HST/STIS Optical Transit Transmission Spectra of the hot-Jupiter HD209458b
We present the transmission spectra of the hot-Jupiter HD209458b taken with the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope. Our analysis combines data at two resolutions and applies a complete pixel-by-pixel limb-darkening correction to fully reveal the spectral line shapes of atmospheric absorption features. Terrestrial-based Na I and H I contamination are identified which mask the strong exoplanetary absorption signature in the Na core, which we find reaches total absorption levels of 0.11% in a 4.4Å band. The Na spectral line profile is characterized by a wide absorption profile at the lowest absorption depths, and a sharp transition to a narrow absorption profile at higher absorption values. The transmission spectra also shows the presence of an additional absorber at 6,250Å, observed at both medium and low resolutions. We performed various limb-darkening tests, including using high precision limb-darkening measurements of the sun to characterize a general trend of Atlas models to slightly overestimate the amount of limb-darkening at all wavelengths, likely due to the limitations of the model’s one-dimensional nature. We conclude that, despite these limitations, Atlas models can still successfully model limb-darkening in high signal-to-noise transits of solar-type stars, like HD209458, to a high level of precision over the entire optical regime (3,000-10,000 Å) at transit phases between 2 and 3 contact.
Subject headings:methods: data analysis - planetary systems - stars: individual(HD209458)
Transiting hot-Jupiter planets offer a tremendous opportunity to study the characteristics of extrasolar planets. During a transit event, both the opaque body of the planet as well as its atmosphere blocks light from the parent star. A precise determination of the radius of the planet can be made from the total obscuration, while partial transmission of light through the exoplanet’s atmosphere, along with its wavelength dependence, allows for the detection of composition and structure (Charbonneau et al., 2002; Ballester, Sing, & Herbert, 2007). In the middle of the visible spectrum, transits can probe atmospheric pressures from about 0.1 bar to 1 bar, containing the troposphere (lower atmosphere), as well as the stratosphere and mesosphere (middle atmosphere). One exoplanet in particular, HD209458b, has been ideal for these studies and holds the distinction of the first detection of an extrasolar planetary atmosphere (Charbonneau et al., 2002) as well as the discovery of an escaping atmosphere (Vidal-Madjar et al., 2003, 2004). These transit studies were performed with the Hubble Space Telescope (HST) using the Space Telescope Imaging Spectrograph instrument (STIS).
Here we expand upon earlier HST STIS analysis (Brown, 2001; Charbonneau et al., 2002; Knutson et al., 2007; Ballester, Sing, & Herbert, 2007) in order to fully probe the line shape of atmospheric Na in HD209458b, and quantify other absorbers in the transmission spectrum. We use STIS data obtained during planetary transit at two spectral resolutions (low and medium). The two datasets are combined to extend the measurements over the entire optical regime, providing a way to simultaneously measure both the narrow core and wide line wing Na absorption. We describe these observations in §2, perform various limb-darkening tests in §3, present analysis of this data in §4, and discuss the results in §5. From our resulting spectra, a detailed atmospheric model fit is given in Sing et al. (2008), which discusses condensation of sodium, as well as the implications of the atmospheric temperatures found. In addition, details of H Rayleigh scattering are presented in Lecavelier et al. (2008) while Désert et al. (2008) explores absorption by atmospheric TiO & VO.
2.1. Data reduction
The HST STIS G750M, G750L, and G430L observations of HD209458b analyzed here are also detailed in Charbonneau et al. (2002), Ballester, Sing, & Herbert (2007), Brown (2001), and Knutson et al. (2007). The G750M data consist of 684 spectra covering the wavelength range of 5,518-6,382 Å, with a resolution R of /5,540 (2 pixels; 1.1 Å), and taken with a wide 52”-2” slit to minimize slit light losses. This observing technique produces spectra which are photometrically accurate near the Poisson limit during the transit event. Four transits were observed, although the first suffered from a database error of the position of the spectrum and, as in Charbonneau et al. (2002), was not used for this analysis.
The dataset was pipeline-reduced with the latest version of CALSTIS and cleaned for cosmic ray detections before performing spectral extractions. The aperture extraction was done in IRAF software with a 30-pixel-wide aperture, no background subtraction, and the optimal extraction algorithm of Horne (1986). This extraction technique produces spectra with 5-6% more flux than simply summing over the cross-dispersion direction, as the stellar counts from the wings of the PSF can be added without additional noise.
The spectra were Doppler corrected to the heliocentric rest frame, with the velocity shifts on the order of one pixel. An additional sub-pixel shift in the dispersion direction was removed in each spectrum by cross-correlation against a template spectrum, which consisted of the mean pixel-shifted spectra. Such sub-pixel shifting are likely due to the jitter of the spacecraft which changes the position of the star within the slit. The shifts are typically on the order of 0.1 pixel within a orbit (the typical guiding accuracy of HST) and 0.5 pixel from orbit to orbit. Several iterations of measuring pixel-shifts, applying those shifts, and producing a new template were performed in order to produce a reliable final template spectra for cross-correlation. With this method, we were able to align the spectra to 0.1 pixel. With different Doppler and pixels-shifts for each spectrum, the PSF of the stellar absorption line profiles can be reconstructed with a much greater sampling than can be obtained from an individual spectrum (see Fig. 1).
The extracted STIS spectra were then used to create a photometric time series covering the G750M bandpass by integrating the flux from each exposure. The resulting photometric light curve exhibits all the systematic instrumental effects noted in Brown (2001). As in both Brown (2001) and Charbonneau et al. (2002), we corrected for these systematic effects by discarding the first exposure of each orbit, discarding the first orbit of each visit, and applying flux corrections by removing a fourth order polynomial fit to the photometric time series phased on the HST orbital period. The photometric corrections were then applied to the spectra themselves, such that different photometric bands could easily be produced.
The Na D wavelength region is also covered by HST STIS G750L observations, described by Knutson et al. (2007), though at much lower resolution. The G750L data set was also reduced, treated in the same manner as the G750M. The cross-correlation analysis, however, only was performed over the blue-half of the data, such that our measured pixel-shifts would be independent of the observed fringes.
2.2. Telluric contamination
Telluric contamination can be seen in a photometric G750M time-series of the Na core where we see a large variation of 4-5% over an HST orbit (see Fig. 2). This variation is observed to be correlated with the HST orbital phase, and repeats in a similar manner within each orbit of a visit, and occurs in all three visits analyzed. The contamination occurs for both Na lines over the same radial velocities, -5 to -20 km s from the Na D line cores, and is consistent with the expected velocity of the earth during the HST observations. Given the size of the variation, it is too large to be due to the known instrumental systematic effects, which only affect the light curves 0.1% during an orbit. In addition, other strong stellar lines such as Fe I do not show any signs of a similar contamination, ruling out possible detector efficiency and count-rate dependent issues as the cause of the observed line core variations. The contamination can also be seen directly in the G750M spectra (Fig. 1), observed as a 0.3Å region in the sodium D cores with little-to-no flux drop during planetary transit, though the actual contaminating region could result from a smaller unresolved region. Absorption by interstellar Na could also be affecting the contaminated region although it’s effect would be constant and should not vary with the HST orbital period. The G750L data-set also shows telluric Na D contamination, with H showing a similar effect as well. With lower resolution, the telluric signature is seen in photometric time-series measurements of the line cores having, as expected, a correspondingly lower amplitude than the medium resolution data.
2.3. Sodium core absorption signature
We performed a double differential photometric measurement, similar to Charbonneau et al. (2002), selecting 23 wavelength bands from 4-100 Å centered on the Na D lines. In the original analysis, Charbonneau et al. (2002) used three different wavelength bands. We chose to use the sum of two bands, each centered on one component of the Na doublet for the two wavelength bands smaller than the Na D doublet separation. For each band, we integrated the spectral flux, producing photometric light curves. We then normalized each visit to their average out-of-transit flux. The two narrowest bands showed terrestrial contamination which modulate with the HST orbital period, which we removed by fitting each visit of the HST phased out-of-transit flux with a fourth-order polynomial applying the fit to the in-transit orbits, as was done in a similar manner for the instrumental systematic effects. The photometric curves were then subtracted from a comparison band composed of the wavelength regions between 5,818-5,843 Å and 5,943-5,968 Å, picked to be identical to the “wide” comparison band in Charbonneau et al. (2002). The relative planetary Na absorption during transit was then computed from the mean of the difference light curve over the in-transit phases between second and third contact, with its associated error computed from the variance of the data. Changing the width of the comparison bands, in the same manner as Charbonneau et al. (2002) produced similar results for corresponding bands. Our resulting absorption profile (see Fig. 3) matches the results of Charbonneau et al. (2002) and, in addition, reveals the strong absorption from the Na D line centers. When left uncorrected for terrestrial-based contamination, the two narrowest bands produce similar absorption values, but with error bars large enough for the absorption to be consistent with a null detection.
A double differential spectroscopic measurement was also performed over the Na region. For the spectroscopic measurement, each spectra was first interpolated, using a cubic spline, onto a common wavelength scale. The spectral flux at each pixel was then normalized by the average out-of-transit flux, then subtracted from the average normalized flux of the “wide” comparison region. The absorption at each wavelength during transit was then measured as performed for the photometric analysis, including telluric corrections for each pixel. The resulting differential spectra shows two statistically significant positive absorption peaks at the Na D lines with each having a large negative absorption core where the the terrestrial contamination is largest (see Fig. 4). The telluric corrections on the Na lines have a modest affect on the absorption values outside the two largest contaminated pixels, as the telluric perturbation originates in a small sub-pixel region, with nearby pixels effected through the 2 pixel instrument resolution. Excluding the two highly contaminated pixels affectively removes the majority of the contamination. In a 4 pixel bin, the average value of the two line cores is consistent with the 4.4 Å band photometry measurement indicating that both approaches to correcting the contamination give consistent values. In our final limb-darkened corrected transmission spectra (see §4.3), we ultimately choose to apply the telluric corrections over the Na region while also leaving out the two highest contaminated pixels. Binning the differential spectra by 3 pixels (1.66 Å) shows the Na D2 line is stronger than the absorption of the D1 line with absorption values 0.0950.02% and 0.0510.02% respectively, and an absorption ratio of D2/D1 = 1.90.9. The differential photometric measurement includes these two pixels as their effects are negligible at large band widths and correctable for the 4.4 and 8.9 Å bands.
2.4. Limb-darkening corrections
Correcting for limb-darkening effects allows a full transmission spectrum to be produced over the entire wavelength range of the STIS data. Similar to Ballester, Sing, & Herbert (2007), we computed nonlinear limb-darkening coefficients to estimate and correct for the limb-darkening effects in the transit light curve. Though other limb darkening laws could in principle be used (for example: linear, quadratic, square-root, or logarithmic), Claret (2000) found the nonlinear law best represents the intensity distributions calculated from 1-dimensional plane parallel atmospheric models used here.
We choose a Kurucz Atlas stellar atmospheric model111http://kurucz.harvard.edu/stars/hd209458 based on the model’s limb-darkening performance, performance vs. other 1D models, model availability, and development within the literature. Limb-darkening calculated from Phoenix models (Claret 2000) were found to predict a stronger limb-darkening, compared to Atlas models, by a few percent in the photometric bands B, V, R, I, J, H and H, but up to 40% weaker in U and u’ bands. As the Atlas models performed better compared to the sun (see §3.2), they were chosen over Phoenix models for our study.
Most studies fitting transit light curves have either chosen to adopt an Atlas stellar atmospheric model to account for limb-darkening effects, or fit for limb-darkening parameters assuming a limb-darkening law. Knutson et al. (2007), who also used an Atlas model for HD209458, found similar planetary parameters when comparing the two methods, suggesting that model based limb-darkening fits can perform well. Knutson et al. (2007) chose to use the limb-darkening calculated from the Atlas models in their results, due to the more precise planetary parameters found, and concerns that fit limb-darkening coefficients could be affected by residual correlation in the light-curve. Such concerns are valid, as we found residual correlated “red” noise ultimately limits the maximum signal-to-noise S/N achievable in this study (see §4.2). In addition, as our limb-darkening corrections can be on a pixel-by-pixel level, a light-curve generated by any one particular pixel will not have sufficient S/N to accurately fit for limb-darkening coefficients.
The four nonlinear coefficients were computed using intensity spectra from a Kurucz 1-dimensional plane parallel model atmosphere calculated at 20 different angles spread uniformly in , fitting for the coefficients in the desired wavelength range. We calculated coefficients for the wavelengths ranges used in the G750M differential measurements, and each pixel of the G750M and G750L dispersions. Using the fit coefficients, we then used the theoretical transits of Mandel & Agol (2002) to determine and correct for limb-darkening effects. The best-fit system parameters of Knutson et al. (2007) were used to calculate the impact parameter and planetary/star radius contrast. For the differential photometric measurement probing the Na line cores, designed by Charbonneau et al. (2002) to be largely limb-darkened independent, all the corrections had a less than 1 effect with corrections to our narrowest band only increasing the absorption by 0.005% (see Fig. 3).
3. Limb-Darkening Tests
3.1. Stellar line vs. continuum limb-darkening strength measurement
When measuring Na in the G750M photometric bandpass, limb-darkening effects increase with narrowing Na bands. Specifically, the stellar limb-darkening is less in the Na line core compared to the surrounding continuum, producing transit light-curves which are slightly more “box” shaped with a depth at mid-transit slightly smaller. When comparing the transit light-curves of narrow regions centered on the Na line to that of a surrounding continuum, with the intention of measuring a difference in apparent planetary radius, the overall effect is to inherently underestimate the signature. Using the G750M spectra, we measured the magnitude of this effect using the stellar absorption lines (Fe I, Ca I, Si I, etc.) and the continuum. No other large planetary atmospheric signature other than Na was detected in the stellar lines of the G750M data (Charbonneau et al. 2002), making them excellent probes of the effects of limb-darkening independent of differing planetary radii. We produced two separate photometric light curves, one that contained only the flux from stellar continuum and one that contained only flux from the stellar absorption lines. The Na region was not included in either photometry. We then normalized the two curves by their out-of-transit flux and took their difference. The average in-transit difference was measured, as in the differential Na analysis, to be -0.00440.0015%. Using the model atmosphere and calculating theoretical transits for the selected wavelengths, we found a theoretical difference of -0.0038% which matches the observed value. This confirms that: (1) the limb-darkening in the stellar lines is smaller than the continuum, (2) the effect is to reduce a planetary absorption signature when measuring within a stellar line and comparing to a nearby continuum, (3) the effect is small for a typical stellar absorption line ( -0.004%), and (4) the strength of the effect is consistent with theoretical 1-D stellar atmosphere predictions. Although the 1-D stellar model used in our analysis does not contain a stellar chromosphere and assumes local thermodynamic equilibrium, the similarity between the model and data suggests that their effects are negligible on the transit light curve at these wavelengths and resolutions.
3.2. Performance of solar-like Atlas limb-darkening models
To gauge the performance and limitations of Atlas atmospheric models, in relation to analyzing planetary transits, we compared the limb-darkening predictions of a solar Atlas model to the measured values of the sun. The sun represents the only test case where sufficiently high-precision optical limb-darkening data exists. HD209458 is a solar-like star, being classified as a G0 V, while the sun has a similar spectral type and is a G2 V. In analyzing the performance of model atmospheres, Bertone et al. (2004) found Atlas models to provide a good fitting accuracy for physical parameters, namely T and log g, for early type main sequence stars, B to F, down to late G/early K stars. For late K and M stars, the models produce systematically poorer fits, due largely to the incomplete treatment of molecular opacity, which becomes important in cooler stars. As HD209458 is slightly warmer than the sun, molecular opacity should correspondingly play a slightly weaker role, and the performance of the Atlas model itself should be similar for such main-sequence stars. Testing a solar Atlas model vs. solar data represents a test of the model itself and the assumptions within the model, as the physical parameters of the sun, which are input into the atmospheric model, are both accurately and precisely measured. The uncertainty in the measured stellar parameters themselves, and its effect on limb-darkened corrected transit light curves, is a separate issue dealt with in §4.1.
Seen in Fig. 5 are high precision solar limb-darkening measurements for 25 precisely chosen continuum wavelengths between 3,000 and 11,000 Å from Neckel & Labs (1994; hereafter NL94) and the corresponding solar Atlas predictions, taken from the non-linear solar Atlas monochromatic coefficients computed by Claret (2000). The Atlas model was calculated at a low resolution, so those wavelengths which matched closest were chosen. The Atlas model is seen to perform well over values between 0.2 and 1.0, slightly overestimating the strength of limb-darkening, consistently at every wavelength, by a couple of percent (see Fig. 6). Our Atlas-solar comparison agrees with earlier studies (Castelli, Gratton & Kurucz 1997). The general overestimation by atlas models is expected, due to the inherent limitations of 1-D models when describing purely 3D turbulent effects. This overestimation has been observed in both a F5 V and K1 V star when comparing Atlas models and 3-dimensional hydrodynamical models to high-precision interferometric measurements (Aufdenberg 2005; Bigot et al. 2006). The largest differences between the model and data exist at the very limb, where Atlas models predict a dramatic increase in limb-darkening strength, a trend not observed in the solar limb-darkening data.
3.3. Simulated Solar Transits
The effect of adopting an Atlas model, to describe limb-darkening in transit light curves, can be seen by simulating transits with the high precision NL94 solar data and comparing them to transits using an Atlas solar model. For this purpose, we modeled transit light curves using the best-fit parameters of the HD209458 system, and both the nonlinear limb-darkening coefficients predicted by the Atlas solar model as well as the solar data (see Fig. 7). With overall stronger limb-darkening, the Atlas models produced systematically deeper transits between 2 and 3 contact and shallower light curves during ingress and egress. The largest differences between the solar and Atlas transits occur during ingress and egress where transit parameter fits are relatively insensitive to the planet-to-star radius contrast, /, which is the desired parameter for this study. This insensitivity combined with its small integrated flux contribution of the limb, in contrast to the rest of the stellar surface, limits the overall affect of the observed large limb model deficiencies during mid-transit. At mid-transit, a 2% overestimation in limb-darkening (corresponding to 0.5) translates to an extra transit flux drop of 0.01%. These trends are seen to be largely reproducible, wavelength-to-wavelength, at a 0.005-0.006% level. The NUV, where the strength of limb-darkening is larger, also exhibits this general overestimation trend, but with a slightly larger scatter compared to the rest of the optical.
We corrected the transit light curve, computed with the NL94 data, for limb-darkening effects as predicted by the Atlas model. This procedure is comparable to our limb-darkening correction procedure adopted for HD209458b, i.e. using the predicted limb-darkening from Atlas models to correct transit light curves which are the result of the actual limb-darkening of a star. These corrected light curves can be seen in the top curves of Fig. 8, where the limb-darkening overestimation by the Atlas models translates into a slightly lower flux ratio at mid-transit, and slightly higher flux ratio just before 3 contact, or just after 2 contact, with this general trend seen at all wavelengths. Thus, introducing the Atlas model produces two systematic effects () a wavelength-to-wavelength flux scatter of up to 0.005-0.006% and () a phase-dependent trend of overcorrecting the transit flux during the middle 2/3 of in-transit times and under-correcting during the remaining 1/3. The first systematic effect is likely due to the internal accuracy of the Atlas models, where uncertainties in opacity database tables and metal line-blanketing, for instance, could reveal themselves. The second systematic effect is clearly related to the general trend of Atlas models over predicting the strength of limb-darkening, at a similar level, in all wavelengths and tied to the treatment of convection in one-dimensional atmospheric models.
To test if the broadband NUV and Na absorption features seen in our data could successfully be recovered using Atlas model limb-darkening corrections, we also simulated transits using the NL94 data, which contained an extra 0.01 R in planetary radii for the NUV and an extra 0.02 R in planetary radii for selected Na-like wavelengths. These simulated absorption transit light-curves were then corrected with those generated with solar Atlas models and the best-fit planetary radius (see Fig. 8). The two simulated absorptions can easily be identified above that of the zero absorption case, with the general phase-dependent trend largely preserved. Therefore, when averaging over a series of in-transit spectra and comparing absorption values at different wavelengths, the values of the relative absorption differences will largely be retained after the Atlas corrections, but the flux level itself could change slightly, depending on the phase sampling (effect ). At the extremes, using only data at mid-transit, 2 contact, or 3 contact, this absolute flux difference is seen to be up to 0.01%. These trends are observed in our absorption simulations. When we average over the in-transit phases, and recover the input absorption signal (see Fig. 9), we get relative absorption values (above the Atlas corrected zero absorption case) of 0.026 0.003% and 0.0460.002% for the NUV-like and Na-like signature respectively. These values closely match the input 0.022% and 0.044% values, indicating that Atlas model corrections can retain relative absorption signals at level of around 0.003%. Selecting subsets which contained only similar orbital phases produced equivalent differential results, indicating effect has a limited impact on relative absorption measurements.
3.4. Application of solar test to HD209458
The residual G430L and G750L Atlas-fit light curves, additionally see Fig. 4 of Knutson et al. (2007), show the same trends as observed in our solar test. Namely, the HD209458 transit light curves show a systematically slightly higher residual flux at mid-transit compared to 2 and 3 contact, at a 0.01-0.02% flux level as in our solar test, with this trend repeated at all optical wavelengths. This indicates the performance of the Atlas models is similar for both HD209458 and the sun. When fitting for the planetary radius, in the case of HD209458, adopting an Atlas limb-darkening model would therefore seem to systematically fit a slightly smaller / ratio at every wavelength, and thus result in smaller planetary radii (given uniform and complete phase coverage). However, this systematic error is much smaller than the uncertainty due to the stellar mass and has a negligible effect on the final determined planetary radius. This is reflected in the analysis of Knutson et al. (2007), who find planetary radii values which differ by less than 1, when using either the method of adopting Atlas models or fitting for limb-darkening coefficients.
Our analysis shows that, over the entire optical regime 3,000-10,000 Å, it is possible to use Atlas models to accurately measure the relative value of planetary radii to around a 0.005-0.006% precision level in solar-type stars. This precision level is comparable to our highest S/N achieved when averaging over large wavelength ranges (>1000 Å) and multiple exposures (see §4.2). Thus, the systematic errors introduced by assuming Atlas models are negligible for our purposes of probing relative transit depths for signals >0.01%. The success of using Atlas models in analyzing transits of the K0 V star HD189733 (Pont et al. 2007), further highlights their capabilities. As a relatively cooler K star, molecular opacity plays a correspondingly larger role in HD189733 than the sun or HD209458, yet an Atlas model provides superior fits compared to leaving the limb-darkening coefficients as free parameters in transit fits (F. Pont, private communication). As more high-precision measurements become available across a wider wavelength range, care will have to be taken when comparing transit parameters determined by separate analysis, which make different limb-darkening assumptions.
4.1. Stellar parameter uncertainties
Uncertainty in the stellar parameters (T, log g, log[M/H], v) can lead to a range of possible stellar models and thus a range of predicted limb-darkening. As limb-darkening derives mainly from intensity differences between blackbodies at different temperatures, changes in the T of the star have the largest effect on the calculated limb-darkening. For HD209458, the range of T found in the literature ranges from 6,000-6,100 K (6,030140 K Allende Prieto & Lambert 1999; 6,00050 K Mazeh et al. 2000; 6,11726 K Santos, Israelian, & Mayor 2004; 6,099 K Fischer & Valenti 2005) and we have adopted a T of 6,100 for this study.
We estimate the uncertainty of limb-darkening inferred from stellar parameter uncertainty by estimating how large a temperature increase or decrease is necessary to produce a difference flux of 0.02% at mid-transit between bandpasses, which is near the absorption signal detected in the NUV region. In our wavelength regime, the flux at mid-transit in the NUV is the most sensitive to changes in limb-darkening, making this test an upper-limit to the T change needed at longer wavelength bandpasses and other phases. From Claret (2000), we use non-linear limb-darkening for the photometric bandpasses U and B calculated at three different temperatures, and measure the transit depth that results. The U and B wavelength ranges roughly correspond to the 0.03% flux difference observed in our transmission spectrum between the NUV (3,000-3,700 Å) and nearby optical (4,000-5,500 Å). Using the best-fit HD209458 parameters, we calculate that a T change from 6,000 K to 5500 K changes the U band mid-transit depth by 0.05% and the B band by 0.03%, resulting in a 0.02% change in relative flux depth. Likewise, changing the T from 6,000 K to 6,500 K changes the mid-transit depth by 0.05% in the U band and 0.03% in the B band, also resulting in a 0.02% change. Thus, an uncertainty of only 50 K for the T of HD209458 corresponds to a NUV limb-darkening uncertainty of only 0.002%, a level well below our S/N level.
4.2. Red noise
We quantify the level of systematic ‘red noise’ in our transmission spectrum following the procedures detailed in Pont, Zucker, & Queloz (2006). In the absence of red noise, averaging over successive measurements increases the S/N in a predictable manner, with the standard deviation of the average varying inversely with the square root of the number of measurements, N. In the presence of red noise, however, the standard deviation does not decrease as quickly, when averaging over larger number of measurements, and in the limit of completely correlated noise, becomes a constant of N.
To estimate the level of correlated noise in our data, we take the out-of-transit spectra, binned over N pixels in wavelength, and calculate the variance and standard deviation from a distribution of points binned by N successive measurements. This is repeated for an increasingly larger number of N and N bin sizes. We checked different binning combinations to ensure correlated noise did not appear at our binning frequency. Plotted in Fig. 10 is a sample of red noise estimation from the G750L data in the 6,200 Å region. Typically, photon noise is seen to dominate down to precision levels of 0.02%, where the effects of red noise start to become visible. For most of the optical, binning over large wavelength regions and multiple exposures allows us to reach precision levels of 0.006%, although after binning beyond 30 measurements, the S/N ratio usually does not significantly increase.
As binning over larger wavelength bands has diminishing returns, the presence of red noise gives our transmission spectra a similar S/N level at moderate wavelength bins as compared to those larger wavelength bins. This is reflected in Fig. 11, where all five 1 error bars calculated to show the significance of observed broadband features are similar to each other, though they differ in wavelength breadth. The broadband errors are also similar to the typical 1 uncertainty levels when binning over 16 pixels, 0.011%.
4.3. Broadband absorption signatures, optical transit transmission spectra
Using the G750M and G750L spectra, we used a limb-darkened corrected transit spectral ratio to probe the full wavelength dependence of atmospheric absorption features, producing an optical transmission spectra. The relative planetary radii, when comparing between different wavelengths, are largely independent of the uncertainties of the stellar parameters and can be determined much more precisely than the actual radii values themselves (Knutson et al. 2007). Putting the low resolution G750L data together with the G430L data (Ballester, Sing & Herbert 2007), allows a probe of the region from 3,000-10,000 Å with the Na D lines located in a high S/N region in the middle.
Our low resolution transmission spectra was produced by interpolating all the systematic error corrected spectra onto a common wavelength scale. We then produced both an average out-of-transit spectra and an average limb-darkened corrected “in”-transit spectra (using phases between 2 and 3 contact), with the ratio of the two providing our ratio spectrum. The error was computed taking into account both photon noise and red noise, as outlined in section 1.7. The G750L spectral region blue-ward of 5,548 Å at the edge of the spectrum was omitted as it contains a region of very rapidly decreasing response whose spectral ratio value is 0.03% lower, when compared to the higher S/N overlapping G430L region. This omitted G750L region is seen to have a larger amount of red noise, limiting the accuracy levels in the region to 0.02-0.03%, which likely explains the flux difference between the two data sets. We used the best fit value of 1-(/) 1.455% from Knutson et al. (2007) as our baseline transit depth reference, subtracting our spectral ratio from that value to construct a plot of the atmospheric absorption profile (Fig. 11). We also performed the same procedure on the G750M data, though a shift of +0.00023 was needed to generate an average absorption level consistent with that of the low resolution data. As the medium resolution data was taken three years before the low resolution data, long-term differences in star spots, for instance, could easily account for the small measured difference in absolute absorption level. The effects from the uncertainties in the transit parameters were tested by varying the period, inclination, stellar radius, stellar mass by 1 (as reported in Knutson et al. 2007) and producing a new transmission spectra. Due to limb-darkening, changing the inclination is seen to have a larger affect than the other parameters, though all produce negligible affects on the final transmission spectrum. For instance, even for the NUV at 3,000 Å which contains strong limb-darkening, changing the inclination by 1 still only has a 0.002% effect on the final transmission spectrum.
The wavelength range of the G750L grating extends in the red past 1m, though with significant detector fringing (Knutson et al., 2007). The data reduction procedures used here were insufficient to correct for the large fringing effect on a pixel-by-pixel basis. Consequently, those regions which showed signs of significant fringing were left out of this analysis, corresponding to wavelength regions longer than 8,000Å.
5. Discussion and Conclusions
Our optical transit transmission spectrum combining all three gratings (see Fig. 11), gives a consistent and more complete view of the observed absorption features present in HD209458b. The low resolution transmission spectrum reveals three prominent broadband absorption features: (1) a NUV absorption below 4,000 Å; (2) a strong broadband Na feature; and (3) an additional absorption feature at 6,250 Å. The medium resolution data shows: (4) the strong Na core absorption (0.065% in a 4.4Å line-core band) and (5) confirms the presence of the absorption feature at 6,250 Å. The NUV absorption region was first reported by Ballester, Sing, & Herbert (2007), and is interpreted along with wavelengths shorter than 5,000 Å by Lecavelier et al. (2008) to be Rayleigh scattering by H. While the long wavelength continuum redward of 6,200 Å can be explained by absorption by TiO and VO (Désert et al., 2008).
Seen at low resolution, the wide Na wings and additional absorption at 6,250Å place the medium resolution data on an apparent plateau, 0.045% above that of the minimum absorption levels seen around 5,000Å and redward of 7,000Å. As such, the total Na core absorption reaches to 0.11% within a 4.4Å band above the minimum level at 5,000Å. This strong Na absorption is much closer to the original cloudless predictions (Seager & Sasselov, 2000; Brown, 2001; Hubbard et al., 2001), albeit with a more complicated Na line absorption profile (Sing et al., 2008). The large Na line-core absorption would seem to disfavor high altitude clouds or haze cutting into the absorption signature, as recently seen on HD189733 by Pont et al. (2007). The sharp transition from broad Na features at lower absorption depths to sharp narrow features at high absorption depths, however, indicates condensation of Na is likely in the upper atmosphere, which would deplete those higher altitudes of atomic Na (Sing et al., 2008).
The complicated Na D line shape and telluric contamination illustrate some of the difficulties in observing this atmospheric absorption signature in HD209458b. Ground based spectroscopic measurements, such as the Na detected in HD189733b (Redfield et al., 2008), require airmass corrections and are only sensitive to the Na D line cores where the atmospheric atomic Na in HD209458b is substantially depleted. Furthermore, telluric Na contamination has a non-negligible impact on the signature, further masking the small signal.
As seen here with Na, transit spectra at multiple resolutions are needed to properly interpret complex transmission features. Data at low resolution, covering a broad wavelength range, places the overall features in context, while data at medium or high resolution is better suited to identify specific absorption features and probe planetary atmospheres over a large pressure ranges. Our tests show that for exoplanets with solar type stellar hosts, such transmission spectra can be corrected for limb-darkening effects to a high precision with current atmospheric models.
Space-based observations on exoplanetary transits offer the extraordinary ability to provide exoplanetary transmission spectra at multiple resolutions, leading to detailed atmospheric composition information. As the signal-to-noise, resolution, and wavelength coverage of such spectra improves, multiple species can be detected and atmospheric properties inferred. The data quality of the spectra used here and results herein help indicate the full potential of the transit method, which can be further exploited with the impending repair of HST and future launch of the James Webb Space Telescope.
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