Probing the Substellar Regime with SIRTF

The past 5 years have witnessed the remarkable birth of a new research field of astronomy—the physical study of substellar objects (mass below 0.075 M_⊙; Baraffe et al. 1998) outside the solar system. Large‐scale optical and near‐infrared surveys of the sky (Deep Near Infrared Survey of the Southern Sky [DENIS], Two Micron All Sky Survey [2MASS], and Sloan Digital Sky Survey [SDSS]) have revealed very cool objects that are close to us but nevertheless were unknown. The overwhelming majority of substellar objects in the field, however, cannot be detected by DENIS and 2MASS because they cool very rapidly with time and become extremely faint at wavelengths shorter than about 4 μm (Burrows et al. 1997). SIRTF (Fanson et al. 1998) will allow deeper probes of in the substellar regime, extending the census of substellar objects in the field to lower masses and temperatures.

Many studies show that the number of substellar objects increases toward lower masses. The functional form of this relationship, the initial mass function (IMF), can be approximated by a power law, dN/dM ∼ M^-α (Salpeter 1955). For masses between 0.1 M_⊙and 0.01 M_⊙ (i.e., ∼100M_Jup and 10M_Jup, respectively), several surveys in young open clusters have found α in the range 0.4–1.0 (Hillenbrand & Carpenter 2000; Luhman et al. 2000; Martín et al. 2000; Najita, Tiede, & Carr 2000; Zapatero Osorio et al. 2000; Béjar et al. 2001). The density of field brown dwarfs discovered by DENIS and 2MASS suggests a slightly steeper IMF with α = 1.3 (Reid et al. 1999). The number of substellar objects in each cluster, or in the field, is still small. Hence the statistical uncertainties are large, and it is not possible to discern whether there are significant variations in the IMF from one region to another. SIRTF has the potential to reveal many nearby ultracool substellar objects and, hence, constrain the IMF in the solar neighborhood. In this paper, we discuss what we think are appropriate observational strategies that will be needed to detect such objects with SIRTF. Following a discussion of the expected spectra of ultracool substellar objects, we provide estimates of the counts of such objects in the Galactic disk that can be detected by SIRTF, and we provide a comparison with similar efforts using ground‐based searches. Special attention is paid to the identification of free‐floating very low mass objects in the immediate vicinity of the Sun. Our main conclusions are that ultracool substellar objects can be identified in the SIRTF/Infrared Array Camera (IRAC) color‐color diagram. Their density can be constrained with a modest amount of telescope time. The coolest objects will be detected only in channel 2. Confirmation will require follow‐up observations with SIRTF or with ground‐based 10 m class telescopes.

The spectra presented here were computed from model atmospheres for solar‐composition substellar objects. These models will be described in detail in a forthcoming paper (M. Marley et al. 2001, in preparation). Here we highlight the results most relevant to estimating the detectability of such objects with SIRTF.

The near‐infrared spectra of L and T dwarfs are sculpted by the molecular bands of water and methane. With decreasing effective temperature, these bands continue to suppress the optical and near‐infrared flux. At temperatures below ∼700 K, substellar objects emit very little flux shortward of 4 μm (see Fig. 1). In fact, the coolest known brown dwarf, Gl 570D, has T_eff = 790 ± 50 K (Burgasser et al. 2000). Its spectrum is similar to that of Gl 229B.

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It is unlikely that the DENIS and 2MASS surveys will detect any objects significantly cooler than Gl 570D. With J = 15.33 mag and M_J = 16.5 mag, this object is near the detection limit of 2MASS (J ∼ 16 mag; and J ∼ 15 mag for DENIS). A substellar object 200 K cooler would have an absolute J‐band magnitude about 1.5 mag fainter (Saumon et al. 1996; Burrows et al. 1997); to be detected by these surveys it would have to be 2 times closer, at 3 pc. There are six stellar systems within 3 pc of the Sun, and there could be a similar number of brown dwarfs. However, the chances that 2MASS will detect them may be negligible if the near‐infrared spectrum is depleted by strong water bands.

Preliminary models (Marley 2001), illustrated here in Figure 2, provide a glimpse of what these substellar objects may look like. Water clouds will first appear in objects with T_eff below ∼600 K. The clouds will first form as tenuous stratus clouds high in the atmosphere and then form lower in the atmosphere in cooler objects where they will be thicker and more substantial. For T_eff below ∼300 K, ammonia clouds will form. Jupiter's water clouds are hidden below two higher cloud layers and are poorly understood. Thus SIRTF provides the opportunity to detect the first substellar mass objects outside our solar system in which water clouds dominate the visible atmosphere.

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Water clouds will substantially alter the infrared spectra of these objects. T dwarfs such as Gl 229B are blue in J−K. Once water clouds form, the J−K color will move redward from J−K ∼ 0 to J−K ∼ 1 (Ackerman & Marley 2001). Introduction of a new spectral class is likely to be necessary for classifying objects cooler than the T dwarfs. Based on near‐IR colors (JHK) alone, it would be very difficult to distinguish the ultracool substellar objects from background M stars with similar colors. Brown dwarfs with clear atmospheres, like the T dwarfs, are bright at 4–5 μm (Marley et al. 1996; Burrows et al. 1997). As with Jupiter, M. Marley et al. (2001, in preparation) find that the coolest brown dwarfs are also bright in this spectral region, even when water clouds are present (Fig. 2). Thus, a search with SIRTF at 4–5 μm has the potential to easily discover such objects.

SIRTF observations can also test current models for the spectra of intermediate‐age brown dwarfs. At our request, calculations of substellar evolutionary tracks in the SIRTF/IRAC passbands were made by the Lyon group (F. Allard, I. Baraffe, & G. Chabrier 2000, private communication). We have compared them with the models used in this paper. The Lyon models extend to higher temperatures than our models but do not descend to temperatures lower than about 250 K. In Figure 3 we present a comparison between the two sets of models for an age of 0.1 Gyr and masses between 1M_Jup and 30M_Jup, which span a temperature range from 280 K to 1900 K, respectively. There is general agreement among the two sets of models that the substellar objects are very red, but the exact position of the objects in the color‐magnitude diagram is clearly model dependent. The treatment of methane absorption is particularly important for model predictions of fluxes in IRAC channel 1. SIRTF observations of brown dwarfs in the Pleiades cluster (age ∼ 0.1 Gyr) and in the solar neighborhood could provide a powerful test of the theoretical models.

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The DENIS, 2MASS, and SDSS surveys combined have demonstrated that free‐floating brown dwarfs outnumber brown dwarf companions to stars by about a factor of 10. Together, these surveys have already discovered more than 200 free‐floating brown dwarfs (Burgasser et al. 1999; Delfosse et al. 1999; Fan et al. 2000; Gizis et al. 2000; Kirkpatrick et al. 2000; Leggett et al. 2000; Martín et al. 1999) but only three companion brown dwarfs to stars (Burgasser et al. 2000; Kirkpatrick et al. 2000). Moreover, high‐precision radial velocity surveys have revealed a brown dwarf "desert" within a few AU of G and K main‐sequence stars (Halbwachs et al. 2000). They determine that there exists a secondary mass cutoff between 0.01 M_⊙ and 0.1 M_⊙. Other searches for brown dwarf companions to stars have found only a few outstanding examples in samples of hundreds of stars (Becklin & Zuckerman 1988; Oppenheimer 1999). These companions are very interesting but seem to be rare.

The spatial resolution of SIRTF (FWHM = 2 3 with IRAC), and the lack of a coronagraph, will not allow a Jupiter‐mass planet at 5 AU separation to be resolved, even for the closest stars. Jupiter‐mass planets may be common around stars, but they are unlikely to be found outside a 20 AU radius of the parent star. The ice condensation region is located at about 5 AU, with little dependence on the spectral type of the star, and gravitational instabilities in the disk are unlikely to be effective beyond 20 AU (Boss 2000). Direct images of massive disks around T Tauri stars indicate that in general the density is too low to allow for the formation of a giant planet beyond 20 AU (e.g., Krist et al. 2000). On the other hand, deep imaging surveys of Orion and IC 348 suggest that free‐floating planetary‐mass objects probably are very numerous (Najita et al. 2000; Zapatero Osorio et al. 2000).

These considerations suggest that a wide‐field imaging survey with SIRTF could be more effective in detecting a large sample of substellar objects than pointed searches for companions. We have used the SIRTF planning observations tool (SPOT) for a case study of a hypothetical survey. We have chosen total exposure times of 720 s per pointing (divided into 24 exposures of 30 s for dithering and cosmic‐ray removal). For these integration times, the total observing time estimated by SPOT to create an IRAC map covering 1 deg² takes comes to 33.3 hours. In this simulated observation, the 5 σ sensitivities for point sources under conditions of low background (high Galactic latitude regions away from the ecliptic) are 2.91 μJy in channel 1 (effective wavelength 3.56 μm, similar to the ground‐based L band), 3.88 μJy in channel 2 (effective wavelength 4.51 μm), 11.3 μJy in channel 3 (effective wavelength 5.69 μm), and 13.2 μJy in channel 4 (effective wavelength 7.98 μm).

The main contribution to source confusion at these flux limits comes from background galaxies. We have estimated the number of galaxies and stars at the IRAC passbands using the predictions of Franceschini et al. (1991) and a modified version of the galaxy model of Wainscoat et al. (1992). We obtain a density of galaxies that is consistent with the 7 μm ISOCAM counts obtained by Taniguchi et al. (1997). Our calculations show that in IRAC channel 2 (the most sensitive passband for substellar objects) we expect to detect approximately 3800 stars (for high Galactic latitude) and 78,000 galaxies per square degree. If each galaxy is assumed to occupy 3 × 3 pixels (36 × 3 6), then the galaxies will cover approximately 7% of the pixels. At fainter detection limits, the crowding from galaxies is correspondingly greater. Thus, more sensitive observations offer relatively diminishing returns for a much greater investment of observing time.

According to the fluxes predicted by the synthetic spectra, substellar objects can be identified unambiguously from IRAC photometry. In fact, a 5 σ detection in channel 2 and no detection in the other channels is formally sufficient. As shown by Figure 4, any object with log F(4.5 μm)/F(3.6 μm)>0.3 can be considered a good brown dwarf or planet candidate. Neither stars nor galaxies contaminate the substellar locus. The location of flared and flat disks in Figure 4 is based on results on the spectral index for T Tauri star disks by Kenyon & Hartmann (1995). The location of 30 Doradus has been derived from Infrared Space Observatory Short Wavelength Spectrometer measurements by Sturm et al. (2000), and the flux values for L* galaxies at z = 0.1–5 are based on simulations by Fazio et al. (1998).

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Figure 4 also indicates that Population III¹ brown dwarfs with effective temperatures below 400 K are readily identified from their colors alone according to evolutionary models by Burrows et al. (1993). Still warmer (and more massive) Population III brown dwarfs occupy a region in the color‐color plot that coincides with redshifted L* galaxies and with stars having debris disks which are intermediate between Vega‐type disks and the disks around classical and weak‐line T Tauri stars. Additional information will therefore be needed to make a positive identification. Two epochs of IRAC observations would facilitate an identification of the most nearby Population III brown dwarfs, based on their high proper motion. More distant candidates for massive Population III brown dwarfs will have to be followed up with instruments with higher intrinsic angular resolution, e.g., ground‐based 8–10 m class telescopes and the Next Generation Space Telescope (NGST).

We have estimated the number counts of substellar objects in the disk of the Galaxy using the following ingredients: (1) Theoretical fluxes computed from synthetic spectra (see Fig. 2). (2) Sensitivities for low background from the IRAC manual. We have adopted a 5 σ confidence level for our detection limit in each channel. (3) A solar neighborhood density of 0.057 stellar systems pc⁻³ (Reid et al. 1999). (4) Power‐law mass functions with α = 1.5, 1.0, and 0.5 from 100M_Jup to 1M_Jup. (5) A constant star formation rate over the lifetime of the Galactic disk (from 0 to 10 Gyr). (6) An exponential vertical distribution for distances beyond 50 pc, and a scale height of 325 pc, consistent with the counts of M dwarfs.

A Monte Carlo code provided the cumulative number of substellar objects. In Figure 5, we show the cumulative distributions of objects with masses in the range 25M_Jup to 1M_Jup for two different slopes of the IMF power law. For an IMF with α = 1.5, we predict that SIRTF could detect about 30 isolated planetary‐mass objects (objects with masses below the deuterium limit at 0.013 M_⊙; Saumon et al. 1996) per square degree. For α = 1.0, the number of such objects decreases to about four per square degree.

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We consider a case study in which 600 hours of SIRTF time would be dedicated for an IRAC survey to search for substellar objects at high ecliptic latitude (to minimize the zodiacal light background). Using SPOT we have estimated that an area of 18 deg² could be covered with 5 σ sensitivity of 3.88 μJy in channel 2. The cumulative distribution of substellar objects that such a survey would find (for α = 1.5) is given in Figure 6. We compare with another survey which is less sensitive but covers a larger area (64 deg²). Both surveys require the same amount of SIRTF observing time according to the SPOT program. The larger survey is less efficient owing to larger overheads and the contribution of detector noise when the exposure times are shorter. More than 150 substellar objects with temperatures cooler than 600 K could be revealed in 18 deg². If the IMF is shallower, the number of objects would naturally be less. For α = 1.0 we predict about 20 objects cooler than 600 K, and for α = 0.5 we predict only three of them. SIRTF observations can constrain the field mass function down to masses below the deuterium mass limit by counting the number of ultracool substellar objects.

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Follow‐up observations of the substellar objects discovered by SIRTF are essential, particularly for the candidates that are detected only in channel 2. Figure 7 illustrates the ratio between the density of objects detected in channel 2 and the density of objects detected in channel 1. We call this quantity R²₁, i.e., the number of objects detected in channel 2 over number of objects detected in channel 1. It is independent of the mass function but very dependent on the temperature of the model spectra. The lower the temperature of the objects, the more likely that they will be detected only in channel 2; i.e., the value of R²₁ becomes higher. For T_eff≥900 K, R²₁<1 owing to the better sensitivity of channel 1 (a factor of 1.5) and the relatively flat spectrum of substellar objects in the 3–5 μm range for those temperatures (Fig. 1). For T_eff<900 K, R²₁ increases monotonically and becomes larger than 10 for T_eff<500 K. For T_eff = 200 K we obtain R²₁ ∼ 10⁴. Ultracool substellar objects are much more likely to be detected only in channel 2 and not in channel 1 or in any of the other two channels which have much lower sensitivity. The preference for channel 2 is mainly due to the pronounced peak at 5 μm of the spectral energy distribution (Figs. 1 and 2).

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Confirmation of the substellar objects is feasible using deeper SIRTF imaging and ground‐based observations. Detailed analysis may have to wait for larger telescopes such as the California Extremely Large Telescope and NGST. For example, a 10M_Jup object with an age of 1 Gyr at a distance of 50 pc is expected to have T_eff = 437 K and a flux in channel 2 of 9.2 μJy. This is well above the 5 σ threshold of our case study. In channels 1, 3, and 4 the same object should give fluxes of 0.60 μJy, 0.86 μJy, and 1.29 μJy, respectively. A deep exposure of 1.4 hours will provide a 5 σ detection in channel 1. The near‐infrared magnitudes of such object will be J = 24.0 mag, H = 23.4 mag, and K = 25.5 mag. A 5 σ detection in J band with a 10 m telescope would take about 2 hours. Longer exposure times would be required for the other bands.

SIRTF observations in nearby star‐forming regions will not be as sensitive to faint ultracool substellar objects as observations in unbiased space. This is due to the much higher mid‐infrared background in the star‐forming regions than in regions far from the Galactic plane. On the other hand, SIRTF searches in star‐forming regions can probe very low masses. For example, at 1 Myr, a Jupiter‐mass object is expected to have T_eff ∼ 500 K (Burrows et al. 1997). Such objects could be detected with SIRTF/IRAC up to distances of about 200 pc, which includes many active star‐forming regions, such as Chamaeleon, Lupus, ρ Oph, and Taurus‐Auriga. The density of these planetary‐mass objects will critically depend on the shape of the IMF down to 1M_Jup and on their spatial distribution. Thus, while SIRTF searches at high Galactic latitude are more efficient for detecting ultracool substellar objects (down to T_eff ∼ 200 K), searches in star‐forming regions could be more efficient to detect younger (warmer) planetary‐mass objects.

We have shown that IRAC channel 2 is very efficient for detecting ultracool substellar objects. The precise position of substellar objects in an IRAC color‐magnitude diagram is model dependent, suggesting that SIRTF observations of known brown dwarfs will be very useful to test the validity of the models. Preliminary models indicate that the atmospheres of substellar objects cooler than about 500 K are dominated by water clouds, which make the objects fainter at optical and near‐infrared wavelengths than previously thought. The 5 μm window is an excellent region for detecting them because their atmospheres are more transparent. We present a case study of a hypothetical SIRTF survey with a 5 σ sensitivity of 3.88 μJy in IRAC channel 2. We show that substellar objects can be identified in an IRAC color‐color diagram. Any object with log F(4.5 μm)/F(3.6 μm)>0.3 can be considered as a good substellar candidate. Neither stars nor galaxies contaminate the substellar locus. We predict a density of 30 isolated planetary‐mass objects per square degree for an IMF with a slope α = 1.5. For shallower IMF slopes, the number of substellar objects diminishes. Thus, a SIRTF wide and moderately deep survey can determine the field substellar IMF down to very low masses. Follow‐up observations of ultracool substellar candidates are feasible with SIRTF or with ground‐based 10 m class telescopes.