I will now describe the observational constraints on the evolution of potential proto-planetary disks through the disk-clearing phase. As already emphasized, I will focus on dust disk evolution, mentioning gas where it should not be forgotten, but not discussing gas in any detail. Three spatial regimes in the disk are considered: inner disk dissipation traced by near-infrared continuum data, mid-disk dissipation depicted by mid-infrared data, and outer disk dissipation traced by millimeter wavelength data.
There is a well-demonstrated empirical connection between accretion and outflow diagnostics measured by high-dispersion optical spectroscopy which probes the kinematics of warm gas in the vicinity of young stars (e.g., Hartigan et al. 1995; White & Hillenbrand 2004). A similar empirical connection (e.g., Hartigan et al. 1990; Kenyon & Hartmann 1995) exists between the same spectroscopic emission lines and the blue continuum excess measured as spectroscopic veiling, both signatures of accretion directly onto the star, and photometric near-infrared (1-3 ¡m) continuum flux excess arising in the innermost (<0.05-0.1 AU), and thus the hottest, disk regions. These correlations affirm the basic connection between accretion from a disk and ejection in an outflow.
Furthermore, both the spectroscopic signatures of accretion and the near-infrared excess are separately demonstrated to correlate inversely with stellar age over small age ranges. Detailed modeling of the accretion temperature, density, velocity, and geometric structure is required to convert emission line strengths and profiles into mass accretion rates. More common than emission line profile studies is the measurement from high dispersion spectroscopy of continuum veiling, which can also be converted to a mass accretion rate after making assumptions about the bolometric correction to derive a total accretion luminosity, and about the infall geometry.
Treatments of the trends in the accretion rate with age have been presented by Muze-rolle et al. (2000) and Calvet et al. (2005a). At least several stars appear to show measurable accretion signatures beyond 10 Myr. Existing trends have been inferred by considering the individually derived ages of stars based on their HR diagram. They are thus subject to the criticism that age spreads in individual clusters such as Taurus, Chamaeleon, or the TW Hydra association may be overestimated, and that comparisons between the mean accretion rates and mean stellar ages in each cluster may be more appropriate. Similar criticisms are also levied below against treatments of near-infrared excess behavior with age.
For the near-infrared continuum analysis, we utilize measured flux above expected photospheric values to infer disk presence. Increasingly complex inner disk geometries have been advanced over the last decade (e.g., Mahdavi & Kenyon 1998) which complicate the expectations regarding the magnitude of a near-infrared excess, given other constant parameters for the star and the disk. In the analysis discussed here, we do not consider such geometric complications and assess simply whether there is, or is not, evidence for disk emission at near-infrared wavelengths for our sample.
In calculating the color excess due to the disk, one must make two corrections from observed colors. First, it is necessary to derive and subtract the contribution from the foreground or large scale circumstellar extinction. Second, from the remaining color, a correction for the underlying stellar photosphere is performed in order to arrive at the intrinsic color excess due to the disk. In formulaic terms, using H — K color as an example, the disk excess is quantified as
A(H — K) = (H — K )observed — (H — K )reddening — (H — K )photosphere •
Similar indices can be derived for J — K or K — L colors which also probe inner disk regions, though they sense dust at slightly different temperatures. In order to effect the above extinction and photospheric corrections, and hence assess intrinsic color excesses, several different sets of information are required: 1) a spectral type, for intrinsic stellar color and bolometric correction determination, 2) optical photometry, for dereddening and locating stars on the HR diagram, assuming known distance, and 3) infrared photometry, for measurement of disk "strength."
It should be borne in mind that disk strength, quantified as above from measurement of the absolute value of the infrared excess, is still a relative quantity. For any given star/disk system, the infrared excess is affected by both stellar properties (mass, radius) and disk properties (accretion rate, inclination, geometry). Meyer et al. (1997) and Hillenbrand et al. (1998; both in collaboration with Calvet) provide detailed discussions of these dependencies apropos near-infrared excesses. The effects of stellar and disk parameters on overall spectral energy distributions are discussed more comprehensively by D'Alessio et al. (1999).
Now what about that pesky other axis of stellar age? Instead of discussing in detail all of the inherent uncertainties in locating stars in the HR diagram (Fig. 2), and in inference of stellar ages and masses from those diagrams, I will simply assume fiducial cluster ages based on the median apparent age of stars in the mass range 0.3-1.0 Mq. With both a disk diagnostic and a method of cluster age estimation we can now explore the evidence for disk evolution.
Our best effort at empirically measuring the timescale for the evolution of inner cir-cumstellar accretion disks is represented in Figure 3, which was produced from a sample of —3000 stars located —50-500 pc from the Sun. To be included in the sample, each star was required to have the spectral type, optical photometry, and infrared photometry necessary for calculation of A(H — K) or A(K — L), as described above. It should be noted that there are far fewer stars with available L-band photometry than available (J)HK photometry. There are several important points made by these example plots.
First, even at the earliest evolutionary stages at which stars can be located in the HR diagram, the optically-thick inner disk fraction does not approach unity. There are several well-known examples of objects near the stellar birthline without any evidence for disks. This may be influenced by selection effects in that protostars and objects in transition from the protostellar to the optically revealed stage generally lack the spectroscopic data required for inclusion in our sample. However, the result is more apparent in the H — K excess figure than in the K — L excess figure. If a real effect (as opposed to an effect introduced by bias in the samples selected for L-band photometry), this strongly indicates that some disk evolution does happen very early on for some stars, before they become optically visible.
Second, beyond one Myr of age, existing samples are less biased by complications of extinction and self-embeddedness, and hence are more representative of underlying stellar populations as a whole (if not close to complete for most of the regions plotted). At these ages, there is a steady decline with time in the fraction of stars showing near-infrared excess emission (i.e., optically thick inner disks), as well as large scatter at any given age. We will return to the issue of the scatter later. The conversion of diagrams like Figure 3 into frequency distributions of accretion disk lifetimes is the next step, o.a s o o cS
Figure 3. Inner accretion disk fraction vs. stellar age inferred from H — K excess (top panel) and K — L excess (bottom panel) measurements, binned by cluster or association. All young stars which we are able to locate in the HR diagram based on information in the literature (about 3500) and having inferred masses 0.3-1.0 Mq are included in this figure. Individual clusters are treated as units of single age, corresponding to the median age inferred from the HR diagram. A cut of A(H — K) > 0.05 mag is used to define a disk. Standard deviation of the mean (abscissa) and Poisson (ordinate) error bars are shown. The linear and exponential fits were derived for ages <30 Myr; the linear fit has a negative slope close to unity with rms 0.3.
Figure 4. Terrestrial zone disk fraction vs. stellar age inferred from N-band excess measurements for ~50 stars, taken from Mamajek et al. 2004.
Figure 4. Terrestrial zone disk fraction vs. stellar age inferred from N-band excess measurements for ~50 stars, taken from Mamajek et al. 2004.
and really what we want to know rather than disk frequency with age; this analysis is presented in Hillenbrand, Meyer, & Carpenter (2006).
Third, based on assessment of modern data, the median lifetime of inner optically thick accretion disks may be as short as 2-3 Myr, with essentially no evidence for HKL excess present in the median star beyond 5 Myr. Clearly, there are exceptions such as the noted cases of ~10 Myr-old accretion disks.
Other discussions of inner disk lifetimes have used different techniques and more limited samples of stars (e.g., Walter et al. 1988; Strom et al. 1989; Skrutskie et al. 1990; Beckwith et al. 1990; Strom 1995; Haisch et al. 2001). As with most scientific inquiries, the results derived depend on the details of both the samples and the analysis. Within the proposed random and systematic uncertainties, all of the above studies are comparable in their results. Previous general conclusions regarding inner disk lifetimes in the 3-10 Myr age range are, broadly speaking, similar to our findings of <2-3 Myr for the evolution of the mean disk. Further, although most disks appear to evolve relatively rapidly, a small percentage appear to retain proto-planetary nebular material for factors of 5-10 longer than the average disk.
As emphasized above, near-infrared wavelengths measure hot dust in the innermost disk regions, the presence of which is well correlated empirically with independent (spectro-scopic) evidence for accretion onto the star. Because only a small amount of dust is required to make the inner disk optically thick, near-infrared continuum excesses tell us little about the bulk of the disk mass or surface area, which radiates at much cooler temperatures, and hence, longer wavelengths. Further, because the dynamical time is a function of radius in the disk, there is some expectation in the scenario that disk dissipation involves sticking collisions that eventually generate planetesimals—for disks to evolve in the inner regions first and the outer regions later (e.g., Hollenbach et al. 2000).
5.2. Mid-disk dissipation
Thus, studying disk frequency with age (or better yet, disk lifetime) as a function of disk radius is of great interest.
Mid-infrared wavelengths, ~ 10-90 ¡m, probe disk radii ~1-5 AU, equivalent to the outer terrestrial and inner gas giant planetary zones of our solar system. To date, observational sensitivity has been the primary hindrance to measurement of disk evolution at these wavelengths. The sensitivity required at mid-infrared wavelengths is, in fact, orders of magnitude more in flux density units than that needed in the near-infrared due to the Rayleigh-Jeans fall-off of the stellar photosphere. Despite the large number of non-detections or upper limits, previous mid-infrared observations of small samples of young stars have revealed evolutionary trends.
The most recent statistical results using ground-based equipment (e.g., Mamajek et al. 2004; Metchev et al. 2004), when considered in the same excess fraction format as Figure 3, show similar morphology with ~10 Myr needed for depletion of 90% of optically thick terrestrial zone dust. Figure 4 is reproduced from Mamajek et al. 2004. The implication is that the terrestrial zone disk dissipation times are perhaps consistent with, or at most factors of a few longer than, inner disk dissipation times. If true, the combined near-and mid-infrared results suggest that disk evolution is both rapid and relatively independent of radius. However, as was true in the analysis of inner disk lifetimes, a decreasing fractional excess that is never unity is suggestive of a dispersion in disk lifetimes—in this case over an order of magnitude in age.
The Spitzer Space Telescope offers dramatic improvement to heretofore available mid-infrared continuum excess probes of dust evolution. Spitzer is sensitive to nearby stellar photospheres between 3.5 and at least 24 im with additional sensitive capability out to 70 ¡m. Spitzer thus enables meaningful statistical studies of primordial (and debris— see Meyer, this volume) disk evolution within and beyond the terrestrial planet zone. Advances over the previous IRAS/ISO and ground capability are already revolutionizing the field. Restricting the discussion to only 8 ¡m results, Silverstone et al. (2006) study both field stars and cluster/association members <30 Myr old, Young et al. (2004) present results for a single 30 Myr-old cluster NGC 2547, and Stauffer et al. (2005) discuss the 120 Myr-old Pleiades cluster. All of these papers reaffirm the basic Mamajek findings that terrestrial zone dust is depleted within 10 Myr, and add needed statistics. Further Spitzer results are forthcoming.
At longer wavelengths, 25-60 ¡m, data from the IRAS and ISO satellites were even more limited in addressing disk evolution problems, again due to the sensitivity requirements of such investigations. These platforms were not capable of detecting the stellar photospheres of young stars at the necessary 150 pc distance. However, some results at 60 ¡m have been presented in the same form as Figure 3 (e.g., Meyer & Beckwith 2000; Robberto et al. 1999), again suggesting consistency with the Mamajek et al. (2004) results at 10 ¡m. However, Spangler et al. (2001) and Habing et al. (2001) argue, based on ISO data, for a much longer mid-infrared disk dissipation timescale, on the order of hundreds of Myr. That there may be some confusion in these two studies between primordial and debris disks as a single, continuous evolutionary path is not expected over this long timescale (see, Decin et al. 2003 for a critical assessment).
Again, Spitzer will revolutionize the field due to its increased sensitivity and spatial resolution over previous capabilities. Results at 24 ¡m for the 5 Myr-old Upper Sco association (Chen et al. 2005) and for the 10 Myr TW Hya association (Low et al. 2005) have appeared thus far. However, the mix of spectral types in these early studies relative to the roughly solar-type stars discussed above make rigorous comparisons of the disk dissipation statistics with radius premature.
5.3. Outer disk dissipation Moving outward in wavelength and hence downward in temperature, millimeter wavelength emission probes the cold outer (^50-100 AU) disk regions and is optically thin. Most millimeter observations (e.g., Andrews & Williams 2005) have been directed towards stars younger than ~107 year, but because of the distance of these populations, they generally place only upper limits on dust masses beyond the youngest phase (e.g., Duvert et al. 2000). Recent application of a clever technique to push below formal detection limits has resulted in more stringent constraints on the typical disk masses in several very young clusters (Carpenter 2002; Eisner & Carpenter 2003), finding mean dust masses of 5 x 10~5 Mq (which can be augmented by an assumed gas-to-dust ratio to infer a total mass). Because of the more dispersed nature of older stars, there remain few such stringent constraints on typical dust masses in the 3-10 Myr-old age range.
Dust mass surveys of older (107-109 year), closer, candidate debris disk stars (e.g., Zuckerman & Becklin 1993; Jewitt 1994; Wyatt et al. 2003; Carpenter et al. 2005) also reveal mostly upper limits due to current sensitivity challenges, but also several detections of very proximate stars with dust masses as low as 10~8 Mq. In an analysis of the ensemble of upper limits, Carpenter et al. (2005) find marginal evidence for continuous evolution in the dust masses at expected primordial disk ages, from the 1-2 Myr young clusters to the 3-10 and 10-30 Myr field stars, which may in fact have already transitioned from primordial to debris disks.
Assessment of primordial disk evolution at radii of several tens to hundreds of AU, where the bulk of the disk mass resides, thus awaits dramatically improved millimeter and sub-millimeter sensitivity. Such is on the horizon with the commissioning of CARMA and ALMA.
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