Jump to content

Newton Gravity for spiral galaxy


David Levy

Recommended Posts

 

Newtons laws does not prove otherwise. Your attempts to make it do so is by ignoring any conflicting mass. Such as dust and dark matter

Newton lows perfectly fits to what we see.

Yes, if you add dust and dark matter it won't fit.

However, don't you think that dark matter is only a theory?

If there is a dark matter it should be anywhere.

Let me use an example of a salt in an ocean.

The percentage of the salt in the ocean is the same even for one drop.

Therefore, if there is a dark matter, it should also be applicable in our solar system!

However, in this case, it's quite clear that Newton low shouldn't fit also for the solar system.

Therefore, if Newton low works perfectly on a solar system without dark matter; it also should work perfectly on spiral galaxy without dark matter.

 

Hence, would you kindly help me to distinguish between theories and real proves?

So far most of the arguments for the assumption that there are mass between the spiral arms were based on theories. For example:

-Density wave theory

-Plasma

-Dark matter

-MOND

-It takes a few million years for a star born in the spiral arm to drift out.

With regards to real evidence, So far the most real evidence was M100.

However, based on the article about M100 it is quite clear that this is not the case.

Therefore, I would mostly appreciate your support in focusing on real evidence.

Edited by David Levy
Link to comment
Share on other sites

Newton lows perfectly fits to what we see.

Yes, if you add dust and dark matter it won't fit.

 

People who have actually done the maths, rather than guessing, would disagree.

 

However, don't you think that dark matter is only a theory?

 

"16. 10 points for arguing that a current well-established theory is "only a theory", as if this were somehow a point against it."

http://math.ucr.edu/home/baez/crackpot.html

 

If there is a dark matter it should be anywhere.

 

It is anywhere and everywhere. The distribution has been mapped fairly thoroughly.

 

Let me use an example of a salt in an ocean.

The percentage of the salt in the ocean is the same even for one drop.

 

Nope. The percentage of salt varies all over the place. (A bit like dark matter.)

 

Therefore, if there is a dark matter, it should also be applicable in our solar system!

 

It is.

 

However, in this case, it's quite clear that Newton low shouldn't fit also for the solar system.

 

If you were capable of doing the maths, you would know this wasn't true (partly because there isn't enough dark matter in the solar system compared to the mass of the Sun).

 

Hence, would you kindly help me to distinguish between theories and real proves?

 

Theory is the best possible explanation science can give. Proof doesn't exist in science. OK?

 

So far most of the arguments for the assumption that there are mass between the spiral arms were based on theories.

 

And that is why they are good arguments.

 

Therefore, I would mostly appreciate your support in focusing on real evidence.

 

You ignore evidence. And science. And refuse to do any real calculations. Stop wasting everyone's time.

Link to comment
Share on other sites

 

Thanks Strange

 

It is anywhere and everywhere. The distribution has been mapped fairly thoroughly.

Nope. The percentage of salt varies all over the place. (A bit like dark matter.)

So, do you agree that dark matter is everywhere?

If the dark matter is like a salt, and there is a salt in every drop of the ocean, than there must be dark matter everywhere. Even in the solar system – and in the same ration (more or less)

If you were capable of doing the maths, you would know this wasn't true (partly because there isn't enough dark matter in the solar system compared to the mass of the Sun).

How come?

Why do you claim that there isn't enough dark matter in the solar system?

Based on Wiki: http://en.wikipedia.org/wiki/Dark_matter

"the total mass–energy of the known universe contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. Dark matter is estimated to constitute 84.5% of the total matter in the Universe, while dark energy plus dark matter constitute 95.1% of the total mass–energy content of the Universe"

So, the ratio between an ordinary matter to dark matter is at least 5 to one.

Hence, in the solar system the dark matter mass should be at least five times the mass of the Sun.

Even if it is only one to one; Please try to confirm Newton low in this condition…

 

Theory is the best possible explanation science can give. Proof doesn't exist in science. OK?

And that is why they are good arguments.

However, if the current theory contradicts Newton low, don't you think that you should reconsider this theory (or Newton low...)? Edited by David Levy
Link to comment
Share on other sites

If the dark matter is like a salt, and there is a salt in every drop of the ocean, than there must be dark matter everywhere. Even in the solar system – and in the same ration (more or less)

 

For large enough values of "more or less" maybe. The density of dark matter near the center of the galaxy is much greater than around the solar system.

 

Why do you claim that there isn't enough dark matter in the solar system?

Based on Wiki: http://en.wikipedia.org/wiki/Dark_matter

"the total mass–energy of the known universe contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. Dark matter is estimated to constitute 84.5% of the total matter in the Universe, while dark energy plus dark matter constitute 95.1% of the total mass–energy content of the Universe"

So, the ratio between an ordinary matter to dark matter is at least 5 to one.

Hence, in the solar system the dark matter mass should be at least five times the mass of the Sun.

Even if it is only one to one; Please try to confirm Newton low in this condition…

 

That is average amount of dark matter compared to matter. In the solar system the density of normal matter is much, much higher than average (almost entirely due to the Sun). So, even if we assume that dark matter is evenly distributed, there will be a much, much higher ratio of matter to dark matter in the solar system.

 

I started working this out, but found someone has already done it. The total mass of dark matter in the solar system is about 1/1000000000000000000th of the mass of the sun.

http://cdms.berkeley.edu/Education/DMpages/FAQ/question36.html

 

However, if the current theory contradicts Newton low, don't you think that you should reconsider this theory (or Newton low...)?

 

Current theory doesn't contradict Newton's law. But note that people have tried to explain dark matter by using modifed theories of gravity (e.g. MOND) but they just don't fit the data. Most notably, if you make the theory work for galaxies it doesn't work for galaxy clusters (and vice versa). The best you can achieve by modified the way gravity works is to reduce the amount of dark matter needed.

 

Also, if dark matter wasn't responsible for the orbital speeds in galaxies, then you would need a new explanation for all the other evidence for dark matter.

Link to comment
Share on other sites

 

First let me highlight my appreciation for your knowledge and support!

"The radius of the sun's orbit is about 2.5x1017 km, so the total mass of dark matter within that orbit is 6x1040 kg. This is the mass of 3x1010 (30 billion) stars like the sun! The entire galaxy only contains ~100 billion stars, so the dark matter does have a significant effect on the sun's orbit through the galaxy. For objects farther out near the edge of the galaxy, the dark matter is actually the main thing keeping them in their orbits. This is more or less how dark matter was discovered by astronomer Vera Rubin and others: the orbital speeds of galactic stars and gas clouds don't match our expectations from the visible matter".

Wow!

Now I can understand the source for the dark mass idea.

As I have stated, Newton low gives full explanation for Spiral galaxy. Hence, there is no need for this dark mass

However, it is quite amazing phenomenon.

The science couldn't find a solution for the sun orbit velocity in the Milky Way galaxy.

Therefore, it was concluded that there must be dark mass inorder to explain this rotation curve.

Now, when I have offered a solution for this rotation curve – I need to explain also the idea of dark mass.

This is an impossible mission for me!

The best you can achieve by modified the way gravity works is to reduce the amount of dark matter needed.

Yes, that is correct. Do you agree to reduce the dark matter to zero?

 

Also, if dark matter wasn't responsible for the orbital speeds in galaxies, then you would need a new explanation for all the other evidence for dark matter.

Yes, I have a perfect explanation for everything we see.

I can promise that if you are ready to ignore completely the current concepts and theories, you will find that there are simple explanations for everything we see and will see.

Therefore, I have asked you to focus only on evidences. I have no ability to compete with the current theories.

From time to time I read about puzzled scientists. They are confused with the last evidence which they have just discovered. However, they are puzzled because the last evidence doesn't fully align with the current theories. So, they try to find new theory to close the gap. Therefore, you must be a master in science inorder to understand the full set of theories and updates.

Edited by David Levy
Link to comment
Share on other sites

As I have stated, Newton low gives full explanation for Spiral galaxy.

 

You have stated this. But it is wrong.

 

Yes, that is correct. Do you agree to reduce the dark matter to zero?

 

No. As I say, the best attempts can reduce the amount needed, not eliminate it. But there is no othjer evidence for the modifed gravity theories (but there is other evidence for dark matter).

 

Yes, I have a perfect explanation for everything we see.

 

It is very sweet that you think so. Your mum must be very proud.

 

Now, if you could actually do the calculations (instead of guessing) then you might impress others as well.

 

I can promise that if you are ready to ignore completely the current concepts and theories

 

As current theories are the current theories for a very good reason (they work and fit the evidence) I won't be doing that.

 

Therefore, I have asked you to focus only on evidences. I have no ability to compete with the current theories.

 

You cannot compete with current theories because you ideas are unsupported and contradicted by the evidence.

Link to comment
Share on other sites

 

You cannot compete with current theories because you ideas are unsupported and contradicted by the evidence.

No, it is not.

Newton low is fully aliened with any available evidence for spiral galaxy.

Please try to find one – only one real evidence - which contradicts my idea!

Edited by David Levy
Link to comment
Share on other sites

 

No, it is not.

Newton low is fully aliened with any available evidence for spiral galaxy.

Please try to find one – only one real evidence - which contradicts my idea!

 

One: there are stars between the spiral arms. (As shown by observation.)

 

Two: The galaxy does not rotate as a solid disk. (The evidence contradicts that idea as well: the orbital speeds do not vary linearly with distance)

 

Three: you have not done any calculations to support your idea. All you have done is shown Newton's law and then asserted that IF you did the calculations then you would get the answer you want. But people have done the calculations and don't get the answer you claim.

 

Four: Newton's law works. (Except when the full accuracy of GR is requried.)

Link to comment
Share on other sites

 

No, it is not.

Newton low is fully aliened with any available evidence for spiral galaxy.

Please try to find one only one real evidence - which contradicts my idea!

We have actually, If you properly use Newton strictly, including all the baryonic matter. (Stars, gas etc, no dark matter)

 

You will end up with spiral arms moving slower the farther you move out from the center of the galaxy.

 

Not only that, when you measure the speed of a measured bar galaxy, the calculate the escape velocities, based strictly upon baryonic matter, those galaxies should fly apart. Their observed speeds exceed the escape velocity of strictly baryonic matter models.

 

Then you have gravitational lensing, in regions where there isn't enough baryonic matter to account for them.

 

Lastly DM assists the early large scale structure formation. The BAO observed in the CMB, utilize dark matter, this is another aspect that MOND could not account for.

 

Now MOND tried fixing the above, by modifications to Newtons inertia laws, in one method, in the other they tried via the fine structure constant. They showed good results , far better than strictly Newtonian, in some cases better than LCDM. In other cases worse.

 

MOND is still around, however it is losing favor, in order to make MOND work in the GR regime, you need TeVeS. Which runs counter to general relativity.

 

All in all though LCDM and MOND as two competing models, provided us incredible insight, and far tighter constraints.

 

If you wish to pursue MOND let me know, I have some excellent introduction aids on MOND.

 

 

Now onto density waves, This in and of itself does not require dark matter. However it does require matter between the spiral arms. (Keep in mind density wave theory is in excellent agreement with observations). To be honest I can't think of a single competing model. Might be one, most likely there is, just never heard of any.

 

Treat all stars and plasma, dust, baryonic matter as a gas. Then apply the interactions of forces, due to a rotating body to that gas. (Cosmology uses the ideal gas laws as it provides a good approximation).

 

Normally the rotations of a gravitating body, would lead to the winding problem. Any spiral arms would within a few rotations wind up and disperse or become indistinguishable. However, if you have analyze the gravitational attraction between stars, at different radii, this would result in regions of higher density.

 

Now these higher regions are described as sound waves, mainly due to its velocity of influence follows the rules of perturbations in a medium. In This case, it's normal to relate it as being the change in vacuum regions. (Ideal gas laws)

 

Now as the galaxy rotates the density waves also rotate, however they rotate faster than the stars themself move. Consequence of f=ma.

 

Dust and plasma takes less force to move than stars.

 

The areas behind the density waves is where the spiral arms a located , the density wave leads the spiral arms. Think of the spiral arms as the turbulence region resulting from the wave. This turbulence and higher density, causes a greater star formation rate.

 

As the density rate is faster than stars move and it generates stars in its path, it can catch up to previously formed stars as well as leaves younger stars behind. The gas itself is dragged behind.

The thing to keep in mind, is that since the galaxy first started forming, and today different ratios of heavier star formation elements became available. So today, the spiral arms can produce pop 1 stars. In the start of formation of our galaxy, we were just a gas cloud with no rotation and no spiral arms. However pop 2 stars are being formed.

 

As the galaxy gains rotation, conservation of angular momentum, The density wave starts. As the available gas changes to heavier elements, different star classifications of stars can now be birthed.

 

 

That's density wave in a nutshell. However without DM, it would suffer the same Keplar curve on galaxy rotation, ie be slower the further out you go. You need DM to keep its rate the further out you go consistent

 

 

A possible analagy, is full a tub with water, then place a variety of different grains of sand with different granularity and weight. When you pull the plug, notice how the lighter grains move compared to the heavier grains.

This is a natural consequence of f=ma

(I prefer that analogy, to the traffic Jam analogy, commonly used to describe density wave theory)

Link to comment
Share on other sites

We have actually, If you properly use Newton strictly, including all the baryonic matter. (Stars, gas etc, no dark matter)

That's great news.

I always wonder why you didn't do it so far.

You will end up with spiral arms moving slower the farther you move out from the center of the galaxy.

Not only that, when you measure the speed of a measured bar galaxy, the calculate the escape velocities, based strictly upon baryonic matter, those galaxies should fly apart. Their observed speeds exceed the escape velocity of strictly baryonic matter models.

It seems that you have a severe error in your modeling.

I will explain:

You have to understand correctly the structure of spiral galaxy.

In each structure, there are different forces.

So, the spiral galaxy is divided into three main sections.

-spiral arms section

-Center; The area between the supper massive black hole to the first Inwards ring of the spiral arms.

-Outwards – The aria from the far end of the spiral arms and outwards.

In each section, there are different forces and different equivalent host mass:

So far I have mainly concentrated in the spiral arms. It should be quite simple to set the modeling of this section.

However, the center should be much more difficult. I have spent hours in order to find the basic mechanism for this area. Even so, I need more data (especially on the bar) inorder to be sure that I do understand the complexity of this section.

The outwards section should be the simplest one. However, so far I didn't make any calculation for this area.

Link to comment
Share on other sites

Actually the error isn't mine its your. Mass distribution is relatively uniform in the power law distribution, according to the virial theorem. You really need to realize your premise of no mass between the spiral arms is 100% wrong.

 

Until you accept that it is pointless, continuing. Your attempts does not change this fact. Nor can it hand wave away the problem of the escape velocities.

Quite frankly I will take the results of thousands of scientists over a few centuries of observation and measurements, over anything you state.

 

The density wave model ACCURATELY describes the spiral arms. Your model does NOT

Quite frankly you can see a clear hydrodynamic model with pulling the plug. Look at the whirlpool. Do you not see density waves forming?

 

This is similar to how density waves behave at Saturn and spiral galaxies,

Link to comment
Share on other sites

Really, according to you.

 

Do yourself a favor. Calculate the acceleration a force has on particle as opposed to a star.

 

Now apply that to a gas nebulae as opossed to the stars within that nebulae. Which will move faster?

You want to apply Newton, apply all three laws.

PS density wave is Newtonian

Link to comment
Share on other sites

 

Thin disk (Population I)

 

The thin disk of the Milky Way has sustained ongoing star formation for ~10^10 years. Consequently it contains stars with a wide range of ages, and the thin disk may be divided into a series of sub-populations of increasing age.

 

The spiral-arm population is the youngest in the disk; it appears to trace the spiral pattern of the Milky Way. This population is concentrated very close to the disk plane, with a scale height of ~100 pc. Representative objects include H I and molecular clouds, H II regions, protostars, stars of types O & B, supergiants and classical cepheids. The metallicity of this population is somewhat higher than that of the Sun (MB81).

 

Attempts have been made to reconstruct the large-scale distribution of the H I from 21-cm observations. The radial distribution is less centrally concentrated than the disk stars, and the inner ~3 kpc are almost free of neutral hydrogen (MB81); thus the Milky Way is one of those galaxies with a central hole in H I. It is now realized that non-circular motions seriously confuse `galactic velocity tomography'.

 

The disk population proper is more smoothly distributed and does not seem to trace the spiral structure. This population may be further subdivided into young, intermediate, and older categories, with ages of ~1, ~5, and ~10*10^9 years, respectively (MB81). The characteristic scale-height of this population increases with age, ranging from ~200 to ~700 pc, while the metallicity declines to perhaps ~20% of the solar value. Representative objects include stars of type A and later, planetary nebulae, and white dwarfs.

 

http://www.ifa.hawaii.edu/~barnes/ast626_95/pcmw.html

 

 

It should be emphasized that there are almost as many stars between the spiral arms as in the spiral arms. The reason why the arms of spiral galaxies are so prominant is that the brightest stars are found in the spiral arms. Spiral arms are the major regions of star formation in spiral galaxies and this is where most of the major nebulae are found.

 

http://www.atlasoftheuniverse.com/milkyway.html

.

 

Link to comment
Share on other sites

Normally the rotations of a gravitating body, would lead to the winding problem. Any spiral arms would within a few rotations wind up and disperse or become indistinguishable.

Winding up problem;

As I have already proved in my mathematical calculations, in order to keep the velocity curve, stars must drift inwards or outwards.

Please see pg. 4.

If the stars are drifting inwards the spiral arm, or even if they keep their distance from the center, than it should lead to winding problem. This is clear.

However, if the stars are drifting outwards from the center than there is no winding problem!

This proves that all the stars in spiral galaxy are drifting outwards!

Actually this is one of the most important aspects for spiral galaxy. There is no spiral galaxy without one drifting direction! It isn't a wave. There is no posibility for drifting inwards and outwards. In spiral galaxy all the stars must drift outwards!

Somehow, the science verified several aspects of spiral galaxy. Never the less, so far I couldn't find even one article about this important issue. (I'm aware about several theories, but not real verification).

Even today, there is no clear indication if the Sun is drifting outwards from the center.

Why?

If you can find even one star (only one star out of the billions stars in spiral arm section) which drifts inwards, than it is a solid proof that I have a severe error in my understanding of spiral galaxy structure.(Please - no theory. Only real evidence!)

Edited by David Levy
Link to comment
Share on other sites

One: there are stars between the spiral arms. (As shown by observation.)

Which observation? Is it M100 or the Saturn ring? Is there any real evidence for this observation? If so, please advice.

 

However, based on Newton lows and my mathematical calculations, it is expected to get the following results:

-All stars in spiral arms must drift outwards

-There are no stable stars between the spiral arms. (If there is a star – than this star had been kicked out from the galaxy)

I would mostly appreciate to get any REAL evidence which confirms or rejects those expectations.

Edited by David Levy
Link to comment
Share on other sites

!

Moderator Note

 

David - unless you start engaging with criticisms (especially those backed up by references) this thread will be locked due to soap-boxing.

 

1. Your calculations are invalid as they are too simplified and hand-wavy and they are also unsound as they are based on false premises - please address these issues.

 

2. When a member presents a piece of information with references - it is not acceptable to state it is false because it fails to accord with your theory; in fact, it is not correct to say it is false whatever theory it contradicts. Science is empirical - data rules! If data does not accord with theory then either it is being mis-interpreted or the theory is incorrect - but we can never dismiss data because it contradicts theory.

 

Link to comment
Share on other sites

Which observation? Is it M100 or the Saturn ring? Is there any real evidence for this observation? If so, please advice.

 

You have been given several links detailing the density of stars between the arms. You have appare ntly chosen to ignore these.

 

However, based on Newton lows

 

 

LAWS, It's LAWS, not lows.

 

and my mathematical calculations

 

You haven't done any caclulations. You have reproduced Newtons laws and then gussed that it would support your idea. If you actually did the calculations, you would find it didn't.

 

I would mostly appreciate to get any REAL evidence which confirms or rejects those expectations.

 

 

No you woyuldn't. You would just ignore it again.

Link to comment
Share on other sites

 

IC342 Galaxy. The large dots in and around the spiral are galaxies. that misty-looking spiral is madeup of billions of stars. Where are the boundaries between the arms with no stars in? Lighter parts are the youngest brightest stars

Hello StringJunky

Thanks for the example.

However, based on Wiki, and Nasa there is no confirmation for the assumption that there are stars between the spiral arms.

It is stated:

http://en.wikipedia.org/wiki/IC_342

"The dust of the Milky Way makes it difficult to determine the precise distance; modern estimates range from about 7 Mly[5] to about 11 Mly.[2]"

By: http://apod.nasa.gov/apod/ap130718.html

It is stated:

"Even though IC 342's light is dimmed by intervening cosmic clouds, this deep telescopic image traces the galaxy's obscuring dust, blue star clusters, and glowing pink star forming regions along spiral arms that wind far from the galaxy's core. IC 342 may have undergone a recent burst of star formation activity and is close enough to have gravitationally influenced the evolution of the local group of galaxies and the Milky Way."

So, Why are you using this example?

Can you please advice if and where there is a confirmation for the assumption of stars between the arms?

 

 

You have been given several links detailing the density of stars between the arms. You have appare ntly chosen to ignore these.

Hello Strange

Thanks again for your great support.

I do appreciate all your efforts, and I do not ignore any massage!

I have got from you and other members full explanation about the theory.

However, you have claimed that the assumption of having stars between spiral arms is confirmed by a real observation.

Unfortunately, so far I couldn't find it in any article which all of you have pointed.

It might be my mistake that I have missed it.

There are millions over billions spiral galaxies.

If there are stars between the spiral arms, we should see it in at least one galaxy.

So please, would you kindly direct me to one (only one) article which confirms this assumption by real observation in one of the spiral galaxies.

Edited by David Levy
Link to comment
Share on other sites

We've provided articles. You provide an article that states density wave is wrong. Your turn

Did you not understand the term Halo? Which lies outside the galactic plane. Have You even looked at the regions in the papers we posted. Or looked at the rotation curve metrics or virial theorem?

 

Here lets make it even more obvious....

 

http://hubblesite.org/reference_desk/faq/answer.php.id=39&cat=galaxies

 

key word Halo, this includes halo stars....

http://www.mpa-garching.mpg.de/~weiss/aa_533_a59.pdf

 

http://www2.lowell.edu/workshops/expdisks2014/presentations/Davis_Poster.pdf

 

http://www.astro.caltech.edu/~george/ay20/Chiappini-MilkyWay.pdf

 

 

http://www.ifa.hawaii.edu/~barnes/ast110/MilkyWay.pdf

http://www.google.ca/url?sa=t&source=web&cd=21&ved=0CDcQFjAKOAo&url=http%3A%2F%2Fwww2.cose.isu.edu%2F~hackmart%2Fmilkyway.pdf&rct=j&q=milky%20way%20pdf&ei=DY7uVJaQEabPsQTV1oCoBQ&usg=AFQjCNG2DpEcZ8Lk2HCxy1Dq1hMIAodtqQ&sig2=lfUKuHq68OqGPoXSsMzJng

In the last link page 11 is full of stars that lie in the galactic halo.

 

You should also note the density to luminosity relations.

 

If this isn't enough to satisfy you prove us wrong With a Peer reviewed paper.

Link to comment
Share on other sites

 

Take your pick If you try to tell me there is a clear delineation between the arms I'll give up.

Thanks StringJunky

Who am I to decide if there is delineation or there isn't?

I have only asked to get one article in which the science states that in spiral galxy X (as an example) there is no delineation between the arms. So, it is clear that there are stars between the spiral arms.

Only one article!

 

 

We've provided articles. You provide an article that states density wave is wrong. Your turn

Thanks Mordred

I will read it carefully and advice.

Edited by David Levy
Link to comment
Share on other sites

Thanks StringJunky

Who am I to decide if there is delineation or there isn't?

I have only asked to get one article in which the science states that in spiral galxy X (as an example) there is no delineation between the arms. So, it is clear that there are stars between the spiral arms.

Only one article!

The 'glow' around the Sombrero galaxy is made up of stars but less populated than in the disk. It should be clear that there is no delineated areas absent of stars because it pervades around and throughout the disk.

 

post-14463-0-28873600-1424930857_thumb.jpg

 

 

This image of the Sombrero galaxy or M104 was taken by the NASA/ESA Hubble Space Telescope.

 

The galactic disc shows spiral arms similar to that of the Milky Way. Above and below the disc the galactic halo can be seen clearly. This halo is a sphere which contains fewer stars by volume as compared to the galactic disc.

 

http://www.esa.int/spaceinimages/Images/2008/06/A_galaxy_and_its_halo

Edited by StringJunky
Link to comment
Share on other sites

Guest
This topic is now closed to further replies.
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.