TESS Discovery of an Ultra-short-period Planet around the Nearby M Dwarf LHS 3844

TESS observed LHS 3844 between 2018 July 25 and August 22, in the first of 26 sectors of the two-year survey. The star appeared in CCD 2 of Camera 3. The CCDs produce images every 2 s, which are summed on board the spacecraft into images with an effective exposure time of 30 minutes. In addition, 2 minute images are prepared for subarrays surrounding preselected target stars, which are chosen primarily for the ease of detecting transiting planets. LHS 3844 was prioritized for 2 minute observations on account of its brightness in the TESS bandpass (T = 11.877), small stellar radius, and relative isolation from nearby stars (Muirhead et al. 2018; Stassun et al. 2018). LHS 3844 will not be observed again in the TESS primary mission.

The 2 minute data consist of 11 by 11 pixel subarrays. They were reduced with the Science Processing Operations Center (SPOC) pipeline, originally developed for the Kepler mission at the NASA Ames Research Center (Jenkins 2015; Jenkins et al. 2016). For LHS 3844, the signal-to-noise ratio of the transit signals was 32.4, using the definition of Twicken et al. (2018). The 30 minute data were analyzed independently with the MIT Quick Look Pipeline (C. X. Huang et al. 2018, in preparation). A transit search with the Box Least Square algorithm (BLS; Kovács et al. 2002) led to a detection with a signal-to-noise ratio of 31.6, using the definition of Hartman & Bakos (2016).

For subsequent analysis, we used the 2 minute Pre-search Data Conditioning light curve from the SPOC pipeline (Stumpe et al. 2012), which was extracted from the photometric aperture depicted in the lower right panel of Figure 1. The resulting light curve is shown in the top panel of Figure 2. To filter out low-frequency variations, we fitted a basis spline to the light curve (excluding the transits and 3σ outliers) and divided the light curve by the best-fit spline. The result is shown in the second panel of Figure 2. The interruption in the middle of the time series occurred when the spacecraft was at perigee, when it reorients and downlinks the data. There was also a 2 day interval when the data were compromised by abnormally unstable spacecraft pointing. In addition, we omitted the data collected in the vicinity of "momentum dumps," when the thrusters are used to reduce the speed of the spacecraft reaction wheels. These lasted 10–15 minutes and took place every 2.5 days.

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LHS 3844 was observed by the ground-based MEarth-South telescope array as part of normal survey operations (Irwin et al. 2015; Dittmann et al. 2017b). A total of 1935 photometric observations were made between 2016 January 10 and 2018 August 25. No transits had been detected prior to the TESS detection, but when the data were revisited, a BLS search identified a signal with a period and amplitude consistent with the TESS signal (Figure 2). The MEarth data (Figure 3) also revealed the stellar rotation period to be 128 ± 24 days, based on the least-squares periodogram of Irwin et al. (2006) as implemented by Newton et al. (2016, 2018).⁴⁸

Additional ground-based transit observations were performed as part of the TESS Follow-up Observing Program (TFOP). A full transit was observed on UT 2018 September 06 in the I_C band, using the El Sauce Observatory Planewave CDK14 telescope located in El Sauce, Chile. Five more transits were observed in the Sloan i' band using telescopes at the Cerro Tololo International Observatory (CTIO) node of the Las Cumbres Observatory (LCO⁴⁹ ) robotic telescope network (Brown et al. 2013). The transit of UT 2018 September 08 was observed with a 0.4 m telescope, and the transits of UT 2018 September 08, 09, 10, and 16 were observed with a 1.0 m telescope. The data are shown in the lower panels of Figure 2. Together, they confirm the fading events are occurring and localize the source to within 2'' of LHS 3844.

We obtained optical spectra on UT 2018 June 18⁵⁰ and September 08 using the CTIO HIgh ResolutiON (CHIRON) spectrograph on the 1.5 m telescope of the Cerro Tololo Inter-American Observatory Small and Moderate Aperture Research Telescope System (Tokovinin et al. 2013). We used the image slicer mode, giving a resolution of about 80,000. The signal-to-noise ratio of each spectrum is about 7, and the spectral range is 411–877 nm. The first observation was a pair of 30 minute exposures centered at an orbital phase of 0.355. The second observation comprised three 30 minute exposures centered at phase 0.880. The data were analyzed as described by Winters et al. (2018b), using a spectrum of Barnard's Star as a template. The spectra show no evidence of additional lines from a stellar companion, no sign of rotational broadening, no detectable Hα emission, and no radial-velocity variation.

Additional spectroscopy was performed with the CORALIE spectrograph (Queloz et al. 2000; Pepe et al. 2017) on the Swiss Euler 1.2 m telescope at La Silla Observatory in Chile. Spectra were obtained on UT 2018 September 10 and 11, at phases 0.211 and 0.645, near the expected radial-velocity extrema. Radial-velocity calibration was performed with a Fabry–Pérot device. With exposure times of 45 and 60 minutes, the signal-to-noise ratio per pixel was about 3 in the vicinity of 600 nm. Cross-correlations were performed with a weighted M2 binary mask from which telluric and interstellar lines were removed (Pepe et al. 2002). Only a single peak was detected. The difference in radial velocities was 60 ± 110 ${\rm{m}}\,{{\rm{s}}}^{-1}$, i.e., not statistically significant.

To place an upper limit on the radial-velocity variation using both data sets (see Table 1), we fitted for the amplitude of a sinusoidal function with a period and phase specified by the TESS transit signal. The free parameters were the amplitude K, and two additive constants representing the zero-points of the CHIRON and CORALIE velocity scales. The result was $K=-{28}_{-60}^{+64}\ {\rm{m}}\,{{\rm{s}}}^{-1}$, which can be interpreted as a 3σ upper limit of 0.96 ${M}_{\mathrm{Jup}}$ on the mass of the transiting object.

Table 1.  Radial Velocities of LHS 3844

BJD	Orbital Phase	RV	${\sigma }_{\mathrm{RV}}$	Instrument
	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)
2458287.9183	0.33	−10.626	0.056	CHIRON
2458287.9393	0.375	−10.667	0.108	CHIRON
2458369.6266	0.833	−10.719	0.031	CHIRON
2458369.6476	0.878	−10.732	0.046	CHIRON
2458369.6686	0.924	−10.724	0.048	CHIRON
2458371.653268	0.211	−10.600	0.090	CORALIE
2458372.780028	0.645	−10.540	0.068	CORALIE

Note. The 100 ${\rm{m}}\,{{\rm{s}}}^{-1}$ difference between the average CHIRON and CORALIE velocities is due to differences in the instrumental zero-points, and is not indicative of velocity variation.

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Using an empirical relationship between mass and K_s-band absolute magnitude (Benedict et al. 2016), and the parallax from Data Release 2 of the Gaia mission (Gaia Collaboration et al. 2016, 2018; Lindegren et al. 2018), the mass of LHS 3844 is 0.151 ± 0.014 ${M}_{\odot }$. The uncertainty is dominated by the scatter in the mass–K_s relation. Based on this mass determination, and the empirical mass–radius relationship of Boyajian et al. (2012), the stellar radius is 0.188 ± 0.01 ${R}_{\odot }$. These results are consistent with the empirical relationship between radius and absolute K_s magnitude presented by Mann et al. (2015), which gives 0.189 ± 0.006 ${R}_{\odot }$. The bolometric luminosity is $(2.72\pm 0.4)\times {10}^{-3}$ ${L}_{\odot }$, based on the observed V and J magnitudes and the bolometric correction from Table 3 of Mann et al. (2015). Based on these determinations of R_⋆ and L_⋆, the Stefan–Boltzmann law gives an effective temperature of 3036 ± 77 K. The spectral type is M4.5 or M5, based on a comparison with MEarth survey stars of known spectral types on a color–magnitude diagram (Gaia G versus H − K_s).

As a check on the preceding calculations, we fitted stellar atmosphere models to the spectral energy distribution, based on the apparent magnitudes and the Gaia parallax, including the correction proposed by Stassun & Torres (2018). This yielded a luminosity of $(2.56\pm 0.4)\times {10}^{-3}$ ${L}_{\odot }$, an effective temperature of 2900 ± 75 K, and stellar radius of 0.201 ± 0.012 ${R}_{\odot }$. These values are all consistent with the stellar parameters derived above.

We jointly analyzed the light curves from TESS, MEarth, and TFOP, using the formalism of Mandel & Agol (2002) as implemented by Kreidberg (2015; batman). We assumed the orbit to be circular and used a quadratic limb-darkening law allowing the coefficients to be free. Because of the differing bandpasses of TESS, MEarth, and the TFOP instruments, each data set was allowed to have different values for the limb-darkening parameters. We imposed a prior constraint on the mean stellar density based on the results of Section 3.1. The model was evaluated with a 0.4 minute sampling and averaged as appropriate before comparing with the data. We used the emcee Markov Chain Monte Carlo code of Foreman-Mackey et al. (2013) to determine the posterior distributions for all the model parameters. The results are given in Table 2. Figure 2 shows the best-fitting model. The best-fit planet radii is 1.32 ± 0.02 ${R}_{\oplus }$ indicating that it is likely to be rocky (see, e.g., Rogers 2015, Wolfgang et al. 2016).

Table 2.  Stellar and Planet Parameters for LHS 3844

Parameter	Value	Source
Catalog information
R.A. (h:m:s)	22:41:59.089	Gaia DR2
Decl. (d:m:s)	−69:10:19.59	Gaia DR2
Epoch	2015.5	Gaia DR2
Parallax (mas)	67.155 ± 0.051	Gaia DR2
${\mu }_{{\rm{R}}.{\rm{A}}.}$ (mas yr−1)	334.357 ± 0.083	Gaia DR2
${\mu }_{\mathrm{Decl}.}$ (mas yr−1)	−726.974 ± 0.086	Gaia DR2
Gaia DR2 ID	6385548541499112448
TIC ID	410153553
LHS ID	3844
TOI ID	136
Photometric properties
TESS (mag)	11.877	TIC V7
Gaia (mag)	13.393	Gaia DR2
Gaia RP (mag)	12.052	Gaia DR2
Gaia BP (mag)	15.451	Gaia DR2
VJ (mag)	15.26 ± 0.03	RECONSa
RKC (mag)	13.74 ± 0.02	RECONSa
IKC (mag)	11.88 ± 0.02	RECONSa
J (mag)	10.046 ± 0.023	2MASS
H (mag)	9.477 ± 0.023	2MASS
Ks (mag)	9.145 ± 0.023	2MASS
Derived properties
${M}_{\star }$ (${M}_{\odot }$)	0.151 ± 0.014	Parallax +Benedict et al. (2016)b
${R}_{\star }$ (${R}_{\odot }$)	$0.189\pm 0.006$	Parallax +Mann et al. (2015)c
$\mathrm{log}{g}_{\star }$ (cgs)	5.06 ± 0.01	empirical relation + LCd
${L}_{\star }$ (${L}_{\odot }$)	0.00272 ± 0.0004	Mann et al. (2015)
${T}_{\mathrm{eff}\star }$ (K)e	3036 ± 77	3
MV (mag)	$14.39\pm 0.02$	Parallax
MK (mag)	$8.272\pm 0.015$	Parallax
Distance (pc)	$14.9\pm 0.01$	Parallax
${\rho }_{\star }$ (${\rm{g}}\,{\mathrm{cm}}^{-3}$)	$31.73\pm 0.39$	empirical relation + LCd
Light-curve parameters
P (days)	$0.46292913\pm 0.0000019$
Tc ($\mathrm{BJD}-2457000$)b	$1325.72558\pm 0.00025$
T14 (minutes)b	$31.27\pm 0.28$
${T}_{12}={T}_{34}$ (minutes)b	${3.73}_{-0.7}^{+0.4}$
$a/{R}_{\star }$	$7.109\pm 0.029$
${R}_{p}$/${R}_{\star }$	$0.0635\pm 0.0009$
$b\equiv a\cos i/{R}_{\star }$	$0.186\pm 0.064$
i (degree)	$88.50\pm 0.51$
Limb-darkening coefficients
c1, MEarth (linear term)	${0.15}_{-0.10}^{+0.16}$
c2, MEarth (quadratic term)	0.29 ± 0.20
${c}_{1},{TESS}$	${0.17}_{-0.11}^{+0.14}$
${c}_{2},{TESS}$	${0.26}_{-0.19}^{+0.22}$
${c}_{1},i$	${0.64}_{-0.14}^{+0.12}$
${c}_{2},i$	${0.18}_{-0.12}^{+0.18}$
Planetary parameters
${R}_{p}$ (${R}_{\oplus }$)	$1.303\pm 0.022$
a (au)	$0.00622\pm 0.00017$
${T}_{\mathrm{eq}}$ (K)	$805\pm 20$
$\langle {F}_{j}\rangle$ (109 $\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$)	$0.0954\pm 0.00070$

Notes.

^aThe optical photometry is from the RECONS survey, and was measured according to the procedures described in Jao et al. (2005) and Winters et al. (2015). ^bWe adopted the error bar based on the scatter in the empirical relations described by Benedict et al. (2016). ^cWe adopted the error bar based on the scatter in the empirical relations described by Mann et al. (2015). ^dWe fitted the transit light curves with a prior constraint on the stellar mass and radius derived from Gaia and broadband photometry. ^eThe effective temperature was determined from the bolometric luminosity and the stellar radius.

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We also performed a fit to the TESS data only, without any prior constraint on the mean stellar density, in order to allow for a consistency check between the two density determinations. Based on the stellar parameters derived in Section 3.1, the mean density is 31.36 ± 0.23 ${\rm{g}}\,{\mathrm{cm}}^{-3}$, while the light-curve solution gives ${30.0}_{-2.8}^{+7.4}$ ${\rm{g}}\,{\mathrm{cm}}^{-3}$. The agreement between these two results is a sign that the transit signal is from a planet, and is not an astrophysical false positive. A related point is that the ratio τ/T between the ingress/egress duration and the total duration is ${0.11}_{-0.02}^{+0.01}$, and less than 0.14 with 99% confidence. This information is used in Section 3.4 to help rule out the possibility that the fading events are from an unresolved eclipsing binary. In general, $\tau /T\gtrsim {R}_{p}/{R}_{\star }$, even when the photometric signal includes the constant light from an unresolved star (Morris et al. 2018).

Many transit-like signals turn out to be from eclipsing binaries that are nearly along the same line of sight as the intended target star, such that the light from the binary is blended together with the constant light of the intended target star. These cases can often be recognized by measuring any motion of the center of light ("centroid") associated with the fading events (Wu et al. 2010). To do so, we modeled the time series of the X and Y coordinates of the center of light in the TESS images as though they were light curves, after removing long-timescale trends by fitting out a cubic spline. Based on the fitted depths of the "centroid transits" we were able to put $3\sigma$ upper limits on centroid shifts of ${\rm{\Delta }}X\lt 2\times {10}^{-4}$ and ${\rm{\Delta }}Y\lt 6\times {10}^{-4}$ pixels, corresponding to 4.4 and 13.2 mas. Thus, there is no evidence for photocenter motion.

As mentioned previously, not all transit-like signals are from transiting planets. Below, we consider the usual alternatives to a transiting planet, and explain how the available data render them very unlikely.

• 1.  
  The signal is an instrumental artifact. This is ruled out by the detection of the transit signals with ground-based telescopes (Section 2).
• 2.  
  LHS 3844 is an eclipsing binary star. This is ruled out by the upper limit on radial-velocity variations, corresponding to a secondary mass of 0.96 ${M}_{\mathrm{Jup}}$ (Section 2.3). In addition, the absence of detectable phase variations in the TESS light curve requires that any companion be substellar. An 80 ${M}_{\mathrm{Jup}}$ companion would have produced ellipsoidal variations of order 0.1% (see, e.g., Shporer 2017), which can be excluded.
• 3.  
  Light from a distant eclipsing binary, or a distant star with a transiting planet, is blended with that of LHS 3844. We can rule out this possibility thanks to the star's high proper motion (800 mas yr⁻¹). Because the star moves quickly relative to background stars, images from previous wide-field surveys allow us to check for faint stars along the current line of sight. No sources are detected within 6 mag of LHS 3844, the brightness level that would be required to produce 0.4% flux dips. In addition, the ground-based observations require the fading source to be within $2^{\prime\prime}$ of LHS 3844 (Section 2.2), and the TESS images reveal no detectable motion of the stellar image during transits (Section 3.3).
• 4.  
  LHS 3844 is physically associated with an eclipsing binary star. The light-curve analysis (Section 3.2) requires the eclipsing object to be smaller than 16% of the size of the eclipsed star. Since the spectrum is that of an M4-5 dwarf, any secondary star would need to be of that size or smaller, implying that the eclipsing object is smaller than $0.16\times 0.19\,{R}_{\odot }$ or 3.0 ${R}_{\oplus }$. This rules out a stellar binary.
• 5.  
  LHS 3844 is a binary star and the transiting planet is around the secondary star. The companion would have to be faint and close to LHS 3844 in order to escape detection by Gaia (Rizzuto et al. 2018; Ziegler et al. 2018). Another indication that any secondary star needs to be faint is that the Gaia parallax and apparent magnitude are consistent with the properties of a single M dwarf. However, if the transiting planet is around such a faint companion, then the true transit depth must be less than about 2% in order for the transiting object to be smaller than 16% the size of the eclipsed star. Thus, in order to produce the 0.4% transit we observe, a secondary star would have to contribute at least 20% of the total flux in the TESS aperture while still escaping detection by Gaia and seeing-limited imaging.

Thus, almost all of these scenarios are ruled out, except for the possibility that the planet is actually orbiting a low-luminosity secondary star. This scenario seems contrived, and is a priori unlikely because of the low companion fraction for mid-M dwarfs (Winters et al. 2018b), the small parameter space for companions that could produce the transits we observe, the lower probability for an M dwarf to host a larger planet compared to a 1.3 R_⊕ planet (Berta et al. 2013; Mulders et al. 2015), and the tendency of selection effects to favor finding transits around primary stars (Bouma et al. 2018). Probably the only way to rule out this possibility, or more exotic scenarios, is through precise Doppler monitoring and adaptive optics imaging. The vespa code (Morton 2015), applied to LHS 3844, confirms that the false positive probabilities due to background eclipsing binaries and hierarchical eclipsing binaries are extremely low (it returns a false positive probability of order 10⁻¹⁶).