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GEOPHYSICAL RESEARCH LETTERS, VOL. 27, NO. 4, PAGES 501-503, FEBRUARY 15, 2000

The Faint Young Sun Paradox' An Observational Testof an Alternative Solar ModelEric J. GaidosJet Propulsion Laboratory, California Institute of Technology,Pasadena, CaliforniaManuel GiidelPaul Scherrer Institute, Villigen, SwitzerlandGeoffreyA. BlakeDivision of Geology & Planetary Science, California Institute of Technology, Pasadena, California

Abstract. We report the results of deep observations atradio 3.6cm)wavelengthsf henearby olar-typetar7r xUrsa Majoris with the Very Large Array (VLA) intendedto test an alternative theory of solar luminosity evolution.The standard model predicts a solar luminosity only 75%of the present value and surface temperatures below freez-ing on Earth and Mars at 4 Ga, seemingly in conflict withgeologicevidence or liquid water on these planets. An al-ternative model invokes a compensatory mass loss througha decliningsolar wind that results n a more consistentearlyluminosity. The free-free emission rom an enhanced windaround nearby young Sun-like stars should be detectable atmicrowaverequencies.ur observationsf 7r xUMa, a 300million year-old solar-massstar, place an upper limit on themass oss ate of 4 - 5 x 10 Moyr -. Total mass ossfrom sucha star over 4 Gyr would be less han 6%. If thisstar is indeed an analog of the early Sun, it casts doubt onthe alternative model as a solution to the faint young Sunparadox, particularly for Mars.Introduction

The paradox of the faint young Sun is one of the out-standingproblems n understanding he early climates of theEarth and Mars. Standard stellar evolution theory predictsthat the solar luminosity at the beginning of the Arcbeaneon (3.8 Ga) was approximately 5% of its presentvalue[Gough, 981]. The lower nsolation t the distances f Earthand Mars should have resulted in surface temperatures be-low 0C, in apparent conflict with geologic ecordswhichsuggestwarmer temperatures and liquid water at the sur-face of both worlds [Saganand Mullen, 1972; Karhu andEpstein, 1986]. Elevated evelsof CO2, a greenhouse as,may have maintained surface temperatures above freezingon the early Earth and Mars [Owenet al., 1979;Cesset al.,1980; Walker et al., 1981; Kasting and Grinspoon, 991].Carbonates from a massivecarbon dioxide greenhousehaveyet to be discovered on Mars, and the CO2 levels postu-lated for the Archean Earth may be in conflict with the geo-chemical ecord Rye et al., 1995]. This has ed to theories

Copyright2000 by the AmericanGeophysical nion.Papernumber1999GL010740.0094-8276/00/1999GL010740505.00

involvingmethane CH4) and ammonia NHa) as greenhousegases Kasting, 997;Saganand Chyba, 997].An alternative model of solar evolution, originally con-structed to explain the anomalousdepletion of lithium in theSun and similarstars)has he potential o resolvehe para-dox [Hobbs t al., 1989; Schramm t al., 1990]. The modelinvokesmass lossof ,,5-10% over the age of the Sun to re-move ts outermost,Li-rich layers Boothroyalt al., 1991].The luminosity of a star on the main sequence caleswith itsmass as a power-law with index 3-4. Thus, a small amountof mass loss could compensate for much of a star's lumi-nosity evolution due to the thermonuclear consumption ofhydrogen Graedelet al., 1991]. Conservation f angularmomentum would impel the expansionof planetary orbits,moderating the fiu at a planet to an even greater degree[Whitrnireet al., 1995]. To explain warm Archeancondi-tions, the mass ossmust occur over a timescale of ,, 1 Gyr.The massoss ate mustalsobe ,, 10 x - 10-Mo yr ,three to four orders of magnitude higher than the presentsolar wind. Agreement betweensolar oscillation requenciesand the standard solar model may limit mass loss to thefirst 0.2 Gyr of solar history, an uninteresting timescale inthis context Guzikand Cox, 1995]. Evolution n solarwindintensity would be a natural consequence f the decline insolarchromosphericctivity over4.6 Gyr[Walter and Barry,1991; Staufferand Soderblom, 991],but the magnitudeofthe change s unknown. A much stronger early wind wouldby itself have profound consequences ecauseof its erosionof terrestrialplanet atmospheresKassand Yung,1995].The qualitative record of ion implantation record in me-teorites and lunar samples suggestsa more intense ancientwind [Geissand Bochsler,1991] but doesnot extend be-yond 0.1 Gyr. Observationsof young, solar-type stars canbe used o test the plausibility of significantearly solar massloss. Detection of mass osswould imply similar behavior bythe early Sun. Likewise, restrictive upper limits on the rateof mass loss from these stars would cast doubt on the the-ory. Stellar wind plasma produces ree-free continuum emis-sion at ram- to cm-wavelengths,but at flux levelswhich areobservationally hallenging Mullan et al., 1992]. The ex-pected flux density from a mass-losingmain sequencestarat 10parsecs1 pc = 2 105AU, theEarth-Sun istance)sonly60Jy (1 Jy = 10 2aergs ec-cm-2Hz-sr-).Windemissionat mm and longer wavelengthswill have a charac-teristicpower-law nergyspectrumwith index2/3 [Panagiaand Felli, 1975; Wright and Barlow, 1975].

501

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502 GAIDOS ET AL.' FAINT YOUNG SUN PARADOX-910

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Figure 1. Mass oss s. time n a power-law odel or 3% and7% total mass loss. The first case is required for liquid water onearly Mars, the second s the limit to avoid a runaway greenhouseon Earth Whirmire et al. [1995]. The modern Sun, a new limitfromVLA observationsf the solaranalogrt UMa, and previouslimits for two other Sun-like stars are marked. The sensitivity ofa single observation by the proposed Atacama array is also noted.

While wind emission is more intense at millimeter wave-lengths the signal must compete with higher sky backgroundand at present,observations t cm wavelengthsare the mostpromising. Limits to mass osshave already been establishedfor moremassiveA and F stars [Brownel al., 1990]and ac-tive, lessmassiveM stars [Lira and While, 1996; van denOord and Doyle, 1997]. Microwaveemission etected romvery young (less han 100 Myr) solar-mass tars s thoughtto be coronalgyrosynchrotronadiation [Gary and Linsky,1981; Giidel el al., 1995]. Searchesor emissionrom slighlyolder stars where this radiation is much weaker have beenunsuccessfulr ambiguousBowersand Kundu, 1981; Garyand Linsky,1981; Whilmire el al., 1995; Giidelel al., 1995].Giidel el al. (1998), obtaining he most sensitiveobserva-tions prior to this work, placed imits on the flux (and thusmass oss) rom three youngsolar-typestars.Observations

We have obtained still more sensitive observations at 3.6cm (X-band)of the solar nalogrt UMa, 14.3pc distant,with the Very Large Array (VLA) in Socorro,New Mexico.This star was one of the three previously observedby Giideland is one of a sample of nearby young solar-mass stars se-lected as analogsof the Sun during the Hadean eon (3.8-4.5Ga) [Gaidos,1998]. Two tracks of the star were obtainedon February14 and 15 with the array in its C/D (compact)configuration using 27 antennae for a total on-source ntegra-tion time of 12.2 hours. We believe these are the most sen-sitive observationsobtained to date of a main-sequencestarother than the Sun. Simultaneous observations were madeof bright point sources or phase and flux calibration whencombining the signal from the individual antennae. Thedata were reduced using the Astronomical Image Process-ing System (AIPS) softwarepackage. The combinedmap

has a resolution of 7.9 X 5.1 arc-seconds and a la noiselevel of 6.4/Jy.Results and Discussion

Nosource asdetectedt the ocation f rtUMa (SIM-BAD ICRS 2000coordinates).A 40/Jy sourcewasdetected15 arc-seconds to the southeast. The offset of this sourcefrom the star was confirmed by measuring its separationfrom an emission-line galaxy with both optical and radiopositions. A plausible counterpart is the nearby low-massbinarysystemHU 628BC [A1-Shukri l al., 1996].A possiblesource1-2.5 arc-seconds o the NE of the star appears at the2a level (12 /Jy) in the Februaryobservationsut at the5a level (40/Jy)in prevousVLA observationsGiidel, pri-vate communication).The offset s significant nd we haveno reason to believe the radio source is associated with thestar. Even if it is, any variable component is due to flar-ing and we place an upper limit of 12/Jy on the total fluxdensity from a wind.A spherically symmetric stellar wind with density fallingas -2 froma starat a distance losingmass t a rateM-to(unitsof 10-tMyr t ) will have he luxdensity pectrum[Wrighl and Barlow,1975; Panagiaand Felli, 1975]

36mm 10 c Jy. (1)The quiescent emission from the star's 20,000 K chromoso-phere optically hick at thesewavelengths)s small,roughly0.3 Jy. Flaring activity may roughly double this contribu-tion. Correcting for this amount, our detection limit corre-spondso a mass ossof 4- 5 x 10-ttMyr -t.

Angular momentum, as well as mass, is lost through anionized, magnetized stellar wind, linking the spin-down ofthe rotation rate f with the mass oss,

(2)where RA is the Alfven (sonic) radius and m is a be-tween0 and 1 dependingon magnetic ield geometry We-ber and Davis, 1967; Slepierg, 988]. At the Allyen radius,uM - BR, whereBr is the radialmagneticieldand u isthe solar wind velocity. In a multipole field, small changesin distance can compensate or large changes n uM, thusRA will vary only slightly over the history of the Sun. Then,M ,-, , where a

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is only3 x 10-aM)yr . Observationsy an upgraded LA(www.nrao.edu/vla/html/Upgrade/Upgrade_home.shtml)rthe proposedAtacama Large Millimeter Array (ALMA)[Woottenand Yun, 1999]will be unable o detect this loss,but will be able to rule out any mass loss rates significantto the climate of the early Earth.Acknowledgments. E.J.G. is supportedby the NASAAstrobiology program. G.A.B. acknowledges support from theNASA Exobiology program. The National Radio Astronomy Ob-servatory is a facility of the National Science Foundation oper-ated under cooperative agreement by Associated Universities, Inc.The SIMBAD database is maintained by the Centre Donnes as-tronomiques de Strasbourg, France.

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Geology & Planetary ScienceDivision, Caltech 150-21, Pasadena,CA 91125. (email: gab@gps.caltech.edu)E. J. GaidosJet Propulsion Laboratory, Caltech 170-25, Pasadena, CA 91125.(email: gaidos@gps.caltech.edu)M. G iidelPaul Scherrer Institute, W'firenlingen und Villigen, CH-5232 Vil-ligen PSI, Switzerland. email: guedel@astro.phys.ethz.ch

(ReceivedSeptember 4, 1999; acceptedOctober27, 1999.)