Clément Ranc
email: ranc@iap.fr

Keywords: gravitational lensing, micro -planets and satellites, detection

Characterizing a planet detected by microlensing is hard if the planetary signal is weak or the lens-source relative trajectory is far from caustics. However, statistical analyses of planet demography must include those planets to accurately determine occurrence rates. As part of a systematic modeling effort in the context of a > 10-year retrospective analysis of MOA's survey observations to build an extended MOA statistical sample, we analyze the light curve of the planetary microlensing event MOA-2014-BLG-472. This event provides weak constraints on the physical parameters of the lens, as a result of a planetary anomaly occurring at low magnification in the light curve. We use a Bayesian analysis to estimate the properties of the planet, based on a refined Galactic model and the assumption that all Milky Way's stars have an equal planet-hosting probability. We find that a lens consisting of a 1.9 +2.2 -1.2 M J giant planet orbiting a 0.31 +0.36 -0.19 M host at a projected separation of 0.75 ± 0.24 au is consistent with the observations and is most likely, based on the Galactic priors. The lens most probably lies in the Galactic bulge, at 7.2 +0.6 -1.7 kpc from Earth. The accurate measurement of the measured planet-to-host star mass ratio will be included in the next statistical analysis of cold planet demography detected by microlensing.

During fall 2020, the hundredth exoplanet detection through gravitational microlensing was added to the NASA Exoplanet Archive database . Although modest in amount when compared to the 4,379 confirmed exoplanets to date and distributed in more than 3,237 planetary systems (Schneider et al. 2011), this milestone enables an unprecedented look at the demography of cold exoplanets orbiting their host stars on wide orbits, with a typical semi-major axis of ∼ 0.5-10 au. Microlensing detections dominate the population of confirmed planets below one Saturn mass and located beyond the "snow line", i.e., the inner boundary of the protoplanetary disk where planet formation is most efficient, according to the core accretion theory (Lissauer 1987(Lissauer , 1993;;Pollack et al. 1996). So, this sample represents a relatively new and unique opportunity for planet formation theories to compare predictions with observations, in a region of the parameter space largely unexplored by other planet detection techniques.

The first comparison of the microlensing planet occurrence rate with population synthesis models (Ida & Lin 2004;[START_REF] Mordasini | Planetary Population Synthesis[END_REF]) identified a discrepancy between predictions of the core accretion theory's runaway gas accretion process and observations (Suzuki et al. 2018). In particular, the observational results do not show any dearth of intermediate-mass giant planets, while the models predict 10 times fewer planets in the planet-to-host mass ratio range 10 -4 < 𝑞 < 4 × 10 -4 . Resolving this discrepancy may have important implications in our understanding of the role played by the runaway gas accretion phase in the delivery of water to inner planetary orbits (Raymond & Izidoro 2017). The MOA collaboration is currently performing a systematic retrospective analysis including more than ten years of survey observations performed at the Mount John in New Zealand, to strengthen and expand the previous statistical results on microlensing planet occurrence rate (Gould et al. 2010;Sumi et al. 2010;Cassan et al. 2012;Shvartzvald et al. 2016;Suzuki et al. 2016;Udalski et al. 2018).

So far, this systematic analysis of previous survey data led to the discovery of several missed exoplanets (e.g., [START_REF] Kondo | [END_REF]. The discovery presented in this article takes place in the context of this systematic modeling of past detections. We report the discovery of a new giant planet from the analysis of the microlensing event MOA-2014-BLG-472, initially detected by alert systems. The planetary signal for this event is not created by a caustic crossing. As a result, the planetary anomaly in the light curve has a low magnification, and the constraints on the physical parameters of the lens are weak. However, including planets like MOA-2014-BLG-472Lb in statistical studies on planet demography is crucial for the completeness of planetary occurrence rates.

This article describes the full analysis of MOA-2014-BLG-472. In Section 2, we recount the discovery of the event, describe the observations and select the data set used to model the event. In Section 3, we describe the full light-curve modeling process. In Section 4, we use a galactic model to derive the physical properties of the source and lens. Section 5 provides a summary of the analysis and concludes the article.

OBSERVATIONS AND DATA REDUCTION

The microlensing event MOA-2014-BLG-472 was discovered by the Microlensing Observations in Astrophysics (MOA, phase II; Sumi et al. 2003) collaboration and first alerted on 2014 August 16 at UT 11:40, i.e., HJD ≈ 6885.99 . The event is located at the J2000 equatorial coordinates (RA, Dec.) = (18 h 00 m 19 s .40, -28 • 08 56 .29) in the MOA-II field 'gb10.' MOA observations were performed using a 1.8 m telescope (and its 2.2 deg 2 field of view camera, Sako et al. 2008) at the Mount John University Observatory in New Zealand with a cadence of 15 min in the custom wide-band MOA 𝑅/𝐼-band filter, referred to as 𝑅 MOA . An anomaly was detected in real time by the MOA observers who issued an internal MOA alert on 2014 September 4. MOA's implementation of the DIA method (Bond et al. 2001) has been used to extract the photometry of MOA observations. The Optical Gravitational Lensing Experiment (OGLE, phase IV; Udalski et al. 2015) was also monitoring this event and triggered an alert on the Early Warning System (EWS) website on 2014 August 26 at UT 11:06, naming the event OGLE-2014-BLG-1783. This event lies in the OGLE-IV field 'BLG504.08,' and has been observed with the 1.3 m-telescope located at Las Campanas Observatory in Chile (and its 1.4 deg 2 field of view camera), with a cadence of 1 hour -1 . The anomaly has been detected by OGLE independently in their data, and an internal alert was sent on 2014 August 26 at UT 11:22. OGLE's member Jan Skowron HJD = HJD -2, 450, 000. circulated among all the collaborations the first model performed, in real time, indicating a likely planet (with mass ratio of 0.0056) on 2014 September 20.

The final data sets consist of 13, 789 data points from MOA observations and used to model the microlensing light curve. We select five observing seasons (2 before and 2 after the event's year) to prevent missing some potential variability in the baseline. The microlensing event has a weak maximal amplification of only 0.25 mag. However, due to the source star being a Red Clump giant (𝐼 ∼ 15.2 mag), it is still well detectable/observable. Figure 1, shows the magnification of the source flux as a function of time. The peak of magnification occurs at HJD ≈ 6910, and a clear anomaly starts at HJD ≈ 6885, first slowing down the magnification rise, then suddenly hiking up the magnification faster than a single-lens magnification pattern. Moreover, the anomaly occurs at an extremely low magnification, 𝐴 < 1.1. The Figure 1 displays 5-hour bins for clarity purposes, but all the data are used during the modeling process.

As a consequence, the error bars are expected to play a major role in the final uncertainties on the physical parameters. Since the photometry pipelines typically underestimate the error bars, for each data set, we normalized the error bars on magnitudes, 𝜎, so that the 𝜒 2 per degree of freedom is 𝜒 2 /d.o.f. = 1, and the cumulative sum of 𝜒 2 is approximately linear. This procedure assumes a best-fit model, and can be repeated as new plausible models are found. During the broad initial search in the parameter space, the error bars are not changed. Then, while exploring local 𝜒 2 -minima, we use the normalization law (Yee et al. 2012)

𝜎 𝑖 = 𝑘 √ 𝜎 2 + 𝑒 2 min , (1)
where 𝜎 is the normalized error bar, the constant 𝑘 is the rescaling factor, and the constant 𝑒 min mostly modifies the highly magnified data. For MOA-2014-BLG-472, we use 𝑘 = 1.205 and 𝑒 min = 2.763 × 10 -3 .

3. LIGHT-CURVE MODELS

Single-lens Model

We start modeling the event MOA-2014-BLG-472 by fitting the observations with a Paczyński light curve (Paczyński 1986), described by three independent parameters: the time (𝑡 0 ) and projected separation (𝑢 0 ) when lens and source are closest on the sky, and the Einstein radius crossing time,

𝑡 E = 𝜃 E 𝜇 rel , (2)
where 𝜇 rel is the lens-source relative proper motion in the geocentric reference frame and 𝜃 E is the angular Einstein radius. These three parameters can be approximately estimated without any sophisticated numerical techniques. First, the peak of the event shown in Figure 1 provides HJD ≈ 6910. Second, the peak-to-baseline flux ratio provides an estimate of the magnification at the peak of the event, 𝐴 peak ≈ 1.3. Using Taylor series for the expression of the magnification yields 𝑢 0 ≈ 1 at the peak. Third, we derive the expected magnification at 𝑡 = 𝑡 0 + 𝑡 E , and search for the corresponding flux in the light curve to find

𝑡 E ≈ 12 d.
Above, we derived estimates for model parameters by assuming that the flux measurement comes entirely from the source star, which is almost never true. During the modeling process, the three parameters 𝑡 0 , 𝑢 0 and 𝑡 E yield the magnification at any given date. To evaluate the goodness-of-fit of a model, two additional parameters are required to compute the observable: one describes the unlensed source flux 𝑓 s,𝜆 𝑖 , for any passband, 𝜆 𝑖 ; the other is the excess flux, 𝑓 b,𝜆 𝑖 , resulting from the combination of any (and possibly several) 'blend' stars. The blend can be either the lens itself or an unrelated star or stars. At any time 𝑡, the total flux of the microlensing target is

Φ 𝜆 𝑖 (𝑡) = 𝐴(𝑡) 𝑓 s,𝜆 𝑖 + 𝑓 b,𝜆 𝑖 , (3)
where 𝐴(𝑡) is the source flux magnification at the date 𝑡, and 𝜆 𝑖 is the MOA 𝑅 passband.

Starting from the parameter estimated above, we use a Levenberg-Marquardt algorithm (Levenberg 1944) to find the best fit model parameters to be used as a starting position when searching for binary-lens models. We then use a Markov chains Monte Carlo (MCMC) algorithm to determine the uncertainties. At this stage, we remove the data during the anomaly, since a point-source point-lens model (hereafter 'PSPL') cannot (by definition) produce any anomaly. The median parameters and their credible intervals are: 𝑡 0 = 6910.1 ± 0.1, 𝑢 0 = 0.9 ± 0.1, and 𝑡 E = 14 ± 1 d. For comparison with the other models presented in this article, the 𝜒 2 value computed with the entire dataset is 𝜒 2 = 14744. The best fit PSPL model is shown with a solid dark blue line in Figure 1. In this figure, the data are binned for more clarity. We choose 5-hour bins, such that for each bin, 𝑛, consisting of N 𝑛 data, the plotted uncertainty, 𝜎 𝑛 , and magnification, 𝐴 𝑛 , are defined as

𝜎 𝑛 = N 𝑛 ∑ 𝑗=1 𝜎 2 𝑗 -1/2 and 𝐴 𝑛 = 𝜎 2 𝑛 N 𝑛 ∑ 𝑗=1 𝐴 𝑗 𝜎 2 𝑗 .
(4)

We do not use any binned data during the fitting process, though.

We introduce two additional parameters to assess whether the anomaly in the light curve may be explained by the non-inertial nature of the observer reference frame. These are the Northern and Eastern components of the microlens parallax vector in the geocentric frame, 𝝅 E , respectively 𝜋 E,𝑁 and 𝜋 E,𝐸 , as defined in Gould (2004). The direction of vector 𝝅 E is the same as the instantaneous lens-source relative proper motion at HJD = 6910, and its magnitude is the lens-source relative parallax in units of the angular Einstein ring radius, i.e.,

𝜋 E = 𝜋 rel 𝜃 E , (5)
where 𝜋 rel = 1 au/𝐷 L -1 au/𝐷 S , 𝐷 L is the distance to the lens and 𝐷 S the distance to the source. Starting from the best fitting static model, we use a MCMC to find the best model with parallax, and estimate the uncertainties. We now include all the observations, since we search for a parallax signal that could explain the anomaly. Including the parallax in the model improves the 𝜒 2 by Δ𝜒 2 = -380. The median and credible intervals of the parameters are: 𝑡 0 = 6909.80 ± 0.05, 𝑢 0 = 2.8 ± 0.4, 𝑡 E = 6.2 +0.8 -0.7 d, 𝜋 E,𝑁 = 0 ± 2, and 𝜋 E,𝐸 = 2.2±0.3. The results from the MCMC show that the constraint on 𝜋 E,𝑁 is very weak, allowing a broad range of acceptable values, including the solution 𝜋 E,𝑁 = 0.0 at a level < 1-𝜎. The very large value of 𝜋 E = 2.7 +1 -0.5 results from the inability for the model to fit the anomaly. This can be seen in Figure 1 that shows the best fit PSPL model with microlens parallax (hereafter 'PSPL ⊕ 𝜋 E ') with a thick brown dashed line. The static binary-lens model presented in Section 3.2 is preferred by Δ𝜒 2 = -588 and fits the anomaly.

Binary-lens Models

In Section 3.1, we showed that the event MOA-2014-BLG-472 is not well described by a single-lens model, because the anomaly that occurs at 𝑡 ≈ 6890 cannot result from a parallax

-11.846185 -11.9 ± 0.2 1) Median of the marginalized posterior distributions, with error bars displaying the 68.3 per cent credible interval around the median.

𝑓 b,𝑅 / 𝑓 s,𝑅 (3) 0.454891 0.4 ± 0.2 𝐼 S . . . 15.8 ± 0.2 (
(2) Instrumental source magnitude in MOA 𝑅-band filter.

(3) Ratio of MOA 𝑅-band instrumental blend and source flux. We do not convert the blend flux from the 𝑅 to the 𝐼 passband because the nature of the blend is unknown. effect on a single lens. Hence, we search for plausible binary-lens, single source models. Three additional parameters are required: the mass ratio of the secondary to primary lens component 𝑞 = 𝑀 2 /𝑀 1 , where 𝑀 2 (𝑀 1 ) is the mass of the secondary lens (the mass of the primary lens, respectively); the separation in Einstein radius, 𝑠; and the counterclockwise angle of the lens-source relative motion projected onto the sky plane with the lens binary axis (from the secondary to the primary lens), 𝛼. For a binary lens model, we choose 𝑢 0 as the distance of closest approach between the lens center of mass and the source.

We start exploring the parameter space searching for PSBL solutions using the best-fit PSPL model parameters, and the initial condition grid search method introduced in Bennett (2010). In practice, for each set of {𝑠, 𝑞}, we scan over -𝜋 ≤ 𝛼 ≤ 𝜋 with a 1.1 • step. During this process, the best-fit PSPL model parameters {𝑡 0 , 𝑢 0 , 𝑡 E } are kept fixed. We used 8 grid points in log 𝜖, from -4.0 to -0.5, with a 0.5 grid spacing, where 𝜖 = 𝑞/(1 + 𝑞) is the planetary mass fraction. The separation values range from 0.1 to 10.0, evenly spaced on a grid of log 𝑠, that includes:

• 53 grid points for log 𝜖 ≤ -2.0,

• 70 grid points for log 𝜖 = -1.5,

• 85 grid points for -1.0 ≤ log 𝜖.

For each model, we compute the 𝜒 2 value and start 25 new fits from the best 25 models found on the grid. We only select one initial condition per {𝑠, 𝑞} couple, i.e., we use the best 𝛼 value for a given set of {𝑠, 𝑞}. At this stage, we release all the parameter constraints, and we use an adaptative version of the Metropolis algorithm optimizing the size of the proposal function during the exploration of the parameter space with a Monte Carlo method. The analysis of this set of fits leads us to identify four different models that meet our criterion Δ𝜒 2 = 𝜒 2 -𝜒 2 min ≤ 500, for further in depth investigation. We use these models to define four classes of models in the next step, consisting in sampling the posterior distribution using several MCMC chains.

The two best fitting models have the same caustic topology, with close values of 𝑠 and 𝑞. One is the best-fit model presented in Table 1. According to the second class of best models (Δ𝜒 2 ≈ 115), the magnification peak would be due to one off-axis planetary caustic characterized by 𝑠 = 0.62798 and 𝑞 = 8.8766 • 10 -3 . However, this model does not fit the anomaly: ∼ 80% of the 𝜒 2 difference compared to the best-fit model comes from observations during the anomaly, and ∼ 20% comes from data between the anomaly and the event peak. This particular model is simply unable to reproduce the gradient of magnification during the anomaly, and must be rejected. The third class of models (Δ𝜒 2 ≈ 153) involves a wide separation caustic. In this scenario, the main peak of the event is due to the central caustic, the source trajectory is passing in between the two components of the caustic, but this model does not properly fit the gradient of magnification during the anomaly: ∼ 69% of the 𝜒 2 increase compared to the best-fit model occurs during the anomaly, and 24% between the anomaly and the peak of the event. It is worth noting that the description of the tails of the event given by this model is also poorer. The fourth best model is substantially worse than the three others, does not fit the anomaly, nor the event peak, and is characterized by Δ𝜒 2 ≈ 423 (98.6% of this value comes from data in the interval HJD = 6865-6910).

After checking the convergence of the MCMC chains, we use 50, 000 samples to diagonalize the covariance matrix and optimize the posterior sampling. Figure 2 displays the source trajectory relative to the caustics obtained with the best-fit model. Table 1 shows the median of the marginalized posterior distributions. The error bars correspond to the 68.3 per cent credible interval around the median, derived from the 16 and 84 per cent percentile of the one dimensional marginalized posterior distribution. One-dimensional cumulative functions and two-dimensional covariances (and nonlinearities) between the model parameters are shown in Figure 3.

Table 1 and Figure 3 only include the 𝑢 0 > 0 solution, but there is an exact degeneracy with a model characterized by (𝑢 0 , 𝛼) ↦ → -(𝑢 0 , 𝛼), due to the symmetry of the lens. In practice, the other parameters remain unchanged, so the physical properties of source and lens are identical. Moreover, there is no close-wide (𝑠 ↦ → 1/𝑠) discrete degeneracy, for the anomaly is due to the planetary caustic instead of the central caustic. In other words, the source apparent trajectory passes in the middle of minor image caustics, in a region where the magnification is lower than what would be observed if the lens were single. This feature is not easily reproductible with another lens geometry, which is, in part, the reason why there are not many competing models for this event. Figure 2 shows the magnification residuals between the PSBL and PSPL models, as well as magnification maps around the caustics computed with an adaptation of the library luckylensing (Liebig et al. 2015). The de-magnification regions appear in blue in this figure.

Although MOA-2014-BLG-472 is a low-magnification event, an anomaly is clearly identified at 𝑡 ≈ 6890. Due to the possibility that this anomaly is shaped by the effect of the physical size of the source, we introduce one more model parameter: the source radius crossing time, 𝑡 ★ = 𝜌 𝑡 E = 𝜃 ★ /𝜇 rel , where 𝜌 is the source angular radius in units of 𝜃 E , i.e.,

𝜌 = 𝜃 ★ 𝜃 E , (6)
with 𝜃 ★ the source angular radius. Hereafter, we refer to the resulting 'finite-source binarylens' model as 'FSBL.' Finite source effects in microlensing light curves are usually sensitive to the stellar limb darkening (Albrow et al. 1999), however only if the source star crosses the caustic, which is not the case in MOA-2014-BLG-472.

We tried to extract constraints on 𝑡 ★ in two ways. One using an MCMC algorithm with no constraint on the parameters, and a large proposal step function. The other fixing 𝑡 ★ on a grid (25 nodes for 0.04 d ≤ 𝑡 ★ ≤ 1.05 d), and searching for solutions with an MCMC algorithm. These two approaches do not provide any useful limit on 𝑡 ★ . In fact, the upper limit on 𝑡 ★ provided by the light curve is found between 1.0 and 1.5 d, corresponding to a 𝜒 2 increase of respectively ∼ 1 and ∼ 7. In Figure 6, this upper limit falls at the edge between the 3 and 4-𝜎 confidence regions of the posterior distribution, i.e., the final constraint on 𝑡 ★ exclusively comes from the galactic prior, rather than from the observations. This result is mainly due to the source trajectory relative to lens. As shown in Figure 2, the PSBL solutions correspond to a caustic consisting in three very small parts of the source plane (a 'central caustic' and two 'planetary caustics'). Along its trajectory, the source remains almost equidistant from the two planetary caustics, leaving the anomaly poorly magnified. However, a detailed analysis unambiguously rules out the PSPL model by Δ𝜒 2 = 𝜒 2 PSPL -𝜒 2 PSBL = 968. Despite the relatively short timescale of the event, we also considered PSBL models, including the microlens parallax (hereafter "PSBL ⊕ 𝜋 E "). Although better by Δ𝜒 2 ≈ -12, this model converges towards the unphysical large value 𝜋 E = 2.5 +0.9 -1.0 (𝜋 E,𝑁 = 2.4 +0.9 -1.2 and 𝜋 E,𝐸 = 0.3 ± 0.1), and leaves the other parameters almost unchanged (all the parameters are within 1-𝜎 of the static model). This means that a model with parallax does not change the interpretation of the lens. The best PSBL ⊕ 𝜋 E model is shown in green in Figure 1. To assess whether the parallax detection is reliable, we compute the Bayesian information criterion (BIC) to take into account the effect of the additional free parameters in the models. The best PSBL model with parallax is now marginally preferred by ΔBIC ≈ -0.03. As a consequence, we cannot claim that the microlens parallax can be reliably measured using MOA observations of this event.

SOURCE AND LENS PHYSICAL PROPERTIES

Nature of the source star

As shown previously in Section 3, the source angular size is not detected in the light curve. Moreover, we do not have any color information about the source. Despite a lack of observational information, this section shows that the nature of the source can be determined: it is most likely a red clump giant (RCG) star located in the Galactic bulge.

First, we build a color-magnitude diagram (CMD) using the MOA-II 𝑅-and 𝑉-passband with stars within 2 arcmin around MOA-2014-BLG-472. Since the source brightness in 𝑅 Figure 5. Empirical law between OGLE 𝐼 magnitude and the instrumental 𝑅 MOA magnitude of stars located at an angular separation less than 2 arcmin from MOA-2014-BLG-472. RCG stars (black dots) only are used in the linear fit (except the outliers displayed as red squares). Black circles corresponds to stars that do not belong to the RCG (most of them are foreground main sequence stars). The cyan region is an envelop holding 100,000 randomly chosen samples. band found in Section 3 turns out to be the same as RCG stars, we assume that the source belongs to the RCG. Doing so, we implicitly reject the scenario with a foreground main sequence source. Although not impossible, this scenario is unlikely because the probability for a star to be lensed is proportional to 𝐷 2 S [START_REF] Paczynski | [END_REF]. Also, the foreground is much less populated by main sequence stars at a magnitude 𝐼 ≈ 16, than the background.

The second step is to calibrate the instrumental MOA-II 𝑅 MOA magnitude by crossreferencing stars from the MOA-II DOPHOT catalog with stars in the OGLE-III catalog. We use these stars to build a catalog with magnitudes in the standard Kron-Cousins 𝐼 and Johnson 𝑉 passbands (Szymański et al. 2011). In OGLE-III catalog, we identify 7446 stars located less than 2 arcmin from MOA-2014-BLG-472, while we find 1222 stars in the MOA-II catalog. Figure 4 shows the resulting OGLE-III (𝑉 -𝐼, 𝐼) CMD. Following the method described in [START_REF] Nataf | [END_REF], we identify RCG stars to derive their centroid (red circle in Figure 4). A total of 818 stars are cross-matched, including 251 RCG stars (see Figure 4). Since we assume a source that belongs to the RCG, we select those stars to derive an empirical linear law between OGLE-III 𝐼 and MOA-II 𝑅 MOA magnitudes. Figure 5 displays the aforementioned cross-matched stars, the RCG stars used in the linear fit, and outliers. The outliers are identified by following the methodology described in Section 3 of Hogg et al. (2010), taking alternatively into account the error bars of 𝐼 and 𝑅 MOA . We remove from the final fit the RCG stars that are classified as outliers in both cases. During this process, we note that an underestimate of the photometric error bars seem to be responsible for being classified as an outlier. The final linear fit is then performed following Section 7 of Hogg et al. (2010), taking into account two-dimensional uncertainties. The resulting empirical law reads, 𝐼 = 𝑎 0 + 𝑎 1 𝑅 MOA , with 𝑎 0 = 27.58 ± 0.06 and 𝑎 1 = 0.992 ± 0.005. These values correspond to the median of the marginalized posterior distributions (i.e., the two values do not necessarily represent a good fit), sampled with a MCMC algorithm. The error bars display the 68.3 per cent credible interval around the median, derived from the 16 and 84 per cent percentile of the corresponding marginalized posterior distribution. Figure 5 shows the envelop that holds 100,000 randomly chosen samples.

The third step is to use the calibration law found in step 2 to derive the 𝐼-band source magnitude. Figure 4 shows the source location in the OGLE CMD (cyan point), when its color is assumed to be the same as the CMD centroid at the corresponding brightness ±0.4 mag, and with the same dispersion. In practice, for each value of the source brightness derived from the previous step, the source color is described by a Gaussian distribution, which mean coincides with the centroid of RCG stars, and with a standard deviation derived from the color dispersion of RCG stars that have the same brightness as the source ±0.4 mag. Under this assumption, the following paragraphs explain how we estimate the source radius from its brightness and color.

To do so, we measure the extinction and reddening of stars within 2 arcmin around MOA-2014-BLG-472. The centroid of the RCG stars is (𝑉 -𝐼) RCG = 2.27 ± 0.02 and 𝐼 RCG = 15.8 ± 0.1. The absolute magnitude of a source located in the Galactic bulge is 𝑀 I,RCG = -0.17 ± 0.05 (Chatzopoulos et al. 2015;[START_REF] Nataf | [END_REF]) and its intrinsic color is (𝑉 -𝐼) RCG,0 = 1.06 (Bensby et al. 2013). We use a new Galactic model (Koshimoto et al. 2021;[START_REF] Koshimoto | A Tool for Gravitational Microlensing Events Simulation[END_REF] to estimate the distance modulus of the source, 𝜇 = 14.60 +0.21 -0.15 , corresponding to 𝐷 S = 8.34 +0.86 -0.57 kpc. As expected, these values are consistent with the assumption we made of a RCG source. The new Galactic model improves several aspects of previous ones (Bennett et al. 2014;Zhu et al. 2017), for instance by taking into account the change in the velocity dispersion within the disk, with respect to the distance to the Galactic center. Since the extinction and reddening mostly occurs during the first kiloparsecs away from Earth, the dereddened source magnitude is 𝐼 s,0 = 𝐼 𝑠 + 𝑀 I,RCG + 𝜇 -𝐼 RCG , i.e., 𝐼 s,0 = 14.4 ± 0.3, and (𝑉 -𝐼) s,0 = 1.06 ± 0.14. The corresponding extinction 𝐴 𝐼 = 1.39 +0.16 -0.22 , and color excess 𝐸 (𝑉 -𝐼) = 1.2 ± 0.1 found are in good agreement with the 𝐴 𝐼 = 1.47 and 𝐸 (𝑉 -𝐼) = 1.21 derived from Gonzalez et al. (2012).

Finally, the angular source size can be estimated using the empirical relation (Boyajian et al. 2014), log 2𝜃 ★ mas = 0.501414 -0.2𝐼 s,0 + 0.419685 (𝑉 -𝐼) s,0 ,

inferred from stars with colors corresponding to 3900 K < 𝑇 eff < 7000 K (Bennett et al. 2017). In Equation 7, 'mas' denotes milli-arcsec. The resulting source angular radius yields the source radius, 𝑅 ★ = 𝜃 ★ 𝐷 S , and the source radius crossing time, 𝑡 ★ = 𝜃 ★ /𝜇 rel , shown in Figure 6. With 𝜃 ★ = 5.8 +1.2 -1.0 𝜇as ('𝜇as' denotes micro-arcsec) and 𝑅 ★ = 10.5 +1.8 -1.5 R , we check that the source is a red giant star of the Galactic bulge, as we assumed.

The exact origin of the blend flux remains unknown. The ratio of the blend flux to the source flux for the binary-lens models, 𝑓 b,𝑅 / 𝑓 s,𝑅 , is 0.4 ± 0.2 (see Table 1). It may be due to one or several stars, including the lens, blended into the point spread function. As a consequence, the blend flux cannot be used to characterize further the nature of the lens.

Nature of the lens

The main difficulty of the lens characterization is that the light-curve modeling returns only one parameter that is sensitive to the mass and distance, namely, the Einstein timescale defined in Equation 2. The mass-distance dependence of 𝑡 E appears in the expression of the angular Einstein radius; i.e.

𝜃 E = √ 4𝐺 𝑀 𝑐 2 𝐷 S 𝐷 S 𝐷 L -1 , (8)
where 𝑀 is the lens mass, 𝐷 S and 𝐷 L are the distances to the source and lens, 𝑐 is the speed of light, and 𝐺 is the gravitational constant. We use a galactic model of the Milky Way to predict the distribution of angular Einstein radii, source distances and lens-source relative parallaxes as introduced in Equation 5,

𝜋 rel = 1 au 𝐷 L - 1 au 𝐷 S , (9)
from the event coordinates. This model assumes that all stars have an equal planet hosting probability. Then, we use these predictions as priors to derive the total mass of the lens using Equations 8 and 9, i.e.,

𝑀 = 0.1228 M 𝜃 E 1 mas 2 𝜋 rel 1 mas -1 , (10)
and the distance to the lens,

𝐷 L = 1 kpc 𝜋 rel 1 mas + 𝐷 S 1 kpc -1 -1 . (11)
Since the angular Einstein radius measurements via microlensing is typically > 1 per cent, the precision of the lens mass estimation is expected to be > 2 per cent; we choose the significant digits of the constant in Equation 10 accordingly. Finally, the host-star and planet masses can be found from the measurement of the mass ratio in Section 3.2, i.e.,

𝑀 1 = 𝑀 1 + 𝑞 and 𝑀 2 = 𝑞𝑀 1 + 𝑞 . ( 12
)
The results of the Bayesian analysis are summarized in Table 2. The lens likely consists of a 1.9 +2.2 -1.2 M J Jupiter-mass planet orbiting a 0.31 +0.36 -0.19 M Mdwarf star. As expected, the lack of source size measurement is responsible for large uncertainties on the mass of each component of the lens system. The planet-host star projected separation is 0.75 ± 0.24 au. If we assume a circular orbit, this value translates into a mean semi-major axis 0.96 ± 0.31 au. This planetary system lies at a distance 7.2 +0.6 -1.7 kpc. In Figure 7, the light gray shading indicates the thin and thick disk contribution to the posterior distribution (black solid curve), while the dark gray shading indicated the spheroid and bulge contribution to the posterior distribution. Although these profiles raise the possibility of a lens lying in the disk, they suggest that a bulge lens is much more likely.

SUMMARY AND DISCUSSION

We have reported the discovery of a new Jupiter-mass planet, MOA-2014-BLG-472Lb, discovered through a low magnification anomaly during the microlensing event MOA-2014-BLG-472. The anomaly was due to the source star passing in between the two off axis components of a close caustic, consistent with a planet-to-host-star mass ratio 𝑞 = 5.75 +0.45 -0.42 × 10 -3 . Since microlensing in the Milky Way is most often caused by M-dwarfs lenses, this mass ratio corresponds typically to the domain of giant planets. The projected separation between the planet and the host star is 𝑠 = 0.47 ± 0.02 Einstein radius.

The 𝑠 ↔ 1/𝑠 degeneracy does not exist for this event, because the anomaly is not due to the central caustic. An exact geometrical degeneracy exists, leaving the lens physical parameters unchanged, though. Due to its low magnification (maximum 𝐴 ≈ 1.4), and anomaly occurring at an extremely low magnification (𝐴 ≈ 1.06), we did not detect features resulting from the angular size of the source. Without this measurement, we cannot use the light curve to measure 𝜃 E . However, we used a Galactic model to predict the distribution of the Einstein radius, source distance, relative lens-source proper motion, and microlens parallax. The resulting constraints on the lens physical properties are weak, but a low mass ratio in conjunction with a likely low-mass host enables us to put the mass of the companion in the planetary mass regime.

Including planets like MOA-2014-BLG-472Lb in statistical studies on planet demography is crucial for the completeness of planetary occurrence rates. The event MOA-2014-BLG-472 (including the anomaly) was intensively monitored by the MOA survey. Interestingly, although the physical parameters of MOA-2014-BLG-472Lb are not tightly constrained, the mass ratio, 𝑞, and the projected separation, 𝑠, are both precisely measured, and not degenerate. Events without close-wide degeneracy are not so common in statistical analyses. Since MOA-2014-BLG-472 does not suffer from it, it is an important add on to the new MOA sample of microlensing planets, that will be used in the next statistical analysis.

  modified version of L A T E X modern style in AASTeX63New Giant Planet beyond the Snow Line for an Extended MOA Exoplanet Microlens Sample

Figure 1 .

 1 Figure1. Magnification during the microlensing event MOA-2014-BLG-472 and the best pointsource binary-lens model (PSBL; solid magenta line). For comparison, the black solid line, brown dashed line and green solid line respectively show the rejected point-source point-lens (PSPL), PSPL including parallax, and PSBL with parallax models. MOA observations are displayed in blue. The inset shows a zoom in on the anomaly. In the lower panel, the residuals from the PSPL model are plotted in magnification units. For clarity, the plot uses 5-hour bins to display the data (these bins are not used in the fit).

Figure 2 .

 2 Figure 2. Caustic topology of the best-fit PSBL model. The color scale of the main plot refers to the magnification difference between the best PSBL and best PSPL models (except in the white regions around the caustic components, where the residuals are highest and not displayed). The caustic consists of three parts, located in the red circles. The insets display a zoom in on magnification maps in the vicinity of the caustic components in the source plane (dotted line). For convenience, we use two different logarithmic color scales for the central and planetary caustics. The black line shows the source-lens trajectory, and the black dots the source position at HJD = 6890 (anomaly peak) and HJD = 6910 (event peak). Blue regions denote a de-magnification compared to a single lens.

Figure 3 .

 3 Figure3. Correlation between the parameters for the PSBL model. The three shaded areas show the 1-3𝜎 credible regions, respectively, from the darkest to lightest color. Plots in the diagonal display the marginal cumulative distribution of each parameter (solid line), the median of the distribution (dot), and the 68.3 per cent credible interval centered on the median. Plot prepared using the python package MOAna (Ranc 2020).

Figure 4 .

 4 Figure 4. The black dots show a CMD in the standard Kron-Cousins 𝐼 and Johnson 𝑉 photometric systems of OGLE-III stars selected within 2 arcmin around the target. The RCG centroid is indicated by the red circle, and the RC stars are shown as black stars. The source brightness and the estimated source color are shown by the cyan point. The color dispersion of the RC stars mostly accounts for the source color error. The cyan horizontal line reminds us that we only measured the source brightness, and the source color fully follows from the assumption that the source belongs to the RC. The green dots show the Hubble Space Telescope CMD from Holtzman et al. (1998) shifted to the bulge distance and extinction derived for the MOA-2014-BLG-472 line of sight.

Figure 6 .

 6 Figure 6. Correlation between the parameters for the best-fit model. The three shaded areas show the 1-3𝜎 confidence regions, respectively, from the darkest to lightest color. Plots in the diagonal displays the marginal cumulative distribution function of each parameter (solid line), the median of the distribution (dot), and the 68.3 per cent credible interval centered on the median. Plot prepared using the python package MOAna (Ranc 2020).

Figure 7 .

 7 Figure 7. One-dimensional marginalized posterior probability density function of the host star mass (upper left panel), distance to the lens (upper right panel), planet mass (lower left panel), and projected separation (lower right panel). Two shaded areas are separated by a dark blue line. They show the contribution of the thin and thick disks (light gray), and the spheroid and bulge (dark gray) to the posterior distribution (black line). The upper right panel also displays the prior distribution on the source distance (red dashed line), derived from the galactic model. The lower right panel includes the probability density function of the deprojected separation (orange line), < 𝑎 >, and snow line position (light blue line), 𝑎 snow .

Table 1 .

 1 Parameters for the Best-fit PSBL Model and the Corresponding Statistical Values from the Posterior Probability Distribution Function

	Parameter	Units	Best-fit	MCMC results (1)
	𝜒 2		13776.36	. . .
	𝑞/10 2		0.568450	0.575 +0.045 -0.042
	𝑠		0.475423	0.47 ± 0.02
	𝑡 E	days	14.787693	14.6 ± 0.8
	𝑡 0	HJD	6910.008646	6910.01 ± 0.04
	𝑢 0		0.924277	0.94 +0.08 -0.07
	𝛼	deg	-145.685730	-145.4 ± 0.9
	𝑅 MOA,s

Table 2 .

 2 Lens and Source Properties Derived from the Bayesian Analysis of Section 4 Median of the marginalized posterior distributions, with error bars displaying the 68 per cent credible interval around the median.

	Parameter	MCMC results †	Units
	Host mass 𝑀 1	0.31 +0.36 -0.19	M
	Planet mass 𝑀 2	1.9 +2.2 -1.2	M J
	Projected separation 𝑎 ⊥	0.75 ± 0.24	au
	Deprojected separation 𝑎	0.96 ± 0.31	au
	Lens distance 𝐷 L	7.2 +0.6 -1.7	kpc
	Einstein radius ‡ 𝜃 E	0.24 +0.09 -0.08	mas
	Lens-source proper motion ‡ 𝜇 rel,G	6.0 +2.3 -2.0	mas yr -1
	Source magnitude 𝐼 S,0	14.4 ± 0.3	mag
	Source color (𝑉 -𝐼) s,0	1.06 ± 0.14	mag
	Extinction 𝐴 𝐼	1.39 +0.16 -0.22	mag
	Reddening 𝐸 (𝑉 -𝐼)	1.2 ± 0.1	mag
	Source angular radius 𝜃 ★	5.7 +1.2 -1.0	𝜇as
	†

‡ Galactic prior.

https://exoplanetarchive.ipac.caltech.edu/

Published at https://github.com/smarnach/luckylensing.

ACKNOWLEDGMENTS

The authors thank the anonymous referee, whose comments and suggestions improved the manuscript. CR thanks Anne Shrestha for stimulating discussions. This work was carried out within the framework of the ANR project COLD-WORLDS supported by the Agence Nationale de la Recherche (French National Agency for Research) with the reference ANR-18-CE31-0002. The work of CR, DPB, NK, YH and AB was supported by NASA under award number 80GSFC17M0002. JS acknowledges support from the National Science Center, Poland grant MAESTRO 2014/14/A/ST9/00121. The MOA project is supported by JSPS KAKENHI grant No. 19KK0082 and 20H04754. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. Software: Astropy (Collaboration et al. 2018), Luckylensing (https://github.com/ smarnach/luckylensing), Matplotlib (Hunter 2007), MOAna (Ranc 2020), NumPy (Oliphant 2015), SciPy (Jones et al. 2001).

DATA AVAILABILITY

The original data underlying this article can be accessed from the NASA Exoplanet Archive MOA Resources, https://exoplanetarchive.ipac.caltech.edu/docs/MOAMission.html. The derived data generated in this research will be shared on reasonable request to the corresponding author until they are added to the NASA Exoplanet Archive, at https: //exoplanetarchive.ipac.caltech.edu/docs/contributed_data.html.


Naira Mkrtchyan

Lauranne Alciato

Michel Kalamarides

Daniele Bernardeschi

Olivier Sterkers

Isabelle Bernat

Mustapha Smail

Nadya Pyatigorskaya

Ghizlene Lahlou

Hearing recovery after surgical resection of non-vestibular schwannoma cerebellopontine angle tumors

Introduction

The most common cerebellopontine angle (CPA) tumor is vestibular schwannoma (VS) which represents approximately 6% of all intracranial [START_REF] Lin | The prevalence of "incidental" acoustic neuroma[END_REF] and 91% of CPA tumors [START_REF] Brackmann | Rare tumors of the cerebellopontine angle[END_REF]. Meningiomas are the second most common tumors of the CPA affecting 6% to 15% of patients [START_REF] Brackmann | Rare tumors of the cerebellopontine angle[END_REF]. Lower cranial nerve and trigeminal schwannomas are rare lesions and represent 0.7% and 1% of CPA tumors, respectively [START_REF] Moffat | Unusual cerebello-pontine angle tumours[END_REF].

Regardless of the tumor histology, hearing loss is one of the most common symptoms of CPA tumors [START_REF] Nakamura | Facial and cochlear nerve function after surgery of cerebellopontine angle meningiomas[END_REF][5][START_REF] Batra | Auditory and facial nerve function following surgery for cerebellopontine angle meningiomas[END_REF][START_REF] Lanzino | Recovery of useful hearing after posterior fossa surgery: the role of otoacoustic emissions: case report[END_REF]. To date, when there is an indication for surgical treatment of these tumors, the choice of surgical approach is guided by the tumor size, growth, location and hearing level [START_REF] Lanzino | Recovery of useful hearing after posterior fossa surgery: the role of otoacoustic emissions: case report[END_REF][START_REF] Tator | Preservation of hearing in patients undergoing excision of acoustic neuromas and other cerebellopontine angle tumors[END_REF]. Although preservation of facial nerve function is still the main goal of surgery, hearing preservation should be considered whenever possible [5,[START_REF] Batra | Auditory and facial nerve function following surgery for cerebellopontine angle meningiomas[END_REF][START_REF] Tator | Preservation of hearing in patients undergoing excision of acoustic neuromas and other cerebellopontine angle tumors[END_REF][START_REF] Cohen | Hearing preservation in cerebellopontine angle tumor surgery: the NYU experience 1974-1991[END_REF].

Apart from VS, where hearing preservation was obtained in 43% of patients in a large series [START_REF] Daoudi | Improving facial nerve outcome and hearing preservation by different degrees of vestibular schwannoma resection guided by intraoperative facial nerve electromyography[END_REF] and significant hearing recovery is not an expectable result, hearing recovery could be a reasonable expectation in non-VS CPA tumors since the they arise outside the acoustic-facial bundle. Up to now, only a few case reports have been published on hearing recovery after surgical resection of non-VS CPA tumors [START_REF] Nakamura | Facial and cochlear nerve function after surgery of cerebellopontine angle meningiomas[END_REF][START_REF] Lanzino | Recovery of useful hearing after posterior fossa surgery: the role of otoacoustic emissions: case report[END_REF][START_REF] Goebel | Hearing improvement after conservative approach for large posterior fossa meningioma[END_REF][START_REF] Maurer | Restoration of hearing after removal of cerebellopontine angle meningioma: diagnostic and therapeutic implications[END_REF][START_REF] Vellutini | Reversible hearing loss from cerebellopontine angle tumors[END_REF][START_REF] Christiansen | Reversible hearing loss in tumours of the cerebello-pontine angle[END_REF][START_REF] Lewis | Pearly tumor of the cerebellopontine angle, report of a case with reversible deafness[END_REF].

In this study, we evaluated the hearing results in non-VS CPA tumors with particular regard to those patients who had significant hearing recovery, trying to analyze the incidence of such events and the possible surgical implications.

Materials and methods

This article follows the STROBE (STrengthening the Reporting of OBservational studies in Epidemiology) [START_REF] Von Elm | The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) Statement: Guidelines for reporting observational studies[END_REF] guidelines for the reporting of observational studies.

Study population

This monocentric retrospective study, conducted in a tertiary referral center, included patients who experienced significant hearing recovery after non-VS CPA tumor removal through a retrosigmoid approach between 2012 and 2020. All patients gave their informed consent for the use of their clinical data. The study complied with Public Health code (CNIL #2211758).

The inclusion criterion was a post-operative hearing improvement of more than 30 dB in pure-tone audiometry (PTA) and/or a 50% gain in the speech discrimination score (SDS).

Exclusion criteria were neurofibromatosis type II (NF2) related tumors, meningiomatosis, pseudotumors of the CPA (arachnoid and epidermoid cysts), tumors of the central nervous system extending to the CPA (pilocytic astrocytoma, choroid plexus papilloma, ependymoma, ganglioglioma) and revision surgical procedures.

Pre-operative assessment

Before surgery, all patients underwent a clinical examination (facial nerve function was evaluated according to the House-Brackmann (HB) grading system [START_REF] House | Facial nerve grading system[END_REF]), hearing assessment and neuroradiological examinations (high-resolution computed tomography and magnetic resonance imaging [MRI]).

Audiometric tests

All patients were evaluated before surgery and post-operatively (at 1 month and at the last visit) by the same audiologist using similar testing equipment and procedures (pure-tone and monosyllabic speech audiometry). Audiometric data included PTA, calculated as the mean of the thresholds at frequencies of 0.5, 1, 2 and 3 kHz and SDS, calculated using a standardized presentation up to 40 dB sensation level or maximum comfortable loudness (whichever was lower). The differences between pre-and post-operative PTA and SDS were calculated (respectively PTA and SDS). Hearing function was graded according to the American Academy of Otolaryngology -Head and Neck Surgery (AAO-HNS) guidelines: Class A: PTA≤30 dB and SDS≥70%; Class B: PTA>30 dB and ≤50 dB and SDS≥50%; Class C: PTA>50 dB and SDS≥50%; Class D: PTA any level and SDS<50%) [START_REF]Committee on Hearing and Equilibrium Guidelines for the Evaluation of Hearing Preservation in Acoustic Neuroma (Vestibular Schwannoma): Committee on Hearing and Equilibrium[END_REF]. Hearing recovery was defined as described above corresponding to a change in the AAO-HNS hearing class from non-useful (Class D) to useful or normal hearing (Class A and B).

Pre-operative and post-operative auditory brainstem responses (ABR) using click were collected. Five waves (I-V) were recorded in the first 10 ms after broad-band and high-intensity stimuli. Three 90 dB acquisitions were made, followed by a decrease by 10 dB ranging up to the hearing threshold. ABR were classified as: Synchronous: reproducible ABR waves in three 90 dB stimulations and good visualization of wave V which decreased in intensity and increased in latency with decreasing stimulus intensity; Augmented inter-peak latency: good visualization of the ABR waves, but with a I-V inter-peak interval in the homolateral ear increasing by more than 0.5 ms compared to the contralateral ear; or Asynchronous: no visualization of a reproducible wave V, even at high-intensity stimulation. A detailed analysis of ABR curves has been carried out.

Tumor imaging

Pre-operative MRI allowed morphological characterization of the tumors for diagnostic orientation, measurement of their sizes and analysis of the acoustic-facial bundle position. The MRI protocol included at least a high-resolution 3D T2-weighted image (wi) to analyze the position of the acoustic-facial bundle and a 3D T1-wi after gadolinium chelate injection, allowing tumor characterization and measurements of tumor size in three axial directions (anterior-posterior, medio-lateral and superior-inferior). Brainstem displacement with or without mass effect in the fourth ventricle was collected. Meningiomas were classified according to the modified Desgeorges and Sterkers classification: Posterior petrous (P); Meatus and auditory canal invasion (M); Anterior petrous (A); Anterior petrous and meatus (AM); Posterior petrous and meatus (MP), and anterior and posterior petrous but also meatus (AMP) [START_REF] Peyre | Posterior petrous bone meningiomas: surgical experience in 53 patients and literature review[END_REF].

Surgery

We used two classifications usually used for VS. The quality of resection was classified following the Monfared classification as gross-total resection (no tumor remnant was visible at the end of surgery), near-total resection (the tumor remnant measured less than 5x5x2 mm over the brainstem and the facial nerve) or sub-total resection (the tumor was resected 80% to 90% by volume and 60% to 70% by surface area) [START_REF] Monfared | Facial Nerve outcome and tumor control rate as a function of degree of resection in treatment of large acoustic neuromas: Preliminary Report of the Acoustic Neuroma Subtotal Resection Study (ANSRS)[END_REF]

Post-operative assessment

Complications of surgery were assessed. Post-operative facial (HB) and lower cranial nerve functions were evaluated at the last follow-up. Audiometric tests and ABRs were performed at the last visit.

Statistical analysis

Results are presented as mean ± SD for continuous variables and as numbers and percentages for categorical variables.

Statistical analysis was performed using Prism (GraphPad Software, San Diego, CA, USA). The pre-operative and postoperative audiological results were compared using two-way ANOVA and Mann-Whitney tests. Differences between groups were considered to be significant for p≤0.05.

Results

Patients

Among 99 patients operated on between December 2012 and January 2020 for non-VS CPA tumors, 69 were eligible for this study, from whom 60 were operated on with a retrosigmoid approach (Fig. 1). A significant post-operative hearing recovery was found in eight patients who were included in this study, representing 13.3% (8/60) of all non-VS CPA tumors operated on with a conservative approach. Patient characteristics for inclusion are detailed in the flow chart (Fig. 1).

Baseline characteristics

Baseline characteristics of the 8 patients with hearing recovery are described in Table 1. Their mean age was 58±9.9 years [40-72 years]. The right side was involved in half of the cases. One patient had pre-operative grade II HB facial nerve function. All patients had a significant degree of pre-operative hearing loss. For all patients but one, who had a sudden hearing loss which was unresolved after 5 days of corticosteroid therapy, the hearing loss was progressive, with an average evolution of 1 year. Patients were not premedicated with steroids or other drugs in the pre-operative period.

Tinnitus and balance disorder were present in one and four cases, respectively. Two patients were experiencing hemifacial hypoesthesia. Regarding lower cranial nerve function, one patient, affected by a lower cranial nerve schwannoma, had a X and XI palsy. One of the patients had morning headaches suggesting early intracranial hypertension.

Pre-operative assessment

Hearing

Complete audiological data were available for all eight patients (Table 1). The mean pre-operative PTA was 58±20.7 dB and SDS was 13±17.5%. All patients presented with class D hearing. ABR were asynchronous for all patients, but in 3 patients, we identified the isolated presence of wave I at 90 dB stimulation.

Imaging

In all cases, the pre-operative MRI allowed a correct diagnosis of tumor histology. The mean tumoral measurements in the three axial directions were 32±5.8 mm, 28±6.9 mm, and 31±5.0 mm for anterior-posterior, medio-lateral and superior-inferior diameters, respectively. Six patients had a significant brainstem compression (Fig. 2), four with and two without fourth ventricle displacement/compression. No hydrocephalus was observed pre-operatively. Four patients showed internal auditory canal invasion.

Regarding the displacement of the acoustic-facial bundle, in two cases, an anterior course was observed, while it was anteriorsuperior in two cases, superior in two others and no nerve deviation and posterior-inferior switch in the two remaining patients. function recovered to grade I (Patient 8). Lower cranial nerve functions were improved in Patient 7, with disappearance of the XI th nerve paralysis, improved laryngeal sensitivity, but persistence of ipsilateral vocal cord palsy.

Imaging

Post-operative imaging was available for seven patients. Three had a residual tumor, located in the jugular foramen in two and in the cavernous sinus in one patient (Table 1). All but one residual tumor were stable; the last one showed growth that was treated with Gamma-knife stereotactic radiosurgery.

Discussion

Analyzing our results, among the 69 patients operated on for a non-VS CPA tumor at our institute, we were surprised to note that the incidence of significant hearing recovery was 13.3% after tumor removal with a retrosigmoid approach. These patients experienced a recovery from non-useful hearing (class D) to useful hearing with intelligibility (class A or B), that probably represents a substantial improvement in their everyday quality of life. During the same period, in nine cases, we used a translabyrinthine approach for non-VS CPA tumor removal (Fig. 1), because of significant pre-operative hearing loss.

It is likely that some of them would have experienced hearing recovery if we had used a retrosigmoid approach in those cases. Therefore, at present, the retrosigmoid approach is the preferred option when dealing with non-VS CPA tumors despite the hearing level and/or the tumor volume, and this has represented an important change in our daily practice.

In the literature, there are a few reports [START_REF] Nakamura | Facial and cochlear nerve function after surgery of cerebellopontine angle meningiomas[END_REF][START_REF] Lanzino | Recovery of useful hearing after posterior fossa surgery: the role of otoacoustic emissions: case report[END_REF][START_REF] Goebel | Hearing improvement after conservative approach for large posterior fossa meningioma[END_REF][START_REF] Maurer | Restoration of hearing after removal of cerebellopontine angle meningioma: diagnostic and therapeutic implications[END_REF][START_REF] Vellutini | Reversible hearing loss from cerebellopontine angle tumors[END_REF][START_REF] Christiansen | Reversible hearing loss in tumours of the cerebello-pontine angle[END_REF][START_REF] Lewis | Pearly tumor of the cerebellopontine angle, report of a case with reversible deafness[END_REF] on hearing recovery after CPA tumor removal (Table 3), most being case reports generally concerning meningiomas, arachnoid and epidermoid cysts. We decided not to include the cysts in our series because they were not "true" tumors with different biological and histopathological behaviors. Only one study reported a large series of CPA meningiomas [START_REF] Nakamura | Facial and cochlear nerve function after surgery of cerebellopontine angle meningiomas[END_REF] and found some degree of hearing improvement in 40 of 421 cases. Unfortunately, they used the Hannover Audiological Classification making comparison with the present study difficult.

Although preservation of hearing in surgical treatment of VS has been emphasized and discussed in the literature [START_REF] Daoudi | Improving facial nerve outcome and hearing preservation by different degrees of vestibular schwannoma resection guided by intraoperative facial nerve electromyography[END_REF], little is known about auditory function in non-VS tumors of the CPA. However, extrapolating data on hearing preservation in VS surgery to the post-operative evolution of hearing for non-VS CPA tumors is probably a mistake. First, in VS, pathophysiological evidence indicates that hearing loss is explained by compression of either the cochlear nerve and/or the labyrinthine artery in the internal auditory canal (IAC) with a direct association between VS tumor size and hearing loss [START_REF] Remenschneider | Is the cause of sensorineural hearing loss in patients with facial schwannomas multifactorial?[END_REF].

In the case of labyrinthine artery compression, vascular damage to the cochlea with no conceivable recovery could explain the hearing loss. The significant recovery of hearing obtained in this series suggests that the vascular etiology was not involved, similar to a report by Lanzino et al. [START_REF] Lanzino | Recovery of useful hearing after posterior fossa surgery: the role of otoacoustic emissions: case report[END_REF] who described hearing recovery after marsupialization of a CPA arachnoid cyst in a patient who had recordable pre-operative otoacoustic emissions (OAEs) with an asynchronous ABR. The presence of OAEs pre-operatively may predict the integrity of vascular supply to the cochlea and correlation studies would be necessary to define their function in pre-operative care [START_REF] Mom | Otoacoustic emissions in clinical and surgical practice[END_REF]. Similarly, the presence of wave I in the pre-operative ABR, which indicates the cochlear synapse function, could have the same significance and be a good prognostic factor for hearing recovery [START_REF] Huo | Prognostic factors of long-term hearing preservation in small and medium-sized vestibular schwannomas after microsurgery[END_REF]. Indeed, we found the presence of wave I pre-operatively even in the case of asynchronous ABR, and it could be helpful to use OAEs as an additional tool to select cases with a greater chance of hearing recovery.

In addition, histological evidence of invasion of the cochlear nerve by VS was reported by Neely et al. [START_REF] Neely | Histologic findings in two very small intracanalicular solitary schwannomas of the eighth nerve[END_REF]. In contrast, in non-VS CPA tumors, although the pathophysiology evidence is poor, hearing loss is probably due to cochlear nerve compression without invasion [START_REF] Christiansen | Reversible hearing loss in tumours of the cerebello-pontine angle[END_REF], which would not cause irreversible damage to the nerve and the cochlea, making hearing improvement possible. Indeed, we know that damage to the cochlear nerve cannot be repaired, but compression by a tumor may cause neurapraxia that, once the pressure is alleviated, allows return of axonal transmission and hearing recovery. Thus, the decompression of the cochlear nerve by the tumor removal could allow spectacular recovery of the SDS, as illustrated in our series.

Regarding other post-operative functional outcomes, a good post-operative facial nerve function was obtained in all patients, despite the presence of relatively large lesions, underlining the fact that, when dealing with large CPA lesions, the facial nerve is not at increased risk during a retrosigmoid approach compared to a translabyrinthine approach. Finally, the choice of the extent of resection in our series was mainly decided after considering lower cranial nerve function. In two cases, the lesion arose from these nerves and a gross-total resection might have led to lower cranial nerve injury.

Surgery is not the sole option for treating these lesions. Gamma-knife stereotactic radiosurgery has been employed in the treatment of meningiomas [START_REF] Jahanbakhshi | Gamma Knife stereotactic radiosurgery for cerebellopontine angle meningioma[END_REF] and lower cranial nerve tumors [START_REF] Ruangkanchanasetr | Toxicity of Gamma Knife radiosurgery may be greater in patients with lower cranial nerve schwannomas[END_REF]. Results on hearing preservation have been published [START_REF] Jahanbakhshi | Gamma Knife stereotactic radiosurgery for cerebellopontine angle meningioma[END_REF] and a mention of hearing improvement has been reported in that series without any audiological data. Because of the volume of tumors in our cases, radiosurgery was not indicated as first-line treatment. In addition, chemotherapy with bevacizumab could be associated with an improvement in hearing in NF2-related VS, but this treatment is reserved for patients with NF2 and no indications are accepted for other kinds of CPA tumor. The mechanism of hearing recovery is thought to be a decrease in intraneural edema and vascular shrinkage of the tumor which would decrease the compression on the nerve and blood vessels [START_REF] Plotkin | Hearing improvement after bevacizumab in patients with neurofibromatosis type 2[END_REF].

There are some important limitations that could affect the generalizability of our findings. First, the retrospective nature of this study encompasses biases that are difficult to overcome. Also, we did not use intraoperative auditory monitoring in this study. Looking at our cases, pre-operative ABR were asynchronous in almost all patients making this kind of monitoring impossible. Monitoring with cochlear nerve action potentials (CNAP) would have provided interesting information about the variation of this potential during manipulation of the tumors with the possibility of individualizing some surgical steps/maneuvers important for hearing recovery [START_REF] Simon | Neurophysiologic intraoperative monitoring of the vestibulocochlear nerve[END_REF]. Finally, we tried to highlight anatomic, audiological or radiological factors to compare the different groups presented in the flow chart (Fig. 1), but the heterogeneity of their presentation and the relatively small number of patients did not allow us to constitute a statistically significant control group.

Conclusion

We would like to alert readers to the potential for significant post-operative hearing recovery in non-VS CPA tumors and stress the importance of considering a conservative surgical approach, even in cases of severely impaired hearing and large tumors. Relying on tumor size and hearing status for choosing the translabyrinthine approach (as classically performed for VS) should not be adopted in non-VS CPA tumors. Larger multi-center studies examining this topic would help corroborate our results.

  . The Jackler classification was used to describe the acoustic-facial bundle position with regard to the tumor: Facial nerve course pattern I: anterior-inferior shift of the VII-VIII bundle; Facial nerve course pattern II: anterior shift of the VII-VIII bundle; Facial nerve course pattern III: superior shift of the VII-VIII bundle; Facial nerve course pattern IV: posterior shift of the VII-VIII bundle [21, 22]. The anatomopathological results were listed, and the meningiomas were graded from I to III according to the World Health Organization (WHO) classification (2007 or 2016).

Fig. 1

 1 Fig. 1 Flow chart of the study population ΔPTA: difference between pre-and post-operative pure tone average; ΔSDS: difference between pre-and post-operative speech discrimination score.

Fig. 2

 2 Fig. 2 Axial and coronal views of MRI scans (cerebellopontine angle meningioma) from Patient 1 Pre-operative Fast imaging employing steady-state acquisition in axial (A, upper left) and coronal (B, lower left) images showing a stage IV tumor with brainstem compression; and post-operative axial (C, upper right) and coronal (D, lower right) images showing a total tumor resection with acoustic-facial bundle visualization.

Fig. 3

 3 Fig. 3 Evolution of hearing between the pre-operative period and the final post-operative visit A: Pre-and post-operative mean of thresholds of the tonal audiogram at 500, 1000, 2000, and 3000 Hz, showing a significant improvement of thresholds (p=0.0152, p=0.0054, p=0.0002 and p=0.0017, respectively; two-way ANOVA with SIDAK's multiple comparison test). B: Significant improvement of the pre-and post-operative speech discrimination score (p=0.0002, Mann-Whitney test).

Surgery

All patients were operated on with a retrosigmoid approach using a continuous facial nerve monitoring system (NIM3 ® , Medtronic, Minneapolis, MN, USA).

Intraoperative displacement of the acoustic-facial bundle by the tumor was as follows: two patients had facial nerve course pattern I, one had pattern II, and five had pattern III. Gross total resection was achieved in four cases, and sub-total resection in four (Table 1). MRI analysis of the VII-VIII bundle displacement matched the intraoperative observed displacement in five cases.

Regarding the histological analysis, the most common lesion was CPA meningioma (n=6), followed by lower cranial nerve schwannoma (n=2) (Table 1). Four of the six meningiomas were classified as grade I in the WHO classification, and the other two as grade II. The proportion of grade I and grade II in our series was comparable to the proportion in the entire cohort (52 grade I WHO and 8 grade II WHO).

Post-operative assessment

Hearing

The mean follow-up was 21±23.5 months [1-54 months]. At the last visit, PTA was 3622.2 dB, with a significant improvement at all frequencies (p<0.0001, two-way ANOVA, n=8, Fig. 3A), and SDS was 8516.9% (p=0.0002, Mann-Whitney test, n=8, Fig. 3B). There was no significant difference between the hearing results at 1 month and at the last visit, or the mean PTA (209.7 dB vs 1810.6 dB, p=0.25, Mann-Whitney test), or the mean SDS (958.8% vs 9218.9%, p>0.999, Mann-Whitney test). Table 1 shows the results for all patients at the last visit.

After surgery, all patients but one recovered from a pre-operative hearing class D to a post-operative class A; the last patient recovered to class B.

Concerning ABRs, three of the five available post-operative ABRs became synchronous, one became synchronous with increased interpeak interval I-V, and only one remained asynchronous.

Complications

Regarding early post-operative complications, one patient experienced a post-operative cerebrospinal fluid leak (7 days after surgery) which required revision surgery.

One patient had a well-tolerated post-operative paralysis of the X and XI nerves (Patient 5) and another had reversible grade II facial paralysis that required no further treatment (Patient 1). The patient presenting pre-operative grade II HB facial nerve