Evidences for the Dark Matter

 

Dark matter is known  as the “missing mass,” dark matter’s existence was first inferred by Swiss American astronomer Fritz Zwicky, who in 1933 discovered that the mass of all the stars in the Coma cluster of galaxies provided only about 1 percent of the mass needed to keep the galaxies from escaping the cluster’s gravitational pull. 

In this blog we will discuss 5 different pieces of evidence for the existence of the dark matter 

1. BENDING OF LIGHT

Gravitational lensing:-

The amount of bending is proportional to the mass of the object that causing the bending, 

Light gets bent due to the mass of the object.

In this image light from the distant galaxy is lensed due to galaxy clusters, so we get lensed images here on the earth.

But we are getting an extra lensed image than usual but the Amount of bending is proportional to the mass of the object, so there is evidence of missing mass, We get the factor of the Dark matter here.

We can derive the formula for this 

As 

2. ROTATIONAL CURVE

The following graph is of the solar system rotation curve 

1.The velocity of any planet depends upon the mass of the star

    Eg. the velocity of the earth depends upon the mass of the sun.

2.The velocity of the planet also depends upon the distance from the force center (Parent Star).

    I.e  v^2=GM/r , v^2=1/r

When an astronomer Vera Rubin looked for the doppler shift diagram for the M31 Galaxy she found that the graph of velocity is not decreasing as the calculated graph does. It goes on a flat curve with no crest on the graph. She found that There is mass beyond the galaxy. And it varies with the 1/r2. That ununderstood mass is known as Dark matter

This is the velocity graph of the High-speed31 galaxy that clearly shows that the graph is not decreasing it goes on flat i.e there must be mass beyond the solar system.

3. VIRAL VELOCITIES IN CLUSTERS

In 1930 the astronomers measured the mass of galaxies in clusters in clusters there are galaxies then dust particles the galaxies are of 2 types 

1.Slow speed galaxies 

2.High-speed galaxies

They found that the inferred mass using the viral theorem argument was 400 times greater than the Mass that counted by just taking the galaxies and gas using the mass to light ratio. 

Viral Theorem is the average kinetic energy is related to potential energy.

They conclude that there must be some missing mass i.e. Dark Matter is present.

4. DARK MATTER AT THE COSMOLOGICAL SCALE 

When we looking at the sky we look at the past. 

The last part we are looking at (CMB) having more density fluctuations 

And the temperature also increases and decreases according to the density fluctuations 

I.e say 𝛅T/T ≈ δρ/ρ  ≦1/10^4

Primordial plasma oscillates depends on the gravitational pull + Radiation pushes

If we add more matter which is not related to light( Dark Matter )  it will oscillate more 

Because if you add more dark matter the photons cannot leak out of small gravitational waves  therefore power drop less steep 

Because every peak in the wave tells us how much dark matter is there.

This is the perfect evidence of the dark matter because we are looking at the cosmological scale 

We know how much is there as it is the physics of the forced damped oscillators 

5. THE COSMIC NET 

Until the universe was matter-dominated everything was Radiation. When the universe become matter-dominated could density fluctuations 

δmax=δρ/ρ  grow after matter radiation equality.

These things grow proportional to the scale factor.

δ α a  as, a (scale factor)

 Between matter radiation equality and today’s universe 

  a/a(equality) ≈ 1+z(equality)/1+z(today)≈ 1100/1 ≈ 103

δmax of cmb～10^(-4)⟶ 0.1

 This structure what we see corresponds to density fluctuations that are significantly larger than one

δmax of cmb～10^(-4)⟶ 0.1 vs δcluster≳1

All these conflicts can be resolved if we add the correct amount of dark matter 

Ωh2≅ 0.12

This is the correct amount of dark matter if we add this, it completes the proper structure of the 

universe .

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