Exoplanet Transits Registered at the Universidad de Monterrey Observatory. I. HAT-P-12b, HAT-P-13b, HAT-P-16b, HAT-P-23b, and WASP-10b

In principle, the final light curve for each date can be fitted independently with a transit model in order to obtain the parameters of the system. However, in practice, the amount of noise present would result in large uncertainties for the model parameters because of the modest telescope aperture used. Therefore, in order to decrease the noise in the light curve to be modeled and obtain better results, we decided to combine all available light curves for a given target. This is warranted because nearly all light curves obtained for a particular target have the same exposure times and similar number of comparison stars, which yielded similar scatter. However, in doing so, we were concerned that long-term brightness variations of the target stars might affect our resulting combined light curves since deeper transits are measured for a given planet size when the host star is dimmer. This could be caused by starspot or other activity. Since we had differential photometry of the target stars with the same comparison stars over multiple epochs, we were able to record brightness variations of the host star or of a particular comparison star. The largest brightness variation of a target star was observed for HAT-P-16 and amounted to ∼4%. Our observations were not frequent enough to detail if these brightness variations showed a trend or were periodic. However, these are within the observing noise limitations for individual transit depths and their effect is also diminished in the process of averaging multiple light curves. Combining all transit light curves into one should theoretically improve the scatter by a factor of $\sim \downharpoonleft n$ and have a tendency to cancel out any systematic leftover trends that may be present after the reduction of the individual light curves.

In order to combine the light curves, we first need to co-register them by finding the mid-transit time for each event. In order to fit the observed transit light curves, we first created initial standard model light curves. These were constructed numerically as a tile-the-star procedure using the software package Binary Maker II (Bradstreet 2005). The initial system parameters used were obtained from the available literature and the linear limb-darkening function coefficient for this system was taken from Claret (2000). Small adjustments to the duration and depth of the model transits were necessary to optimize the fits and extract the best mid-transit time possible for each individual light curve. This was done by applying small (a few percent) multiplicative factors to both the depth and duration of the model transit. Precise model parameters were not required as this first approximation fit to the individual "noisy" light curves was only intended to derive the mid-transit time for the event. Best-fit models were obtained by minimizing the ${\chi }^{2}$ of the data. Again, to be conservative we used the average scatter of the photometry (mean point-to-point difference) to estimate the uncertainties because this value is larger than the formal error for each photometric measurement.

Once the initial mid-transit times for each system were obtained, a combined light curve was created by placing all the photometry points in a common time reference frame, centered on the mid-transit time for each event, and by averaging the data points falling within predetermined bins. This method generates a light curve more suitable for modeling since it contains fewer data points, exhibits less noise, and also maintains the general shape of the transit curve. However, care must be taken in selecting the bin size in order to simultaneously have sufficient amount of data in each bin, and also sufficient data points to define the critical ingress and egress portions of the light curve. Initially, we attempted to use bins defined with a fixed amount of time (we found out that two-minute bins best satisfied both criteria) but determined that this approach was unsuitable since some bins ended up containing more data points than others. This would result in the data points of the combined light curve to be modeled having unequal weights. Therefore, we decided to define bin sizes by the number of points to be averaged. For each system, we chose a fixed number of photometric points (ranging from 8 for HAT-P-12 to 19 for HAT-P-13) for the bins such that it would yield an average spacing of about two minutes between them. We then calculated the average flux value and average time from mid-transit for each bin to construct the combined light curve to be modeled. In obtaining these average values we weighed each point by the inverse of its individual uncertainty measurement.

Further refinements were performed to the individual light curve mid-transit times by subjecting the combined light curve to the same ${\chi }^{2}$ fit to the preliminary model and obtaining general multiplicative factors to both the depth and duration of the model transit for each system. These factors were then used on the individual light curves to derive improved mid-transit times and also generate a new combined light curve. This process was iterated until there was convergence between the individual mid-transit times and the best-fit multiplicative factors for the combined light curve. Table 1 also presents the observed transits and the final mid-transit times derived from fitting the models as explained above.

In all cases the resulting combined light curve exhibits a much reduced scatter compared with the individual observed light curves. Scatter values decreased by factors of 3.3–4.2 in the combined light curves, depending on the number of individual light curves combined, seeing conditions, magnitude limits, exposure times, etc. However, the value for the scatter of all of the combined light curves seems to level off at around 0.0010 (0.1%) for our system. This noise level seems to be close to the limit inherent in observing through an atmosphere as light curves produced with larger telescopes have difficulty improving on this value.

We derived an improved orbital period for the all the systems by performing a least-squares linear fit to our data and all other transit times available in the literature, weighing the individual mid-transit times by their uncertainties. See the individual discussions for each system in Section 5 for the references. When necessary we have converted the reported time frames (usually Barycentric Julian Date or Heliocentric Julian Date based on Coordinated Universal Time: BJD_UTC or HJD_UTC) to the improved Dynamical Time-based system (BJD_TDB) as suggested, for example, in Eastman et al. (2010). Our analysis for the studied systems yields the ephemeris shown in Table 2. In all instances the uncertainty is reduced. No clear transit-timing variations (TTVs) from a single period, which would suggest the presence of other planets in the systems, can be claimed at this time from this data. Other works have searched for an approximately constant period decrease (∼0.01 s yr⁻¹) due to tidal effects for close orbiting planets, which appears as a gradual deviation from a linear ephemerides model usually fitted with a quadratic model (e.g., Adams et al. 2010). However, this requires observations over a large number of years and has been inconclusive for several objects due to uncertainties in transit timings (e.g., Ricci et al. 2015).

We registered six transits for HAT-P-12 through a standard Johnson-Cousins Ic filter between 2011 and 2014 (see Table 1 and Figure 1(a)) that we used to derive the combined light curve shown at the bottom of Figure 1(a). Average point-to-point variation values ranged between 0.0031 and 0.0045 (0.31%–0.45%) for the individual light curves, while the value for the combined one was 0.0012 (0.12%), for an improvement of a factor of 3.3. Our observations also show that the host star did not vary in brightness with respect to the comparison stars when out of transit, which lends confidence to combining the individual light curves. For the calculation of the period and epoch we used, aside from our six observations, four mid-transit times of Hartman et al. (2009; as presented by Lee et al. 2012), three from Lee et al. (2012), and one from Sada et al. (2012). Our result (P = 3.2130589 ± 0.0000003 days and ${T}_{{\rm{c}}}$ = 2454419.19584 ± 0.00009 BJD_TDB) agrees with the one obtained by Lee et al. (2012) and with the one by Todorov et al. (2013), both of which also included reanalyzed amateur light curves from the ETD website. No long-term TTVs are evident at this time (see Figure 1(b)) and there are few mid-transit times available for the determination of short-term variations.

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Hartman et al. (2009) derive an orbit with zero eccentricity from the radial velocity data presented in the discovery paper. Recently, Knutson et al. (2014) include a few more radial velocity measurements, but they also calculate an eccentricity for the orbit that is consistent with zero. Thus, we also adopt a circular orbit for this system in our modeling. Our results (see Table 4) are in general agreement with those obtained by Hartman et al. (2009), Lee et al. (2012), and Sada et al. (2012). However, the recent analysis of a near-IR transmission spectrum from Hubble Space Telescope data by Line et al. (2013) yields a planet-to-star radius ratio that is ∼2.5% smaller than the others.

Table 4.  Modeled Main System Parameters

Name	i (°)	a/${R}_{*}$	$R{\rm{p}}/{R}_{*}$	e	ω (°)
HAT-P-12	${88.17}_{-0.28}^{+0.34}$	${12.00}_{-0.33}^{+0.36}$	${0.1400}_{-0.0012}^{+0.0012}$	Assumed Circular Orbita
HAT-P-13	${82.81}_{-0.59}^{+0.60}$	${5.61}_{-0.22}^{+0.23}$	${0.0860}_{-0.0012}^{+0.0012}$	0.0133 ± 0.0045	${197}_{-37}^{+32}$ b
HAT-P-16	${88.03}_{-0.74}^{+1.00}$	${7.65}_{-0.24}^{+0.22}$	${0.1058}_{-0.0008}^{+0.0008}$	0.040 ± 0.003	${215}_{-5}^{+6}$ c
HAT-P-23	${87.4}_{-2.0}^{+1.7}$	${4.26}_{-0.14}^{+0.13}$	${0.1113}_{-0.0009}^{+0.0010}$	0.096 ± 0.024	${121}_{-9}^{+11}$ d
WASP-10	${88.26}_{-0.22}^{+0.26}$	${11.55}_{-0.17}^{+0.18}$	${0.1605}_{-0.0012}^{+0.0011}$	0.0473 ± 0.0032	${166}_{-9}^{+10}$ e

Notes.

^aConsistent with Hartman et al. (2009) and Knutson et al. (2014). ^be and ω set from Knutson et al. (2014) after their solution for other planets in the system. ^cSolved using combined radial velocity data from Buchhave et al. (2010), Moutou et al. (2011), and Knutson et al. (2014). ^dSolved using combined radial velocity data from Bakos et al. (2009) and Moutou et al. (2011). ^ee and ω set from Knutson et al. (2014) after their solution for a linear trend in the radial velocities.

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We observed nine transits of this system between 2010 and 2014 (see Table 1 and Figures 2(a) and (b)). Average point-to-point variation values ranged between 0.0032 and 0.0044 (0.32%–0.44%) for the individual light curves, while the value for the combined one was 0.0010 (0.10%), for an improvement of a factor of 3.9. Eight of these observations were recorded through a standard Johnson-Cousins Ic filter and another one through a Sloan z' filter (not shown). This last one was used only to help define a linear period for the system and not to derive a combined light curve. Besides the transiting planet, radial velocity measurements of this system have revealed the presence of a second planet in the system that is not known to transit the disk of the star (Bakos et al. 2009) and perhaps a third one (Winn et al. 2010; Knutson et al. 2014) as well. So far the gravitational influence of this second planet has not been definitely observed as mid-transit-timing variations on the transiting planet. Initially, there were claims of possible statistically significant TTVs (Nascimbeni et al. 2011; Pál et al. 2011), but as the number of registered transits grew, this claim started to be in doubt (Fulton et al. 2011; Southworth et al. 2012). Aside from the issue of analyzing a small number of mid-transit times to find possible statistically significant deviations from a linear period, the transits of HAT-P-13b, in particular, are fairly shallow (∼0.75%) and have long ingress and egress times (∼30 minutes). This results in relatively large uncertainties (±∼60 s in the best of circumstances, and usually 50% larger) in the mid-transit time determinations from ground-based light curve observations. Payne & Ford (2011), for example, suggest that mid-transit timings would need to have uncertainties at least four to six times smaller than current observations to confidently use the TTVs to help constrain the orbit of the perturbing planet. This seems hard to achieve from ground-based observations. Because of this, in this work we have chosen to fit a linear period and epoch to the available data. Our observations also extend the timeline of recorded transits to six years and reduce the uncertainties compared with previous works. The result is of use to predict future transits of HAT-P-13b. Besides our nine mid-transit times (see Table 1), we have also used 31 others available from light curves published in Bakos et al. (2009; as presented in Pál et al. 2011), Szabó et al. (2010), Nascimbeni et al. (2011), Pál et al. (2011), Fulton et al. (2011), and Southworth et al. (2012). Our derived linear period and epoch (P = 2.9162433 ± 0.0000012 days and ${T}_{{\rm{c}}}$ = 2455176.53893 ± 0.00022 BJD_TDB; see Figure 2(c)) is in general agreement with the latest determination by Southworth et al. (2012).

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In our combined light curve modeling for this system we adopted the eccentricity, e, and angle of periastron, ω, from the calculations of Winn et al. (2010) and Knutson et al. (2014) because the software cannot derive these values from radial velocity measurements in which there are noticeable gravitational effects from another planet. Our results (see Table 4) are similar in value and uncertainties to those derived originally in Bakos et al. (2009) mainly because we adopted their spectroscopically derived values for ${T}_{\mathrm{eff}*}$, $\mathrm{log}\;g*$, and [Fe/H].

We recorded four transits of the HAT-P-16 system between 2010 and 2013 using a standard Ic filter (see Table 1 and Figure 3(a)). Average point-to-point variation values ranged between 0.0030 and 0.0042 (0.30%–0.42%) for the individual light curves, while the value for the combined one was 0.0010 (0.10%), for an improvement of a factor of 3.6. Our derived linear period and epoch (P = 2.7759704 ± 0.0000007 and T_c = 5027.59292 ± 0.00019) also used mid-transit times from Buchhave et al. (2010) and Ciceri et al. (2013). The amateur mid-transit times used by Ciceri et al. (2013) were not included in this study. The result is consistent with previous estimates and reduces the uncertainties further because of the increased time coverage. There are too few observations available for this system to definitively detect a TTV signal. No clear sign of one is evident from Figure 3(b).

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In modeling our combined light curve we also used radial velocity information from Buchhave et al. (2010), Moutou et al. (2011), and Knutson et al. (2014) to solve for the eccentricity, e, and argument of periastron, ω. The results shown in Table 4 for HAT-P-16 clearly confirm the results of Buchhave et al. (2010).

We obtained 11 transits for HAT-P-23 through a standard Rc filter (see Table 1 and Figures 4(a) and (b)) from observations between 2011 and 2014 and derived a resulting light curve which, upon analysis, yields results in line with those obtained with combining only the first four light curves as presented in Ramón-Fox & Sada (2013). Average point-to-point variation values ranged between 0.0036 and 0.0053 (0.36%–0.53%) for the individual light curves, while the value for the combined one was 0.0010 (0.10%), for an improvement of a factor of 4.2. The period and epoch (P = 1.2128867 ± 0.0000002 days and T_c = 4852.26548 ± 0.00017 BJD_TDB) were derived with our 11 mid-transit times (including slight mid-transit times revision for the four from Ramón-Fox & Sada 2013) and the ephemeris given in the original discovery paper by Bakos et al. (2011). No other transits were found in the refereed literature. A six-year baseline allows us to constrain the uncertainty further, and no deviations from a single linear period are evident from the available data (see Figure 4(c)).

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Unlike in the analysis by Ramón-Fox & Sada (2013), where only a combined light curve from four individual transits was modeled and the orbital parameters e and ω were fixed, in the present work we also included the available radial velocity information in order to constrain the model parameters. These were taken from Bakos et al. (2011) and from Moutou et al. (2011), who determined the system's spin–orbit inclination. The simultaneous analysis of the combined light curve and radial velocity information for the system allowed for a more realistic estimation of the uncertainties for our resulting parameters (see Table 4) than in Ramón-Fox & Sada (2013). Our inclination and scaled semimajor axis of the system agree with those of Bakos et al. (2011) and Ramón-Fox & Sada (2013), and the eccentricity and argument of periastron also agree with Bakos et al. (2011) with reduced uncertainties due to the inclusion of the Moutou et al. (2011) radial velocity data set.

We do note a difference in the planet-to-star radius ratio ${R}_{{\rm{p}}}/{R}_{*}$ for the system. Our value is about 4.5 ± 1.0% lower than the one initially derived in Bakos et al. (2011), and in general agreement with Ramón-Fox & Sada (2013). Through our observing campaign, we noticed that the star in this system varied in brightness by ∼3%, probably due to starspot activity, and suspected that perhaps our individual light curves would have different transit depths due to this. However, our analysis to find a correlation between individual transit depths and stellar brightness variations yielded null results. Thus, we conclude that the combination of individual transit data was a valid attempt at deriving a typical light curve for the transiting system that can be analyzed to obtain the main parameters for the system.

Our smaller planet-to-star radius ratio is in line with the expectation of Fortney et al. (2008), which predicted a smaller planet size (∼8.4% smaller than observed by Bakos et al. 2011) from their theoretical models for a planet of this mass. However, we could not improve on the uncertainty regarding the inclination of the system, which would have helped answer the question regarding the projected angle between the orbital plane and the stellar equatorial plane outlined in Moutou et al. (2011).

Recently, O'Rourke et al. (2014) performed near-IR secondary eclipse photometry of HAT-P-23 and concluded from their mid-eclipse time observations that this system likely has a circular orbit. Our decreased uncertainty for the orbital value of e still advocates for non-circularity, although more radial velocity information is still desirable to settle the issue.

We observed nine transits of WASP-10 through a standard Ic filter (see Table 1 and Figures 5(a) and (b)) between 2008 and 2014. Average point-to-point variation values ranged between 0.0031 and 0.0047 (0.31%–0.47%) for the individual light curves, while the value for the combined one was 0.0010 (0.10%), for an improvement of a factor of 3.4. Another transit observed through a z' filter (2009 September 16—not shown) was also obtained but was not used in the construction of the combined light curve. However, it was used to help derive a period for the system. Our result (P = 3.0927295 ± 0.0000003 days and T_c = 4664.03804 ± 0.00006 BJD_TDB) was derived from our 10 light curves plus 30 others obtained from Christian et al. (2009), Johnson et al. (2009), Dittmann et al. (2010), Maciejewski et al. (2011a; which included four modified measurements from Krejčová et al. 2010), Maciejewski et al. (2011b), Sada et al. (2012), and Barros et al. (2013). Maciejewski et al. (2011a, 2011b), in particular, perform transit-timing analysis of the data and found small periodic variations presumably due to another planet in the system. However, Barros et al. (2013), upon thorough reanalysis of the data, do not find such variations and attribute them to starspot occultation features, especially during ingress and/or egress, or to systematics. We provide 10 other mid-transit times that extend the observational baseline to 7 years and reduces the uncertainty in the linear period fit.

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This system exhibits a very deep transit (∼3%) with sharp and well-defined short ingress and egress times (∼20 minutes), and it is located on a field with several comparison stars of similar magnitude. This makes it particularly well suited for observation and modeling. This has been done by not only Christian et al. (2009), but also by Johnson et al. (2009), Dittmann et al. (2010), Krejčová et al. (2010), Maciejewski et al. (2011b), and Barros et al. (2013). Our results, in particular, match those of Johnson et al. (2009), who analyzed a single high signal-to-noise light curve. For our modeling, we adopted the eccentricity, e, and angle of periastron, ω, values from Knutson et al. (2014) since they discovered a radial velocity trend in the data that suggests the presence of another planet, and the software is not designed to handle such a circumstance. However, it must be said that Husnoo et al. (2012) advocate for a circular orbit for this system, and the recent observation of a secondary eclipse for WASP-10 by Cruz et al. (2015) was insufficient to differentiate between a circular and an eccentric orbit.

The star in this system was initially suspected (Dittmann et al. 2010) and later confirmed (Smith et al. 2009; Maciejewski et al. 2011a, 2011b; Barros et al. 2013) to exhibit starspot activity that affects not only the radial velocity measurements and mid-transit timings, but also the modeling of the system parameters. Our light curves show no clear evidence of starspot activity to the noise level of the individual light curves, and we detected less than ∼2% intensity variation of the star between our observations. Thus, we felt confident that our combined light curve yielded modeling results that are in line with all other work.