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An accreting X-ray pulsar contains a magnetized neutron star whose magnetic field channels the accreting gas toward its magnetic poles. Rotation carries the bright accretion regions through the observer's view and produces pulses. The input angular momentum can change the spin period; this differs from the rotational energy source of an isolated pulsar.

Aperture synthesis reconstructs the sky's brightness from complex visibilities measured at different interferometric baselines. Each measurement constrains a Fourier transform component of the brightness, rather than supplying a little photograph. Combining many such components can distinguish sources that each individual antenna leaves unresolved. The remarkable economy is that changing separations and the rotation of Earth can provide many measurements with only a few physical antennas.

Martin Ryle's Cambridge group made aperture synthesis a practical method of astronomical imaging at the Mullard Radio Astronomy Observatory. Cambridge's institutional history connects that work with the One-Mile Telescope and its larger successors.^[ref]

In his 1974 lecture Radio Telescopes of Large Resolving Power, Martin Ryle recalled the problem of distinguishing weak extragalactic sources and resolving their structure. He explained sequential wavefront sampling using one simultaneously observed element as a wave phase reference, and the saving obtained by letting Earth rotate the apparent baseline.^[ref]

The 1974 Nobel Prize in Physics distinguished Martin Ryle's observations and inventions, especially aperture synthesis, from Antony Hewish's role in discovering pulsars. The latter is a separate astronomical discovery, with its own observational history.^[ref]

A binary pulsar is a pulsar in a binary star: the companion's gravity changes the emitting neutron star's motion and hence its pulse arrival times. The companion need not itself be a detectable pulsar. Pulsar timing turns that motion into a measurable orbit, making the system useful for stellar mass determination and tests of general relativity.

The geometric light-travel contribution from the pulsar's position within the binary orbit. To construct an eccentric Kepler orbit, use eccentric anomaly $E$, orbital eccentricity $e$, mean anomaly $M=2\pi (t-T_0)/P_b$, and argument of periapsis $\omega$. Here $T_0$ is passage through periapsis. Coordinates in the orbital plane are $X=a_1(\cos E-e)$ and $Y=a_1\sqrt{1-e^2}\sin E$. Rotate through $\omega$ and project by $\sin i$ to obtainThe first equation is Kepler's equation: equal time intervals give equal increments of $M$, not of $E$. Since $1-e\cos E>0$ for $0\le e<1$, each $M$ has a unique $E$ on the corresponding unwrapped orbit. A constant delay is absorbed into the arbitrary arrival-time origin. The circular limit is ${\Delta }_R=x\sin (M+\omega )$, so its amplitude measures $x$. For $e>0$, the delay's offset and amplitude also depend on $\omega$; its maximum is not generally $x$.

Jocelyn Bell Burnell helped build Antony Hewish's radio telescope for finding compact sources through interplanetary scintillation in the solar wind. Operating it and inspecting its chart recorder output in 1967, she recognized an unusual recurring trace, checked earlier charts, and obtained fast recordings resolving pulses in late November. Her observation, recognition and persistent analysis were indispensable.^[ref]

The 1968 paper by Antony Hewish, Jocelyn Bell Burnell (bylined S. J. Bell), J. D. H. Pilkington, P. F. Scott and R. A. Collins reported $1.337\mathrm{s}$ spacing and proposed compact-star oscillations. Its radio telescope had 2,048 full-wave dipole antennas in sixteen rows. Four receivers selected declinations; two array halves formed an east-west interferometer. The $81.5\mathrm{MHz}$ receivers passed $1\mathrm{MHz}$. Observations used $0.05\mathrm{s}$ receiver time constant and Rapidigraph chart recorder with $0.03\mathrm{s}$ time constant; radio second pips calibrated timing.^[ref]

Antony Hewish checked sidereal time recurrence. Jocelyn Bell Burnell recalls that P. F. Scott and R. A. Collins reproduced the pulses with another telescope and receivers, while J. D. H. Pilkington measured pulsar dispersion delay: independent checks of instrument independence and intervening plasma.^[ref]

A useful numerical comparison uses the approximate sidereal time day of $1436.07\min$. Relative to a $1440\min$ schedule, the same sky direction transits about $3.93\min$ earlier each day, or $39.3\min$ after ten days. This compares successive passages through the receiving beam; it is a different clock from the roughly $1.3\mathrm{s}$ pulse spacing within one passage. Sky recurrence alone cannot rule out every transmitter or reflection, and pulsar dispersion delay alone does not uniquely establish an emission mechanism. Their strength lies in independent constraints agreeing.

The discovery lesson is that an unexpected signal must survive changes of readout, instrument and observing date. Increasing chart recorder speed exposed structure hidden in a compressed trace; it did not make the source begin pulsing. The pulsar interpretation now separates the rotating clock, beam geometry, pulsar magnetosphere emission and pulsar dispersion delay. The initial observation established periodic arrival, not a direct measurement of the neutron star's surface motion or radius.

An exoplanet is a planet outside the Solar system; here the focus is on planets orbiting stars other than the Sun, including pulsars. Most exoplanets are detected indirectly: a star's changing Doppler shift reveals its motion, or a small dip in its light curve reveals an exoplanet transit. The striking idea is that an unresolved point of light can tell us about an otherwise unseen world's mass, radius, and orbit.

The measurements answer different questions. Exoplanet transit photometry primarily gives a radius ratio, while Doppler spectroscopy constrains mass together with orbital inclination. Combining them with the host star's properties gives a mean mass density, ${\bar{\rho }}_p=3M_p/(4\pi R_p^3)$, useful for exoplanet interior models. Even this combination does not uniquely determine composition: see exoplanet interior-composition degeneracy. Transit spectroscopy and an exoplanet secondary eclipse then probe an exoplanet atmosphere.

The discovery history has two distinct milestones. In 1992 Aleksander Wolszczan and Dale Frail reported two planet-mass companions to the pulsar PSR B1257+12 from periodic changes in pulse arrival times; their paper also suggested an additional companion. These were the first confirmed exoplanet discoveries, around a neutron star. ^[ref]. Wolszczan's contemporary conference account, archived by NASA, likewise distinguishes the two reported companions from a possible third. ^[ref].

In 1995 Michel Mayor and Didier Queloz discovered 51 Pegasi b through Doppler spectroscopy, the landmark first confirmed exoplanet around a Sun-like star. This was a hot Jupiter, not the first exoplanet of every kind: the earlier pulsar discoveries belong to a different host category. ^[ref]. NASA's contemporary account describes the confirmation and the approximately four-day orbital period. ^[ref].

The surprise was a pulsar whose apparent period would not stay fixed. Russell Alan Hulse's Arecibo search used a multichannel receiver, pulsar dedispersion and computer searches over period and pulse width. Follow-up at higher time resolution retained the changing period, excluding inadequate sampling as its explanation. The observed variation exceeded the expected terrestrial Doppler shift; a predicted reversal from decreasing to increasing period appeared on 16 September 1974.^[ref]

The 1975 analysis fitted an eccentric Kepler orbit to Doppler shifts inferred from about 200 five-minute period measurements over ten days. That discovery fit was not yet the later precision arrival-time experiment.^[ref] An orbit explains both signs of the apparent period change without requiring the stellar rotation to alternate between speeding up and slowing down.

Interplanetary scintillation is rapid variation in the received strength of a compact astronomical radio source, produced by propagation through fluctuating Electron density in the solar wind. Its dependence on source angular size can help distinguish compact sources. It is a propagation effect, distinct from intrinsic periodic emission by a pulsar.

An astronomer whose Princeton group studies pulsars through radio observations.^[ref]

If a single approximately stationary emitting region changes coherently through a causal disturbance, a disturbance travelling no faster than the speed of light takes at least $L/c$ to coordinate a scale $L$. Light-travel differences also smear simultaneous emission from different depths. Under those assumptions, observed intrinsic variability on a time scale $\Delta t$ suggests $L\lesssim c\Delta t$.

For a chosen example $\Delta t=0.010\mathrm{s}$, multiplication by $c=299,792.458\mathrm{km}{\mathrm{s}}^{-1}$ gives $L\lesssim 2998\mathrm{km}$. This is an order-of-magnitude causality bound on a coordinated emitting scale. It is not a measured stellar radius, and even the relation between $L$ and a diameter depends on geometry. A pulsar beam crossing is a geometric clock, and pulsar dispersion delay, scattering and instrumental response can broaden its observed pulse. The recurrence period, observed pulse width and intrinsic variability time must therefore be distinguished before applying the bound. Relativistically moving emitters require further arrival-time corrections.

Awarded in equal shares to Martin Ryle and Antony Hewish for pioneering radio astrophysics: Ryle for observations and inventions, especially aperture synthesis, and Hewish for his decisive role in discovering pulsars.^[ref]

Awarded in equal shares to Russell Alan Hulse and Joseph Hooton Taylor Jr. for discovering a new type of pulsar that opened new possibilities for studying gravity.^[ref]

The semimajor axis $a_1$ of the pulsar's orbit about the binary barycenter, projected along the line of sight and divided by the speed of light. The orbital inclination $i$ is zero for a face-on orbit. Thus $x$ is a time, often quoted as the numerical number of light-seconds in $a_1\sin i$, not the true binary separation. The relative-orbit semimajor axis is instead $a=a_1+a_2$; conservation of momentum gives $a_1=a{m}_2/(m_1+m_2)$.

Combining Kepler's third law with that barycenter relation gives the timing form of the binary mass function, also valid for eccentric Kepler orbits:Choose $x=2\mathrm{s}$ and $P_b=8\mathrm{h}$ for an original example: $a_1\sin i=599,585\mathrm{km}$ and $f\simeq 0.0773M_{\odot }$, where $M_{\odot }$ is a solar mass. For a specified pulsar mass $m_1=1.4M_{\odot }$, the smallest allowed companion mass occurs at $\sin i=1$ and is approximately $0.698M_{\odot }$. A different assumed $m_1$ changes this bound. One measured $f$ does not determine both masses and orbital inclination.

A pulsar is a rotating magnetized neutron star whose directed emission is observed as periodic pulses. Rotation supplies the energy of an ordinary radio pulsar.

A pulsar turns stellar rotation into an observable clock: the neutron star's emission can continue while its beam sweeps past the observer only briefly. The pulse spacing measures a repetition period; identifying that period with stellar rotation requires a physical model. The discovery of the first pulsar established a remarkably regular astronomical signal before its engine was understood. Today, pulsar dispersion delay also makes these clocks probes of the intervening interstellar medium.

Pulsar dedispersion aligns radio wave arrival times in separate frequency channels before combining them. For an original illustrative model chooseBoth bracketed ratios are dimensionless, so $D$ supplies all the time units. The reference is $150\mathrm{MHz}$: delays are $0$ there, $0.13333\mathrm{s}$ at $100\mathrm{MHz}$, and $0.26833\mathrm{s}$ at $80\mathrm{MHz}$. These are chosen model values, not measurements of the first pulsar. Subtracting the delay aligns the peaks; summing channels first spreads a short pulse over a longer interval and reduces its peak. Finite channel width and incorrect delay parameters leave residual smearing.

Phase folding of a light curve collects samples at equal trial phase. Consider a noiseless illustrative pulsar with one pulse every $P=1.4\mathrm{s}$ and arrival times $t_n=nP$, after pulsar dedispersion. At $P_{\mathrm{trial}}=P$, all arrivals fold to one phase. But $P/2$ also puts all arrivals at one phase: folding discarded the fact that alternate proposed cycles contain no pulse. At $2P$, the arrivals instead occupy two phases, $0$ and $1/2$. Thus a sharp folded profile alone need not identify the fundamental period.

Check the original time sequence, adjacent arrival intervals and pulse occupancy as well as the folded profile. With $N$ arrivals and a slightly wrong trial period, the unwrapped drift isFor $N=100$ and $P_{\mathrm{trial}}=1.401\mathrm{s}$, this is about $-0.07066$ cycle. Splitting the observation into early and late pieces reveals the drift that one full folded average can blur. Separately, regular discrete sampling can create aliasing: observing at a spacing comparable with the pulse width can miss narrow pulses even when the recurrence period is much longer. Neither this toy exercise nor one sharp profile replaces time-standard calibration and propagation corrections.