2016 NASSP OTII Pulsarsavntraining.hartrao.ac.za/images/Schools/2017March/... · 2016 NASSP OTII...
Transcript of 2016 NASSP OTII Pulsarsavntraining.hartrao.ac.za/images/Schools/2017March/... · 2016 NASSP OTII...
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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●
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Neutron Star
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Pulsars
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Slow Pulsar
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Pulsar
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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
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First observation of pulses
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Sources of pulses
● Initially sources of pulses was unknown● Pulsations in a star are ~days rather than seconds● Must be a compact object
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How fast can star spin?
● Lower limit to period● Centrifugal acceleration < gravitational acceleration at the
equator (derive this)
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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.
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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.
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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
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Exercise
The fastest known pulsar was discovered in 2004 and spins with a frequency of 716 Hz.
What is its minimum density?
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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
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Neutron star masses
Ozel & Freire 2016, Annual Reviews of Astronomy and Astrophysics
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Moment of Inertia
Calculate the moment of inertia of the “canonical” pulsar with
M = 1.4 solar masses and radius of 10 km
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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
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Loss of rotational energy
Pulsars are observed to spin-down – period increases slowly
We can estimate the rate of loss of rotational energy
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Loss of rotational energy
(Be able to derive this!)
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Magnetic field
If we assume that the power radiated by the spinning magnetic dipole = loss of rotational energy we can calculate the magnetic field
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Characteristic Age
We can estimate the age of a pulsar assuming that it was born spinning much faster than it is currently spinning
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Derived quantities
We can measure P and dP/dT and then deduce three properties of the pulsar
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P Pdot diagram
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Evolution on P Pdot diagrahm
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Effect of ISM on Pulsars
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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
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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
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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
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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)
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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?
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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
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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.
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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
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Coherent vs Incoherent Dedispersion
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Interstellar Scattering
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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)
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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
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Antenna Gain
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Modified radiometer equation