A NEW ANALYSIS OF THE EXOPLANET HOSTING SYSTEM HD 6434

The methodology of the TERMS project requires that we have an adequate understanding the host star properties, particularly the mass and radius. To characterize HD 6434, we obtained a high-resolution spectrum using the CHIRON high resolution spectrograph installed on the CTIO 1.5 m telescope on 2014 July 7 (Tokovinin et al. 2013; Brewer et al. 2014). A 400 s exposure, between 4200 and 8800 Å, was taken of the object with a resolution of R = 90,000, resulting in a signal to noise of ∼100.

We use the Spectroscopy Made Easy (SME) package (Valenti & Fischer 2005) in iterative mode (Valenti et al. 2009) to determine the stellar properties. The iterative approach determines stellar properties from the observed spectrum and compares them to those predicted by the Yonsei-Yale model evolutionary isochrones (Demarque et al. 2004) in order to arrive at an internally consistent solution. The stellar values for HD 6434 are shown in Table 1, including both referenced and derived parameters from our CHIRON spectra analysis. The stellar temperature derived from spectral synthesis and the radius derived from evolutionary modeling are within 1σ agreement with those estimated from empirically calibrated ($V-J,H,K$) color–temperature relations, ${T}_{{\rm{eff}}}$ = 5739 K, and surface brightness relations, ${R}_{*,\mathrm{SB}}=1.10\pm 0.04\;{R}_{\odot }$ (Boyajian et al. 2013; Boyajian et al. 2014). The derived parameters are consistent with the star being a G1IV m-2 star per Gray (1989), who specifically targeted metal-poor stars.

Table 1.  Stellar Parameters

Parameter	Value	Source
V	7.71 ± 0.12	Carney (1978)
B − V	0.61 ± 0.01	Carney (1978)
Distance (pc)	41.4 ± 1.03	Hipparcos
Age (Gyr)	11.27 ± 2.12	SME
[Fe/H] (dex)	−0.48 ± 0.05 (0.35)	Hypatia
${T}_{{\rm{eff}}}$ (K)	5690 ± 92	SME
$\mathrm{log}g$ (cgs)	4.29 ± 0.06	SME
$v\mathrm{sin}i$ (km s−1)	2.2 ± 0.5	SME
M* (${M}_{\odot }$)	0.89 ± 0.04	SME
R* (${R}_{\odot }$)	1.14 ± 0.05	SME

Download table as:  ASCIITypeset image

In comparison to Santos et al. (2001), we find that our SME ${T}_{{\rm{eff}}}$ is 100 K lower and $\mathrm{log}g$ is 0.27 lower. Similar to Santos et al. (2001), Mayor et al. (2004) had a larger ${T}_{{\rm{eff}}}$ value of 5835 K, $\mathrm{log}g$ of 4.60, similar $v\mathrm{sin}i$ of 2.3 km s⁻¹, and a smaller M_* estimate of 0.79 ${M}_{\odot }.$ Moro-Martín et al. (2007) also had a higher value for ${T}_{{\rm{eff}}},$ the same as Mayor et al. (2004), although their stellar mass estimate was between ours and Mayor et al. (2004) at 0.84 ${M}_{\odot }.$

To date, more than a dozen different groups, such as Ecuvillon et al. (2004) and Battistini & Bensby (2015), have measured +23 elemental abundances within the photosphere of the HD 6434 host star. Every group that measures stellar abundances normalizes their data with respect to a solar scale, however, those scales vary and therefore makes comparing multiple data sets difficult. Therefore, we renormalized the solar abundance scales for all of the data sets to be on a consistent scale with respect to Lodders et al. (2009), per the analysis within the Hypatia Catalog (Hinkel et al. 2014). The median [Fe/H] determination in HD 6434 was −0.48 dex, with a variation of 0.35 dex between the groups. The maximum, renormalized [Fe/H] measurement originated from Gilli et al. (2006) with −0.31 dex while the minimum measurement was from Laird (1985) with −0.66 dex. Comparatively, the SME [Fe/H] determination for HD 6434 performed here is −0.61 ± 0.07 dex when renormalized. The standard error on [Fe/H] is ∼0.05 dex, meaning that the spread between groups is a factor of over five times larger than the typical error. The large group-to-group discrepancy within the literature, due to the variations between the methods and systematic offsets, means that HD 6434 was not included in the analysis or reduced version of the Hypatia Catalog (Hinkel et al. 2014).

Many elements that are considered important for habitability, such as carbon, oxygen, magnesium, and silicon, were measured within the photosphere of HD 6434, namely [C/Fe] = 0.22 ± 0.09 (0.43) dex, [O/Fe] = 0.35 ± 0.09 (0.28) dex, [Mg/Fe] = 0.3 ± 0.07 (0.03) dex, and [Si/Fe] = 0.13 ± 0.05 (0.07) dex, where both the typical errors are included along with the respective spreads in parenthesis. In addition to [Mg/Fe], there were an additional ten elements for which the spread was smaller than the average error for that element: [N/Fe] = 0.08 dex, [S/Fe] = −0.14 dex, [Sc ii/Fe] = 0.025, [Cu/Fe] = −0.06 dex, [Zn/Fe] = 0.0 dex, [Y/Fe] = 0.24 dex, [Yii/Fe] = 0.27 dex, [Zr/Fe] = 0.27 dex, [Zr ii/Fe] = 0.32 dex, [Ba ii/Fe] = 0.16 dex, [Nd/Fe] = 0.13 dex, and [Eu/Fe] = 0.15 dex. In general, the volatile and neutron-capture element-ratios within HD 6434 were super-solar. However, element-ratios for those at the iron-peak were markedly sub-solar. While this conclusion may prove interesting when considering the presence of the b-planet around the host star, we must remember that the spread in the individual elements, in conjunction with the large spread in iron, makes any firm interpretation tentative until the methodologies can be better understood.

To examine the stellar variability of HD 6434, we performed a weighted Lomb-Scargle (L-S) Fourier analysis of our photometry (see Kane et al. (2007) for more details). The L-S Fourier analysis was first applied to the Hipparcos photometry by Mayor et al. (2004), and like them, we do not find any peaks of significance at the measured orbital period of the planet. There is a peak of moderate significance at 24.13 days, however given the evolved G1 classification of the star (see Section 2.1), it could possibly be due to the stellar rotation period.

The strongest peak in the Fourier analysis of the Hipparcos photometry is at 5.12 days. A Fourier analysis of our CTIO 1.0 m photometry (see Figure 1) are unable to confirm the 24 day period since the data sampling do not cover a complete orbital period of the planet. The power spectrum does, however, reveal a significant periodic signature at 5.32 days, similar to the Hipparcos signature at 5.12 days. The nature of such a periodic signature is difficult to explain from a stellar astrophysics perspective and requires further study. The horizontal lines in Figure 1 indicate significance values starting at false-alarm probability (FAP) ranging from 10% to 0.01% FAP. The FAP are extremely low for these calculations because the number of data points is high and the range of frequencies that we sample in the Fourier analysis is large. In addition, the FAP is slightly underestimated due to non-Gaussian sources of noise in the photometry, although this effect is minimal. As a final check, we also examined a single night of CTIO 0.9 m photometry for less than 0.5 day periodic signatures but no features of significance were detected in the Fourier analysis.

Zoom In Zoom Out Reset image size

We utilized publicly available data from the Hipparcos satellite. Hipparcos acquired a total of 142 measurements of HD 6434 over a period of 1146 days during the course of its mission lifetime (Perryman et al. 1997; van Leeuwen 2007). Analysis of these Hipparcos data show that they have a 1σ rms scatter of 0.018 mag and a mean measurement uncertainty of 0.012. The data are thus consistent with HD 6434 being photometrically stable at the ∼1% level.

The TERMS team first monitored HD 6434 with the CTIO 1.0 m telescope and Y4KCam CCD detector during 2011 Oct 22–30. The observations were conducted off-transit to establish a baseline and were done using the Johnson-Morgan B-band filter. Relative photometry was performed using the TERMS Photometric Pipeline (see the Appendix) with respect to one stable comparison star: CD-40 236. Note we had originally identified two references stars within the science frames, but found that the CD-40 237 was a variable star and therefore unusable. The data have a 1σ rms of 0.007 mag.

Additional time was required in order to monitor the target during the predicted transit window. Time was allotted on the CTIO 0.9 m telescope during 2012 October 18–20. The same reference star and filter were used. Due to poor weather, one additional night was needed to determine whether HD 6434 transited during the predicted transit window. The night of 2014 September 22 was purchased on the CTIO 0.9 m telescope and observations were conducted by David James, again using the same reference and filter. The CTIO 0.9 m data have a 1σ rms of 0.016 mag.

The phase-folded photometric results are given in Figure 3, where all of the data within the window were taken on the CTIO 0.9 m telescope. The solid black lines shows the predicted transit behavior of the planet, including the transit duration (0.01 phase or 0.25 days) as dashed black lines (see Table 3) at a predicted depth of 0.9%. These properties were determined using the stellar (Table 1) and orbital planetary ephemerides (Table 3). The central transit window (0.031 phase or 0.69 days) was calculated using the error on the stellar radius and improved planetary properties, given by dotted lines. The uncertainty on the transit midpoint (0.021 phase or 0.46 days) is given by the solid red line.

Zoom In Zoom Out Reset image size

To verify the trend in the 657 observations within the transit window, we plot the mean (0.9994 mag) as an orange triangle. Additionally, we have divided the data into two 1σ bins, which translates to a width 0.01 in phase-space, and determined the means of each of those bins, 1.0055 and 0.99994 mag, given as dark blue triangles, respectively. The means of the two 1σ bins, in conjunction with the overall mean of the data, serve to verify the comparatively stable relative flux observations seen within the transit window. The data has a 1σ rms scatter of 0.009 mag, which would have captured a transit event with significant certainty. We can rule out the possibility of a HD 6434b transiting in front of the host star to a depth of 0.9%. Additionally, given that these measurements cover 75.4% of the predicted central transit window, centered on the transit window, without a significant decrease in the relative flux, we can rule out a grazing transit to a depth of 1.6% due to the limitations of the impact parameter.

The reduction performed by the TPP is done in two steps. Initially, the over-scan region of each science frame is trimmed. If the image is produced from multiple CCD chips, a mosaic can be created from the individual frames. The current chip geometry options are 1 × 1, 1 × 2, 2 × 1 and 2 × 2. Once the user has specified the bounds for the trimming, the frames are cropped, stitched together, and saved to a sub folder such that the original frames are never changed. An example of the GUI is shown in Figure 4 (left). Once the reduction preferences are set up, the options can be saved to a text file and loaded in the future.

Zoom In Zoom Out Reset image size

The second part of the reduction creates the master-bias and -flat frames, then removes their effects from the science images containing the object(s) of interest. The user loads trimmed images⁶ and is able to filter the entire data set based on two sets of keywords. For example, by first sorting by the header-keyword "flat" will reduce the file list to only frames containing sky/dome flats. A second sort, for example on the keyword "R," can then be used to further reduce the list of files that contains dome/sky flats acquired with the R filter. Each frame can be examined individually, added or removed from the list, such that only high quality data are kept for reduction. The user is then able to create a master-bias and -flat frames (or load them if they have already been made). The master-bias is created by taking the average of all the trimmed bias frames selected. After the bias has been subtracted, the trimmed flats are normalized and averaged to produce the master-flat. After creating/loading the master-bias and -flat frames, the user can use the GUI to specify a new file list in order to specify the target frames. The science frames are reduced by subtracting the master-bias and dividing by the master-flat.

The photometric routine utilizes the APER code, which is based on previously developed work per DAOPHOT and its implementation, in IDL. The stars observed with the TERMS project are bright and therefore are often purposefully unfocused in order to avoid having saturated pixels in the object profile, making point-spread function fitting not applicable. The user specifies the location of the target and reference stars by using mouse-clicks, see Figure 4 (right). The center of the star is found though a centroid algorithm, where pixels containing less then the median value of the total count are excluded from the calculation in order to remove the effects of the background. The calculation for the centroid is analogous to one for center of mass:

$$\begin{eqnarray}&&{C}_{r}=\displaystyle \frac{1}{{F}_{\mathrm{tot}}}\displaystyle \sum _{i=0}^{n}{F}_{i}{r}_{i}\end{eqnarray} \tag{ 1 }$$

where C is the center, F is the pixel value for frame i, F_tot is the total value of all pixels in the region once the background has been removed, and r is the pixel coordinate (x, y) on the CCD. We have determined that such an approach works well for non-crowded fields. Photometry may be performed for up to 12 objects (target + reference stars) across the entire image data set.

Aperture photometry, used for subtracting the background signal, is then performed about the center. Ideal aperture and sky annuli are obtained with the Aperture Suggestion Routine built into the TPP. Once initiated with an aperture range, inner sky radius, and outer sky radius, the TPP selects random images and linearly changes the pixel size of the aperture, producing flux as a function of aperture radius. This approach is resembles to a curve-of-growth analysis (Figure 5), such that when the photon count levels off at a certain point, an increase in aperture size only introduces additional counts from the background and not the actual target. The Aperture Suggestion Routine allows for aperture, inner-, and outer-sky radii to be determined consistently for all science frames.

Zoom In Zoom Out Reset image size

The TPP has two built-in routines which are not necessary for the data analysis but can be useful in particular situations. The first routine is a simple IDL wrapper for astrometry.net (Hogg et al. 2008). This enables the user to obtain accurate R.A. and decl. J2000 coordinates, which at times may be unknown, and use them to determine the location of potential target stars.

The secondary supplementary routine available is a plotting function, implemented in order to provide the observer at the telescope with fast analysis of the data as they are being obtained. The plotting routine allows the user to graph parameters like flux, airmass, x/y pixel coordinates, time, as well as any customizable variables, for up to 12 stars. Furthermore, relative photometry can be performed on any target, using any combination of up to 12 stars within the data set.

We have thoroughly tested the TPP against published data sets, both from within the TERMS team and from external sources, to verify that the photometric analysis accurate and repeatable. Furthermore, given the Aperture Suggestion Routine, our results are also easily reproducible and do not depend on the person reducing the data. We have used the TPP while "in the field," reducing data taken on previous nights in order to inform upcoming observations, and have had excellent success. The TTP has been tested and used with telescopes from Lowell Observatory (not shown here) as well as the CTIO 1.0 and 0.9 m telescopes. Please contact the author if you would like a copy of the TPP for these or additional telescopes.