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.

Getting started

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

pip install photerr

Note that PhotErr requires Python >= 3.8.

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)

This uses all of the default settings for the LSST model, which includes 10 years of observations. If instead, you want to calculate errors for LSST year 1, you can pass the nYrObs argument to the constructor:

errModel = LsstErrorModel(nYrObs=1)

Another parameter you might want to tweak is the name of the bands. By default, the LsstErrorModel assumes that the LSST bands are named u, g, etc. If instead, the bands in your catalog are named lsst_u, lsst_g, etc., then 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!

The other big thing you may want to change is how the model handles non-detections, which are any "observed" fluxes with negative values. By default ndMode="flag", which means that the error model will flag these values using the flag set by ndFlag, which defaults to np.inf. However, you can also set ndMode="abs", in which case the error model takes the absolute value of the fluxes before calculating magnitudes. This is useful if you don't want to worry about non-detections, but it results in a non-Gaussian error distribution for low-SNR sources. You can also set ndMode="sigLim", which clips all magnitudes at the n-sigma limit set by the sigLim parameter. For example, if nMode="sigLim" and sigLim=1, then all bands will be clipped at their 1-sigma (coadded) limit.

Besides the parameters described above, there are many other you can tweak to fine tune the error model. To see all available parameters, you can either call help on the error models params object,

help(errModel.params)

or look at the docstring of the corresponding parameters object,

from photerr import LsstErrorParams
help(LsstErrorParams)

All model parameters can be overridden using keyword arguments to the error model constructor.

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, PhotometricErrorModel, which is not defaulted for any specific survey. To instantiate PhotometricErrorModel, there are several required arguments that you must supply. To see a list and explanation of these arguments, see the docstring for ErrorParams.

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 the parameters from Ivezic (2019). 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. 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
Sam Schmidt