Colour dependent photometric residuals

Starting by matching calibrated and corrected (for mag bias, spatial structure, and field offset) ZTF g and r-band photometry to PS1 (after removing galaxies), I investigate a number of fields for residual photometric trends.

In the figure above we see that there is only moderate structure in the g-band residuals with g-r colour, but strong structure in the r-band. This strongly suggests that additional colour corrections are required to better calibrate ZTF PSF photometry.. The source is likely the difference between PS1 and ZTF colour response (which creates second order effects with airmass, reddening, etc.)

For the r-band we see that there is a systematic dog leg of residuals around g-r = 1.2. We mark and select the two groups of stars with similar colours, but very different systematic residuals, for further study.

In the figure above we see that the blue points (with positive g_ztf - g_ps1 systematic residuals), are distributed over a spread of magnitudes while the green points (with strongly negative residuals) are generally faint source which form a discrete feature in the CMD. The second plot shows that the residuals are not very dependent on the source brightness in this field.

To better determine the nature of these two groups stars I matched all the bright source (13.5 < mag < 18) in ZTF field 297 to Gaia DR2. This gives us accurate distances, proper motions and additional colours.

From the figure above we see that the green sources are very nearby. Field 297 has a central Galactic latitude b=-75 degrees. Thus, the green points show the foreground disk M-dwarf stars, while the blue points are thick disk and red points are in fact blue thick disk and halo stars.

In the figure above we plot the absolute mags using PS1 and Gaia photometry for the stars in ZTF field 297. The PS1 data shows us that the blue points and green have significantly different absolute magnitudes. The Gaia photometry shows us that these two groups of sources actually have very different colours, yet the PS1 (g - r) colours are unable to distinguish foreground late M-dwarfs from early M-dwarfs in the thick disk. This suggests that additional colours (such as PS1 i-band), are needed to properly calibrate red ZTF stars as shown below.

The plots above suggest that PS1 i-band data can be used to remove residual trends. However, for stars with g - r < 1.0, the PS1 (g - r) mags should be best.

Residual trends in Other ZTF Fields

Among the fields in the plot above we see a trend where fields closer to the Galactic plane (e.g. 682, blue pts) have less significant trends in their residual.

This flattening trend becomes more extreme in crowded fields nearer to the Galactic plane. For example, ZTF field 487 (l=36.56, b=3.03), exhibits very different residual structure than the halo fields as shown below.

ZTF field 487 has very significant variations in reddening across the field as shown by the quadrant colour distributions below. This complicates interpretion of the cause of the residuals.

To some extent the structure may be similar, but the lack of blue stars may make it less evident. Additionally, the crowded Galactic plane fields have far more calibrators leading to more accurate colour coefficients and zero points. It is possible that the redder average colours of the calibrators in these fields also reduces the residual colour trend. Even internal to the quadrants there are varying degrees of reddening in this field.

The other Galactic plane fields shown below also do not exhibit the strong colour dependent residual photometric structure in r-band that is seen in the halo fields above. However, in these cases the stellar population is very different.

The foreground disk stars still produce a feature in the r-band residuals of the Galactic plane fields (at g-r ~1.45). The exact location of this feature varies slightly in (g-r) between the fields. This is likely due to the slight amount foreground reddening for these foreground stars that also varying with Galactic latitude and longitude. This feature is expected to be more evident at fainter magnitude limits where the number of M-dwarfs dominate.

The variations of the colour dependency of photometric residuals with field will make corrections difficult. It may be necessary to perform colour corrections on a field or even CCD or quadrant basis.

Conclusions for residual colour trends

There is also evidence for trends in the residuals for calibrated and corrected g-band photometry. However, these appear much smaller. The lower amplitude may be due to ZTF g-band being closer to PS1 g-band than ZTF r-band is to PS1 r-band.

Residual trends with PSF shape

Note 1: chi may be more useful than FWHM since it is possible to average over all observations, while FWHM varies significantly between each observation with seeing (thus requiring normalization).
Note 2: values noted as Chi^2 below are actually just Chi.

In the plot above we see that the average PSF chi values vary with the colours of the stars. This strongly suggesting that PSF shape also varies with colour.

Another means of quantifying the PSF shapes of sources is their sharpness. Here this is define as:

Another expectation is that the PSF shape will vary with location. This variation is accounted for in ZTF using the linear model.

If we look at the spatial distribution of average chi or sharpness we see that both are also dependent on location. Likewise, the average PSF Fit chi varies with position. The structure in these plots mirror each other since the PSF shape dominates each quantity. Interestingly, we see that the smallest chi values are in the corners (rather than the center where more calibrator stars are expected).

When we look at the average chi distribution over a full CCD field (CCD 07) we see the circular structure evident in the photometric residual maps is present. That is to say, at least some of the photometric residuals we see are likely due to poor PSF fitting. The same structure is seen in multiple fields.

To separate the colour trend from the spatial trend, we fit the trend (as shown above) and subtract it. The resulting colour-corrected trend is shown below.

As expected we get a cleaner view of the spatial trend in chi. This is almost certainly due to variation in the PSF shape with position.

Trends in photometric residuals with Chi and Sharpness

Stetson and Harris (1988, AJ, 96, 909, Fig. 28) suggest that the distribution of Chi values with magnitude should be close to 1, and have no trend in magnitude. However, as shown in the figure above, in r-band, this is clearly not the case within some ZTF fields. This is likely, in part, related to the variation in Chi with colour in feilds where the average star colour varies strongly with brightness.

To check this we take a closer look at a quadrant with strong structure (ccd 16 quadrant 2). This has a typical CMD. However, the r_ZTF - r_PS1 residuals do not show significant structure with g - r colour. This is very different from the less crowded halo fields above. Note, the is a systematic offset averages out when stars with r > 18 are included.

The lack of a difference between the SEDs of mid and late M-dwarfs within the r-band filter does not affect fields near the Galactic plane since these stars are sparse in the foreground and reddened to much fainter magnitudes when at greater distances.

When we plot the variation in Chi from the PSF fits vs source magnitude we see clear trends that correlate with the trend in r-band residuals. This is very different from halo field 297 (shown above) where no obvious trends were seen. The relationship here between Chi and r-band residuals is thus not straight forward in crowded Galactic plane fields due to a magnitude and colour dependence.

Looking the distribution of sharpness values, we see that there are clearly two separate sets of points within a quadrant which are offset. However, both exhibit the same linear trend between sharpness and residuals. In addition, there is a clear variation in sharpness with source magnitude (likely caused by the brighter fatter effect), pointing to variations in the PSF shape with magnitude.

Examining the spatial distribution of sharpness from the two sets of points above we see a very clear separation (Note, this quadrant is on the edge of the camera). The plot suggests a distinct change in PSF shape that gives rise to a systematic offset in sharpness and thus residuals. A change in PSF shape is also suggested by the residuals of difference images for this field/quadrant.

By correcting the residuals for the sharpness trend seen above for each of two sets of points we arrive at the figure above. Notable is the removal of the halo of outlier sources at faint magnitudes is corrected by using the linear relationship between sharpness and residuals. Nevertheless, the relationship between sharpness and photometric residuals was seen to vary between quadrants. The relationship is poorly defined in many quadrants (as the residuals are too small) and appears to vary in slope for the same quadrant+filter when observed in different fields. This suggests a simple correction to remove residuals based on sharpness or chi statics is not possible.

Overall Conclusions

Note: all of the photometry used here already has the underlying spatial structure removed, so the PSF-based effects can only be seen chi and sharpness statistics.

In crowded fields, where the colour dependence of the photometric residuals is smaller than halo fields, there are trends in PSF fit chi and sharpness values with source brightness. These trends are strongly correlated with the residual difference between the calibrated ZTF and PS1 magnitudes.

In summary, improved ZTF photometric calibration relative to PS1 requires additional colour information as well as fitting and removal of the remaining trends in residuals with colour and brightness per field. Parameters such as chi and sharpness can be used to further improve the calibrations, but these are quadrant and field dependent.