I am wondering whether some of the physically smaller stars, for example white dwarfs, might exhibit intrinsic light variations on the sub-second scale- say, at a frequency of the order of 0.05 seconds? Factoring in the speed of light, for a star to vary at this rate it would have to have a diameter less than about 15,000 km - approximately Earth size.
I am tentatively (here) trying to scope a project (perhaps a BSM project?) that could detect such variations. I am unaware as to whether anyone has pursued such a study before, but perhaps I haven't searched the literature hard enough. If not, this would be a project of pure discovery.
I am pretty vague as to what the undelying mechanism of the variation might be - perhaps some kind of star-quake which ruptures the very strange "degenerate" surface of a white dwarf? Anyway, such questions need only be pursued if the putative variation is in fact detected by observation.
Note the deliberate use of the word "intrinsic" - I am deliberately excluding from discussion such objects as milli-second pulsars and the like ... I don't think of these as intrinsically varying.
My thoughts along these lines were prompted by the claimed ability of CMOS astro-cameras to capture and download images rather more rapidly than can a comparable CCD astro-camera. Bearing in mind the Nyquist criterion, this led me to wonder whether it might be possible to image a star with a CMOS camera, at a fairly rapid cadence - in this case at 0.025 seconds?
There are several ZWO CMOS cameras on the market which claim to be able to image faster than this rate (and by use of ROI maybe could operate even faster). For example the ASI 174 MM cooled camera claims to be able to operate at 128 FPS.
One practical problem with the above idea is that an image cadence of 40 per second would not necessarily give the camera sufficient time to collect enough light in individual images to achieve a satisfactory SNR. Moreover, the apparent faintness of white dwarves just compounds this "light-gathering" problem.
My own scope is an 8-inch SCT and my guess is that the above scenario is way beyound its capabilities, and I suspect that is even more true of the "small refractors" in the BSM network. Not sure about other telescopes in the AAVSO Network?
I would appreciate any comments please as to whether such a project as described above makes sense theoretically? I am trying to think "outside the box" here, but perhaps not too far outside ...
Also, would anyone like to take a stab at calculating the aperture needed to make the above project technically feasible?
Certainly there are objects with very fast variation, such as cataclysmic variables where you have orbital motion, stellar rotation, and hot spot eclipses. There are lots of time scales available on other normal stars as well, such as astroseismic multimode vibration/pulsation. If the entire star is involved in the variation, then the smaller the star, the faster the potential variation. In cataclysmic variables with mass transfer, the region producing the light can be much smaller than a typical star.
Very little work has been done on rapid cadence photometry. There are multiple issues. First, most of the small stars tend to be faint, and if you want to have enough signal/noise so that you can be sure the variation is real and not just noise, you need big aperture. Working at 0.1sec exposures means you work a factor of 100 (or 5 magnitudes) brighter than when you are taking 10 second exposures.
Second, and probably most important, is scintillation. There are nice tables showing how scintillation affects observations; it is a function of exposure time, airmass and telescope aperture. In general, I don't recommend exposures less than 5-10 seconds with amateur-class telescopes, if you want 0.01-0.02mag precision. Even at 5 seconds, though, there are few targets that have been observed.
The CMOS cameras are certainly capable of short exposures. I've used the ZWO ASI-183mm camera here with 0.1second exposures, and it works fine. Windowing/region of interest exposures can be much shorter, though the smaller the field, the harder to find a comp star. One of the big problems is overhead, as the current system both calibrates each image as it is taken, as well as doing plate solving, before storing to hard drive. You can take a 0.1second exposure, but it is many seconds before you can take the next 0.1second exposure. I'm working on reducing that overhead, but for a true take-them-as-fast-as-possible setup, we'd have to do a lot more work. Not impossible, but also a low priority software effort at this time. Doing some testing with your home system is a good idea! Certainly, planetary photographers have software that will allow you to take very high cadence time series, so software other than the ACP/MaximDL setup we use with the BSM systems might be better for such a project.
Thanks for your comments (and prompt response).
1. You have definitely confirmed for me that aperture is the big issue here. When I do a few back-of-the-envelope calculations, it becomes pretty clear that seriousaperture would be needed - around 100-inch and upwards to get a 5-magnitude boost over and above an amateur scope. Way beyond amateur capability!
2. About scintillation: On the face of it, that would definitely be an issue (assuming one could get the aperture) but, at sub-second exposures, I wonder if the problem would be tamed somewhat? In other words, given that we are talking here about the movement of/in air cells, can the atmosphere scintillate all that quickly?
3. Regarding ROI and comparison stars: Good point, but initially at least, to detect these kinds of phenomena it would only be necessary to check for the existence of a variation(not so much its actual magnitude - comparative measurement could come later). Also, it would not be necessary initially to go into multi-wavelength measurements - just V would do.
4. Another thought: Would it be possible (asuming that the above problems could be sorted) to compare a companion white dwarf (eg. proxima Centauri) with its parent star - if it has one? There would need to be some way of scaling down the apparent magnitude of the parent star to something like the magnitude of the companion to avoid over-exposure of the parent. If this could be done, it might also help with the scintillation problem, because, more than likely, we would be viewing both stars through the same air cell at the same time.
5. Finally, I'm not sure I explained myself properly when talking about "Earth-sized stars": It seems to me that there is a lower limit to the variation frequency that can be observed, of a star that appears to us as a point source; it depends on the size of the radiating object - that is, even if a star of diameter 15,000 kilometres in fact varies faster than 20 times a second, we will not be able to detect this except as a 20 cycle-per-second variation, because of the light transit time across the disk of the star. Does this make sense?
If you are interested in scintillation, and have a little math background, I recommend the theoretical papers by Andy Young in the 1960's and 1970's (including a Sky and Telescope article) on seeing and scintillation (mostly in JOSA), and the resultant empirical paper set by Dravin et al:
The basic answer is yes, the atmosphere can change that quickly. I can readily think of several ways of defeating scintillation:
- use a larger telescope. That averages over the number of atmospheric cells, and is why high cadence light curves from 4-8m class telescopes always look smoother. You also get higher signal/noise!
- use longer exposures. Not an option if you are going high cadence!
- only observe on the meridian, and of sources that transit close to the meridian. The less air you look through, the lower the scintillation noise.
- go to a mountaintop. The less air you look through, the lower the scintillation noise.
- find a way to anticorrelate observations.
The latter might be feasible. If you can use two telescopes, pointed at the same object and with synchronous exposures, you can keep only the signal that is correlated between the two systems. That way, you get rid of most of the scintillation noise and are left with the true signal. This is not easy to do in practice. Another method (as you suggest) is to observe two close sources, so that the observations are simultaneous and through the same air column. Based on interferometry, these two stars would have to be very close together, typically 50arcsec or less - not a common occurrence.
When I was in school, we were taught that there are many different time scales in astronomy, such as the dynamical time scale (kind of a sound-crossing timescale) and the evolutionary time scale. The light-crossing time scale typically says that variability has to be longer than the time necessary for light to travel across a source, otherwise you won't see the correlated variation (as you mention). This would be a small fraction of a second for something the size of the earth. Larger sources can seemingly vary faster than this, depending on a number of factors such as beaming.
High-cadence work can be fun, but just realize that discerning true variation from noise, especially if the variation is not periodic, is very difficult and takes some thought. I don't think it is possible with the current BSM network, but an individual can create their own system to get results.