Mid-to-late M Dwarfs Lack Jupiter Analogs Emily K. Pass1 , Jennifer G. Winters1,2 , David Charbonneau1 , Jonathan M. Irwin1,3, David W. Latham1 , Perry Berlind1, Michael L. Calkins1 , Gilbert A. Esquerdo1 , and Jessica Mink1 1 Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 2 Thompson Physics Lab, Williams College, 880 Main Street, Williamstown, MA 01267, USA 3 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK; emily.pass@cfa.harvard.edu Received 2023 January 5; revised 2023 March 14; accepted 2023 April 24; published 2023 June 12 Abstract Cold Jovian planets play an important role in sculpting the dynamical environment in which inner terrestrial planets form. The core accretion model predicts that giant planets cannot form around low-mass M dwarfs, although this idea has been challenged by recent planet discoveries. Here, we investigate the occurrence rate of giant planets around low-mass (0.1–0.3Me) M dwarfs. We monitor a volume-complete, inactive sample of 200 such stars located within 15 pc, collecting four high-resolution spectra of each M dwarf over six years and performing intensive follow-up monitoring of two candidate radial velocity variables. We use TRES on the 1.5 m telescope at the Fred Lawrence Whipple Observatory and CHIRON on the Cerro Tololo Inter-American Observatory 1.5 m telescope for our primary campaign, and MAROON-X on Gemini-North for high-precision follow up. We place a 95% confidence upper limit of 1.5% (68% confidence limit of 0.57%) on the occurrence of MP sin i> 1MJ giant planets out to the water snow line and provide additional constraints on the giant planet population as a function of MP sin i and period. Beyond the snow line (100 K < Teq< 150 K), we place 95% confidence upper limits of 1.5%, 1.7%, and 4.4% (68% confidence limits of 0.58%, 0.66%, and 1.7%) for 3MJ−15° and the CTIO HIgh ResolutiON (CHIRON; R= 80,000) spectrograph at the Cerro Tololo Inter-American Observatory 1.5 m telescope for sources with δ<−15°. Exposure times were selected based on a target per- pixel signal-to-noise ratio (S/N) of 15 in the TiO bands around 7100Å, ranging from 60 to 5400 s; however, in practice our observations span a range of S/Ns, with a typical value of 11 for our TRES observations and 8 for our CHIRON observa- tions. Forthcoming entries in this series will discuss the active subsample, the binary subsample, and present galactic kine- matics for all stars (Pass et al. 2023; J. G. Winters et al. 2023, in preparation). In this work, we consider only the single, inactive subsample, as with four observations per star, we cannot easily distinguish variations due to an orbiting planet from other sources of variation. As we perform intensive follow-up vetting of each candidate flagged as potentially variable from our four- observation campaign, selecting the single, inactive subsample allows us to minimize the time spent intensively monitoring candidates that are ultimately false positives. We discard all binaries separated by less than 4″, as light from both stars would fall in the spectroscopic aperture under typical seeing. To avoid a large number of false positives due to activity- induced radial velocity variability (e.g., Tal-Or et al. 2018), we neglect active stars for which we measure Hα emission stronger than a median equivalent width (EW) of –1Å using the method of Medina et al. (2020). We use the notation that a negative EW indicates emission. This –1Å threshold has been used to distinguish between active and inactive M dwarfs in previous work such as Newton et al. (2017). Of the stars without close binaries, we classify 123 as active based on this Figure 1. The mass distribution of our stars. We contrast this sample with Bonfils et al. (2013; B13), the largest radial velocity survey of M dwarfs in the literature, as well as Sabotta et al. (2021; S21)’s recent results from the CARMENES survey. Previous studies of giant planets around M dwarfs have been dominated by early Ms, with masses that are not so dissimilar to those of Sun-like stars. More poorly studied are low-mass, fully convective M dwarfs. Our sample is volume complete and contains 200 such stars with masses of 0.1–0.3 Me. Previous studies have dramatically smaller samples over this mass range (46 in B13 and 15 in S21) and are not volume complete. Note that this figure compares total sample size; for a comparison of effective sample size as a function of planetary mass and period, an interested reader may compare our Figure 3 with Figure 15 of B13 and Figure 3 of S21. 2 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. criterion; this group includes the known giant planet hosts GJ 83.1 (Hα EW =−2.3Å) and LHS 252 (Hα EW =−1.8Å). While “inactive” M dwarfs may still have activity-induced variability that masquerades as a planet (e.g., Lubin et al. 2021), this phenomenon is less ubiquitous and can be evaluated on a case-by-case basis through intensive follow up of the small number of inactive candidates. After making these cuts, 200 M dwarfs remain in our sample (Figure 1), of which we observe 122 with TRES and 78 with CHIRON. 3. Data Reduction 3.1. Radial Velocities We extract the spectra using the standard TRES (Buchhave et al. 2010) and CHIRON (Tokovinin et al. 2013) pipelines and measure radial velocities using an updated version of the method presented in Winters et al. (2020), which itself is based on Kurtz & Mink (1998). In addition to utilizing the TiO bandhead features from 7065 to 7165Å (TRES echelle order 41 and CHIRON echelle order 44), we also consider five additional red echelle orders—36, 38, 39, 43, and 45 for TRES and 36, 37, 39, 40, and 51 for CHIRON, which represent wavelengths with low telluric contamination and high informa- tion content for low-mass M dwarfs. These orders fall within 6400–7850Å. We obtain an initial radial velocity estimate for each spectrum by cross-correlating with a template of Barnard’s Star in the manner described in Winters et al. (2020). This method also produces an estimate of v sin i. We then shift and stack our observations to create a high-S/N template spectrum of the average slowly rotating, low-mass M dwarf observed by TRES. To stack the observations, we first create an error- weighted mean spectrum for each star. We then median combine the spectra of all 122 stars that were observed with TRES. Prior to coaddition, we mask regions with telluric depths greater than 2% in a representative TAPAS spectrum (Bertaux et al. 2014) or skyline emission greater than 5× 10−17 erg s−1 cm−2Å−1 in the UVES sky emission atlas (Hanuschik 2003). Our final template neglects wavelengths at the edges of orders that do not include information from at least ten M dwarfs. In creating this average low-mass M dwarf template, we note that the information content Q (Bouchy et al. 2001) in TRES echelle order 45 differs by a factor of two across our sample, with the highest values obtained for cold, metal-rich stars and the lowest values obtained for hot, metal-poor stars. To minimize radial velocity uncertainties caused by template mismatch, we therefore create six different average templates for TRES. Each star is initially classified by the Q we measure in order 45, dividing the sample equally into six preliminary bins. We then reclassify each star by determining the preliminary template that maximizes the cross-correlation coefficient, recreating the templates based on these refined classifications, and repeating until the classifications converge. This iterative process prevents stars from being misclassified in cases where their Q is not representative of their spectral type (for example, when noise leads to inflated estimates of Q). We perform a similar analysis for CHIRON, although we create only three templates so that we attain an acceptable S/N given the smaller number of observations available for coaddition. We compute the cross-correlation function as the weighted sum: å å å = + + + + + r a b w a w b w , 1j i i j i i j i i j i j i i i j 2 2)( ( ) ⎜ ⎟ ⎛ ⎝ ⎞ ⎠ where a is the observed flux, b is the template flux, and w are the variance weights (or wi= 0 for masked telluric or skyline features). This sum is evaluated jointly across the six echelle orders. Both a and b are blaze corrected, normalized, continuum subtracted, and oversampled by a factor of 32. Our code also includes the ability to broaden b rotationally to analyze rapidly rotating stars, but there are no such stars in this study due to our Hα activity cut. The errors used to calculate w consider photon noise and read noise in a, and are scaled based on the blaze correction. Lastly, we determine the radial velocity shift by fitting a Lorentzian to the cross-correlation peak. 3.2. Uncertainties We calculate theoretical radial velocity uncertainties using the equation derived in Bouchy et al. (2001): å d l l = ¶ ¶c b w 1 , 2 i i i i i RV 2 2( ) ( ) where b is once again the template flux and w are the variance weights. In the photon-noise limit, this equation simplifies to δRV= c/(Q× S/N). Alternatively, we can estimate the radial velocity uncertainty directly from the cross-correlation function using the equation from Zucker (2003): d = -  - - c N r r r r1 , 3RV eff max max max 2 max 2 1 ( )⎜ ⎟ ⎛ ⎝ ⎞ ⎠ where we have replaced N with º å åN w wi i i ieff 2 2( ) to account for our error weighting. In this equation, rmax denotes the cross-correlation peak and r max represents its second derivative. Generally, we find good agreement between these two uncertainty estimators, although they differ when template mismatch is a significant source of uncertainty (e.g., in the high-S/N limit or when there is substantial rotational broad- ening, although the latter is not relevant for the sample discussed here). We make the conservative choice to always adopt the larger of the two. To validate our uncertainties, we also compute the cross- correlation function for each of the six echelle orders individually and compare the resultant radial velocities using the chi-squared estimator: åc = - = w v v , 4 k k k 2 1 6 rad, rad 2( ) ( ) where the variance weights ( d=w 1k k 2) are determined using the above uncertainty calculations for each order. For both TRES and CHIRON, the resulting distribution of χ2 across all observations shows good agreement with a chi-squared 3 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. distribution with five degrees of freedom, as we would expect for properly estimated uncertainties. An independent source of uncertainty comes from the barycentric correction, which ideally would be calculated at the photon-weighted midpoint of the observation. As we lack information on the temporal flux distribution over an exposure, we adopt the geometric midpoint as the observation time. This approximation can produce a systematic error of up to 2 m s−1 per minute of difference between the geometric and photon- weighted midpoints, as shown in Tronsgaard et al. (2019; see their Equation (8)). That work found that the offset between these midpoints is typically around 5% of the exposure length. For completeness, we therefore add a radial velocity uncer- tainty term in quadrature corresponding to a 5% offset to the midpoint time; however, we find that this contribution is ultimately negligible in the total error budget. We note that our uncertainty estimates thus far do not account for the long-term instability of the spectrograph. Over the observation campaign, one zero-point offset occurred for CHIRON and two for TRES due to hardware and software changes to the instrument. To determine the amplitudes of these offsets, we create an ensemble of all our observations from each spectrograph, subtracting the error-weighted mean radial velocity of each star to put the observations on a common zero-point. We then use these ensembles to measure the amplitude of the radial velocity discontinuities and apply a correction to subsequent measurements. For CHIRON, this offset is +50 m s−1 at BJD= 2,458,840 days. For TRES, these offsets are +45 m s−1 at BJD= 2,458,700 days and −20 m s−1 at BJD= 2,459,218 days. To evaluate the stability of each spectrograph outside of these events, we consider the standard deviation of the most precise observations—namely, observations with uncertainty estimates between 5 and 18 m s−1. If our observations were unaffected by a noise floor, we would expect the standard deviation to fall somewhere within this 5–18 m s−1 range. Note that the delta degrees of freedom (ddof) in this calculation is not 1; this would underestimate the standard deviation, as we have subtracted the error-weighted mean of each star. The ddof is also not equal to the number of stars; this would overestimate the standard deviation, as all observations are used to inform the error-weighted means, not just observations with small estimated uncertainties. We make a more reasonable estimate of the ddof by assuming that each star contributes ∑wj/∑wi, where wj are the variance weights of the observations with estimated uncertainties below 18 m s−1 and wi are the variance weights of all observations. The maximum value of this expression is 1, which occurs when the error-weighted mean radial velocity is fully informed by observations with small estimated uncertainties. For CHIRON, our calculation includes 137 observations, has ddof = 47.4, and results in a standard deviation of 20 m s−1. For TRES, we have 48 observations with small estimated uncertainties, ddof = 16.2, and a standard deviation of 21 m s−1. As these results are greater than 18 m s−1, it appears that instrumental instability is indeed setting a noise floor. These results are consistent with Winters et al. (2020), who found typical rms velocity residuals of 20 m s−1 using orbital solutions for bright, slowly rotating low-mass M dwarf binaries observed by TRES. As uncertainties below 20 m s−1 may therefore be underestimated due to instrumental instability, we do not allow our estimates to be smaller than this floor. Our radial velocity measurements and uncertainties for all 200 stars are available in a machine-readable format, with the format of this file shown in Table 1. 4. Data Analysis 4.1. Identification and Follow Up of Candidate Variables We use the metric P(χ2) to evaluate whether each radial velocity time series is consistent with an unvarying model given the uncertainties determined in the previous section. In this context, the chi-squared estimator is given by: åc d = - á ñ = v v , 5 i i i 2 1 4 rad, rad 2 RV, 2 ( ) ( ) with Nobs− 1= 3 degrees of freedom. 〈vrad〉 denotes the error- weighted mean of the radial velocity time series. We flag a signal as significant if the variability is inconsistent with the null hypothesis with 99% confidence (P(χ2)< 1%). In other words, we are searching for statistically significant excess radial velocity jitter; if such jitter is detected, further follow up is necessary to verify that this jitter is due to a planet and not an astrophysical or statistical false positive. Given our sample size of 200 stars, we expect an average of two statistical false positives due to random chance. We conducted a preliminary analysis of our data in early 2021, from which we identified two stars—LHS 2899 and G 125-34— as candidate variables based on this P(χ2)< 1% cut. Based on the significance of the variability in the initial four observations, we proceeded to collect an additional 41 observations of LHS 2899 and 46 observations of G 125-34 with TRES between 2021 April and 2022 May. At the time of the preliminary analysis, we had yet to obtain a fourth observation for some stars in the sample; our follow up of LHS 2899 and G 125-34 therefore occurred concurrently with our main observation campaign, which was completed on 2022 May 11. When analyzing Table 1 First Five Lines of the Online, Machine-readable Table Listing our Radial Velocity (RV) Measurements and Their Uncertainties Name Inst BJD −2,457,640 (day) Relative RV (m s−1) RV Error (m s−1) P(χ2) 1 2 3 4 1 2 3 4 1 2 3 4 GJ 1001 C 689.8474 1067.8194 1083.7259 1545.6148 28 6 −17 −16 20 33 22 20 0.343 GJ 1002 T 293.9686 466.6685 469.5924 1049.9704 18 −8 8 −24 29 98 31 29 0.761 LEP 0011+5908 T 122.6580 476.6877 1102.8183 1856.7702 4 −6 –28 28 21 25 36 35 0.723 GJ 12 T 34.7181 280.9609 1014.9527 1828.8724 36 13 −33 −24 35 29 40 31 0.468 GJ 15B T 1.9447 301.9763 1009.9604 1851.8027 −26 −16 5 62 20 26 29 27 0.063 Note. In the instrument column, T denotes TRES and C denotes CHIRON. (This table is available in its entirety in machine-readable form.) 4 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. Table 2 Stellar Properties and Radial Velocity Variability for Our 200 Stars Name 2MASS ID M* L* P(χ2) Name 2MASS ID M* L* P(χ2) (Me) (Le) (Me) (Le) GJ 1001 00043643-4044020 0.262 0.0079 0.343 LHS 2385 11163766-2757186 0.186 0.0045 0.013 GJ 1002 00064325-0732147 0.115 0.0015 0.761 LHS 2395 11193058+4641437 0.112 0.0014 0.547 LEP 0011+5908 00113182+5908400 0.107 0.0012 0.723 LHS 2415 11285624+1010395 0.286 0.0091 0.929 GJ 12 00154919+1333218 0.249 0.0075 0.468 LHS 306 11310835-1457201 0.157 0.0035 0.078 GJ 15B 00182549+4401376 0.157 0.0034 0.063 SCR 1138-7721 11381671-7721484 0.118 0.0017 0.291 LHS 112 00202922+3305081 0.119 0.0016 0.706 SIP 1141-3624 11412152-3624346 0.173 0.0041 0.322 GJ 1013 00313539-0552115 0.275 0.0088 0.250 GJ 442B 11463269-4029476 0.164 0.0037 0.055 L 291-115 00331349-4733165 0.126 0.0020 0.667 GJ 445 11474143+7841283 0.252 0.0076 0.495 GJ 1014 00355557+1028352 0.132 0.0024 0.022 GJ 447 11474440+0048164 0.173 0.0041 0.593 LHS 1134 00432603-4117337 0.210 0.0057 0.175 GJ 1151 11505787+4822395 0.164 0.0038 0.122 LHS 1140 00445930-1516166 0.179 0.0044 0.619 L 758-107B 12111697-1958213 0.272 0.0085 0.577 GDR 20049+6518 00492565+6518038 0.140 0.0028 0.609 GJ 465 12245243-1814303 0.274 0.0092 0.480 GJ 1025 01005643-0426561 0.198 0.0051 0.763 GJ 1158 12293453-5559371 0.233 0.0066 0.845 GJ 1028 01045368-1807292 0.136 0.0025 0.683 LHS 337 12384914-3822527 0.152 0.0033 0.712 GJ 1031 01081826-2848207 0.207 0.0055 0.478 LHS 2597 12393641-2658111 0.114 0.0015 0.621 GJ 1035 01195227+8409327 0.155 0.0034 0.686 GJ 480.1 12404633-4333595 0.185 0.0047 0.737 GJ 61B 01365042+4123325 0.187 0.0047 0.166 LHS 2608 12421964-7138202 0.242 0.0071 0.395 LP 991-84 01392170-3936088 0.133 0.0023 0.449 LHS 2674a 13065025+3050549 0.133 0.0023 0.384 LHS 5045 01525159-4805413 0.217 0.0061 0.611 LHS 2718 13200391-3524437 0.259 0.0079 0.151 L 173-19 02003830-5558047 0.275 0.0086 0.461 LHS 350 13225673+2428034 0.265 0.0080 0.442 LHS 1326 02021620+1020136 0.112 0.0013 0.092 GJ 1171 13303106+1909340 0.146 0.0031 0.728 LHS 1339 02054859-3010361 0.206 0.0057 0.154 LHS 2784 13424328+3317255 0.281 0.0088 0.203 GJ 105B 02361535+0652191 0.263 0.0079 0.035 LP 911-56 13464607-3149258 0.104 0.0009 0.400 GJ 1050 02395066-3407557 0.287 0.0097 0.620 GJ 1179A 13481341+2336486 0.122 0.0019 0.807 SCR 0246-7024 02460224-7024062 0.137 0.0026 0.675 LTT 5437 13571306-2922252 0.279 0.0091 0.101 LHS 1443 02463486+1625115 0.101 0.0009 0.724 SSS 1358-3938 13580529-3937545 0.129 0.0023 0.713 LP 831-1 02543950-2215584 0.246 0.0074 0.540 LHS 2830 13581392+1234438 0.220 0.0061 0.780 LHS 1481 02581021-1253066 0.184 0.0048 0.731 G 165-58 14155637+3616368 0.241 0.0071 0.351 LTT 1445A 03015142-1635356 0.258 0.0080 0.956 GJ 545 14200739-0937127 0.263 0.0079 0.036 LHS 1490 03020638-3950516 0.111 0.0014 0.993 LHS 2899 14211512-0107199 0.237 0.0067 0.030 GJ 1055 03090015+1001257 0.133 0.0024 0.095 LEP 1422-7023 14221943-7023371 0.121 0.0019 0.541 GJ 1053 03105861+7346189 0.128 0.0023 0.028 LEP 1455+3006 14551146+3006454 0.170 0.0040 0.914 GJ 1057 03132299+0446293 0.160 0.0035 0.632 GJ 2112 15221293-2749436 0.180 0.0043 0.356 LHS 1516 03141241+2840411 0.108 0.0012 0.640 GJ 585 15235112+1727569 0.171 0.0041 0.560 GJ 1059 03230175+4200269 0.124 0.0021 0.419 GJ 589B 15352039+1743045 0.129 0.0023 0.586 LHS 176 03353849-0829223 0.119 0.0017 0.725 GJ 589A 15352059+1742470 0.296 0.0103 0.961 GJ 1061 03355969-4430453 0.123 0.0019 0.946 GJ 590 15363450-3754223 0.211 0.0056 0.460 L 228-92 03385590-5234107 0.146 0.0031 0.257 GJ 1194A 15400352+4329396 0.295 0.0103 0.486 LHS 1593 03472091+0841464 0.134 0.0025 0.283 GJ 1194B 15400374+4329355 0.204 0.0050 0.962 GJ 1065 03504432-0605400 0.198 0.0051 0.614 GJ 609 16025098+2035218 0.250 0.0074 0.727 LP 357-56 03544620+2416246 0.116 0.0013 0.746 GJ 611B 16045093+3909359 0.145 0.0029 0.115 2MA0406-0534 04060688-0534444 0.224 0.0061 0.164 GJ 618B 16200321-3731485 0.164 0.0034 0.079 LHS 1629 04063732+7916012 0.134 0.0024 0.242 LHS 3241 16463154+3434554 0.108 0.0011 0.928 GJ 1068 04102815-5336078 0.129 0.0023 0.597 LP 154-205 16475517-6509116 0.168 0.0039 0.355 GJ 1072 04505083+2207224 0.139 0.0026 0.499 GJ 643D 16552527-0819207 0.210 0.0056 0.226 GJ 1073 04523448+4042255 0.212 0.0057 0.935 LHS 3262 17032384+5124219 0.180 0.0044 0.641 LHS 1723 05015746-0656459 0.166 0.0039 0.931 GJ 1214A 17151894+0457496 0.178 0.0042 0.828 LHS 1731 05032009-1722245 0.290 0.0097 0.798 GJ 1220 17311725+8205198 0.158 0.0035 0.494 UPM 0505+4414 05050591+4414037 0.145 0.0030 0.630 LHS 3324 17460465+2439049 0.278 0.0092 0.919 G 86-28 05103956+2946479 0.261 0.0082 0.858 GJ 693 17463427-5719081 0.280 0.0092 0.413 LEHPM 2-1009 05273058-5129158 0.129 0.0022 0.195 BARNARDS 17574849+0441405 0.155 0.0033 0.168 GJ 203 05280015+0938382 0.231 0.0065 0.089 GJ 1223 18024624+3731048 0.139 0.0027 0.579 LHS 5108 05325194+3349474 0.202 0.0053 0.471 LP 449-10 18064856+1720472 0.196 0.0051 0.951 GJ 213 05420897+1229252 0.221 0.0061 0.243 G 140-51 18163154+0452456 0.174 0.0040 0.066 GJ 2045 05421271-0527567 0.122 0.0019 0.712 LHS 461B 18180345+3846359 0.165 0.0038 0.904 LEP 0556+1144 05565722+1144333 0.125 0.0020 0.597 GJ 712 18220671+0620376 0.294 0.0100 0.244 LHS 1805 06011106+5935508 0.275 0.0085 0.470 GJ 1227 18222719+6203025 0.162 0.0037 0.022 LHS 1809 06022918+4951561 0.134 0.0024 0.693 SCR 1841-4347 18410977-4347327 0.111 0.0013 0.398 GJ 1088 06105288-4324178 0.296 0.0097 0.088 GJ 1230B 18410981+2447195 0.195 0.0042 0.069 G 192-22 06140240+5140081 0.264 0.0083 0.667 LP 867-15 18421107-2328582 0.259 0.0081 0.262 LP 779-34 06151198-1626152 0.190 0.0049 0.067 GJ 725B 18424688+5937374 0.265 0.0084 0.470 L 308-57 06210665-4905379 0.172 0.0040 0.301 LHS 5341 18430697-5436481 0.240 0.0071 0.033 GJ 232 06244132+2325585 0.152 0.0032 0.482 G 184-31 18495449+1840295 0.162 0.0037 0.497 5 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. observations of all stars after data collection was completed, we found that the stability of the TRES zero-point worsened in 2021–2022, motivating us to augment our 20 m s−1 noise floor with a dynamic floor using the radial velocity jitter in the TRES standard stars over each observing run (S. Quinn, private communication). These standards are quiet, Sun-like stars that are known to have very low intrinsic radial velocity variation based on observations from more precise instruments. We use these standards to determine the rms scatter in each observing run, which we add to our uncertainties in quadrature. In theory, we should also be able to correct for zero-point offsets using these standards; however, they are Sun-like stars and analyzed in bluer orders than our M dwarf spectra, and we find that the offsets in the M dwarfs are not entirely commensurate with those seen in the standards. With this refinement to our uncertainty estimation, the P(χ2) in the initial four observations of LHS 2899 increased from <1% to 3%, no longer meeting our follow-up criterion. For the purposes of our statistical study, it is therefore not necessary to establish whether the variability of LHS 2899 is a planet or a false positive; however, for completeness we will nonetheless discuss it here. G 125-34 retained its P(χ2)< 1% designation and no other signals became significant with this change. P(χ2) values for all stars are given in Table 2. For both G 125-34 and LHS 2899, the significance of the candidate variability increased with the TRES follow-up observations, with a final P(χ2) = 4.3× 10−5 for G 125-34 and P(χ2) = 1.0× 10−5 for LHS 2899. A periodogram analysis yielded candidate periods for orbital solutions, although the precision and quantity of the data were insufficient to prove or disprove the presence of a planet definitively. The preferred planetary solutions were a 0.22MJ planet on a 77 day orbit for G 125-34 and a 0.70MJ planet on a 337 day orbit for LHS 2899. To reach definitive conclusions about the dispositions of these candidates, we obtained five observations of LHS 2899 and 13 observations of G 125-34 using the MAROON-X spectrograph (Seifahrt et al. 2018), an extreme precision radial velocity instrument on the 8.1 m Gemini-North telescope, over a two month interval. These observations were reduced by the Table 2 (Continued) Name 2MASS ID M* L* P(χ2) Name 2MASS ID M* L* P(χ2) (Me) (Le) (Me) (Le) SCR 0642-6707 06422703-6707193 0.110 0.0013 0.731 GJ 732A 18533991-3836442 0.289 0.0093 0.368 GJ 1092 06490542+3706533 0.177 0.0042 0.027 GJ 1232 19095098+1740074 0.189 0.0049 0.077 GJ 1093 06592868+1920577 0.123 0.0018 0.822 LEP 1916+8413 19162483+8413411 0.150 0.0031 0.256 G 107-48 07073776+4841138 0.163 0.0037 0.720 GJ 754.1B 19203346-0739435 0.259 0.0087 0.187 L 136-37 07205204-6210118 0.265 0.0083 0.946 GJ 754 19204795-4533283 0.175 0.0042 0.022 SCR 0736-3024 07365666-3024160 0.196 0.0051 0.535 LHS 475 19205439-8233170 0.275 0.0085 0.107 GJ 283B 07401922-1724449 0.101 0.0008 0.737 GJ 1235 19213867+2052028 0.194 0.0050 0.084 LHS 1950 07515138+0532572 0.154 0.0034 0.255 GJ 1236 19220206+0702310 0.223 0.0064 0.066 GJ 1103 07515465-0000117 0.192 0.0049 0.176 GJ 1238 19241634+7533121 0.121 0.0018 0.073 GJ 1105 07581269+4118134 0.284 0.0090 0.653 G 125-34 19484080+3555178 0.237 0.0067 0.008 GJ 299 08115757+0846220 0.138 0.0027 0.428 GJ 770C 19542064-2356398 0.166 0.0036 0.719 GJ 300 08124088-2133056 0.282 0.0091 0.117 GJ 1248 20035098+0559440 0.267 0.0090 0.332 LHS 2025 08313011+7303459 0.279 0.0088 0.620 GJ 774B 20040195-6535586 0.220 0.0062 0.858 GJ 2070 08342587-0108391 0.246 0.0074 0.103 GJ 1253 20260528+5834224 0.158 0.0034 0.321 LEP 0840+3127 08401597+3127068 0.299 0.0098 0.130 GJ 1251 20280382-7640164 0.169 0.0039 0.979 LEP 0844-4805 08443891-4805218 0.200 0.0053 0.148 GJ 1256 20403364+1529572 0.189 0.0048 0.096 GJ 324B 08524084+2818589 0.278 0.0089 0.957 LP 816-60 20523304-1658289 0.238 0.0069 0.743 LHS 2088 08595604+7257364 0.158 0.0035 0.573 LHS 3593 20533304+1037020 0.180 0.0044 0.014 LP 60-179 09025284+6803464 0.265 0.0081 0.038 GJ 810B 20553706-1403545 0.140 0.0028 0.078 GJ 1123 09170532-7749233 0.224 0.0063 0.686 GJ 2151 21031390-5657479 0.242 0.0071 0.751 LEP 0921-0219 09214812-0219433 0.272 0.0090 0.679 LEP 2124+4003 21243234+4003599 0.130 0.0022 0.660 GJ 359 09410199+2201291 0.145 0.0030 0.782 LHS 510 21304763-4042290 0.205 0.0053 0.445 GJ 1128 09424635-6853060 0.176 0.0043 0.258 WT 795 21362532-4401005 0.197 0.0052 0.162 LHS 5156 09424960-6337560 0.210 0.0057 0.788 LHS 512 21384369-3339555 0.280 0.0088 0.075 LHS 272 09434633-1747066 0.154 0.0036 0.478 LEP 2146+3813 21462206+3813047 0.178 0.0043 0.093 GJ 1129 09444731-1812489 0.299 0.0099 0.318 LP 698-42 21471744-0444406 0.157 0.0035 0.539 LHS 2224 10092996+5117197 0.181 0.0044 0.831 LHS 516 21565513-0154100 0.144 0.0030 0.060 GJ 1132 10145184-4709244 0.192 0.0049 0.765 LHS 3746 22022935-3704512 0.251 0.0074 0.275 LEP 1015+1729 10155390+1729271 0.287 0.0091 0.367 GJ 1265 22134277-1741081 0.168 0.0040 0.699 LEHPM 2-2758 10384782-8632441 0.252 0.0075 0.097 GJ 1270 22294885+4128479 0.259 0.0078 0.381 GJ 1134 10413809+3736397 0.205 0.0054 0.408 L 645-74B 22382544-2921244 0.254 0.0076 0.066 LHS 288 10442131-6112384 0.106 0.0012 0.959 LHS 3844 22415815-6910089 0.151 0.0031 0.496 LHS 2303 10442927-1838063 0.125 0.0021 0.853 GJ 1277 22562466-6003490 0.172 0.0040 0.573 LHS 2310 10473868-7927458 0.251 0.0075 0.605 LEHPM 2-2163 23303802-8455189 0.138 0.0027 0.240 GJ 402 10505201+0648292 0.282 0.0091 0.056 GJ 1286 23351050-0223214 0.118 0.0017 0.160 GJ 403 10520440+1359509 0.278 0.0087 0.164 LHS 547 23365227-3628518 0.171 0.0040 0.968 LHS 296 11011965+0300171 0.164 0.0037 0.692 GJ 905 23415498+4410407 0.140 0.0026 0.125 (This table is available in machine-readable form.) 6 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. MAROON-X team using the SERVAL pipeline (Zechmeister et al. 2018) and are shown in Figure 2. The final observation of LHS 2899 and the final three observations of G 125-34 were taken in a different MAROON-X observing run from the prior observations, with a zero-point offset of −1.5± 1.0 m s−1 for the blue arm and +1.5± 1.0 m s−1 for the red arm; the uncertainty in this offset is responsible for the larger error bars for these later observations. The radial velocity time series for both stars are flat at the 1 m s−1 level, definitively ruling out all orbital solutions consistent with the TRES data. LHS 2899 and G 125-34 are statistical false positives, with their significance in the TRES follow-up observations likely the result of non- Gaussian outliers. There are no giant planet detections in our 200 star sample. 4.2. Occurrence Rate Constraints For a given star, j, the probability that we do not detect a planet is Pnull(μ)j= 1− μ× Cj, where μ is the planetary occurrence rate in a given bin and C is the survey completeness in that bin. The probability that we do not detect any planets around any of our stars is then the product: m m= -P C1 . 6 j jnull ( ) ( ) ( ) To determine a 95% confidence limit on the occurrence rate, we numerically solve for μ given that Pnull(μ)= 0.05. While we use this form of the equation to generate our Figure 3, note that in the limit where the binomial approximation m m- » - C1 1C jj( ) applies (i.e., where μ< 1 and μCj= 1, which is appropriate for this study), this equation can be rewritten as m m= -P 1 N null eff( ) ( ) , where Neff, the effective sample size, is given by Neff=∑jCj. This form is a convenient simplification, as it only requires the average completeness instead of the completeness for each star in the sample, and it motivates our use of Neff as the color bar axis in this figure. We conduct an injection and recovery analysis to determine C as a function of MP sin i and orbital period. We derive our occurrence rate constraints under the assumption of circular orbits, following the precedent of past works (e.g., Howard et al. 2010b; Mayor et al. 2011). This assumption has been shown to be reasonable for e< 0.5 (Endl et al. 2002; Cumming & Dragomir 2010). While many eccentric cold Jupiters meet this criterion (Buchhave et al. 2018), more highly eccentric giant planets are known (e.g., Robertson et al. 2012; Moutou et al. 2015). Notably, giant planet formation via gravitational instability may produce large orbital eccentricities (Jennings & Chiang 2021). We consider the limitations of the circular orbit assumption in the following section. We consider 100 periods spaced logarithmically between 10−1 and 105 days and 100 values of MP sin i spaced logarithmically between 10−1 and 101 MJ. For each mass and period, we generate 100 artificial radial velocity time series for each star using the observation times and radial velocity uncertainties of the real data, drawing phases from a random uniform distribution. For each hypothetical planet, every star is assigned a completeness C between 0 and 1, indicating the fraction of trials in which the simulated observations were variable at the P(χ2)< 1% level. The sample size Neff is the sum of these fractions. This completeness assumes that we would gather sufficient MAROON-X follow-up observations to verify that any signal flagged at P(χ2)< 1% significance is a true planet. Our injection and recovery results are shown in Figure 3, which also includes the period axis recast in terms of the zero- albedo equilibrium temperature, ps=T L a16eq 2 1 4[ ( )] , and instellation, s=S T4 eq 4 . This transformation requires the masses and luminosities of each star; we adopt the masses from Winters et al. (2021), which are based on the K-band relation from Benedict et al. (2016), and estimate the bolometric luminosities from the photometry collated in Winters et al. (2021) and distances from Gaia parallaxes (Gaia Collaboration et al. 2018, 2021; Lindegren et al. 2021). In Figure 2. Radial velocity time series for the two candidate variables. The left panels show LHS 2899 and the right panels show G 125-34, while the upper panels show TRES observations and the lower panels show MAROON-X observations. The lower panels cover a much smaller range in time and radial velocity; the overlap is indicated by the red rectangles. Radial velocities from the blue arm of MAROON-X are shown in blue with thick crosses and from the red arm in red with thin crosses. The red arm achieves uncertainties as low as 70 cm s−1. The lack of radial velocity variability in the extreme precision MAROON-X observations refutes all possible orbital solutions consistent with the variability in the TRES data. 7 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. particular, we consider the bolometric corrections from both Pecaut & Mamajek (2013) and Mann et al. (2015), adopting the average of the luminosities calculated from these two methods. These masses and luminosities are included in Table 2. There are two regimes in Figure 3, with a transition around Teq≈ 50 K. At short periods, the sensitivity is determined by the radial velocity semiamplitude of the orbit. The slope of the transition region between detectable and undetectable planets represents the interplay between the radial velocity semiam- plitude and typical radial velocity uncertainties. At long periods, the sensitivity drops off rapidly due to the finite length of the observing campaign. 4.3. Eccentric Orbits To quantify the impact of the circular orbit assumption, we repeat the analysis of the previous section but under the assumption that all planets have e = 0.5 in one trial or e = 0.8 in another. For each simulated planet, we draw the argument of periastron from a random uniform distribution. Figure 4 shows the change in sensitivities compared to the circular orbits case Figure 4. The difference in survey sensitivity between the assumption of circular orbits and the assumption that all planets have e = 0.5 (left panel) or e = 0.8 (right panel). This difference is given in terms of ΔNeff, the change in the number of stars around which we could detect the planet, with a positive value indicating an increase in the effective number of stars for the eccentric case over the circular case. Given that our total sample contains 200 stars, the circular orbit assumption is generally appropriate for most regions of parameter space; the largest percent decrease in effective sample size is only 13% and 30% for the e = 0.5 and e = 0.8 assumptions, respectively. There are also previously inaccessible regions of parameter space to which we gain sensitivity when considering eccentric planets (in particular, the regime of super-Jupiters on wide orbits). Figure 3. The completeness of our survey, annotated with 95% confidence upper limits on the occurrence rate of giant planets around low-mass M dwarfs as a function of planetary mass and period/instellation/zero-albedo equilibrium temperature under the assumption of circular orbits. In regions where we are highly sensitive (i.e., short periods and large masses), we constrain the occurrence rate to <1.5% with 95% confidence. The color bar indicates Neff, the effective number of stars around which we are sensitive to the hypothetical planet. The arrows in the right-hand plot show instellations equivalent to that of the water snow line (Podolak & Zucker 2004; white), Jupiter (brown), and Neptune (blue). We are sensitive to MP sin i = 1 MJ planets at the water snow line for 83% of stars (occurrence rate < 1.8% with 95% confidence) and at Jupiter-like instellations for 70% of stars (occurrence rate < 2.1%). We remain sensitive to MP sin i = 1 MJ planets at Neptune-like instellations around 19% of stars (occurrence rate < 7.7%). 8 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. in terms of ΔNeff, the change in the number of stars around which the planet is detectable. We find that ΔNeff is generally small; the sample size is never decreased by more than 15 stars in the e = 0.5 trial and 39 stars in the e = 0.8 trial. There are other regions of parameter space in which the sample size is increased by similar amounts. Moreover, the percent decrease in effective sample size does not exceed 13% or 30%, respectively. Even in the limit where all giant planets are highly eccentric, the circular orbit assumption will produce reasonable occurrence rate constraints. Compared to a planet on a circular orbit, an eccentric planet achieves a higher radial velocity semiamplitude but spends more time at relative radial velocities near zero. As we approach the sensitivity limit from the detectable side, the decreased likelihood of observing the eccentric orbit in a peak/ trough renders a previously detectable planet undetectable. As we approach the sensitivity limit from the undetectable side, the increased amplitude of the peaks/troughs renders a previously undetectable planet detectable. 4.4. Summary of Analysis To summarize the above reduction and analysis, we do not detect any giant planets in our sample of 200 low-mass, inactive M dwarfs. More specifically, our four measurements for each star do not vary in excess of our P(χ2) = 1% detection limit for 198 stars, and we initially flagged the remaining two stars as candidate radial velocity variables. We collected additional observations of these two candidates with TRES, but were unable to establish the provenance of the signals conclusively. We then obtained observations of the two stars using MAROON-X. The MAROON-X radial velocities show no variation at the 1 m s−1 level over a two month interval, indicating that the candidate variability from the TRES observations are statistical false positives. After refuting these candidates, none of our stars exhibit radial velocity variability that exceeds our detection threshold. Nevertheless, our injection and recovery analysis indicates that we are very sensitive to a variety of giant planets (Figure 3). We can therefore place strong upper limits on the occurrence rate of these planets, as we discuss in the following section. The median mass of stars in our sample is 0.18Me, with a median radial velocity precision of 29 m s−1 and a median observation baseline of 3.1 yr. 5. Discussion 5.1. Occurrence of Warm Jupiters As shown in Figure 3, we have nearly complete sensitivity to MP sin i> 1MJ planets out to the water snow line. In regions of complete sensitivity, we place a 68% confidence upper limit of 0.57% and a 95% confidence upper limit of 1.5%. Jupiter- and super-Jupiter-mass planets interior to the snow line of low-mass M dwarfs are therefore exceedingly rare. How does this compare to studies of all types of M dwarfs? The Bonfils et al. (2013) sample contains one planet in this regime: Gliese 876 b (Marcy et al. 1998; Delfosse et al. 1998). While that work published their survey sensitivity in specific bins that differ from the one currently under discussion (their Table 11), inspection of their Figure 15 indicates that they are nearly complete across this parameter range, with Neff equal to roughly 96 stars. If the true occurrence rate of such planets around all M dwarfs was equal to our 68% confidence upper limit of 0.57%, binomial probability yields a 32% chance that Bonfils et al. (2013) would detect one planet in this bin, with a 58% chance of detecting zero and a 10% chance of detecting two or more planets. Our results are therefore in reasonable agreement with Bonfils et al. (2013) without invoking a decrease in warm Jupiter occurrence around low-mass M dwarfs relative to all M dwarfs, although our occurrence constraints are tighter given that our sample is twice as large. We also note that Gliese 876 has a mass of 0.37Me; i.e., while it is more massive than the M dwarfs in our sample, it is not a particularly massive M dwarf. That said, a decrease in warm Jupiter occurrence around low-mass M dwarfs relative to all M dwarfs is also consistent with our data. Other constraints on the occurrence rate of giant planets around early M dwarfs are available from transit surveys, although they are limited to hot Jupiters and their bins are not as directly comparable to ours due to the observable of these studies being radius, not mass. Gan et al. (2023) found an occurrence rate of 0.27± 0.09% for hot Jupiters around early (0.45�M*� 0.65) M dwarfs from TESS, with this statistic defined over the ranges 7 R⊕� RP� 2 RJ and 0.8� P� 10 days. A similar occurrence rate of such planets around our low-mass M dwarfs is fully consistent with our null detection. 5.2. Occurrence of Giant Planets at the Snow Line Planet formation theories predict an enhancement in giant planet occurrence at the water snow line (Pollack et al. 1996; Ida & Lin 2008; Morbidelli et al. 2015), a phenomenon that has been observed around Sun-like stars; specifically, Fulton et al. (2021) found that giant planet occurrence in the California Legacy Survey of FGKM stars follows a broken power law, with a peak that approximately coincides with the location of the snow line and which represents a factor of 4 increase in occurrence relative to giant planets interior to the snow line. While this sample does contain a small number of M dwarfs, it is dominated by FGK stars, with 83% of the stars in the sample having stellar masses above 0.6Me and 98% having stellar masses above 0.3Me (see Figure 4 of Rosenthal et al. 2021). As an aside, we note that Fulton et al. (2021) do not make specific statements about the occurrence of giant planets at the snow line of their M dwarfs. In their Figure 7, they do present occurrence rates as a function of stellar mass for giant plants that are more massive than Saturn and that orbit between 1–5 au, including a bin for 0.3–0.5Me M dwarfs. In this bin, they find an occurrence rate of roughly 5%, with the 68% confidence interval ranging from 5% to 12%. However, this 1–5 au bin represents much lower instellations for M dwarfs than for Sun-like stars. Using the scaling relation asnow= 2.7(M*/Me) 1.14 au from Childs et al. (2022; adapted from Mulders et al. 2015), the snow line of a 0.4Me star occurs at 0.95 au and decreases further to 0.68 au for a 0.3Me star. Therefore, while the 1–5 au bin is centered on the snow line for Sun-like stars, it does not represent the occurrence rate of giant planets at the snow line of M dwarfs. Rather, it represents the occurrence rate of giant planets on wider orbits. To investigate the occurrence rate of giant planets at the snow line of low-mass M dwarfs in our sample, we consider a bin corresponding to zero-albedo equilibrium temperatures of 100 K < Teq< 150 K, which we subdivide into mass categories of sub-Jupiters (0.3MJ 1MJ planet detections in our study is not necessarily in tension with their occurrence rate. However, those authors note that their value is actually more like a lower limit on the occurrence rate, as they use lower limits in the P= 102–103 day range where microlensing sensitivity declines, and they claim their findings are consistent with the nearly twice as large measurement of this occurrence rate from Montet et al. (2014), another radial velocity survey. As these studies focus on more massive M dwarfs (recall that the microlensing lens distribution is centered at M* = 0.5Me, while the mean stellar mass in the Bonfils et al. (2013) sample is 0.35Me), our lack of detections of any giant planets beyond the snow line may be indicative of a decrease in cold Jupiter occurrence around low-mass M dwarfs relative to all M dwarfs. It is difficult to compare our results directly with Montet et al. (2014), as they report their occurrence rate only in the bin 1MJ1MJ planets around low-mass M dwarfs at very wide orbital separations from direct imaging (Gaidos et al. 2022) and disk studies (Curone et al. 2022). These results hint that giant planet occurrence may peak at lower instellations around low-mass M dwarfs as compared to Sun-like stars. Such a distribution could indicate a pathway for giant planet formation governed by processes unrelated to the water snow line, such as disk instability (Boss 2006; Mercer & Stamatellos 2020). Other possible mechanisms to move giant planets to wide orbits include scattering by planet–planet interactions (e.g., Rasio & Ford 1996) or outward migration in resonance (e.g., Crida et al. 2009). 5.5. Notable Systems For Sun-like stars, Rosenthal et al. (2022) found that 41% of stars with a close-in, small planet also hosted an outer giant, in contrast to a 17.6% occurrence of outer giants overall. We are therefore particularly attentive to the sensitivity curves for the ten stars in our sample with published small planets: GJ 1214 (Charbonneau et al. 2009), GJ 1132 (Berta-Thompson et al. 2015; Bonfils et al. 2018), LHS 1140 (Dittmann et al. 2017; Ment et al. 2019), GJ 1265 & LHS 350 (Luque et al. 2018), LHS 3844 (Vanderspek et al. 2019), LTT 1445A (Winters et al. 2019, 2022; Lavie et al. 2023), GJ 1061 (Dreizler et al. 2020), GJ 1057 (Bauer et al. 2020), and GJ 585 (Harakawa et al. 2022). While we do not have the radial velocity sensitivity to recover these small planets, we can provide constraints on the existence of further out giant planets to inform our under- standing of exoplanetary system architectures. In Figure 5, we show our sensitivity to giant planets around each of these small-planet hosts. For all stars, we are likely to detect a planet that is Jupiter-like in mass and instellation, with our sensitivity varying from just under 50% for LHS 350 to nearly 100% for GJ 1061. As we only have four observations of each star, the sensitivity curves are bumpier than the smooth results of Figure 3; for a given star, there are specific periods in which a planet could feasibly evade detection, although these hiding spots are averaged out when we consider the sample as a whole. For the purposes of Figure 5, we have rerun our analysis with 1000 samples in mass and period to allow the nonhomogeneity of the sensitivity curves to be more readily appreciated. While we cannot definitively rule out the existence of a giant planet beyond the snow line for any individual system, Jupiter-analog companions to inner terrestrial planets —i.e., planetary system architectures like our own—cannot be commonplace for low-mass M dwarfs. If 41% of these stars had a planet that was Jupiter-like in mass and instellation (a percentage motivated by the outer giant companion occurrence rate around Sun-like stars from Rosenthal et al. 2022), there is a 98% chance we would have detected this planet around at least one of the ten stars. An abundance of lower-mass giant companions beyond the snow line (e.g., MP sin i � 0.3MJ) is not ruled out by our observations: if all ten stars had a 0.3MJ planet at the Jovian instellation, there is a 78% chance that we would have detected at least one, but this chance drops to 43% when we lower the incidence to 41%. 5.6. Implications for Terrestrial Planets What does a lack of outer Jovians imply for the inner terrestrial planets in these systems (notably, the only terrestrial planets amenable to atmospheric study for at least the next decade)? While simulations on this topic are beyond the scope of this work, one can look to the large body of literature discussing the impact of Jupiter on the evolution of our own solar system. Models such as Walsh et al. (2011) suggest that 11 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. the migration of Jupiter and Saturn led to the truncation of the planetesimal disk at 1 au, ultimately limiting the size of the terrestrial planets. Meanwhile, Izidoro et al. (2015) suggest that Jupiter acted as a dynamical barrier to the inward migration of gas giant cores, preventing them from migrating into the inner solar system from beyond the snow line and explaining why our solar system lacks a super-Earth (although note Bryan et al. 2019, who found that the presence of super-Earths correlates positively with the presence of an outer Jovian). Similarly, Bitsch et al. (2021) argue that a Jovian beyond the snow line can block the inward flow of water-rich pebbles, resulting in a drier inner stellar system. Systems without an outer Jovian may therefore have wetter (and potentially, larger) small planets; notably, Luque & Pallé (2022) recently identified a population of water worlds among the small planets that transit M dwarfs (although note Ment & Charbonneau 2023, who found that Figure 5. Our sensitivity to giant planets around the ten stars in our survey that are known to host a low-mass planet. The darkest blue line denotes a detection probability of 50%. The contours illustrate where our survey places 84% and 97.5% constraints on the existence of a planet. A hypothetical planet with the instellation and mass of Jupiter is indicated with a red X. Dashed lines show the locations of the known small planets. LHS 3844 b is located off the left edge of the plot. 12 The Astronomical Journal, 166:11 (14pp), 2023 July Pass et al. volatile-rich small planets are less common around mid-to-late M dwarfs). Giant planets are thought to also set the terrestrial water budget in our own solar system, with Raymond & Izidoro (2017) arguing that Jupiter and Saturn were responsible for delivering Earth’s small amount of water through planetesimal scattering. Childs et al. (2022) note another implication of a lack of outer Jovians: without such a planet, a stellar system is unlikely to have an asteroid belt or a mechanism of delivering asteroids to inner terrestrial planets, and these asteroid impacts may be necessary for the origin of life (e.g., Osinski et al. 2020). Using modeling from Childs et al. (2019), they further argue that lower-mass giant planets (specifically, they replaced Jupiter with a planet of mass 0.14MJ) are unable to sustain suitable asteroid bombardment; more massive giant planets are needed. In the case of Earth, large asteroid impacts are thought to be responsible for the production of a reducing atmosphere (Sinclair et al. 2020b), which ultimately led to the emergence of prebiotic chemistry (Benner et al. 2019). 6. Summary We present a null detection of giant planets in the volume- complete sample of 200 nearby, inactive 0.10–0.30Me M dwarfs. We place a 95% confidence upper limit of 1.5% (68% confidence limit of 0.57%) on the occurrence of MP sin i> 1MJ planets out to the water snow line (Teq> 150 K) around these low-mass M dwarfs. At the snow line (100 K < Teq< 150 K), we place 95% confidence upper limits of 1.5%, 1.7%, and 4.4% (68% confidence limits of 0.58%, 0.66%, and 1.7%) for 3MJ