Entering magnitudes instead of fluxes into Phoebe?

[kaleetock]

Hi! I am a new Phoebe user trying to enter magnitudes instead of fluxes into Phoebe using the following command:

b.add_dataset('lc', times=ts_2pv, magnitudes=mags_2pv, dataset='lc02')

This does not give an error, but then when I try to print them using

print(b['magnitudes@lc02@dataset'])

it says "Parameter Set: 0 parameters" and when I try to plot them it tells me that there is nothing to plot.

If I rename my "magnitudes" to "fluxes" in the data entry step, it will both print and plot my data (though in that case I get an error when I call run_compute). Any wisdom would be greatly appreciated!

[kecnry]

Phoebe currently works strictly in fluxes, so you'll need to convert your magnitudes to fluxes before attaching the dataset.

Support for converting within phoebe is on our list of feature requests, so might be available in a future release. If you'd be interested in helping develop or test that, let us know!

[kaleetock]

Ok, I converted my calibrated magnitudes to calibrated fluxes (to within a scale factor. I think.). If I did that correctly, it still would only work for a Bessel-V filter. If I confirm the conversion and find the corresponding conversions for other filters, I'll be happy to share.

However, in the meantime, I'm still struggling with Phoebe. My bar is low: I just want to put in my data and get out something resembling the lightcurve I know is there. I made a Colab at the link below. What am I doing wrong? Thanks so much for any wisdom!

https://colab.research.google.com/drive/18yYTiyjlhSojgELV_2PjIlPlQmdg8krn?usp=sharing

[kecnry]

A few suggestions:

• run_compute runs the forward model only - it takes all the input parameters and creates a synthetic model.
• if you also pass compute_times/compute_phases when adding the dataset, then the synthetic model can be computed in evenly spaced time/phases rather than those matching the dataset
• the main difficulty you have in plotting the observations and the synthetic model is the flux scaling. My suggestion would be to use pblum_mode='dataset-scaled' for now, and later down the road consider if you want to actually fit for passband luminosities (which I would suggest if you eventually do MCMC).

You may also find some of the notebooks and recordings from the 2021 workshop useful. Just keep in mind some of these do use unreleased features (although we tried to state when that was the case) and are not kept up to date as the code changes going forward. Since the workshop was so recent, it should still be quite current and you shouldn't really run into any changes yet.

[kaleetock]

Thank you so much for the links and workshop videos; these will keep me busy for a while! :)

Could you let me know how to convert between W m^-2 and W m^-2 Hz^-1 ? I gather one multiplies by a frequency, but which frequency?

Thanks again for the references and resources! :)

[mfitzasp]

We can convert magnitudes to Janskys and then Janskys to W/m2/Hz but we don't know how to go from W/m2/Hz to W/m2 for a given filter. It appears PHOEBE wants W/m2. Is it as simple as multiplying by the central frequency (1/Hz) of the filter?

[aprsa]

Let me try and elucidate this. PHOEBE works in fluxes to avoid problems with calibrations (see the IAU resolution B2). If you have magnitudes, you need two constants that are, fortunately, quite inconsequential unless you are trying to get distances figured out as well. The first is m₀, the magnitude zero-point, and the second is f₀, the flux that corresponds to the zero-point magnitude. In a nutshell, to convert from magnitudes to fluxes:

• if you have differential (relative) magnitudes, select m₀ for each passband to be close to the quarter-phase magnitude and then do f_k = 10^{-2/5 (m_k-m₀)} for all observed m_k;
• if you have all-sky (absolute) magnitudes and do not care about absolute fluxes, select a single m₀ for all passbands that is close to a single passband's quarter-phase magnitude; then transform all magnitudes to fluxes using that same m₀ by the same equation as above;
• if you have all-sky (absolute) magnitudes and do care about absolute fluxes (i.e. to determine distance, reddening, etc), you need to calibrate m₀ and f₀ appropriately, which is outside the scope of PHOEBE. You need to concern yourself with the bolometric correction (cf. the resolution above) and the actual passband calibration, which is instrumental and had to have been used when calibrating magnitudes in the first place.

If you can provide me with your actual use case, I might be able to provide further guidance.

One last thought on the units: PHOEBE calculates intensities from each surface element, which are in W/m³, and then integrates them into fluxes, which are in W/m², that are then compared to observations. Intensity is a local passband quantity that varies across the star; flux is a global passband quantity that varies with time.

[mfitzasp]

We do have absolute magnitudes. They are colour-term corrected such that the filters are very good representations of the standard filtersets and have very high confidence that they are accurate measurements of absolute magnitude on the standard scale. We have ugriz and BV filters, although at the moment we are playing around just with the B and V filter data to see if we can get PHOEBE to work. Due to the large number, and quality, of the filters and telescopes available for us to observe and we are currently using an Algol detached binary as a test object, it would be good to see if we could transform the absolute magnitudes into absolute fluxes to estimate the distance and reddening.

[mfitzasp]

No problem, thank you very much! Looking forward to it! It would be nice to get my head around the conversions (even if the helper function makes it realtively straightforward anyway).

Thanks for your help!

[mfitzasp]

Hope you are doing well, I was wondering if you had thought about this more in the intervening handful of months :)

[aprsa]

Thanks for the ping on this -- I'll refresh my memory next week and see if I can come up with something coherent soon.

[mfitzasp]

No problem! Thanks for taking a look :)

[mfitzasp]

Hi! I was wondering if you'd had a chance to look at this? I appreciate there are a hundred other higher priorities though :)

[aprsa]

I've been on this for the last week and I have a jupyter notebook essentially ready that demonstrates all the points I raised earlier. It is quite intricate and I will try to briefly summarize it here, and -- once the notebook is polished -- I'll send out the link to it; I just didn't want to leave this hanging even longer than it already has been. We're preparing a workshop that starts in less than a month so time is a commodity in short supply these days. Also note that there's a bug with latex markup that doesn't render some of the equations below; hopefully they resolve it soon and markup starts to work automagically.

• The measured quantity on a photometric CCD telescope system is passband flux (as opposed to flux density). In particular, it is the count of detected photons per second in a given amount of time. This photon count will depend on all instrumental aspects of the observational setup: filter transmission, optics, CCD QE, ... These are instrumental passband fluxes and they differ from site to site.
• Next, we need to reconcile site differences. For that we observe standard stars and we measure their own instrumental passband fluxes. For each standard we have a published value of the corresponding flux density that we will have to match. In order to do that, we need to calculate instrumental flux density of the calibration star. How we do that depends on the processing pipeline. I would argue that the best way would be to do this:

$$ f_\lambda^\mathrm{instrumental} = \frac{\int_\lambda \lambda I(\lambda) P(\lambda) d\lambda}{\int_\lambda \lambda P(\lambda) d\lambda} = \frac{f_\mathrm{pb}^\mathrm{instrumental}}{\int_\lambda \lambda P(\lambda) d\lambda}, $$

       where $I(\lambda)$ is the (unknown) spectral energy distribution of the observed calibration source and $P(\lambda)$ is the passband response.

• This instrumental flux density is passband-independent -- it is a constant value across the entire wavelength span. If integrated over the passband-weighted response, it would yield the same integral as the source. We can now calibrate it: we know what $f_\lambda$ of the calibration source should be (for example, from the STmag calibration), so we have a simple scaling factor that maps $f_\lambda^\mathrm{instrumental} \mapsto f_\lambda$ that we can apply to the actual source of interest.
• We now have calibrated flux density $f_\lambda$. But this is flux density, not flux, and we need to convert it back to passband flux so that PHOEBE can use it. Thus:

$$ f = \frac{1}{hc} \int_\lambda \lambda f_\lambda P(\lambda) d\lambda = f_\lambda \left( \frac{1}{hc} \int_\lambda \lambda P(\lambda) d\lambda \right) \equiv f_\lambda A_\mathrm{photon}. $$

• So how do magnitudes come into all of this? The exact same way. We either refer to passband magnitudes or magnitude densities (more frequently known as monochromatic magnitudes). They are computed from:

$$ m - m_0 = -\frac 52 \log \frac{f}{f_0}, $$

       where $m_0$ and $f_0$ are calibration constants (for example, $f_0 = 1 , , \mathrm{erg}/\mathrm{cm}^2/\mathrm{s}/\overset{\circ}{A}$ corresponds to $m=-21.1$ for the STmag system).

• In order to properly convert magnitudes to fluxes, we thus need to know how the conversion from observed fluxes to flux densities was done under the hood. Here I covered what I think is the most intuitive way. Other ways include bolometric weighing (i.e. energy- rather than photon-weighted), effective wavelength correction, etc. Then we simply need to undo that and we will get proper fluxes that PHOEBE can work with.

Thank you for bearing with me with the delay in responding. This semester has been just crazy...

[kaleetock]

Thank you so much for this comprehensive response. The latex mostly works on Github where I am reading this, so all is well. My semester has been crazy too, and I'm looking forward to digesting the explanations above once it is properly finished. (One of these days I'll make it to the summer workshop--this summer doesn't work, unfortunately.)

Thanks again so much!

[aprsa]

In the hope it helps, here is a notebook that should elucidate some of the finer points of flux calibration. I'd love to receive any and all feedback on it.

[kaleetock]

Thank you so much for the notebook! I appreciate the graphs and can tell that it will be helpful once I dig into it. :)