## Visible Matter and Dark Matter

 Question 1 How much mass is there in our Galaxy? Question 2 How much visible matter is there in our Galaxy? Question 3 How much matter is missing ? Question 4 Is it possible to explain the missing mass by using the NFW profile ? Question 5 Is it possible to explain the missing mass by using the Hernquist profile ? Question 6 Is it necessary to explain the missing mass by introducing dark matter ? Question 7 Is there dark matter in the Universe ?

### Background

1. The problem with the movement of the Sun is that its observed speed does not match with the calculated (expected) speed based on the visible mass in both the bulge and the disk. This calculated speed is too low. To match both more mass has to be assumed. The question is what is the nature of this mass.
2. In order to do a proper simulation of the movement of the Sun through our Galaxy the amount (and distribution) of matter and dark matter in our own galaxy is important.
3. In order to do a proper simulation of the movement of the planet Mercury the amount of visible matter and dark matter in the neighbourhood of the Sun is important.

For an older discusion (8/10/2005 until 16/12/2005) read this:
Dark matter may not exist

For a reaction on the above discussion in German read this:
"Dunkle Materie" und "Dunkle Energie" sollen die ART retten...

### Description

Visible matter constitutes all the mass (stars) that are directly visible including all planet sized objects and even smaller. Visible means objects that emit light. Mass considered are the elements of the periodic table.
Dark matter constitutes mass that is not described by the periodic table.
Visible is a typical human parameter. From a philosophical point of view physical behaviour has nothing to do with human behaviour. The laws of nature are independent of human involvement.

There are three methods to calculate the mass of a Galaxy.

1. By measuring the Luminosity at distance r from the centre of the galaxy and by using the Mass-luminosty relation, which gives the mass at distance r. The sum of all the distances gives the total visible mass of the galaxy.
Next by using Newton's Law and assuming that the sum of all forces is zero you can calculate the galaxy rotation curve. This is what is called the calculated or expected galaxy rotation curve based on visible mass
2. By measuring the orbital speed of the galaxies as a function of the distance from the centre. This is the visible rotation curve. Next by using Newton's Law in the form of: a = m(r) * v^2 / r over a small distance dr assuming that the total galaxy is in equilibrium (is stable). The result is a delta mass at distance r from the centre. The sum of all those masses gives the total calculated mass of the galaxy.
3. By making observations about the movement of a cluster of Galaxies. The same method can be used to study globular star clusters. See Virial Theorem The method involved assumes that the stars or galaxies involved form a rather close system. For galaxies this is a difficult assumption. What makes this extra difficult are the speeds and distances involved.

The problem with the first two methods is that they do not give the same results:

• The expected galaxy rotation curve and the visible rotation curve are different.
• The speed of the expected rotation curve based on visible mass is lower
• The shape of the visible rotation curve is flat.
• The shape of the visible rotation curve seems to continue outside the visible region.

The current accepted solution is to include dark matter in the form of a halo.

For an example of a galaxy rotation curve go to the following Galaxy Rotation Curve from Wikipedia.
This example looks like this:

 ``` XXBBBBBBBBB BBBBBBBBB X A BBBBBBBBBB BBBB X A X A X AA X AAA X AAAAAAAAA X AAAAAAAAAAAAAAAA X X---------------------------------------- Figure 1 ```
Beneath the example is the text:
Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Dark matter can explain the velocity curve having a 'flat' appearance out to a large radius
The problem with this example is that if you want to simulate the predicted curve (A) you need a disk of almost zero mass. In fact the shape (A) is almost identical as the speeds of the planets around the Sun or of a point mass. That is a wrong assumption if you want to simulate a galaxy.

### Simulation Programs of Galaxy Rotation Curves, with and without dark matter.

1. In Quick Basic:
• For a copy of the program select: MASS_GAL.BAS. The purpose of the program is to calculate the galaxy rotation curves as a function of the height and shape of the disk. The program does not support dark matter.
• For a listing of the program select: MASS_GAL.HTM.
• To execute the program select: MASS_GAL.ZIP.
• For an explanation of the program See: program2.htm
2. In Visual Basic
3. in Excel
• There are 3 programs in Excel to simulate Galaxy Rotation Curves: grotc.xls, grotc1.xls and grotcexp.xls.
The difference is in the shape of the disk.
• For a copy of all 3 programs select: grotc.xls.
. The programs also supports dark matter.
• For a description of this programs and a "Read me First" select grotc.xls.htm or grotcexp.xls.htm
• For similar programs in Excel to calculate Galaxy Rotation Curves select: circ11.xls, circ12.xls and circ11.xls to circ16.xls.
The purpose of those programs is to calculate disk density profiles to simulate (flat) galaxy rotation curves.
• For a description of those programs and a "Read me First" select circ11.xls.htm

### Answer question 1 - Total Mass

Accordingly to the document: Galactic Structure, Fundamental Parameters etc the shape and size of both the Andromeda Galaxy (M31) and the Milky Way are identical. The Galaxy rotation curve is flat and the speed of the Sun is roughly 250 km/sec.
Using that information it is possible to calculate the mass of the Galaxy.
There are three ways to do that:
1. Assuming that the Galaxy consists wholly out of a bulge. That means there is no disk. In fact this is an Elliptical Galaxy. See Test1 in Circ11.xls. The total mass is 1,77 10^42 Kg.
2. Assuming that the Galaxy only has a disk. See Test2 in Circ11.xls. Total mass is 1,16 10^42 Kg
3. Assuming that the Galaxy has both a bulge and a disk. See Test3 Test4 Test6 in Circ11.xls. The total mass is 1,16 10^42 Kg. Radius is 200000 Lightyears or 61 Kpc.

### Answer question 2 - Visible Mass

Accordingly to the document Deriving the Galactic Mass from the Rotation Curve the size of the visible disk is 30 kpc or 100000 lightyears. The speed at that distance is 100 km/sec.
Test5 of program Circ11.xls simulates more or less this behaviour. The total visible mass (0,5 + 1,39) = 1,92 10^41 Kg. This is a factor 6 too Low compared with the above results.

### Answer question 3 - Missing Mass

In the Question 2 the Visible disk size is 100000 Lightyears. In question 1 the size of the disk studied is 200000 Lightyears.
In program Circ16.xls the total mass size for different disk sizes are studied. i.e. 25000 Ly, 50000 Ly, 100000 Ly and 200000 Ly.
The result is respectivily: 1,4 2,9 5,8 and 11,6 10^41 Kg
Comparing the two results of 100000 Lightyears shows that an amount of 5,8 - 1,92 = 3,9 10^41 Kg is missing.

### Answer question 4 - Dark Matter NFW profile.

It is relative simple to solve the missing mass problem by introducing dark matter which is described the NFW profile
The NFW profile uses two parameters: rs and rhos.
For more detail (Specific page 17) See: See http://lanl.arXiv.org/pdf/astro-ph/0301144 Test 6
For more detail See: Circ12.xls NFW profile

### Answer question 5 - Dark Matter Hernquist profile.

It is relative simple to solve the missing mass problem by introducing dark matter which is described the Hernquist profile
The Hernquist profile uses two parameters: Mh or Mass Halo and a.
For more detail (Specific page 2) See: http://lanl.arXiv.org/pdf/astro-ph/0506015 Test 6
For more detail See: Circ14.xls Hernquist profile

### Answer Q6 - Is Dark Matter required to solve the missing mass problem ?

Observations reveal that the Galaxy Rotation Curve observed (which is flat) and the expected Galaxy Rotation Curve based on visible mass (which drops after a certain distance) do not match. This is called the missing mass problem.
The solution for the missing mass problem is to introduce a Halo of dark matter outside the bulge.

This dark matter solution can be only be considered if "you" are sure that there is no other explanation. IMO the most obvious solution is ordinary matter in the form of planet sized objects in the disk. That means in invisible visible matter. Using this assumption it is very easy to simulate a flat galaxy rotation curve, specific by assuming that the disk is much larger that based on visible observations.
This solution is not so strange. If you consider the solair system than all the planets, including the objects in the Kuiper belt, belong to the category of invisible visible matter.

The mathematical shape of both the NFW or Hernquist profile is rather by good luck or with a wet finger. The method to establish the two parameters of each is rather artfical.
• In program Circ12.xls (NFW profile) the starting point is a flat galaxy rotation curve. In figure 1 above this is the line marked B. In order to find the curve marked A you first increase the peak of the NFW profile by changing the two parameters rs and rhos and then you move the peak to the right position. This approach is not very scientific.
• In program Grotcexp1.xls Test4 (NFW profile) en in Test7 (Hernquist profile) the reverse approach is followed. Starting point is the curve marked A.
in order to find the curve marked B, with the NFW profile, you first select the position of the peak by changing the parameter rs and then you change the hight of peak by changing the parameter rhos such that the Galaxy rotation curve becomes flat.
With the Hernquist profile you increase the parameter "a" first and secondly the parameter "Mh" (Mass Halo). This approach is rather by try and error and is not very scientific.
The problem with both profiles is that there is no way to demonstrate which one is correct. In fact both can be wrong.

### Answer Question 7 - Is there darkmatter in the Universe ?

The current accepted theory holds that the total amount of matter in the Universe 83% is dark matter (nonbaryonic) and that only 17% is ordinary visible matter (baryonic), that means the type of matter that are the building blocks of the stars and planets.
In Wikipedia there is also a distinction between baryonic and nonbaryonic dark matter with the text:
A small proportion of dark matter may be baryonic dark matter
That means a small part of the 83% can be baryonic.

The Galaxy Rotation problem is no reason to assume that there is (nonbaryonic) dark matter inside the galaxies. As argumented in this document the simplest explanation is only ordinary matter inside the bulge and the disk and that the disk is much larger.
Gravitational Lensing is also no prove that there is (nonbaryonic) dark matter in the Universe. Gravitational Lensing or in general the bending of light is a demonstration that there is extra mass between the source and the observer. Again the most simple explanation is ordinary matter.

The real questions to ask is for our Milkyway Galaxy:
• How much ordinary visible (baryonic) matter is there. This matter includes the star. They transmit energy in the form of light.
• How much ordinary invisible (baryonic) matter is there. This matter includes the black holes, all the planets all the pluto sized objects and smaller.
• How much nonbaryonic matter is there.
Secondly the same questions but now for: the Local Group
Third the same questions but now for the full Universe. To get a glimpse of this complexity study: Friedmann's equation
The answers for all 3 questions can be different, and the outcome of the first will influence the second.
IMO the readers of this document should not be amazed that in the future the necessity of including nonbaryonic darkmatter in any Galaxy will be zero.

1. The Dark Matter problem Authors: A. Bosma
In these notes I will briefly summarize our knowledge about the dark matter problem, and emphasize the corresponding dynamical aspects.
2. More literature: Dark Matter in disk Galaxies Authors: A. Bosma
The Mass and Extent of the Galactic Halo Authors: Dennis Zaritsky
3. Dark Matter by Bill Keel .
4. What is dark matter by Scott I Chase.
5. What is dark matter by Scott I Chase. Select Item 9
6. What is dark matter Frequently asked questions in cosmology
7. Dark Matter in the Universe by Vera Rubin
8. Science News: A Galactic Centre Mystery Movie with Fast-moving stars in the centre of our Galaxy
9. Disk galaxy rotation curves and dark matter distributionInteresting article. Start reading with Summmary and Conclusion at page 17. The article is in favour of MOND.
10. Galaxy rotation curves without nonbaryonic dark matterBy J. R. Brownstein and J. W. Moffat. This article shows more than 150 Curves. The article is in favour of MOND.

### Reflection as of August 2013

1. For comments about "Dark Matter" in Wikipedia read this: Dark Matter
2. For comments about "Galaxy Rotation Curves" in Wikipedia read this: Galaxy Rotation Curve
3. For comments about "Big Bang Nucleosynthesis" in Wikipedia read this: Big Bang Nucleosynthesis
There are three articles which raise doubt that dark matter is involved as building material of galaxies.
• Do elliptical galaxies have dark matter halos? http://astrobites.org/2013/04/04/do-elliptical-galaxies-have-dark-matter-halos/
The text of this document reads:
The authors found that the mass-to-light ratio is constant for different sizes of Einstein rings, showing that there is no sign of large amounts of dark matter surrounding these galaxies! If there is dark matter in these galaxies, it’s mixed in with the luminous matter.
• Gravitational lensing evidence against extended dark matter halos http://arxiv.org/abs/1303.6896
The text in this document reads:
Our results thus suggest that, if dark matter is present in early-type galaxies, its amount does not exceed the amount of luminous matter and its density follows that of luminous matter, in sharp contrast to what is found from rotation curves of spiral galaxies.
Also:
The main goal of the present paper is to test the hypothesis that early-type lens galaxies are embedded in extended dark matter halos, as are generally found around spiral galaxies.
As far as I know, no one has found (detected) dark matter (WIMPS etc) around spiral galaxies.
The whole concept of dark matter halos around spiral galaxies is deduced to explain galaxy rotation curves, not on observations.
1. Suppression of star formation in the galaxy NGC 253 by a starburst-driven molecular wind http://www.nature.com/nature/journal/v499/n7459/full/nature12351.html
2. Hubble Finds Source of Magellanic Stream: Astronomers Explore Origin of Gas Ribbon Wrapped Around Our Galaxy http://www.sciencedaily.com/releases/2013/08/130808123318.htm
Accordingly to dutch paper NRC the amount of baryonic mass involved includes 10^8 Sun masses.

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Created: 8 September 1997
modified: 20 January 2002