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

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?

• – uhoh Jan 1 '20 at 16:00

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 $$F(\nu) \propto \nu^{\alpha}$$, 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.

• Thanks for the speedy answer! In a really small telescope like a 2.4 inch I have crudely estimated that +16.5 magnitude is only about a photon per second plus/minus a factor of ten, so for a hobbyist I think that it's either run all night with a photomultiplier tube and some elaborate pulse timing electronics, or get a fairly decent sized telescope and have a potentially useful photocurrent. – uhoh Jan 1 '20 at 18:00