H-band Light Curves of Milky Way Cepheids via Difference Imaging

The DEHVILS survey started in northern spring 2020 with the primary goal of using UKIRT to build a NIR sample of SNe Ia. The survey aims to measure the local growth of structure parameters and provide an "anchor" sample for next-generation high-redshift samples such as those from the Vera C. Rubin Observatory and the Nancy Grace Roman Space Telescope. DEHVILS has observed over 100 SNe Ia in YJH in its first year of operations and, with collaborators at the University of Hawai'i, over 300 SNe Ia in J.

UKIRT's WFCAM has already observed ∼17,900 square degrees of sky in J as part of the UKIRT Hemisphere Survey (Dye et al. 2018) and ∼6200 square degrees in zYJHK as part of the UKIRT Infrared Deep Sky Survey (Lawrence et al. 2007). Thanks to the large-area footprint and WFCAM's ∼1° field of view, the photometry can be calibrated relative to the 2MASS Point Source Catalog (PSC; Skrutskie et al. 2006) at the ∼1% level (Hodgkin et al. 2009). DEHVILS also uses observations of CALSPEC standard stars (Bohlin 1996) with in-focus and defocused observations to measure the calibration and linearity of the UKIRT system.

DEHVILS targeted 12 MW Cepheids from the aforementioned HST program that were observable from Hawai'i. Though these Cepheids will normally saturate at the minimum UKIRT exposure times, by defocusing the telescope we can avoid the nonlinear regime. We present the analysis for seven of these variables whose observations have been completed. Each target was observed for 11–20 epochs spread over 2–3 months between 2020 May and October.

Table 1 presents the mean H magnitudes and periods of these objects. The magnitudes and associated uncertainties are from the 2MASS PSC (Skrutskie et al. 2006) while the periods are from Riess et al. (2021). The Cepheid periods were derived while applying the phase correction procedure that is described briefly in Section 4.2 and in more detail in the appendix of Riess et al. (2018a). The procedure relies on multiband literature photometry, whose sources are shown in Tables 2 and 4 of Riess et al. (2021). The long baseline of the photometry used (∼20–25 yr) yields negligible uncertainties in the derived periods.

WFCAM is a wide-field infrared camera consisting of four detectors (arranged in a 2 × 2 array), each with a field of view of 0.21 square degrees and a plate scale of 04 per pixel. The detectors cover $13\buildrel{\,\prime}\over{.} 65$ on a side and are spaced $12\buildrel{\,\prime}\over{.} 65$ apart. Available filters include zYJHK (Casali et al. 2007).

In a given exposure, the relevant Cepheid was observed by one of the four WFCAM detectors. We obtained two images per epoch for a given Cepheid, rotated 90° from each other. The left panel of Figure 1 shows a typical image of one of our targets.

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Images of a given Cepheid were aligned by updating their World Coordinate System (WCS) information prior to running the DIA pipeline. The first image from the first epoch of a given object was adopted as the reference WCS. At least 12 bright, isolated stars were identified in all images of a given field and their (x,y) positions were used to derive geometric transformations using IRAF (Tody 1986), with iterative rejection of outliers.

This work used a modified version of the difference-imaging pipeline from Oelkers et al. (2015) and Oelkers & Stassun (2018, 2019) (hereafter OS-DIA) to measure the photometry of each Cepheid. The OS-DIA pipeline was originally designed to measure stellar photometry from defocused images generated by the Chinese Small Telescope Array (CSTAR), and was adapted to extract light curves from TESS full-frame images (FFIs) (Oelkers et al. 2015; Oelkers & Stassun 2018). The pipeline reduced more than 10⁶ images from CSTAR, and has generated more than 100 million light curves from TESS FFIs with a precision that has met the expectation of initial prediction models (60 ppm hr^−0.5; Ricker et al. 2014; Oelkers et al. 2015; Sullivan et al. 2015).

The OS-DIA pipeline uses a Dirac δ-function kernel to transform reference images and account for "non-Gaussian, arbitrarily shaped PSFs," such as those seen in the defocused WFCAM images of this work. This kernel type provides more flexibility when characterizing non-Gaussian PSFs because each individual kernel basis is independently solved for, which results in a kernel map that is not required to be Gaussian in shape. Light curves of all objects are extracted from the differenced images via aperture photometry and detrended using the light curves of sources with low dispersion that have similar magnitudes and are nearby to the variable objects on the detector. We employed the OS-DIA pipeline on the WFCAM images with a spatially constant 5 × 5 pixel kernel after our initial testing showed first- and second-order spatially varying kernels provided little improvement in photometric precision but significantly increased the runtime of the pipeline. Figure 2 shows a typical kernel for one of our images and its efficacy at convolving the reference image to match the PSF of the image to be differenced.

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We made a number of modifications to the OS-DIA pipeline to improve its performance on our defocused images. First, we used the coordinates of the center of the reference image to query the TESS Input Catalog (TIC; Stassun et al. 2018) to get a list of sources that appeared in the image. However, since the WFCAM images were defocused, there was a consistent offset between the TIC coordinates and the WFCAM initial WCS. We removed this offset by visually identifying the stellar centroids that would capture the stellar flux completely within our photometry apertures, which varied between 26–41 pixels depending on the defocused nature of the Cepheid.

We median-combined all the images of a given Cepheid to generate the reference frame used for subtraction. This differs from the procedure in Oelkers & Stassun (2018, 2019) which only used the first image in the series as the reference image.

We modified the selection procedure to identify stars which could be used to solve for the reference kernel. We only selected stars which had pixel positions farther than at least 100 pixels from the edge, and had photometric uncertainties less than 0.05 mag after an initial execution of aperture photometry on the reference frame. Additionally, we purposefully excluded the Cepheid from the list of stars that could be used for the kernel generation since its variability would likely degrade the kernel solution.

Finally, we modified the original OS-DIA light-curve-detrending procedure applied to the Cepheids. Normally, this pipeline uses a median-combined subset of 100 stars of similar magnitude to the target star which decreases the photometric dispersion when combined and subtracted from the target light curve. This traditional approach was used to evaluate our photometric precision as discussed in Section 3.3. However, we were unable to use this method for the Cepheids as there are few (if any) stars with similar magnitudes in each frame. Instead, we selected all stars within 250 pixels of the Cepheid as "trend" stars. Next, we subtracted the reference frame magnitude of each trend star from its full light curve, and median-combined the trend light curves with a 2σ clipping to create a reference trend. This reference trend was then subtracted from the light curve of the corresponding Cepheid.

We characterized the photometric quality of the differenced light curves for stars other than the Cepheids as follows. We first subtracted the mean magnitude of each star in every field from the corresponding detrended light curve and then computed the median absolute value of the resulting offsets, performing iterative 5σ clipping to exclude outliers. The results for one representative field are shown in Figure 3. We achieved a photometric precision limit of ∼0.01 mag for bright (8 ≲ H ≲ 11 mag) stars. We investigated whether the achieved photometric precision was in line with expectations by performing aperture photometry on the raw images of the RX Cam field using the corresponding input star list to the pipeline. We determined the S/N of each object taking into account contributions from photon statistics, sky background, and readout noise. As shown by the solid black line in Figure 3, the photometric precision expected from S/N considerations closely follows the noise floor. The objects with excess rms (0.07–0.2 mag for 11.5 < H < 13.3) are either uncharacterized variables or located near the edges of the reference image, where the quality of the image subtraction and subsequent photometry procedures are less reliable.

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In the case of the Cepheids, we phased their light curves adopting the periods listed in Table 1 and fit them using templates from Inno et al. (2015), ⁸ which is linear in amplitude and mean magnitude, and nonlinear in initial phase offset. We adopted a strategy of first searching for the initial phase offset that achieved a global least-squares minimum, simultaneously solving for amplitude and mean magnitude for each trial value of the initial phase. Then, the initial phase offset and parameter uncertainties were fine-tuned using the Gauss–Newton algorithm. This strategy ensures both accuracy and speed. The best-fit model amplitudes and initial phase offsets, along with their uncertainties, are listed in Table 2.

We used the residuals from the light-curve fitting to estimate a global statistical uncertainty of 0.027 mag for the Cepheid photometry. This larger value relative to the brightest non-Cepheids in the frame likely arises from our limited ability to detrend the former light curves. Overall, the phase correction uncertainties are dominated by the light-curve-modeling errors, and thus were estimated by the scatter of the light-curve-fitting residuals.

We compared three of our Cepheid light curves (V0386 Cyg, TX Cyg, and RX Cam) with those obtained by Monson & Pierce (2011) to provide context into our template fitting and data reduction. We executed a bootstrap simulation sampling from both sets of light curves independently (with replacement) 1000 times. We scaled the amplitude of the Cepheid template (described in Section 4.2) during each bootstrap simulation and selected the amplitude which minimized the least-squares residuals of the fit. The results are presented in Figure 5.

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We found the amplitudes for V0386 Cyg to be 0.25 mag in this work and 0.21 mag from Monson & Pierce (2011), which are consistent within 1.0σ using the photometric uncertainties of the light curves and 1.3σ using the standard deviation of the bootstrap simulations. We found the amplitudes for TX Cyg to be 0.27 mag in this work and 0.31 mag from Monson & Pierce (2011), which are consistent within 1.0σ using the photometric uncertainties of the light curves and 1.0σ using the standard deviation of the bootstrap simulations. Lastly, we found the amplitudes for RX Cam to be 0.17 mag in this work and 0.23 mag from Monson & Pierce (2011), which are consistent within 1.5σ using the photometric uncertainties of the light curves and 1.4σ using the standard deviation of the bootstrap simulations. We interpret these results as being statistically consistent.

We obtained corrections to "mean light" for the random-phase HST Wide Field Camera 3 (WFC3) F160W observations of these Cepheids reported in Riess et al. (2021). One set of corrections was based on V- and I-band light curves from the literature (see Tables 3 and 4 in Riess et al. 2021) while the other was based on our H-band light curves. The procedure to obtain the phase corrections is described in detail in the Appendix of Riess et al. (2018b), but we briefly summarize the procedure below.

First, any available observations in the VIJH bands that contain epochs close to the HST observations of a given Cepheid are assembled. These bands are used because they are similar in central wavelength and bandpass to the HST WFC3 bands F555W, F814W, and F160W, and thus can be easily transformed. The assembled observations are then combined into a single data set, which is fit with a Fourier series to obtain a model of Cepheid variability. Riess et al. (2018b) consider two models of variability: one where the period is kept constant and another where the period is allowed to vary along with the other model parameters. For the set of phase corrections presented here, the constant period model was used.

The variability model is then used to convert observation times to phase, and a cubic spline (or a Cepheid template if the number of observations is limited) is used to interpolate the light curves in a single band and determine magnitude at the observed phase, m_ϕ . m_ϕ is used to define a phase correction curve ${C}_{\phi }=\overline{m}-{m}_{\phi }$. The H-band phase was allowed to vary freely and was not shifted relative to the V-band phase. Photometric transformations from Riess et al. (2016) are then used to convert the phase corrections from the ground-based to the HST photometric system.

Figure 6 compares the two sets of phase corrections. We find good agreement with the phase corrections based on VI light curves, with a small mean difference of −1 ± 6 mmag.

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