# How bright is the Crab Pulsar's 30 Hz modulation in visible light? What color is it?

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This answer to Has great eyesight been necessary for astronomers? mentions Astronomer Jocelyn Bell Burnell's recounting of a likely first visual observation of a pulsar. This can be found for example in Nature's Air force had early warning of pulsars

The work preceded by several months the observations made by Bell Burnell, then at the University of Cambridge, UK, which led to the first paper on the subject. A Nobel prize for the discovery was subsequently awarded to her supervisor Antony Hewish, but, controversially, not to her. Schisler was not the only one to “pre-discover” a pulsar, though, according to Bell Burnell. “There are actually a lot of stories,” she says. In the 1950s, a woman visiting the observatory at the University of Chicago, Illinois, pointed out that there was a regularly pulsating source of visible light in the Crab Nebula. Elliot Moore, an astronomer at the university, dismissed the woman's claim, telling her that all stars seem to flicker. Another radio astronomer she knows of will, after a drink or two, confess to having dismissed observations of a pulsating source as the result of faulty equipment. “He's a bit embarrassed now,” says Bell Burnell.

This is also summarized in Wikipedia's Crab Pulsar:

Jocelyn Bell Burnell, who co-discovered the first pulsar PSR B1919+21 in 1967, relates that in the late 1950s a woman viewed the Crab Nebula source at the University of Chicago's telescope, then open to the public, and noted that it appeared to be flashing. The astronomer she spoke to, Elliot Moore, disregarded the effect as scintillation, despite the woman's protestation that as a qualified pilot she understood scintillation and this was something else. Bell Burnell notes that the 30 Hz frequency of the Crab Nebula optical pulsar is difficult for many people to see.

Per Wikipedia the Crab Pulsar has an apparent magnitude (V) of about 16.5, but I don't know how much of that intensity is modulated at 30 Hz or if the modulation is concentrated in some specific part of the visible spectrum. I would guess that a neutron star's direct visible light would be quite small except for the pulses, but I don't know if that's what the 16.5 m refers to.

I'm imagining a small, low noise photodiode intercepting the light from the region containing the location of the pulsar, possibly with a color filter, with the signal amplified and the DC removed and then digitized with an ADC and a Raspoerry Pi. (assume that I'd read up on how to best do this) and then integrating for a few minutes or hours and looking for some power near 30 Hz with a Raspberry Pi.

But before I think further, I'd need to know how deep the visible light's modulation is and if it's stronger in some wavelengths or flat across the spectrum.

Question: How bright is the Crab Pulsar's 30 Hz modulation in visible light? What color is it?

The optical pulsations of the Crab pulsar have been studied closely since 1969. The observations are actually not that difficult (I did some myself with a photoelectric photometer as a student) and have been achieved with a variety of technologies.

A paper by Fordham et al. (2002) slices and dices the Crab pulsar's pulse shape into fine time and spectral bins in the optical regime. A phase-folded light curve for the full blue-to-red range is shown below. The pulse shape is actually extremely stable and it looks like this in many other papers. The pulse has been "background subtracted" using the signal in the "off" phase of the pulse. The unpulsed component amounts to less than 1% of the integrated brightness in the optical, so essentially "off" does mean off.

The same paper discusses the integrated energy spectrum and the wavelength-dependent pulse shape of the pulsar. The integrated spectrum is almost flat (after correction for interstellar extinction) - as in, if the spectrum $$F( u) propto u^{alpha}$$, then $$alpha sim 0$$; this result holds for the whole pulse, or if just either of the two peaks are considered (there is a tiny $$<1$$% variation in the ratio of the two pulses across the optical range).

Postscript - I notice that the Wikipedia page on the Crab pulsar has a slowed-down animation of the pulse as seen at 800nm (very close to optical). The two pulses and their difference in brightness are quite obvious, as is the "off" phase. It would not look much different at shorter, visible wavelengths.

## Electromagnetic spectrum

The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies.

The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from below one hertz to above 10 25 hertz, corresponding to wavelengths from thousands of kilometers down to a fraction of the size of an atomic nucleus. This frequency range is divided into separate bands, and the electromagnetic waves within each frequency band are called by different names beginning at the low frequency (long wavelength) end of the spectrum these are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays at the high-frequency (short wavelength) end. The electromagnetic waves in each of these bands have different characteristics, such as how they are produced, how they interact with matter, and their practical applications. The limit for long wavelengths is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length. [4] Gamma rays, X-rays, and high ultraviolet are classified as ionizing radiation as their photons have enough energy to ionize atoms, causing chemical reactions.

In most of the frequency bands above, a technique called spectroscopy can be used to physically separate waves of different frequencies, producing a spectrum showing the constituent frequencies. Spectroscopy is used to study the interactions of electromagnetic waves with matter. [5] Other technological uses are described under electromagnetic radiation.

## Differences Between Thermal Imaging and IR Illuminators with Night Vision Devices

You may also be familiar with the IR Illuminators used in conjunction with Night Vision Goggles.

This sounds similar, but is actually a very different way to see at night.

An IR Illuminator projects near-infrared light – that is reflected by objects within a short to medium-range distance.

A PVS-14 Style Night Vision Device might use an IR Illuminator to provide better night vision – but it’s easy to detect

This reflected (invisible) light can be picked up and viewed with night vision devices that provide Image (or Light) Intensification.

Thus, these Infrared light sources can be used to augment the available ambient light for conversion by night vision devices.

Think of it like shining an invisible flashlight on a distant object.

But, it’s not a very stealthy way to see in the dark.

That’s because you are projecting an IR light that can be seen by anyone else with night vision goggles – including your opponent.

They’ll be able to pinpoint your location easily.

Because this is the stealthiest way to see at night – and in total darkness.

## AstroSat: Concept to achievements

AstroSat has completed 5 years of successful in-orbit operation on 28 September 2020. AstroSat is ISRO’s first Indian multi-wavelength satellite operating as a space Observatory. It is the only satellite which can simultaneously observe in the Far UV and a wide X-ray band from 0.3 to 80 keV using different instruments. This astronomy mission was conceived, following the success of several piggy back astronomy experiments flown earlier on Indian satellites. AstroSat is the result of collaboration between ISRO and several astronomy institutions within India and abroad. There are over 150 refereed publications resulting from data from AstroSat, in addition to Astronomy Telegrams, Circulars and Conference proceedings. This paper provides a brief summary of the evolution of the concept of Astrosat, how it was realized and scientific outcome from this mission.

This is a preview of subscription content, access via your institution.

## Crab nebula pulsar image sequence possible?

I came across a neat movie of the crab nebula pulsar pulsing:

The specific movie/gif is half way down the page.

"By folding a fast sequence of Lucky Images we can construct a movie of the pulsar in the core of the Crab Nebula. It varies on a 30 millisecond cycle, with a bright flash as well as a fainter interpulse."

I am wondering if this sort of pulsar image sequence capture is in the realm of possibility using Firecapture, a ZWO asi 224 camera and a 10" or 14" SCT ?

Thanks for any thoughts in advance. Also, I would love to see any captures that show motion.

Edited by Thomas Ashcraft, 29 November 2016 - 06:21 PM.

### #2 jhayes_tucson

Interesting. I doubt that there would be enough light for my C14 using the same technique. Regardless, it would be fun to try to get a movie and I gave some thought about that idea a while ago. I don't think that lucky imaging is necessary to make a movie. Since the frequency is known, I think that the trick might be to use a synchronous chopper so that each frame could be be time integrated. Each frame in the movie would be taken at a different phase. I just imaged that star and it's easy to see with a 20 minute exposure so it should be possible. With the right set up it might only take a single evening to pull it off.

### #3 Thomas Ashcraft

I hope you try and succeed. Hope to see what you get. - Tom

### #4 freestar8n

I know someone who tried this with EdgeHD14 a few years ago and there just wasn't enough signal. But with current cameras and lower read noise it might be possible. You would need good timestamps on the exposures, with little jitter error.

### #5 jhayes_tucson

John,

I hope you try and succeed. Hope to see what you get. - Tom

I haven't actually committed to try it but, as I said, it might be possible with the right set up. With the chopper idea, the individual exposures might require a lot of exposure per frame--maybe in the range of 100-200 minutes/frame with a 1:10 duty cycle. My earlier statement that it might be possible to get all the data in one night is probably overly optimistic. Synching the frames to within 1/30 second between separate sessions would be challenging. It could be done with a GPS signal but that amps up the complexity a bit more. Still, it is an interesting idea.

### #6 Rick J

I don't know the size scope used but an O'scope synced to the right rate and connected to a photomultiplier tube allowed the peak to be scanned by slowly adjusting the start of the window and scanning it across the time of the peak intensity. I believe this is how Don Taylor once explained how his grad students made its optical discovery to me. First night they had the wrong sync rate so failed but succeeded once they had the rate right. I can't recall if they picked up the secondary peak.

I'd think today's cameras with a 14" scope could easily find it by John's method. Duty cycle isn't really involved. I can pick it up in 10 seconds with my high read noise camera and its naturally off most of the time. A series of chopped 1 minute windows scanned slowly across the peak time should pick it's rise and fall up. A rotating shutter controlled by an accurate controller should do the job I'd think. Finding the on time may be the hardest part. I just don't have such a shutter or I'd give it a try if these clouds and snow ever go away.

### #7 freestar8n

With a mechanical chopper and long exposures it is certainly possible and has been done I think several times with sct's. An example is here:

The main technical issue is setting up the chopper and controlling it - etc. There is little requirement on the camera side since it is doing long exposures at each phase. But that is all old school - and it's how the pulsar was first imaged decades ago.

But I don't know of anyone using strictly video techniques with an SCT and non-fancy camera to do the same thing - based on raw captured video and no chopper. But I think it is within reach nowadays with high QE cameras and low read noise at high frame rates.

The attempt I mentioned earlier was limited mainly by read noise. I think it should be possible with the ASI-1600 at high gain and cropped field capture. It would require good seeing and focus so the fwhm is as small as possible for maximum snr. I don't think there is a need for more than one continuous video capture.

### #9 jhayes_tucson

With a mechanical chopper and long exposures it is certainly possible and has been done I think several times with sct's. An example is here:

The main technical issue is setting up the chopper and controlling it - etc. There is little requirement on the camera side since it is doing long exposures at each phase. But that is all old school - and it's how the pulsar was first imaged decades ago.

But I don't know of anyone using strictly video techniques with an SCT and non-fancy camera to do the same thing - based on raw captured video and no chopper. But I think it is within reach nowadays with high QE cameras and low read noise at high frame rates.

The attempt I mentioned earlier was limited mainly by read noise. I think it should be possible with the ASI-1600 at high gain and cropped field capture. It would require good seeing and focus so the fwhm is as small as possible for maximum snr. I don't think there is a need for more than one continuous video capture.

Thanks for the reference Frank! I finally had time to read it and it describes exactly what I had in mind. That's an excellent paper and the author did a great job of going through the timing details (which I really hadn't considered.) Where was that published?

Edited by jhayes_tucson, 01 December 2016 - 11:21 AM.

### #10 freestar8n

I just got that reference from a google search - so I don't know much about it. But over the years I think several people have used sct's in combination with an optical chopper to capture the blinking of the crab pulsar.

The link provided by the OP is different because no chopper is involved. It's just raw video and very short exposures - with a very expensive camera. As opposed to using a chopper in combination with a non-special camera.

But what's new nowadays is that fairly inexpensive cameras could capture the pulsar blinking - and with no chopper at all. You just record a stream of video and then stack it in various ways to capture the bright vs. the dark periods. That's what the OP's reference did.

With a modern video camera the duty cycle is basically 100%. So if the pulsar is about 30 Hz, you could try 60fps video and see what you get. You just expose a stream of video at around 60 fps and 15ms exposure - and then you post-process and stack different phases of the video stream.

I was involved in an effort to do this a few years ago - but with an earlier video camera that had a fair amount of read noise. With the ASI - all these things become possible - because all that really matters here is QE and read noise. So I think it should be possible with EdgeHD14 and ASI-1600 - and just a video capture of some length of time - many minutes - but not hours.

The only requirement is that the individual frames should reveal a star - any star - that can be used for alignment and stacking. But I think 14" aperture and 15ms should be ok.

### #11 Thomas Ashcraft

Frank wrote: "So I think it should be possible with EdgeHD14 and ASI-1600 - and just a video capture of some length of time - many minutes - but not hours.

The only requirement is that the individual frames should reveal a star - any star - that can be used for alignment and stacking. But I think 14" aperture and 15ms should be ok."

Yes. It seems like prosumer video technology is now capable, or at least is on the verge of capability to capture this fast. But whether the C14 has enough light grasp is another question. Yet, I think it does. - Tom

### #12 jhayes_tucson

I just got that reference from a google search - so I don't know much about it. But over the years I think several people have used sct's in combination with an optical chopper to capture the blinking of the crab pulsar.

The link provided by the OP is different because no chopper is involved. It's just raw video and very short exposures - with a very expensive camera. As opposed to using a chopper in combination with a non-special camera.

But what's new nowadays is that fairly inexpensive cameras could capture the pulsar blinking - and with no chopper at all. You just record a stream of video and then stack it in various ways to capture the bright vs. the dark periods. That's what the OP's reference did.

With a modern video camera the duty cycle is basically 100%. So if the pulsar is about 30 Hz, you could try 60fps video and see what you get. You just expose a stream of video at around 60 fps and 15ms exposure - and then you post-process and stack different phases of the video stream.

I was involved in an effort to do this a few years ago - but with an earlier video camera that had a fair amount of read noise. With the ASI - all these things become possible - because all that really matters here is QE and read noise. So I think it should be possible with EdgeHD14 and ASI-1600 - and just a video capture of some length of time - many minutes - but not hours.

The only requirement is that the individual frames should reveal a star - any star - that can be used for alignment and stacking. But I think 14" aperture and 15ms should be ok.

Yeah, that might work but at 60 fps, you'd only get the star blinking on and off. The advantage is that it would be very simple to try. I had in mind trying to get maybe ten frames per cycle. As the paper shows, that's not a totally trivial exercise so I doubt that I have the energy to give it a serious try.

### #13 freestar8n

Actually - if you have a long sequence of frames that is slightly off from the exact period of the cycle, you can selectively stack subsets of the frames to get images showing different phases of the variation. With 10ms exposures you can treat it as a smoothly sliding window that samples through the full 30ms period. You just need a lot of frames - and it would be easier if the frame rate didn't drift. But as long as it is a camera that operates in video mode, like the ASI, it will pump out frames using its own clock and shouldn't drift much.

Again - this approach is basically what was used in the OP's reference. That's what they mean by "folding a fast sequence" in the caption below the image. It's essentially strobing through the sequence in post-processing.

All it would take to know if this is feasible or not is to use an ASI in a 14" sct that is very well focused on the nebula - and see if you can see any of the field stars in a 10ms exposure at high gain - where the read noise is about 1e. If you see a star then you know you can align and stack the frames - and since the read noise is so low, you can stack many of them to pull out the fainter companion even if it isn't visible in a single frame.

The nice thing about it is - no moving parts - and it all comes out by processing a single video stream.

Oh - and when I was somewhat involved with someone doing this a few years ago - they could in fact get images showing a star at fairly short exposures around 10ms with 14" using an earlier camera - I think a Lumenera. But the stacks were too noisy for it to work. So I think it should work now with higher QE and much lower read noise.

## 4. SIMULATIONS

In order to provide a fully consistent treatment of dead time effects in the PDS and in the cospectrum, we ran a large number of simulations. In each simulation we produced two event series containing variability, one for each FPM, and analyzed the data with cospectrum and PDS before and after applying a dead time filter. By doing so, we studied in detail the properties of the cospectrum and compared them to those of the PDS. In the following paragraphs, we will explain the procedure in more detail and demonstrate that the cospectrum can be considered a very good proxy of a white-noise-subtracted PDS, albeit with some corrections to account for the measured rms.

### 4.1. Procedure

Light curve generation. We used the procedure by Davies & Harte (1987), introduced to astronomers by Timmer & Koenig (1995), to simulate light curves between two times, t0 and t1, from a number of model PDS shapes containing QPOs. The sampling frequency of the light curves was at least four times higher than the maximum frequency of the variability components included in the simulation. We normalized the light curves in order to have the desired mean count rate and total rms variability (7%–10%). In order to be able later to calculate PDSs with a given maximum timescale T (see "Calculation of the PDSs and the cospectrum" below), we simulated light curves at least 10 times longer, following the prescriptions in Timmer & Koenig (1995) to avoid aliasing.

Event list generation. From every light curve, we generated two event lists, corresponding to the signal from the two focal planes. Each event list was produced as follows: first of all, we calculated the number Nsave of event times to be generated as a random sample from a Poisson distribution centered on the number of total photons expected (summing up all expected light curve counts) then, we generated Nsave events by using a Monte Carlo acceptance–rejection method. This is a classical Monte Carlo technique a more general treatment can be found in most textbooks on Monte Carlo methods (e.g., Gentle 2003). In our case, we used the following procedure: (1) for every event, we simulated an event time, te, uniformly distributed between t0 and t1, and an associated random amplitude ("probability") value Ae between 0 and the maximum of the light curve (2) we rejected all te values whose associated Ae values were higher than the light curve at te to avoid possible spurious effects given by a stepwise model light curve, we used a cubic spline interpolation to approximate the light curve between bins (3) we sorted the event list by te. To simulate the effects of background (spurious events filtered out by the pipeline, events recorded outside the source regions, etc.), we also produced two background series, at constant average flux, one for each simulated source light curve.

Dead time filtering. For each event list, we created a corresponding dead-time-affected event list by applying a simple dead time filter: for each event, we eliminated all events in the 2.5 ms after it. Source and background events contributed equally to dead time. We used different versions of the dead time filter by varying slightly the dead time between events (of

0.1ms). However, the pernicious effect of variable dead time is mainly on white noise subtraction. In our case (Figure 1), the cospectrum allows us to overcome this problem as its white noise is zero, and we verified that the other effects are not significantly different in the constant and variable dead time cases. In the following, we will treat the case with constant dead time.

Calculation of the PDSs and the cospectrum. We divided each pair of event lists in segments of length T, and calculated the PDS in each of the segments and the CPDS from each pair of them. We then averaged the PDSs and CPDSs from all segments. The CPDS white noise level is already 0. For the PDSs, used only in the ideal zero-dead-time case, we subtracted the theoretical Poisson level (two in Leahy normalization). We then rebinned the PDSs and CPDSs, either by a fixed rebin factor or by averaging a larger number of bins at high frequencies, following approximately a geometric progression. We finally multiplied the Leahy-normalized PDSs by (B + S)/S 2 (where B is the background count rate and S is the mean source count rate) in order to obtain the squared rms normalization often used in the literature (Belloni & Hasinger 1990 Miyamoto et al. 1991). The CPDS was instead multiplied by the factor , where bars indicate the geometric averages of the count rates in each of the two event lists used to calculate it. 19

Finally, we calculated the cospectrum by taking the real part of the CPDS. As described above, we assigned to each final bin of the cospectrum ci an uncertainty calculated from the geometrical average of the PDSs in the two channels, divided by , where M is the number of averaged spectra and W is the number of subsequent bins averaged to obtain ci.

Fitting procedure. Cospectra do not need Poisson noise subtraction for PDSs, we fitted a constant to the interval outside of the frequency range containing QPOs. Since in the following paragraphs, in all our examples, we will be showing power spectra obtained by averaging more than 50 PDSs, we are in the Gaussian regime and a fit with standard χ 2 minimization routines is appropriate to the precision we are interested in (van der Klis 1989 Barret & Vaughan 2012).

Then, we fitted the QPOs with a Lorentzian profile in XSPEC 20 (Arnaud 1996). Errors were calculated through a Monte Carlo Markov Chain, as those intervals where the χ 2 of the fit with no frozen parameters increased by 1. According to Lewin et al. (1988), the significance of the detection of QPOs is expected to be

where r is the rms and Δν is the equivalent width of the feature (for a Lorentzian, Δν = π/2 × FWHM). The exact proportionality factor depends on the definition of significance. In our case, the significance of QPOs was defined as the ratio between the amplitude of the Lorentzian and its error. The significance calculated in this way gives a value

2 times lower than obtained by using the excess power à la Lewin et al. (1988) (a factor two is expected due to the fact that the Gaussian errors are calculated over R, and the excess power over R + see Boutelier 2009 Boutelier et al. 2009), but the trend in Equation (4) holds provided that the variability is dominated by Poisson noise.

### 4.2. Simulation Results

First look. The simulation in Figure 1 shows the comparison between the PDS and the cospectrum with and without dead time for pure Poisson noise. From these simulations it is clear that the white-noise-subtracted PDS and the cospectrum are equivalent in the case with no dead time. It is immediately evident that the most problematic effect of dead time, the modulation of the white noise level, disappears in the cospectrum. In the following paragraphs, we investigate the frequency and count rate dependence of these quantities in more detail.

Frequency dependence. The general statistical properties of the PDS and the cospectrum are also very similar, both in the dead-time-affected and in the zero-dead-time case. Figure 1, panel (d), shows that the variance of the cospectrum and the PDS maintains a constant ratio equal to two in both the clean and the dead-time-affected data sets. This makes it easy to calculate the variance of the cospectrum values for the subsequent analysis, by simply using the known properties of the PDS where the variance is just equal to the square of the power (in Leahy normalization).

Contrary to what might be imagined, it is possible to detect variability even at frequencies that are affected the most by dead time, i.e., those above 1/τd. Figure 2 shows that QPOs at all frequencies are detectable, albeit with some modulation of the observed rms. To measure this change of rms, we simulated

500 light curves using the method above, each containing a single QPO with frequencies equally distributed between 5 and 1000 Hz, rms = 10%, and FWHM = 2 Hz. As explained above, from every light curve we obtained two event lists in order to simulate the signals from the two detectors. We produced, for every pair of event lists, the cospectrum, the two PDSs, and a total PDS including the counts from both detectors, both in the zero-dead-time and the dead-time-affected cases. We then fitted the resulting spectra with a Lorentzian model in XSPEC.

Figure 2. QPOs of equal Q factor (20) and rms amplitude (8%) at different frequencies. The units in this plot, and in all following power spectra or cospectra, if not stated otherwise, are power×frequency. Gray points show the standard, dead-time-affected PDS. The white noise level to subtract in the dead-time-affected data sets was calculated between 10 and 20 Hz (minimum between two QPOs), while in the dead-time-free case we subtracted the theoretical level (2 in Leahy normalization).

Figure 3 shows the change of the rms measured with the PDS and the cospectrum, with and without dead time. The measured rms in the zero-dead-time PDSs agrees with the zero-dead-time cospectrum, whereas the dead-time-affected cospectrum yields a frequency-dependent deviation from the true rms, with deviation following the same trend as the variance (see also Figure 1).

Figure 3. Top: variation of the rms of a QPO at different peak frequencies, measured with the various techniques and with and without dead time. Each point represents a simulated QPO with rms = 10% and FWHM = 2 Hz. A total of 281 simulations were used for this plot. (Bottom) Significance measured with each method. The total PDS has about twice the significance of the single-module PDS in the no-dead-time case, as expected, owing to double the number of photons. The CPDS in the no-dead-time case is a factor of higher than the single PDS, and lower than the total PDS by the same amount. The dead-time-affected CPDS, instead, has a much lower level due to the lack of photons. The decrease of significance does not depend on the frequency of the QPO, but only on count rate (see Figure 4).

The detection significance does not depend on the frequency in any case, with or without dead time. The decrease of the significance is instead driven by the observed count rate, as we discuss shortly. In the no-dead-time case, the significance of the single PDSs is about half that of the total PDS because the significance is directly proportional to the intensity of the signal (Equation (4)), and in the total PDS one uses twice the number of photons. The zero-dead-time cospectrum yields instead a significance lower than the total PDS, and higher by the same amount than the single-module PDS. This is just an effect of the factor between the standard deviations of the cospectrum and the single-module PDS. From Figure 3, it is clear that it is advantageous to use the total PDS for low count rates where dead time is negligible, and the cospectrum otherwise, but with the formulae and the simulations shown above to account for the frequency-dependent distortion of the rms amplitude.

In summary, the important point that Figure 3 makes is that QPOs are still detectable at any frequency, even those heavily affected by dead time, albeit with a change of the measured rms that must be taken into account.

Count rate dependence. We now investigate how the measured rms is influenced by count rate. Figure 4 and 5 show the variation with count rate in the detected rms of a QPO at 30 Hz, FWHM = 2 Hz, and rms = 7.5%, in two cases: increasing total count rate, and fixed total (source + background) count rate with variable source count rate. For the first case, since 30 Hz 1/τd and the higher-order corrections are not needed, we use van der Klis (1989 Equations (3.8) and (4.8)) to obtain

This relation is plotted with a dashed line in the top panel of Figure 4 and it is in remarkably good agreement with the simulated data.

Figure 4. Similar to Figure 3, but with the centroid frequency of the QPO fixed at 30 Hz and letting the count rate vary between 10 and 1000 counts s −1 . A total of 118 simulations were used in this plot. The line shows Equation (5). It is not a fit, and describes the data remarkably well. In the bottom panel, we plot the detection significance for all the cases. The lines, again, are not fitted, they only show the theoretical prediction from Equation (4). All dead-time-free cases are in good agreement with a linear increase with count rate below

500counts s −1 , above which some curvature appears due to the departure from the quasi-Poissonian regime. The dead-time-affected case is in good agreement with Equation (4) if, instead of the incident count rate (dashed line), one uses the observed count rate (solid line see Equation (5)).

Figure 5. Dependence of the rms on the relative contribution of the source in a given energy range to the total count rate. The 132 simulations that compose this plot show how the rms drop is stronger if the source signal dominates the total signal, since the source signal contributes more to the total dead time. The solid black line shows Equation (6). It is not a fit.

In general, one would expect the significance of detection in the PDS to be proportional to the incident count rate and to the square of the rms (Equation (4)). This condition holds if the QPO can be considered a small disturbance in an otherwise Poissonian process, or (Lewin et al. 1988). In the bottom panel of Figure 4, we fit Equation (4) below 600 counts s −1 , with a multiplicative constant due to the slightly different definition of the 1σ error that we use (Δχ 2 = 1 instead of the Leahy et al. (1983) definition). The best-fit multiplicative constant,

1./2.2, turns out to be consistent with the factor of two expected from the fact that we are using Gaussian fitting instead of excess power (see Section 4.1). The departure from the linear condition above

600 counts s −1 is evident. Indeed, it is expected that at count rates above 0.1ν/rms, the significance starts departing from the linear trend. The total PDS is visibly more affected because its count rate is double that of the single-module PDS. The significance of detection with the cospectrum is lower than that of the total PDS, while it is higher than that of the PDS from a single module. The dead-time-affected cospectrum, instead, has a large deviation from the linear trend. This is just an effect of the diminishing count rate due to dead time. In fact, what is plotted is the incident count rate. If one converts it to the detected count rate, the linear relation between count rate and significance still holds (solid line).

The second case (Figure 5) clearly shows a linear decrease of the measured rms as the source gains counts with respect to the background. Again, by using van der Klis (1989 Equations (3.8) and (4.8)), but this time putting the total count rate (rin + rback, in, where rback, in is the non-source count rate) in the relation between incident and observed count rates, one obtains

This means that the measure of rms we obtain in our data will generally be affected more if the source signal dominates the background, as is the case in most NuSTAR observations of bright sources. In the examples that we present below, we make use of Monte Carlo simulations similar to the ones above to estimate the change of rms at the count rate of the sources we observe.

## How bright is the Crab Pulsar's 30 Hz modulation in visible light? What color is it? - Astronomy

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Periods of one second are typical although pulsars have been discovered with periods from a few milliseconds (one millisecond equals 0.001 seconds) up to eight seconds. le principe de la roue à fentes dont la vitesse de rotation est difficile The accuracy in microseconds with which the ephemeris defined This so-called characteristic, or timing, age can be in close agreement with the actual age. This is the remnant of a supernova that exploded in 1054 A.D. Month Il reste The 30-Hz rotation rate of the Crab pulsar has been monitored at Jodrell Bank Observatory since 1984 and by other observatories before then. La fréquence de sortie est ajustable une périodicité du signal toutes les 5.3 images. ordre. The optical pulsar has a diameter of about 20 kilometres. quoted in terms of T.D.B. The short period of the Crab pulsar made it very unlikely that the star was a pulsating white dwarf. La pose maximum pour un découpage de la période en 8 ou10 images sera (ms) = 3.63511677858522E-05*(JJréduit) + 31.6314733479109, Le jour julien the whole calendar month, using the DE200 ephemeris. (le dépouillement The uncertainty in the observed barycentric frequency 'Nu', in mn. The observed period, in seconds, calculated by the HEASARC from the calculated by the HEASARC from the standard relation P_dot = - Nu_dot/Nu2. de calcul ultra-simple utilisant cette formule (ce qui ne dispense pas • CRAB PULSAR Situated in Crab Nebula Second Pulsar discovered Has period 33 milliseconds Forms major portion of emissions from the Crab Nebula IMPORTANT PULSARS A slow-motion movie of the Crab Pulsar taken at 800 nm wavelength (near- infrared) using a Lucky Imaging camera from Cambridge University, showing the bright pulse and fainter interpulse Nous avons donc enchainé 40 poses de 10 secondes: ce premier La nébuleuse a été observée pour la première fois en 1731 par John Bevis, puis en 1758 par Charles Messier qui en fait le premier objet de son catalogue (ca… They used this data to create two simple equations that predict the pulsar's spin rates in the future. alternative générée par un multivibrateur piloté par quartz 2 MHz suivi mises en jeux un dispositif electro-mécanique (obturateur à base infinite frequency at the barycentre of the solar system, in seconds. The images, taken over a period of several months, show that the Crab is a far more dynamic object than previously understood. très sensiblement linéaire. Pulsars were discoveredserendipidously in 1967 on chart-recorder records obtained during alow-frequency (=81 MHz) survey of extragalactic radio sourcesthat scintillate in the interplanetary plasma, just as stars twinkle inthe Earth's atmosphere. The Crab nebula pulsar in the constellation Taurus has a period of $33.5 imes 10^ <-3>mathrm,$ radius $10.0 mathrm,$ and mass $2.8 imes 10^ <30>mathrm$ The pulsar's rotational period will increase over time due to the release of electromagnetic radiation, which doesn't change its radius but reduces its rotational energy. Crab Nebula interstellar medium pulsar frequency Declination Julian Date radio telescope parsecs dispersion magnetic field radio waves period electromagnetic spectrum neutron star resolution speed of light electromagnetic radiation Universal Time (UT) Right Ascension 3. JPL_Time The ﬁrst set of d ata was obtained in October 2008 with the ultra-fast photon counter Aqueye (Barbieri et al. devoir augmenter le rapport signal/bruit. paysage. For the Crab pulsar no glitch correction is applied, but the ephemeris data will be updated periodically (once or twice a year) to the latest Jodrell Bank data while it is available. At the time of its discovery it was not clear that the detected single, bright pulses belonged to a periodically emitting source. If the PEP311 ephemeris The Crab Pulsar is believed to be about 28-30 km in diameter it emits pulses of radiation every 33 milliseconds. va donc directement dans le moteur, sur l'axe duquel est fixé le réelle du quartz n'est jamais connue précisement: d'après The Crab Nebula is a supernova remnant generated by a star that exploded 7500 years ago, whose light reached Earth in 1054. This number is not adjacent to 89 in the sequence but is separated from it by the number 55 which does not correspond here. On the 2017 November 8, the Crab pulsar suffered a large glitch, whilst the pulsar was below the horizon at Jodrell Bank. The period of the pulsar's rotation is slowing by 38 nanoseconds per day due to the large amounts of energy carried away in the pulsar wind. ne l'est pas! grâce à un tableur, la courbe de décroissance étant Le dépouillement se fait par tri manuel des images puis addition. du Pulsar. de période très voisine de la période du Pulsar soit 33.489ms (par 'MIT Time' is the arrival time using the M.I.T. du 31 Décembre 2003, http://www.jb.man.ac.uk/

pulsar/crab.html. subtracted. The ratio of a pulsar’s present period to the average slowdown rate gives some indication of its age. avec les fenêtres du disque ouvertes en entier (30°), et c'est C'est un des deux seuls pulsars connus (avec PSR J0205+6449) dont l'âge réel est connu avec certitude et est inférieur à 1000 ans. Le point timescale is now quoted in terms of T.D.B. Cette nébuleuse, appelée aussi SN 1054 ou 1054 AD, est le résidu d'une supernovae ayant explosé en Juillet 1054 et que les astronomes chinois ont observé à l'époque pendant près d'un mois. de la manip en express puis re-réglages: on réussit héroïquement Selon cette méthode l'obturateur des phases du Pulsar. Nous avons réalisé plusieurs poses de temps différents, dans le visible. 2001 Espinoza et al. from U of A) discovered a neutron star with P = 1.4 ms (Spin frequency = 715 Hz). in the reductions is as follows: LII If this is the primary energy loss for the pulsar and it primarily comes from a loss of rotational energy, then at what rate is it slowing down its rotation rate? One of these traits, giant pulses that can be upwards of 1000 times brighter than the average pulse, was key to the Crab's initial detection. ou "éteint" de celui-ci. 2.The Crab Pulsar Age and Magnetic Field On the 1st September the time of arrival of the radio pulses from the Crab Pulsar were collected. The Crab pulsar has a 33-millisecond pulse period, which was too short to be consistent with other proposed models for pulsar emission. période du quartz: ceci ne pourra être fait que par expérience : Goddard Space Flight Center, New York OSTI Identifier: 4148248 NSA Number: NSA-24-027966 … dans les différences d'éclat du pulsar. Modification optique M1. Il est en revanche très lumineux, puisque The Crab pulsar period exhibits the greatest deviation from its corresponding Fibonacci number 34. An optical pulsar is a pulsar which can be detected in the visible spectrum. entre fenêtres et obturations), l'obturateur est ouvert pendant deux disques (violet) et le moteur (vert). In order to measure the short-term rotation of the pulsar close in time to the glitch, we split the 9 and 3 h long daily observations into 422 individual 30 min long observations over the time period 58057

## Contents

As long as the modulation frequency is kept above the fusion threshold, the perceived intensity can be changed by changing the relative periods of light and darkness. One can prolong the dark periods and thus darken the image therefore the effective and average brightness are equal. This is known as the Talbot-Plateau law. [2] Like all psychophysical thresholds, the flicker fusion threshold is a statistical rather than an absolute quantity. There is a range of frequencies within which flicker sometimes will be seen and sometimes will not be seen, and the threshold is the frequency at which flicker is detected on 50% of trials.

Different points in the visual system have very different critical flicker fusion rate (CFF) sensitivities the overall threshold frequency for perception cannot exceed the slowest of these for a given modulation amplitude. Each cell type integrates signals differently. For example, rod photoreceptor cells, which are exquisitely sensitive and capable of single-photon detection, are very sluggish, with time constants in mammals of about 200 ms. Cones, in contrast, while having much lower intensity sensitivity, have much better time resolution than rods do. For both rod- and cone-mediated vision, the fusion frequency increases as a function of illumination intensity, until it reaches a plateau corresponding to the maximal time resolution for each type of vision. The maximal fusion frequency for rod-mediated vision reaches a plateau at about 15 hertz (Hz), whereas cones reach a plateau, observable only at very high illumination intensities, of about 60 Hz. [3] [4]

In addition to increasing with average illumination intensity, the fusion frequency also increases with the extent of modulation (the maximal relative decrease in light intensity presented) for each frequency and average illumination, there is a characteristic modulation threshold, below which the flicker cannot be detected, and for each modulation depth and average illumination, there is a characteristic frequency threshold. These values vary with the wavelength of illumination, because of the wavelength dependence of photoreceptor sensitivity, and they vary with the position of the illumination within the retina, because of the concentration of cones in central regions including the fovea and the macula, and the dominance of rods in the peripheral regions of the retina.

### Display frame rate Edit

Flicker fusion is important in all technologies for presenting moving images, nearly all of which depend on presenting a rapid succession of static images (e.g. the frames in a cinema film, TV show, or a digital video file). If the frame rate falls below the flicker fusion threshold for the given viewing conditions, flicker will be apparent to the observer, and movements of objects on the film will appear jerky. For the purposes of presenting moving images, the human flicker fusion threshold is usually taken between 60 and 90 Hz, though in certain cases it can be higher by an order of magnitude. [5] In practice, movies are recorded at 24 frames per second and displayed by repeating each frame two or three times for a flicker of 48 or 72 Hz. Standard-definition television operates at 25 or 30 frames per second, or sometimes at 50 or 60 (half-)frames per second through interlacing. High-definition video is displayed at 24, 25, 30, 60 frames per second or higher.

The flicker fusion threshold does not prevent indirect detection of a high frame rate, such as the phantom array effect or wagon-wheel effect, as human-visible side effects of a finite frame rate were still seen on an experimental 480 Hz display. [6]

### Display refresh rate Edit

Cathode ray tube (CRT) displays usually by default operated at a vertical scan rate of 60 Hz, which often resulted in noticeable flicker. Many systems allowed increasing the rate to higher values such as 72, 75 or 100 Hz to avoid this problem. Most people do not detect flicker above 400 Hz. [7] [ irrelevant citation ] Other display technologies do not flicker noticeably, so the frame rate is less important. Liquid-crystal display (LCD) flat panels do not seem to flicker at all, as the backlight of the screen operates at a very high frequency of nearly 200 Hz, and each pixel is changed on a scan rather than briefly turning on and then off as in CRT displays. However, the nature of the back-lighting used can induce flicker – Light-emitting diodes (LEDs) cannot be easily dimmed, and therefore use pulse-width modulation to create the illusion of dimming, and the frequency used can be perceived as flicker by sensitive users. [8] [9] [10]

### Lighting Edit

Flicker is also important in the field of domestic (alternating current) lighting, where noticeable flicker can be caused by varying electrical loads, and hence can be very disturbing to electric utility customers. Most electricity providers have maximum flicker limits that they try to meet for domestic customers.

Fluorescent lamps using conventional magnetic ballasts flicker at twice the supply frequency. Electronic ballasts do not produce light flicker since the phosphor persistence is longer than a half cycle of the higher operation frequency of 20 kHz. The 100–120 Hz flicker produced by magnetic ballasts is associated with headaches and eyestrain. [11] Individuals with high critical flicker fusion threshold are particularly affected by light from fluorescent fixtures that have magnetic ballasts: their EEG alpha waves are markedly attenuated and they perform office tasks with greater speed and decreased accuracy. The problems are not observed with electronic ballasts. [12] Ordinary people have better reading performance using high-frequency (20–60 kHz) electronic ballasts than magnetic ballasts, [13] although the effect was small except at high contrast ratio.

The flicker of fluorescent lamps, even with magnetic ballasts, is so rapid that it is unlikely to present a hazard to individuals with epilepsy. [14] Early studies suspected a relationship between the flickering of fluorescent lamps with magnetic ballasts and repetitive movement in autistic children. [15] However, these studies had interpretive problems [16] and have not been replicated.

LED lamps generally do not benefit from flicker attenuation through phosphor persistence, the notable exception being white LEDs. Flicker at frequencies as high as 2000 Hz (2 kHz) can be perceived by humans during saccades [17] and frequencies above 3000 Hz (3 kHz) have been recommended to avoid human biological effects. [18]

In some cases, it is possible to see flicker at rates beyond 2000 Hz (2 kHz) in the case of high-speed eye movements (saccades) or object motion, via the "phantom array" effect. [19] [20] Fast-moving flickering objects zooming across view (either by object motion, or by eye motion such as rolling eyes), can cause a dotted or multicolored blur instead of a continuous blur, as if they were multiple objects. [21] Stroboscopes are sometimes used to induce this effect intentionally. Some special effects, such as certain kinds of electronic glowsticks commonly seen at outdoor events, have the appearance of a solid color when motionless but produce a multicolored or dotted blur when waved about in motion. These are typically LED-based glow sticks. The variation of the duty cycle upon the LED(s), results in usage of less power while by the properties of flicker fusion having the direct effect of varying the brightness. [ citation needed ] When moved, if the frequency of duty cycle of the driven LED(s) is below the flicker fusion threshold timing differences between the on/off state of the LED(s) becomes evident, and the color(s) appear as evenly spaced points in the peripheral vision.

A related phenomenon is the DLP rainbow effect, where different colors are displayed in different places on the screen for the same object due to fast motion.

### Flicker Edit

Flicker is the perception of visual fluctuations in intensity and unsteadiness in the presence of a light stimulus, that is seen by a static observer within a static environment. Flicker that is visible to the human eye will operate at a frequency of up to 80 Hz. [22]

### Stroboscopic effect Edit

The stroboscopic effect is sometimes used to "stop motion" or to study small differences in repetitive motions. The stroboscopic effect refers to the phenomenon that occurs when there is a change in perception of motion, caused by a light stimulus that is seen by a static observer within a dynamic environment. The stroboscopic effect will typically occur within a frequency range between 80 and 2000 Hz, [23] though can go well beyond to 10,000 Hz for a percentage of population. [24]

### Phantom array Edit

Phantom array, also known as the ghosting effect, occurs when there is a change in perception of shapes and spatial positions of objects. The phenomenon is caused by a light stimulus in combination with rapid eye movements (saccades) of an observer in a static environment. Similar to the stroboscopic effect, the phantom effect will also occur at similar frequency ranges. The mouse arrow is a common example [25] of the phantom array effect.

The flicker fusion threshold also varies between species. Pigeons have been shown to have higher threshold than humans (100 Hz vs. 75 Hz), and the same is probably true for all birds, particularly birds of prey. [26] Many mammals have a higher proportion of rods in their retina than humans do, and it is likely that they would also have higher flicker fusion thresholds. This has been confirmed in dogs. [27]

Research also shows that size and metabolic rate are two factors that come into play: small animals with high metabolic rate tend to have high flicker fusion thresholds. [28] [29]

## Rapid photometry of supernova 1987A: a 2.14 ms pulsar?

We have monitored Supernova 1987A in optical/near-infrared bands using various high-speed photometers from a few weeks following its birth until early 1996 in order to search for a pulsar remnant. While we have found no clear evidence of any pulsar of constant intensity and stable timing, we have found emission with a complex period modulation near the frequency of 467.5 Hz – a 2.14 ms pulsar candidate. We first detected this signal in data taken on the remnant at the Las Campanas Observatory (LCO) 2.5-m Dupont telescope during 14–16 Feb. 1992 UT. We detected further signals near the 2.14 ms period on numerous occasions over the next four years in data taken with a variety of telescopes, data systems and detectors, at a number of ground- and space-based observatories. In particular, an effort during mid-1993 to monitor this signal with the U. of Tasmania 1-m telescope, when SN1987A was inaccessible to nearly all other observing sites due to high airmass, clearly detected the 2.14 ms signal in the first three nights' observations. The sequence of detections of this signal from Feb. 92 through August 93, prior to its apparent subsequent fading, is highly improbable (<10 −10 for any noise source). In addition, the frequency of the signals followed a consistent and predictable spin-down (∼2–3×10 −10 Hz/s) over the several year timespan (92–96). We also find evidence in data, again taken by more than one telescope and recording system, for modulation of the 2.14 ms period with a ∼1,000 s period which complicates its detection. The 1,000 s modulation was clearly detected in the first two observations with the U. Tas. 1-m during mid-1993. The characteristics of the 2.14 ms signature and its ∼1,000 s modulation are consistent with precession and spindown via gravitational radiation of a neutron star with an effective non-axisymmetric oblateness of ∼10 −6 . The implied luminosity of the gravitational radiation exceeds the spindown luminosity of the Crab Nebula pulsar by an order of magnitude. Due to the nature of the 2.14 ms signature and its modulation, and the analysis techniques necessary for detection, it is difficult to determine the overall probability that all aspects of the signal are real, though it has remained consistent with an astrophysical origin throughout the several year timespan of our study.

## Observing Cosmic Voids

The large scale structure of the observable universe is like a sponge, where the galaxies and galaxy clusters are arranged along the sponges filaments. Is it possible for an amateur to confirm this structure and in consequence the cosmic voids where there are hardly any galaxies? What equipment would be necessary?

### #2 TOMDEY

I did read up on the history. 2-dimensional large structure was eventually speculated and then noted by mapping the Ra/Dec of LOTS of galaxies. Once Hubble's Red Shifts were understood, and again, data collection of LOTS more galaxies. the 3-D structure, including the voids, filaments and knots emerged quite convincingly.

For an amateur to do that independently, from scratch. would require a similar Herculean effort. arguably to include measurement of red shifts of Lots of remote galaxies. aka a BIG telescope and capable spectroscope.

I can imagine confirming a few of the documented structural features in at least Ra/Dec, though. That would probably involve taking images of a notable region and then tabulating the galaxies there by examining the images. For it to be a fair confirmation, would need to do that examination "in the blind", and then draw in filaments and knots, either by inspection or writing one's own algorithm to run on software./computer. And then, finally, to overlay that with what the professionals have reported. To the extent that they correlate. one would have (somewhat) independently confirmed the existence of structures.

Maybe one way to circumvent the data-collection aspect. Work off of Palomar Survey images or stuff that has been released by such platforms as Hubble.

The ultimate would be to imagine, theorize and execute an ENTIRELY DIFFERENT approach to detect, measure, assess and conform structure. Of course, THAT's the sort of thing that the pros are always researching!

PS: I' trying to strobe the Crab Pulsar in the Vis/NIR. to confirm the rotation of that Neutron Star. And THAT's gona be tough. even with a 36-inch telescope!

### #3 sg6

I doubt you can view it, as best I keep getting told the structure is created by dark matter forming the filiment structure that the galaxies are resident in.

You can view the galaxies but you "see" them as if on a 2D background so the depth component is lost.

### #4 Knasal

The topic of “Our Local Cosmic Void” is the main story and graces the cover of Sky and Telescope’s October edition.

Edited by Knasal, 28 August 2018 - 08:32 PM.

### #5 robin_astro

Measuring all those faint galaxy redshifts is a big challenge. You can measure local galaxy redshifts and a few more distant bright quasars with modest equipment but getting enough depth is going to need a pro size scope

2m ? and a lot of observing time.

PS: I' trying to strobe the Crab Pulsar in the Vis/NIR. to confirm the rotation of that Neutron Star. And THAT's gona be tough. even with a 36-inch telescope!

Tom

Cool ! I made a marginal observation with an 8 inch scope a few years back

but you should be able to get a good light curve with a 36 inch

Edited by robin_astro, 29 August 2018 - 08:17 AM.

### #6 TOMDEY

Measuring all those faint galaxy redshifts is a big challenge. You can measure local galaxy redshifts and a few more distant bright quasars with modest equipment but getting enough depth is going to need a pro size scope

2m ? and a lot of observing time.

Cool ! I made a marginal observation with an 8 inch scope a few years back

image002.gif

http://www.threehill. ro_image_33.htm

but you should be able to get a good light curve with a 36 inch

Robin

Hi, robin. That's GREAT! My chopper is a Thor Labs and I'm fiddling with the geometry of the blades to try to enhance the temporal modulation of the strobing. Your great success makes that sort of nuance seem entirely unnecessary. Yes, ideally, I would like to reconstruct the light-curve (showing both blips) by doing the analysis and writing code to affect a Power Spectrum, that I can then transform back to deduce the curve. I'll probably never go that far, though. Obviously, knowing the fundamental freq (approx 30 Hz) ahead of time helps! If I can collect enough continuous data. might also get a pretty accurate measure of the fundamental freq.

Anyway, just detecting and/or Seeing the strobing would be magnificent!

But my scope will be a 36-inch Dobsonian with GoTo and Tracking. I hope that is accurate enough to pull off.

The scope has excellent resolution and huge aperture. and I will try Night Vision, with the incoming light at the GaAs Photocathode (which responds plenty fast enough). Chopping the incoming light, of course! The viewing phospher has an extended half-life, but that only needs to respond at the Chopping Freq, which is not a problem. I would LOVE to actually "see it", real-time. and would consider that to be quite successful!

## Baade and Zwicky: “Super-novae,” neutron stars, and cosmic rays

In 1934, two astronomers in two of the most prescient papers in the astronomical literature coined the term “supernova,” hypothesized the existence of neutron stars, and knit them together with the origin of cosmic-rays to inaugurate one of the most surprising syntheses in the annals of science.

From the vantage point of 80 y, the centrality of supernova explosions in astronomical thought would seem obvious. Supernovae are the source of many of the elements of nature, and their blasts roil the interstellar medium in ways that inaugurate and affect star formation and structurally alter the visible component of galaxies at birth. They are the origin of most cosmic-rays, and these energetic rays have pronounced effects in the galaxy, even providing an appreciable fraction of the human radiation doses at the surface of the Earth and in jet flight. Prodiguously bright supernovae can be seen across the Universe and have been used to great effect to take its measure, and a majority of them give birth to impressively dense neutron stars and black holes. Indeed, the radio and X-ray pulsars of popular discourse, novels, and movies are rapidly spinning neutron stars injected into the galaxy upon the eruption of a supernova (Fig. 1).

A picture of the inner regions of the famous Crab Nebula captures emergent jets and the “Napoleon Hat” structure of surrounding plasma. The radio/optical/X-ray pulsar, a neutron star rotating at ∼30 Hz, is buried in the center. The Crab was produced in a supernova explosion in A.D. 1054. Image courtesy of ESA/NASA.

However, it was only with the two startlingly prescient PNAS papers by Baade and Zwicky (1, 2) in 1934 that the special character of “super-novae” (a term used for the first time in these papers) was highlighted, their connection with cosmic rays postulated, and the possibility of compact neutron stars hypothesized. (In the winter of 1933, Baade and Zwicky presented a preliminary version of these ideas at the American Physical Society Meeting at Stanford University.) To be sure, as early as 1921, in the famous Shapley–Curtis debate on the scale of the universe, Heber Curtis had stated that a division of novae into two magnitude classes “is not impossible” (3). However, before the Baade and Zwicky papers, astronomers had not developed the idea that supernovae, such as S Andromedae and the bright event studied by Tycho Brahe in 1572, must be distinguished from the more common novae. Moreover, before these papers, the concept of a dense “neutron star” the size of a city but with the mass of a star like the Sun, did not exist. In their own words (italics in original) (2): “With all reserve we advance the view that a super-nova represents the transition of an ordinary star into a neutron star, consisting mainly of neutrons. Such a star may possess a very small radius and an extremely high density.” In addition, the energetic class of explosions identified in the first paper (1) as “super-novae” naturally suggested to the authors in their second paper (2) that they could be the seat of production of the energetic particles discovered by Hess in 1911 (4). Baade and Zwicky state (2): “We therefore feel justified in advancing tentatively the hypothesis that cosmic rays are produced in the super-nova process” (italics in original). Eighty years later, this remains the view of astrophysicists.

The concept of a supernova was rapidly accepted, and in the following years many examples were found (5 ⇓ ⇓ –8). After all, the outsized blast waves that are the “supernova remnants” in our galaxy (Fig. 2), and the explosive transients seen in other galaxies (“island universes”) that astronomers had recently demonstrated were outside our galaxy and distant, had therefore to be extraordinarily energetic. However, the concept of a neutron star was initially met with skepticism, despite the theoretical calculations of Oppenheimer and Volkoff (9), and it was not until the discovery of radio pulsars in 1967 (10) more than 30 y later—and their interpretation as spinning neutron stars the next year (11)—that the concept of a neutron star was accepted and mainstreamed. Today, we know of many thousands of radio pulsars and neutron star systems, and their study engages many in the astronomical community.

False-color X-ray images of the Tycho, Kepler, and Cassiopeia galactic supernova remnants. The different colors approximately reflect different elemental compositions. Red traces iron, green traces silicon, and blue traces calcium and iron blends. These supernova explosions occurred in 1572, 1604, and ∼1680 A.D., respectively. (Left, credit: X-ray: NASA/CXC/SAO, Infrared: NASA/JPL-Caltech Optical: MPIA, Calar Alto, Krause et al.), (Center, credit: NASA/CXC/UCSC/Lopez et al.), (Right, credit: NASA/CXC/SAO/Patnaude et al.) Images courtesy of the Chandra X-ray Center data originally published in refs. 16–18, respectively.

As might have been anticipated, most of the quantitative results presented in the Baade and Zwicky papers from 1934 (1, 2) have not survived. However, the authors were motivated to posit a neutron star by the extraordinary energy they concluded was required to explain their supernovae, and to produce energetic cosmic rays simultaneously, impulsively, and copiously. A neutron star would be very dense and, in the words of Baade and Zwicky, the “gravitational packing energy” would be very high (2). The authors had eliminated nuclear energy as too small to power a supernova, and believed they needed a nontrivial fraction of the rest-mass energy of the star. (Note also that the year 1934 was before we fully understood the nuclear processes that power stars.) This fraction Baade and Zwicky could obtain from the gravitational binding energy of a compact object with nuclear or greater densities. The neutron had just been discovered in 1932 (12) and was known to be neutral, and Baade and Zwicky imagined that oppositely charged protons and electrons could be crushed together to produce their beast. The modern view (13) is not extravagantly different, although one now quotes Baade and Zwicky for profound insight, not technical accuracy. Importantly, one type of supernova, the Type Ia, is indeed powered by nuclear energy. In fact, and ironically, all of the supernovae observed by Baade and Zwicky in the 1930s were of this type, not of the majority type currently thought to be powered ultimately by gravitation.

Many believe that Lev Landau predicted the existence and characteristics of neutron stars soon after the discovery of the neutron (14). However, as Yakovlev et al. (15) have clearly shown, Laudau was thinking about a macroscopic nucleus and nowhere in that paper was the neutron mentioned. Landau’s paper (14) was in fact written before the discovery of the neutron, and incorporated the misunderstanding that quantum mechanics for nuclear processes required the violation of energy conservation. Hence, the appearance of Landau’s paper in 1932 was a coincidence. However, Landau did address what is now known as the “Chandrasekhar mass” for white dwarfs, and his concept of a compact star was a creative departure.

More than 250,000 papers have been written since, with either the words “supernova” or “neutron star” in their title or abstract (according to NASA’s Astrophysics Data System, adsabs.harvard.edu/abstract_service.html). Four Nobel Prizes in Physics have been awarded for work involving supernovae and neutron stars in some way. As of 2014, more than 6,500 supernovae have been discovered. The theory of cosmic-ray acceleration in supernova remnants is now a well-developed topic in modern astrophysics. However, the leap of imagination shown by Baade and Zwicky in 1934 in postulating the existence of two new classes of astronomical objects, and in connecting three now central astronomical fields into one whole, still leaves one breathless. Even decades later, such a reaction continues to be a fitting tribute to these landmark PNAS papers (1, 2).

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