle: there are no special places or times, it has looked like it does now for some considerable time.

de Sitter Space has constant negative curvature, and it is this curvature that means that geodesics, the paths of typical galaxies through our visible universe follow hyperbolae.

Pairs of geodesics separate exponentially in both forwards and backwards time. It is this forwards separation that explains redshift.

The separation in backwards time is generally overlooked, but this balances things out with blue shifted galaxies, new arrivals in our visible universe.

class gotu.spiral.Cosmo(cosmo=None)

Mimic an astropy Cosmology object

It’s a Sciama-DeSitter Universe.

Static, but doesn’t look static.

Old and big in a state of equilibrium.

The O*0 attributes give the current estimates of the share of the critical mass (also at z=0) in various buckets.

Ogamma for photons (primarial CMB) Om for non-realtivistic matter Ob for baryonic Odm for dark matter. Ode for dark energy.

Dark matter is not part of this cosmology.

Instead assume this turns up as black holes in the centre of galaxies.

In the default astopy cosmology, many functions take a redshift parameter or z value as a parameter. In FLRW, big bang, cosmologies, an exact Hubble-law is assumed, so a corresponds to a time and a distance as well as just redshift.

In a Sciama-DeSitter universe there is only an asymptotic relation between distance and redshift, for each emitter an observer sees.

There is also an asymptotic relation in backwards time, with emitters arriving highly blue shifted in our visible universe.

Where z is in effect a time, we return the value for z=0.

check_critical_density()

Critical density formulae

The critical density only depends on the Hubble distance.

It is the mass per unit volume such that the total mass has Schwartzchild radius equal to the Hubble distance.

As such, it is determined by the Hubble constant.

is_flat()

de Sitter Space has constant negative curvature

Hence, it is not flat.

class gotu.spiral.LLPegasi

Beautiful spiral with an 810 year period.

Dust around a binary system showing a clear spiral structure.

The gap between bands and their rate of expansion are consistent with the pair’s 810 year orbit based on their angular separation.

Distance is 1300 * u.pc

temperature 1800K

class gotu.spiral.SkyMap(gals=None, n=1566, fudge=None)

Yet another table viewer?

parsing csv and figuring out what it means.

or just give me lists of fields i can pick form for any purpose?

Or yet another universe viewer.

And so we descend into the world of coordinate systems.

Something astronomers understand very well.

See gotu.wits for more on this subject.

Maybe SkyMap allows systems to evolve over time, according to the paradigm.

async cmbsim()

Calculate some CMB related numbers

This is really just a test of planck_radiance_law_wavelength, checking that the energy gives the same Ogamm0 as is implied by the temperature.

create_sample(gals=None, n=None, t0=0)

Create a new sample of galaxies

This also initialises some parameters, based on the sample.

The goal is to set the stellar masses to match the baryonic matter as given by the cosmology Ob0. This is then scaled so that the sum of the central masses equals the mass of the universe.

gals: if given, a list of galaxies to include.

find_distant(results)

Find objects we no longer care about

async local_mode_sim()

Simulation of the gravity waves from the local cluster

sample_mass()

Return the sum of the masses of the sample

In solar masses.

set_mcent()

Set up central mass of all spheres based on stellar mass

tofu(u, balls=None, name=None)

Work in natural units, c=G=Hubble Distance=1

Time in Hubble times.

waves()

What waves would be generated by the catalog?

class gotu.spiral.SpanishDancer

Spanish Dancer

class gotu.spiral.Spiral

Model a spiral galaxy

Or any rotating mass?

Want to convert this to use astropy units.

accretion()

Accretion rate

amplitude(R=None)

amplitude of the gravitational wave wave

Returns the amplitude of the wave if there was just one such object in the sphere radius R. Scale by the actual density to get useful numbers.

Suppose rho is the number of such objects per unit volume, the the full wave will be:

a = 4 * pi rho Sum M r^2 dr / r for 0 < r < R

Which simplifies to:

a = 4 * pi * rho * M Sum r dr for 0 < r < R

or:

a = 2 * pi * rho * S * R ** 2 [1]

Now:

N = rho * 4/3 * pi * R**3

So if N==1, rho = 4 * pi / (3* R**3), substituting in [1]

a = 3 S / 2 R

Where S be the Schwartzchild radius of Mcent.

R is the radius out to which bodies can contribute to the sum.

To get the full wave, scale by the number of objects in the region of radius R.

bondi()

The Bondi Sphere

Equate the root mean square velocity of hydrogen atoms in the medium, sqrt(3kT/m_h) with the escape velocity sqrt(2GM/B).

critical_radius()

Radius of Mcent based on critical density

Convert Mcent to the radius of the sphere it would occupy based on critical density.

density()

Return density of Mcent if it is a black hole

eddington(z=None)

Eddington Sphere

Easiest to calculate if we know the redshift.

galaxy()

Set parameters for a galaxy

inspiral(tt)

The gravitational wave this galaxy arriving could generate

Provides a time domain model.

tt are the times in seconds before the peak of the wave.

ringdown(tt, zboost=0)

The gravitational wave this galaxy arriving could generate

tt are the times in seconds before the peak of the wave.

rmin_check()

The length of the roots of the spirals

This can be used to set the B value.

Assume that the spiral roots end at radius r0

And assume the roots are moving with the inertial frame at that radius.

The rate of precession will match that of the inertial frame at that radius.

schwartzchild()

Schwartzchild radius in lightyears

spheres3()

Bondi, Eddington and Schwartzchild

We have mass in lightyears, the Schwartzchild radius.

To get the mass in kilograms, S = 2GM/c^2, M = Sc^2/2G

tb()

blue shift period

tofu(u)

Work in natural units, c=G=Hubble Distance=1

Time in Hubble times.

umax()

the last time u that the source can be seen

notice e^umax = 1/(e**tstar = e**(-tstar) so umax = -1 * tstar. t for umax is infinite and u for tstar is -infinity

v(r)

Velocity at radius r

A = 0.0005 K = Mcent CC = -10

??

vinert(r, v)

Inertial part of the velocity

Part of velocity relative to inertial frame.

Notes

K is central mass. A = 0.0005

z_calc()

1.27e7 theta / M

M mass in suns

zgrav(r)

Gravitational redshift at radius r

r in hubble times

eddington tells us the radius given z in terms of the schwartzchild radius, s.

r = s / (1 - (1+z)**-2)

so:

1-(1+z)**-2 = s/r

1-(s/r) = 1/((1+z) **2)

1/(1-s/r) = (1+z)**2 = 1 + 2z + z*z) 0 = 1 - 1/(1-s/r) + 2z + z * z

class gotu.spiral.Sun

gotu.spiral.cpr()

Started as Mathematica code from the new paradigm.

adapted to python over time.

See spiral class for more information over time.

gotu.spiral.e2tofu(u, theta, phi)

Work in natural units, c=G=Hubble Distance=1

Time in Hubble times.

gotu.spiral.e2uoft(t, theta, phi)

Work in natural units, c=G=Hubble Distance=1

Time in Hubble times.

gotu.spiral.from_heasarc(kwargs)

Create a Spiral from a Heasarc record

gotu.spiral.hubble_tension(cmb=<Quantity 67.66 km / (Mpc s)>, near=None)

Explore hubbe tension

gotu.spiral.mass_length()

Equivalence of mass and length based on Schwartzchild radius

This is for use with astropy constants.

for example: >>> u.solMass.compose(mass_length())

gotu.spiral.near_galaxies()

parse galaxy.txt from

https://heasarc.gsfc.nasa.gov/w3browse/all/neargalcat.html

gotu.spiral.planck_radiance_law_wavelength(wavelength, T=None)

Energy emitted in wavelength at temperature T

wavelength: a float, wavelength in meters T: temperature, a quantity with units K

returns astropy Quantity object with units

gotu.spiral.schwartzchild(m)

Mass in kg to schwartzchild radius in lightyears