robin_astro

If you are only interested specifically in the sky brightness in each photometric band though why not measure it directly from images taken through each filter using stars as flux references? (Though you would still need to correct the stellar fluxes for the effects of atmospheric extinction) Cheers Robin

The spectrum of a star varies significantly in both intensity and the shape of the spectrum with altitude depending on the air mass, due to atmospheric extinction. A simple slit spectrograph will give you the data you need (The sky background comes for free with any astronomical spectrum and has to be subtracted to give the spectrum of the target) but you will need some way of absolute calibrating the result. For astronomical objects this is done by measuring a reference star and calibrating against a published spectrum defined as measured at the top of the atmosphere. To measure the sky brightness at the Earth's surface though you would not want to include the atmospheric extinction contribution in your measurement so you would need to separate out the instrument component and just correct for that. Christian Buil's webpage here holds some clues to how this could be done http://www.astrosurf.com/buil/isis/guide_response/method.htm Cheers Robin

A favourite tweet from one of the ASAS-SN team, Though when looking at some of the differences between observers in the variable star databases, I sometimes wonder if it should be an elephant (as in the room)

The problem with binning/smoothing/stacking is you can reduce the contrast of any outliers making them more difficult to spot. In many (most?) measurements it is the systematic errors which limit accuracy and outliers add systematic errors which are much more insidious and difficult to recognise compared with any effect of slightly lower SNR. (A hot/cold pixel moving in and out of the aperture can look a lot like an eclipsing variable!) Ideally it is better to analyse the subs separately, dealing with any outliers at this stage eg with a sigma clip (or if present in all of them with a bad pixel map) Cheers Robin

ISIS is very powerful and although it is possible to use ISIS to process Star Analyser spectra, only a masochist would probably use it for this. It is really designed for highly automated rigorous processing of spectra from slit (or fibre fed) spectrographs to produce research quality spectra. For the beginner, programs like Visual Spec and RSpec are much easier to use with the Star Analyser.

The dispersion (Angstrom/pixel) will stay the same provided you do not change the distance of the grating from the sensor so you can just use the zero order with the dispersion you calculated from the Balmer lines. (4 Aur is A1v so perfect for this) See video # 24 here to see how to do it in RSpec https://www.rspec-astro.com/more-videos/ Cheers Robin

That's much better. (No more of that terrible chromatic aberration) Your identification of the O2 telluric band looks ok so your wavelength calibration should be roughly correct. Capella is a G type star (G3iii) though so the spectrum is mostly a forest of blended metal lines at this resolution and will not show obvious Hydrogen lines. It is best to use a main sequence A star to start with so you can use the clear Balmer lines to focus on and produce an accurate wavelength calibration which can then be transferred to any other target. Capella should look like something like this after correcting for instrument and atmospheric response. Try overlaying a G star spectrum from the library in RSpec on your spectrum and see if anything lines up. The colour camera will make this more difficult though because of the humps and bumps in the camera response where the filters overlap. (The big dip at ~5700A in your spectrum for example) Cheers Robin

Only provided you preserve the precision in the result. For example averaging a series of 16 x 8 bit images to produce an 8 bit precision result is not the same as summing them and expressing the result to 12 bit precision

Yes the dimensions are assumed to remain constant under rotation but the mean frequency of the photons is based on transitions in a large population of randomly oriented atoms so is not orientation dependent. These kinds of arguments could equally be applied to almost any observation, even those of flat earthers. 😃. In the absence of evidence, only Ocam's razor can save us from these. Relativity explained anomalous observations. I would argue unless there is evidence to the contrary there is "nothing to see here". Cheers Robin

True and since my apparatus is made up of solid components the inter-atomic forces which define its dimensions would have to be anisotropic in an anisotropic speed of light universe. This was not the argument put forward in the original article though which claimed that in a relativistic universe it was impossible to measure the speed of light independently in both directions. I claim that my apparatus can do this without needing to resort to a round trip or two observers with "synchronised" clocks.

Most people normally run the Star Analyser without guiding, taking short exposures and stacking them but the distance from grating to sensor is not that critical so this might allow you sufficient leaway to mount the grating before the OAG say and you can still guide on a field star zero order if you want. You can use my calculator hosted on the RSpec website to explore the range. https://www.rspec-astro.com/calculator/ (Closer gives a more concentrated but lower resolution spectrum for fainter objects while a larger distance gives more resolution up to a point for brighter objects. Avoid going too close and getting warnings but you can increase the distance until you get a warning about problems fitting the spectrum in the field.) Cheers Robin

Hi Steve, 50mm spacing is a fine starting point for your sensor There are a few obvious issues 1. Yes you have severe chromatic aberration which is varying the focus along the spectrum and causing the fishtail effect. Fast achromatic refractors are not good for spectroscopy. The Newtonian will be much better. 2. It looks like you have some sort of Bayer pattern in the image. Does your software think it is a colour image ? 3. Your first two spectra may be over exposed. Err on the underexposed side to start with which makes it easier to see and focus on the features in the spectrum. eg see the faint spectrum of a cool star at the top left of the wide field image which shows molecular bands before it goes way out of focus into a broad fishtail at the IR end Cheers Robin

Indeed. This is conceptually similar to my suggestion here. I am still to hear a convincing argument that this cannot demonstrate that the speed of light is isotropic to any given degree of precision. (My tests have already demonstrated this to 10^4) Robin

This was with a LHIRES III telescope mounted slit spectrograph at ~0.4A resolution. It is a notoriously unstable instrument so I superimposed precise wavelength markers on the star spectrum with a calibration lamp. I talk about it briefly here at 18:36 min https://britastro.org/video/13862/14769 Ultimately though slit spectrographs are not so good for precise radial velocity measurement where you are trying to measure the centroids of lines accuracy because the shape of the line can change significantly depending on where exactly you place the star relative to the central line of the slit. Fibre fed spectrographs are better in this respect because the fibre scrambles the profile. (As well as the big advantage of mounting them off the telescope in a temperature controlled environment) These (and the echelle advantages) are the key things that allowed Christian to get about 2 orders of magnitude more precision than here. He is also an extremely skilled observer ! Cheers Robin

Yep it gives you a double hit. You use all the photons and cross correlation over a wide wavelength range gives you incredible precision (again helped by the choice of star, G/K/M dwarf stars have a lot of lines)

I think the current state of the art is the ESPRESSO spectrograph on the VLT which was specified for 10cm/s precision and recently got down to 30cm/s when measuring Proxima Centauri-b and were able to detect activity due to star spots https://arxiv.org/abs/2005.12114 Robin

For bright targets I suspect you will find the systematic errors are much larger than the photon statistics. In Christian's case he believes they are fibre noise and spectrograph thermal stability. In the professional case ISTR is the stability of the star which makes sub m/s precision difficult

As an example here are some measurement I made of the variations in the radial velocity of red supergiant Deneb due to non radial pulsations which are several km/s and as far as is known are chaotic in nature, compared with the much more stable main sequence star Vega.

The answer is yes it is done to this precision by professionals for measuring the wobble due to exoplanets. As you say you do have to make corrections for many factors and chose your star as the stability of the star puts a lower limit on the measurement. (Fortunately In the search for planets capable of supporting life the stars are likely to be stable, like our sun for life to evolve). You might be interested in this measurement by Christian Buil which describes in detail how it can be done even by an amateur to a 1 sigma precision of 5m/s http://www.astrosurf.com/buil/exoplanet2/51peg.htm Cheers Robin

Give me a grant and I will build an instrument to improve the precision (The bigger the grant the greater the precision 😀 )

Actually I have already done it when testing the stability of my ALPY spectrograph. (To a precision of better than 1 in 10^4) The spectrograph consists of a lamp filled with excited neon atoms, a transmission diffraction grating and a camera recording the spectrum, all mounted rigidly in a line. I pointed it in a number of different directions including east and west for example. There was no detectable movement in the position of the centroid of spectral lines on the camera sensor as measured from the counts in in each pixel. ie the measured wavelength was constant . For this to be true in an anisotropic c universe either the dimensions of the instrument must depend on the orientation in a complex way (the camera sensor is orthogonal to the light beam) or the mean frequency of the photons (the clock) changed depending on the orientation of the instrument which seems unlikely given the random orientation of the atoms in space. Cheers Robin

I would say the relationships between wavelength, frequency and velocity and between the wavelength and the diffraction pattern are more universal as it is independent of the physical nature of the wave. (It is effectively just geometry)

It depends on the size of the effect of course but in principle as a thought experiment you could use a rigid stick so the two are guaranteed to be comoving. Perhaps though in a universe where the speed of light is anisotropic the length of the stick depends on the orientation 😉

Since the speed of light connects frequency and wavelength and diffraction depends on wavelength shouldn't anisotropic c move the position of the spectral lines from my spectrograph calibration lamp when pointing in different directions? Robin