Imaging Survey for Faint Companions with Shaped Pupil Masks 1

Imaging Survey for Faint Companions with Shaped Pupil Masks 1 Jian Ge, John Debes, Anne Watson & Abhijit Chakraborty 55 Davey Lab, Department of Astronomy & Astrophysics, Penn State University, University Park, PA 1680 Abstract A combination of Spergel s innovative gaussian-shaped pupil masks with future space-based and ground-based adaptive optics telescopes will offer great sensitivity for direct imaging of faint companions including brown dwarfs and extra-solar planets around nearby stars. Here we propose a quick way to fully achieve its potential for deep contrast imaging surveys with a great speed in a conventionally designed telescope. In our approach, two Gaussian pupil masks set on each side of the secondary obscuration, slightly penetrating the telescope spider structures, are placed in a cryogenic pupil plane in an infrared (IR) camera to allow the collimated telescope beams to pass through. This simple design will enable ~10-6 deep contrast imaging while enjoying diffraction-limited imaging from the full telescope aperture for discovering faint companions closest to the primary. The survey speed with this design will be at least 3-4 times faster than a conventional coronagraph due to its simple alignment. This contrast should allow an image survey for Jupiter-like planets to ~ 0 pc in the thermal IR with next generation large groundbased and space based telescopes. A combination of this shaped pupil mask with an apodizing focal plane mask will enable deeper contrast than the pupil mask alone. However, it takes a much longer time to align the system, so this mode will be used for characterization of faint companion systems from the candidates identified from the survey. A prototype gaussian pupil mask in the Penn State near IR Imager and Spectrograph (PIRIS) has been tested at the Mt. Wilson 100 inch telescope with high order natural guide star adaptive optics (AO) and has demonstrated its tremendous potential. The contrast is about 10-3 -10-4 beyond 7 λ/d. The contrast is about 5 times better than the direct AO image, and comparable to an IR coronagraph in the same instrument. Recent lab experiments show that 3 10-6 at ~ 4 λ/d can be reached with a combination of a Gaussian pupil mask with an apodizing focal plane mask. Key Words: Extra-solar Planets, Brown Dwarfs, gaussian-shaped mask, adaptive optics, telescope, survey, imaging 1. Introduction The search for Brown Dwarfs (BD) and planets as close companions to nearby stars has produced spectacular results in recent years. Doppler radial velocity (RV) techniques have been able to find more than 100 extra-solar planets with masses between 0.5 to 15 M Jup within 4 Astronomical Units (AU) of ~7% of nearby F,G,K and M stars (for a current list of systems and their properties see http://www.obspm.fr/encycl/encycl.html). Combining these RV results with data on spectroscopic binaries produces a distribution of companions from 1 to 1000 M Jup that is characterized by a minimum or Brown Dwarf desert at 10-30 M Jup, i.e. fewer than 0.5% of these stars have a BD companion within 4 AU (Marcy et al. 000). In contrast the frequency of stellar companion to G dwarfs is about 57% (Duquennoy et al. 1991) and to M dwarfs is about 4% (Fischer et al. 1993). The reason for the decline in the frequency of close-in BDs is not known and could be due to the mechanism of formation of stars and planetary systems. It is 1 Send correspondence to Jian Ge, email: jian@astro.psu.edu, Tel: 814-863-9553, Fax: 814-863-3399

possible that the dynamics of protoplanetary disks prevent the formation of BDs. Contrary to what has been discovered within 4 AU to the primaries, many BDs in the field and with wide separations from their primaries have been detected from the large scale surveys like the MASS and the SDSS (Reid et al. 1997; Kirkpatrick et al. 1999; Leggett et al. 000). Gizis et al. (001) have shown that the occurrence of L and T dwarfs at much larger separations of > 1000 AU from F-M main sequence stars is much higher, about 10 times more frequent than at < 3 AU. They also estimated that G dwarfs have the same number of stellar companions with separation < 3 AU and > 1000 AU. The primaries of most BDs with large separation are relatively massive (solar type) which suggest that low mass primaries (M types) are unable to retain their companions. The extreme limit for L dwarf binaries is about 10 AU (Reid et al. 001). Previous surveys for planets and BDs have limitations. The Doppler technique for RV surveys is an indirect method which detects companions through measuring stellar radial velocity perturbation by the gravity pull of possible planet and/or BD candidates. Hence, it cannot provide information about planet properties such as orbital location (therefore the total mass), size and atmosphere. Previous imaging surveys for BDs provide little information about BDs between 4-1000 AU. This is because previous imaging techniques either cannot provide contrast sufficient to detect very faint companions close to the central bright objects or cannot provide a required survey speed to carry out a large scale survey. Therefore, new high contrast imaging techniques are critical for carrying out surveys for faint companions very close to the nearby stars. In this paper, we will describe a new technique based on shaped pupil coronagraphs for high contrast imaging surveys for faint companions around nearby stars. The original concept of the Gaussian shaped pupil coronagraph was proposed by David Spergel at Princeton University (Spergel 000). This technique takes advantage of high contrast achieved by varying the shape of the pupil mask inside of an astronomical camera system. This technique is especially suitable for imaging surveys since it can provide both speed and high contrast.. Specially Shaped Pupil Coronagraph In this shaped pupil coronagraph, a specially shaped mask is placed in the pupil plane of an Figure 1. An ideal Gaussian-shaped pupil design (left, a=b=1, α=.7), and its corresponding point spread function at a focal plane (right).

instrument to create a specially shaped point spread function (PSF) in the final focal plane. Some of the image area is much darker than the other areas to allow deep searches for faint companions. In the family of the shaped masks, a Gaussian shaped aperture is a conventional one to use. In a Gaussian shaped aperture, its top and bottom edges are described by Gaussian curves: y top bot where a, b, and α control the depth and azimuthal area of deep contrast, and R is radius of primary. The Fraunhofer diffraction pattern that results from the shaped pupil produces a region of high contrast. We define contrast as z = I(ε,η)/I(0), the ratio of the intensity at a particular point (I(ε,η)) in an image to the peak intensity I(0). The size, depth of contrast, and angular coverage can be altered by the choice of free parameters a, b, and α. Figure 1 shows an example of a Gaussian-shaped aperture with a=b=1, α=.7, and its point spread function at the focal plane. The contrast along the horizontal line passing the image center is shown in Figure along y x R = ar[ e e α / α x R = br[ e e α / α ] ] Figure. Horizontal cuts along the symmetry axis of diffraction patterns of different sized openings. Increasing α deepens the null. Figure 3. (left) The log of normalized contrast vs. α. As α increases the contrast ratio decreases sharply, but at the cost of where the contrast begins. (right) The dependence of search angle θ with increasing α. A larger α restricts the total region of high contrast. with those with other α values. This figure also shows that the inner working distance, the location where high contrast occurs, strongly depends on the α value. Smaller α value gives less image contrast, but closer working distance. The dependence of α, a and b for the contrast and search angle is illustrated in Figures 3 and 4. Increasing α increases contrast while decreasing the angular coverage of the high z region. Decreasing a and b increases angular coverage at the expense of contrast and throughput. This is explored in more details in Debes et al. (00a). The efficiency of an imaging survey using a Gaussian shaped pupil mask depends on the search angle, the inner working distance, the image contrast and the total throughput of the mask. It is

important to optimize the image performance by carefully choosing the design parameters, a, b and α. In addition, since the telescope wavefront and optics errors contribute to the halo components of a point source image, it is important to include the wavefront effects in the design, Figure 4. Same as for Figure 3 but for varying a,b where a=b. Decreasing a or b can increase search angle but decreases throughput and degrades contrast. i.e. the optimal design is the one that the theoretical contrast limit matches the halo level while it provides high throughput and large search area. Since the deep contrast is achieved by the diffraction of the pupil mask, the overhead time for aligning a shaped pupil coronagraph is negligible. On the contrary, the overhead for aligning the focal plane mask along the optical axis in the conventional coronagraph approach usually takes at least a few times longer than the typical exposure time for the target. Furthermore, the high contrast possible with a Lyot coronagraph strongly depends on good alignment. Any deviation degrades the possible contrast. Therefore, the shaped pupil coronagraph is an ideal instrument for high contrast imaging surveys for faint companions with the ground-based and space-based telescopes. The coronagraphs involving careful focal plane mask alignment may be a good tool for follow-ups. 3. Observing Results with a Prototype Gaussian Mask A Gaussian shaped mask was designed and placed in the cold pupil plane of the Penn State near IR Imager and Spectrograph (PIRIS) to create a shaped pupil coronagraph for demonstrating its high contrast near-ir imaging capability (Ge et al. 00; Debes et al. 00a,b). Figure 5 shows the design of the mask used in the PIRIS. The mask was fabricated through photo chemical machining by the NewCut Inc. in New York. Part of the physical mask is also shown in Figure 5. The placement of Gaussian apertures avoided the support structure of the telescope to maximize contrast. A total of 1 apertures were situated symmetrically in each quadrant of the pupil mask to allow a total of 5% throughput. To maximize the azimuthal coverage so that in any one image roughly half of the azimuthal area was in a high contrast region, we varied the height of the top and bottom of the apertures. Nearby bright stars, ε Eridani (V=3.7, d=3. pc) and µ Her A (V=3.41, d=8.4 pc) were observed with the shaped pupil coronagraph. Figure 6 shows a logarithmic scaled image of the PSF of the Gaussian shaped pupil and a theoretically produced PSF. The PSF is not azimuthally symmetric and the high contrast region extends roughly over 180º. The majority of light in the diffraction pattern is spread into the four wings, leaving higher contrast regions between them. No faint companions were detected, but fairly stringent limits can be imposed on what kind of companions

would have been detected between 1 arcsec and 10 arcsec from the central star in the high contrast regions (Debes et al. 00b). ~ 4 mm Part of prototype pupil mask Figure 5. (left) Picture of the design tested at Mt. Wilson and at the lab. (right) part of the Gaussian mask fabricated through photo chemical etching. For comparison, Figure 7 shows the differences in the three imaging modes we conducted with the PIRIS (direct AO imaging, Lyot coronagraph imaging and shaped pupil coronagraph imaging) plus a simulation of the performance of our pupil mask design with no scattered light or atmospheric turbulence. The shaped pupil coronagraph performs better than AO alone and is ~ times worse than the Lyot coronagraph beyond 1 arcsec. This is without any attempt to block the light of the central star. Comparison of normalized contrast versus λ/d to other coronagraphs and Figure 6. (left) Logarithmically scaled image of ε Eridani showing the PSF of the Gaussian pupil mask produced by the PIRIS at the Mt. Wilson 100-inch telescope. (right) a theoretically produced PSF of a perfect Gaussian pupil mask (Debes et al. 00a).

to deep HST WFPC observations of ε Eridani show that our Gaussian pupil and coronagraphic mode performs similarly in terms of contrast to previous work done (Schroeder et al. 000; Hayward et al. 001; Luhman et al. 00). It is also evident that several effects degrade contrast. A large part of this degradation is due to the scattered light in the telescope and the AO. A faint companion around µ Her A was detected with high S/N in both the shaped pupil mode and direct AO imaging mode. Figure 8 shows the raw K-band image which clearly shows the faint companion. This companion was previously detected in the R and I band AO images at Mt. Wilson, and used to explain a radial velocity acceleration corresponding to a ~ 30 yr orbit (Cumming et al. 1999; Cochran et al. 1994; Turner et al. 001). Our observations confirm the dimmer object to be a proper motion companion and thus physically bound to the brighter star. Based on the age, absolute magnitudes in R, I, H and K of the companion, we used Figure 7. Graph of the different observing modes of PIRIS. The Gaussian pupil coronagraph performs about five times better than AO alone and two times worse than a Lyot coronagraph. the models of Baraffe et al (1998; 00) to conclude that its mass should be ~ 0.13 M Sun. This observation demonstrates the feasibility of our shaped pupil coronagraph for detecting faint companions around bright objects. Raw image in the K band µ Her 1".31 Figure 8. (left) the K band image of µ Her taken with a prototype Gaussian-shaped pupil mask at the Mt. Wilson 100 inch telescope in 001. (right) the relation between luminosity, mass and age of low mass stellar and substellar objects (Baraffe et al. 1998; 1999). The location for µ Her is plotted. The Mt. Wilson experiments demonstrate that the residual wavefront errors from the telescope system due to imperfect optics and the uncorrected distorted wavefront by the atmospheric

turbulence are the major sources limiting the image contrast. Improving wavefront quality is necessary for further increase in the image contrast. At Mt. Wilson, the typical Strehl ratio (SR) in the K band was about 0.1 during the experiments due to the bad seeing and misalignment of the optics. There is a potential for significant improvement in the image quality. For instance, the typical measured SR is 0.36 in the I band during the summer observing season (Ge et al. 1998). The SR of ~ 0.8-0.9 in the K band should be reachable at this site. With this kind of image, a contrast of ~ 10-5 at 5-10 λ/d with a shaped pupil coronagraph is probably reachable. Further improvement in the contrast needs implementation of a higher order AO system. Based on this kind of image quality, which represents the best case for most of the AO systems with large ground-based telescopes, the theoretical contrast level of ~ 10-6 is probably required for the design of a shaped pupil coronagraph for deep imaging surveys. Although this contrast level is much less than that required for detecting an Earth-like planet with the future Terrestrial Planet Finder (TPF) (~10-10 ), it is sufficient for surveys for BDs and young planets around nearby stars. In addition, less demanding in contrast opens up more design freedoms for improving the throughput and angular coverage of the shaped pupil coronagraph. In the following, we introduce a new mask design optimized for imaging surveys to be used at the Mt. Wilson 100-inch for searching for faint companions, which illustrates the potential of a shaped pupil mask for imaging surveys at future ground-based and space-based telescopes. We will also discuss the performance of the survey mask, the survey strategy, and follow-up characterization of faint companions with a hybrid coronagraph we proposed for the first time. 4. Survey Mask Design Figure 9. Overlay of the design with the pupil of the Mt. Wilson 100-inch telescope. Figure 10. The gaussian apertures avoid the secondary and all but a small fraction of the support structure. Results of simulations for the new survey mask design. The left graph shows the horizontal cut along the high contrast axis. The design will achieve high contrast ~ times closer than previous Gaussian pupil mask designs. The right graph shows the entire PSF with contour levels at 10-6, 10 -, and.8 of peak flux.

For this design, getting the highest contrast possible close to the central object is the most important goal. One drawback to the multi-aperture design that avoids all of the support structure is that it necessitates a halving of the aperture width which decreases the resolving power of the design. A design that retains a majority of that resolution while avoiding the secondary obstruction will have its theoretical contrast degraded only slightly by the presence of any support structure that appears in the aperture (See Debes et al. 00a). Figure 9 shows the design overlayed with a scaled version of the Mt. Wilson telescope pupil. It shows that the design avoids a majority of the support structure and secondary obstruction, while retaining the width of the pupil. In two areas the support structure overlaps the aperture. The total throughput of the design is 34.6%, much higher than our prototype. Using IDL simulations of the telescope plus pupil, we can predict the theoretical performance of the design. Insufficient AO correction will degrade these results due to a halo of uncorrected light, which can be estimated by previous observations (see Figure 7). Figure 10 shows a horizontal cut of the PSF of the design. We took an average of points centered around 10λ/D to determine the z along the high contrast axis. For this design we determined an average z=5.89 10-7. Figure 10 also shows a contour plot of the design with the different levels of contrast. The high contrast starts at ~ 5λ/D, which is roughly two times closer than our previous Gaussian pupil mask design. This will allow faint companions to be seen much closer to the central star, at the limit of AO performance. In the near-ir bands we will be using this closest region of high contrast translates to 0.5 arcsec, 0.66 arcsec, and 0.88 arcsec in the J, H, and K bands, respectively. The theoretical contrast possible at these separations represents two orders of magnitude improvement in contrast, compared to a 10-m telescope with a circular aperture. 5. Survey Strategy A successful survey of this kind on the ground is highly dependent on a high order of AO correction, a sensitive camera, and the presence of the specially shaped pupil mask design. Even more important is a telescope that has a large amount of time free for a survey of large nature. This rules out the 10m telescopes for two reasons. While in theory the larger primary mirror gives large gains in how close to an object in angular space the large contrast appears, no AO system currently in use on 10m telescopes has a high enough order of correction. Secondly, the large amount of time needed for a large survey makes a 10m telescope in high demand unfeasible. The best fit for this kind of survey is moderate size telescopes equipped with high order AO systems such as the Mt. Wilson 100- inch telescope. The future combination of high order AO with the shaped pupil coronagraph allows quick imaging of thousands of nearby stars for planet and/or BD companions. Since the PSFs of the shaped pupil coronagraph have two quadrants of deep contrast, we need two shaped pupil masks setting perpendicular to each other to allow searches for all directions. Because the imaging does not require any careful alignment of the instrument with the targets, it saves overhead time associated with Figure 11: PSFs of shaped pupil coronagraphs without (left) and with a Gaussian transmission mask (Hybrid, right). The pupil mask is a truncated Gaussian with α=.7 (Spergel 001; Debes et al. 00a), The focal plane mask has a Gaussian transmission with a FWHM of 4 λ/d.

the usual conventional Lyot coronagraph setting up. This overhead time is at least a few times longer than typical exposure time. Therefore, the survey speed can be much improved by using the shaped pupil coronagraphs. Once candidates are discovered through the quick imaging survey, careful imaging with higher contrast is required for detailed studies. These studies can be carried by new kind of coronagraphs such as band-limited coronagraph proposed by Kuchner and Traub (00), or hybrid coronagraph proposed by us. In recent studies, Kuchner and Traub (00) found that a band-limited mask, another kind of graded coronagraphic image mask, can, in principle, provide perfect elimination of on-axis light, while simultaneously maximizing the Lyot stop throughput and angular resolution. A bandlimited mask has a transmission function chosen to diffract all the light from an on-axis source to a region within ε of the edges of the pupil, so that a well-chosen Lyot stop can block identically all of that diffracted light. Such an image mask typically consists of a series of dark rings or stripes. In the absence of other limiting factors, this design can completely block the light from an on-axis source, while providing up to 80% throughput for off-axis planets, and an inner working distance of 3 λ/d. 6. Characterization of Planets and BDs with a Hybrid Coronagraph The hybrid coronagraph is a combination of a specially shaped pupil mask with a focal plane mask to allow high contrast imaging closer to the central source than can be achieved with the pupil coronagraph alone. Our recent simulations confirm the additional improvement on image contrast by simply adding an apodizing focal plane mask. Figure 11 shows the PSFs with and without a simple Gaussian transmission mask at the telescope focal plane. Figure 1 shows the cross-section of the on-axis PSF. Apparently, the image contrast close to the central object for the hybrid coronagraph has been improved by a few orders of magnitude over the shaped pupil coronagraph alone within ~ 8 λ/d. Figure 1 also shows the image contrast for a conventional Lyot coronagraph with the same throughput as the Figure 1. Comparison of image contrast among three coronagraphs, Gaussian pupil coronagraph (GAPM), Lyot coronagraph and hybrid coronagraph with the same throughput. They are all designed to be used at the Mt. Wilson 100-inch telescope. hybrid coronagraph. It appears that the hybrid one can provide better contrast than the Lyot one. In fact, considering an optimal function, e.g. prolate spheroidal function, for the pupil shape, the improvement can be -3 orders of magnitude (Kasdin et al. 00). This opens up new possibilities for potential detection of lower mass planets closer to the central object than the shaped pupil coronagraph. Apparently this new hybrid coronagraph concept represents a new family of coronagraphs. The shaped pupil and band-limited coronagraphs represent extreme members of this family.

Recent lab experiments were conducted to study optical performance for the three kinds of coronagraphs: the Gaussian shaped pupil coronagraph, Lyot coronagraph and Hybrid coronagraph, with the same instrument throughput. Figure 13 shows the results. For the ideal coronagraph designs which does not include the telescope central obscuration and spiders structure, the hybrid and Lyot coronagraphs provide a few times better contrast than the Gaussian shaped coronagraph alone. The best contrast with the hybrid one is about 3 10-6 at ~ 4λ/D at. Figure 13. The measured image contrasts for Gaussian shaped pupil, Lyot and hybrid coronagraphs. The left show the results from ideal coronagraph designs without considering telescope structures. The right shows the results of the realistic designs for the Mt. Wilson 100-inch telescope including telescope central obscuration and spiders. µm. For the Mt. Wilson design, which includes the telescope obscuration and spiders structure, the hybrid and Lyot ones still provide a factor of a few times better contrast than the Gaussian shaped coronagraph. The best contrast is about 1 10-5 at ~ 4λ/D at. µm. The results for both the ideal and Mt. Wilson designs are slightly worse than the theoretical results shown in Figure 1. This is caused by scattered light from imperfect optics in the experiments. If the ground-based telescope with AO can provide diffraction-limited wavefront (or Strehl ratio is higher than 0.8), then the performance at the telescope should be similar to what we can achieve in the lab. This kind of contrast should allow a survey for young planets and BDs with the ground-based telescopes in the near future. 7. Conclusions Recent development of shaped pupil coronagraphs opens up new possibilities for efficient imaging surveys for faint companions, especially planets and BDs, around nearby stars on the ground-based AO telescopes and future space-based telescopes. The combination of a specially made focal plane mask with a specially shaped pupil mask will provide further contrast for characterization of these companions. Acknowledgement The authors would like to acknowledge D. McCarthy for loaning part of the optics for PIRIS, R. Brown (LPL) for the PICNIC array, C. Ftalas for coronagraphic masks, and A. Kutyrev for IR filters. Several important discussions with D. Spergel, J. Kasdin, R. Vanderbei, M. Kuchner, and W. Traub were critical for understanding of Gaussian apertures and band limited masks. We

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