Cepheids in M31: The PAndromeda Cepheid Sample

The galaxy M31 was observed from 2009 August 31 to 2010 January 21, 2010 July 23 to 2010 December 27, 2011 July 25 to 2011 November 22, and 2012 July 28 to 2012 October 31, with usually two visits per night in the g_P1, r_P1, and i_P1 bands (see Tonry et al. 2012 for information on the PS1 filter system). The general exposure time is 60 s per frame, and each epoch (visit) is a stack of typically seven frames in the r_P1 band and five frames in the g_P1 and i_P1 bands. The creation of this visit stack is described in the next section. Figure 1 shows the distribution of the number of frames making up one epoch. In total, there are 420 epochs in the r_P1 band, 262 epochs in the i_P1 band, and 56 epochs in the g_P1 band. Due to masking (which will be discussed in the following section), the light curves usually have less epochs, so this is the maximum number of epochs. In addition, we disregard epochs that are based on less than three frames. In total, PAndromeda has taken 2511 frames in the r_P1 band with a combined exposure time of 157,904 s (≈43.86 hr), 1260 frames in the i_P1 band with a total of 75,840 s (≈21.07 hr), and 246 frames in the g_P1 band with a combined exposure time of 15,048 s (≈4.18 hr).

Zoom In Zoom Out Reset image size

The gigapixel camera (GPC) consists of 60 orthogonal transfer arrays (OTAs), where each OTA is made up of an array of 8 × 8 cells. One OTA has an FOV of 21' × 21'. The pixel scale is 025 pixel^–1. The PS1 image-processing pipeline (IPP; Magnier 2006) provides us with astrometrically aligned frames (the frames are also bias- and flat-field-corrected). During the alignment, the exposures are remapped to a common grid, the so-called skycells. Only the first data reduction steps are done by the IPP; the other steps, done by ourselves, are discussed in the next section. Compared to K13, we changed the layout and size of the skycells so that they now cover 6647 pixels × 6647 pixels (i.e., 277 × 277) and use the intrinsic pixel scale of 025. Also, we defined the skycells such that they overlap (by 6'), in order to have a simple way to check our data reduction for consistency. The covered area is ∼7 deg² in the r_P1 and i_P1 bands and ∼6.8 deg² in the g_P1 band. The central six skycells were split during our data reduction into four smaller skycells with 3524 pixels × 3524 pixels (i.e., 147 × 147), for reasons discussed in the next section. The area covered in the g_P1 band is smaller, since skycells 003, 004, 005, 006, 012, and 028 are not used due to the lack of data in their skycells. The area in K13 (with ∼2.6 deg²) is much smaller than the area analyzed here. The skycell layout for this work (hereafter K18a), as well as for K13, is shown in the Appendix.

The data reduction is based on our previous pipeline used in K13. The overall approach of using difference imaging (Alard & Lupton 1998) is the same. Apart from changing certain details, the biggest change is to mask a large fraction of the images in order to minimize systematic errors that are due to the poor PS1 image quality. The trade-off for less systematics is a larger statistical error caused by the rigorous masking. This was mainly done to help with the microlensing search (Lee et al. 2012), which was originally the main scientific goal of PAndromeda. As far as Cepheid light curves are concerned, the fact of having more statistical noise is usually negated by the large increase in epochs. But some area is lost or has substantially less epochs due to the masking. Therefore, we do not recover all Cepheids found in K13 and all eclipsing binaries found in Lee et al. (2014a).

As mentioned in the previous section, our data reduction starts with astrometrically aligned frames provided by the IPP (Magnier 2006) that are already debiased and flat-field-corrected. Our pipeline (see also Lee et al. 2012; Koppenhoefer et al. 2013; K13) uses the AstroWISE data-management environment (Valentijn et al. 2007). In the first step, where we ingest the frames provided by IPP into the AstroWISE database, we apply multiple masks. We use most of the masking flags already provided by IPP. The quality of these original masks was not sufficient, so we improved those masks and provided them to the IPP in order to reprocess all of our raw data using these new mask files. This step was necessary since the masks are based on the defects on the OTA cell level, and applying the masks before the skycell regridding is computationally more efficient. We also use the ghost masks provided by IPP but significantly increase the masking, since the position of the ghost model is sometimes off. We also mask satellite tracks using the linear Hough transform algorithm that is implemented in AstroWISE, and we use manually created masks that we have for a few hundred frames. Saturated pixels are also masked. Since there are offsets between the OTAs, we only use the dominant OTA in each skycell and mask the other OTAs. This implies that we mask up to 75% for the rare case where four OTAs are in one frame with the same area. This OTA masking is quite extreme, but it ensures that there are no systematic jumps inside a frame and that we can photometrically align the frames to each other. After applying these masks, we only use those frames that have more than 20% unmasked pixels in the central region of the frame (pixels 1661–4985 in x and y). The mean masking over all frames in all skycells is 64% in the r_P1 and i_P1 bands and 65% in the g_P1 band. The mean masking per skycell ranges from 48% to 83% in the r_P1 band, 48% to 82% in the i_P1 band, and 43% to 85% in the g_P1 band.

As can be seen in Figures 27–29, the central six skycells are each divided into four smaller skycells. The point-spread function (PSF) varies slightly over the FOV of the GPC. The PSF is broadest on the edges of the GPC but also blurred in the center of the GPC. Over the PAndromeda observing campaign, the center of the GPC was pointed on different skycells. Due to this, the central six skycells showed the largest PSF variation. By splitting them into smaller frames, the variation inside these new skycells is significantly reduced. This ensures that our PSF photometry, which uses a constant PSF model for a skycell, performs well.

In order to perform difference imaging, we need to construct so-called reference frames. A reference frame is a stack of the images with the best PSF. The frames are photometrically aligned so that the sky background and zero point are the same. Masked areas in one frame (if the masked region is not too large) are replaced from another frame with an almost similar PSF. The frames are assigned weights according to the inverse of the squared product of the seeing and the mean error. The reference frame is the weighted stack of these frames. In the r_P1 and i_P1 bands, we use 100 frames for the reference frame. For the g_P1 band, we use 40 frames. Additionally, we require the original position angle to be zero or a multiple of 90° in the r_P1 and i_P1 bands. The reason for this is that we want to limit the increased noise caused by, e.g., chip gaps or bleeding to the four cardinal directions. The observing strategy required the second visit in one night to have a position angle of 90°. Unfortunately, there were also a significant number of frames taken with a random position angle. We disregard those for the reference frame in the r_P1 and i_P1 bands but have to use them in the g_P1 band, because in this band we do not have enough data. In K13, we used the 70 best-seeing frames, but here we also selected according to masking. Since we increased the masking drastically, we have to make sure that the reference frames cover as much area as possible. Everything that is masked in the reference frame will be lost, even if there are frames that have data in these masked regions. Due to the fact that the masking fraction and the seeing are not correlated, we first select seven times more frames for the reference frame where the masking is the lowest and then select the best-seeing frames from those frames. The frame that is used to photometrically align the other frames is one of the 10 best-seeing frames that overlaps the most with the other frames. The reason for this is that the alignment works better the more area the frames have in common. Since we wanted to limit the area lost due to the new strict masking, we also require that a frame does not increase the masking in the reference frame too much. Pixels that are masked in all but one frame will still be dominant in the reference frame. During the creation of the reference frame, each frame contributing to it is checked if including it in the stack would decrease the unmasked area in the reference frame by more than 1%. If that is the case, the frame will be dropped from the reference frame. Therefore, the final reference frame can include less than 100 (r_P1 and i_P1 bands) or 40 (g_P1 band) frames, respectively. Each reference frame is calculated twice. The first time, the sources are detected using SExtractor (Bertin & Arnouts 1996). The reference frame is inspected, and if there are, e.g., satellite tracks missed by the algorithm or ghosts, etc., we create manual masks for the input frames. This first reference frame is then used to photometrically align the input frames for the creation of the final second reference frame. In the second run, we use DAOPHOT (Stetson 1987) to detect the sources. Due to the crowding in M31, SExtractor sometimes determines a wrong position of a star, while DAOPHOT is optimized for high crowding. We perform PSF photometry on the positions identified with DAOPHOT on a background-subtracted reference frame. The neighboring stars are iteratively subtracted in order to account for the crowding. As in K13, we fit a bicubic spline model to determine the background (sky and M31). For each skycell, we determine a PSF model but do not vary it over the reference frame. The flux calibration is done as in K13; however, we do not use the Sloan Digital Sky Survey (SDSS; Abazajian et al. 2009) for the calibration but rather the PS1 PV2 catalog (Chambers et al. 2016). The reason for this is that the SDSS catalog is very sparsely populated in the central region of M31. With the PV2 catalog, we have a lot of comparison stars, so that we are able to also correct for PSF variation over the field by modeling the zero point with a spline.

For the difference imaging, we also need to create so-called visit stacks, which are stacks of all frames from one visit. Ideally, there should have been two visits of M31 per night, one in the first half of the night and one in the second half. The data taken have significant deviations from that. Sometimes the second visit was done right after the first, or there were three visits or visits with less frames. Also, the total integration time per visit changed several times in order to balance the total exposure time between the r_P1 and i_P1 bands. So, instead of automatically splitting the data of one night into two visit stacks, we grouped all the frames by hand into visit stacks with a stack depth as homogeneous as possible. The frames of a visit stack are photometrically aligned such that the sky background and zero point are the same. The weighted stack of these frames is photometrically aligned to the reference frame such that the visit stack and reference frame have the same zero point and sky background. Note that the visit stack has a smaller signal-to-noise ratio, since the reference frame is much deeper and the PSF is different, i.e., usually worse. As described in K13, the PSF of the reference frame is aligned to the visit stack by determining a convolution kernel when calculating the difference frame. Compared to K13, we decreased the size of the area one convolution kernel uses in order to better account for differences not only in PSF size but also PSF shape. We also masked out all sources brighter than 18 mag in the r_P1 band, since those bright sources are not relevant for our science cases and are producing residuals in the difference frame. The PSF photometry on the difference frame uses the PSF constructed from the convolved reference frame.

In order to obtain the flux in one epoch of the light curve of a resolved source, the flux in the difference frame is added to the flux in the reference frame. Since the skycells overlap, the light curve can be constructed as a combination of measurements from different skycells. For the case where a resolved source has measurements of one epoch in multiple skycells, we use the measurement with the smallest error. For our Cepheid detection, we only use epochs in the light curve that have a signal-to-noise ratio larger than two and where the visit stack has more than two frames (the published light curves include those epochs for consistency). In total, we have detected 7,226,125 unique sources, where 3,348,137 unique sources have data in at least the r_P1 band. For all sources that have r_P1-band data, we determine the periodicity of the light curve with SigSpec (Reegen 2007). In K13, we explained in detail how we determined the periods and period errors. We have not changed any parameter of the period determination, since the procedure described in K13 works very well. For the period error determination, we increased the number of bootstrapping samples from 1000 in K13 to 10,000. The error rescaling factor described in K13 that was necessary due to the change of the pixel scale is as expected, 1.0, and therefore not necessary anymore. We use the AB magnitude system throughout this paper and in the published data.

As described previously, we need to identify a certain number of Cepheids manually so that we are able to construct a three-dimensional parameter space that enables us to find Cepheids in as unbiased a way as possible. Of course, the manual selection of Cepheids by light-curve shape is biased to some degree. It is especially difficult to determine the variable type for noisy light curves. As described previously, we start with 21,313 sources but only select those where the period significance determined by SigSpec is larger than 25. This leaves us with 10,562 light curves. From these, we preselected 2807 by using only those that are not noisy, and the light curves that even remotely resemble Cepheids, i.e., Mira-like light curves, were also selected. The selection is only based on the shape of the light curves in all available bands. So, we do not look at the position in the PLR. In order to be as unbiased as possible, four of the authors independently assigned flags to those 2807 light curves. We then matched the four classifications and reviewed cases where we disagreed. We disregarded sources where we could not reach a consensus of opinion. We end up with 1966 light curves that are manually classified as Cepheids based only on their light-curve shape. We apply the color cut described in the next subsection and clip 295 sources, leaving us with 1671 Cepheids. The color cut can be seen in Figure 2. The number of clipped sources is quite high considering that they were manually identified to have a Cepheid-like light curve. The color cut used in K13, shown with cyan lines, would cut less objects, but the new color cut (magenta lines) works better in selecting Cepheids in the complete sample.

Zoom In Zoom Out Reset image size

As already mentioned, we use a color cut for a better identification of Cepheids. We use the reddening-free Wesenheit and the r_P1 – i_P1 color for the selection, since we do not have g_P1 data for all light curves. In order to define the color cut, we use the same approach as in K13. Theoretical pulsation models provide us with the information on how the instability strip edges depend on the effective temperature (T_eff) and luminosity (L). We then use isochrones to translate the instability strip defined by T_eff and L to the observable color and Wesenheit. In K13, we used the Fiorentino et al. (2002) instability strip but had to extend the edges by 0.2 mag in order to also include fainter but obvious Cepheids that would otherwise not have been covered, which makes the reliability of the instability strip parameters somewhat doubtful. Now we use the Anderson et al. (2016) instability strip edge models. As can be seen in Figure 3, those also include fainter and cooler Cepheids. We include all their models from Tables A.1 to A.6, i.e., all three metallicities (Z = 0.014, 0.006, and 0.002) and all three rotations (ω_ini = 0.0, 0.5, and 0.9). The Anderson et al. (2016) instability strip edges are used to define an area in which we require our Cepheids to reside. The area is defined by lines connecting the points (3.755, 4.8), (3.890, 1.5), (3.550, 4.8), (3.740, 2.934), and (3.812, 1.5), as shown in Figure 3. In the next step, we use the PARSEC isochrones (Bressan et al. 2012; Chen et al. 2014, 2015; Tang et al. 2014) and require the T_eff and L of the isochrones to be within the area defined by the instability strip edges. This defines an area in the Wesenheit–color diagram, as seen in Figure 4. This region, which is defined by lines connecting the points (0.111, 16.450), (−0.010, 20.350), (−0.126, 25.900), (0.033, 25.134), (0.092, 23.222), (0.194, 20.430), (0.294, 19.003), (0.536, 16.680), and (1.067, 14.223), is used to perform the color cut. The area shown in Figure 4 is also valid for all metallicities used in the Anderson et al. (2016) models. In order not to clutter up the plot, we only show the solar-metallicity isochrones. The isochrones can also be used to determine the instability strip in other filter bands. We use this in K18b, where we identify our Cepheid sample in HST data. Since the color cut uses the intrinsic color, we have to correct for the extinction. As in K13, we use the Montalto et al. (2009) color-excess map and the foreground extinction toward M31 determined by Schlegel et al. (1998) (E(B − V)_fg = 0.062) combined with the correction factor 0.86 from Schlafly & Finkbeiner (2011). The Montalto et al. (2009) map gives the color excess for a line of sight going completely through M31. Therefore, we only correct by half the color excess, assuming the Cepheid is only affected by half the dust. This corresponds to a probability argument, where sources are in front of an infinitely thin dust layer or behind, e.g., the extinction correction in the r_P1 band, as

$$\begin{eqnarray}&&\overline{{A}_{{r}_{{\rm{P}}1}}}=(0.5\cdot E(B-V)+0.86\cdot 0.062)\cdot {R}_{r,{\rm{P}}1},\end{eqnarray} \tag{ 2 }$$

where R_r,P1 = 2.5535 (R_i,P1 = 1.8928 and R_g,P1 = 3.5258) for a reddening law of R_V = 3.1. The assumption that the Cepheid is obscured by only half the dust can be refined in some cases. An object satisfies the color selection if it is within the area defined above, also considering its errors. So each object is not a point in the Wesenheit–color space but rather a box, where the height of the box is the error of the Wesenheit. The width of this box is the error of the color combined with the full color excess of that object. So the right side of the box is where only the foreground extinction has been corrected, and the left side is where the foreground plus the full color excess is used. In an edge-on view this corresponds to a location on the top of the disk, where only the foreground extinction has to be considered, or the bottom, where additionally the full color excess has to be taken into account. In case this box intersects the color-cut area defined by the instability strip edges, half the width of the box that is inside the color-cut area and is due to the color excess is used to correct the extinction. So we use the color-cut area to narrow down the range of color excess the object can have.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In the following, we use the extinction-corrected magnitudes, i.e., r_P1 denotes the extinction-corrected magnitude. The uncertainty caused from the color excess is not propagated into the magnitude errors.

Fundamental-mode (FM) and first-overtone (FO) Cepheids, as well as type II (T2) Cepheids, occupy different locations in the A₂₁–φ₂₁–P space, which can be used to identify the Cepheid type (see, e.g., Udalski et al. 1999; Vilardell et al. 2007; K13). As in K13, we use two projections of this space, i.e., A₂₁–P (see Figure 5) and φ₂₁–P (see Figure 6), for the type classification. In K13, we used the A₂₁–P projection to distinguish between FM and FO Cepheids and the φ₂₁–P space to separate T2 and FM Cepheids. Here we additionally use an area in the φ₂₁–P projection to find T2 Cepheids. The different Cepheid types could also be identified in the PLR, but by using this three-dimensional space, i.e., using the Fourier parameters, we only use the light-curve shape to determine the Cepheid type. The FO and FM PLRs have a small separation compared to their dispersions. Therefore, defining a line in the PLR that would distinguish both Cepheid types would bias the resulting PLRs. In the three-dimensional Fourier space, we also see overlaps between the different Cepheid type sequences. To address this issue, we require the Cepheids to be completely inside the defined areas, including their errors. Consequently, some Cepheids are in a transition region and therefore cannot be assigned a definite Cepheid type. We label those as the unclassified (UN) Cepheid type. In K13, we called the Cepheids that were clipped in the Wesenheit relation UN Cepheids. As we will discuss later, we still perform outlier clipping in the Wesenheit PLR and call the clipped Cepheids UN Cepheids. Therefore, in this paper, UN Cepheids can arise from two reasons. We do not distinguish between the two and call both UN Cepheids. We separate the areas by defining the following linear parameterization:

$$\begin{eqnarray}&&{m}_{\mathrm{FO}}=\displaystyle \frac{0.14-0.34}{\mathrm{log}(7.5)-\mathrm{log}(3.0)},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{t}_{\mathrm{FO}}=0.34-\mathrm{log}(3.0)\cdot {m}_{\mathrm{FO}},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{m}_{{\rm{T}}\mathrm{2,1}}=0.00,\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{t}_{{\rm{T}}\mathrm{2,1}}=5.05,\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{m}_{{\rm{T}}\mathrm{2,2}}=\displaystyle \frac{0.48-0.25}{\mathrm{log}(30.0)-\mathrm{log}(10.0)},\end{eqnarray} \tag{ 7 }$$

and

$$\begin{eqnarray}&&{t}_{{\rm{T}}\mathrm{2,2}}=0.25-\mathrm{log}(10.0)\cdot {m}_{{\rm{T}}\mathrm{2,2}}.\end{eqnarray} \tag{ 8 }$$

In order for a Cepheid to be assigned the FO type, the following two equations have to be true (see Figure 5):

$$\begin{eqnarray}&&{A}_{21}+{A}_{21,e}\lt \mathrm{log}(P)\cdot {m}_{\mathrm{FO}}+{t}_{\mathrm{FO}}\end{eqnarray} \tag{ 9 }$$

and

$$\begin{eqnarray}&&P\lt 7.5\,\mathrm{days}.\end{eqnarray} \tag{ 10 }$$

For it to be a T2 Cepheid, the equations (see Figure 6)

$$\begin{eqnarray}&&P\gt 11.95\,\mathrm{days},\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{\varphi }_{21}-{\varphi }_{21,e}\gt \mathrm{log}(P)\cdot {m}_{{\rm{T}}\mathrm{2,1}}+{t}_{{\rm{T}}\mathrm{2,1}},\end{eqnarray} \tag{ 12 }$$

and

$$\begin{eqnarray}&&P\lt 53.0\,\mathrm{days}\end{eqnarray} \tag{ 13 }$$

or the equations (see Figure 5)

$$\begin{eqnarray}&&{A}_{21}-{A}_{21,e}\gt \mathrm{log}(P)\cdot {m}_{{\rm{T}}\mathrm{2,2}}+{t}_{{\rm{T}}\mathrm{2,2}}\end{eqnarray} \tag{ 14 }$$

and

$$\begin{eqnarray}&&P\gt 10.0\,\mathrm{days}\end{eqnarray} \tag{ 15 }$$

have to be true, i.e., (Equation (11) AND Equation (12) AND Equation (13)) OR (Equations (14) AND (15)). For it to be considered an FM Cepheid, at least one of the equations (see Figure 5)

$$\begin{eqnarray}&&{A}_{21}-{A}_{21,e}\gt \mathrm{log}(P)\cdot {m}_{\mathrm{FO}}+{t}_{\mathrm{FO}}\end{eqnarray} \tag{ 16 }$$

and

$$\begin{eqnarray}&&P\gt 7.5\,\mathrm{days}\end{eqnarray} \tag{ 17 }$$

has to be true, and additionally, at least one of the equations (see Figure 6)

$$\begin{eqnarray}&&P\lt 11.95\,\mathrm{days},\end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray}&&{\varphi }_{21}+{\varphi }_{21,e}\lt \mathrm{log}(P)\cdot {m}_{{\rm{T}}\mathrm{2,1}}+{t}_{{\rm{T}}\mathrm{2,1}},\end{eqnarray} \tag{ 19 }$$

and

$$\begin{eqnarray}&&P\gt 53.0\,\mathrm{days}\end{eqnarray} \tag{ 20 }$$

has to be true. Also, at least one of the equations (see Figure 6)

$$\begin{eqnarray}&&{A}_{21}+{A}_{21,e}\lt \mathrm{log}(P)\cdot {m}_{{\rm{T}}\mathrm{2,2}}+{t}_{{\rm{T}}\mathrm{2,2}}\end{eqnarray} \tag{ 21 }$$

and

$$\begin{eqnarray}&&P\lt 10.0\,\mathrm{days}.\end{eqnarray} \tag{ 22 }$$

has to be true; i.e., for an FM Cepheid, the logical connection is (Equation (16) OR Equation (17)) AND (Equations (18) OR Equation (19) OR Equation (20)) AND (Equation (21) OR Equation (22)). In case the Cepheid cannot be classified as FM, FO, or T2, it is classified as UN. Figure 7 shows that the type classification of the manually selected Cepheid sample performs reasonably well considering the dispersion in the PLRs.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In order to facilitate the automatic classification of Cepheids, additional selection criteria are needed. The combination of color cut and three-dimensional parameter space selection alone does not suffice to obtain a clean Cepheid sample. Table 1 summarizes the selection criteria and provides information on how many objects are rejected in each step. The cuts could be applied in any order without changing the resulting sample. The published Cepheid catalog also includes the tables and light curves of the clipped objects, as well as information on the clipping reason in the form of a bit flag. Some fits or, e.g., the final type determination are performed after certain cuts have been applied in order to save computation time. Therefore, the catalog of the clipped objects might not have all the information. The selection criteria are applied to the manually classified Cepheid sample, as well as the sample that is selected using the three-dimensional parameter space (3D sample). Table 1 provides the number of clipped objects for each sample. The selection criteria are applied first to the manual sample so that the three-dimensional parameter space can be defined (as explained in the next section). The selection criteria are then applied again to the resulting 3D sample. The selection criteria in Table 1 are applied to the r_P1 and i_P1 bands, while the criteria in Table 2 are applied to the g_P1 band. Objects clipped due to the criteria in Table 1 are removed from the final Cepheid sample, while objects clipped only in the g_P1 band (Table 2) are flagged and therefore not used for the g_P1 PLR or the g_P1 sample in general.

Table 1.  Selection Criteria Used in the r_P1 and i_P1 Bands

	Band	Selection Criterion	Manual	3D	Flag
I	All	Color cut	295/1966	1922/3390	1
II	rP1 and iP1	15 mag ≤ m(t) ≤ 25 mag	0/1671	0/1468	2
III	rP1 and iP1	0.1 mag ≤ max(m(t)) − min(m(t)) ≤ 1.75 mag	1/1671	72/1468	4
IV	rP1 and iP1	$\tfrac{\mathrm{median}(| m(t)-{m}_{i}| )}{\max (m(t))-\min (m(t))}\leqslant 0.3$	20/1671	343/1468	8
V	rP1 and iP1	max(Θi − Θi+1) ≤ 0.25	0/1671	1/1468	16
VI	All	Same type from light-curve bootstrap ≥90%	3/1671	73/1468	32
	rP1 and iP1	Final sample	1640	1046

Note. The number of remaining Cepheids for the manual and 3D sample does not have to add up to the final number, since some cuts are performed at the same time and some objects fulfill multiple criteria. The columns Manual and 3D provide the number of clipped objects and the total number of objects still present at this step. The Flag column provides a bit flag so that the reason for the clipping can be found in the published data. The magnitude of the fitted light curve is denoted as m(t), while the observed magnitudes are called m_i. Here Θ_i is the phase of the ith observed epoch, and Θ_i+1 is the next largest phase (which is not necessarily the next epoch).

Download table as:  ASCIITypeset image

Table 2.  Selection Criteria Used in the g_P1 Band, Otherwise See Table 1

	Band	Selection Criterion	Manual	3D	Flag
I	All	Color cut	295/1966	1922/3390	1
II	gP1	15 mag ≤ m(t) ≤ 25 mag	162/1671	391/1468	2
III	gP1	0.1 mag ≤ max(m(t)) − min(m(t)) ≤ 2.00 mag	198/1671	504/1468	4
IV	gP1	$\tfrac{\mathrm{median}(| m(t)-{m}_{i}| )}{\max (m(t))-\min (m(t))}\leqslant 0.3$	24/1671	362/1468	8
V	gP1	max(Θi − Θi+1) ≤ 0.25	175/1671	246/1468	16
VI	All	Same type from light-curve bootstrap ≥90%	3/1671	73/1468	32
	gP1	Final sample	1302	595

Download table as:  ASCIITypeset image

Criterion I, the color cut discussed previously, is an important selection criterion for the 3D sample. Selection criterion II is a magnitude cut that ensures that the fitted light curve does not overshoot. As can be seen in Table 1, this cut is not used for the r_P1 and i_P1 band, but the cut is relevant for the g_P1 band (Table 2). This is not surprising, since the g_P1 band has relatively few epochs, and the light curves therefore have gaps that facilitate overshoots in the light-curve fitting. Criterion III is an amplitude cut, where we reject small amplitudes because those are difficult to distinguish from noise. Amplitudes are smaller for longer wavelengths (Madore & Freedman 1991), and therefore we have a different upper amplitude cut in the g_P1 band. In criterion IV, we make a noise cut by comparing the median absolute deviation of the observed magnitudes with the fitted magnitudes in relation to the amplitude of the light curve. Large gaps in the light curve cause problems in fitting the light curve. As mentioned previously, the gaps might cause overshoots, but even without overshoots, the shape of the light curve might not be determined well enough for the type classification or the determination of the Fourier parameters A₂₁ and φ₂₁. Therefore, we introduce criterion V, where we require that the largest gap is smaller than a quarter phase of the light curve. As we mentioned previously, we perform 10,000 bootstrapping realizations for determining the magnitude error and the errors of the Fourier parameters A₂₁ and φ₂₁. For each of those realizations, we determine the Cepheid type and require in criterion VI that the Cepheid type is the same in more than 9000 realizations. There are also two additional flags (64 and 128) not mentioned in Tables 1 and 2. Flag 64 is assigned to seven manually classified Cepheids, and they are removed from the Cepheid sample because of their location in the 3D parameter space. The reason for this is explained in the next subsection. Flag 128 is assigned 19 times in the final Cepheid catalog (so those Cepheids are still included in the catalog) in order to mark Cepheids where the light curve from visual inspection does not look like a typical Cepheid light curve. We keep those Cepheids in the sample so that the selection of Cepheids is as objective as possible. The results do not change if we disregard those Cepheids.

Similar to K13, we use the 3D parameter space A₂₁–φ₂₁–P to select light curves that have a shape typical for a Cepheid. The advantages of this approach are that it is less biased than visual selection and the selection is reproducible. Nevertheless, the approach requires the manual sample in order to define this 3D space. In K13, we spanned a grid in this 3D space and selected those grid points where one manually classified Cepheid resides. By doing this, we had to choose six parameters, i.e., the grid size and starting point for each dimension. Here we improve the method by using only three parameters. We define a sphere around each point in the manual sample. In order for an object to be selected, it has to be inside at least one of the spheres that are made up by the manual sample in the A₂₁–φ₂₁–P space. One of the free parameters is the radius of the sphere, and the other two are the normalizations of the other two dimensions, i.e., how each dimension is scaled compared to the other dimensions. We choose A₂₁–(2π)⁻¹φ₂₁–log(P) as the new 3D space. We choose it such that the values of the manual sample have a similar range. The reason for this is that we can use a sphere and do not have to use an ellipsoid. For example, if we use a radius of 0.2 in A₂₁–φ₂₁–P space, that would be a large difference in A₂₁, while it is only a small change in φ₂₁ and almost no change in P. In order to determine the radius of the sphere, we use the manual sample. We calculate for each Cepheid in the manual sample the distance in A₂₁–(2π)⁻¹φ₂₁–log(P) space to the next closest Cepheid. The cumulative distribution function of this distance is then used to choose the radius of the sphere. We select a radius of 0.088 for the sphere (99.5% of Cepheids are closer than this distance to their next neighbor). Seven Cepheids have a larger distance to the next neighbor. We choose to cut those seven Cepheids because they are in a region of the 3D space that is sparsely sampled, and if they were to be included, the radius of the sphere would have to be increased significantly, which makes the selection worse (a larger radius means a more fuzzy selection). If the seven Cepheids were left in the sample but the 0.088 radius were used, then the seven Cepheids would be rejected by the 3D selection process if the manual sample were subjected to the 3D selection (which it is not because it is used to define it). So, for consistency reasons, the seven Cepheids are excluded. As described in the previous subsection, the seven Cepheids are flagged with the 64 bit flag. In the Appendix, the location of those seven Cepheids in the 3D space can be seen in Figures 32–34. The 3D classification finds an additional 3390 Cepheid candidates. As can be seen in Figure 8, 1922 of those are clipped due to the color cut.

Zoom In Zoom Out Reset image size

Figure 9 shows the Wesenheit PLR of the combined manual and 3D sample after all selection criteria have been applied. As can be seen, there are outliers. There are different reasons for these outliers: crowding, misclassification, misidentification, blending, and extinction. In K15, we discussed those reasons in more detail, but we want to point out that the crowding problem is significantly more severe in these ground-based optical data than in the HST data. In order to remove the outliers from the sample, we perform an iterative κ–σ clipping with the median absolute deviation of the residuals as the magnitude error. This method that we developed in K15 is very robust and is also used in K18b, as well as in Riess et al. (2016) and Hoffmann et al. (2016). As in K15 and K18b, we use κ = 4. The clipped Wesenheit PLR shown in Figure 10 has no outliers anymore. In Figure 11, we show all Cepheids that were clipped, as well as the UN Cepheids. The UN Cepheids in this figure were assigned the UN type because the Cepheids are occupying a transitional region where the type classification is unsecure (see Section 3.3). In K13, the UN type was assigned only to the clipped Cepheids. Here the UN type is assigned to all Cepheids shown in Figure 11. After this point, we do not distinguish between the two reasons a Cepheid could have been assigned the UN type. The 3D parameter space of the final clipped sample is shown in Figures 12 and 13. In these figures, we already do not distinguish between the two UN type origins. The 3D parameter space is more densely sampled, and of course, it is similar to the manual sample shown in Figures 5 and 6, since the additional Cepheids have been selected by this 3D space. It can also be seen that in the final sample, the transitional region between Cepheid types is more prominently populated, and therefore there are more UN Cepheids in these regions than in the manual sample.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The skycell layout discussed in Section 2.1 is shown in Figures 27–29 for K18a. Figures 30 and 31 show the skycell layout in K13.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The bit flag 64 is assigned seven times, as explained in Section 3.5. The seven manually classified Cepheids have a larger distance to their respective next Cepheid neighbor in 3D space. Figures 32 and 33 show the location of these seven Cepheids in the amplitude ratio (A₂₁) and phase difference (φ₂₁) diagrams. Figure 34 shows where these seven Cepheids reside in the period Wesenheit diagram.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Since our data have more epochs and cover a larger time span than K13, the periods are also more precise. The long periods show a larger relative change in Figure 35, since for these periods, we now cover multiple pulsation cycles. We compare the r_P1- and i_P1-band magnitudes in Figures 36 and 37 for the 1445 Cepheids that are in both samples. There is no offset, but some Cepheids show a large magnitude change. The large magnitude differences are explained with a bad SExtractor position (on which the forced photometry was carried out) in K13 due to crowding. Most of these had a source position between two stars, and the brighter magnitude from this sample is now correct, since the position is correctly identified. But there are also a few cases where the new magnitude is fainter. This happens when there are two very close stars where the PSFs overlap and the pulsation was previously wrongly attributed to the brighter source. In Figure 38, we show how the Cepheid type changes. Of the 1445 Cepheids that are in both samples, 1224 do not change the Cepheid type. As can be seen, most change from UN to FM and from FM to UN, and almost all changes except for nine cases involve the UN type. A cross-match table is provided on the CDS.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Tables 6–11 give a description of the published data. The tables include the clipped sources, but not all fits have necessarily been performed for those objects, depending at which point the object was cut. In those cases, the columns show −1 or −99 as a default value. Some values can also be so small that they are shown as 0.0 in the tables. The errors of some values have been determined by different methods. We use the errors shown in Table 6. The method used to determine the magnitude errors is described in Section 3. A distribution of magnitudes is obtained, and the error is calculated from this distribution in two slightly different approaches. The first method is to determine the error from the ±σ/2 range around the mean magnitude from the light-curve fit. The other method is to determine the error from the 1σ range of the distribution regardless of the fitted mean magnitude from the light curve. The two errors are the same if the mean of the distribution is the same as the mean magnitude from the light-curve fit. This also implies that the difference of these two error estimates is a tracer of how symmetric the distribution is around the mean magnitude from the light curve. A good example for this is the period error, where the distribution is obtained by using the bootstrapping method on the light curve and the error is calculated with the two methods. The period calculated from the light curve can be so much on the edge of the distribution of periods obtained from the bootstrapping that it is outside the 1σ range of the distribution, and therefore the error from the ±σ/2 range around the mean period is not defined anymore. The period of a light curve that is changed drastically when bootstrapping the light curve would show this behavior. Note that these Cepheids do not have poor period estimates but rather all epochs are important for the period determination. The error from the 1σ range can always be calculated, and therefore it is used as the period error. The ±σ/2 range period error would not be defined for all Cepheids. The different error estimates are not used in this work to perform additional cuts, but we include them in the published data for the interested reader.

Table 6.  Description of main.dat

Column #	Label	Explanation
1	PSO id	PS1 identifier
2	id	Identifier used through the K18a data
3	R.A.	Right ascension (J2000.0)
4	Decl.	Declination (J2000.0)
5	${P}_{{r}_{{\rm{P}}1}}$	Period in the rP1 band (determined with SigSpec)
6	${P}_{e,{r}_{{\rm{P}}1}}$	Period error in the rP1 band determined with half the width of
		the 1σ interval of the period distribution obtained by the bootstrapping method
7	rP1,0	Extinction-corrected rP1-band magnitude (mean flux of the
		light curve converted to magnitudes)
8	re,P1	Magnitude error in the rP1 band
		determined by the method described in Section 3
9	iP1,0	Extinction-corrected iP1-band magnitude
10	ie,P1	Magnitude error in the iP1 band (see Section 3)
11	gP1,0	Extinction-corrected gP1-band magnitude
12	ge,P1	Magnitude error in the gP1 band (see Section 3)
13	W	Wesenheit magnitude as defined in Equation (1)
14	We	Wesenheit magnitude error
		determined with the same method as re,P1; see Section 3
15	A21	Amplitude ratio of the first two Fourier components
		in the rP1 band (see K13 Equation (5))
16	Ae,21	Error of the amplitude ratio A21
		obtained from the error of the Fourier decomposition
17	${\varphi }_{21}$	Phase difference of the first two Fourier components
		in the rP1 band (see K13 Equation (6))
18	φe,21	Error of φ21 (same method used as for Ae,21)
19	sample	Manual in case the Cepheid was classified manually and 3D in case the Cepheid
		was classified with the 3D parameter space
20	${\mathrm{flag}}_{{r}_{{\rm{P}}1},{i}_{{\rm{P}}1}}$	Bit flag for the rP1 and/or iP1 bands as described in Section 3.4
21	${\mathrm{flag}}_{{g}_{{\rm{P}}1}}$	Bit flag for the gP1 band (see Section 3.4)
22	type	Cepheid type (see Section 3.3)
23	catalog	Flag indicating whether the object is part of the catalog (C)
		or has been clipped/rejected (R)

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset images: 1 2

Table 7.  Description of lc-info.dat

Column #	Label	Explanation
1	id	Identifier used through the K18a data
2	${\mathrm{epo}}_{{r}_{{\rm{P}}1}}$	Number of epochs in the rP1-band light curve
3	${\mathrm{epo}}_{{i}_{{\rm{P}}1}}$	Number of epochs in the iP1-band light curve
4	${\mathrm{epo}}_{{g}_{{\rm{P}}1}}$	Number of epochs in the gP1-band light curve
5	${P}_{{i}_{{\rm{P}}1}}$	Period in the iP1 band
6	${P}_{{g}_{{\rm{P}}1}}$	Period in the gP1 band
7	${\mathrm{sig}}_{{r}_{{\rm{P}}1}}$	SigSpec significance of the rP1-band period (see Section 3 in K13)
8	${\mathrm{sig}}_{{i}_{{\rm{P}}1}}$	Significance of the iP1-band period
9	${\mathrm{sig}}_{{g}_{{\rm{P}}1}}$	Significance of the gP1-band period
10	${\mathrm{epo}}_{\mathrm{use},{r}_{{\rm{P}}1}}$	Number of epochs used for the Cepheid light curve in the rP1 band
		(all epochs are required to have a signal-to-noise ratio larger than two, and
		the corresponding visit stack has to have more than two frames)
11	${\mathrm{epo}}_{\mathrm{use},{i}_{{\rm{P}}1}}$	Number of epochs used for the Cepheid light curve in the iP1 band
12	${\mathrm{epo}}_{\mathrm{use},{g}_{{\rm{P}}1}}$	Number of epochs used for the Cepheid light curve in the gP1 band
13	${\min }_{r}$	Minimum magnitude (i.e., brightest magnitude)
		of the Fourier fit to the light curve in the rP1 band
14	mini	Minimum magnitude of the Fourier fit to the light curve in the iP1 band
15	ming	Minimum magnitude of the Fourier fit to the light curve in the gP1 band
16	maxr	Maximum magnitude (i.e., faintest magnitude)
		of the Fourier fit to the light curve in the rP1 band
17	maxi	Maximum magnitude of the Fourier fit to the light curve in the iP1 band
18	maxg	Maximum magnitude of the Fourier fit to the light curve in the gP1 band
19	rP1	rP1-band magnitude (i.e., not extinction-corrected as the rP1,0 magnitude but
		also determined with the mean flux of the light curve converted to magnitudes)
20	iP1	iP1-band magnitude
21	gP1	gP1-band magnitude
22	${A}_{21,{i}_{{\rm{P}}1}}$	Amplitude ratio in the iP1 band (analog to A21 but for the iP1 band)
23	${A}_{21,{g}_{{\rm{P}}1}}$	Amplitude ratio in the gP1 band
24	${A}_{e,21,{i}_{{\rm{P}}1}}$	Error of the amplitude ratio in the iP1 band
		(analog to ${A}_{e,21}$, i.e., error from the Fourier decomposition)
25	${A}_{e,21,{g}_{{\rm{P}}1}}$	Error of the amplitude ratio in the gP1 band
26	${\varphi }_{21,{i}_{{\rm{P}}1}}$	Phase difference of the first two Fourier coefficients in the iP1 band
		(analog to ${\varphi }_{21,{g}_{{\rm{P}}1}}$)
27	${\varphi }_{21,{g}_{{\rm{P}}1}}$	Phase difference in the gP1-band
28	${\varphi }_{e,21,{i}_{{\rm{P}}1}}$	Error of the phase difference in the iP1 band (analog to ${\varphi }_{e,21}$;
		the method described in Section 3 is used to determine the error)
29	${\varphi }_{e,21,{g}_{{\rm{P}}1}}$	Error of the phase difference in the gP1 band
30–40	${a}_{i,{r}_{{\rm{P}}1}}$	Fourier coefficients in the rP1 band as defined in Equation (3) in K13
		(the order of the fit is N = 5, so there are 11 Fourier parameters)
41–51	${a}_{i,{i}_{{\rm{P}}1}}$	Fourier coefficients in the iP1 band
		(the order of the fit is N = 5, therefore there are 11 Fourier parameters)
52–62	${a}_{i,{g}_{{\rm{P}}1}}$	Fourier coefficients in the gP1 band
		(the order of the fit is N = 3, but there are still 11 columns where the columns
		for the higher orders are set to a default value of −1)
63–73	${a}_{i,e,{r}_{{\rm{P}}1}}$	Fit error of the Fourier coefficients in the rP1 band
74–84	${a}_{i,e,{i}_{{\rm{P}}1}}$	Fit error of the Fourier coefficients in the iP1 band
85–95	${a}_{i,e,{g}_{{\rm{P}}1}}$	Fit error of the Fourier coefficients in the gP1 band
96	${\mathrm{gap}}_{{r}_{{\rm{P}}1}}$	Largest phase (Θ) gap in the folded rP1-band light curve (${\rm{\Theta }}\in [0,1]$)
97	${\mathrm{gap}}_{{i}_{{\rm{P}}1}}$	Largest phase gap in the folded iP1-band light curve
98	${\mathrm{gap}}_{{g}_{{\rm{P}}1}}$	Largest phase gap in the folded gP1-band light curve
99	catalog	Flag indicating whether the object is part of the catalog (C)
		or has been clipped/rejected (R)

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset images: 1 2

Table 8.  Description of other.dat

Column #	Label	Explanation
1	id	Identifier used through the K18a data
2	pretype	Cepheid type before the outlier clipping (see Section 3.6)
3	${\mathrm{mult}}_{{r}_{{\rm{P}}1}}$	Number of different skycells in which the Cepheid is in the rP1 band
4	${\mathrm{mult}}_{{i}_{{\rm{P}}1}}$	Number of different skycells in which the Cepheid is in the iP1 band
5	${\mathrm{mult}}_{{g}_{{\rm{P}}1}}$	Number of different skycells in which the Cepheid is in the gP1 band
6	${\mathrm{decrise}}_{{r}_{{\rm{P}}1}}$	Decline/rise factor in the rP1 band as defined in Section 5 in K13
7	${\mathrm{decrise}}_{{i}_{{\rm{P}}1}}$	Decline/rise factor in the iP1 band
8	${\mathrm{decrise}}_{{g}_{{\rm{P}}1}}$	Decline/rise factor in the gP1 band
9	${\mathrm{IV}}_{{r}_{{\rm{P}}1}}$	Noise factor in the rP1 band as defined by selection criterion IV in Table 1
10	${\mathrm{IV}}_{{i}_{{\rm{P}}1}}$	Noise factor in the iP1 band as defined by selection criterion IV in Table 1
11	${\mathrm{IV}}_{{g}_{{\rm{P}}1}}$	Noise factor in the gP1 band as defined by selection criterion IV in Table 2
12	$E(B-V)$	Color excess from the Montalto et al. (2009) map
		but improved where possible by the instability strip as discussed in Section 3.2
13	${\mathrm{err}}_{{r}_{{\rm{P}}1}}$	Magnitude error in the rP1 band determined from the 1σ range method
14	${\mathrm{err}}_{{i}_{{\rm{P}}1}}$	Magnitude error in the iP1 band determined from the 1σ range method
15	${\mathrm{err}}_{{g}_{{\rm{P}}1}}$	Magnitude error in the gP1 band determined from the 1σ range method
16	${\mathrm{err}}_{{ok},{r}_{{\rm{P}}1}}$	Percentage ($\in [0,1]$) of rP1-band epochs used in all 10,000 light-curve realizations
		(see Section 3; epochs can be cut if the sum of the drawn reference frame flux
		and difference frame flux is negative or the signal-to-noise ratio is smaller than two)
17	${\mathrm{err}}_{{ok},{i}_{{\rm{P}}1}}$	Percentage of iP1-band epochs (analog to ${\mathrm{err}}_{{ok},{r}_{{\rm{P}}1}}$)
18	${\mathrm{err}}_{{ok},{g}_{{\rm{P}}1}}$	Percentage of gP1-band epochs (analog to ${\mathrm{err}}_{{ok},{r}_{{\rm{P}}1}}$)
19	${\mathrm{err}}_{m,{r}_{{\rm{P}}1}}$	Mean rP1-band magnitude of the distribution used to calculate the error
20	${\mathrm{err}}_{m,{i}_{{\rm{P}}1}}$	Mean iP1-band magnitude of the distribution used to calculate the error
21	${\mathrm{err}}_{m,{g}_{{\rm{P}}1}}$	Mean gP1-band magnitude of the distribution used to calculate the error
22	${\mathrm{err}}_{\mathrm{sd},{r}_{{\rm{P}}1}}$	Standard deviation of the rP1-band distribution used to calculate the error
23	${\mathrm{err}}_{\mathrm{sd},{i}_{{\rm{P}}1}}$	Standard deviation of the iP1-band distribution used to calculate the error
24	${\mathrm{err}}_{\mathrm{sd},{g}_{{\rm{P}}1}}$	Standard deviation of the gP1-band distribution used to calculate the error
25	${A}_{e,21,m,r}$	Amplitude ratio error in the rP1 band determined from the 1σ range method
26	${A}_{e,m,21,i}$	Amplitude ratio error in the iP1 band determined from the 1σ range method
27	${A}_{e,m,21,g}$	Amplitude ratio error in the gP1 band determined from the 1σ range method
28	${A}_{e,21,c,r}$	Amplitude ratio error in the rP1 band determined from the ±σ/2 range method
29	${A}_{e,c,21,i}$	Amplitude ratio error in the iP1 band determined from the ±σ/2 range method
30	${A}_{e,c,21,g}$	Amplitude ratio error in the gP1 band determined from the ±σ/2 range method
31	${\varphi }_{e,m,21,r}$	Phase difference error in the rP1 band determined from the 1σ range method
32	${\varphi }_{e,m,21,i}$	Phase difference error in the iP1 band determined from the 1σ range method
33	${\varphi }_{e,m,21,g}$	Phase difference error in the gP1 band determined from the 1σ range method
34	${\varphi }_{e,c,21,r}$	Phase difference error in the rP1 band determined from the ±σ/2 range method
35	${\varphi }_{e,c,21,i}$	Phase difference error in the iP1 band determined from the ±σ/2 range method
36	${\varphi }_{e,c,21,g}$	Phase difference error in the gP1 band determined from the ±σ/2 range method
37	${P}_{e,{i}_{{\rm{P}}1}}$	Period error in the iP1 band determined with the 1σ range method
38	${P}_{e,{g}_{{\rm{P}}1}}$	Period error in the gP1 band determined with the 1σ range method
39	${P}_{e,c,{r}_{{\rm{P}}1}}$	Period error in the rP1 band determined with the $\pm \sigma /2$ range method
40	${P}_{e,c,{i}_{{\rm{P}}1}}$	Period error in the iP1 band determined with the $\pm \sigma /2$ range method
41	${P}_{e,c,{g}_{{\rm{P}}1}}$	Period error in the gP1 band determined with the $\pm \sigma /2$ range method
42	${P}_{e,{ok},{r}_{{\rm{P}}1}}$	Percentage ($\in [0,1]$) of the 10,000 bootstrapped light curves in the rP1 band
		for which SigSpec was able to determine a period
43	${P}_{e,{ok},{i}_{{\rm{P}}1}}$	Percentage ($\in [0,1]$) of the 10,000 bootstrapped light curves in the iP1 band
		for which SigSpec was able to determine a period
44	${P}_{e,{ok},{g}_{{\rm{P}}1}}$	Percentage ($\in [0,1]$) of the 10,000 bootstrapped light curves in the gP1 band
		for which SigSpec was able to determine a period
45	${A}_{e,21,m,b}$	Amplitude ratio error in the rP1 band determined from the 1σ range method
		where the distribution is obtained from 10,000 bootstrapped light curves
		from the measured light curve (i.e., not the method described in Section 3,
		where the reference frame flux is drawn from a distribution)
46	${A}_{e,21,c,b}$	Amplitude ratio error in the rP1 band determined from the $\pm \sigma /2$ range method
		with bootstrapping
47	${\varphi }_{e,21,m,b}$	Phase difference error in the rP1 band determined from the 1σ range method
		with bootstrapping
48	${\varphi }_{e,21,c,b}$	Phase difference error in the rP1 band determined from the $\pm \sigma /2$ range method
		with bootstrapping
49	${b}_{\mathrm{FM}}$	Percentage ($\in [0,1]$) of how often the FM type is assigned in the 10,000 realizations
		(i.e., criterion VI in Section 3.4; the Cepheid type is the pretype,
		i.e., the type before the outlier clipping)
50	${b}_{\mathrm{FO}}$	Percentage of how often the FO type is assigned
51	${b}_{{\rm{T}}2}$	Percentage of how often the T2 type is assigned
52	${b}_{\mathrm{UN}}$	Percentage of how often the UN type is assigned
53	$E{(B-V)}_{\min }$	Smallest possible color excess determined from the Montalto et al. (2009) map
		and the instability strip edges, as described in Section 3.2
54	$E{(B-V)}_{\max }$	Largest possible color excess
55	catalog	Flag indicating whether the object is part of the catalog (C)
		or has been clipped/rejected (R)

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset images: 1 2

In addition to the K13 cross-match table mentioned in the previous subsection, we also provide a cross-matching table for the Vilardell et al. (2006) sample with 416 Cepheids, the DIRECT sample with 332 Cepheids (Kaluzny et al. 1998, 1999; Stanek et al. 1998, 1999; Mochejska et al. 1999; Bonanos et al. 2003), the WECAPP sample with 126 Cepheids (Fliri et al. 2006), and the Riess et al. (2012) sample with 68 Cepheids. Due to the masking discussed in Section 2.1, we cannot match all literature Cepheids. With a matching radius of 2'', we match 349 Cepheids of the Vilardell et al. (2006) sample of 416 Cepheids. Eight of the Vilardell et al. (2006) sample have two matches within the 2'' radius. There are 277 Cepheids in the K18a sample, and 72 are clipped. Of the 332 DIRECT Cepheids, we match 316. There are 14 Cepheids with two matches inside the 2'' matching radius, 267 are in the K18a sample, and 49 are clipped. Of the 126 WECAPP Cepheids, we match 64. Thirty are in the K18a sample while 34 are clipped, and two Cepheids have two matches inside the 2'' matching radius. We match 61 of the 68 Riess et al. (2012) Cepheids. Three have two matches within the 2'' radius, and 55 are in K18a, while nine are clipped. In Figure 39, we show the comparison of the literature periods with those that are in our K18a sample (i.e., the clipped Cepheids are not included). The Vilardell et al. (2006) sample and the WECAPP sample have the most epochs of the literature samples, and therefore the periods match very well to our K18a periods. Since our K18a sample covers a larger baseline, the long periods are determined more precisely than in the literature samples.

Zoom In Zoom Out Reset image size