PhotErr

PhotErr is a photometric error model for astronomical imaging surveys. It implements a generalization of the high-SNR point-source error model from Ivezic (2019) that is more accurate in the low SNR regime and includes errors for extended sources, using the models from van den Busch (2020) and Kuijken (2019).

PhotErr currently includes photometric error models for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), as well as the Euclid and Nancy Grace Roman space telescopes.

If you use this package in your research, please cite the following paper

@misc{crenshaw2024,
      title={Probabilistic Forward Modeling of Galaxy Catalogs with Normalizing Flows}, 
      author={John Franklin Crenshaw and J. Bryce Kalmbach and Alexander Gagliano and Ziang Yan and Andrew J. Connolly and Alex I. Malz and Samuel J. Schmidt and The LSST Dark Energy Science Collaboration},
      year={2024},
      eprint={2405.04740},
      archivePrefix={arXiv},
      primaryClass={astro-ph.IM}
}

Getting started

PhotErr is available on PyPI and can be installed with pip:

pip install photerr

Note that PhotErr requires Python >= 3.10.

Once installed, you can import the error models. For example, to use the default LSST error model,

from photerr import LsstErrorModel
errModel = LsstErrorModel()
catalog_with_errors = errModel(catalog, random_state=42)

The error model expects an input catalog in the form of a pandas DataFrame with true magnitudes, and it returns another DataFrame containing observed magnitudes and photometric errors. Any extraneous columns in the DataFrame (e.g. a redshift column), remain in the new DataFrame - their presence does not effect the error model.

If compatibility with Astropy Tables, Ordered Dictionaries, etc., would be useful to you, let me know!

You can also calculate limiting magnitudes:

errModel.getLimitingMags() # coadded point-source 5-sigma limits
errModel.getLimitingMags(nSigma=1, coadded=False) # single-image point-source 1-sigma limits

Tweaking the error model

There are many parameters you can tweak to fine tune the error model. To see all available parameters, check the docstring of either the error model or parameters object. For example,

from photerr import LsstErrorModel
help(LsstErrorModel)

All model parameters can be overridden using keyword arguments to the error model constructor. Below, we explain in detail a few of the more commonly tweaked parameters.

Changing the observing duration

The example above uses the default settings for the LSST model, which includes 10 years of observing time. If instead you want to calculate errors for LSST year 1, you can pass the nYrObs argument to the constructor:

errModel = LsstErrorModel(nYrObs=1)

Changing the band names

Another parameter you might want to tweak is the name of the bands. By default, the LsstErrorModel assumes the LSST bands are named u, g, r, etc. If instead, the bands in your catalog are named lsst_u, lsst_g, lsst_r, etc., you can instantiate the error model with a rename dictionary:

errModel = LsstErrorModel(renameDict={"u": "lsst_u", "g": "lsst_g", ...})

This tells LsstErrorModel to use all of the default parameters, but just change the names it gave to all of the bands. If you are changing other dictionary-parameters at the same time (e.g. nVisYr, which sets the number of visits in each band per year), you can supply those parameters using either the new or old naming scheme!

Directly setting limiting magnitudes

By default, PhotErr tries to use the provided information to calculate limiting magnitudes for you. If you would like to directly supply your own $5\sigma$ limits, you can do so using the m5 parameter. Note PhotErr assumes these are single-visit point-source limiting magnitudes. If you want to supply coadded depths, you should also set nYrObs=1 and nVisYr=1, so the calculated coadded depths are equal to those you provided.

Handling non-detections

The other big thing you may want to change is how the error model identifies and handles non-detections.

The error model has a parameter named sigLim, which sets the limit for non-detections. By default sigLim=0, which means only negative fluxes count as non-detections, however if you set sigLim=1, any magnitudes beyond the 1-sigma limit in each band will count as a non-detection. You can set sigLim to any non-negative float.

The ndMode parameter tells the error model how to handle the non-detections. By default ndMode="flag", which means the model will flag non-detections with the value set by ndFlag, which defaults to np.inf. However, you can also set ndMode="sigLim", in which case the model will set all non-detections to the n-sigma limits set by the sigLim parameter described in the previous paragraph. Remember that sigLim also sets the detection threshold, so in effect, any galaxy magnitudes beyond the detection threshold will be set equal to the detection threshold.

One other option is provided by the absFlux parameter. If absFlux=True, the absolute value of all fluxes are taken before converting back to magnitudes. If combined with sigLim=0, this means every galaxy will have an observed flux in every band. This is useful if you do not want to worry about non-detections, but it results in a non-Gaussian error distribution for the flux of low-SNR sources.

Errors for extended sources

PhotErr can be used to calculate errors for extended sources as well. You just have to pass extendedType="auto" or extendedType="gaap" to the constructor (see explanation below for the differences in these models). PhotErr will then look for columns in the input DataFrame that correspond to the semi-major and -minor axes of the objects, corresponding to half-light radii in arcseconds. By default it looks for these in columns titled "major" and "minor", but you can change the names of these columns using the majorCol and minorCol keywords.

You can also calculate limiting magnitudes for apertures of a given size by passing the aperture keyword to errModel.getLimitingMags()

Scaling the errors

If you want to scale up or scale down the errors in any band(s), you can use the keyword scale. For example, LsstErrorModel(scale={"u": 2, "y": 2}) will have all the same properties of the default error model, except the errors in the u and y bands will be doubled. This allows you to answer questions like "what happens to my science if the u band errors are doubled."

Note it is the flux error that is doubled. This also only scales the band-specific error. The band-independent systematic error floor, sigmaSys is still the same, and so at high-SNR near the systematic floor the errors won't scale as you expect.

Other error models

In addition to LsstErrorModel, which comes with the LSST defaults, PhotErr includes EuclidErrorModel and RomanErrorModel, which come with the Euclid and Roman defaults, respectively. Each of these models also have corresponding parameter objects: EuclidErrorParams and RomanErrorParams.

You can also start with the base error model, ErrorModel, which is not defaulted for any specific survey. To instantiate ErrorModel, there are several required arguments that you must supply. To see a list and explanation of these arguments, see the docstring for ErrorModel. However, the easiest way to create a new model is to supply nYrObs, nVisYr, gamma, and m5. You might need to fit gamma to match the expected errors, however a good default guess is 0.04.

Explanation of the error model

The point source model

To derive the Ivezic (2019) error model, we start with the noise-to-signal ratio (NSR) for an object with photon count $C$ and background noise $N_0$ (which depends on seeing, read-out noise, etc.):

$$ NSR^2 = \frac{N_0^2 + C}{C^2}. $$

If we define $C = C_5$ when $NSR = 1/5$, then we can solve for $N_0$ and write

$$ NSR^2 = \frac{1}{C_5} \left( \frac{C_5}{C} \right) + \left[ \left( \frac{1}{5} \right)^2 - \frac{1}{C_5} \right] \left( \frac{C_5}{C} \right)^2. $$

Defining $x = \frac{C_5}{C} = 10 ^{(m - m_5) / 2.5}$ and $\gamma = \left( \frac{1}{5} \right)^2 - \frac{1}{C_5}$, we have

$$ NSR^2 = (0.04 - \gamma) x + \gamma x^2 ~~ (\text{mag}^2). $$

In the high signal-to-noise ratio (SNR) limit, $NSR \ll 1$, and we can approximate

$$ \sigma_\text{rand} = 2.5 \log_{10}\left( 1 + NSR \right) \approx NSR. $$

This approximation yields Equation 5 from Ivezic (2019). In PhotErr, we do not make this approximation so that the error model generalizes to the low SNR regime. In addition, while the high-SNR model assumes photometric errors are Gaussian in magnitude space, we model errors as Gaussian in flux space. However, both of these high-SNR approximations can be restored with the keyword highSNR=True.

The LSST error model uses parameters from Ivezic (2019), Bianco 2022, and from this Rubin systems engineering notebook. The Euclid and Roman error models follow Graham (2020) in setting $\gamma = 0.04$, which is nearly identical to the values for Rubin (which are all $\sim 0.039$).

In addition to the random photometric error above, we include a system error of $\sigma_\text{sys} = 0.005$ which is added in quadrature to random error. Note that the system error can be changed using the keyword sigmaSys.

After adding photometric errors to the catalog, PhotErr recalculates the photometric error from the "observed" magnitudes. This is so that the reported photometric errors do not provide a deterministic link back to the true magnitudes. This behavior can be disabled by setting decorrelate=False.

The extended source model

The Ivezic (2019) model calculates errors for point sources. To model errors for extended sources, we use Equation 5 from van den Busch (2020):

$$ NSR_\text{ext} \propto NSR_\text{pt} \sqrt{\frac{A_\text{ap}}{A_\text{psf}}}, $$

where $A_\text{ap}$ is the area of the source aperture, and $A_\text{psf}$ is the area of the PSF. Note the PSF FWHM is assumed to scale like $\text{airmass}^{0.6}$. We set the proportionality constant to unity, so that when $A_\text{ap} \to A_\text{psf}$, we recover the error for a point source.

We include two different models for calculating the aperture area. The "auto" method from van den Busch (2020) calculates the semi-major and -minor axes of the aperture ( $a_\text{ap}$ and $b_\text{ap}$) from the semi-major and -minor axes of the galaxy ( $a_\text{gal}$ and $b_\text{gal}$, corresponding to half-light radii):

$$ a_\text{ap} = \sqrt{\sigma_\text{psf}^2 + (2.5 a_\text{gal})^2}, \quad b_\text{ap} = \sqrt{\sigma_\text{psf}^2 + (2.5 b_\text{gal})^2}, $$

where $\sigma_\text{psf} = \text{FWHM}_\text{psf} / 2.355$ is the PSF standard deviation. The formula for the area of an ellipse is then used to calculate the aperture area: $A_\text{ap} = \pi a_\text{ap} b_\text{ap}$.

The "gaap" method for extended sources (Kuijken 2019) is nearly identical, except that it adds a minimum aperture diameter in quadrature when calculating $a_\text{ap}$ and $b_\text{ap}$, and then clips aperture diameters above a certain maximum.

Calculating errors for extended sources requires columns in the galaxy catalog corresponding to the semi-major and -minor axes of the galaxies (with the length scale corresponding to the half-light radius). You can set the names of these columns using the keywords majorCol and minorCol.

Authors

John Franklin Crenshaw
Ziang Yan

Contributors guide