Post on 15-Jul-2020
References
Discovery of pulsars● http://www.bigear.org/vol1no1/burnell.htm
Pulsars from Essential Radio Astronomy● http://www.cv.nrao.edu/~sransom/web/Ch6.html●
Neutron Star
Pulsars
Slow Pulsar
Pulsar
Discovery of Pulsars
Pulsars discovered in 1967 by PhD student Jocelyn Bell during a low frequency survery of scintillating extragalactic radio sources.
They were discovered on chart record data
First observation of pulses
Sources of pulses
● Initially sources of pulses was unknown● Pulsations in a star are ~days rather than seconds● Must be a compact object
How fast can star spin?
● Lower limit to period● Centrifugal acceleration < gravitational acceleration at the
equator (derive this)
How fast can a star spin?
This is a conservative limit lower limit. A rapidly spinning star becomes oblate whichincreases the centrifugal acceleration and increases the gravitational acceleration at the equator.
Example
The first pulsar CP 1919+21 has a period of 1.3 s. What is its minimum density?
This is within the limit for a white dwarf.
Crab pulsar
Guest star seen by the Chinese in 1054
P = 0.033 s
When the crab pulsar was discovered (P = 0.033 s) its period implied a density too high for white dwarfs.
It confirmed the Baade and Zwicky hypothesis that neutron stars were the remains of supernova remnants
Exercise
The fastest known pulsar was discovered in 2004 and spins with a frequency of 716 Hz.
What is its minimum density?
Radius
A star of mass less than the Chandrasekhar mass is stable as a white dwarf.
For stars with M > Mch the maximum radius is
If the density of the star is greater than nuclear density
Neutron star masses
Ozel & Freire 2016, Annual Reviews of Astronomy and Astrophysics
Moment of Inertia
Calculate the moment of inertia of the “canonical” pulsar with
M = 1.4 solar masses and radius of 10 km
Rotational energy
The rotational energy is related to the moment of inertia by
Calculate the rotational energy of the Crab Pulsar with P = 0.033s
Loss of rotational energy
Pulsars are observed to spin-down – period increases slowly
We can estimate the rate of loss of rotational energy
Loss of rotational energy
(Be able to derive this!)
Magnetic field
If we assume that the power radiated by the spinning magnetic dipole = loss of rotational energy we can calculate the magnetic field
Characteristic Age
We can estimate the age of a pulsar assuming that it was born spinning much faster than it is currently spinning
Derived quantities
We can measure P and dP/dT and then deduce three properties of the pulsar
P Pdot diagram
Evolution on P Pdot diagrahm
Effect of ISM on Pulsars
Refractive index
The electrons in the ISM form a cold plasma with a refractive index
Where ν is the frequency of the observed radiation and νp the plasma frequency is given by
Where ne is the electron density
Calculate the plasma frequency for ne=0.03 cm-3
Refractive index
If ν < νp then μ imaginary – waves don't propogate
If ν > νp → μ < 1 → waves propogate with group velocity
For most radio observations ν >> νp and so
Dispersive delay
For a broadband pulse the higher frequencies will have a higher group velocity and arrive earlier. This diagram shows an observation made with KAT7 of the Vela pulsar
Dispersive delay
If the distance to the source is d then the dispersion delay is given by
In astronomical units
Where DM, the dispersion measure is given by (in pc. cm-3)
Dispersive Delay
The dispersive delay between pulses at ν1 and ν2 is given by
Refer to the exercise in the ipython notebook on dispersion measure
Exercise:
The pulsar J1644-4550 (with a DM of 478) is observed with MeerKAT in half-band mode with a bandwidth of 428 MHz centered on 1284 MHz. What is the delay between the top and bottom of the band?
Incoherent dedispersion
The effect of dispersion can be removed by splitting the bandwidth up into a number of channels.
Each channel can be the corrected for dispersion. This process is known as incoherent dedispersion
From Lorimer and Kramer
Channel smearing
If the channel bandwidth is small compared to the observing frequency
B << ν then the smearing across the channel is given by
With incoherent dedispersion there is a residual smearing across each channel.
Coherent dedispersion
The residual smearing across each channel can be removed using coherent dedispersion.
The effect of a the ISM is modelled as a transfer function. Convolve the raw voltage data with the inverse transform function. This method is computationally expensive
Coherent vs Incoherent Dedispersion
Interstellar Scattering
Example
The MSP pulsar J1939+2134 is observed using MeerKAT in full-band mode with a bandwidth of 856 MHz centered on 1822 MHz
J1939+2134 has a period of 1.56 ms and a DM = 71.
The bandwidth is divided into 2048 channels.
What is the residual smearing at the lowest end of the band?
(v = 1366 MHz)
Pulsar Sensitivity
● How many pulsars can we observe with a certain antenna?● Exercise on Monday …
● Factors:● Area of dish● Number of dishes● Bandwidth● Observing time● System temperature
Antenna Gain
Modified radiometer equation