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The Phase-Dependent Infrared Brightness of the Extrasolar Planet ʊ Andromedae b

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Science  27 Oct 2006:
Vol. 314, Issue 5799, pp. 623-626
DOI: 10.1126/science.1133904

Abstract

The star υ Andromedae is orbited by three known planets, the innermost of which has an orbital period of 4.617 days and a mass at least 0.69 that of Jupiter. This planet is close enough to its host star that the radiation it absorbs overwhelms its internal heat losses. Here, we present the 24-micrometer light curve of this system, obtained with the Spitzer Space Telescope. It shows a variation in phase with the orbital motion of the innermost planet, demonstrating that such planets possess distinct hot substellar (day) and cold antistellar (night) faces.

Last year, two independent groups (1, 2) reported the first measurements of the infrared light emitted by extrasolar planets orbiting close to their parent stars. These “hot Jupiter” (3) planets have small enough orbits that the energy they absorb from their hosts dominates their own internal energy losses. How they absorb and reradiate this energy is fundamental to understanding the behavior of their atmospheres. One way to address this question is to monitor the emitted flux over the course of an orbit to see whether the heat is distributed asymmetrically about the surface of the planet.

We have observed the υ Andromedae system with the 24-μm channel of the Multiband Imaging Photometer for Spitzer (MIPS) (4) aboard the Spitzer Space Telescope (5). We took 168 3-s images at each of five epochs spread over 4.46 days (97% of the 4.617-day orbital period of υ Andromedae b) beginning on 18 February 2006 at 12:52 UTC. After rejecting frames with bad pixels near the star and those with Spitzer's “first frame effect” (1) (2% to 8% of the data, depending on epoch), we measured the flux of the system and that of the surrounding sky by using both subpixel, interpolated aperture photometry and optimal photometry (6, 7) on each frame.

The detection of eclipses (8) from the hot Jupiter planetary systems HD 209458b (1), TrES-1 (2), and HD 189733b (9) demonstrate that a small fraction (∼0.1%) of the total infrared light we observe from these systems is actually emitted from the planet rather than the star. Thus, if we can measure the flux of a system at a signal-to-noise ratio (S/N) > 1000, temperature differences between the day and night faces of the planet will appear as an orbital modulation of the total system flux. With a star as bright as υ Andromedae, our 3-s exposures each have S/N ∼ 500, so that our SNR expectation is Math at each epoch.

The MIPS instrument acquires data by placing the stellar image in a sequence of 14 positions on the detector. The detector's response varies with position at about the 1% level. This variation is stable and reproducible, so we calculated correction factors as follows: At each epoch, we computed the mean measured system flux at each position and took the ratio with the mean in the first position. We then averaged this ratio over all epochs for each position. This results in corrections < 2% between positions, with uncertainties ∼ 6 × 10–4. Bringing the photometry to a common normalization allowed us to average over all the frames in each epoch to achieve S/N ≈ 4350 at each epoch.

As with most infrared instruments, MIPS's sensitivity varies in time. We corrected for such drifts by dividing the system flux value by the measured background in each frame. The background at 24 μm is thermal emission from the zodiacal dust. This dust pervades the inner solar system, absorbing light from the sun and reradiating it at infrared wavelengths. At 24 μm, its emission is strong enough for use as a flux standard, a technique used successfully in measuring the eclipse of HD 209458b (1). However, the present work requires one additional correction. The zodiacal background is the integrated emission by dust along the line of sight between the telescope and the object. The observed value thus undergoes an annual modulation as that line of sight varies with the telescope's orbit about the sun. The best available model (10) predicts a linear drift over the brief interval of our observations. However, we cannot use the Spitzer model directly, because it is calculated for a line of sight from Earth to the object in question. The difference in position between the Earth-trailing telescope and Earth itself is large enough that the slope of the variation may be slightly different. Thus, we fit for the linear drift directly, simultaneously with any model lightcurve fits.

The phase curve for the υ Andromedae system shows a variation (Fig. 1) in absolute photometry, even before any corrections for instrumental or zodiacal drifts are made. After the calibration with respect to the zodiacal background was applied, this variation is revealed to be in phase with the known orbit of the innermost planet of the system, our principal result.

Fig. 1.

The light curve of the υ Andromedae system. (A) The phase variation in the υ Andromedae system flux before any corrections are applied for instrument or zodiacal drifts. Variations in the system flux are significant even at this point. (B) By comparing to the zodiacal background and fitting for the linear drift in the background due to the telescope's motion, we obtained the phase curve shown. In each case, phase is shown modulo unity, with zero phase occurring when the planet is closest to Earth. The amplitude units are expressed in terms of the system flux at the first epoch. Error bars indicate the residual statistical error at each epoch.

A simple model can be fit to the phase curve (Fig. 2), assuming local, instantaneous thermal reradiation of the absorbed stellar flux. In the simplest model, the phase of the variation is not a free parameter but is rather set by the measured radial velocity curve (11), although phase offsets are possible for models in which the energy is absorbed deep within the atmosphere and redistributed about the surface (12, 13). There is weak (2.5σ) evidence for a small phase offset in this data (Fig. 2), but the large offsets predicted from some models are excluded at high significance. Fitting the peak-to-trough amplitude to the observations yields a best-fit value for the planetstar flux ratio of 2.9 × 10–3 ± 0.7 × 10–3. This is very similar to the result at this wavelength for HD 209458b (1). However, the latter is a measure of the absolute flux from the planet divided by that from the host star, whereas the present result is a measure of the flux difference between the projected day and night sides, divided by the flux of the (different) host star.

Fig. 2.

Comparison of the phase curve and the no-redistribution model. The solid points show our final phase curve, after applying calibrations, in time order from left to right. The open points are repetitions of these, displaced horizontally by one orbit, to better illustrate the phase coverage over two cycles. The solid line is an analytic model for the planetary emission in which energy absorbed from the star is reradiated locally on the day side with no heat transfer across the surface of the planet, the so-called no-redistribution model [and in excellent agreement with the more detailed version in (17)]. The assumed inclination in this case is 80° from pole-on, and the relative planet/star amplitude is 2.9 × 10–3. If we allow for a phase shift relative to the radial velocity curve, we obtain a slightly better fit, as shown by the dotted curve. The best fit is obtained with a phase lag of 11°, but zero lag is excluded only at the 2.5σ level. Error bars indicate the residual statistical error at each epoch.

Another difference between the cases of υ Andromedae b and HD 209458b is that we do not have a strong constraint on the orbital inclination in this system, so we must include the unknown inclination in the model fit (Fig. 3). At higher inclinations, parts of both the night side and the day side are always visible, so the true contrast between the day and night sides must be larger than the amplitude of the observed variation. This contrast is ultimately driven by the light absorbed from the star, which therefore provides an upper limit. We know the distance of the planet from the star and the stellar properties, so we can estimate the contrast that would result if all of the observed flux were reradiated from the day side and nothing from the night side. If we assume the planet's radius is <1.4 Jupiter radii (as observed for other planets of this class), then we can constrain the expected amplitude to be <3.4 × 10–3 (2σ) for a simple black-body, no-redistribution model with zero albedo. Thus, a consistent picture of the atmospheric energetics emerges as long as the orbital inclination is >30°.

Fig. 3.

The influence of inclination on the inferred day-night contrast. The solid contours bound the 1, 2, and 3σ confidence regions for the day-night flux difference (in units of the stellar flux), determined as a function of assumed orbital inclination (measured relative to a face-on orbit). The large shaded regions indicate those values excluded at 3σ. The lower shaded region is excluded because the planet does not transit in front of the star. The vertical dashed line indicates the expected upper limit to the contrast, obtained when the night side is completely dark and all of the stellar flux is reradiated from the day side, in accordance with the no-redistribution model and assuming zero albedo. At the right, we show the true mass of the planet given the assumed inclination (based on the minimum mass derived from the radial velocity curve), in units of Jupiter masses.

A natural question to ask is whether there are any plausible alternative models for the observed variation. The estimated rotation period of the star is too long to explain our phase curve as the result of a normal starspot (which is darker than other parts of the stellar surface). One could posit a feature on the stellar surface similar to a starspot but induced by a magnetic interaction between the star and the planet, and therefore moving synchronously with the planet. However, Henry et al. (14) place an upper limit of 1.6 × 10–4 on the amplitude of optical variation with the planetary orbital period, so infrared variability from the star should be even weaker than this. Some evidence for such magnetospheric interactions is found in observations of chromospheric calcium H and K lines (15) and has even been seen in the υ Andromedae system. However, the energy input needed to explain the Ca lines is ∼1027 ergs s–1, much less than the minimum planetary luminosity we infer here (∼4 × 1029 ergs s–1). Indeed, one can make a quite general argument that our observations cannot be powered by the same mechanism, because any heating of the star due to magnetic interaction with the planet ultimately extracts energy from the planetary orbit. Thus, one may calculate an orbital decay time Math Math where M* and Mp are the stellar and planetary masses, MJ is the mass of Jupiter, a is the semimajor axis, R is the radius of the Sun, and Ė is the observed heating rate. Heating at the level necessary to explain our observations would result in the decay of the planetary orbit on time scales < 107 years, yet the estimated age of the system is 3 Giga year. As such, the chromospheric heating of the star is unlikely to be related to the effect seen at 24 μm.

This observation reveals the presence of a temperature asymmetry on the surface of an extrasolar planet. The first measurements of eclipses (1, 2) yielded measurements of the absolute flux levels emerging from the day sides of two extrasolar planets. When compared with models of radiative transfer in such atmospheres (1620), those observations are consistent with a situation intermediate between no redistribution and full redistribution. A similar comparison is possible in this case (Fig. 4). Our observed day-night flux difference is comparable to the flux emerging at full phase in the models of (16), which suggests that there is little redistribution of energy to the night side.

Fig. 4.

Comparison of the measured amplitude and a planetary spectral model. (A) The solid curve shown is a model (16) foraplanet of radius 1.4RJ, irradiated with parameters appropriate to the υ Andromedae system observed at full phase. This results in a temperature ∼ 1875 K (22). The model is in agreement with the observations (solid circle) at the 2σ level (error bar is 1σ). (B) The normalized spectral response curve of the MIPS 24-μminstrument extends from 20 μm to 30 μm.

In conclusion, the observation of the phase curve of υ Andromedae b indicates that substantial temperature differences exist between the day and night faces of the planet, consistent with a model in which very little horizontal energy transport occurs in the planetary atmosphere. Furthermore, it indicates that the opportunities for direct extrasolar planetary observations are better than previously thought, because useful data can be obtained even in cases where the planetary orbit is not so fortuitously aligned that the system exhibits transits or eclipses.

References and Notes

  1. The usual estimate given for planetary temperatures is the equilibrium temperature, Teq, defined as the effective temperature of a uniformly bright planet radiating energy at a rate that balances the irradiation received from the star. Teq is thus determined by the stellar effective temperature, Teff, stellar radius, R*, and distance of the planet from the star a: Math Math in the case of υ and b with albedo = 0.05. However, in a proper no-redistribution model, the temperature distribution is not uniform but rather hottest at the substellar point and coolest at the limb, and the full-phase temperature average over the planetary surface is better approximated by Math. This is the temperature we adopt, which is 1875 K in this case.
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