2.1.

GPIES Observations

A GPIES campaign observation is comprised of 20 to 40 sequential H-band ($1.6\mu \mathrm{m}$) integral field spectrograph (IFS) images, each with a 60-s exposure. Each exposure is automatically reconstructed into a spectral cube ($x$, $y$, and $\lambda$), which we refer to as “raw images.” A record of the instrument, observatory, and ambient environment states, along with a time stamp and target identification information, are saved in the image header. At the end of an observing sequence, individual raw IFS images automatically undergo calibration and PSF-subtraction and are combined into a single “final” IFS image by the GPIES data pipeline.^30–33

An important metric used for monitoring GPI’s performance is contrast, the minimum detectable planet-to-star flux ratio at a given projected separation from the host star. The $5\sigma$ contrast at a given separation is defined as five times the local standard deviation of the noise in an annulus centered at that separation. This calculation first takes place for each wavelength slice in a cube, and then the values for the central 50% of the spectral band are median-combined to produce a single contrast curve that is associated with the observation.^31,33 Typical “raw contrast” values at 0.4 arc sec are $\lesssim {10}^{-4}$. The “final contrast” is typically 10 to 50 times better than the raw contrast.

The raw and final data products are logged in the GPIES database as they are produced.³⁴ This includes the raw and final $5\sigma$ contrast measured at 0.2 arc sec, 0.4 arc sec, and 0.8 arc sec separations. For simplicity, we consider only the raw and final contrast at 0.4 arc sec separation. At smaller separations, performance can be affected by coronagraph misalignment, and at larger separations, images may be background limited.¹¹ In total, we have access to 28,387 raw images and 719 final images, which were gathered between November 2014 and January 2019.

2.2.

GPI AO Telemetry

GPI’s AO system¹⁰ consists of a Shack–Hartmann wavefront sensor (WFS) and two DMs. The WFS uses $2\times 2\text{pixel}$ quad-cell centroiding to measure the slope of the wavefront across each subaperture in the full telescope aperture, which is 43 subapertures wide. Each subaperture samples 18 cm of the wavefront, and these measurements are performed at a rate of 1 kHz on stars brighter than eighth magnitude in I-band and 500 Hz on fainter stars. The phase of the wavefront is reconstructed in Fourier modes.³⁵ Low-order modes are sent to the woofer DM and the tip/tilt stage; high-order modes are sent to the tweeter DM. The real-time control computer estimates the modal coefficients for tip, tilt, and focus and removes them from the signal that drives the control loop.

Several types of AO data are periodically recorded for analysis purposes, 2 to 5 times per target, at the discretion of the observer. A full telemetry set contains a record of the WFS measurements, DM, and tip/tilt commands, along with any other offsets applied. The datasets used here are 10- to 22-s long, and a total number of 2009 AO telemetry sets were recorded between September 2014 and January 2019.

A direct measurement of the AO system’s performance is the residual wavefront error (${\sigma }_{\mathrm{WFE}}$), defined as the error measured by the WFS after applying a correction with the DM. An instantaneous approximation of ${\sigma }_{\mathrm{WFE}}$, based on the RMS subaperture slopes, is saved to the header of each raw IFS frame (see Sec. 3.1). We also estimated the ${\sigma }_{\mathrm{WFE}}$ from reconstructed wavefront telemetry as discussed in Sec. 3.2.

2.3.

Gemini Observatory Data

There are multiple temperature sensors placed in and around the telescope dome at GS. Each sensor records the temperature every 5 min. The approximate locations of the interior sensors relevant to this study are displayed in Fig. 1. At each location, there is one sensor directly attached to the metal truss surface (Minco S651PDX24B³⁶) and another that is suspended freely in the air next to it (Omega RDT-805³⁷). On M1, there are two individual sensors mounted directly on the outer rim. The “M1-Y” sensor is attached to the side that tips downward when the telescope slews to a lower elevation, while the “M1+Y” sensor is attached to the side that tips upward. The precision of the temperature data is $\sim 1\%$ at 25°C, according to the sensor specifications. Although precise, the sensors may be subject to constant bias offsets, as will be discussed in Sec. 3.1. Additionally, the outside air temperature is recorded by a weather tower adjacent to GS.

Fig. 1

Schematic of GS telescope and observatory dome. Arrows mark the locations of temperature sensors.

The ${ϵ}_0$ and ${\tau }_0$ values at the time of observation were provided by the observatory’s Differential Image Motion Monitor (DIMM) and Multi-Aperture Scintillation Sensor (MASS), respectively.³⁸ These instruments are not located in the dome, but rather in a separate tower $\sim 80\mathrm{m}$ away. Consequently, they are insensitive to mirror or dome seeing, a crucial point for our study.

3.1.

Filtering, Matching, and Calibrating GPI Science Data and Temperature Readings

IFS raw and final datasets were filtered as follows. To ensure high signal-to-noise images and telemetry, we included in our sample only bright stars (I-band magnitude $<7$). This also guaranteed that the AO system was operating at 1 kHz for all images in the sample. We also excluded images that were taken in the worst seeing conditions or when there was no recent measurement ($\lesssim 40\min$) from the MASS/DIMM. According to the MASS/DIMM, the median seeing recorded at Cerro Pachon from the years 2014 to 2019 was ${ϵ}_0=0.9\mathrm{arc}\sec$ and ${\tau }_0=1.5\mathrm{ms}$. We only kept the images corresponding to the best 85% seeing conditions: ${ϵ}_0<1.2\mathrm{arc}\sec$ and ${\tau }_0>0.8\mathrm{ms}$. These seeing cuts combined culled almost 80% of the remaining dataset, in large part because no MASS/DIMM values were available after early 2017. Next, we rejected final images in which the field of view (FOV) rotated by less than twice the FWHM of the PSF for a planet orbiting its star at $0.4\mathrm{arc}\sec ({\theta }_{\mathrm{FOV}}>12.2\mathrm{deg})$ (${\theta }_{\mathrm{FOV}}>\frac{2\lambda }{D\rho }$, where $\lambda =1.65\mu \mathrm{m}$, $D=8\mathrm{m}$, and $\rho =0.4\mathrm{arc}\sec$). The final contrast depends on the FOV rotation because the GPI data pipeline relies in part on the angular differential imaging observing technique. Sequences with a lower FOV rotation suffer loss of sensitivity due to self-subtraction during the PSF subtraction process. After all of these cuts, 2977 raw frames and 120 final images remained. The remaining data represent 57 different observing nights between September 2014 and February 2017.

Finally, not all sequences attained the same total integration time. To normalize all values to an equivalent of a full sequence (38 min), we scaled final contrast by $\sqrt{t_i/38\min }$, where $t_i$ is the total integration time. This scaling was verified to hold after the minimum ${\theta }_{\mathrm{FOV}}$ was achieved, based on a multihour c Eri dataset.

The approximate ${\sigma }_{\mathrm{WFE}}$ that is stored in the IFS headers is overestimated because the calibration between the RMS displacement of the WFS centroids and the actual wavefront error was never measured. We obtained the linear relationship:

Fig. 2

Comparison of residual wavefront error derived from AO telemetry, ${\sigma }_{\mathrm{AO}\text{telemetry}}$, to the instantaneous approximation saved to the IFS image headers, ${\sigma }_{\mathrm{IF}\text{Sheader}}$ (black points). The linear fit is overlaid (red line) and was used to correct ${\sigma }_{\mathrm{IF}\text{Sheader}}$ in subsequent analysis.

We also filtered and calibrated the GS temperature data. Bad or missing data in the GS temperature logs are recorded with a null value; these entries were removed. We cross-checked the M1 temperatures against simultaneous readings from the GPI AO bench temperature sensor and the dome air and truss sensors. Both M1 sensors revealed significant offsets. The observatory staff calibrated these two sensors on August 3, 2017. Unfortunately, the offsets were not recorded during the calibration process. To correct the historical data, we determined the zero-point offset for each sensor in the following way: first, we split the data into before and after calibration sets—from January 1, 2014, to August 2, 2017, and from August 4, 2017, to December 31, 2018—and then folded them by year. Next, we fit a line to the before calibration data from August 4 to December 31 and subtracted the fit from the after calibration data. In the final step, we calculated the DC offset that made the mean of the difference equal to zero. The average offset value for each sensor is displayed in Table 1. The dome air temperature reported by the various truss air temperature sensors also showed moderate systematic offsets. The lower-truss sensor reading most closely matched the temperature reported by the weather tower, while the upper- and mid-truss sensors reported temperatures 1°C to 2°C cooler. Because the calibration of these sensors was not independently checked as M1 sensors were, we chose to use only the readings from the lower-truss sensor. However, we stress that absolute temperatures were not essential in this study as we investigated only the relationship between GPI performance and relative temperature changes.

Table 1

Calculated temperature offsets for GS temperature sensors (Tcorrected=T0+offset).

Ultimately, a single value of each environment parameter (M1 temperature, dome temperature, ${\tau }_0$, and ${ϵ}_0$) was associated with each raw and final image for all subsequent analysis. We averaged the two corrected M1 sensors to produce an instantaneous M1 temperature. We matched each raw science frame with its closest-in-time temperature readings. If no temperature was recorded within 30 min of the observation, we excluded the image from our sample; this removed $\sim 25$ of the raw images. Finally, we matched final science frames with the average M1 and dome temperatures and the average seeing recorded during the entire observation sequence.

3.2.

Characterizing Turbulence with AO Telemetry

We quantified the characteristics of mirror turbulence by examining the spatial and temporal PSDs of the wavefronts at the entrance pupil (i.e., before AO correction). In theory, it is possible to directly measure mirror seeing with open-loop measurements from the WFS. But in practice, open-loop wavefront errors are too large to be measured by GPI’s WFS. Thus, rather than directly measuring the open-loop phase, we reconstructed the “pseudo open-loop” phase from closed-loop AO telemetry. A detailed description of this process can be found in Refs. 39 and 40. The closed-loop residual phase measured by the WFS, ${\mathrm{\Phi }}_{\mathrm{WFS}}$, is given by

Tip and tilt were already removed from the signal by the real-time control computer; however, some static aberrations remained. To estimate the low-order static aberrations, we calculated the time-average phase map and fit it with the first six Zernike polynomials, under the assumption that any low-order turbulence-induced wavefront error would average to zero over the 10- to 22-s time series. We used the Python optical simulation package Poppy⁴¹ to calculate normalized Zernike coefficients.

We then used the two-dimensional discrete Fourier transform (DFT) to decompose the phase signal at each timestep into its Fourier modes. Given the open-loop phase $\varphi (x,y,t_i)$ and the aperture $a(x,y)$, the modal coefficients at each time step $t_i$ are

Fig. 3

(a) Spatial and (b) temporal PSDs of pseudo open-loop wavefront errors derived from AO telemetry recorded while observing c Eri on December 19, 2015. We superimposed the temporal PSD obtained after applying the Savitzky–Golay filter (black) with the original temporal PSD (gray). Power law fits (red line) were performed in the inertial range of the PSDs.

The length scales captured by GPI range from 0.36 to 8 m, where 0.36 m is twice one subaperture diameter and 8 m is the full aperture diameter. We fit a power law of the form $\mathrm{PSD}={10}^{{\alpha }_{\mathrm{s}}}{\mathrm{f}}^{{\beta }_{\mathrm{s}}}$ from the middle region of the spectrum $(0.3{\mathrm{m}}^{-1},1.0{\mathrm{m}}^{-1})$, which is highlighted in Fig. 3. This selection ensures that our parameters are free from tilt and outer scale effects at lower spatial frequencies and WFS aliasing effects at higher spatial frequencies.

This process was repeated to estimate the average temporal PSD of the DM actuators:

4.1.

Temperature Conditions at Gemini South

We first investigated the typical temperature conditions at GS using temperature records from the years 2015 to 2019, which include all nights, not only those with GPI data. We excluded nights with only partial records. We required at least 10 measurements recorded in a 24-h period and at least 4 h between $T_{\max }$ and $T_{\min }$. A total of 1001 nights, out of an original 1221, remained. Figure 4(a) shows a histogram of $(T_{\max }-T_{\min })$ of the outside air for each calendar day, split at sunset. The distribution peaks at 4°C but occasionally reaches 15°C, illustrating the wide range of day–night temperature swings that the observatory must cope with. We measured the nighttime instantaneous temperature differences between M1, dome air, and ambient air to identify potential sources of dome seeing. We only considered nights in which GPI took on-sky data. We plot their density histograms in Fig. 4(b) and their cumulative densities in Fig. 4(c). The reported median temperature of the dome is 0.7°C cooler than ambient, while the reported median temperature of M1 is 1.2°C warmer than ambient. However, as discussed previously, while the calibration of the M1 sensors has been validated, those of the outside air sensor and the dome air sensor have not. Thus, while the distributions of dome–ambient and M1–ambient difference are correct, the medians could be biased. From the standard deviations of the two distributions (1.6°C and 2.0°C, respectively), we can conclude that the dome more quickly tracks ambient temperature than M1.

Fig. 4

Temperatures at the GS Observatory. (a) Histogram of the daily min–max range of outside air temperatures. (b) Histogram of instantaneous temperature differences between dome air or M1 and outside air at night, for those nights when GPI was observing, with DC offset corrections as described in Sec. 3.1. (c) Cumulative density plot of the data in (b).

Figure 5 shows the median 24-h temperature profile of M1, dome air, and outside air for nights in which GPI took on-sky data. It shows that the min-to-max range of M1 is small compared with the min-to-max range of the ambient air. We postulate that M1 typically remains warmer than ambient air during the night, resulting in additional mirror seeing and in GPI AO performance degradation. The exact thermal balance of any observatory is complex. M1 may never be in good equilibrium after sudden jumps in the ambient temperature, which on Cerro Pachon are frequently $>4^{\mathrm{o}}\mathrm{C}$ in a day. There could also be potential sources of heat such as electronics in or near the mirror cell. This is an ongoing area of study at the Gemini Observatory.

Fig. 5

Median 24-h temperature profile at GS for nights on which GPI took on-sky data. The black, red, and blue lines represent the median temperature of M1, dome air, and the outside air, respectively. Vertical dashed lines mark the approximate length of the shortest and longest nights of the year.

4.2.

Effect of Temperature Differentials on Residual Wavefront Error and Contrast

Next we explored the correlation between the instantaneous ${\sigma }_{\mathrm{WFE}}$ recorded in the GPI image headers and the temperature differences between M1 and the outside air. The result, which is displayed in Fig. 6, shows that ${\sigma }_{\mathrm{WFE}}$ becomes larger as the temperature difference between M1 and the outside air increases. Some vertical scatter is present due to additional contributions from other sources affecting performance, such as stellar magnitude or atmospheric seeing conditions. With appropriate calibration, measurements from the observatory seeing monitors could potentially be used to correct for some of the atmospheric seeing contribution; this analysis is left to future work. Nonetheless, the performance limit imposed by mirror seeing is clearly captured by the lower envelope of the data, which corresponds to the best seeing conditions. The model⁴³ we used to capture the relationship between ${\sigma }_{\mathrm{WFE}}$ and $\mathrm{\Delta }{T}_{\mathrm{M}}$ is

Fig. 6

${\sigma }_{\mathrm{WFE}}$ versus $\mathrm{\Delta }{T}_{\mathrm{M}}$. The temperature difference between M1 and ambient sets the lower limit on ${\sigma }_{\mathrm{WFE}}$. The red line indicates a fit of the bottom 25th percentile of the data, which are the points shaded in black.

We also quantified the effects of mirror seeing on contrast performance, which is the quantity of interest when imaging planets. Previous correlation studies of GPI performance showed that raw contrast and final contrast both scaled with ${\sigma }_{\mathrm{WFE}}^2$ at close-to-intermediate separations.^10,11 Therefore, we expected that raw contrast and final contrast to have the following relationship:

Fig. 7

Image contrast versus $\mathrm{\Delta }{T}_{\mathrm{M}}$. (a) Raw contrast while (b) is final contrast. Blue line is the fit of the best 25th percentile of the data (black points). On nights when the temperature of the mirror diverged by more than 3°C from the outside air temperature, both raw and final contrast degraded by $\sim 3\times$.

4.3.

Effect of Temperature Differentials on Turbulence Power Spectra

Evidently high-contrast imaging performance is reduced significantly when M1 is not in thermal equilibrium; however, this relationship alone cannot identify the underlying cause. As discussed in Sec. 1, GPI’s AO system was designed assuming Kolmogorov turbulence models of the local atmosphere. Perhaps M1 is an extra source of turbulence, resulting in turbulence conditions for which the AO system is no longer optimized. The GS seeing monitors, located outside the dome, cannot directly measure mirror turbulence. However, GPI’s well-characterized AO system may be able to. In this section, we check for relationships between the structure of the spatial and temporal PSDs and $\mathrm{\Delta }{T}_{\mathrm{M}}$ measured during the entire GPIES campaign. The spatial PSD is calculated with all temporal frequencies, and we fit only spatial frequencies between 0.3 and ${1.0\mathrm{m}}^{-1}$. The temporal PSD is calculated using all spatial frequencies, and we fit only temporal frequencies between 2 and 40 Hz. Therefore, keep in mind that we cannot rule out effects at other length scales or frequencies. After the data selection outlined in Sec. 3.1, a total of 582 AO telemetry sets remained. We then averaged the parameters that were extracted from the fits for all telemetry sets taken while integrating on the same star, leaving 122 measurements.

The parameters extracted from our fits, log($\alpha$) and ($\beta$), are plotted as a function of $\mathrm{\Delta }{T}_{\mathrm{M}}$ in Fig. 8. We find that there is no clear dependence between $\beta$ and $\mathrm{\Delta }{T}_{\mathrm{M}}$. The ${\beta }_s$ data are uniformly scattered on the expected power-law for spatial Kolmogorov turbulence ($-11/3$), indicating that mirror seeing does not exhibit significant deviations from Kolmogorov behavior at these length scales. The ${\beta }_t$ data also exhibit uniform behavior, but at a slightly higher value than the expected power-law for temporal Kolmogorov turbulence ($-8/3$). This shows that the temporal power spectrum is flatter than what is expected from Kolmogorov, implying an excess of high temporal frequencies with respect to simply translating a Kolmogorov phase screen. Disentangling the relative contributions of noise versus small-spatial-scale boiling is left to future work.

Fig. 8

Power law index ($\beta$) and log [amplitude ($\alpha$)] derived from fits of spatial and temporal PSDs are plotted as a function of $\mathrm{\Delta }{T}_{\mathrm{M}}$. The points are the mean of each campaign sequence. The black points highlight those datasets with the best 25th percentile contrast, as defined in Fig. 7. The power law expected for spatial Kolmogorov turbulence ($-3.67$) and for temporal Kolmogorov turbulence ($-2.67$) is marked with a line. Only the strength of the turbulence as measured by the spatial PSD shows clear dependence on $\mathrm{\Delta }{T}_{\mathrm{M}}$.

Now we focus on $\alpha$, which is directly related to the total seeing.⁴⁵ We expect the total seeing to increase as the mirror temperature difference increases, and indeed we find a positive trend between ${\alpha }_s$ and $\mathrm{\Delta }{T}_{\mathrm{M}}$, albeit at low signal to noise. This, combined with the flat dependence of ${\beta }_s$ on $\mathrm{\Delta }{T}_{\mathrm{M}}$, shows that the power spectrum is shifted vertically upward when $\mathrm{\Delta }{T}_{\mathrm{M}}$ increases, implying that the intensity of turbulence gets increased at all length scales in the inertial range. Surprisingly, this behavior is less obvious with ${\alpha }_t$, but we hypothesize that our inability to probe smaller length scales and/or other noise sources could be obscuring the trend.