# Limits on the Gas Disk Content of Two “Evolved” T Tauri Stars

Alan G. Aversa  Steward Observatory, 933 N Cherry Ave., Tucson AZ 85721

###### Abstract

We derived upper limits of the circumstellar gas disk masses around the T
Tauri stars St 34 and RX J0432.8+1735 in order to place constraints on
theories of planet formation and to explore the evolution of the gas-to-dust
ratio during the epoch of disk dissipation around young sun-like stars. Since
sub-millimeter lines of 12CO trace of the cold, outer regions of circumstellar
disks, we observed 12CO $J=2-1$ emission with the 10 m Sub-Millimeter
Telescope (SMT) for two carefully chosen targets. St 34 is a rare classical T
Tauri star with an age of $8\pm 3$ Myr, and RX J0432.8+1735 is a rare weak-
emission T Tauri star with far-infrared excess. Both exhibit radial space
motion enabling us to distinguish disk emission from ambient cloud material.
Assuming a 12CO excitation temperature of 20 K, a 12CO line-width of 5 km s-1,
and optically-thin emission, we derive $3\sigma$ upper limits on the H2
circumstellar disk mass for St 34 and RX J0432.8+1735 to be $<4.20$ M⊕ for
both disks. Placing these results in the context of other studies, we discuss
their implications on planet formation models.

##  1 Introduction

Circumstellar disks of gas and dust, a natural result of the conservation of
angular momentum, are a common outcome of the star formation process. Kenyon &
Hartmann (1995) find that over half the low mass ($<$ 2 M⊙) pre–main-sequence
T Tauri stars in the Taurus-Auriga star formation region have more infrared
emission than expected from a normal stellar photosphere, indicating the
presence of a dusty circumstellar disk heated by the parent star as well as
active accretion. T Tauri stars fall into two categories: Weak-Line T Tauri
Stars (WTTSs), characterized by low H$\alpha$ equivalent widths, and Classical
T Tauri Stars (CTTSs), with higher H$\alpha$ equivalent widths indicative of
ongoing gas accretion. These circumstellar disks generally have the following
properties (Dutrey et al., 2007; Andrews et al., 2009): mass surface densities
$\Sigma(r)\propto r^{0\,\mathrm{to}\,-1.0}$, surface temperatures $T(r)\propto
r^{0\,\mathrm{to}\,-0.6}$(depending on disk flaring), and Keplerian rotational
velocities $V(r)\propto r^{0.5}$.

Gas giant planet formation depends upon the gas content of the circumstellar
disk from which they form. Primordial inner disks traced by hot dust disappear
after about 3 Myr with a range of $1-10$ Myr (Meyer et al., 2007). If gas
content and dust content in disks dissipate through similar mechanisms
(Damjanov et al., 2007), then we would expect gas to disappear on these same
timescales. To understand the timescales of planet formation, we must
understand how long a gas disk persists around its parent star. Accretion
rates (higher in CTTSs than WTTSs) also trace the time evolution of gas
content as gas must be present to accrete. Durisen et al. (2007) suggest that
gravitational instabilities in gas disks could account for their rapid ($<3$
Myr) dissipation, locking up mass in planets. In contrast, simulations of the
evolution of gas disk surface density for a 1 M☉ star due to photo-evaporation
indicate that gas disks disappear in about 6 Myr (Alexander et al., 2006;
Dullemond et al., 2007). Because there are various theoretical results for the
gas dispersal mechanisms and associated timescales, we might expect to observe
diverse properties for gas disks around T Tauri stars.

Ideally, sub-millimeter interferometric images of T Tauri stars would yield
the most information about circumstellar disks, including their orientation,
geometry, and gas content. Yet observations of this sort have only been
published for a few nearby stars (e.g., Sub-Millimeter Array (SMA)
observations of TW Hya; Qi et al., 2004). Infrared photometric campaigns with
Spitzer, such the Cores to Disks (Evans et al., 2003) and the Formation and
Evolution of Planetary Systems (FEPS; Meyer et al., 2006) Spitzer Legacy
projects, provide knowledge of the dust circumstellar disks based upon IR
excesses at many wavelengths including $24\micron$, which trace dust within a
few AU of the parent star, and at $70\micron$, which trace cooler dust at
larger radii. Silverstone et al. (2006) surveyed 74 stars with ages between
3-30 Myr finding no stars with mid–IR excess that were not gas rich accreting
T Tauri stars. Padgett et al. (2006) however identified a handful of WTTS
(lacking signatures of accretion) with evidence for mid– and far–IR excess
emission. Photometric IR observations do not, however, constrain the total gas
content in circumstellar disks because of a potentially highly variable gas-
to-dust ratio. Observing the rotational energy transitions of 12CO, a proxy
for molecular hydrogen (H2), and assuming the ISM abundance ratio
$\left[\mathrm{H}_{2}/\mathrm{CO}\right]\approx 10^{4}$ enables one to trace
the majority of cold gas in disks out to radii many times larger. Is the
timescale for gas dissipation similar to the timescale for dust dissipation
around T Tauri stars? This is the central question we address with our new
observations.

Expanding on previous works (e.g. Pascucci et al., 2006; van Kempen et al.,
2007), we search for 12CO $J=2-1$ emission for two “evolved” T Tauri stars in
Taurus to place constraints on their gas circumstellar disk masses. St 34 is
evolved in the sense that it is $8\pm 3$ Myr old, whereas RX J0432.8+1735 is
evolved in the sense that—although it is much younger ($1.0\pm 0.5$ Myr)—it
has already lost its inner accretion disk. In §2, we describe our selection of
sources and observations, then in §3 we derive upper limits on our sources’
gas disk masses. Lastly, in §4 we describe the implications of our results,
and in §5 we list our conclusions.

##  2 Observations

###  2.1 Selection of Sources

We observed the 12CO $J=2-1$ emission of the Taurus region objects St 34 and
RX J0432.8+1735, T Tauri stars with known 24 or $70\micron$ excesses (Kenyon &
Hartmann, 1995; Padgett et al., 2006, see Table 2.1). In order to detect gas
in their circumstellar disks, we must be able to distinguish emission from the
disk and surrounding molecular cloud. From available candidate “evolved” (in
age or shape of spectral energy distribution) T Tauri stars, we selected those
least likely to be contamined by the ambient CO emission from the parent
molecular cloud based on the Dame et al. (1987) CO survey. The radial
velocities of our sources differ from the systemic velocities of any CO
emission in the vicinity of our sources by $\sim 2-3$ km s-1.

Table 1: Candidate Source Summary

Object | $\alpha$ | $\delta$ | Heliocentric RV | Source $V_{\mathrm{LSR}}$aaWe corrected the heliocentric radial velocities (RVs) from the literature into local standard of rest ($V_{\mathrm{LSR}}$) radial velocities assuming the sun moves toward J2000 $(\alpha=18\fh 0,\delta=30\fdg 0)$ at 20 km s-1. | Cloud $V_{\mathrm{LSR}}$bbDetermined by the 12CO $J=1-0$ emission from the Dame et al. (1987) survey | $T_{\mathrm{eff}}$ | $\log{L^{\star}}$ | Mass | Age | General
---|---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) | (km s-1) | (km s-1) | (km s-1) | (K) | ($\log{L_{\sun}}$) | ($M_{\sun}$) | (Myr) | Reference
RX J0432.8+1735 | 04 32 53.23 | 17 35 33.68 | $18.6$ | 7.3 | 10.2 | 3499ccWichmann et al. (2000) |  $\sim-6.1\times 10^{-2}$ggEstimated by integrating the spectral energy distribution (SED) of RX J0432.8+1735 in Padgett et al. (2006) |  $\cdots$ |  $1\pm 0.5$ddD’Antona & Mazzitelli (1997) | a
St 34 | 04 54 23.70 | 17 09 54.00 | $17.9\pm 0.6$ | 6.6 | 8.37 | 3415 | $1.03\pm 0.06$ |  $0.37\pm 0.08$eeFor both binary components |  $8\pm 3$e,fe,ffootnotemark:  | b

fffootnotetext: Isochronal age is given. The Li depletion age for both binary
components is $>25$ Myr.

References. — For RVs, see Wichmann et al. (2000); White & Hillenbrand (2005).
For general references, see (a) Padgett et al. (2006) and (b) White &
Hillenbrand (2005).

####  2.1.1 St 34

St 34 (HBC 425) is a binary system of two CTTSs, separated by $\lesssim 0.78$
AU (White & Hillenbrand, 2005) based on the orbital solution for the system
(Downes & Keyes, 1988) in the Taurus-Auriga T association (Kenyon & Hartmann,
1995). Both components of the spectroscopic binary have roughly equal mass and
spectral types of M3 (White & Hillenbrand, 2005). White & Hillenbrand (2005)
observed St 34 in the optical with the HIRES spectrograph at Keck and derived
an isochronal age of $8\pm 3$ Myr for both components of the binary. Since
they did not detect any lithium (7Li) in the spectrum, St 34 must have
reached—assuming the stars are completely convective—an internal temperature
$>2\times 10^{6}$ K and since depleted all of its lithium. St 34 has a low
accretion rate of $2.5\times 10^{-10}$ M☉ yr-1, and the maximum radial
velocity difference between the two binary components of St 34 is 58.4 km s-1
(White & Hillenbrand, 2005). St 34, being one of the oldest known pre–main-
sequence (PMS) star still accreting from a proto-planetary disk, also has a
low dust mass of $\sim 2\times 10^{-10}$ M☉ for radii $\lesssim 0.7$ AU
(Hartmann et al., 2005).

####  2.1.2 RX J0432.8+1735

RX J0432.8+1735 is a WTTS of spectral type M2 (Martín & Magazzù, 1999). Based
on the PMS tracks of D’Antona & Mazzitelli (1997) RX J0432.8+1735 is estimated
to be $1.0\pm 0.5$ Myr old. Padgett et al. (2006) observed RX J0432.8+1735
with Spitzer and noticed that its $24\micron$ flux is in excess of the
expected photospheric value by a factor of 3. Its lack of IR excess $\leq
12\micron$ suggests there may be a large inner hole in the disk. Based on
ROSAT observations, Carkner et al. (1996) discovered that RX J0432.8+1735 is
also an X-ray source. As RX J0432.8+1735 is classified as a WTTS star with no
estimates of its accretion rate, we assume it is not accreting.

###  2.2 Observing Procedure

On 26-27 November 2007, we observed the 12CO $J=2-1$ (230.53799 GHz) emission
line of our two T Tauri stars with the 10 m Heinrich Hertz Sub-Millimeter
Telescope (HHT) on Mt. Graham, Arizona. Observations were obtained with a 1 mm
dual polarization (Vpol, Hpol), sideband-separating, ALMA prototype receiver.
The upper sideband was tuned to 12CO $J=2-1$ while the lower sideband was
tuned to 13CO $J=2-1$. We used the Forbes Filter Bank (FFB) backend in 4 IF
mode, an upper and lower sideband each with 1 MHz and 250 kHz of spectral
resolution, respectively. The channel width, $\Delta\nu_{\mathrm{ch}}$, of our
spectrometer was $0.33$ km s-1. The 1 MHz resolution data were used to
determine main beam efficiencies $\eta_{\mathrm{mb}}$, and the $250$ kHz
resolution data were used to measure the 12CO line.

Table 2: Observation of Main Beam Efficiencies $\eta$ Planet | $\eta_{\mathrm{Vpol}}$ | $\eta_{\mathrm{Hpol}}$ | $\eta_{\mathrm{Vpol}}/\eta_{\mathrm{Hpol}}$
---|---|---|---
MarsaaAll Mars brightness temperature errors assumed to be 5% | $0.80\pm 0.05$ | $0.72\pm 0.04$ | $1.10\pm 0.09$
Mars | $0.80\pm 0.05$ | $0.71\pm 0.04$ | $1.12\pm 0.09$
Saturn | $0.93\pm 0.04$ | $0.70\pm 0.03$ | $1.33\pm 0.08$
Saturn | $0.94\pm 0.04$ | $0.69\pm 0.03$ | $1.36\pm 0.09$
Venus | $0.89\pm 0.03$ | $0.66\pm 0.03$ | $1.35\pm 0.08$
Venus | $0.88\pm 0.03$ | $0.66\pm 0.03$ | $1.34\pm 0.08$
Mars | $0.87\pm 0.05$ | $0.66\pm 0.04$ | $1.31\pm 0.10$
MarsbbEnd of first night | $0.87\pm 0.05$ | $0.66\pm 0.04$ | $1.33\pm 0.10$
MarsccBeginning of second night | $0.88\pm 0.05$ | $0.68\pm 0.04$ | $1.29\pm 0.10$
Mars | $0.89\pm 0.05$ | $0.68\pm 0.04$ | $1.31\pm 0.11$
Mars | $0.84\pm 0.04$ | $0.70\pm 0.04$ | $1.21\pm 0.10$
Mars | $0.88\pm 0.05$ | $0.68\pm 0.04$ | $1.29\pm 0.10$
Venus | $0.93\pm 0.03$ | $0.68\pm 0.03$ | $1.38\pm 0.09$

Using CLASS in the GILDAS data reduction package, we estimated the main beam
efficiencies by observing the planets shown in Table 2. Typical sideband
rejections, ignored in the calibration, were $>10$ dB. The main beam
efficiency $\eta$ was computed following Mangum (1993) and corrected for
single-sideband observations:

$\eta=\frac{T_{A}^{\star}(\mathrm{planet})}{J(\nu_{s},T_{\mathrm{planet}})-J(\nu_{s},T_{\mathrm{cmb}})}\times\left[1-\exp{\left(-\ln{(2)}\frac{\theta_{\mathrm{eq}}\theta_{\mathrm{pol}}}{\theta_{\mathrm{mb}}^{2}}\right)}\right]^{-1},$
(1)

where

$J(\nu,T_{b})=\frac{h\nu/k}{e^{\frac{h\nu}{kT_{\mathrm{mb}}}}-1}$ (2)

is the Planck function at brightness temperature $T_{b}$ and frequency $\nu$,
$T_{A}^{\star}$ is the single-sideband antenna temperature of the planet,
$T_{\mathrm{planet}}$ is the planet’s observed brightness temperature,
$T_{\mathrm{cmb}}=2.73$ K, $\theta_{\mathrm{eq}}$ and $\theta_{\mathrm{pol}}$
are respectively the planet’s equatorial and poloidal diameters in arcseconds,
and $\theta_{\mathrm{mb}}=33\arcsec$ at $\nu=230$ GHz. We adopted an average
Venus brightness temperature $T_{b}$ from Kuznetsov et al. (1982) of $287\pm
20$ K. For all other planets’ $T_{b}$, we used the JCMT online
database111http://www.jach.hawaii.edu/jac-bin/planetflux.pl. We derived a
ratio $\eta_{\mathrm{Vpol}}/\eta_{\mathrm{Hpol}}$ of the two IF’s mean main
beam efficiencies for both nights of $1.24\pm 0.04$. We used this ratio to
scale the Hpol polarization’s antenna temperature up to match the level of the
Vpol polarization’s antenna temperature. After fitting a baseline to each
spectrum, we averaged the sum of the scaled Hpol brightness temperatures and
the Vpol brightness temperatures: $\frac{1}{2}\langle
T_{A}^{\star}(\mathrm{Hpol,scaled})+T_{A}^{\star}(\mathrm{Vpol})\rangle=T_{A}^{\star}(\mathrm{sum})$.
Thus we computed the corrected main beam temperature as

$T_{\mathrm{mb}}=\frac{T_{A}^{\star}(\mathrm{sum})}{\eta_{\mathrm{Vpol}}}.$
(3)

The average beam efficiencies were $\langle\eta_{\mathrm{Hpol}}\rangle=0.68\pm
0.01$ and $\langle\eta_{\mathrm{Vpol}}\rangle=0.88\pm 0.01$ for both nights.

Since we had null detections for our two sources, we must assume a line-width
to calculate upper limits on the integrated intensity. We assumed typcial a
line-width of $\Delta\nu=10$ km s-1 ($=7.69$ MHz). If we assume the CO line is
well described by a Gaussian line shape, then the uncertainty in the
integrated intensity is given by

$\sigma_{I}=\sigma_{T_{\mathrm{mb}}}\sqrt{\frac{3\Delta\nu_{\mathrm{ch}}\Delta\nu}{\sqrt{\ln{2}}}},$
(4)

where $\sigma_{I}$ and $\Delta v$ are the CO line fluxes and the the full
width at half maximum (FWHM) and $\Delta v_{\mathrm{ch}}$ is the channel
spacing 0.33 km s-1; see Appendix I of Schlingman et al. (in prep.). The
observations are summarized in Table 3.

Table 3: Observational Summary

Source | Integration Time | $\sigma_{T_{\mathrm{mb}}}$ | $\sigma_{I}$ | $\log_{10}{(F_{\nu})}$ | $\overline{N}(T\mathrm{ex}=10,20,100\mathrm{~{}K})$ | $M_{\mathrm{H}_{2}}(T_{\mathrm{ex}}=10,20,100\mathrm{~{}K})$
---|---|---|---|---|---|---
| (sec) | (K) | (K km s-1) | ($\log_{10}{(\mathrm{W~{}cm}^{-2})}$) | (1013 cm-2) | (M⊕)
RX J0432.8+1735 | 3600 | 0.019 | 0.046 | $<-23.02$ | $<12.7,7.47,6.53$ | $<3.59,1.10,1.84$
St 34 | 6120 | 0.019 | 0.046 | $<-23.02$ | $<12.7,7.47,6.53$ | $<3.59,1.10,1.84$

Note. — $T_{\mathrm{mb}}$ is the main beam corrected brightness temperature
and $I$ is the corresponding intensity assuming a line width of 5 km s-1. $F$
is the $3\sigma$ line flux upper limit.

Note. — That $\sigma_{T_{\mathrm{mb}}}$ for both objects is the same is a
fluke.

##  3 Results & Analysis

The main-beam corrected spectra of our observations are shown in Figure 1.

Figure 1: Spectra of St 34 (left) and RX J0432.8+1735 (right). The vertical
line labeled “Cloud” represents the estimated background cloud velocity
determined by the Dame et al. (1987) CO $J=1-0$ survey, and the vertical line
labeled with the source’s name indicates that source’s $V_{\mathrm{LSR}}$. For
St 34, we show with an arrow the difference between the radial velocities of
its binary components with an arrow centered on the systemic velocity.

While 9$\arcmin$ is a rough spatial scale for comparison to the 33$\arcsec$
beam of the SMT, and since we did not detect a 12CO line in any of our
sources, the on-cloud results from SMT are consistent with Dame et al. (1987).
It is unlikely that high spatial frequency variations of 33$\arcsec$ scales
over 9$\arcmin$ regions have systemic velocity shifts of 2-3 km-1

Since we did not detect any 12CO line, we convert our $3\sigma$ noise into an
upper limit on the flux. A knowledge of the flux will enable us to estimate
upper limits on gas disk mass.

The observed flux is the double-integral of the observed intensity $I_{\nu}$
over frequency $\nu$ and solid angle $\Omega$:

$F=\int\int
I_{\nu}\,d\nu\,d\Omega=\int\int\frac{2k\nu^{3}T_{b}}{c^{3}}\,dv\,d\Omega.$ (5)

Assuming the brightness temperature does not vary substantially over the
telescope beam and that the line is a Gaussian with line-width $\Delta v$,
then the upper limit on the $3\sigma$ line flux $F$ is

$F<\frac{2k\nu^{3}(3\sigma_{T_{\mathrm{mb}}})}{c^{3}}\frac{\pi\theta^{2}}{4\ln{2}}\sqrt{\frac{4\ln{2}}{\pi}}\times\Delta
v=(5.05\times
10^{-15})\sigma_{T_{\mathrm{mb}}}\mathrm{erg~{}s}^{-1}\mathrm{~{}cm}^{-2}.$
(6)

The $3\sigma$ upper limits on $F$ are listed in Table 3.

Similarly, we can derive the column density in the optically thin limit to be

$\overline{N}(T_{\mathrm{ex}})=\frac{8\pi
k\nu^{2}}{hc^{3}g_{u}A_{ul}}\mathcal{F}(T_{\mathrm{ex}},E_{u},\nu)\int
T_{\mathrm{mb}}\,dv,$ (7)

where

$\mathcal{F}(T_{\mathrm{ex}},E_{u},\nu)\equiv\frac{J_{\nu}(T_{\mathrm{ex}})Q(T_{\mathrm{ex}})\exp{\left(\frac{E_{u}}{kT_{\mathrm{ex}}}\right)}}{J_{\nu}(T_{\mathrm{ex}})-J_{\nu}(T_{\mathrm{cmb}})},$
(8)

$A_{ul}$ is the Einstein A coefficient (spontaneous emission) and has units of
s-1.

Similar to the analysis of Pascucci et al. (2006), we assume an excitation
temperature $T_{\mathrm{ex}}\approx 20$ K. Then in our case for 12CO $J=2-1$,
$\mathcal{F}(T_{\mathrm{ex}},E_{u},\nu)\approx 28.00$. The Einstein
$A_{ul}=6.91\times 10^{-7}$ s-1 and partition function
$Q(20\mathrm{~{}K})=15.9$ (CDMS222http://www.ph1.uni-koeln.de/vorhersagen/).

We compute and tabulate in Table 3 the 12CO number densities and H2 gas masses
in the optically thin limit. Gas disk masses were derived from Scoville et al.
(1986),

$M_{\mathrm{H}_{2}}<\overline{N}(T_{\mathrm{ex}})\times\Bigg{\\{}\left[\frac{\mathrm{H}_{2}}{\mathrm{CO}}\right]\mu_{G}m_{\mathrm{H}_{2}}\frac{\pi\theta^{2}}{4}d^{2}\Bigg{\\}}\mathrm{~{}g}=110\sigma_{T_{\mathrm{mb}}}\mathrm{~{}M}_{\earth},$
(9)

where $\left[\mathrm{H}_{2}/\mathrm{CO}\right]\approx 10^{4}$, $\mu_{G}=1.36$
is the mean molecular weight, $m_{\mathrm{H}_{2}}$ is the mass of an H2
molecule, and $d\approx 140$ pc is the distance to Taurus.

##  4 Discussion

Theories of gaseous planet formation require knowledge of (1) how much gas
there is in circumstellar disks initially and (2) the rate at which gas is
depleted over time. To answer the first question, upper limits on the amount
of gas in very young protostellar disk systems puts limits directly on the
amount of mass available for gaseous planet formation in the systems observed.
Answers to the second question, requiring large samples over a wide range of
ages, are also necessary because of the competition between the timescale for
planet formation and gas disk dispersion timescales (for a recent review, see
Meyer, 2009).

There are several ways of constraining gas disk masses, each with its own
advantages and disadvantages. To understand gas disk timescales, one can also
analyze H$\alpha$ emission line profiles and determine gas accretion rates and
thus constrain the gas mass surface density at the inner edge of the disk
tracing perhaps global disk evolution (e.g. Fedele et al., 2009). Using UV
tracers of gas emission, Ingleby et al. (2009) describe HST observations
searching for evidence of hot gas in emission finding no evidence for H2
emission for WTTS in their sample. Ultraviolet absorption line from a
continuum source (e.g. Roberge et al., 2005) can help constrain cold mass in
disks, but it requires a continuum source that is bright in the far UV and an
edge-on geometry; therefore, it is observationally feasible only in special
circumstances. Near IR fluorescent H2 traces gas with excitation temperatures
$T_{\mathrm{ex}}>2000$ K (Bary et al., 2003) and mid-IR ro-vibrational lines
(e.g. Najita et al., 2007; Thi et al., 2001; Pascucci et al., 2006),
especially the $28.2~{}\mu$m and $17\mu$m Spitzer bands, trace gas up to
50-200 K. Our observations of rotational lines of CO trace cooler gas at
larger orbital radii. The disadvantage of such measurements is that CO can
freeze out at the coldest temperatures corresponding to the outer limits of
the disk $\gtrsim 30$-100 AU. Hughes et al. (2010) present evidence for
evolving gas to dust ratios in transitional disks which exhibit evidence for
optically-thick outer disks but possess inner holes and gaps.

St 34, being $8\pm 3$ Myr old, might have a lower gas surface density than
typical CTTSs. It is still accreting gas (White & Hillenbrand, 2005), albeit
at a low rate, but retains at least a low density inner disk. Our
non–detection in a search for cold gas implies that most of its outer disk
must have disappeared or frozen out onto grains. White & Hillenbrand (2005)
show that St 34 has an accretion rate $\langle\dot{M}\rangle=8.3\times
10^{-10}$ M☉ yr-1, so after 1 Myr much more gas than our upper limit of $4.20$
M⊕ would accrete ($\sim 276$ M⊕). Perhaps St 34 recently lost its outer disk
through photoevaporation (e.g. Gorti & Hollenbach, 2009) and we are witnessing
the “last gasp” of accretion onto the star. This is possible but not likely,
as it requires current observations to be taking place at a very special time.

Conversely, RX J0432.8+1735—being a much younger, $1.0\pm 0.5$ Myr WTTS—must
have either evaporated its disk or formed planets from its gas disk faster
than normal. Its being a WTTS is consistent with our null detection of its gas
content, although remnant amounts of gas less than a few $M_{\earth}$ could
still exist in its outer disk. That RX J0432.8+1735 is relatively young and
does not have detectable gas content could be significant considering that
there are older systems, such as Hen 3-600, a binary system at between $1-10$
Myr of age with apparent WTTS and CTTS components (Jayawardhana et al., 1999);
TW Hya, a CTTS at 8-10 Myr (Webb et al., 1999); and DM Tau at $\sim 8$ Myr
(Guilloteau & Dutrey, 1994). Thus something about the disk evaporation physics
is dramatically different in RX J0432.8+1735 than these oldest systems.

In Figure 2 we compare our sources’ gas disk masses and ages with the gas mass
upper limits of those sources $\leq 30$ Myr from Pascucci et al. (2006) and
with the gas mass determinations (solid circles) of BP Tau (13CO $J=2-1$;
Dutrey et al., 2003); DL Tau, DO Tau (12CO $J=2-1$; Koerner & Sargent, 1995);
and DM Tau, DR Tau, GG Tau a, GM Aur, GO Tau, LkCa 15, RY Tau (12CO $J=3-2$
and 13CO $J=3-2$; Thi et al., 2001). We note that this is not an exhaustive
compilation from the literature, but representative of recent results.
Assuming a 1:10 gas-to-dust ratio (D’Alessio et al., 2005), we would expect RX
J0432.8+1735 and St 34 to have at most 0.420 M⊕ and 0.420 M⊕ of dust,
respectively, for $T_{\mathrm{ex}}=20$ K. For St 34, Hartmann et al. (2005)
estimates a disk mass of 665 M⊕ located in a circumbinary disks between the
“wall” (the region defined to surround the two components of the St 34 binary;
$\sim 0.7$ AU) and $7$ AU. Assuming this mass is representative of a total
disk mass in St 34 out to $7$ AU, this would be consistent with a small ($<10$
AU), optically-thick CO disk with a gas-to-dust ratio of $\sim 100$; we do not
detect this due to beam dilation (cf. Pascucci et al., 2006).

St 34 has infrared excess for wavelengths longer than 3.6 $\mu$m (Hartmann et
al., 2005) and RX J0432.8+1735 has infrared excess for wavelengths longer than
24 $\mu$m (Padgett et al., 2006), yet St 34 is a binary CTTS with an accreting
inner disk and RX J0432.8+1735 is a WTTS. Binaries tend to disrupt inner gas
disks (Jensen, 1996) and may decrease disk lifetimes (Monin et al., 2007).
However, Armitage & Clarke (1996) have argued that close binaries affect
angular momentum exchange in the natural evolution of accretion disks
resulting in longer lived outer disks. Indeed Thébault et al. (2004) find that
planet formation around binaries might require a long-lived but massive disk.
Since circumbinary disks allow for long gas disk lifetimes, St 34 might have
had more time to form planets.

Figure 2: Gas circumstellar disk mass versus age of selected sources: our RX
J0432.8+1735 and St 34 upper limits (labeled); upper limits from the Pascucci
et al. (2006) sample (unlabeled upper limits) with ages $\leq 30$ Myr (the
Kelvin-Hemholtz contraction timescale for a 1 M☉ star); and exact mass
determinations (solid circles) of BP Tau (13CO $J=2-1$; Dutrey et al., 2003);
DL Tau, DO Tau (12CO $J=2-1$; Koerner & Sargent, 1995); and DM Tau, DR Tau, GG
Tau a, GM Aur, GO Tau, LkCa 15, RY Tau (12CO $J=3-2$ and 13CO $J=3-2$; Thi et
al., 2001). We assume errors in stellar ages to be 50%.

##  5 Conclusions

Assuming optically thin disks ($\tau\ll 1$), an excitation temperature
$T_{\mathrm{ex}}=20$ K, and a line-width $\Delta v=10$ km s-1, we do not
detect significant amounts of gas around three T Tauri stars: $<4.20$ M⊕ for
the PMS binary St 34 and $<4.20$ M⊕ for RX J0432.8+1735. St 34, a CTTS, is
still accreting gas although it is $8\pm 3$ Myr old, and the gas disk of RX
J0432.8+1735, a WTTS of $1.0\pm 0.5$ Myr, has disappeared quickly. Future
observations of larger samples will be required to understand the diversity of
disk lifetimes as a function of stellar properties.

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