An Indirect Evidence for the Existence of Dark energy/Dark Matter by Considering a Pulsar

We all know that a pulsar is a rapidly rotating neutron star. Especially, the density of a pulsar is very high. Because, it consists of almost neutrons with high concentration densities. When a neutron star is rapidly rotating it calls as a pulsar.  Similar to Earth, pulsar has axis of rotation and magnetic axis. But pulsar emits high energy electromagnetic waves along the direction of the magnetic axis. Usually those EM waves are highly energized Gamma radiations. Since the pulsar emits highly energized gamma radiations along the magnetic axis, an observer able to see the pulsar’s photons discretely. Because the axis of rotation and magnetic axis are different in the alignments. Then the magnetic axis creates a symmetric cone which is symmetric along the axis of rotation. Then only when the magnetic axis is towards the Earth, observer on Earth can see the photons coming from the pulsar. But not otherwise. 
My attempt is to investigate my own ideas those related with several cosmological subject fields. Let’s consider the time duration between two consecutive detections of gamma photons 
is Δt > 0. Then, 
The angular velocity of the pulsar = ω = 2*π/Δt …………………………………(1) 
Usually the pulsars those we can observe are very distant objects from the Earth. Then there is a relative velocity due to the universal expansion according to the Big Bang theory. That means the universal expansion causes a red shift of the incoming photons from the pulsar to the Earth. But due to the tangential velocity component at the magnetic pole of the pulsar when the gamma radiations were emitting, there is another red shift/ blue shift of the incoming gamma photons.
You all know that scientists able to use a spectrometer to analyze the electromagnetic waves coming from the distant universe. By using the resolution images, they are capable to identify the chemicals in the distant object’s surface if they analyze the emission spectrum. Similar to that after analyzing the emission spectrum of the pulsar, researcher is capable to calculate the wavelengths of two different regions of the emission spectrum. But according to the Doppler Effect, researcher cannot estimate the exact wavelengths of the chemicals of the pulsar by neglecting the Doppler Effect. Thus he should take red shift due to the universal expansion plus the red shift/blue shift due to the pulsars rotation along the axis of rotation. 
Let’s consider an emission spectrum of the pulsar’s EM waves that has taken at time T. 
Let, f1 is the frequency of emission line L1 that has estimated using the emission spectrum taken at time T. f0 is the exact frequency of the considering photon that has emitted by the pulsar. 
Let, f2 is the frequency of emission line L2 that has estimated using the emission spectrum taken at time T. f’0 is the exact frequency of the considering other photon that has emitted by the pulsar. 
But the photons associated with line L1 and L2 have received simultaneously. Then, according to the relativistic Doppler Effect: 
Where, Vb is the relative velocity of the pulsar due to the universal expansion that might caused by the Big Bang incident. Also, Vp is the tangential velocity of the pulsar when the detecting photon was emitting by the pulsar. θ is the angle between the line joining the Earth and the pulsar and the line parallel to the tangential velocity direction of the pulsar when the detecting photon was emitting. C is the speed of light. 
Also,
Depending on the detection of the photon at time T, Vp may negative or positive.
By equation (2) and (3): 
f1/f2 = f0/f’0 ……………………………………………….(4)
By analyzing the spectrum, we can calculate the value of f1/f2 . let’s consider f1/f2 = x. 
Then f0/f’0 = x. But f0 and f’0 are non-shifted frequency values. Then by comparing laboratory measurements of photon frequencies of various chemicals with the value x; we can identify what should be the chemicals associated with the frequency f0 and f’0. Then we can estimate the values of f0 and f’0. Then by the equation (2), we can calculate the value of 
But in order to calculate Vb, we should know the distance between the Earth and the pulsar when the detecting photon (came from the pulsar) was emitting by the pulsar. There are several ways to calculate the distance to a faraway object. 
Let’s consider the below method. 
By using spectral classes, researcher has the capability to identify the color of the particular pulsar and then she able to measure the surface temperature of the particular pulsar. By Hertzsprung-Russell diagram the researcher able to calculate the absolute brightness (M) of the pulsar. After measuring the apparent brightness (m) of the pulsar, by using the equation 
(5.log10 D = m-M -10) he able to calculate the distance to the pulsar (D) at the detecting photon emitted moment. 
Especially this method is valid exactly only for the pulsars those are comparably closer to the Earth. Then we can say the value of Vb when the detected photon was emitting by the pulsar and the present moment are same (according to the Hubble’s law). Also then only we can say the value of D when the detected photon emitted by the pulsar and the value of D at the present moment are roughly same. 
Then by the Hubble’s equation for universal expansion, Vb = H. D, 
we can calculate the value Vb 
Then by equation (5), we can calculate the value Vp. cos θ = k…………………………..(6)
But by the diagram number (1); we can identify that we are capable to detect the EM waves coming from the pulsar: only when the tangential velocity direction of the pulsar and the gamma radiations coming direction are perpendicular to each other. The above statement is true ONLY IF THE CONE (MADE DUE TO THE MOTION OF MAGNETIC AXIS OF THE PULSAR) IS SYMMECTRIC AROUND THE AXIS OF ROTATION OF THE PULSAR. 
 we can conclude that there is some external force acting on the pulsar or pulsar

---

is influenced by its own change of its internal magnetic force acting on it. By considering the nearby visible matter to the pulsar, the variations of the value ‘y’ from the value

---

different times, spectroscopic data of infrared radiations around the pulsar and the internal magnetic field strength calculated through the variations of the gamma rays coming from the pulsar; researcher is capable to identify whether is there any un-visible matter/energy around 

the pulsar or not. Because by considering the difference between y and 

---

time to time; 
he may able to estimate theoretically the net force(F1) that should be acting on the pulsar due to the surrounding visible matters. But experimentally the researcher able to calculate the net gravitational force (F2) acting on the pulsar by observing the surrounding visible matters. If there is any difference between F1 and F2; he is capable to conclude that there is some another 
un-visible gravitational force acting on it. That should be an indirect evidence for the dark matter and dark energy. This argument is perfect if he can verify that there is no any change of the internal magnetic force or there is no any other external magnetic force acting on it as below. But if there is any internal (self-exist) change of magnetic field or any external change of magnetic field that is acting on the pulsar, the researcher able to use the Maxwell’s laws to detect whether is there any such a change of magnetic field or not. If there is any external/internal magnetic field change of the pulsar, then by analyzing spectrum of the infrared radiations coming from the pulsar’s surface; he may calculate the force due to the change of the magnetic field. Then, ifThe theoretically calculated force associated with the difference between y and 

---

Calculated external gravitational force acting on the pulsar + calculated force acting due to the change of the magnetic force on the pulsar ->
The researcher is proud to investigate that ‘The researcher has found indirect evidence for the existence of dark matter/dark energy ’
Moreover, by using luminosity, temperature and other properties of the pulsar, the researcher able to calculate the radius of it. By using equation (1), he may able to calculate the tangential velocity (Vp) of the pulsar when the beam of gamma rays is towards us. Then by using equation (5), he may able to calculate the value of θ. Then that angle value will help the researcher to identify where should be the Dark energy/Dark matter strong in the strength.

Hi I am Geerasee. I am a contributing writter at Nerdynaut. Click to know more about me.

by Geerasee