2016 NASSP OTII Pulsars

Sarah Buchner October 2016sbuchner@ska.ac.za

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