THE SOLAR NEIGHBORHOOD XXIX: THE HABITABLE REAL ESTATE OF OUR NEAREST STELLAR NEIGHBORS

The modern sample of all known stars and brown dwarfs within 5 pc of the Sun (Henry 2010, 2013), listed in Table 1 (assembled photometry in Table 2) was first published in the Observer's Handbook 2010. The sample, which is updated yearly, was created using the combination of several ground-based and space-based parallax programs, including the General Catalogue of Trigonometric Stellar Parallaxes (van Altena et al. 1995), Hipparcos (Perryman et al. 1997), RECONS (Henry et al. 1997, 2006; Deacon et al. 2005; Jao et al. 2005; Costa et al. 2005), the Hubble Space Telescope (Benedict et al. 1999, 2002), Gatewood (1989, 1994), and Gatewood et al. (1992, 1993). To be included in the sample, a system must have a weighted mean trigonometric parallax measurement of 200 mas or greater with an error of 10 mas or less. To create this sample the parallaxes compiled were combined and weighted based on the individual measurement errors. The spectral type, with reference, for each star or star system is given with the astrometric data, including right ascension, declination, the weighted mean trigonometric parallax, and the number of parallaxes included in the weighted mean, in Table 1. The closing date for the sample is 2012.0.

The 5 pc sample contains 67 stars, including the Sun, and 4 presumed brown dwarfs (spectral types L or T) in 50 systems. Of the 50 systems, 34 are single, 11 are binaries, and 5 are triples, giving a multiplicity fraction of 32%. This fraction is consistent with previous volume-limited surveys (35%; Reid & Gizis 1997). The majority (85%) of stars in the sample are main sequence stars; the exceptions include Procyon (GJ 280A), which has a slightly evolved spectral type of F5IV-V, five white dwarfs, and the four L/T dwarfs. The spectral type breakdown includes 1 A, 1 F, 3 Gs (including the Sun), 7 Ks, 50 Ms, 1 L, 3 Ts, and 5 white dwarfs. We do not include white dwarfs and brown dwarfs in subsequent calculations of habitable real estate as they are objects that are cooling continually, resulting in unsustainable HZs on long (∼Gyr) timescales.

Due to the sparse population of all but the M stars in the 5 pc sample, it is difficult to draw meaningful statistics to estimate which stellar spectral types possess the most habitable real estate. Therefore, we extend our sample to 10 pc for A, F, G, and K stars. Using the Hipparcos catalog, which is complete to V = 9 (Perryman et al. 1997), we selected all objects with a parallax greater than 100 mas for inclusion into the sample. We expect that the extended 10 pc sample is complete for spectral types A through K, given M_v = 9.0 for a M0.0V star (Henry et al. 2006). However, rather than using spectral type as a selection criterion, we used a color cutoff of V − K ⩽ 3.5 as the dividing line between K and M dwarfs (Kenyon & Hartmann 1995). As with the 5 pc sample, weighted mean parallaxes from the General Catalogue of Trigonometric Stellar Parallaxes, the Hipparcos catalog and other sources are listed with the astrometry data for the extended 10 pc sample in Table 3, as well as spectral types and references. Available photometric data are listed in Table 4. We note that there are no O-type or B-type stars within 10 pc. Because the M star population is not complete out to 10 pc (Henry et al. 2006), we approximate the total M star population by scaling by a factor of eight from the 5 pc sample. For clarity, we refer to the additional AFGK stars from 5–10 pc as the "extended 10 pc sample" and our estimates of all AFGKM stars within 10 pc as the "estimated 10 pc sample." In total, the stellar population of the estimated 10 pc sample consists of 66 AFGK stars in 57 systems. Broken down by spectral type, the sample contains 4 A stars, 6 F stars, 21 G stars, 35 K stars, and an estimated 400 M stars within 10 pc.

The UBVRI photometry used in this paper, listed in Tables 2 and 4, was extracted from sources in the literature with preference given to large surveys and measurements consistent with photometry obtained as part of the CTIO Parallax (CTIOPI) program, which uses the Johnson–Kron–Cousins system. R and I magnitudes from the USNO-B1.0 catalog (Monet et al. 2003) are incorporated in the extended 10 pc sample and both are rounded to the nearest 0.1 mag. R magnitudes are averaged from the first and second epochs.

The majority of JHK photometry is taken from the Two Micron All Sky Survey (2MASS) database, identified as those values with errors listed explicitly in Tables 2 and 4 (Cutri et al. 2003). In cases of close binaries with magnitude difference measurements in the literature (e.g., Henry & McCarthy 1993; Henry et al. 1999), the optical and 2MASS photometry is used with the published magnitude differences to split the component fluxes into individual magnitudes. Note that stars brighter than ∼5 mag are saturated in 2MASS images and typically have relatively large photometric errors (⩾0.2 mag). Where possible, we use JHK measurements in the literature for these stars (Johnson et al. 1966, 1968; Glass 1975; Mould & Hyland 1976). These magnitudes, listed in their unconverted form in Tables 2 and 4 and with specific references listed in the error columns, were then converted to 2MASS magnitudes using color transformations from Carpenter (2001). Of the 16 multiple systems in the 5 pc sample, 8 have spatially unresolved photometry in some or all passbands and are marked as "Joint" in the Notes section of Table 2. Similarly, 10 of the 19 multiple systems in the extended 10 pc sample have spatially unresolved photometry in some or all passbands and are listed as "Joint" in the Notes section of Table 4.

Although spectral types are often used to estimate stellar effective temperatures, the various methods for determining spectral types are inhomogeneous and often depend upon the spectral range used. As an alternative, we fit synthetic stellar spectra to broadband energy distributions to determine effective temperatures and radii. In particular, we use photometric measurements spanning UBVRIJHK (0.3 to 2.4 μm) in conjunction with model spectra generated using the PHOENIX code (Hauschildt et al. 1999). This prescription is only used for single stars and for stars in multiple systems in the 5 pc and extended 10 pc samples with at least four spatially resolved photometric measurements in different filter bandpasses. Estimates for unresolved multiples are discussed in Section 4.3.

These available models span the temperature ranges of T_eff of 10,000 K–7000 K in 200 K increments and 6900 K–2000 K in 100 K increments. The model spectra have a resolution of 2 Å and range from 10 Å to 500 μm. The models were convolved with UBVRIJHK filter responses to create synthetic photometry. For the UBVRI synthetic photometry, we took zero points from Bessell et al. (1998) and filter responses from CTIO.⁵JHK filter responses and zero points were from 2MASS.⁶ The zero points adopted are listed in Table 5. We adopt log g values of 4.5 or 5.0 for all stars.

Solar metallicity is adopted for all stars except GJ 191 (Fe/H = −0.98; Woolf & Wallerstein 2005) and GJ 451 (Fe/H = −1.16; Valenti & Fischer 2005), for which we adopt metallicities of −1.0. The assumption of solar metallicity for the remainder of our 10 pc sample is based on the 36 FGK stars that overlap with Valenti & Fischer (2005). These stars have an average metallicity of Fe/H = −0.048 with a standard deviation of 0.168 dex.

The flux values in the model spectra are given as a surface flux that must be scaled by a radius to a known distance for fitting with observed integrated flux values. A stellar radius grid from 0.001 R_☉ to 3.00 R_☉ with a step size of 0.001 R_☉ is calculated for each model spectrum. Each spectrum and radius combination is then convolved with filter response and the zero point data referenced above to derive consequent fluxes observed at Earth. These integrated fluxes are then fit via a χ² minimization routine, written in IDL and described in Equation (3), to compare the model flux with the observed flux across each filter bandpass. Here, O is the observed integrated flux from the photometric measurements, E is the estimated integrated flux from the model grids, ν is the number of photometric points (degrees of freedom), and σ is the average error in the photometric measurement. Examples of fits for AFGKM stars in the 5 pc sample are shown in Figure 1:

$$\begin{equation} \chi _\mathrm{red}^2 = \frac{\chi ^2}{\nu } = \frac{1}{\nu } \sum {\frac{(O - E)^2}{\sigma ^2}} . \end{equation} \tag{ 3 }$$

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The output is an effective temperature from the model and a radius that best fits the measured photometric data. We assume no interstellar extinction for our sample, and choose four photometric points as the minimum number needed to make a fit. When deriving radii, all stars in the sample are assumed to be spherical and radiate isotropically, which is not the case for rapidly rotating stars that may be oblate and experience gravity darkening (e.g., Altair, see Monnier et al. 2007; Vega, see Aufdenberg et al. 2006). This is most common among stars earlier than mid-F spectral type, as these stars are fully radiative and consequently do not possess an efficient rotational braking mechanism (e.g., Wilson 1966). However, all but one of the early-type stars (i.e., earlier than spectral type F5) within 10 pc have projected rotational velocities less than 100 km s⁻¹, which correspond to projected oblateness values ≲2% (Absil et al. 2008). These apparently slow rotating stars include Sirius A (GJ 244, A1V, 16 km s⁻¹; Royer et al. 2002), Procyon A (GJ 280, F5V-IV, 4.9 km s⁻¹; Fekel 1997), Vega (GJ 721, A0V, 24 km s⁻¹; Royer et al. 2007), and Fomalhaut (GJ 881, A4V, 93 km s⁻¹; Royer et al. 2007). We note that despite having a small vsin i value, Vega is believed to be rapidly rotating with a nearly pole on orientation (Aufdenberg et al. 2006). An additional rapidly rotating star is Altair (GJ 768, A7V, 217 km s⁻¹; Royer et al. 2007) which has an oblateness of 18% determined from interferometric measurements by the CHARA Array (Monnier et al. 2007). As expected, our derived radii and effective temperatures for Altair and Vega are intermediate to the polar and equatorial values listed in Monnier et al. (2007) and Aufdenberg et al. (2006), respectively. Because the EHZ boundaries are a function of the square root of the total luminosity (see Section 4.2), our adopted methodology should yield reliable estimates of the habitable real estate these stars provide, even if the stellar temperatures vary with stellar latitude.

As a consequence of the limited temperature resolution of the PHOENIX grids used (ΔT = 200 K from 10,000 K to 7000 K and ΔT = 100 K from 6900 K to 2000 K), the fitting routine can determine a slightly larger radius coupled with a cooler temperature, or vice versa. Systematic uncertainties in the PHOENIX models are such that a ΔT of less than 100 K is unreliable (P. H. Hauschildt 2009, private communication). As the Stefan–Boltzmann law shows R_⋆²T_eff⁴ ∼ L_⋆, the luminosity determined from the spectral energy distribution (SED) remains the same as long as the radii and effective temperatures move in opposite directions, and therefore the EHZ, being a function of the square root of the luminosity, does not change. Of key importance, the output radii and temperatures determined here allow us to compare our results directly to those found via interferometric techniques.

Of the stars investigated, 28 have spatially resolved angular diameters from long baseline interferometric instruments such as CHARA, the Palomar Testbed Interferometer, and VLTI (Table 6). Fifteen of these measurements are from the recent effort of Boyajian et al. (2012). Because these measurements determine sizes to within a few percent, we use them to test the accuracy of the radii determined in our fitting process. The published radii are on average 7.4% larger than our derived radii, which shows a systematic effect. Our derived model T_eff's are on average 2.4% hotter than derived from interferometric measurements. A comparison of our model versus published values is shown in Figure 2. The temperature uncertainties correspond to spectral type uncertainties of 1–2 spectral subclasses, similar to the error associated with most spectral classification methods. As the average values indicate, the overprediction of temperature leads to the expected under-prediction of radius, and the combination yields a more accurate luminosity, and thus consistent EHZ. Given this agreement, we adopt our model values for T_eff and R/R_☉ in final calculations of the habitable real estate.

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A few stars are worthy of note. Procyon is slightly evolved (F5.0IV-V) and has a highly constrained log g of 4.05 ± 0.04 (Fuhrmann et al. 1997) measured via high-resolution spectroscopy in concert with masses determined using astrometry from the Procyon–white-dwarf orbit. We adjusted the log g to 4.0 for this star and recomputed the T_eff and R. This, nevertheless, yielded values within the model grid resolution identical to those of log g = 4.5. The model spectra used in this work have a low temperature limit of 2000 K, which is the value derived for the three intrinsically faintest stars in this sample: SCR 1845−6357A (M8.5V), DEN 1048−3956 (M8.5V), and LP 944−020 (M9.0V).

Kasting et al. (1993) use a one-dimensional climate model to calculate HZs around single main sequence stars. A one-dimensional climate model characterizes a planet's global temperature by dividing the planet into latitudinal bands, and treats the planet as uniform with respect to longitude. These one-dimensional radiative-convective models are a good approximation of global temperature, but more complicated three-dimensional global climate models are needed to account for the complex physical interactions associated with oceans, clouds, and land surface processes. These inputs add parameters such as land/ocean surface coverage and clouds, which can vary from planet to planet, complicating the overall goal to characterize the EHZ of a star. Here we use the one-dimensional model to generalize the EHZ, and adopt a modified version of the one-dimensional model based on the "Venus and early Mars criterion" from Selsis et al. (2007). In that work, they argue that empirical evidence shows that Venus has not had water on its surface for at least 1 billion years, and Mars had water on its surface around 4 billion years ago. The solar fluxes at those times were 8% and 28% lower, respectively (Baraffe et al. 1998). Venus (0.72 AU today) and Mars (1.52 AU today) would need to be at distances of ∼0.75 AU and ∼1.77 AU, respectively, to receive these levels of solar flux today.

Selsis et al. (2007) provide a method for estimating the inner and outer edges of HZs for stars with T_eff = 3700 K–7200 K. The stars in the sample discussed here range in temperatures from 2000 K to 10,000 K. We have therefore chosen to derive new relations for the HZ boundaries that span the entire stellar temperature regime of our sample, and thereby provide a consistent methodology for all stars in the sample.

In defining our EHZ inner and outer boundaries, we assume a planet with an atmosphere, radius, mass, and Bond albedo (0.3) that matches Earth's (Kasting 1996). This leads to the EHZ Equations (4) and (5), used to determine the empirical surface temperature of an Earth-like planet that satisfies the "Venus criterion" (we adopt 0.80 AU on the suggestion of J. Kasting 2010, private communication) and "Mars criterion" (1.77 AU). The resulting inner and outer radii of the EHZ correspond to equilibrium temperatures of 285 K to 195 K, respectively.

$$\begin{equation} R_{{\rm EHZ\, inner}}=\frac{R_\star }{2}{(0.7)}^{1/2}\left (\frac{T_{{\rm eff}}}{285\,{\rm K}}\right)^2 \end{equation} \tag{ 4 }$$

$$\begin{equation} R_{{\rm EHZ\, outer}}=\frac{R_\star }{2}{(0.7)}^{1/2}\left (\frac{T_{{\rm eff}}}{195\,{\rm K}}\right)^2 . \end{equation} \tag{ 5 }$$

Note that these only depend on R_⋆ and $T_{{\rm eff}}^2$, or essentially the square root of the star's luminosity. Values for both samples are listed in Tables 7 and 8. Only stars used in the cumulative EHZ calculations are listed, except for the cases of Sirius (GJ 244A) and Procyon (GJ 280A), which provide useful benchmarks.

Although stars in multiple systems are often avoided in planet searches, planets have been found in binary and multiple systems (e.g., Patience et al. 2002; Raghavan et al. 2006; Eggenberger et al. 2007). The potentially dynamically disruptive effects of any close stellar companion must be considered when assessing the possibility of formation, long-term dynamical stability, and ultimately the habitability of planets in multiple star systems. The α Centauri triple system, at a distance from the Sun of 1.34 pc for the G2V–K0V pair (GJ 559 AB) and 1.30 pc for the wide M5V companion (GJ 551), includes the nearest set of Sun-like stars, and provides a test case to study the habitability of multiple stars. The G–K pair has an orbit with a semimajor axis of 1757 and eccentricity of 0.518 (Pourbaix et al. 2002). This gives periastron and apastron distances of 11.33 AU and 26.67 AU, respectively. Barbieri et al. (2002) show for α Centauri A that planets can form in stable orbits on a timescale of 5 Myr. Using numerical simulations, they show that not only could planets form, but in some models they formed directly in the HZ. Quintana et al. (2007) similarly find that binary separations greater than 10 AU did not inhibit the formation of terrestrial planets at 2 AU. Consistent with this, Wiegert & Holman (1997) show that the orbit of a planet can be stable as long as the ratio of the semimajor axis of the binary to that of the planet is more than 5:1.

The 36 multiple systems in the 5 pc and extended 10 pc samples consist of 27 binaries, 6 triples, and 3 quadruple systems (GJ 423, GJ 570, and GJ 695), for a total of 84 stars/brown dwarfs. However, nine are not main sequence stars, and are excluded because of their evolutionary states (e.g., sub-giants, white dwarfs, and brown dwarfs). Additionally, 16 are M star companions in the extended 10 pc AFGK sample. Because the habitable real estate of M stars out to 10 pc is estimated by scaling the 5 pc results, we do not consider these M stars in our EHZ calculations. This leaves 59 stars in multiple systems with potential HZs. For clarity, we emphasize that the EHZ of each star in a system is calculated separately.

Of the 59 stars, 43 (73%) have at least 4 spatially resolved photometric measurements in different filter bandpasses. For these stars, the same prescription used in Section 4.2 is used to calculate the EHZs. For the 16 stars that are not photometrically spatially resolved from their nearest companion(s), we estimate the EHZ locations based on spectral type information for the components. Using the assembled spectral types listed in Tables 1 and 3, we estimate the components' V − K color using the spectral type versus V − K colors relations of Kenyon & Hartmann (1995), and estimate the location of the EHZs using the relations described in Section 5.2.

To assess the dynamical stability of any planets in these EHZs, we compare the locations of the outer EHZ boundaries to the binary separations listed in Table 9. We consider a planet to be dynamically stable if the periastron distance of a star's nearest companion is greater than five times the outer EHZ boundary. In cases where the periastron distance cannot be calculated (because its full orbit solution is not known), we use the projected separation. Fortunately, these exceptions are all large separation multiples, and thus minor errors in the adopted separation are likely irrelevant for dynamical stability considerations. The ratios of periastron distances to outer EHZ boundaries are illustrated in Figure 3. For each star and its nearest companion, the ratios range from 0.001 to 164,107. 49 of the 59 stars have ratios to their nearest companions of greater than 5, and thus EHZs in which planets should be in dynamically stable orbits. The remaining 10 stars (GJ 53A, GJ 222A, GJ 244A, GJ 280A, GJ 423A, GJ 423B, GJ 713A, GJ 713B, GJ 866A, and GJ 866C) are considered to have EHZs in which planets would not be in dynamically stable orbits, so are excluded in our estimate of total EHZ real estate. Seven of these have ratios less than 1.0, hinting at the possibility of circumbinary planets. However, the majority of the EHZ outer radii are only a few times the binary separations, making it unlikely that these systems would have dynamically stable circumbinary planets in the EHZ. Nonetheless, it is worth noting that a few massive planets have been reported in circumbinary orbits (Lee et al. 2009; Qian et al. 2010).

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Table 9. Orbital Properties of Multiple Systems

Star	Sep	a	e	i	Ω	ω	P	T	Ref.
				(°)	(°)	(°)	(yr)
GJ 15 AB	40''	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Eggen (1996)
GJ 34 AB	⋅⋅⋅	1199	0.497	34.76	98.43	88.59	480	1889.6	Strand (1969)
GJ 53 AB	⋅⋅⋅	101	0.561	106.8	47.3	152.7	21.75	1975.74	Drummond et al. (1995)
GJ 65 AB	⋅⋅⋅	206	0.615	127.3	150.5	285.4	26.52	1971.88	Worley & Behall (1973)
GJ 66 AB	⋅⋅⋅	782	0.534	142.8	13.1	18.37	483.66	1813.5	van Albada (1957)
GJ 105 AC-B	165''	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Golimowski et al. (2000)
GJ 105 AC	33	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Golimowski et al. (2000)
GJ 166 A-BC	83''	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Baize & Petit (1989)
GJ 166 BC	694	⋅⋅⋅	0.410	108.9	150.9	327.8	252.1	1849.6	Heintz (1974)
GJ 216 AB	95''	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Eggen (1956)
GJ 222 AB	⋅⋅⋅	0688	0.451	95.94	126.36	111.57	14.11	1999.9	Han & Gatewood (2002)
GJ 234 AB	⋅⋅⋅	104	0.371	51.8	30.7	223	16.12	1999.38	Ségransan et al. (2000)
GJ 244 AB	⋅⋅⋅	756	0.592	136.5	55.57	147.27	50.09	1894.13	Gatewood & Gatewood (1978)
GJ 250 AB	58''	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Eggen (1956)
GJ 280 AB	⋅⋅⋅	4496	0.365	31.9	284.8	88.8	40.38	1967.86	Irwin et al. (1992)
GJ 412 AB	28''	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Gould (2003)
GJ 423 AC-BD	⋅⋅⋅	2533	0.421	112.1	101.3	127.3	59.84	1995.05	Heintz (1996)
GJ 423 AC	⋅⋅⋅	0056	0.53	94.9	263.5	143.0	1.832	1986.50	Mason et al. (1995)
GJ 423 BD	*274,000 km	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.015	⋅⋅⋅	Mason et al. (1995)
GJ 432 AB	17''	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Henry et al. (2002)
GJ 442 AB	254	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Poveda et al. (1994)
GJ 473 AB	⋅⋅⋅	0926	0.295	103.00	143.48	347.2	15.64	1992.30	Torres et al. (1999)
GJ 559 AB	⋅⋅⋅	1757	0.518	79.2	204.85	231.65	79.91	1875.66	Pourbaix et al. (2002)
GJ 551-GJ 559 AB	218	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Poveda et al. (1994)
GJ 566 AB	⋅⋅⋅	494	0.51	139	347	203	151.6	1909.3	Söderhjelm (1999)
GJ 570 A-BC	⋅⋅⋅	3234	0.20	72.53	317.31	252.1	2130	1689	Hale (1994)
GJ 570 BC	⋅⋅⋅	0151	0.756	107.6	195.9	127.56	0.846	1996.51	Forveille et al. (1999)
GJ 570 ABC-D	2583	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Burgasser et al. (2000)
GJ 663 AB	⋅⋅⋅	130	0.916	99.79	−85.8	−90.2	470.9	1677.9	Irwin et al. (1996)
GJ 663 AB-GJ 664	742	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Luyten (1957)
GJ 666 AB	⋅⋅⋅	1042	0.779	35.64	131.78	333.44	693.24	1907.2	Wieth-Knudsen (1957)
GJ 667 AB	⋅⋅⋅	181	0.58	128	313	247	42.15	1975.9	Söderhjelm (1999)
GJ 695 AD	143	⋅⋅⋅	0.32	68.0	81.8	92	65	1951.0	Turner et al. (2001); Heintz (1994)
GJ 695 AD-BC	34''	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Raghavan et al. (2010)
GJ 695 BC	⋅⋅⋅	136	0.178	66.2	60.7	174.0	43.2	1965.4	Couteau (1959)
GJ 702 AB	⋅⋅⋅	455	0.499	121.16	302.12	14.0	88.38	1895.94	Pourbaix (2000)
GJ 713 AB	⋅⋅⋅	0124	0.428	74.42	230.30	119.3	0.768	1984.83	Farrington et al. (2010)
GJ 725 AB	⋅⋅⋅	1388	0.53	66.0	136.9	234.6	408	1775.0	Heintz (1987)
GJ 783 AB	71	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Poveda et al. (1994)
GJ 820 AB	⋅⋅⋅	2443	0.414	52.7	173.4	153.17	691.61	1689.14	Baize (1950)
GJ 845 A-BC	4023	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Scholz et al. (2003)
GJ 845 BC	0732	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	McCaughrean et al. (2004)
GJ 860 AB	⋅⋅⋅	2383	0.410	167.2	154.5	211.0	44.67	1970.22	Heintz (1986)
GJ 866 AC	⋅⋅⋅	∼001	0.000	∼117	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	1991.71	Delfosse et al. (1999)
GJ 866 AC-B	⋅⋅⋅	0346	0.446	112	161.5	337.6	2.25	1997.53	Delfosse et al. (1999)
GJ 881-GJ 879	197	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Poveda et al. (1994)
GJ 1245 AC-B	7969	⋅⋅⋅	0.320	135.0	80.0	38.0	15.22	1983.1	Tokovinin (1997)
GJ 1245 AC	0800	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Tokovinin (1997)
SCR 1845-6357 AB	1170	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	Biller et al. (2006)

Note. ^*asin (i).

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Using our initial assumptions of a terrestrial "Earth-like" planet as the basis for our EHZ, we estimate the habitable real estate using linear AU separations from the central star, essentially the width of the EHZ. In Table 10 we present the EHZ width totals for each spectral type in the 5 pc and total 10 pc samples.

The cumulative EHZ width for stars in the 5 pc subsample is 8.8 AU, including 2.6 AU for the three G stars (including the Sun) and 2.9 AU for the seven K stars. The 48 M dwarfs in the 5 pc sample en masse provide 3.3 linear AU available for habitable planets, or 38% of the available EHZ. The dominant contribution of M dwarfs to the EHZ width is demonstrated clearly using the estimated 10 pc sample. The total EHZ width for the estimated 10 pc sample is 71.5 AU, including 13.2 AU for the 3 A, 4.9 AU for the 4 F stars, 11.9 AU for the 14 G stars, and 15.4 AU for the 34 K stars. The estimated 384 M stars en masse provide 26.1 AU of linear EHZ. This accounts for 36.5% of the total EHZ. Thus, by spectral type, M stars en masse provide the largest EHZ real estate.

Given the rapid pace of exoplanet discovery, it would be helpful to have a tool to easily and accurately predict the location of the EHZ to determine whether or not a planet resides within it. Predicting the EHZ of a star based on spectral classification can be problematic due to the inhomogeneity in classification and spectral types being determined over different wavelength ranges. As shown in Henry et al. (2006), the V − K color is a useful temperature diagnostic for the A through M stars that dominate the solar neighborhood. This relation can also be very helpful in determining a rough estimate of the EHZ based on observable photometry, and may be easily scaled to larger populations.

We use the results from the 5 pc and extended 10 pc samples to derive a relation between V − K color and the size and location of the EHZ. As in the computation of total habitable real estate, we removed binary stars with unresolved photometry as well as stars known to be evolved. We do, however, use stars such as Sirius (GJ 244) and Procyon (GJ 280) for which EHZs have been determined, even though their companions corrupt their EHZs. Their white dwarf companions do not significantly contribute to their luminosities or V − K, and their inclusion improves the statistics of our fit. We fit a second order polynomial, described by Equation (6), to the V − K colors and computed EHZ widths shown in Figure 4:

$$\begin{equation} {\rm Log}({\rm EHZ}_\mathrm{width (AU)}) = 0.648 - 0.457 (V-K) + 0.021(V-K)^2 . \end{equation} \tag{ 6 }$$

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Using the same method, a relationship for V − K color and the inner and outer radii of the EHZs are described by Equations (7) and (8), respectively. These relations are only valid for main sequence stars:

$$\begin{equation} {\rm Log}({\rm EHZ}_\mathrm{inner (AU)}) = 0.593 - 0.457(V-K) + 0.021(V-K)^2 \end{equation} \tag{ 7 }$$

$$\begin{equation} {\rm Log}({\rm EHZ}_\mathrm{outer (AU)}) = 0.922 - 0.457(V-K) + 0.021(V-K)^2 . \end{equation} \tag{ 8 }$$

As a check on these relations, we use these to calculate the total EHZ width by spectral type of the estimated 10 pc sample and compare these values to the direct calculations described in Sections 4.2 and 4.3. We find the total EHZ widths from the empirical relations differ on average from the calculated total widths by −12.7%, −6.4%, 1.6%, 4.7%, and 0.3% for A, F, G, K, and M stars respectively; negative values correspond to underpredictions of the EHZ width totals. The higher percentage differences for A type and F type totals are due to the relatively small populations within 10 pc and the effects of large 2MASS photometric errors due to brightness. The results imply that this relation is useful for quickly estimating the amount of habitable real estate for a population with known V − K values. We also test how well the predicted inner and outer boundaries from our relations agree for any given star. On average, these predictions yield values consistent to 3% with a dispersion of 22% for both inner and outer boundaries for AFGKM stars in our samples. These dispersions can be interpreted as the uncertainty in the locations of these boundaries from these relations.

Of the 14 confirmed planetary systems within 10 pc of the Sun for which orbits have been determined, 5 contain multiple planets (GJ 139, GJ 506, GJ 581, GJ 667C, and GJ 876). All 14 systems are listed in Table 11 with published values for semimajor axis and eccentricity, as well as calculated inner and outer radii of the EHZ from this work. Three of the systems, GJ 581, GJ 667C, and GJ 876 have planets in the EHZ.

GJ 581, an M2.5V star at a distance of 6.25 pc, has six proposed planets, but the existence of GJ 581g and GJ 581f are currently debated (see: Vogt et al. 2010a; Andrae et al. 2010; Gregory 2011; Anglada-Escudé 2010; Tuomi 2011). If real, GJ 581g, with a semimajor axis of 0.146 AU, orbits in the EHZ in a presumed circular orbit. Using CHARA, von Braun et al. (2011) recently measured the size of the star and derived HZ boundaries of R_in = 0.11 AU and R_out = 0.21 AU. Our EHZ is somewhat closer in to the star, R_in = 0.083 AU and R_out = 0.179 AU, but still places GJ 581g in the EHZ. The differences are due to our calculated luminosity (L = 0.11 L_☉) being 8% lower than von Braun et al. (2011), as they adopted an extinction of A_V = 0.174 for GJ 581, which they note as unexpected for a star at this distance. GJ 581d, with semimajor axis of 0.22 AU and eccentricity of 0.38, also moves in and out of the EHZ of GJ 581.

GJ 667C, an M1.5V star at a distance of 7.23 pc, hosts two planets, and possibly four (Anglada-Escudé et al. 2012). Although GJ 667Cb does not lie within the EHZ, GJ 667Cc (msin i of 4.5 M_⊕) lies within the EHZ for the majority of its orbit. With a semimajor axis of 0.123 AU and eccentricity <0.27, it may lie completely within the EHZ once the eccentricity is more highly constrained.

GJ 876, an M3.5V star at a distance of 4.66 pc, hosts four planets (Rivera et al. 2010). Our calculations show an EHZ spanning 0.090–0.191 AU. Rivera et al. (2010) report orbital fits for two planets near the EHZ with semimajor axes of 0.13 AU (GJ 876c) and 0.21 AU (GJ 876b), and eccentricities of 0.25 and 0.03, respectively. As shown in Figure 5, this allows for GJ 876c to be in the EHZ of its host star for the full duration of its orbit, while GJ 876b lies just outside the EHZ. Although these planets are not considered terrestrial (msin i of 0.56 and 1.89 M_J), the possibility exists that they could have terrestrial-like moons that could be habitable.

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The previous sections provide estimates of EHZs based on the requirement of liquid water on a planetary surface. Of course, a planet's location in the EHZ of a host star does not guarantee its habitability. A host of other factors, such as planet size, atmosphere, magnetic fields, and even plate tectonics, play vital roles in determining the habitability of a planet in the EHZ. Without a sufficiently thick atmosphere, biologically harmful radiation can penetrate to the surface of a planet. On Earth, atmospheric CO₂ levels are kept in check by the carbon-silicate cycle. Known to regulate climate temperatures through a negative feedback, this cycle allows for as much as 60 bars (Kasting 1996) of CO₂ to be locked away in rock and sediments. This slow carbon-silicate cycle requires that water be present, because without water, the atmospheric CO₂ cannot be sequestered as carbonate. A magnetosphere on Earth also plays an important role by deflecting harmful charged particles. Tectonic activity may be one of the key factors in keeping a planet habitable (Doyle et al. 1998). Without water, the lithosphere of a planet may become a stagnant lid, halting tectonic activity and the sequestration of CO₂.

There is a temporal constraint on habitability as well, as the HZ may change considerably over the lifetime of a star (Kasting et al. 1993; Kasting 1996; Tarter et al. 2007; Selsis et al. 2007). Putting these complications aside, the requirement of liquid water on the surface of a planet is a good first order approximation to habitability.