JSTOR

1. INTRODUCTION

More than 30 extrasolar planets have been discovered around nearby stars by measuring their Keplerian radial velocity Doppler shifts (see, e.g., Marcy, Cochran, & Mayor 2000). Two radial velocity teams recently discovered a planet orbiting the star HD 209458 (Henry et al. 2000; Mazeh et al. 2000). The planet has and AU and an eccentricity consistent with zero (Mazeh et al. 2000). Photometric observations revealed a dimming of this star’s light consistent with planetary transits (Charbonneau et al. 2000; Henry et al. 2000). This first detection of a transit signal of a 51 Pegasi b‐type planet allows determination of the planet’s mass (by knowing the inclination) and radius (from the depth of the transit), giving in this instance a mass and radius of and (Mazeh et al. 2000). This inflated physical size of the planet is consistent with models for hot extrasolar planets (hereafter called inflated Jupiters; Guillot 1999). Ten percent of short‐period planets (hereafter called 51 Pegasi b‐type planets) are expected to transit solar‐sized stars (Charbonneau et al. 2000).

Doppler measurements from the Keck HIRES spectrometer of the star HD 187123 indicate the presence of a short‐period planet (Butler et al. 1998). Transit photometry can yield the mass and radius of this planet if the orbit is viewed nearly edge‐on. The radial velocity data allow the transit time to be predicted to within the accuracy of the determination of the planet’s orbital period. The planet orbiting HD 187123 has and should be inflated like the planet orbiting HD 209458 since they have comparable semimajor axes (0.04 and 0.05 AU, respectively). A maximum central transit depth of 0.018 mag would be produced for an adopted stellar radius of 1.14 R_⊙. Photometric precision of better than 0.006 mag is required for a statistically significant detection (at the level for the most favorable transit geometry). The goal for this work was photometric precision of 0.001 mag measured over at least the duration of a central transit of a 51 Pegasi b‐type planet of a solar‐like star (approximately 3 hours). In this work, photometric precision is defined as the actual measured standard deviation of the differential magnitude measured over the duration of the observations.

2. DIFFERENTIAL PHOTOMETRIC METHOD

Differential stellar photometry, the measurement of the difference in brightness of two or more stars, has several advantages for the detection of planetary transits. Differential photometry is a simple technique that does not require reduction to a standard magnitude system by the use of separately observed standard stars. It is the most accurate technique for measuring small changes in brightness (Henden & Kaitchuk 1990). If the stars to be compared are near one another on the celestial sphere and similar in color, the first‐order (air‐mass dependent only) extinction and the second‐order (color dependent) extinction corrections are unnecessary. Traditionally, differential photometry is performed with a single‐channel photometer, a nonimaging instrument that measures a single star’s brightness. A differential measurement then consists of a pair of measurements of two stars taken sequentially through two different values of air mass. In contrast, charge‐coupled device (CCD) differential photometry allows the simultaneous measurement of the brightness of all stars in a given field through virtually identical values of air mass. Differential CCD photometry has been demonstrated to achieve precision of 0.0008 mag for a 9 hour time series with 1 m class telescopes (Gilliland 1991). Differential photometry is robust to small changes in atmospheric transparency (i.e., light clouds) and the efficiency of the instrumentation (such as that caused by optical vignetting). The first‐order extinction is given by , where is the magnitude of the object star that would be measured in the absence of the Earth’s atmosphere, X is the air mass, is the V band first‐order extinction coefficient in magnitudes per unit air mass, and is the measured magnitude in the V band. The first‐order extinction coefficient is usually determined nightly by observing a star through a range of air masses. The second‐order extinction depends on the color difference between the object star and a comparison star and is defined by the equation . In this equation, is the second‐order extinction coefficient in units of magnitudes per air mass per unit difference in B−V color.

A backside‐illuminated and thinned CCD was selected because these high quantum efficiency devices are less sensitive to intrapixel sensitivity variations (Buffington, Booth, & Hudson 1991) than frontside‐illuminated devices. For frontside‐illuminated CCDs, photons must pass through the polysilicon parallel transfer electrodes running in the row direction. These electrodes are used to clock charge out to the serial output registers. In a frontside‐illuminated device the photons have to pass through these structures which are opaque to some wavelengths of visible light and lead to spatial quantum efficiency variations within each pixel. Backside‐illuminated devices accept photons directly into the bulk silicon from the “backside” of the CCD where no parallel transfer electrodes are present.

3. THE SPOT FILTER

The Keck radial velocity survey of Marcy et al. has chosen relatively bright stars (few stars in the survey are as dim as 10 mag) in order to obtain the high signal‐to‐noise spectra necessary to determine radial velocities with 3 m s ⁻¹ precision in short integration times. There are only several hundred thousand stars as bright as 10th magnitude on the 41,253 deg² that make up the celestial sphere, or approximately five bright stars per square degree. The comparably bright comparison stars required for standard stellar differential photometry are therefore lacking in any reasonably sized CCD field of view. It was decided to overcome this comparison star scarcity problem by employing a neutral density spot filter to reduce the flux from the object star relative to the comparison stars, rather than attempting precision differential measurements over a large field (Borucki et al. 2000).2 By using a spot filter, placed in the converging beam very near the detector focal plane and positioned to attenuate the light from the bright object star, integration times on the order of several minutes are possible for the stars that have known planetary companions. For the results reported herein, 250 s integrations are required to suppress atmospheric scintillation noise to the 0.0007 mag level (Young 1974). For the special case of HD 187123, its proximity to the galactic plane in the constellation of Cygnus and its relative faintness, , makes the likelihood of suitable nearby comparison stars much higher.

The filter used for this work was fabricated by the Lick Observatory optical shop from a 5 mm core cut from a Schott neutral density filter of NG3 glass and nominal thickness 2.00 mm (giving transmittance, or 5.23 mag of attenuation) and placed in a 5 mm hole bored in a second Schott neutral density filter of 2.00 mm thick NG12 glass (giving 0.79 transmittance, or 0.26 mag of attenuation). Note that the spot filter diameter of 5 mm is very large compared to a typical stellar FWHM of less than 0.1 mm. The large size of the spot allows for less precise positioning of the object star. By selecting this construction method, differences in the thickness and index of refraction of the two filter components that might lead to focus differences between the object and comparison stars were minimized. Room‐temperature vulcanizing silicon rubber was used as the adhesive to join the two components.

4. OBSERVATIONS

The Anna L. Nickel 40 inch telescope of the University of California’s Lick Observatory, Mount Hamilton, California, was used to make measurements of HD 187123 on the nights of 1999 September 5 and September 8. The detector employed was a CCD array of 24 μm pixels, backside‐illuminated, thinned, and mounted at the Cassegrain focus. The read noise was 1.7 electrons per pixel. The plate scale was 0 3 per pixel. Table 1 lists the journal of observations. The ephemeris of transit centers for HD 187123 (assuming a circular orbit; G. Marcy 1999, personal communication) is , where is the time of transit center in Julian days and n is an integer. The uncertainties in the transit center reference epoch and period are 0.01 day and 0.003 days, respectively.

TABLE 1 Journal of Observations

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5. DATA REDUCTION

CCD frame bias was removed by the Lick data system at the time of exposure. Images were stored to hard disk during observing and periodically transferred via file transfer protocol (FTP) to a laptop computer. Commercial compact disc writing software was then used to archive each night’s data to a separate CD‐ROM before the end of an individual run. The laptop was also used to view images and perform simple data quality checks. National Optical Astronomy Observatories Image Reduction and Analysis Facility (NOAO IRAF) was used for image trimming (to remove the overscan region) and CCD calibration (flat‐fielding).

Flat fields were constructed from median combining 17 “dome” exposures using incandescent lamps (Stone 1992) illuminating the inside of the telescope dome. Twilight flats were taken but not used due to the difficulty of obtaining sufficient digital counts under the spot during the relatively brief summer twilight. The spot filter design resulted in an achieved attenuation of a factor of 25 for objects under the spot. This is less than the expected attenuation of a factor of 97 obtained by taking the difference in the neutral density of the components of the spot filter. Presumably, the smaller than expected attenuation was due to the spot filter location just above the focal plane and consequent light leakage around the edges of the filter from the converging telescope beam. The attenuation under the spot resulted in a factor of 25 fewer digital counts per pixel under the spot than in the background in all images, including flat‐field frames. Since the typical maximum digital counts in the background of a flat‐field frame was 20,000 (chosen to be safely below the analog‐to‐digital converter saturation level and any nonlinear response regime of the CCD), 800–1000 digital counts per pixel were typically obtained under the spot.

To achieve photometric precision of 0.001 mag, it is required that the Poisson noise, σ, be less than 1 part in one thousand ( ). Here N is the number of photoelectrons collected per pixel in the combined flat‐field exposures, implying one million photoelectrons are required per pixel. In practice, a less stringent requirement than this is realized since each star’s brightness is measured over apertures no smaller than 6 pixels in radius or an area of about 113 pixels. For a gain of 4.4 electrons per analog‐to‐digital unit (ADU), the averaged flux in a flat‐field pixel under the spot was photoelectrons. This results in a contribution to the errors of 0.0004 mag from the Poisson noise in the flat fields. For stars not under the spot, the contribution to the errors from the Poisson noise due to the flat‐fielding process is small compared to the errors introduced from Poisson noise in the flux from the stars themselves.

No cosmic‐ray removal or bad pixel masking was performed. The IRAF routines IMEXAM and XIMTOOL were used to select object and comparison stars interactively and to determine the necessary aperture sizes. All stars were given the same aperture size for the entire night, and an initial stellar coordinates file was constructed as input to the aperture photometry routine PHOT in the APPHOT package. Recentering of the apertures was performed for each frame. The PHOT routine “mode” option was selected for background determination since this method is less sensitive to hot pixels. IRAF TXDUMP was used to produce tables of position, fluxes, magnitudes, magnitude errors, and the universal time (UT) of the exposure for each star. A computer program written in Research Systems Incorporated Interactive Data Language (RSI IDL) language was used to read the IRAF output files, reduce the data to differential magnitudes for each star in each frame, and plot the results versus universal time. Diagnostics of flux, centroid position, and background flux for each star were also plotted and examined.

For CCD differential photometry, differential (or first order) extinction is due to differences in air mass between the object and comparison stars in a single exposure. Differential extinction is smallest at low values of air mass (at the zenith, for example) and is largest at high values of air mass (at the horizon, for example). The typical extinction coefficients found at Lick were 0.36–0.47 mag per air mass in the V band. The maximum angular distance between the object star and any single comparison star was 3 54. Combining these extinction coefficients and angular distances with a maximum air mass of 1.5 results in a maximum predicted differential extinction of 0.0006 mag. In practice, comparison stars are arranged around the object star so that some will have a greater air mass than the object star and some less. Generally, for low values of air mass, differential extinction is much less. In fact, differential extinction contributes less than a micromagnitude to the errors in the differential magnitudes at the meridian for stars at the declination of HD 187123. For these reasons, first‐order extinction was ignored.

Because of the long exposure times possible with the spot filter (250 s), dozens of suitable comparison stars down to about a magnitude of 12 were available within the 5 arcmin square field of view. Exposures were taken in the B and V filters, and four stars with a B−V color within 0.1 of the object star (HD 187123) were chosen as comparison stars. Choosing similar‐color comparison stars minimizes the second‐order extinction effect which varies with the air mass X and the difference in B−V color. The size of the second‐order extinction correction is typically 0.03 mag for a B−V difference of 1 over a unit change of air mass (Janes 1996). For the observations reported herein, the largest change in air mass over the night was 0.40 and the largest B−V difference was −0.067 (star 3), which translates to a color‐dependent extinction of −0.0008 mag using the Janes estimate.

The differential magnitude of each star relative to the other four was calculated for each frame for the two nights of observation of HD 187123. For example, star 2 was compared to the sum of the flux from stars 1, 3, 4, and 5. The standard deviation of this differential measure yields an estimate of the variability of the comparison stars (Table 2). There is no evidence for variability of comparison stars 2, 4, and 5 within the errors of the measurements. Star 3 does show a difference in the mean differential magnitude between the two nights at the level. The small change in mean differential magnitude from night to night for each star is also an indication of the photometric stability of the system. The two data sets were taken with one spot installation and reduced using the same normalized master flat fields.

TABLE 2 Comparison Star Photometry

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Even though the first‐order extinction (due to air‐mass differences between the object and comparison stars) and second‐order extinction (due to B−V color differences between the object and comparison stars) corrections have been shown to be smaller than the 0.001 mag precision goal, there was evidence for a residual linear trend with time in the data. A linear fit was calculated and subtracted from the differential magnitude of HD 187123. This residual linear component has a slope of 0.0005 and 0.0004 mag per hour for the nights of 1999 September 5 (UT) and 1999 September 8 (UT), respectively. Figures 1 and 2 show the data after the linear trend is removed. Subtraction of this linear trend improved the measured precision (Table 1).

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Fig. 1.— Data from the night of 1999 September 5 (UT) with the residual linear trend removed. The standard deviation of the night’s data set was 0.0015 mag, somewhat larger than the formal errors shown as error bars for each data point. Superposed are simulated idealized transits. Solid line: the central transit of a Jupiter‐radius planet; long‐dashed line: central transit of an inflated Jupiter; short‐dashed line: the grazing transit of Jupiter‐radius planet; dot‐dashed line: grazing transit of an inflated Jupiter. All cases except a Jupiter‐radius grazing transit would have been detected at the greater than level per data point. The uncertainties in the ephemeris amount to ± 2 ticks on the time axis.

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Fig. 2.— Data from the night of 1999 September 8 (UT) with the residual linear trend removed. The standard deviation of the night’s data set was 0.0023 mag, somewhat larger than the formal errors shown as error bars for each data point. Superposed are simulated idealized transits. Solid line: the central transit of a Jupiter‐radius planet; long‐dashed line: central transit of an inflated Jupiter; short‐dashed line: the grazing transit of Jupiter‐radius planet; dot‐dashed line: grazing transit of an inflated Jupiter. All cases except a Jupiter radius grazing transit would have been detected at the greater than level per data point. The uncertainties in the ephemeris amount to ±2 ticks on the time axis.

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6. HIPPARCOS SATELLITE PHOTOMETRY

A 51 Pegasi b‐type planet such as that orbiting HD 187123 (HIP 97336) with a 3.097 day period and a central transit duration of approximately 3 hours would be expected to be observed in transit for roughly 4% of randomly chosen observation times. The Hipparcos satellite observed HD 187123 a total of 162 times during its mission, albeit not randomly spaced in time (Perryman 1997). The Hipparcos data might therefore be able to constrain the orbital inclination. Hipparcos photometry has been shown to be useful in confirming transit detections and refining the radial velocity–derived orbital period (Robichon & Arenou 2000; Castellano et al. 2000).

The uncertainty in the radial velocity–derived orbital period of 0.003 days (Butler et al. 1998) results in a phase error at the epoch of the Hipparcos measurements greater than the orbital period of HD 187123b of 3.097 days. It is therefore necessary to search at all phases for a transit signal repeating at the known orbital period. The measured standard deviation of the 162 photometric measurements of the ‐magnitude 7.970 star HD 187123 is 0.016 mag, comparable to the 89 measurements of the ‐magnitude 7.772 star HD 209458 with standard deviation of 0.015 mag.

Monte Carlo simulations reveal that for transit depths and durations typical of 51 Pegasi b‐type planet (using a simple detection criterion based on the properties of the known transit signal of HD 209458b in the Hipparcos data), about one in six of possible phases of simulated HD 187123b transits result in successful detections. Similar results are achieved for HD 209458b (fewer data points and slightly less noise) and suggest that a successful transit detection using only the Hipparcos data can be expected for perhaps one in six stars that actually exhibit transits. These results depend critically on the sensitivity of the transit detection algorithm. The Hipparcos data therefore lend no support to the claim made herein of no detection of a transit HD 187123 but remain useful for the confirmation of future detected transits and refinement of the radial velocity derived periods, for those few events that are so phased as to be well sampled.

7. DISCUSSION

Keplerian Doppler variations with a period of 3.1 days of the solar‐like star HD 187123 were first reported by Butler et al. (1998). The Doppler variations imply an orbiting companion of mass or larger in a near‐circular 0.04 AU orbit. The radial velocity method alone cannot determine the inclination of the orbit, hence the ambiguity in the mass. HD 187123 is a solar twin with a visible spectrum that differs from the Sun’s by less than 1% (rms) (Butler et al. 1998). However, HD 187123 is slightly more luminous than the Sun at L_⊙ and has a slightly higher effective temperature of 5830 K (Gonzalez, Wallerstein, & Saar 1999). This combination of effective temperature and luminosity yields an estimated radius of 1.14 R_⊙ (Table 3). At an orbital distance of just 0.04 AU the equilibrium global average effective temperature of the planet around HD 187123 is near 1250 K. It may be that the planet is inflated by the extreme stellar insolation to (Guillot et al. 1999). If this is the case, then the transit depth is increased by about a factor of 2 over that produced by a Jupiter‐radius planet. Central transits have maximum depths given by the simple ratio of the planet’s to the star’s disk areas. Noncentral transits have smaller depths at all wavelengths due to limb darkening. Since HD 187123 is a solar twin (Butler et al. 1998), it is expected to follow a solar limb‐darkening law (Allen 1976). At an inclination of 82 7, solar‐like limb darkening reduces the transit signal to 0.55 that of a central transit in the V band. At this value of inclination, the transit duration is 0.31 that of a central transit. This value of inclination was chosen as a limiting case because at this inclination angle, 95% of orbital inclinations that will produce a transit are included. Figures 1 and 2 demonstrate that transits of inflated Jupiters would have been easily detected if the orbital inclination is between 82 7 and 90° and that Jupiter‐sized planets would be detected only for inclinations very near 90° (Table 4). The simulated idealized transits in Figures 1 and 2 include the effect of solar‐like limb darkening in the transit depth determination but do not include the effect of limb darkening on the transit ingress and egress profiles. A giant terrestrial planet with a mass of has a radius of (Guillot et al. 1999) and would not have been photometrically detectable in transit with the precision reported herein.

TABLE 3 HD 187123 Stellar Properties

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TABLE 4 HD 187123b Planet Properties

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8. CONCLUSION

The recent detection of planetary transits of the star HD 209458 by Charbonneau et al. and Henry et al. amply demonstrates the utility of transit photometry in determining the mass and radius of extrasolar planets. Accurate determination of the radius and atmospheric structure of this and other 51 Pegasi b‐type planets as required to constrain structural models of extrasolar giant planets will depend on continued precision photometry with high time resolution. A novel method for performing this high‐precision, time‐series CCD differential photometry of bright stars has been demonstrated. No transits are observed at the epochs predicted from the radial velocity observations for the star HD 187123. In addition, utilizing detection criteria based on the known transit properties of the only known transiting 51 Pegasi b‐type planet HD 209458b, a search of the Hipparcos satellite photometry revealed no evidence for a transit. Simulations reveal, however, that this is not an unexpected result given the sparse sampling of the Hipparcos data.