Corpuscular Rays in St. Peter's Basilica (the Vatican)

Blog topic: 

A few days ago, I stayed in the Vatican (more about this one day symposium in another post). During the stay, I naturally visited St. Peter's Basilica.

Near Bernini's altar (made from copper stolen from the Pantheon which of course has nothing to do with our story...) I saw corpuscular rays. It may seem like some godly thing (quite appropriate for the location I guess), but from a physicists point of view, it was merely scattering by dust particles. So, I wondered, what could one say about that holy dust?

Here is the sight I saw: 

See the light of god in church, corpuscular rays

The first thing to note is the rather obvious - the dust is colorless! This means that the scattering dust particles are much larger than the wavelength of visible light. Namely, $r \gtrsim 1 \mu m$.

If the particles were to have radii much smaller than the visible wavelength, Rayleigh scattering would have been the dominant scattering process, and it would have given bluish light which scatters more effectively (as is the case with the sky). If the particles radii would have been comparable to the wavelength, we would have witnessed complex behavior, and certainly get some color behavior at some angles (e.g., as is the case with the scattering by small water droplets, which gives rise to colored haloes, arcs, glows and so forth, especially near the forward and backward scattering directions). But again, since we don't see any color, the size must be relatively large.

Next, because the dust is airborne, it cannot be too large. In fact, it cannot be falling at a speed much larger than the typical air motions in the basilica. (say,  a few cm/sec).

Because the sizes are so small, we are obviously dealing with laminar flows (i.e., non-turbulent flows around the dust... if you don't beleive me, you can check the Reynolds number for yourself). Thus, the terminal speed of the dust due to Earth's gravity is obtained by equating the Stokes drag to the gravitational acceleration:

$$ f_{drag} = 6 \pi \mu r v ~~~ =~~~ f_{grav} = m g = {4\pi r^3 \rho g\over 3}, $$ where $\mu$ is the visocity of air. Thus, the terminal speed is: $$ v_{max} = {2 r^2 \rho g \over 9 \mu}. $$ The radius must therefore be smaller than: $$ r \lesssim \sqrt{{9 \mu v_{max} \over 2 r^2 \rho_{dust} g }} \sim 10 \mu m$$

In other words, we know that the holy dust should typically be between 1 and 10 μm, otherwise there would have been at least some color, or the dust would have settled down too quickly.

We can also say something about the amount of dust, but this requires a few rough approximations.

We know that the scattered light (e.g., at 30° in the picture) has roughly the same brightness (give or take a factor of a few...) as the ambient light within the basilica. From photography, we know that outdoors we would typically need a shutter which is perhaps 100 times shorter than in the basilica (say 0.01 sec instead of 1 sec). This means that over a distance of about 10 meters (which is the length that my line of sight passes inside the "corpuscular beam"), the dust scatters light which is perhaps 100 times brighter than the ambient, to the ambient level.

This implies that over one meter, the light beam attenuates by 0.1%. Hence, the total projected area of the dust in a cubic meter of air should be of order 0.001 of a m2. If the typical radius is 3μm, we then need about 30 million particles, which add up to about 4 mg per cubic meter... give or take an order of magnitude.

We could discuss the angular dependence of the light scattering, and reach the conclusion for example that the dust particles don't have a large diffusive component, at least not one which is semi-isotropic since otherwise the backscattering would have been much brighter... but given the late hour I'll quit here.


Comments (9)

  • anon

    I've never been to the Vatican, or even to Rome so the answers to my questions may be obvious.

    It seems a little too fortuitous that you happened to see crepuscular rays in a church which makes me speculate that the church is designed to produce that effect. Certainly, the windows are relatively small and in your picture the sun is shining directly into the interior. What direction do the windows face and what time of day was the picture taken?

    I also have to inquire about the possibility of dust being added to the air to help create the effect. Is there any evidence of that, e.g. excessive dust on horizontal surfaces? Or maybe the secular, modern city of Rome produces such dust by itself.

    Jan 01, 2008
  • anon

    I think that the amount of visitors coming into the church every day is enough to bring in all the required dust, and stir the air to keep the dust afloat. When the church was built some 4 centuries ago, I don't know whether they expected so many visitors!

    Also, there are enough windows facing all directions such that it should not be a rare occurrence for sure (all you need is direct sunlight, which isn't rare in southern Europe...).

    -- Nir

    Jan 01, 2008
  • anon


    first, thumbs up for a great article on a topic that is of interest to my work (underwater visibility).

    I have a question about your climate sensitivity study. Sorry about placing this comment here, but I saw no more other fitting place to put it:

    1. if I read your study correctly then you essentially assume that the causal relationship in the best fit between CO2 and temperature is 100% from CO2 to temperature. Is this a proper reading of your study? If so then we can probably expect the climate sensitivity of CO2 to be significantly lower than in your study, since the causality in the CO2/temperature correlation in reality goes both ways.

    2. how have you dealt with methane and other non-measurable paramters in your climate sensitivity study? If you have assumed methane to be a non-factor where no data exists then this too has the effect of pushing your climate sensitivity estimate too high.

    Jan 05, 2008
  • anon

    If it is this one then the answer is that on each time scale I took all the known contributers to changes in the radiative forcing. It includes for example methane in the 20th century analysis. Of course, the estimates are only as good as the references I used.

    As for your first question, it is true that in addition to some CO2 → temperature effect, there is the opposite one of a temperature affecting the CO2. However, it does not matter for the analysis I have done. The only thing which matter is the assumption that doubling the CO2 is equivalent to a radiative forcing change of 3.8 W/m2, which I assume to be correct...


    p.s., do you scuba dive? Talking about underwater visibility, every scuba diver in Israel knows that the visibility along the mediterranean coast is always rather poor. In the red sea, however, it is always much better. I am not sure I know what the reason is, but I think it is because our mediterranean coast has a lot of find sand coming from the Nile (well, which used to come until the Aswan dam was built).

    Jan 05, 2008
  • anon

    My point is that it is very likely that methane has varied with temperature for a very long time, ever since there were plants on Earth. By not including methane where there is no data the effect is to increase the climate sensitivity. In my view it is possible to estimate previous methane levels by using the ice core data in the past 600.000 years. This gives a methane number ppb/K. This can be used to give a rough estimate of the methane level millions of years into the past, at least back to when plants evolved.

    On CO2: if I understand your study correctly you have done a regression between CO2 and temperature to find a best fit. Using 3.8 W/m2 for a CO2-doubling then enables you to calculate climate sensitivity. But my point is that if warming causes CO2 to increase, then the regression will give a false best fit. To exemplify: suppose that the REAL climate sensitivity to CO2 was 0 K/, and yet e.g. the ice ages show that there is e.g. a 3.8 K/CO2-doubling correlation (i.e. 3.8 K warming causes a CO2-doubling). Then the regression analysis would show that the climate sensitivity was 1 K/W/m2. I.e. the regression is spurious. I can't see that your analysis has taken this into account. Correct me if I am wrong.

    Also one final question: I *assume* that in your study you have operated under the assumption that there is the SAME climate sensitivity for all climate forcings (CO2, cosmis rays etc.). In my view this is highly unlikely. CO2 operates top down, first heating the top of the atmosphere and then finally reaching the oceans. The cosmic ray mechanism starts bottom up on the other hand, first heating the oceans, which then evaporates more water vapor which creates its own greenhouse effect. It seems very likely to me that the climate is much more sensitive to solar forcings than to CO2 or methane. IF you have used this assumption in your study then this will have the tendency to overestimate the climate sensitivty of CO2.

    On scuba diving: No, I run a technology company that develops underwater camera technology. Speaking of Israel. I am going there in late march for a mud spa in the dead sea. Any chance of popping by your university for a chat?

    Jan 06, 2008
  • anon

    Methane: Perhaps. In my analysis, I took previously published estimates for the radiative forcing change between the last ice-age and today. I'd like to think that those estimates also took things like Methane into account. It is not difficult I guess, because there are measurements for it in the ice-cores.

    CO2: Yes, I assumed that the CO2 introduces a radiative forcing imbalance of 3.8 W/m^2 per CO2 doubling. The regression of course does not assume that CO2 is the only radiative forcing change, it is only one of many. This gives a much smaller climate sensitivity.

    Nevertheless, there is of course the following tricky question. CO2 affects climate, and climate affects CO2. Should I therefore include the CO2 in the analysis of the radiative imbalance? The answer is of course that both options are possible, but the meaning would be different. If CO2 is included in the radiative imbalance, it is considered as an external forcing. The result would therefore be Earth's climate sensitivity without the feedback effects of CO2. (This is basically the value that the IPCC uses). Including it (at least in cases were CO2 is a result of feedbacks, such as the warming from the last glacial maximum) would give Earth's full climate sensitivity which does include the CO2 feedback.

    Assumption on sensitivities: Yes, it is assumed that 1W/m^2 from CO2 change is the same as a 1W/m^2 arising from albedo changes, etc. This is of course an approximation, and one of the drawbacks of empirical derivations of climate sensitivity, but when compared with the other option, of estimating the sensitivity using GCM's, I think the former is still a much better option.

    Your visit to the Israel: Sure. Jerusalem is on the way to the dead sea. Only 30 mins away (to the northern tip of the Dead Sea), and 10°C cooler.

    Jan 07, 2008
  • anon

    I think your analysis cannot be TOO far off regardless og the things I have pointed out because, as you yourself have pointed out, the effect of adding cosmic rays to the analysis has reduced the
    overall scattering of climate sensitivities, and the likelihood of this happening by chance is low. Thus the climate sensitivity of *cosmic rays* is probably very close to 1,4 C/doubling.

    However, it may be possible to further improve your analysis by fixing cosmic rays/insolation at 1,4 C and then letting the climate sensitivity of CO2 be a free variable. If you then regress, minimizing climate sensitivity scattering or error, you may end up with a different (and possibly lower) sensitivity for CO2.

    On Israel: that has got to be the Urban Heat Island COOLING effect. :-) Anyhoo, I'll contact you when the time is nigh.

    Jan 11, 2008
  • anon

    CO2 sensitivity: yes, it is already on my list of things to do. Note however that if the CO2 corrections mentioned by Royer et al. to the O18 are correct, then the lack of any CO2 / O18 correlations over the past 550 million years implies that CO2 temperature sensitivity should be around the 1-1.5°C range.

    -- Nir

    Jan 11, 2008
  • anon

    Terrific pages, I came upon them searching for information on the thrust force of soda bottle water rockets.

    Wikipedia has Crepuscular rays instead of your Corpuscular Rays. Perhaps your spelling is off a bit? ( I don't know enough to claim expertise)
    Also your Row boat page is interesting. I'm a sea kayaker and found your discussion interesting and different from the typical hull speed discussions I've found.
    I don't know about rowing per se, but I think I calculated the top speeds of Olympic kayakers in the Beijing Olympics at almost 12 knots, (6.17 m/s) .

    Thanks for sharing.

    Oct 11, 2011