DISCOVERY OF A MAKEMAKEAN MOON

For each of the six frames in which S/2015 (136472) 1 is visible, we subtracted a co-registered median stack of the six frames in which it was not visible. In five of these six difference images, we performed small-aperture photometry to measure the flux from S/2015 (136472) 1; in the sixth, a cosmic ray impinged too close to S/2015 (136472) 1. The typical signal to noise of S/2015 (136472) 1 in these frames is S/N ∼ 25, and the photometry is listed in Table 1; given this signal to noise, we do not currently find any evidence for intrinsic variability in the satellite. Four bracketing short F350LP exposures were also median stacked (without differencing) to measure the flux from Makemake itself in the filter passband. We find that S/2015 (136472) 1 is 7.80 ± 0.04 mag fainter than Makemake in F350LP. In the absence of any color information on the satellite, we adopt this delta-magnitude for V-band photometry. Makemake is H_v = 0.091 ± 0.015 (Rabinowitz et al. 2007), and from this we estimate H_v = 7.89 ± 0.04 for S/2015 (136472) 1. At the time of discovery, the system was at a heliocentric range of 52.404 au, a geocentric range of 51.694 au, and observed at a phase angle of 0781.

Table 1.  S/2015 (136472) 1 Discovery Astrometry and Photometry

JDmid	maga	Δλb	Δβc	ΔR.A.d	ΔDecl.e
2457140.07994	25.21	−0136	0556	0125	0558
2457140.10045	25.06	−0135	0560	0127	0561
2457140.14283	25.19	−0138	0555	0123	0558
2457140.15309	25.27	−0140	0553	0120	0558
2457140.16334	25.12	−0136	0554	0124	0557

Notes.

^aAB-mag in HST WFC3 UVIS F350LP filter. Mean Makemake F350LP magnitude in four 12 s exposures: 17.39; uncertainty in each measurement is estimated to be 0.04 mag. ^bSky-plane offset in ecliptic longitude, secondary to primary; Δλ = (λ₂ − λ₁) × cos(β₁); positional uncertainty in each measurement is estimated to be 0008. ^cSky-plane offset in ecliptic latitude, secondary to primary; Δβ = β₂ − β₁. ^dSky-plane offset in J2000 R.A., secondary to primary; ΔR.A. = (R.A.₂ − R.A.₁) × cos(Decl.₁). ^eSky-plane offset in J2000 Decl., secondary to primary; ΔDecl. = Decl.₂ − Decl.₁.

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We performed preliminary orbit modeling to determine the possible range of system parameters given the limited astrometric information derived from the discovery data. To avoid overfitting the data, we assume a prograde circular orbit for preliminary estimates and adopt a simple pass–fail criterion: if, given a set of orbit parameters, the predicted positions of S/2015 (136472) 1 at the times with measured astrometry (Table 1) are within 0016 (twice the estimated raw astrometric uncertainty of 0008, given S/N ∼ 25, the dithering precision of HST, and the undersampled WFC3 PSF) from the measured locations at those times, and the predicted positions of S/2015 (136472) 1 at the times when it was not detected fall within the masked region in Figure 2, then an orbit is accepted as plausible given the discovery data alone. We densely sampled a large volume of orbital parameter space and determined the maximum plausible range of each orbital parameter of interest under the stated assumptions above.

We sampled bulk density for Makemake over the range 1.4 g cm⁻³ ≤ ρ ≤ 3.2 g cm⁻³ (Brown 2013) and find that the S/2015 (136472) 1 discovery observations alone do not further constrain Makemake's density. Given this range of densities, semimajor axes in 21,100 km ≲ a ≲ 300,000 km, inertial orbital periods in 12.4 days ≲ τ ≲ 660 days, and prograde ecliptic inclinations in 63° ≲ i_E ≲ 87° are acceptable (the mutual inclination of the system is 46° ≲ i_M ≲ 78°, and the inclination with respect to the sky plane is 83° ≲ i_S ≲ 105°; the retrograde mirror solutions to all of these ranges are also acceptable).

Given the existence of previous HST satellite search data of sufficient depth to detect S/2015 (136472) 1, we consider the largest semimajor axis solutions unlikely due to the fact that these orbital configurations place S/2015 (136472) 1 at large separations from Makemake for the majority of the time; with a = 100,000 km, S/2015 (136472) 1 spends ∼90% of the time at detectable separations, whereas with the minimum allowable circular semimajor axis of 21,000 km, S/2015 (136472) 1 spends only ∼50% of the time at detectable separations. On the other hand, semimajor axes in excess of 100,000 km are known to exist for much less massive binary KBOs (e.g., 2001 QW322; Parker et al. 2011). The largest semimajor axis solutions are found for the highest adopted Makemake density, and these solutions are at ∼50% of the Makemake Hill radius for this density.

Given the equations in Noll et al. (2008), if the orbit of S/2015 (136472) 1 has a semimajor axis near its lower limit and the components both have ρ = 2 g cm⁻³, the orbital circularization timescale for a D = 175 km satellite is approximately 60 Myr, while if the semimajor axis is twice this lower limit, the orbital circularization timescale increases to longer than the age of the solar system, ∼6 Gyr. Thus, if S/2015 (136472) 1 is in an orbit with semimajor axis consistent with its discovery separation, its orbit is very likely circular; if the semimajor axis is much larger, eccentric orbits become more plausible.

Given the limited amount of orbital motion about Makemake observed for S/2015 (136472) 1, we must consider the possibility that the detection is a false positive arising from another TNO serendipitously crossing the same line of sight as Makemake. We can strongly rule out this scenario with the following simple analysis. At the time of the discovery observations, Makemake was at a heliocentric ecliptic latitude of ∼285 and a heliocentric range of ∼52 au. Since the parallax produced over the width of HST's orbit will vary by nearly a full UVIS WFC3 pixel for objects within ∼5 au of 52 au, we cap the heliocentric range of potential coincident TNOs to 47–57 au. Using the Canada France Ecliptic Plane Survey L7 synthetic model of the Kuiper belt (Petit et al. 2011), we find that the typical sky density of Hv ≤ 7.8 TNOs with 28° ≤ β ≤ 29° and 47 ≤ R ≤ 57 is ∼0.1 deg⁻². Given three relatively distinct epochs (counting HST observations from program 10860 collected in 2006 November, which did not detect the satellite) of observations capable of detecting S/2015 (136472) 1, the odds of a similarly bright or brighter TNO at a similar heliocentric distance falling within an arcsecond of Makemake in one or more epoch is less than one in 10⁷.

Thermal observations of Makemake collected by the Spitzer (Stansberry et al. 2008) and Herschel (Lim et al. 2010) space telescopes revealed that there were at least two distinct surfaces contributing to the spectral energy distribution; the majority of the emitting surface must be very bright, but a small component must be very dark. It was argued that the presence of distinct dark terrains on the surface of Makemake was at odds with Makemake's very small light curve amplitude unless Makemake is in a pole-on viewing geometry (Brown 2013).

Given the discovery of S/2015 (136472) 1, we reconsider these thermal observations under the hypothesis that much of the dark material in the system does not reside on the surface of a modestly mottled Makemake, but rather covers the entire surface of a uniformly dark S/2015 (136472) 1. Lim et al. (2010) require a dark surface area with equivalent diameter 310 km < D < 380 km, with geometric albedo 0.02 < p_v < 0.12. For p_v = 0.02, the estimated H-magnitude of S/2015 (136472) 1 corresponds to a diameter of ∼250 km, too small to account for all of the dark material, but sufficient to account for a large fraction of it. This would reduce the preference for a pole-on orientation for Makemake's rotation. A very dark surface might suggest an origin distinct from other dwarf planet satellites, perhaps indicating that the satellite is a captured, formerly unbound TNO. Alternatively, a dark satellite surface may be the result of past epochs of interactions with an escaping Makemake atmosphere.

As a simple check, we use NEATM (Harris 1998) to model the thermal flux from the system with the occultation-updated diameter of 1430 km for Makemake and three different surfaces for S/2015 (136472) 1 and compare them against previous thermal observations of the system. Makemake's surface is modeled with a uniform geometric albedo of 0.82 and a beaming parameter of η = 1.9. The three models of S/2015 (136472) 1 include (a) a model with Salacia-like 4% geometric albedo, but an exceptionally low beaming parameter of η = 0.25; (b) a model with an exceptionally low 2% geometric albedo, but a beaming parameter in-family with the results of Lim et al. (2010), η = 0.4; and (c) a model with a 4% geometric albedo and a beaming parameter η = 0.4, but with an absolute magnitude 0.5 mag brighter than observed for S/2015 (136472) 1, capturing the possibility that S/2015 (136472) 1 has a substantial light curve or a systematic error in its discovery photometry. The results are illustrated in Figure 3. These three models all produce between 60% and 80% of the measured 24 μm spectral flux density from the system.

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Follow-up observations of S/2015 (136472) 1 will permit the measurement of Makemake's mass and density. Since we cannot yet predict the future position of S/2015 (136472) 1 with respect to Makemake, it is likely that any recovery efforts will be hampered by an initial period in which S/2015 (136472) 1 is lost in a large fraction of observations before the orbit can be sufficiently well modeled and the recovery rate increased. With sufficient recovery observations, the system mass will be measured. Given a nominal geometric albedo of 4%, S/2015 (136472) 1 would have a diameter of 175 km and for equal densities would contribute ≲0.2% of the system mass; thus, the system mass will be dominated by Makemake. This contribution is further reduced if S/2015 (136472) 1 has an albedo comparable to the small satellites of Pluto (≳50%; Weaver et al. 2016), which would indicate a diameter ≲50 km.

Because of the nearly edge-on configuration of the orbit, there is the potential for a near-future epoch of mutual events between S/2015 (136472) 1 and Makemake. As with the mutual events between Pluto and Charon in the late 1980 s (e.g., Buie et al. 1992; Young et al. 2001), such a configuration could enable detailed investigations of the system and the surface properties of the two components.

Future observations with James Webb Space Telescope (JWST) can test the dark moon hypothesis; Parker et al. (2016) highlight that JWST could characterize the anomalous thermal excess of Makemake in detail. Figure 3 illustrates the 10,000 s 10σ MIRI detection limits in its five longest-wavelength wide filters. At 15 μm, Makemake and all three S/2015 (136472) 1 model surfaces produce detectable spectral flux density, and at this wavelength the spatial resolution of JWST is comparable to the discovery separation of Makemake and S/2015 (136472) 1. Resolved JWST observations in this and the two adjacent filters would enable direct determination of the fraction of the system's dark material that is attributable to the surface of S/2015 (136472) 1. However, the success of such observations relies upon the ability to predict the sky-plane separation of Makemake and S/2015 (136472) 1, requiring that near-term observations of S/2015 (136472) 1 be conducted to accurately measure its orbital properties.

Makemake's high rate of rotation makes its equilibrium figure a Maclaurin spheroid (Ortiz et al. 2012). Given even a small flattening, Makemake's J₂ would likely drive the system to a low primaricentric inclination between the satellite's orbit and the spin pole of Makemake (e.g., Porter & Grundy 2012). We note that the projected long axis of Makemake measured by Ortiz et al. (2012) runs nearly north–south, which is consistent with our determination of the orientation of the orbit plane of S/2015 (136472) 1—and thus consistent with a low primaricentric inclination. If the spin pole of Makemake and the orbit plane of S/2015 (136472) 1 are aligned, we are viewing Makemake nearly equator-on, and the sky-plane elliptical fit presented in Ortiz et al. (2012) likely reflects the true axial ratio of Makemake, implying a flattening of ∼15%. If the dark moon hypothesis is correct, then edge-on rotation for Makemake is not at odds with its low-amplitude light curve, and a low-amplitude light curve in this configuration also implies a rotationally symmetric, close-to-equilibrium figure.

Additionally, if the spin pole of Makemake and the orbit plane of S/2015 (136472) 1 are aligned, Makemake has a very high obliquity with respect to its heliocentric orbit (46°–78°). A current edge-on configuration places Makemake near equinox, and if so, we estimate its thermal parameter Θ (Spencer 1990) to be ∼70 (given a Pluto-like thermal inertia of 20 J m⁻² s^−0.5 K⁻¹; Lellouch et al. 2011), placing it solidly in the regime in which fast rotator approximations apply. Given this high obliquity, however, as Makemake continues around its orbit, it will effectively transition into a slow rotator state at its solstices. Makemake is currently near aphelion, so this potential transition from fast to slow rotator is also currently synched with its heliocentric distance extrema. This could lead to fascinating seasonal evolution on Makemake's volatile-dominated surface.

With the discovery of S/2015 (136472) 1, all four of the currently designated trans-Neptunian dwarf planets (Pluto, Eris, Makemake, and Haumea) are known to host one or more satellites. The fact that Makemake's satellite went unseen despite previous satellite searches suggests that other very large trans-Neptunian objects that have already been subject to satellite searches (such as Sedna and (225088) 2007 OR₁₀) may yet host hidden moons. While Brown (2013) argued that the lack of a satellite for Makemake suggested that it had escaped a past giant impact, the discovery of S/2015 (136472) 1 suggests that unless it resulted from the capture of a previously unbound TNO, it too was subjected to a giant impact and its density will likely reflect that (Stewart & Leinhardt 2012; Barr & Schwamb 2016). The apparent ubiquity of trans-Neptunian dwarf planet satellites further supports the idea that giant collisions are a near-universal fixture in the histories of these distant worlds.