Radio Observations of Neutron Stars

Robert RutledgeMcGill University

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Assignment:Simulate a Power Density Spectrum for

a Millisecond Pulsar

• You have been given time on the SKA to search for a new binary pulsar. Due to an extremely clever theorist in your group, you know exactly where to “point” the telescope. However, due to extremely liberal data policies, your competitors will get the exact same data set! Can you perform the data analysis needed to discover the new binary millisecond pulsar, and publish the correct values, before your competitors do, and present your results at a conference that afternoon?

• In this assignment, you will:

(a) Simulate a lightcurve (intensity vs. time) for one pulsar in a NS-NS binary

(b) Produce a Power Density Spectrum (PDS) of this lightcurve.

(c) Obtain the pulsar Period, the circular orbital velocity from the PDS.

(d) Finally, you will do (c) on the dataset of another team, and present your derived answer to the group.

Why Study Neutron Stars?

• Do we really know so little?

• Why does it matter that we don’t know much about the dense matter equation of state? Isn’t it just a pressure vs. density relationship?

Why Study the Dense Matter Equation of State (dEOS)?

• Comes from the strong nuclear interaction -- one of the “four fundamental forces”. Strong interaction comes from Quantum Chromo-Dynamics.

• The dEOS could be derived from a perfect theoretical understanding of QCD at finite density. This would predict the pressure as a function of density of cold matter above nuclear density.

• However, consider the Yukawa potential: it’s non-superpositional!

V (r) = − g2

4π

e−r/R

rYukawa Potential

for particle exchange interaction

V (r) ≈ λr (r > 1fm)

• More importantly, for gluon exchange between quarks, asymptotic freedom gives us --

Solving Quantum Chromodynamics At Finite Density - Neutron Stars are Unique Astrophysical Laboratories

• 1932: Since discovery of neutron (Chadwick 1932), how the strong force works to mediate attraction between protons and neutrons has been a major question for physics.

• 1930s-1960s: Strong force is a non-superpositional force, multi-body in nature -- parameterization with Skyrme potential had (limited) success explaining the properties of small nuclei.

• 1960s: Discovery of quarks, and development of QCD explained the formation of neutrons, protons, mesons, hyperons.... This is QCD at finite energy (temperature, QCDt). It does an outstanding job of explaining the existence of these particles, and their one-to-one interactions. But we have no exact theoretical apparatus to perform the many-body interaction calculations. Thus we rely on approximate methods of effective-field-theories (Brueckner-Betha-Goldstone Theory, Green’s function theory, and relativistic mean-field theory).

• Today: QCD is not an exact theory at finite density (QCDd). Where this becomes relevant is above nuclear density (>2.35x1014 g cm-3), and for asymmetric matter (many more neutrons than protons).

• It is technically impossible to create cold nuclear matter above nuclear density in terrestrial laboratories. However, in the cores of neutron stars, gravitational force compresses matter to supernuclear densities.

• Thus: Neutron Stars are unique sites of cold QCDd in the universe, precisely as black holes are the unique sites for strong field gravity.

•If we want to solve QCDd, neutron stars will be the astrophysical tool for how we do it.

QCD at Finite Density for Astronomers

•Since the early 1970s: There exists a precise equation for calculating the quark-quark interaction energy for an arbitrarily large system of quarks at arbitrarily large densities. This is known as Lattice QCD. While analytic, it is mathematically intractable (“the sign problem”). A breakthrough in mathematics could solve this problem.

•There are two observables Lattice QCD could predict: the binding energy of nuclei, and the dEOS.

•Computational approaches become more and more limited as T->0 (where matter is non-relativistic). These approaches rely upon cutting off the interaction wave-form for each quark at some size scale, beyond which the interaction strength can be neglected. As T->0, this scale becomes very large, encompassing many other quarks, and increasing the number of calculations required in a computationally intractable way.

Ideal Gas Law and its Equation of State

• Uses the Kinetic theory of gases and statistical mechanics to create the velocity distribution of atoms, based on the Maxwellian distribution arising from atoms with a specific temperature.

• This resulted in the Pressure (density) equation of state for an ideal gas.

• We would like to have a similar first-principles derivation of the equation of state of dense nuclear matter; but we, at present, lack the theoretical capability. This ability requires nothing less than a complete understanding of the multi-body strong force, and is a major goal of physics.

P (ρ)

Fg ∝M(< R)

From Neutron Star Mass-Radius Relation to the Equation of State

•Lindblom (1992) showed that each Dense Matter Equation of State maps to a unique Mass-Radius relationship for neutron stars.

•Ozel and Psaltis (2009) demonstrate how to perform the inverse problem: take the mass-radius relationship, and produce an equation of state. Only ~5-7 such objects are needed, but “with different masses”, to derive a new dense matter equation of state.

•Thus, measurement of the neutron star mass-radius relationship would implicate a unique dEOS.

Short Course: Gravity pulls inward

Pressure Pushes OutwardResult: R=f(M)

P = f(ρ)

Mass-Radius Relationships

• We understand ideal gas pressure very well, and this permits us to very precisely predict the Mass-Radius relationship for “main sequence” stars, which are balanced against gravity by ideal gas pressure. This prediction matches observations very well.

Fg ∝M(< R)

The Mass-Radius Relationship of Neutron Stars

Enough Stellar Evolution to Understand the Formation of Neutron Stars

Enough Stellar Evolution to Understand the Formation of Neutron Stars

Become Black Holes (NSs?)

Become Neutron Stars

Become White DwarfsBased on this,

about 109 neutron stars have been

created inside our own galaxy.

Age

10,000 Yr

1,000,000 Yr

1,000,000,000 Yr

Supe

rnov

a

Supe

rnov

a R

emna

nt D

isap

pear

s

The

rmal

Em

issi

on D

isap

pear

s

Puls

ar E

mis

sion

Dis

appe

ars

Mag

neta

rs G

o D

ark

(spi

n do

wn?

)

Compact Central Objects (CCOs)

Radio Pulsars

Thermally EmittingIsolated Neutron Stars

Magnetars

Enough Stellar Evolution to Understand the Formation of Neutron Stars

Pulsar Magnetic Dipole Emission Model

Erot =12Iω2

ω =2π

P

Erot =−4π2 IP

P 3Erot =

23c3

(BsurR3NS sinα)2

�2π

P

�4Dynamics

Kinematics

Bsur sinα = 3.2× 1019

�PP

sec

�1/2

Gauss

For sin(alpha)=1, the “Pulsar magnetic field strength”

τage =P

2P

The “Pulsar age”

Bsurα

The P-Pdot Diagram

• Dipole model successfully predicts magnitude (and sign) of secular spin-down, consistent with theory

• Also gives (approximate) ages for pulsars (but! in some cases these are systematically wrong by factors of several).

CREDIT: Harding and Lai (2006)

Heuristics from stars• If you take the magnetic flux at the surface of the sun, shrink it down

to size of a neutron star (10 km radius) conserving flux, you get a 1012 G surface magnetic field.

• If you take the spin period of the sun (30 days) shrink it down to the size of a neutron star (10 km radius) you get something which spins in 1 msec!

• Yet, msec pulsars do not appear to be (commonly) formed directly through stellar collapse. They appear to be (commonly) formed through spin-up in a low-mass X-ray binary.

• And the magnetic fields of young neutron stars can be 1000x greater than this, so the dominant mechanism for magnetic field production in neutron stars is complicated MHD during the supernova explosion.

Known problems with the Dipole Model

• The dipole spin-down model predicts a “breaking index”

• The dipole model predicts n=3. The measured values have always been wrong.

• This implies at least another emission mechanism is active.

ν =1P

n =νν

ν2Livingstone et al

How to Detect a Radio Pulsar

• The Characteristic Signal: A Stable periodicity in intensity (pulses!)

Hewish and Bell (1967)

The Power Density Spectrum

• Analysis tool to detect a pulsar.

• Uses the Fourier Transform to “pull out” periodic signal from a light curve.

Interstellar Free Electron Dispersion

• A problem, but solvable by dividing the signal across the band by frequency, and de-dispersing. Adds to the computational load.

• However, DM to Galactic Center is several hundred!

CREDIT: Swinburne U5.7 msec pulsar

t2 − t1 = 4.15 ms DM [(ν1/GHz)−2 − (ν2/GHz)−2]

700

Phot

on F

requ

ency

(M

Hz)

680

660

Time (millisecond)0 2.5 5

Interstellar Free Electron Dispersion

• Here, the DM is high enough that the time delay between 1500 MHz (top of the bandpass) and 1240 MHz (bottom) is over twice the pulse period of this pulsar. Without multi-frequency channel observations, this pulsar could not be detected!

• In Converse: for every multi-channel receiver, there is a DM limit above which they could not detect a pulsar with a given period.

Handbook of Pulsar Astronomy, by Lorimer and Kramer

Computational Facilities

• Any serious radio pulsar survey requires massive computational effort. The parameter space to discover pulsars is enormous: pulsar Period and its derivative, RA, dec, proper motion (2 dimensions) DM. For binary pulsars, there is the additional Porb, projected orbital separation, and orbital ellipticity.

CREDIT: Swinburne CAS

Radio Telescopes: Resolution

•Resolving power (how small of a thing you can “see”) depends on the size of the telescope and the wavelength of the light

λ

size

For radio waves, this is large…

So this must also be large

•“Size” = diameter of telescope for single dish; maximum distance between telescopes for arrays

CREDIT: NRAO

Radio Telescopes: Resolution

Arrays

Green Bank Telescope, WV Very Large Array, NM

Single Dish

Size

Size

CREDIT: NRAO

Green Bank Telescope (USA - 100m x110m)

Parkes (AUS - 64m)

Aricebo (operated by NRAO, in Puerto Rico - 305m)

Which of these has discovered the most pulsars?

What are the important characteristics of a pulsar discovery telescope?

RadioTelescopes

Great for imaging interferometry -- but not the

best instrumentation to detect pulsars with!

Very Large Array

Discovery of the First Pulsar

• Completely Serendipitous: Was Actually Searching Trying to Study the Interstellar Medium

Hewish and Bell (1967)

The First Binary Pulsar(Hulse and Taylor 1975)

The First Binary Pulsar(Hulse and Taylor 1975)

• Because the binary orbit is nearly edge on, the mass of the companion is determined through Shapiro delay, along with the inclination of the orbit along the line of sight.

• Gravitational Radiation produces a decay in the orbital period, which matches the precise prediction of General Relativity

Shapiro Delay• It is only possible to measure the mass

ratio of a pulsar to its companion, if there is just one pulsar in the system.

• However, if the system is nearly edge on, as the pulse train passes close to the companion, it experiences Shapiro delay in the pulses. The magnitude and duration of the delay episode is related to the inclination of the binary orbit to the line of sight, and the mass of the companion. Since these are the only 2 unknowns, this completely determines the system, and permits measurement of the mass of the pulsar (neutron star).

Credit: Bill Saxton/NRAO

The First Millisecond Pulsar

• High time resolution required made these more difficult to detect than the more common radio pulsars.

• Smearing across the radio band is computationally demanding.

• Extremely fast periods made them outstanding clocks to measure spin-down accurately, and doppler shifts in binaries accurately

Backer, Kulkarni et al (1982)

P=1.557 msec

PSR B1937+214

Pulsars

Pulsars Outstanding Clocks for doppler-shift mass measurements

Some systems with masses measured to 1 part in 106

However, not so useful for radius measurements.

A Binary Pulsar, with Two Pulsars

Kramer et al 2007

Almost edge on (strangely, not rare).

Mass Measurements

• There are two major techniques which have already produced mass measurements for neutron stars.

• Doppler-shifts in Pulsar binaries

• Shapiro-Delay in binaries where the seconary’s mass can be determined.

Shapiro Delay• It is only possible to measure the mass

ratio of a pulsar to its companion, if there is just one pulsar in the system.

• However, if the system is nearly edge on, as the pulse train passes close to the companion, it experiences Shapiro delay in the pulses. The magnitude and duration of the delay episode is related to the inclination of the binary orbit to the line of sight, and the mass of the companion. Since these are the only 2 unknowns, this completely determines the system, and permits measurement of the mass of the pulsar (neutron star).

Credit: Bill Saxton/NRAO

Highest Mass Measurement

DeMorest et al (2010)

The Known Population of Radio Pulsars

• There are:approximately 2000 radio pulsars known.

Add to that the 200 X-ray Binaries

Add to that the ~20 Magnetars and Compact Central Objects (CCOs) (see Anna’s Talk)

Add to that ~7 Isolated Neutron Stars (again, Anna).

From 109 Neutron Stars produced in the history of the Galaxy

That leaves 109 Neutron Stars we have not directly observed!

The Known Population of Radio Pulsars

• This implies that there are observational selection effects.

• For radio pulsars: beamed radio emission (you can’t see radio pulsars from every direction); age (pulsars eventually “shut off), typically after billions of years. Also, requires B-fields be strong, and the NSs be spinning fast enough to produce pulses.

• For thermal sources: all “hot” (isolated) neutron stars cool -- regardless of their initial temperature -- after a few 106 years.

The ATNF Pulsar Catalog

• If you are interested in searching for correlations between pulsar observables (age, B, luminosity, P, Pdot) the ATNF catalog contains every known pulsar. You can get it online:

• http://www.atnf.csiro.au/people/pulsar/psrcat/

The Known Population of Radio Pulsars

• Also assumes the neutron stars haven’t left the galaxy!

• 1000 km/sec = 1 kpc per million years.

RR et al (2008)

“Field” Pulsars

Lorimer (2010)

The P-Pdot Diagram

CREDIT: Harding and Lai (2006)

Globular Cluster Pulsars

• What’s a Globular Cluster?

• Why are there pulsars in them?

• Are these pulsars useful?

• Acceleration in the cluster potential. Limits timing capabilities.

Distances to Neutron Stars

• Free electron model

• VLBI parallax

• Timing parallax

• Distance methods to objects containing neutron stars (globular clusters, star formation regions).

Free Electron Model of the Galaxy

• Cordes and Lazio 2002, using measured DMs from pulsars with known distances from other measures, a model of the galactic gas, produced a model of the free electron distribution DM throughout the galaxy (right).

• When DM is measured to a new pulsar, and its direction is known, this model can provide an estimate for the distance (accurate to about 30%).

CREDI

VLBI Parallax

Chatterjee et al (2005)

Parallax measureddistance of B1508+55

d = 2.37+0.23−0.20 kpc

Combined with theproper motion (angular speed across the sky)

v = 1083+103−90 km s−1

Exceeds the escape speed of the Galaxy!

New and Coming Radio Instrumentation

Low Frequency Array (LOFAR)

Constructed by The Netherlands.

Operating primarily in the ~few 100 MHz range, where pulsars are brighter (and interference is the main challenge)

Has begun deployment, even detected its first (previously known) pulsar!

New and Coming Radio Instrumentation

Square Kilometer Array (SKA)

Goal: produce 1 square kilometer collecting area radio telescope.

International Primary Science Team formed, science headquarted at Jodrell Bank.

SKA (Australian concept)

Summary

• Neutron Stars are the only laboratories to explore strong force physics at T=0, and large N. They can permit measuring the dense matter equation of state, which may lead the way to understanding strong force physics.

• Radio pulsars observations have lead to extremely accurate mass determinations. The maximum mass measurement from radio pulsars, in turn, is a major constraint on the dEOS.

Assignment:Simulate a Power Density Spectrum for

a Millisecond Pulsar

• You have been given time on the SKA to search for a new binary pulsar. Due to an extremely clever theorist in your group, you know exactly where to “point” the telescope. However, due to extremely liberal data policies, your competitors will get the exact same data set! Can you perform the data analysis needed to discover the new binary millisecond pulsar, and publish the correct values, before your competitors do, and present your results at a conference that afternoon?

• In this assignment, you will:

(a) Simulate a lightcurve (intensity vs. time) for one pulsar in a NS-NS binary

(b) Produce a Power Density Spectrum of this lightcurve.

(c) Obtain the pulsar Period, the circular orbital velocity from the PDS.

(d) Finally, you will do (c) on the dataset of another team, and present your derived answer to the group.

Assignment:Simulate a Power Density Spectrum for

a Millisecond Pulsar

• Simulate a lightcurve x(tk) with N=2^24 bins (a float array of N bins), where each bin represents 1/(2^11) sec.

• Take a Fast Fourier Transform of x(tk).

• Create a Power Density Spectrum, and plot Power vs. Frequency for a lightcurve generated by:

✤ A sinusoidal pulsing millisecond pulsar (choose a period between 1-10 msec) (this is just a self-test of your software to make sure it works)

✤ Then, create a dataset: a millisecond pulsar in a binary orbit (choose a period of 5 min-1 hour)

• Give x(tk) (for the binary MSP) to your companion team who must then determine the pulsar frequency and the orbital period.

Assignment:Simulate a Power Density Spectrum for

a Millisecond Pulsar

• 3:00pm Begin software development.

• 5:00pm Provide your lightcurve in a ASCII data file of a single column of floating point numbers to your companion team. Report to me the pulsar Period and the orbital velocity you used.

• 5:25pm All teams provide 1 PDF figure of the Power Density Spectrum (Power vs. frequency in Hz), centered on the detected pulse signal. On the figure, state the detected Pulse Period (in millisecond!) and the detected circular velocity v (in km/sec).

• 5:30-6:00 Each team reports their findings (<2 min), and the companion team which provided the data either confirms (or doesn’t!) the reported results.