The Carnegie-Chicago Hubble Program: Calibration of the Near-Infrared RR Lyrae Period-Luminosity Relation With HST

TL;DR

This paper calibrates the near-infrared period-luminosity relation for RR Lyrae stars using HST data, establishing a key step in measuring the Hubble constant with 3% accuracy.

Contribution

It provides a new calibration of the RR Lyrae period-luminosity relation in the near-infrared using HST observations, linking Galactic variables to extragalactic distance measurements.

Findings

Zero point determined with four RR Lyrae stars with HST parallaxes.

Calibration consistent with Gaia DR2 data within uncertainties.

Achieves 3% accuracy in the Hubble constant measurement.

Abstract

We present photometry of 30 Galactic RR Lyrae variables taken with HST WFC3/IR for the Carnegie-Chicago Hubble Program. These measurements form the base of the distance ladder measurements that comprise a pure Population II base to a measurement of Ho at an accuracy of 3%. These data are taken with the same instrument and filter (F160W) as our observations of RR Lyrae stars in external galaxies so as to to minimize sources of systematic error in our calibration of the extragalactic distance scale. We calculate mean magnitudes based on one to three measurements for each RR Lyrae star using star-by-star templates generated from densely time-sampled data at optical and mid-infrared wavelengths. We use four RR Lyrae stars from our sample with well-measured HST parallaxes to determine a zero point. This zero point will soon be improved with the large number of precise parallaxes to be provided by Gaia. We also provide preliminary calibration with the TGAS & Gaia DR2 data, and all three zero points are in agreement, to within their uncertainties.

Tables

Table 1. Table 1 Galactic RR Lyrae Sample

Star	Period (d)	Observations	Type	Blazhko	[Fe/H]	AF160W
SW And	0.442270	a	RRab	*	-0.24	0.021
UY Cam	0.267042	a	RRc		-1.33	0.012
RZ Cep	0.308710	a,c,d	RRc		-1.77	0.043
RR Cet	0.553028	a	RRab		-1.45	0.012
XZ Cyg	0.466599	a,c,d	RRab	*	-1.44	0.053
DX Del	0.472617	a	RRab		-0.40	0.051
SU Dra	0.660420	a,c,d	RRab		-1.80	0.006
CS Eri	0.311331	a	RRc		-1.41	0.010
SV Eri	0.713796	a	RRab		-1.70	0.047
RR Gem	0.397290	a	RRab	*	-0.29	0.030
TW Her	0.399600	a	RRab		-0.69	0.023
BX Leo	0.362860	a	RRc		-1.28	0.013
RR Leo	0.452393	a	RRab		-1.60	0.020
TT Lyn	0.597434	a	RRab		-1.56	0.009
RR Lyr	0.566838	a,b,c,d	RRab	*	-1.39	0.017
UV Oct	0.542580	a,c,d	RRab	*	-1.74	0.050
BH Peg	0.640993	a	RRab	*	-1.22	0.043
RU Psc	0.390385	a	RRc	*	-1.75	0.024
HK Pup	0.734238	a	RRab		-1.11	0.088
RU Scl	0.493339	a	RRab		-1.27	0.010
SV Scl	0.377340	a	RRc		-1.77	0.008
AN Ser	0.522072	a	RRab		-0.07	0.022
V440 Sgr	0.477479	a	RRab		-1.40	0.047
V675 Sgr	0.642289	a	RRab		-2.28	0.072
MT Tel	0.316900	a	RRc		-1.85	0.021
AM Tuc	0.405810	a	RRc	*	-1.49	0.013
AB UMa	0.599577	a	RRab		-0.49	0.012
RV UMa	0.468060	a	RRab	*	-1.20	0.010
SX UMa	0.307118	a	RRc		-1.81	0.006
TU UMa	0.557659	a	RRab		-1.51	0.012

Table 2. Table 2 PSF photometry of individual exposures.

Name	MJDobs	Phase	$F160W$	$F160W$
			mag	$\sigma$
AM Tuc	56900.43533022	0.98375	10.677	0.030
AM Tuc	56900.43553856	0.98426	10.676	0.030
AM Tuc	56900.43574688	0.98477	10.651	0.030
AM Tuc	56900.43642986	0.98646	10.699	0.030

Table 3. Table 3 Mean Magnitudes

Name	$F160W$	$F160W$	$F160W$	$F160W$	$2MASS$
	Spitzer	${\sigma }_s$	Template	${\sigma }_T$	H
	mag	mag	mag	mag	mag
SW And	8.606	0.020	8.598	0.020	8.590
UY Cam	10.851	0.024	10.849	0.025	10.841
RZ Cep	7.972	0.016	8.007	0.017	8.136
RR Cet	8.609	0.025	8.617	0.023	8.652
XZ Cyg	8.665	0.020	8.749	0.025	8.770
DX Del	8.752	0.027	8.750	0.064	8.818
SU Dra	8.701	0.018	8.733	0.019	8.686
CS Eri	8.174	0.024	8.217	0.025	8.175
SV Eri	8.657	0.023	8.718	0.024	8.736
RR Gem	10.334	0.023	10.339	0.021	10.271
TW Her	10.385	0.041	10.352	0.027	10.269
BX Leo	10.688	0.034	10.750	0.058	10.743
RR Leo	9.672	0.021	9.798	0.028	9.737
TT Lyn	8.697	0.020	8.701	0.022	8.656
RR Lyr	6.472	0.035	6.481	0.031	6.598
UV Oct	8.316	0.013	8.292	0.013	8.289
BH Peg	9.180	0.025	9.184	0.029	9.070
RU Psc	9.190	0.025	9.244	0.021	9.156
HK Pup	10.055	0.034	10.038	0.025	10.031
RU Scl	9.252	0.025	9.286	0.020	9.285
SV Scl	10.567	0.024	10.605	0.075	10.599
AN Ser	9.895	0.026	9.895	0.020	9.914
V440 Sgr	9.104	0.025	9.218	0.031	9.230
V675 Sgr	9.088	0.025	9.114	0.022	9.059
MT Tel	8.055	0.055	8.135	0.034	8.193
AM Tuc	10.677	0.028	10.713	0.029	10.704
AB UMa	9.707	0.020	9.694	0.024	9.862
RV UMa	9.889	0.043	9.911	0.034	9.862
SX UMa	10.152	0.028	10.200	0.021	10.150
TU UMa	8.735	0.020	8.747	0.021	8.717

Table 4. Table 4 Absolute Magnitudes

Name	H(mag)	[F160W]	$\sigma$	Blazhko
	$2MASS$	HST		mag
	HST/FGS
XZ Cyg	-0.149	-0.275	0.221	*
SU Dra	-0.554	-0.543	0.245
RR Lyr	-0.537	-0.663	0.076	*
UV Oct	-0.588	-0.569	0.127	*
	TGAS
XZ Cyg	-0.297	-0.423	0.320	*
DX Del	-0.132	-0.198	0.288
SU Dra	-0.538	-0.528	0.425
SV Eri	-0.157	-0.164	0.421
RR Gem	-0.672	-0.754	0.763	*
TT Lyn	-0.226	-0.207	0.568
UV Oct	-0.231	-0.132	0.247	*
BH Peg	-0.055	-0.042	0.341	*
RU Scl	0.173	0.152	0.429
RV UMa	-0.806	-0.775	0.675	*
TU UMa	-0.459	-0.440	0.458
	Gaia DR2
SW And	-0.180	-0.163	0.200	*
RR Cet	-0.456	-0.495	0.112
XZ Cyg	-0.281	-0.407	0.043	*
DX Del	-0.099	-0.166	0.050
SU Dra	-0.582	-0.572	0.051
SV Eri	-0.881	-0.963	0.106
RR Gem	-0.569	-0.510	0.149	*
TW Her	-0.080	0.033	0.073
RR Leo	-0.282	-0.343	0.191
TT Lyn	-0.923	-0.882	0.068
UV Oct	-0.368	-0.349	0.034	*
BH Peg	-0.740	-0.641	0.088	*
HK Pup	-0.838	-0.808	0.128
RU Scl	-0.577	-0.599	0.148
AN Ser	-0.209	-0.236	0.105
V440 Sgr	-0.092	-0.213	0.068
V675 Sgr	-0.786	-0.757	0.115
AB UMa	-0.379	-0.345	0.070
RV UMa	-0.327	-0.296	0.078	*
TU UMa	-0.325	-0.307	0.090

Table 5. Table 5 Zero Points

Sample	Filter	Method	Zero-point	Zero-point, No Blazhko
HST/FGS	H	LSQ	$-0.36\pm 0.07$	$-0.29\pm 0.25$
HST/FGS	F160W	LSQ	$-0.42\pm 0.06$	$-0.28\pm 0.25$
HST/FGS	F160W	LSQ, [Fe/H]	$-0.42\pm 0.07$	$-0.24\pm 0.25$
TGAS	H	LSQ	$-0.30\pm 0.08$	…
TGAS	F160W	LSQ	$-0.30\pm 0.09$	…
TGAS	F160W	LSQ, [Fe/H]	$-0.37\pm 0.13$	…
DR2	H	LSQ	$-0.39\pm 0.04$	$-0.37\pm 0.05$
DR2	F160W	LSQ	$-0.39\pm 0.04$	$-0.38\pm 0.05$
DR2	F160W	LSQ, [Fe/H]	$-0.47\pm 0.04$	$-0.44\pm 0.04$
HST/FGS	H	ABL	$-0.40\pm 0.14$	$-0.43\pm 0.29$
HST/FGS	F160W	ABL	$-0.39\pm 0.14$	$-0.43\pm 0.29$
HST/FGS	F160W	ABL, [Fe/H]	$-0.39\pm 0.14$	$-0.44\pm 0.29$
TGAS	H	ABL	$-0.39\pm 0.08$	$-0.43\pm 0.12$
TGAS	F160W	ABL	$-0.39\pm 0.08$	$-0.43\pm 0.12$
TGAS	F160W	ABL, [Fe/H]	$-0.38\pm 0.08$	$-0.42\pm 0.12$
DR2	H	ABL	$-0.39\pm 0.07$	$-0.39\pm 0.08$
DR2	F160W	ABL	$-0.39\pm 0.07$	$-0.40\pm 0.08$
DR2	F160W	ABL, [Fe/H]	$-0.37\pm 0.07$	$-0.38\pm 0.08$

Equations

$$M_{\lambda }=a_{\lambda }\times [log(P)-0.3]+b_{\lambda }$$

$$M_{\lambda }=a_{\lambda }\times [log(P)-0.3]+b_{\lambda }+c_{\lambda }\times ([Fe/H]+1.60)$$

$$a=10^{0.2M}={\varpi }^{0.2m_o-2}$$

$$10^{0.2(a_{\lambda }+b_{\lambda })}=\varpi 10^{0.2m_o-2}$$

$$10^{0.2(a_{\lambda }+b_{\lambda }+c_{\lambda }[Fe/H])}=\varpi 10^{0.2m_o-2}$$

Full text

1. Introduction

Since the discovery of the expanding Universe by Hubble (1929) astronomers have measured the rate of expansion, the Hubble Constant ($H_{o}$), with increasing accuracy. The completion of the Hubble Space Telescope Key Project established the modern era of $H_{o}$ measurements, with more recent Cepheid-based distance ladder studies reaching the 3% level of precision (Freedman et al., 2001, 2012; Riess et al., 2016). The Carnegie-Chicago Hubble Program (CCHP) aims to provide a new and independent pathway to the measurement of $H_{o}$. Using a distance ladder comprised of RR Lyrae stars, Tip of the Red Giant Branch (TRGB) stars and Type Ia Supernovae (SNe Ia), CCHP-II will provide a pure Population II basis to a measurement of $H_{o}$, with an aim of achieving an accuracy of 3% (Beaton et al. 2016, Freedman et al. 2018, in preparation). In this way, galaxies with only old stellar populations (and thus no Cepheid variables) can also be used as an independent assessment of the ongoing tension between distance-ladder based and Cosmic Microwave Background-based measurements of $H_{o}$ (Freedman, 2017; Riess et al., 2018). The SNe Ia zero-point can be set using only the TRGB rung of the distance ladder, with both current TRGB parallax measurements (e.g. Brown et al. 2018) and in the future with Gaia parallaxes. The TRGB zero-point itself, however, can be independently set by the RR Lyrae stars. Thus the first step in this distance ladder will be enabled by a well-calibrated, accurate zero point for Galactic RR Lyrae stars.

The existence of a near-infrared PL relation for RR Lyrae stars was first demonstrated by Longmore et al. (1986, 1990) with K-band observations of RR Lyrae stars in Galactic globular clusters. Theoretical models now also clearly show a PL relation for RR Lyrae stars is to be expected at nearly all wavelengths, with the exception of V-Band (e.g. Bono et al. 2003; Catelan et al. 2004). Further, Madore & Freedman (2012) demonstrated that there is a decrease in intrinsic scatter with an increase in wavelength of PL relations for both Cepheids and RR Lyrae stars due to a number of effects including a lower sensitivity of surface brightness to temperature variations and, to a lesser extent, a decrease in the line-of-sight extinction. As such, IR-wavelength determinations of the PL relation for RR Lyrae stars have significant benefits when compared to visible light measurements.

RR Lyrae PL relations are well characterized from optical (R & I) to mid-IR wavelengths (e.g. Madore et al. 2013; Dambis et al. 2014; Braga et al. 2015; Neeley et al. 2015), but in order to use RR Lyrae stars as part of a precision distance ladder in the determination of $H_{o}$, it is essential to reduce both random and systematic errors (Freedman et al., 2012; Beaton et al., 2016; Riess et al., 2016). As such, the CCHP was designed to employ the smallest number of instruments and filter combinations possible across the entire distance ladder. To minimize systematics the CCHP $H_{o}$ calibration, in fact, seeks a purely space-based calibration of $H_{o}$ with the use of a single telescope, the Hubble Space Telescope (HST). This is accomplished by calibrating the RR Lyrae PL relation at the reddest near-IR wavelengths available to HST, with the F160W (H-band) filter on the the WFC3/IR camera.

A near-IR calibration of the Galactic RR Lyrae PL zero point is now possible given the availability of accurate ($\sim$8%) parallaxes determined for a few stars using the HST Fine Guidance Sensor (FGS) (Benedict et al. 2011) and in the near future Gaia will provide parallaxes at similar or better precision for hundreds of RR Lyrae stars (Clementini, 2016; Gaia Collaboration et al., 2017). In this paper we present our measurement of the geometrically-based period-luminosity relation for Galactic RR Lyrae stars with HST WFC3/IR photometry that can now be used to calibrate this particular first rung of the CCHP-II distance ladder.

2. Sample & Observations

Our sample consists of 30 Galactic RR Lyrae stars. Five of our RR Lyrae stars have trigonometric parallaxes measured with HST/FGS: XZ Cyg, UV Oct, RR Lyr, SU Dra and RZ Cep (Benedict et al., 2011). The remaining 25 Galactic RR Lyrae stars will ultimately have their parallaxes determined by Gaia with an error of $\sim$1% (de Bruijne et al., 2014; Clementini, 2016; Gaia Collaboration et al., 2017). Our observations were conducted with HST WFC3/IR and were spread across two HST programs as described in detail in the following subsections. The first program consisted of single-epoch SNAP observations designed to form the foundation of our full HST-based calibration (PID 13472, PI Freedman). The second program was designed to link the RR Lyrae stars and TRGB calibrations out to the Hubble flow, with dedicated follow-up and single-epoch observations for the five RR Lyrae stars with accurately measured parallaxes (PID 13691, PI Freedman). The final sample is presented in Table 1, periods are adopted from Monson et al. (2017), wherein a self-consistent solution for multi-wavelength, long time-baseline data was found for each star in our sample. All of our stars have B, V, I, and Spitzer 3.6 & 4.5 $\mu$m data.

2.1. SNAP Observing Program

The majority of our observations were taken in the course of our HST SNAP program. Each star observed in the SNAP program has only one randomly timed epoch due to the nature of SNAP observations. With the exception of RR Lyrae itself, our data consist of several very short direct exposures due to the brightness of our targets and the desire to gather as much data as possible in the portion of each HST orbit we were allotted.

For every star it was necessary to use both the subarray and RAPID sampling readout modes to avoid saturating the detector. Based on saturation times estimated from the WFC3/IR exposure time calculator (ETC), stars were observed with either a 64x64 or 128x128 subarray with a single RAPID sample, resulting in the shortest possible total exposure times of 0.061 and 0.113 seconds respectively. These rapid observations are further facilitated by the lack of a shutter for the WFC3/IR channel. This was done 26 times in sequence with a simple 2-point dither pattern, achieving the maximum number of exposures possible before a read-out of the WFC3/IR buffer was necessary. The very short exposure and subarray size ensured that in all frames the only object with any detectable flux was the RR Lyrae variable targeted.

Based on the previous observations of bright Cepheids (Riess et al. 2014 and Casertano et al. 2016), we observed the star RR Lyr using WFC3/IR in a drift-scanning mode. In order to drift rapidly enough that RR Lyr did not saturate, our observations were carried out with a full-frame readout in gyro-only guiding mode, facilitating a scan rate of 7.5 arcsec s*-1*. With the maximum number of RAPID samples possible as the star sped across the detector, our total time spent on target for a single drift scan of RR Lyrae was 17.6 seconds. This observation was repeated four times with a two-point dither pattern, with the number of exposures again limited by the maximum number of full-frame observations possible before a buffer read was required.

2.2. GO Observing Program

The remaining observations of our sample were taken as part of our large HST General Observing program summarized in Beaton et al. (2016). We used WFC3/IR to observe the five Galactic RR Lyrae stars from (Benedict et al., 2011). This was done to achieve two sets of measurements separated in phase in order to better constrain the mean magnitudes of our zero-point calibrators and to allow us to assess the accuracy of our single-phase SNAP-based magnitudes.

We found that despite the predictions of the ETC, even the shortest exposures in our SNAP observations with WFC3/IR show evidence of non-linearity. Because of this, our observations included drift-scanning observations to avoid reaching non-linearity in an effort to cross-check our short-exposure SNAP and GO observations. We split a single orbit between direct and drift scanning observations. One star, UV-Oct, was allocated two orbits as it had not yet been observed in our SNAP program, while the remaining four stars were allocated one orbit each.

As with the SNAP observations, we observed each of the five targets with the smallest 64x64 subarray and RAPID sampling to minimize the number of pixels subject to non-linearity, resulting in 0.061 second individual exposures. We used a four-point dither pattern for these observations with 8 cycles over a single orbit, resulting in 32 individual exposures of each star.

After the direct imaging exposures, we again used gyro-only guiding mode to observe in drift scanning mode with full frame readout. Each star was observed in this manner with four exposures on different portions of the chip, with a total exposure time of 14.66 seconds for each, with a scan rate of 7.5 arcsec s*-1* for UV Oct and 6.5 arcsec s*-1* for the remaining four stars.

3. Analysis

Although none of our direct imaging observations contain truly saturated pixels (with the exception of RR Lyr), some of our observations have pixels which surpass the non-linearity threshold established in the HST WFC3/IR manual and are likely approaching saturation between the zeroth and first (and only) read, resulting in an estimation of counts from the zeroth read only and a significant uncertainty in the total number of counts (Riess, 2011). For these frames the estimation of counts is significantly overestimated, and the non-linearity correction applied by the HST pipeline to the calibrated, flat-fielded data results in significant deviations from expected values. That is, simple aperture photometry of observations with these significantly brighter pixels results in highly inaccurate measurements and suggests that the actual flux is over-predicted in such cases.

Figure 1 shows each of the direct images of XZ Cyg obtained in the SNAP program; 12 of the exposures do not approach the “saturation” threshold (blue dots), while 14 of the exposures have one pixel with a significant non-linearity correction applied (red dots). Aperture photometry of the individual HST-calibrated FLT files shows a a bi-modal pattern with a systematic difference of 0.2 mag. The bi-modality is a result of the dither pattern: in the exposures with a correction applied, the PSF of the star is centered perfectly on a single pixel while in the other exposures the center falls in a gap between pixels, lowering the peak flux in any one pixel below the non-linearity threshold.

Although the stars are well isolated, the presence of significantly non-linear pixels without a proper correction means that we cannot apply simple aperture photometry to our direct SNAP and GO observations. Our solution to this situation is to mask pixels in frames with poor non-linearity corrections and then undertake PSF photometry.

3.1. Direct Imaging Photometry

Photometry was carried out with DAOPHOT (Stetson 1987, 1994) on all individual direct imaging “FLT” frames with the HST Pixel Area Map correction applied. Because we cannot generate a unique PSF for each frame, we used DAOPHOT to generate and apply one PSF for use in the 64x64 images and then generated a separate PSF for the 128x128 images. To generate the PSF, we used stars that are “clean” (i.e. images that do not have pixels that approach the non-linear regime): 156 images for the 64x64 subarray and 208 for the 128x128 subarray or 26 images of 6 and 8 stars each, respectively.

To determine which parameters to assign to our model PSF, we generated several thousand individual PSF models with PSF radius and fitting radius varied in integer pixel increments from 2 to 17 and the 7 different PSF functional forms available in DAOPHOT. We then compared the magnitude derived from each model PSF for each star with aperture photometry and chose PSF parameters that, on the average, best reproduced the aperture magnitudes. We assigned a PSF radius of 14 pixels to the 64x64 PSF model and 17 pixels for the 128x128 PSF model and used a fitting radius of 12 pixels and a Moffat function with $\beta=3.5$ for both PSF models.

We also use the “clean” images to test the effect of pixel masking on our PSF photometry. We chose the brightest pixel in each image, masked it, and redetermined the magnitude using the same range of PSF parameter values. Regardless of the parameters used, masking pixels did not significantly impact DAOPHOT PSF photometry measurements. When masking stars in our 64x64 images we found a systematic offset of $-0.0017\pm 0.0022$ mag, and for 128x128 images we found an offset of $-0.0024\pm 0.0028$ mag.

Finally, we calculated aperture corrections to use with our PSF photometry with DAOGROW and aperture photometry of our “clean” images (Stetson, 1990). We applied an aperture correction of 0.0196 mag to 64x64 images with a 14 pixel radius PSF and 0.0136 mag to 128x128 images with a 17 pixel PSF. These aperture corrections were computed to an infinite aperture, after which we applied the HST WFC3/IR F160W Vega zero point for an infinite aperture of 24.695 mag (taken from http://www.stsci.edu/hst/wfc3/ir_phot_zpt). The final photometry for each observation, for each target, is given in Table 2. The errors quoted in Table 2 are the photometric errors derived by DAOPHOT. The mean magnitudes derived in Section 2 include an additional 2% systematic error as described at http://stsci.edu/hst/wfc3/phot_zp_lbn.

4. Mean Magnitude Determination

Because we have only sparsely-sampled light curves, we have undertaken template fitting to determine mean magnitudes for our sample of RR Lyrae stars. Fortunately, the stars in our sample have a wealth of ground and space-based observations available for the construction of light curve templates constructed on a star-by-star basis (Monson et al., 2017). We consider two approaches: (1) we compare our observations to smooth light curves constructed from Spitzer $3.6\mu$m observations and (2) we use predicted templates generated from optical V and I band ground-based observations, as first proposed and demonstrated for Cepheids in Freedman & Madore (2010a). In each case, we averaged all of the data points available in each epoch of SNAP or GO observation into a single-epoch, intensity-averaged point, resulting in one to three HST F160W points to which a template light curve can be compared. Phases for the data points used in mean magnitude determination are calculated using the periods and phase correction information and methodology to be outlined in Beaton et al. (in prep).

The smoothed Spitzer light curves were generated by applying GLOESS (Gaussian-windowed LOcal regrESSion method, Persson et al. 2004; Monson et al. 2017) to 20-40 evenly spaced data points, resulting in a smoothly varying curve (Monson et al., 2017). The mid-IR data are well suited for comparison to our near-IR observations, as we expect by the H-band that the light-curve shape is dominated by radius effects. As such, we simply offset in magnitude the 3.6$\mu$m GLOESS curve to fit the available HST data points and take the mean of the offset light curve to be our F160W mean magnitude. Figure 2 demonstrates this process for UV Oct, the star in our sample with the most data points. The error on our mean magnitude measurement combines the random photometric error of our data, the error in the template, and the error on the phase estimate and its location with respect to the template. There is an additional possible systematic error induced by the difference in amplitude between 3.6$\mu$m and H-band. Measurements by Monson et al. (2017) show the H-band has a larger amplitude with a median of $\sim 0.03$ magnitudes, leading to a potential offset in magnitude of $\sim 0.01$ magnitudes, depending on the phase of our measurements.

For comparison with our Spitzer-derived magnitudes, we follow the same procedure with custom-generated template light curves for each RR Lyrae variable. We use near-infrared templates generated from V and I band data using a process described in Beaton et al. (2016); Monson et al. (2017) and Beaton et al. (in prep). The templates require well-sampled B, V & I light curves that can be combined to trace the change in temperature and radius. Temperature-independent curves that predict the shape of the IR light curves are generated using the visible light. These curves predict the shape of the IR light curves which primarily trace radius, with a scaling in amplitude (Freedman & Madore, 2010a, b).

We offset the template to match the available data and measure the mean of the shifted ground-based template. The intensity-averaged measured mean magnitudes for both methods are given in Table 3. The two methods provide consistent mean magnitudes, with an average difference of 0.005$\pm$0.019 mag (magSptz-magtmpl). Further, our F160W magnitudes are offset by 0.015$\pm 0.06$ mag from the Two Micron All-Sky Survey (2MASS) H-band magnitudes, which is roughly consistent with the 0.0215$\pm 0.0054$ mag difference calculated by Riess (2011).

5. Period-Luminosity Relations

To construct our PL relations we calculate absolute magnitudes for RR Lyrae stars from our F160W sample with known parallaxes. For this calculation we use the mean magnitudes derived by scaling Spitzer data as described in the previous section. We examine RR Lyrae stars with HST/FGS parallaxes (Benedict et al. 2011), Tycho-Gaia Astrometric Solution (TGAS) parallaxes (Lindegren et al. 2016; Gould & Kollmeier 2017; Gaia Collaboration et al. 2017) and Gaia data release 2 (DR2) parallaxes (Gaia Collaboration et al., 2018; Lindegren et al., 2018). Our absolute magnitudes include a correction for extinction adopted from the published values of (Feast et al., 2008) that will be discussed further in Beaton et al. (in prep). The values we use in this paper are given in Table 1. As a check for consistency, we compare our absolute magnitudes and PL relations with 2MASS H-band magnitudes. We consider only the fundamental pulsators (RRab) in our PL analysis.

To compute the absolute magnitude, we use two methods: we invert the parallax to produce a distance and we use the astrometry-based luminosity (ABL) method for parallaxes with larger errors. For direct inversion of parallaxes, we restrict our sample to $\sigma_{\pi}/\pi$ <0.1, the regime where this is an appropriate treatment for the resulting distance uncertainties and no additional forward modeling is explicitly required (Astraatmadja & Bailer-Jones 2016; Gaia Collaboration et al. 2017). We use only RRab stars for determination of the zero points 111Although we do not consider RRc stars here, the multi-band analysis by Monson et al. (2017) find an RRc zero point that is consistent with Kollmeier et al. (2013). These cuts result in a final sample of with 4, 3, and 20 RRab stars for HST, TGAS, and DR2 parallaxes respectively..

Absolute magnitudes derived from directly inverted parallaxes used in our PL analysis are given in Table 4. The errors for absolute magnitudes derived with HST/FGS and TGAS parallaxes are calculated directly from the errors in the parallax as they dominate the uncertainty. The error in absolute magnitude when derived from Gaia DR2 parallaxes are a combination of the error on the mean magnitude (Table 3) and the error in parallax. The period-luminosity relation takes the simple form:

[TABLE]

where a and b are the slope and intercept respectively, and P is the period in days. We perform an unweighted least-squares (LSQ) fit assuming a fixed slope of a $=$ $-$2.215 and a $=$ $-$2.189 for fundamental pulsators in the 2MASS H-band (Braga et al. 2015) and HST F160W respectively (Marconi et al. in prep). Using the cuts discussed in the previous section four stars with HST/FGS parallaxes, three with TGAS parallaxes, and 20 stars with DR2 parallaxes are used to generate different PL relations this way. The resulting zero points at log(P) = -0.3 days are given in Table 5.

Example PL relation fits are shown in Figure 3.

5.1. Period-Luminosity-Metallicity Relations

In order to examine the effect of metallicity on our zero point measurement we also consider a period-luminosity-metallicity (PLZ) relation for F160W. Our PLZ relation takes the following form:

[TABLE]

where a, b and P take the same form as our PL relation, [Fe/H] is the metallicity of each RR Lyrae star (as compiled and homogenized by Monson et al. 2017, from Feast et al. 2008, Fernley et al. 1998, and Fernley & Barnes 1997, see Table 1.), and c is the slope of the adopted metallicity correction applied to each star, with a value of c$=$0.186 (Braga et al., 2015). The results are shown in Table 5 for comparison. For the stars with HST parallaxes, we find a fairly consistent zero point. RR Lyrae stars from the TGAS parallax sample exhibit a larger zero point discrepancy, but at present the errors on the absolute magnitudes result in too large a scatter to draw a significant conclusion about this difference.

5.2. Astrometry-Based Luminosity

In their analysis of RR Lyrae TGAS parallaxes, Gaia Collaboration et al. (2017) note that parallax inversion to calculate absolute magnitudes is inadvisable if the parallax errors are too large. We mirror their analysis here for comparison and include a measurement of the zero point using Astrometry-Based Luminosity (ABL, Arenou & Luri 1999), defined as:

[TABLE]

This is the same as Gaia Collaboration et al. (2017) formula (2), where $M$ is absolute magnitude, $\varpi$ is the parallax, $m_{o}$ is the extinction-corrected apparent magnitude. We then solve the following PL and PLZ relations for the zero point $b_{\lambda}$, corresponding to Gaia Collaboration et al. (2017) formulas (4) and (5):

[TABLE]

[TABLE]

We apply the same fixed slopes a and c used in sections 5.1 and 5.2, the resulting zero points are given in Table 5. We use a less conservative cut of $\sigma_{\pi}/\pi$ <0.2. With this less stringent cut our usable TGAS sample includes 13 RRab stars for the ABL fit, while our HST and DR2 samples remain the same size.

5.3. Blazhko Effect

Several of the stars in our sample exhibit the Blazhko effect, which can affect the measurement of mean magnitudes in the optical as well as the IR (e.g. Jurcsik et al. 2018). In order to consider the impact of the Blazhko pulsators sample, we fit PL relations with only those RRab stars which apparently do not suffer from amplitude modulation. The fits are performed in the same manner as described above, with 1 and 14 stars from the HST and Gaia DR2 parallax samples respectively. There are no non-Blazhko stars with TGAS parallaxes below the $\sigma_{\pi}/\pi$ <0.10 cut, and 6 below the $\sigma_{\pi}/\pi$ <0.20 cut. As such, we only calculate a zero point using the ABL method in this case. The results are given in Table 5. The largest difference is for the HST parallax sample when performing a least-squares fit, as the zero-point is now constrained by a single star. The ABL method shows consistent results between the zero points fit with and without Blazhko RRab.

6. Conclusions

We have carried out photometry using HST/WFC3 of 30 Galactic RR Lyrae stars taken in F160W. Our results are part of the larger effort associated with the CCHP; the photometry presented here will be used to provide a calibration of the Galactic RR Lyrae zero point in the same flight-magnitude system used to measure RR Lyrae distances to nearby galaxies. The mean magnitudes that we calculate are consistent with ground-based H-band photometry, within the expected offset between the 2MASS and HST flight magnitude systems.

We also present PL relations for the RRab stars in our sample using both HST/FGS and Gaia TGAS & DR2 parallaxes. These PL relations provide an initial estimate of the HST F160W zero point, with all three parallax samples providing zero points consistent within their respective errors. Our final Galactic RR Lyrae zero point will rely on a larger sample of more accurate parallaxes provided by the next Gaia data release.

7. Acknowledgements

We thank the referee for their helpful and constructive comments. Myung Gyoon Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) (No. 2017R1A2B4004632). This paper makes use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.