Journal of the Korean Astronomical Society http://dx.doi.org/10.5303/JKAS.2016.49.1.9 49: 9 ∼ 18, 2016 February pISSN: 1225-4614 · eISSN: 2288-890X c 2016. The Korean Astronomical Society. All rights reserved. http://jkas.kas.org Euclid ASTEROSEISMOLOGY AND KUIPER BELT OBJECTS Andrew Gould1, Daniel Huber2,3,4, and Dennis Stello2,4 1Department of Astronomy Ohio State University, 140 W. 18th Ave., Columbus, OH 43210, USA [email protected] 2School of Physics, University of Sydney, NSW 2006, Australia; dhuber,[email protected] 3SETI Institute, 189 Bernardo Avenue, Mountain View, CA 94043, USA 4Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark Received April 27, 2015; accepted December 20, 2015 Abstract: Euclid, which is primarily a dark-energy/cosmology mission, may have a microlensing component, consisting of perhaps four dedicated one-month campaigns aimed at the Galactic bulge. We show that such a program would yield excellent auxilliary science, including asteroseismology detections for about 100000 giant stars, and detection of about 1000 Kuiper Belt Objects (KBOs), down to 2–2.5 mag below the observed break in the KBO luminosity function at I 26. For the 400 KBOs below the break, Euclid will measure accurate orbits, with fractional period errors∼ . 2.5%. Key words: astrometry — gravitational microlensing — stars: oscillations — Kuiper belt 1. INTRODUCTION 2. EUCLID CHARACTERISTICS In two earlier papers, we pointed out that WFIRST microlensing observations toward the Galactic bulge We adopt Euclid survey characteristics from Penny et would automatically yield a treasure trove of asteroseis- al. (2013), with some slight (and specified) variations. mic (Gould et al. 2015) and Kuiper Belt Object (KBO) In each case, for easy reference, we place the corre- (Gould 2014) data. These papers contained detailed sponding assumed WFIRST parameters in parenthe- analytic calculations that permit relatively easy scaling ses. Mirror diameter D = 1.2m (2.4 m); pixel size p = 0.3′′ (0.11′′), detector size 8k 8k (16k 16k), me- to other missions and experiments. One very relevant × × mission is Euclid, which is presently scheduled to be dian wavelength λ =1.7 µm (1.5 µm), photometric zero launched in 2020. Unlike WFIRST, Euclid does not yet point Hvega = 23.5 (26.1), exposure time 52s (52s), ef- have a microlensing component, but such a component fective background (including read noise, Hvega,sky = −2 − − is being actively discussed. 20.0 arcsec , and dark current) 209 e (341 e ), full 5 5 Based on a most naive assessment, Euclid would pixel well nmax = 10 (10 ), and single read time appear to be much less effective in extracting non- tsingle = 2.6 s (tsingle = 2.6s). In fact, Penny et al. microlensing science from microlensing data than (2013) do not specify a read time, so we use the same WFIRST. Euclid has 1/2 the telescope diameter of value as for WFIRST to simplify the comparison. Also, WFIRST, 2.7 times larger linear pixel scale, 1/4 as Penny et al. (2013) adopt an exposure time of 54 s, but many visits to each target, and 1/2 the angular area we use 52 to again simplify the comparison. Finally, 16 of the survey. Penny et al. (2013) list nmax = 2 , but this appears However, as we show, such naive assessment would be to be in error. In any case, since the detector is very quite wrong since Euclid will be able to detect oscilla- similar to WFIRST, these two numbers should be the tions in giants that are about 0.8 mag brighter than for same. WFIRST, i.e., to about 0.8 mag above the red clump. The most striking of these differences is the 2.6 mag Hence, it will obtain asteroseismic measurements for (factor 11) difference in zero points because only a fac- roughly 100 000 stars. tor 4 is accounted for by the difference in mirror sizes. For KBOs, Euclid benefits by having an optical chan- The two other principal factors are shorter bandpass nel in addition to its primary infrared (IR) channel, (1.4–2.0 µm vs. 1.0–2.0 µm) and lower peak throughput even though it is expected that the optical exposure (47% vs. 77%), with the latter primarily due to the fact time will be 3 times smaller than for the IR. The op- that Euclid employs a dichroic beamsplitter whereas tical observations gain substantially from their smaller WFIRST does not, and (very secondarily) WFIRST has point spread function (PSF) as well as the fact that IR-optimized gold mirrors, which Euclid does not. KBOs (unlike stars) do not suffer extinction. Hence, Euclid will also be a powerful probe of KBOs. In our calculations we first consider simple 52 s expo- sures, but later take account of the fact that five such Corresponding author: A. Gould exposures will be carried out in sequence over 285 s. ∼ 9 10 Gould et al. 3. ASTEROSEISMOLOGY However, whereas this regime applies to stars H < 3.1. Bright-Star Photometry 11.6 for WFIRST (x-intercept of lower curve of mid- dle panel in Figure 1 of Gould et al. 2015), this From Equation (16) of Gould et al. (2015), the frac- break occurs at a brighter value for Euclid. To eval- tional error (statistical) in the log flux F (essentially, uate this offset, we rewrite Equation (3): Npixel = 2 2 magnitude error) is kfNreadtsingle(D p/λ) A(rDp/λ). Hence, the offset (at fixed r) between the break points on the WFIRST and θ σ(ln F ) = [πn (3 Q)]−1/2r−1 ; r unsat Euclid diagrams is max − unsat unsat ≡ p (1) ∆H = 2.5 log [fDλ/p] /[fDλ/p] =2.8 (8) − E H where p is the pixel size, θunsat is the radius of the closest unsaturated pixel (in the full read), nmax is the That is, this boundary occurs at H = 11.6 ∆H = full well of the pixel, 8.8, which is significantly brighter than the majority− of potential asteroseismic targets. However, inspection of −1 −2/3 −1/3 Q = N + 3(2Nread) , (2) read that Figure shows that the same scaling (σ FH ) applies on both sides of the H = 11.6 “boundary”.∝ and N is the number of non-destructive reads. read The reason for this is quite simple. As we consider When comparing WFIRST and Euclid, the most im- fainter source stars F , the saturated region of course portant factor is r . To determine how this scales H unsat continues to decline. Since the Airy profile at large with mirror size, pixel size, exposure time t, throughput − radii scales as A(x) x 3, the radius of this region f, and mean wavelength λ, we adopt a common PSF ∝ scales as r F 1/3. Hence, the number of semi- function of angle θ, A(Dθ/λ), which is scaled such that unsat ∝ H dx2πxA(x) 1. Then, if a total of K photons fall saturated pixels (each contributing nmax to the total ≡ 2/3 Ron the telescope aperture, the number falling in a pixel photon counts) scales FH , which implies that the ∝ − centered at θ is fractional error scales F 1/3. This breaks down only ∝ H 2 2 at (or actually, close to) the point that the central pixel npixel = p KfA(Dθ/λ)(D/λ) (3) is unsaturated in a full read (at which point the er- −1/2 Setting npixel = nmax, we derive ror assumes standard FH scaling). That is, in ∝ − the case of Euclid, the F 1/3 scaling applies to about −1 2 2 2 H A [nmaxλ /(KfD p )] H < 14.8 ∆H = 12.0, which is still toward the bright runsat = . (4) pD/λ end of potential− targets. 2 Then noting that K = kfNreadtsingleD , where k is a 3.2. Bright-Star Astrometry constant, we obtain From Gould et al. (2015) A−1[n λ2/(kft N D4p2)] r = max single read (5) p unsat pD/λ σ(θ)= , (9) 3πnmax ln(1.78Nread +0.9) Finally, noting that in the relevant range, a broad-band p in the saturated regime. Hence, using the same param- Airy profile scales A(x) x−3, we find a ratio of Euclid eters (for a single Euclid sub-exposure) (E) to WFIRST (W) unsaturated∝ radii, 1/3 σ(θ)E runsat,E (NreadDλf/p)E =2.73. (10) = 0.42. (6) σ(θ)W runsat,W (NreadDλf/p)W ≃ Then taking account of the fact that Euclid has five In making this evaluation we note that (DE/DW ) = such sub-exposures, we obtain σ(θ)E /σ(θ)W = 1.22, 0.50, (pE/pW ) = 2.73, (λE /λW ) = 1.13, and i.e., Euclid is very similar to WFIRST. 0.4(23.52−26.1) 2 (fE/fW ) = 10 /(DE/DW ) = 0.365. The However, as in the case of photometric errors, the last number may be somewhat surprising. It derives boundary of the regime to which this applies is H < 8.8 mainly from WFIRST’s broader passband (1 µm vs. for Euclid (compared to H < 11.6 for WFIRST). And, 0.6 µm and its gold-plated (so infrared optimized) mir- more importantly, for astrometric errors, the functional ror. The other ratio of factors is form of errors does in fact change beyond this break (see Figure 1 of Gould et al. 2015). 3 QE − =1. (7) The reason for this change in form of astrometric 3 Q − W errors can be understood by essentially the same argu- Therefore, we conclude that in the regime that the cen- ment given for the form of photometric errors in the tral pixel is saturated in a single read, a sequence of 5 previous section.