Resolution and Field of View

1. Resolution and Field of View A Self-Centered, Short-Sighted Analysis of VLST Possibilities Gary Bernstein University of Pennsylvania 2/27/04

2. Why Build a Big Telescope? • Collecting area • Replicable with multiple apertures. • Resolution • Replicable with unfilled aperture.

3. What good is resolution? • Morphological information, e.g. high-z galaxy substructure, circumstellar disks. • Confused regions, e.g. stellar pops beyond M31, MBH’s at galaxy centers, high-contrast studies. • Improved S/N for unresolved, sky-limited sources.

4. Exposure times for broadband S/N=10 point sources, with l/D pixel size. • Sky limit for V>29 on 2.5m, V>32 on 10m! • Same for spectroscopy. • Even fainter at l<500 nm • Exposure time to reach sky-limited point is always about 1 hour. When does resolution improve observing speed? 10m resolution is useless for uncrowded V<29!

5. When does resolution improve observing speed? • Longest exposures near 100 hours for HST, Chandra. • Plot shows limit for S/N>10 point sources (500 nm) vs resolution, on 10-meter VLST. • High-res spectra will never be in sky-limited regime of the 2.5-m telescope. • Multiple apertures just as good as one large telescope! • Need lower detector noise for multiple apertures though.

6. When does resolution improve observing speed? • Advantage of single aperture kicks in between 29<V<32. • Only for sources <10 mas (at 500 nm)

7. Figures of Merit for VLST designs • Single targets with size>40 mas or V<29: speed  A; multiple apertures equivalent to large aperture. • Unresolved/crowded single targets V>29: speed  A/dW; large aperture is advantageous (AO?). • Searches or sky-filling targets resolved or V<29: speed  AW • Searches or sky-filling targets unresolved & V>29: speed  AW/dW

8. How Does FOV scale with aperture? • Simple geometric similarity shows that FOV is independent of D if we will accept fixed-angular-size geometric aberrations. • But note that the physical area of detector required scales as D2 A. Fixed-scale pixels will have fixed Npix but large cosmic-ray rate. Fixed-size pixels have Npix D2 • Here AW just scales as total collecting area, and required detector area is also independent of multiple- vs single-aperture choice! • If we want to keep aberrations below the diffraction scale, then the FOV must shrink. Three-mirror telescopes have leading aberrations q5, so W D-0.4. • Now AW D1.6 Npix. Total throughput is dependent on total pixel count, which is higher per unit aperture in multiple-aperture scheme. • But AW/dW D3.6, so sky-limited target surveys prefer single aperture.

9. What about a Multiple-Aperture Telescope? • Equal to single-aperture telescope of same total area when A or AW is figure of merit. • Cost per square meter is lower (?) • Required detector real estate is equivalent. • Much more compact structure  stiffer, easier to hold figure, higher resonant frequencies, faster slews and settling. • More robust because of risk-spreading. • More flexible scheduling, can target telescopes independently. • Faster response • Can specialize units of the fleet, e.g. a wider filter choice available. • Already know how to build these, just need them to be cheaper. • No need to train squad of L2 android astronomers to assemble. • Element cycling is natural path to decade-scale upgrades. • Easier to get wide-field multi-object spectroscopy.

10. Self-centered Science Example: KBOs

13. VLST Opportunities for KBOs • Large samples of V<29 (15 km) KBOs; how does the accretion process depend on dynamical state? • This investigation prefers multiple-aperture VLST. • Directly detect the precursors of comets to V≈34. • Would seem to prefer single-aperture telescope, BUT the dispersion of KBO apparent motions exceeds 10 mas in 30 seconds even in favorable conditions, so enormous bandwidth & computing required to use such high resolution. • Targetted followup: high resolution (or interferometry) for angular sizes; colors, light curves, etc.

14. Weak Gravitational Lensing with VLST • Now apparent that weak lensing sky holds a vast amount of information: • Time history of the dark energy equation of state. • Masses of the neutrinos. • Slope/running index of inflationary spectrum. • Is the WMAP CMB low-l deficit a fluke? • How do dark halo properties connect with visible galaxy properties? • Figures of merit for WL observations: • Number of resolved galaxies per arcmin2 • Fraction of sky covered by survey

16. Instrument Requirements for Weak Lensing • HDF, etc., have very few unresolved galaxies! Additional resolution below 50 mas does not greatly increase WL information. • Deeper images gain galaxies only slowly once we are looking at L* galaxies at Ly break. Helps WL only at small angular scales. • Want to scan as much of sky as possible, good photo-z’s, with HST-ish resolution, so AW is the figure of merit for space observatories. • Multiple-aperture approach seems ideal here.

17. Something to think about… An space-based Vis/NIR survey of the full sky seems inevitable - why not start thinking about it? [Note: full sky 10 bands 0.05” pix=2x1015 pixels!]

18. SPace All Sky Multiband Survey (SPASMS) MultiSNAP? Astrono-MIRV? Constellation V?

19. WL Capabilities of Observatories

20. Summary • Much VLST science will demand 10-meter diffraction-limited resolution of morphology and crowding. Think about AO, unfilled-aperture alternatives for some of this. • But for many survey projects and any high-resolution spectroscopy, a more attractive solution might be to spread the aperture over ~20 telescopes. • SPASM survey would take 2 years and yield stunning ultimate weak lensing results, nearly full inventory of Galactic stars, all >10 km planetesimals in Solar System, and an extremely flexible observatory.