X-rays in the Orion Nebula Cluster: Constraints on the origins of magnetic activity in pre-main sequence stars

A recent Chandra/ACIS observation of the Orion Nebula Cluster detected 1075 sources (Feigelson et al. 2002), providing a uniquely large and well-defined sample to study the dependence of magnetic activity on bulk properties for stars descending the Hayashi tracks. The following results are obtained: (1) X-ray luminosities L_t in the 0.5-8 keV band are strongly correlated with bolometric luminosity with<log L_t/L_bol>= -3.8 for stars with masses 0.7<M<2 Mo, an order of magnitude below the main sequence saturation level; (2) the X-ray emission drops rapidly below this level in some or all stars with 2<M<3 Mo; (3) the presence or absence of infrared circumstellar disks has no apparent relation to X-ray levels; and (4) X-ray luminosities exhibit a slight rise as rotational periods increase from 0.4 to 20 days. This last finding stands in dramatic contrast to the strong anticorrelation between X-rays and period seen in main sequence stars. The absence of a strong X-ray/rotation relationship in PMS stars, and particularly the high X-ray values seen in some very slowly rotating stars, is a clear indication that the mechanisms of magnetic field generation differ from those operating in main sequence stars. The most promising possibility is a turbulent dynamo distributed throughout the deep convection zone, but other models such as alpha-Omega dynamo with `supersaturation' or relic core fields are not immediately excluded. The drop in magnetic activity in intermediate-mass stars may reflect the presence of a significant radiative core. The evidence does not support X-ray production in large-scale star-disk magnetic fields.


Introduction
The astrophysical origin of the surface magnetic activity of solar-type main sequence stars has been established with some confidence (Schrijver & Zwaan 2000). Magnetic fields are generated by differential rotation at the interface (tachocline) between the radiative and convective zones and rise through the convection zone to the surface where they produce active regions, violent flares, coronal heating and other effects. Oscillations in this dynamo account for the 22-year solar cycle. In other main sequence stars, the principal evidence for such a dynamo is the ubiquitous relationship between magnetic activity indicators and surface rotation: more rapidly rotating stars exhibit higher levels of activity until, for some indicators, a saturation of the process is reached.
It is not clear, however, whether this model applies to late-type stars with substantially different internal structure from the Sun's such as PMS T Tauri stars, post-main sequence giants, and low-mass M dwarfs. Such stars may have tachoclines buried deep in the interior or may be fully convective without any tachocline. Yet both T Tauri stars and dM main sequence stars exhibit large active regions and strong flaring indicating that magnetic field generation is operative. Various suggestions have been made to account for this, such as a turbulent dynamo process distributed throughout the convective zone, but with little empirical support. Notably, an activity-rotation relationship is sometimes but not always evident in these stars. But the samples for study have generally been small and the empirical results often discrepant.
It has proved difficult to study the origins of magnetic activity in PMS stars using traditional optical and ultraviolet indicators due to obscuration and confusion arising from gas infall and ejecta. Elevated levels of X-ray emisison, in contrast, are ubiquitous in PMS stars and are relatively unaffected by such problems (see review by Feigelson & Montmerle 1999). However, despite considerable effort with the Einstein and ROSAT missions, the observational basis for understanding the elevated levels of PMS magnetic activity is still murky. Some studies show an X-ray/rotation correlation while others do not, and other confounding correlations with bulk properties are present ( §2.1.3). The theoretical issues are also more complex than with main seqence stars ( §2.2).
The Chandra ACIS study of the Orion Nebula Cluster (ONC), which illuminates the M 42 blister HII region on a near edge of the Orion molecular cloud, provides a unique opportunity to study these issues. Here, a single image reveals ∼ 1000 X-ray emitting PMS stars that span the entire initial mass function and a good portion of the PMS evolutionary tracks. The ONC has been the subject of intense optical and infrared study so that nearly a thousand of its members have been placed on the Hertzsprung-Russell (HR) diagram and over four hundred have photometrically measured rotation periods. Together, the Chandra and optical results give a great increase in sample size for study of the origins of PMS magnetic activity compared to previous efforts.
We find no evidence for the X-ray/rotation correlation strongly present in main sequence stars among ONC stars. Various other effects are found which may constrain alternative explanations for PMS magnetic activity. The most promising interpretation, in our view, is that the magnetic fields are produced by a distributed dynamo within the deep convective zone. Further development of theoretical models is needed in light of our observational results.
The paper begins with a review of the complex empirical and theoretical issues concerning magnetic activity and rotation in late-type stars ( §2). The Chandra ONC dataset is presented ( §3) and the effects of various stellar properties on the X-ray emission are explored ( §4). X-ray/rotation relations are presented in §5 followed by discussion ( §6) and conclusions ( §7). This is the fourth paper in a series on the Chandra observation of the ONC using the ACIS-I detector: Garmire et al. (2000) introduced the field and discussed stars in the BN/KL region; Feigelson et al. (2002, henceforth F02a) give comprehensive tables of the 1075 sources and discuss X-ray emission as a function of mass; and Feigelson, Garmire & Pravdo (2002, henceforth F02b) discuss flaring in pre-main sequence analogs of the early Sun and their implications for the early solar system.

Stellar X-rays and dynamos
We review here past observational ( §2.1) and theoretical studies ( §2.2) studies which provide the foundation for the present study. We find that the situation for main sequence F-K stars is reasonably clear: rotation appears to be the principal observable correlate to X-ray luminosity and, through the Rossby number, rotation can be linked to an α − Ω-type dynamo that successfully explains many features of solar and stellar activity. The Rossby number Ro = P/τ c , the ratio of the rotational period P to the convective overturn time τ c near the base of the stellar convection zone, is a measure of the growth rate of the field in many dynamo theories. Rossby numbers account for mass-dependent structural differences in stellar interiors and are quite stable to reasonable variations in assumptions concerning the physics of the convection zone (Montesinos et al. 2001).
The situation is more confused for giants and dM stars where only weak activity/rotation relationships are seen. It is not clear whether magnetic fields in the these stars with deep convective zones arise from a modified α − Ω dynamo or a distributed turbulent dynamo. For PMS stars, the interpretation is even more uncertain: several dynamo concepts compete with the possibility that the magnetic fields are inherited from the gravitational collapse or arise from star-disk interactions.

Solar-type main sequence stars
The surface magnetic activity of solar-type stars arises from the emergence and reconnection of fields generated in the stellar interior (see Schrijver & Zwaan 2000, for a thorough review). In the X-ray band, this consists of a slowly varying soft X-ray corona and hard emission from violent magnetic reconnection during flares. The first X-ray surveys of latetype stars with the Einstein Observatory revealed a strong X-ray/rotation correlation of the form L s = 10 27 (v sini) 2 erg s −1 where L s is measured in the soft 0.5 − 2.5 keV band and v (sini) is the projected rotation speed in km s −1 (Pallavicini et al. 1981). The Xray/rotation connection for main sequence stars was repeatedly confirmed in many Einstein and ROSAT studies of both field and open cluster stars.
For later comparison with pre-main sequence Orion stars, Figure 1 shows two results from these studies. Panel (a) shows a sample of nearby ≃1 M ⊙ field solar analogs, most with ages between 0.3 and several Gyr. The soft X-ray emission closely follows the relation log L s = 31.1 − 2.64 log P erg s −1 where P is the period in days (Güdel, Guinan, & Skinner 1997;Gaidos 1998). Figure 1b shows the relation between X-ray emissivity and Rossby number from many ROSAT studies of cluster and field stars (Randich 2000, kindly updated by S. Randich). The lines indicate three regimes (Randich et al. 1996): 1. For slowly rotating stars, X-ray emission is approximately linearly dependent on Rossby number as log L s /L bol = −5.0 − 2.1 log Ro.
2. Below log Ro ≃ −0.8, main sequence stars exhibit a 'saturated' X-ray level of log L s /L bol = −3.0. Saturation is well-established for several tracers of magnetic activity in several classes of magnetically active stars (Vilhu & Walter 1987;Fleming, Schmitt, & Giampapa 1995;Krishnamurthi et al. 1998). Considered together, all manifestations of surface magnetic fields should not exceed ∼ 1% L bol , a general limit on the mechanical power in convection (Mullan 1984). But other saturation processes may also be involved such as: a limit of field generation capacity of the underlying dynamo, complete coverage of the surface by strong fields (unity filling factor of photometric starspots), or centrifugal forces on large magnetic loops in rapidly rotating coronae (Randich 1998;Jardine & Unruh 1999).
3. The most rapidly rotating stars with P < 0.5 d lie in a 'supersaturated' regime where X-ray emission drops several-fold below the saturation limit. Cluster 'ultrafast rotators' with v sini ≃ 100−200 km s −1 , rotationally coupled W UMa binary stars, and some dM stars exhibit supersaturation. Again the cause of the diminution of activity is uncertain: perhaps magnetic flux is concentrated toward the poles, centrifugal forces limit the coronal extent, or coronal temperatures lie out of the narrow ROSAT passband in these rapidly rotating stars (Randich 1998;James et al. 2000;Stepień, Schmitt, & Voges 2001;Mullan & MacDonald 2001).
Despite these interpretational difficulties and some discrepancies between different samples, the overall agreement over 3.5 orders of magnitude of X-ray luminosity seen in Figure  1b is probably the clearest empirical indicator of the underlying relationship between magnetic activity and stellar angular momentum (Krishnamurthi et al. 1998). In particular, the dependence of L s /L bol on mass appears to be relatively weak in main sequence stars in contrast to the findings we report here for PMS stars ( §4.3).

dM and giant stars
The α − Ω dynamo model is less convincing for stars with very deep convective zones such as M-type dwarfs and post-main sequence giants; for these stars, the activity-rotation relation is confusing and poorly understood. This departure from solar-type main sequence stars is particularly relevant to PMS stars which are fully convective at the birthline and (except for very low mass stars) develop radiative cores as they descend the Hayashi tracks.
Standard interiors models indicate that the convective zone thickens as mass decreases on the main sequence and the stars become fully convective below mass 0.3 − 0.4 M ⊙ (M3−M4). Yet, no change either in the distribution of rotational velocities or the activity/rotation relation is seen around this spectral type (Delfosse et al. 1998). This may be explained by deficiencies in standard interiors models that neglect to consider how magnetic fields can suppress the onset of complete convection down to ≃ 0.1 M ⊙ (Mullan & MacDonald 2001). There may be a subset of M dwarfs where the surface activity does not depend on rotation; these may be cases where the fields are generated throughout the convection zone. The rotational evolution of dM stars may be simpler than for higher mass stars as there is less opportunity for internal redistribution of angular momentum (Sills, Pinsonneault, & Terndrup 2000).
Considerable study has been made of magnetic activity of giants with masses 1 < M < 3 M ⊙ and bolometric luminosities 3 < L bol < 100 L ⊙ lying at the base of the red giant branch after crossing the Hertzsprung gap, occupying the same region of the HR diagram as < 1 Myr T Tauri stars. Their interiors range from nearly fully radiative G giants to K giants with an outer convective zone occupying 90% of the stellar radius. The strongest effect among these stars is the 'coronal dividing line': giants with spectral types hotter than about K1 typically exhibit log L x ∼ 28 to 30 erg s −1 (log L x /L bol ∼ −7 to -5) while cooler giants are usually X-ray inactive, sometimes with log L x /L bol ≤ −10 (e.g. Ayres et al. 1981;Huensch et al. 1996;Gondoin 1999).
While a rough link between X-ray luminosity and rotation is present because both are low for the cooler giants, the X-ray/rotation diagram for the hotter giants shows mostly scatter, up to three orders of magnitude in L x for a given rotational velocity (Gondoin 1999;Pizzolato, Maggio, & Sciortino 2000). Several stars are known with slow rotation (v sini ≃ 1 − 3 km s −1 ) and high X-ray luminosities (log L x ∼ 29 − 30.5 erg s −1 ). A weak X-ray/rotation correlation may be present for the lower mass (1.0 < M < 1.5 M ⊙ ) giants, but an anticorrelation between L x and v sini may be present among higher mass (1.5 < M < 3.0 M ⊙ ) giants. These authors suggest that the strength of the dynamo in these more massive giants is regulated more by internal differential rotation than the rotation itself. Computations indicate that turbulence-induced differential rotation arises as the convective envelope thickens (Kitchatinov & Rüdiger 1999). However, it is possible that the coronal dividing line arise from differences in magnetic field configurations at the stellar surface rather than differences in dynamo processes (Rosner et al. 1995). A valuable but inconclusive discussion on issues concerning magnetic activity in red giants appears in Strassmeier et al. (1998).

Pre-main sequence stars
High levels of X-ray emission are ubiquitous among PMS stars, with the X-ray luminosity function extending from < 10 28 to 10 31 erg s −1 (see review by Feigelson & Montmerle 1999). This is far above typical main sequence levels of 10 26 − 10 29 erg s−1 but, because their surface areas are greater, their surface fluxes are typically an order of magnitude below main sequence saturation levels. The emission is characterized by high temperatures (kT ≃ 2 keV is typical but 5 to > 10 keV values are not uncommon; F02a), too hot to be produced by an accretion shock. The X-ray emission is usually strongly variable; for example, the Chandra dataset studied here indicates that solar mass ONC stars exhibit flares with L t (peak) ≥ 10 29 erg s −1 every few days (F02b). The emission is thus dominated by flares rather than a soft-spectrum, quiescent corona. The geometry of the reconnecting fields responsible for the flares is quite uncertain. Possibilities include field lines rooted in the stellar surface as in older stars, field lines extending from the star to the disk, and fields in a disk corona.
The relationship between activity and rotation for PMS stars is not well-established. Although elevated X-ray emission is present during all PMS phases, rotation is more easily measured during the later phases when the continuum and sometimes broad emission line excesses of the 'classical' T Tauri phase have subsided. Most of the measured periods are obtained from photometric time series of rotationally modulated cool starspots on 'weaklined' T Tauri stars which are no longer interacting with their circumstellar disks (e.g. Herbst et al. 2002). A handful of bright T Tauri stars also have surface Doppler images (e.g. Donati 1999;Granzer, Schüssler, Caligari, & Strassmeier 2000) and Zeeman magnetic field measurements (Johns-Krull, Valenti, & Koresko 1999). X-ray/rotation studies have concentrated on T Tauri stars in the Taurus-Auriga complex (d ≃ 140 pc), which are often well-studied and not heavily obscured. Promising evidence for a solar-type dynamo emerged from the Einstein Observatory when Bouvier (1990) reported an anti-correlation between F s = L s /4πR 2 ⋆ and rotation period in a sample of 13 classical and 8 weak-lined T Tauri stars. Their X-ray activity is elevated several-fold above active main sequence stars with similar rotations. However, the correlation is weaker and the scatter greater when a larger Einstein sample of 50 Taurus-Auriga stars are considered (Damiani & Micela 1995). Studies of the entire Taurus-Auriga region with the ROSAT All-Sky Survey gave large samples showing apparent correlations between X-ray luminosities and rotational periods and surface velocities (Neuhäuser et al. 1995;Wichmann et al. 2000;. These results will be discussed with respect to our findings in §5.1. The X-ray/rotation relation has also been sought in other nearby star forming regions. ROSAT studies of the Chamaeleon I cloud and the ONC, for example, show most stars lying below the saturation level without an evident X-ray/rotation correlation (Feigelson et al. 1993;Gagné, Caillault, & Stauffer 1995). Two ROSAT samples selected for unusually strong X-ray emission similarly show no X-ray/rotation correlation, with several stars overluminous in X-rays compared to saturated main sequence stars (Preibisch 1997;Alcalá et al. 2000).
In summary, a broad correlation with rotational speed is present in some samples, but considerable scatter is present and the relationship may not be the same as seen in main sequence stars (Figure 1). Note, however, that previous investigations generally had samples too small to permit study of the rotational effects on X-ray activity independent of other properties such as stellar mass 3 .

Theoretical considerations
The standard dynamo theory developed for the solar interior and applied to main sequence and giant stars as outlined above cannot be readily applied to fully convective stars, as it assumes the field is generated and amplified at the interface, or tachocline, between the convective and radiative zones. However, models have been developed where dynamos operate throughout a convection zone (Durney, De Young, & Roxburgh 1993). If sufficiently efficient, such a distributed dynamo could not only explain surface magnetic activity, but could have a considerable effect on the bulk stellar properties. For example, a field with 3% of the energy density of the gas distributed throughout the interior of PMS stars shifts the Hayashi tracks several hundred degrees towards the red compared to standard tracks in the HR diagram (D'Antona, Ventura, & Mazzitelli 2000).

α − Ω solar-type dynamo
In a modern dynamo theory for Sun-like stars (e.g. Parker 1993;Charbonneau & Mac-Gregor 1997;Markiel & Thomas 1999), a toroidal field is generated by strong differential rotation that arises in the thin overshoot layer or tachocline between the radiative and convective zones (the Ω effect). These fields are then twisted and transported through the rotating convective zone to the surface (the α effect). With an appropriate choice of α, such models explain many characteristics of solar activity including the 22-year cycle, the 'butterfly diagram' of active region magnetic orientations, and differential rotation in the solar interior inferred from inversion of helioseismological data (e.g. Charbonneau et al. 1999).
For dynamo mechanisms that scale with the Rossby number, the deep convective zones of PMS stars lead to τ c values an order of magnitude longer than in main sequence stars, giving smaller Ro values and more magnetic field generation at a given rotational period compared to main sequence stars. However, the relevance of Ro for PMS magnetic field generation is not clear. For example, Durney & Robinson (1982) suggest that for a distributed dynamo, the efficiency scales with the depth of the convective region as well as the inverse of the Rossby number.
Two detailed calculations of the convective turnover time τ c , and hence Rossby numbers, for PMS stars have been reported. First, Gilliland (1986) considered nonrotating PMS interiord and finds τ c is ∼ 200 days for fully convective PMS stars at the top of the Hayashi track. In higher mass stars, τ c drops sharply by several orders of magnitudes in ≃ 1 (10) Myr for M = 3 M ⊙ (1 M ⊙ ) stars. In lower mass 0.5 − 1 M ⊙ stars, τ c falls only gradually over 10 7 − 10 8 yr. Second, Kim & Demarque (1996) provide calculations of τ c using updated OPAL opacities, realistic surface boundary conditions, improved models of diffusion and rotational mixing, and angular momentum loss by a magnetized stellar wind. They treat fully convective Hayashi track stars with masses between 0.5 and 1.2 M ⊙ undergoing solid body rotation with equatorial surface velocity of 30 km s −1 (corresponding to a period P ≃ 5 days if R * = 3 R ⊙ ). Surface rotation is assumed to decay with age as t −1/2 (which may often not be correct). They find that τ c rises from around 600 to ≥ 1000 days over several million years in 0.5-1 M ⊙ stars, whereafter it drops to shorter timescales. More massive 1.0 − 1.2 M ⊙ stars start at τ c ≃ 700 − 400 days and only show the decline. This implies that dynamo efficiency is constant (for solar-mass) or grows 1 − 2 orders of magnitude (for sub-solar mass) stars during the first ∼ 10 Myr, whereafter it drops by several orders of magnitude over gigayear timescales.
We use τ c values from Kim & Demarque (1996) in deriving Ro values for ONC stars below. We caution that the calculations of τ c by Gilliland (1986) and Kim & Demarque (1996) differ both in qualitative behavior and quantitatively by factors of 2 − 5 over the age range of interest, and even the relevance of the Rossby number for magnetic field generation or surface magnetic activity in these stars is uncertain.

Distributed dynamos
A distributed dynamo due to turbulence in the convection zone was first discussed in detail by Durney, De Young, & Roxburgh (1993). They emphasize that the turbulent velocity field in a convection zone will generate small-scale magnetic fields that can attain energy densities comparable to the kinetic energy density of convective motions. Rotation may enhance the rate of field generation but is not essential to the process. The principal result of adding an Ω effect from the boundary between a convection zone and a radiative core is to build significant energy densities in large-scale fields, such as those that dominate the solar cycle. They argue that small-scale turbulent fields may coexist with large-scale α − Ω fields generated in the tachocline, and should dominate the large-scale fields in stars with deep convective zones.
Recent calculations have been made of fully convective T Tauri stars rotating nearly as a solid body with differential rotation around 1%, both radially within the convection zone and latitudinally along the surface (Küker & Rüdiger 1997;Kitchatinov & Rüdiger 1999;Küker & Stix 2001). Field amplification occurs throughout the convection zone, and little dependence on bulk rotation is expected. In other models of PMS interiors, magnetic activity is inferred to arise from α − α processes, producing non-axisymmetric and steady fields, in contrast to α − Ω fields which are typically axisymmetric and oscillatory (Moss 1996;Küker & Rüdiger 1999;Kitchatinov 2001). Schrijver & Zwaan (2000, p. 183f) outline a related dynamo concept for stars with deep convective envelopes. At the base of the convective zones where the Alfvén velocity is low, magnetic fields are subject to little buoyancy and reside in the same region for a long time. They are then wound up and greatly strengthened by differential rotation, giving a strong field layer analogous to the tachocline in solar-type stars from which an α − Ω dynamo can be sustained. Mullan & MacDonald (2001) give a valuable discussion concerning whether a sharp change in X-ray emission is expected in a star (or ensemble of stars) that passes from a core-convection zone structure to a completely convective structure. No clear prediction can be made: turning off an efficient α − Ω dynamo should reduce the X-ray emission, but the less efficient α − α dynamo may compensate by operating over a larger volume.
Finally, we note that distributed dynamo theories refer to field generation in the stellar interior and do not specify how these field emerge onto the surface to produce the extremely large starspots and violent X-ray flares observed in PMS stars. A critical issue is whether the surface magnetic saturation level, as measured by L x /L bol , could be substantially lower for a distributed dynamo than a main sequence α − Ω dynamo.

Relic and core magnetic fields
It is possible that the dominant source of magnetic flux in T Tauri stars are 'fossil fields' inherited from the star formation process rather than generated by a dynamo (Mestel 1999). Poloidal magnetic fields of order 10 4 G are roughly expected from compression of interstellar cloud fields (Dudorov et al. 1989;Levy, Ruzmaikin, & Ruzmaikina 1991). In a fully convective PMS star, this fossil interstellar field should quickly decay due to turbulent magnetic diffusivity. However, it is possible that the field may collect into flux ropes which would resist turbulent diffusion until a radiative core develops (Moss 2002).
PMS magnetic fields might also arise in the radiative core (which forms at t ≃ 2 Myr for a 1 M ⊙ star) by capturing flux from the convective zone. Such core fields could persist unchanged for billions of years and could coexist with convective zone dynamo-generated fields (Tayler 1987;Moss 1996;Kitchatinov, Jardine, & Collier Cameron 2001). Relic fields trapped in the larger radiative cores of intermediate mass stars may account for the high surface fields in Am/Ap stars (Mullan 1973;Stepień 2000). Unlike dynamo generated fields, relic fields are likely to have a global dipole component and may be non-axisymmetric (Kitchatinov 2001). A global dipole is needed to produce the large-scale field lines thought to link the T Tauri star to the circumstellar disk at the corotation radius (e.g. Hartmann 1998).

Disk-related fields
T Tauri stars differ from older late-type stars in that they often have a circumstellar disk. While the disk is thermodynamically cold and neutral, sufficient X-rays and cosmic rays likely penetrate and ionize the disk to freeze in magnetic fields and initiate MHD instabilities and dynamo processes (Glassgold, Feigelson, & Montmerle 2000). Some forms of magnetic activity, such as the reconnection flares that dominate the X-ray emission, may thus arise in three locations: at the stellar surface as in other late-type stars; at the corotation interface between large-scale dipolar stellar fields and the inner disk (Shu et al. 1997;Birk et al. 2000); or above the disk in a magnetically active corona (e.g. Levy & Araki 1989;Romanova et al. 1998;Merloni & Fabian 2001). There is a wealth of evidence for strong activity at the stellar surface, but the strong fluorescent 6.4 keV iron line seen in two protostars (Koyama et al. 1996;Imanishi, Koyama, & Tsuboi 2001) may be evidence that X-ray flares occur in close proximity to the disk. This issue of the geometry of reconnecting magnetic field lines in T Tauri systems is discussed in detail by F02b.
3. The X-ray data

Observations
The Orion Nebula Cluster (ONC) is the richest young star cluster within 500 pc with ≃ 2000 members concentrated in a 1 pc (8 ′ ) radius sphere (O'Dell 2001). The full initial mass function from a 45 M ⊙ O star to dozens of substellar brown dwarfs is present. Over 1500 stars are not deeply embedded and have V < 20 magnitudes, ∼ 1000 of which have high-quality photometry and spectroscopy (Hillenbrand 1997, and subsequent updates to the database). This gives locations on the HR diagram from which stellar ages and masses are inferred from theoretical stellar interior models (D'Antona & Mazzitelli 1997). We ignore here the X-ray population of deeply embedded stars which lies behind the ONC around the OMC 1 cloud cores.
The ONC was observed with the ACIS-I imaging array on board Chandra twice during the inaugural year of the satellite, on 12 Oct 1999 and 1 Apr 2000, for ≃ 12 hours on each occasion. The satellite and instrument are described by Weisskopf et al. (2002). The reader should consult F02a for an atlas of the field, full description of the data reduction procedures, and properties of the 1075 X-ray sources found in the field.

Sample and database
Of the 1075 ACIS ONC sources, we consider stars with estimated ages and masses (Hillenbrand 1997) and further eliminate stars with M > 3 M ⊙ 4 The resulting sample of 525 stars is listed in Table 1. Absorption is not large for most of these stars: 47% have A V ≤ 1, 95% have A V < 5, and for 77% the difference between the observed total band (log L t ) and absorption-corrected (log L c ) X-ray luminosities does not exceed 0.3. The log L t values in the 0.5 − 8 keV band thus reflect the true emission with reasonable accuracy. The log L s luminosities in the soft 0.5 − 2 keV band will be more seriously affected by absorption, and are provided only to permit comparison with earlier ROSAT soft band results. Note that the main source of scatter in the X-ray luminosities is the intrinsic variability of the sources during the two observations. Table 1 gives: the ACIS-I CXOONC source name (column 1); associated optical star (column 2, most are designated JW from Jones & Walker 1988); stellar bolometric luminosity, mass and age (columns 3 − 5); a circumstellar disk indicator (column 6); rotational period with reference (columns 7 − 8); estimated Rossby number (column 9); soft and total band Xray luminosities (columns 10−11), and the ratio of total band X-ray to bolometric luminosity (column 12). Columns 1 − 5 and 10 − 11 are extracted from Tables 2 and 3 of F02a. As in F02b, we considered stellar ages below log t = 5.5 yr to be upper limits because of difficulties in establishing the zero-age point in evolutionary calculations (e.g. Wuchterl & Klessen 2001). The disk indicator is based on the criteria given by F02b with data from F02a. A + symbol indicates a near-infrared photometric excess ∆(I − K) > 0.3 and/or association with a Herbig-Haro outflow, far-infrared source or imaged proplyd; a − symbol indicates ∆(I − K) < 0.3 and no association of these types; and . . . indicates insufficient information for classification. The ∆(I − K) measurements are from Hillenbrand et al. (1998).
The photometric rotational periods are extracted from  (2000) and Herbst et al. (2002); and S = Stassun et al. (1999). A few rotation periods have been updated from those given in F02a based on the final results of Herbst et al. (2002), and stars with discrepant reported photometric periods are listed in the Notes to Table 2 of F02a. We do not supplement these with 43 new periods estimated from the projected Doppler surface velocity measured spectroscopically by Rhode, Herbst, & Mathieu (2001). Periods derived from spectroscopy are inaccurate due to the unknown inclinations of individual stars, and a systematic overestimation compared to photometric periods is present.
Column 9 of Table 1 lists Rossby numbers Ro derived from the observed rotation periods and τ c estimated from Figure 3 of Kim & Demarque (1996) in the 0.5−1.2 M ⊙ range ( §2.2.1). Due to these restrictions, only 36 values are given.
Columns (10-12) give the X-ray luminosities log L s (erg s −1 ) in the soft 0.5 − 2 keV band, log L t in the total 0.5 − 8 keV band, and the ratio log L t /L bol where L bol is obtained from Hillenbrand (1997). The log L s and log L t values are obtained from Table 3 of F02a; see their §2.6-2.9 for details. 5 .
In §4-5, we visualize the data from Table 1 using boxplots in addition to two-dimensional scatter plots. Boxplots are a simple nonparametric graphical tool for visualizing and comparing univariate distributions widely used in many fields (Tukey 1977;McGill, Tukey & Larsen 1978). The center of the box indicates the median value and the 'hinges' (ends) of the box enclose the 25% and 75% quartiles of the data. 'Whiskers' (error bars) extend from the box to the largest data value less than 1.5 times the quartile range. Circles show outliers if present; for a Gaussian distribution, about 1 in 100 points will be an outlier. If the 'notches' (indented regions around the medians) of two boxes on the same plot do not overlap, then the two population medians are different with > 95% confidence based on an assumption of asymptotic normality of the standard deviation of the medians (i.e. large-N samples). The width of the boxes is scaled to the square root of the number of points included in each box so that the wider boxes have greater statistical reliability than narrower boxes. The range of each box along the abscissa was chosen by us in an arbitrary manner. The graphics were produced with R (Ihaka & Gentleman 1996), a public-domain statistical software package closely related to the commercial S-Plus package. R software and documentation can be obtained at http://www.r-project.org.

Sample completeness
Although Table 1 is by far the largest dataset of magnetic activity measurements for PMS stars with measured stellar properties, we must consider systematic biases present in the sample: 1. Our sample is first restricted to 979 ONC stars placed on the HR diagram lying within the ACIS field. This sample is estimated to be 100% complete for all ONC stars with M ≥ 0.5 M ⊙ with A V ≤ 0, and for A V < 2.5 100% complete for M ≥ 1 M ⊙ and 50 − 70% complete above the substellar limit (Hillenbrand 1997, , §4.3). The main omission are very-low-mass M stars and brown dwarfs which show up in deep K-band studies (Hillenbrand & Carpenter 2000).
2. Of these 979 stars, our sample is restricted to 525 stars detected with Chandra having ACIS count rates above 0.1−0.4 cts ks −1 in the 0.5−8 keV band, where the higher values are due to reduced sensitivities from the poor point spread function towards the outer portions of the cluster (F02a, §2.12). For most cluster members with typical intrinsic PMS X-ray spectra and low absorptions, this limit corresponds to log L t = 28.0 − 28.5 erg s −1 although some limits reach log L t = 29.0 erg s −1 . Here also a strong bias in mass is present: ≃ 90% (F02a, §5.2) of ONC members with M > 1.5 M ⊙ are present compared to roughly 25% of PMS brown dwarfs (F02a, §5.6).
3. Of these 525 stars, 232 have measured photometric periodicities interpreted as rotationally modulated starspots. By comparing spectroscopically measured v sin i rotational velocities for ONC stars with and without detected photometric starspots, Rhode, Herbst, & Mathieu (2001) have found that the stars with modulated starspots have the same rotational distribution as the underlying ONC population. Also, the latest study of Herbst et al. (2002), which provides most of the photometric rotation periods used here, extends period measurements down to M ≃ 0.1 M ⊙ . The rotation measurements should thus not contribute any further bias to our sample except below M ≃ 0.1 M ⊙ .
4. Both the optical and X-ray data have arcsecond (∼ 500 AU) resolution and thus see the majority of binary and multiple systems as a single star (Mathieu 1994). We assume that both the optical and and X-ray light is dominated by a single primary component. This assumption also tends to deemphasize the presence of lower mass stars from our sample.
We conclude that the principal bias in our sample of 525 stars involves stellar mass and associated variables such as bolometric luminosity. A double bias is present: the underlying optical sample is deficient in low mass stars compared to the underlying cluster, and the X-ray observation is deficient in detecting these stars. A more complete sample would thus have many more objects at low masses with characteristically lower X-ray luminosities. The bias is nearly absent for masses 0.7 < M < 3 M ⊙ . From Table 5 in F02a and Table 1

Sources of uncertainty
As considerable scatter appears in the correlation plots presented below, it is important to discriminate the degree to which these arise from measurement errors or from true astrophysical variance. The broad band 0.5 − 8 keV X-ray luminosities log L t in most cases have rather small (∆ log L t = ±0.1) statistical uncertainties, but the intrinsic variability due to X-ray flaring is frequently ∆L t = ±0.3 during the two 12-hour Chandra observations (F02a, §2.9) and sometimes exceeds 1.0 (F02b). The long-term variability of a star will obviously exceed the variability found during the limited observations available here. We thus expect all samples of PMS stars to exhibit significant scatter in X-ray luminosity, roughly ∆ log L t = ±0.5 for the majority of stars, due to statistics and variability.
Uncertainty or systematic errors may also be present in other stellar parameters. log L bol is relatively well-established with errors about ±0.15 by the photometry and spectrometry of Hillenbrand (1997). Stellar masses and ages depend on the model assumptions of the evolutionary tracks adopted in our study (D'Antona & Mazzitelli 1997). These quantities will systematically change with differing assumptions regarding the equation of state, mixing length theory, accretion, rotation, and the internal magnetic field (D'Antona, Ventura, & Mazzitelli 2000;Palla 2001). The effects of even modest observational error on parameters derived from evolutionary tracks, especially stellar age, may be significant: an uncertainty ∆T ef f = ±100 K and ∆L bol = ±0.1 produces fractional errors around ∆ log M = ±0.1% and ∆ log t = ±0.5 (Siess 2001). Rotational periods generally have almost no statistical uncertainty but sometimes suffer large errors if the wrong peak in a periodogram is chosen. A few stars in our sample with discrepant reported periods of this type are listed in the notes to Table 1 of F02a.
We thus expect scatter in various stellar properties, particularly age, due to observational error, plus possible systematic errors in properties due to model assumptions. In most cases, the latter may produce offsets or stretching of the plotted axes, but will not affect overall strength of a correlation. The greatest danger would arise if both the X-ray luminosity and another property of interest were mutually dependent on magnetic field generation, producing spurious correlations. However, this problem does not appear to be present: PMS model interiors with magnetic fields tends to have cooler surfaces which would yield lower inferred masses (D'Antona, Ventura, & Mazzitelli 2000). In contrast, we find below ( §4.3) that Orion stars with stronger magnetic activity have higher rather than lower masses than those with weak activity.

X-ray dependencies on stellar properties
We present here empirical results relating the X-ray emission, viewed as an indicator of magnetic activity, to the bulk properties of the ONC PMS stars: bolometric luminosity, mass, age, presence of disk, and surface rotation. In some cases we elucidate longstanding relationships found from past studies ( §2.1.3), while in other cases we reveal new phenomenology. The findings are summarized in §6.1.

X-ray and bolometric luminosities
With a sample population far larger than previously available, we can now see why a correlation between L s and L bol has been seen in past studies of PMS stellar populations but with inconsistent quantitative results (e.g. Walter & Kuhi 1981;Feigelson et al. 1993;Casanova et al. 1995;Gagné, Caillault, & Stauffer 1995;Preibisch & Zinnecker 2002;Getman et al. 2002). Figure 2a shows a broad correlation over three orders of magnitude, roughly consistent with the linear relationship log L t ≃ 29.8 + log L bol erg s −1 or, as seen in Figure 4c, log L t /L bol ≃ −3.8. But, due to the selection bias against X-rayfaint low-mass stars ( §3.3), it is likely that the median X-ray luminosity at low L bol values is overestimated here, leading to a steeper true relation. For example, the data could be modelled as L t ∝ L 2 bol with a saturation limit at high luminosities. Although difficult to quantify due to the scatter and bias, examination of the notches in the boxplot (Figure 2b) shows that the overall correlation has very high statistical significance.
Whatever the underlying relationship between X-ray luminosity and L bol , a great deal of scatter is present 7 . At any given L bol value, the dispersion in L t or L t /L bol is such that half of the stars lie greater than a factor of 3 away from the predicted value, and some are discrepant by more than an order of magnitude. This dispersion must be astrophysical in origin as it is too large to arise from observational or absorption effects. It is likely that X-ray flaring is the main contributor to this dispersion, but other dependencies on other variables may also be important.

X-ray emission and stellar size
As most T Tauri stars have similar surface temperatures T ef f , bolometric luminosity is closely related to stellar surface area via L bol = 4πR 2 σT 4 ef f where σ is the Stefan-Boltzman constant. X-ray luminosities which scale with L bol will therefore also scale with stellar surface area, radius and volume. Figure 3 shows one of these relationships: X-ray emission compared with stellar volume in units of V ⊙ = 4πR 3 ⊙ /3. Recognizing that the median levels for the smallest stars is probably overestimated due to undetections ( §3.3), we find that X-ray luminosity scales roughly as L t ∝ V 2/3 ∝ R 2 .
A similar, but considerably steeper, activity-radius effect has been found in a sample dM 1V main sequence stars by Houdebine & Stempels (1997). They find that Hα, Ca II H&K and soft X-ray activity indicators scale with absolute magnitude which, for constant surface temperature, itself scales with radius, surface area and volume. Stated another way, early dMe stars are more luminous, and hence larger, than less active dM stars. The dM X-ray sample is small and suggested a relationship around L x ∝ R 7 . Figure 4 shows scatter diagrams and boxplots of X-ray emission as a function of stellar mass. A comparison of panels (a) and (b) to those in Figure 2 shows that mass is as strong a predictor for X-ray emission as bolometric luminosity, although the X-ray/mass relation has only occasionally been noticed in past studies with discrepant quantitative results (e.g. Feigelson et al. 1993;Neuhäuser et al. 1995;Preibisch & Zinnecker 2002). Given a strong L t − L bol correlation, a similar L t − M relation is expected from a coeval PMS population given the tilt of the isochrones with respect to the isomass lines in the HR diagram. The relationship appears steeper than linear, roughly consistent with log L t ≃ 30.2 + 1.5 log M erg s −1 , but again we recall the selection bias ( §3.3) that should increase the slope of this relation at low masses. This is consistent with the recent Chandra-based result log L t = 30.10 + 1.97(±0.24) log M erg s −1 derived by Preibisch & Zinnecker (2002) in the IC 348 young stellar cluster over a mass range similar to that considered here 8 .

X-ray emission and stellar mass
The log L t /L bol − M diagram (Figure 4c) dramatically reveals an effect distinct from the general L t − M relationship: X-ray emission from the higher mass stars in the sample with 2.0 < M < 3.0 M ⊙ has an enormous dispersion. It is possible that, for M > 2 M ⊙ , the ONC population can be divided into two classes. The majority of these 2 − 3 M ⊙ stars have −5 < log L t /L bol < −3 like virtually all lower mass stars, while a minority 9 show 8 The observed L t −mass correlation may be affected by unresolved binarity, which is likely to be present in over half of the ONC 'stars' under study (Mathieu 1994). However, it seems unlikely that the effect is very significant. If fainter secondary components were responsible for the X-ray emission, then the low-mass systems should show as wide a spread in L t as high-mass systems and the L t -mass correlation would be weak. A ROSAT study of nearby T Tauri stars confirms that the X-ray emission of primaries dominates over the secondaries in resolved wide binaries (König, Neuhäuser, & Stelzer 2001). Note however that we do believe binarity is important for the interpretation of X-ray emission from higher mass (M > 2 M ⊙ ) stars. 9 There is no indication these X-ray-weak stars are foreground interlopers, as their proper motions have 98 − 99% probabilities of cluster membership (Hillenbrand 1997). These stars, however, are older than most ONC stars; it possible that both mass and age are involved in their unusually low magnetic activity. Note that weak evidence for a decay in X-ray emission as PMS stars age was reported for 0.7 < M < 1.4 M ⊙ −7 < log L t /L bol − 5. The latter low X-ray emissivities are ubiquitous for the intermediatemass 3 < M < 30 M ⊙ ONC stars (see Figure 12a in F02a). Two interpretations of this difference in X-ray behavior of intermediate-and low-mass PMS stars are outlined in §6.2.

X-ray emission and circumstellar disks
From the very beginning of X-ray studies of PMS populations, most studies found that accretion and outflows associated with 'classical' T Tauri star-disk interactions were not essential ingredients for elevated X-ray levels. This is often shown as an absence of correlation between X-ray and Hα emission when a full PMS population of weak-lined and classical T Tauri stars is treated, although an X-ray/Hα correlation may be present within the weak-lined T Tauri stars alone where both arise from magnetic activity (e.g. Montmerle et al. 1983;Feigelson et al. 1993;Damiani & Micela 1995;Casanova et al. 1995;Gagné, Caillault, & Stauffer 1995). In contrast, some studies find that weak-lined T Tauri stars (defined by weak Hα emission) are an order of magnitude more X-ray luminous than classical T Tauri stars (Neuhäuser et al. 1995;. But this is likely due to misclassifications and incompleteness in the sampling of X-ray-faint weak-lined T Tauri stars in contrast to the good optical sampling of X-ray-faint classical T Tauri stars (Preibisch & Zinnecker 2002).
We consider here the photometric near-infrared excess measure ∆(I − K) > 0.3 as a discriminant of the presence of a disk, which is not necessarily the same as strong optical emission lines which indicate the presence of an accreting disk. Figure 5 shows no important relationship between X-ray emission and the presence of a disk. (Another view of this result appears in the middle panel of Figure 10 in F02a.) Figure 5c shows that mass, which is a strong correlate of L t , is not an important confounding variable in this result.

X-ray emission and stellar age
Low mass stars evolve in many respects during their descent along the Hayashi tracks: the star contracts; brief periods of deuterium and lithium burning occur; a radiative core forms and grows although most of the star is convective; and star-disk interaction declines or terminates, perhaps releasing the star from rotational coupling with the disk. While most ONC stars appear to have formed within the past 2 Myr, a tail of stellar ages appears to stars by F02b, and is discussed again in §4.5 below. extend beyond 10 Myr, although it is not clear these ages are accurate. Alternatively, the older Myr stars in the field may be interlopers from the older Orion Ia-c OB associations (see discussion in Hillenbrand 1997;Hartmann 2001).
Past study of the evolution of X-ray emission along the Hayashi tracks has been been limited and somewhat confusing. In ROSAT studies of individual PMS clusters, Feigelson et al. (1993) report a tentative drop of soft band L s from < 1 to 10 Myr while Neuhäuser et al. (1995) report a rise with age. Kastner et al. (1997) collect average soft X-ray levels for stars from several clusters of different ages and find that < log L s /L bol > rises an order of magnitude over tens of Myr. We caution that comparisons of mean X-ray luminosities of different clusters is subject to systematic error due to different X-ray sensitivities and different levels of prior knowledge of the cluster memberships. A rise in X-ray emissivity with PMS age is consistent with a model of stellar angular momentum evolution where surface rotation (and presumably the internal magnetic dynamo efficiency) rises as star-disk rotational coupling ends and the star contracts (Bouvier, Forestini, & Allain 1997;Barnes, Sofia, & Pinsonneault 2001). This model is supported by study of the η Cha cluster, a recently identified older PMS cluster with t = 9 Myr stars, where nearly all have unusually short rotational periods and high X-ray luminosities around log L s /L bol ≃ −3 (Mamajek, Lawson, & Feigelson 2000;Lawson et al. 2001). Figure 6 shows the X-ray/age relationship found for the ONC sample discussed here. Recall that ages were estimated from the evolutionary tracks of D' Antona & Mazzitelli (1997) based on the photometry and spectroscopy of Hillenbrand (1997), and that we truncate all extremely young inferred ages at 0.3 Myr. Panels (a) and (b) reveal a small but statistically significant decline in X-ray luminosity from a median level of log L t ≃ 29.6 erg s −1 for ages < 1 Myr to log L t ≃ 29.2 erg s −1 for ages > 10 Myr. A similar but steeper drop in L t is found when the 0.7 − 1.4 M ⊙ solar analogs are considered alone (F02b). We also note that the dispersion in X-ray luminosities decreases monotonically with age from > 3 to 2 orders of magnitude. Panels (c) and (d) show that this fall in X-ray luminosity is roughly equal to the decrease in bolometric luminosity from 0.3 to 10 Myr, so that the X-ray emissivity log L t /L bol is roughly constant at -3.8. But a distinctive change is seen among the oldest ONC stars: with the exception of a single intermediate mass outlier (see §4.3), all of the 13 ONC stars with apparent ages between 10 and 30 Myr have unusually high X-ray emissivities with log L t /L bol ≃ −3 at the main sequence saturation level, similar to the η Cha finding. There are several possible interpretations for these stars. If they are indeed cluster members and are correctly placed in the HR diagram, they suggest an increase of L t /L bol with age. However, if they have been erroneously placed on the diagram, due perhaps to underestimation of their extinction, then L bol would be higher and the L t /L bol ratio consistent with the bulk of the ONC PMS stars.

X-ray emission and surface rotation
The relationships between X-rays and rotation in ONC PMS stars are shown in Figures  7 and 8. They should be compared to analogous graphs of main sequence stars shown in Figure 1 which are discussed in §2.1.1.

X-rays and rotational period
Figures 7 and 1 immediately show two differences between PMS and main sequence magnetic activity: a large fraction of ONC stars have considerably stronger X-ray emission than main sequence with similar rotation periods; and the strong main sequence anticorrelation between X-rays and period is dramatically absent in the ONC population 10 . Instead, a correlation in average luminosities with period is marginally present (compare the boxplot notches in Figure 7b) such that stars with periods P > 10 days are about 4 times more X-ray luminous on average than stars with P < 2 days. This trend is in the opposite direction of the strong anticorrelation seen in main sequence stars, for stars with similar periods; for example, for solar-mass stars shown in Figure 1a, the X-ray luminosity of stars with P > 10 days is ∼ 100 times smaller than those with P ≃ 2 days. The log L t /L bol vs. P diagram similarly does not show any sign of the steep decline in X-ray luminosity with period seen in main sequence stars over a similar period range (compare Figure 7c with Figure 1a).
Perhaps the most challenging characteristic of this finding to explain are the high X-ray luminosities of very slowly rotating PMS stars. Such stars had been occasionally found in the past; for example, Preibisch (1997) noted that the ONC star JW 157 (= P 1659) has a surprisingly high X-ray emissivity log L s ≃ 31.5 erg s −1 for its 17.4 day period, and Lawson et al. (2001) find RECX 10 in η Chamaeleon has log L s /L bol = −2.9 erg s −1 with P = 20.0 days. Both of these are slowly-rotating weak-lined T Tauri stars, although JW 157 appears to be very young (log t < 5.5 yr) while RECX 10 is old (log t = 7.0 yr). The ONC provides a sample of ≃ 30 such stars with P > 10 days and log L t /L bol = −4 ± 1 with a wide range of masses.
We recall that some Einstein and ROSAT studies report X-ray/rotation correlations while others do not ( §2.1.3). Perhaps the clearest case that is discrepant from our result is the ROSAT study of Taurus-Auriga PMS stars by . They find that, for 39 stars in the soft X-ray band, X-ray emission systematically decreases from log L s ≃ 30.6 to 29.1 erg s −1 and log L s /L bol ≃ −3.0 to −4.5 as rotational period increases from ≃ 1 to 10 days. We suspect that this discrepancy arises from incompleteness in the Taurus-Auriga sample; it is difficult to define and study the population of this large cloud complex where star formation has occurred in cores dispersed over 500 square degrees. First, arguments have been put forward that Taurus-Auriga PMS stellar samples are deficient both in high mass stars (Walter & Boyd 1991) and faint low mass weak-lined T Tauri stars (Luhman 2000;Preibisch & Zinnecker 2002). The effects of such missing stars on an X-ray/rotation diagram is unknown. Second, rotational periods of Taurus-Auriga stars were typically obtained from photometric observations of specific PMS stars with observing sessions spanning ≃ 10 − 40 days (e.g. Bouvier et al. 1986Bouvier et al. , 1997 and result in periods for only 39 of 168 stars detected in the study of . In contrast, most ONC periods were obtained from observing runs spanning several months or years (Herbst et al. 2000(Herbst et al. , 2002, and result in periods for 232 of 525 stars in the present ONC study. It is thus possible that an improved study of Taurus-Auriga rotations would show a subpopulation of slow rotators with strong X-ray emission which would remove the X-ray/rotation correlation found by .

X-rays and Rossby number
It is well-known that combining stars of different masses can blur relations between magnetic activity indicators and rotational periods. We address this in two ways. First, examination of individual symbols in the scatter plots in Figure 7, which represent different mass ranges, shows no evidence of the expected decrease in X-ray emission with increasing period within individual mass strata. Second, we consider the X-ray relation to Rossby number, which is very effective in removing mass-dependent effects in the context of α − Ω dynamo models (Noyes et al. 1984;Montesinos et al. 2001). As described in §3.2, we obtain Rossby numbers from the convective turnover times for PMS stars calculated by Kim & Demarque (1996), recognizing that they assume a single rotation rate and are available only for 0.5 − 2 M ⊙ stars. The results are shown in Figure 8; panel (c) is most valuable for its comparison with the main sequence X-ray/Rossby number relation (Figure 1c).
The X-ray/Rossby number plot (Figure 8b) gives a possible explanation for the absence of the expected X-ray/rotation relation. Due to the very short calculated convective turnover times at the base of the deep convection zones of PMS stars, most ONC PMS stars around M ∼ 1 M ⊙ lie in the supersaturated regime rather than the linear regime where X-ray emission inversely correlated with Rossby number. Extremely long rotation periods around 100 days would be needed to move the ONC stars into the linear regime.

Discussion
It is valuable to first recognize why this study may achieve results not available to previous observations. For PMS stars, X-rays from reconnection flares are the most easily observed indicator of surface magnetic activity. Optical emission line indicators useful in other types of stars are often confused by lines due to accreted or ejected matter, and the ultraviolet is ofen obscured by interstellar matter. Doppler imaging and Zeeman effect studies are very valuable for mapping surface fields, but have to date been obtained for only a handful of the brightest T Tauri stars. X-ray emission, on the other hand, is typically elevated 10 2±1 times above solar levels during all phases of PMS evolution (Feigelson & Montmerle 1999). PMS spectra show typical plasma energies around 1 − 3 keV and are sometimes dominated by plasmas as hot as ∼ 10 keV (F02a), and can therefore been studied even in the presence of considerable interstellar absorption. A 2 keV photon has the same penetrability as a 2 µm near-infrared photon, and is comparable to mid-infrared emission above 5 keV (Montmerle & Grosso 2002). Finally, the ONC provides the largest and best defined PMS sample in the nearby Galaxy in the sense that virtually all members of the cluster appear in the optical/infrared sample with very few contaminants from unrelated objects. The ONC has the largest sample of PMS stars with detailed optical photometric, spectroscopic and rotation measurements. While nearly all earlier X-ray telescopes studied the ONC, only Chandra has the sensitivity and resolution to resolve the crowded cluster core (except for multiple systems). Our observations, for example, achieve more than an order of magnitude greater sensitivity than ROSAT observations of the ONC.

Summary of findings
In this light, the principal findings from examination of bivariate relations between X-ray emission and stellar properties for well-characterized ONC stars are: 1. X-ray luminosities are strongly correlated with several closely coupled stellar properties: bolometric luminosities, stellar size (radius, surface area and volume), and mass ( §4.1-4.3). The log L t − log L bol relation, for example, is roughly linear and consistent with an average log L t /L bol ≃ −3.8. This is an order of magnitude below the main sequence saturation level. The log L t −size relations are consistent with X-ray luminosities scaling linearly with stellar surface area. The dispersion about the relation is high and can be largely attributed to X-ray variability and flaring. The relationship between X-ray luminosities and mass is steeper than linear, and a sharp decrease by more than a factor of 10 in X-ray emissivity log L t /L bol is seen in some 2 − 3 M ⊙ stars. This drop becomes ubiquitous for ONC stars with M > 3 M ⊙ .
2. The presence or absence of a circumstellar disk, as measured by near-infrared photometric excess, appears to have no influence on X-ray luminosities or emissivities. ( §4.4) 3. X-ray luminosities shows a mild decline as stars age and descend the Hayashi track ( §4.5). Because L bol also falls, the ratio log L t /L bol is constant for t < 10 Myr and may rise to the main sequence saturation level during 10 < t < 30 Myr.
4. Most importantly for our purposes, X-ray luminosities and emissivities are higher than seen in main sequence stars for any given rotational period, and show a slight rise with rotational period over the range 0.4 ≤ P ≤ 20 days in contrast to the strong decline seen over the same range in main sequence stars ( §5.1). However, the result may be consistent with the main sequence X-ray/Rossby number diagram, as ONC stars appear to lie in the 'supersaturated' regime at low Rossby numbers ( §5.2).

Implications for dynamo models
Clearly PMS stars do not exhibit the standard empirical activity-rotation relationships seen in main sequence stars attributed to an α − Ω dynamo ( §2.1.1). The X-ray emission of an ensemble of mass-stratified PMS stars is unaffected by differences in rotation periods from 0.4 to 20 days, whereas the X-ray emission of main-sequence stars declines by a factor of 10 3 over this same period range 11 . However, these dramatic differences do not necessarily exclude the application of a 11 The comparison between main sequence and PMS activity may appear somewhat paradoxical at first glance: PMS X-ray luminosities (log L t ) are considerably elevated above main sequence levels, particularly for slow rotators, but PMS X-ray emissivities (log L t / log L bol ) are below the main sequence saturation level. This discrepancy is easily understood by recalling that PMS stars around 1 Myr, as in the ONC, typically have an order of magnitude greater surface area and hence bolometric luminosity than main sequence stars of the same mass. standard dynamo ( §2.2.1) because, based on the limited availability of Rossby numbers for ONC stars, it appears that ONC stars lie in the 'supersaturated' regime around log Ro ≃ −2 ( §2.1.1). The slight increase in log L t with log P seen in the full sample (Figure 7b) might represent the rise in X-ray emissivity from the supersaturated to the saturated regime seen in the main sequence populations.
One argument against an α − Ω dynamo is the level of saturation: PMS activity shows a log-mean level of < log L t /L bol >= 3.8 which is ∼ 10 times below the saturation level seen in main sequence stars in the 0.5 −8 keV band. If the same process of magnetic field generation and eruption is involved in both classes of stars, why should the surface activity differ by so much in a systematic fashion? The finding that X-ray luminosities scale approximately with stellar area ( §4.2) suggests saturation at the surface, but we can not eliminate the possibility that X-ray luminosity instead scales with stellar volume, representing a saturation of the internal dynamo.
We are thus led to consider dynamos where the fields are entirely generated and amplified in the turbulent convection zone that fills all or most of the stellar interior ( §2.2.2). Such fields may be generated both on small-scales due to turbulence in the convection zone (Durney, De Young, & Roxburgh 1993), and on large scales driven by a small differential rotation within the interior (Küker & Stix 2001;Kitchatinov 2001, and references therein). While a full suite of calculations is not yet available, the solutions appear to be largely independent of the global rotation rate, consistent with the absence of an log L t − P relation in our findings. These analytical treatments are supported by recent three-dimensional magnetohydrodynamical calculations: fields quickly form and amplify to energy densities > 10% of the turbulent kinetic energy density in both slab geometries (Thelen & Cattaneo 2000) and large-scale differentially rotating spherical geometries (Brun 2002). The cause and level of saturation of these distributed dynamos are perhaps not yet clear 12 .
An important constraint on any explanation for PMS X-rays is the change in behavior seen amoung the more massive 2 − 3 M ⊙ stars considered here ( §4.3). They exhibit an enormous dispersion in X-ray emissivity with some in the log L t /L bol ≃ −4 ± 1 range similar to lower mass stars, both others show log L t /L bol ≃ −5 ± 1. This emissivity drops further to log L t /L bol ∼ −8 for B stars (F02a). We consider two explanations for this effect, both of which may be operative: 1. Following F02a (their §5.2), these very low X-ray emissivities may be misleading due to binarity, where a lower mass secondary produces the observed X-rays and the higher mass p[rimary (which dominates L bol ) is magnetically inactive. The X-ray luminosities of these systems are somewhat higher than the average low-mass PMS ONC stars, implying that the companions have higher than average mass (e.g. 1 M ⊙ rather than 0.3 M ⊙ ). Detailed optical study of the 2 − 3 M ⊙ population could test the binarity hypothesis.
2. The drop in X-ray emissivity among intermediate mass PMS stars by an order of magnitude (or more if the binary hypothesis is correct) may be linked to structural changes in the stellar interior and consequent changes in dynamo activity. Palla & Stahler (1993) show that PMS stars with masses above ≃ 4 M ⊙ arrive at the stellar birthline with radiative interiors undergoing nonhomologous contraction, in contrast to PMS stars below M ≃ 2 M ⊙ with fully convective interiors undergoing homologous contraction. They predict a narrow range of PMS masses, 2.4 < M < 3.9 M ⊙ in their canonical model, where a composite structure of radiative core and convective mantle heated by deuterium burning occurs. The precise boundaries of these structural changes are very sensitive to the initial conditions, so that intermediate-mass ONC stars with somewhat different ages and accretion histories can have very different structures. These internal structure differences may be reflected in the efficiency of the magnetic dynamo, leading to the wide dispersion of log L t /L bol ratios we see in the 2 < M < 3 M ⊙ mass range (Figure 4c). The exact nature of the magnetic fields in these stars is not clear: conceivably different combinations of a distributed dynamo, tachocline dynamo or fossil field could be present in different stars with similar masses.

Implications for other models
While models of relic and core magnetic fields in PMS stars are not fully developed ( §2.2.3), our findings do not support these as the source of fields responsible for the observed X-ray emission. We find only a mild temporal dependence of X-ray luminosity on stellar age ranging from 10 5 to 10 7 yr ( §4.5), during which time the stellar interior undergoes the important transition to a radiative core. The only hint of a dependence on internal structure is the clear dependence of X-rays on stellar mass. However, we cannot determine whether the L t − M relationship arises from an astrophysical mechanism or as a byproduct of more fundamental relationships like L t /L bol ∝ constant, L t ∝ R 2 , or L bol ∝ M. But if a causal link between magnetic activity and mass is present, it conceivably could arise from the increased trapping of relic fields during the gravitational collapse of more massive stars, or from the increased capture of flux in the radiative core of more massive stars.
Our results also lend little support for models where X-ray emission is associated with a circumstellar disk ( §2.2.4) 13 . This result may have important implications for the physics of the circumstellar disk; in particular, X-ray ionization of disk gas and energetic particle bombardment of disk solids should be lower if the X-rays arise from fields close to the stellar surface than if they arise from the immediate vicinity of the disk (Glassgold, Feigelson, & Montmerle 2000, F02b).
Finally, we note that the activity-rotation diagram for PMS stars bears some phenomenological similarity to that obtained for post-main sequence giants and main sequence dM stars ( §2.1.2). For example, intermediate-mass 2 − 3 M ⊙ giants and PMS stars show the same wide range of X-ray luminosities, from log L x < 28 erg s −1 to 31 erg s −1 , unaffected by a wide range of rotational velocities (Pizzolato, Maggio, & Sciortino 2000). dM stars show a strong link between log L x and stellar size (Houdebine & Stempels 1997). However, as several different models still compete to explain activity in these stars, it is unclear whether phenemological similarities between the magnetic activity of PMS, dM and giant stars are astrophysically meaningful.

Concluding comments
With the greatly enlarged sample provided by the ONC, observational constraints on the origins of magnetic activity in low-mass PMS stars are more quantitatively and securely established compared to previous results. But, at present, we can not establish a definitive link between our findings and a unique theory of magnetic field generation in PMS stars.
There are two sources of uncertainty. First, we encounter a degeneracy between the physical properties correlated with X-ray emission. Examination of the evolutionary tracks in the HR diagram immediately reveals that bolometric luminosity, radius, mass and age are mutually dependent in a non-trivial and systematic fashion. We thus can not confidently extract from observations alone which property is astrophysically responsible for the magnetic activity we detect.
Second, theoretical models have often not been sufficiently developed to compare with our empirical findings; additional theoretical calculations are clearly necessary. For example, calculation of Rossby numbers (as in Kim & Demarque 1996) for each star in our sample using its specific mass, age and rotation, would populate the X-ray/Rossby number diagram ( Figure 8) and possibly reveal new constraints and trends. It would also be very useful if PMS dynamo models involving α − Ω, α − α and other distributed field generation processes were produced for PMS interiors with a wide range of masses and rotations for comparison with our findings. Initial models of this type have been reported by Kitchatinov (2001); Küker & Stix (2001) and references therein.
Despite these difficulties, the results seem to favor certain interpretations. The absence of an activity-rotation relation is by itself a good argument for some form of distributed dynamo arising throughout the convective zone, rather than the standard α − Ω dynamo involving a tachocline. The scaling between X-ray emission and the volume of the convective region at lower masses, and the change of X-ray properties in some stars at intermediate masses when a radiative core appears, together support a distributed dynamo for most T Tauri stars.
But we cannot yet exclude alternatives such as a standard dynamo in a 'saturated' or 'supersaturated' regime, where the saturation level occurs at a substantially lower value of L x /L bol than in main sequence stars. If PMS stars indeed all have 'saturated' dynamos, it is possible that little will be learned of their magnetic processes, expecially as we do not understand the causes of saturation even in main sequence stars. Similarly, magnetic reconnection of a mass-dependent fossil field may still be a viable model. However, the findings to not support models where the X-rays are associated with a circumstellar disk, either reconnection of star-disk fields at the corotation radius or reconnection of sheared disk-disk fields.
Additional forthcoming X-ray observations of the ONC should provide critical new insights. A contiguous Chandra ACIS observation spanning ≃ 11 days is planned which will give an order of magnitude increase in sensitivity essential for tracing magnetic activity in M ≤ 0.7 M ⊙ PMS stars, and a sufficiently long time series of all stars to obtain detailed characteristics of PMS X-ray emission. Several relevant studies are planned. The statistical properties of X-ray flares (e.g., the distribution of energies, durations and recurrence rates) may reveal similarities or differences when compared to flares in the Sun and older active stars. Quiescent X-ray levels between flares will be sought, and may show less scatter in correlations with other stellar properties than we find here. We will search for rotationally modulated X-ray emitting structures which might reveal large-scale asymmetries in the magnetic field geometry predicted by α − α dynamos and relic core fields. Conceivably, transitions in the levels and structure of surface magnetic fields reflecting the emergence of a core radiative zone will be seen in comparisons of younger vs. older and less vs. more massive PMS stars.
We are greatly appreciative of the careful and insightful reading of the manuscript by Dermott Mullan (Bartol) and the anonymous referee. EDF also greatly benefited from discussions with participants of stellar magnetism workshops in Santiago, Boulder and Toulouse during 2001−02. Patrick Broos (Penn State), Steven Pravdo (JPL), and Yohko Tsuboi (Penn State/Chuo) played critical roles in the Chandra ACIS Orion project. Sofia Randich (Arcetri) provided valuable help and comments. This work was principally supported by NASA contract NAS 8-38252 (Garmire, PI).