Bolometric Correction for Brown Dwarfs

Balaji Muthusubramanian & Johanna Hartke

April 9, 2014

1 Scientific Justification

Bolometric corrections are essential in estimating the absolute bolometric magnitude and luminosity of a source. The Bolometric correction for a photometric band is defined as the difference between absolute magnitude and the magnitude of the stellar/sub-stellar objects in that band.

BCV = Mbol − MV (1) To correct for the bolometric magnitude, we need to employ a reference point. Generally, this reference point is taken as the Sun:

Mbol, = MV, + BCV, = V + 31.572 + BCV, , (2) where V is the apparent V band magnitude of the Sun.Thus the bolometric magnitude is computed as

Mbol − Mbol, = −2.5log(L/L ). (3) Hence the V magnitude of the star can be corrected by combining equa- tions 1, 2 and 3 as,

MV = −2.5log(L/L ) + V + 31.572 − (BCV − BCV, ) (4)

We can adopt the solar parameters from Allen (2000) to be, MV, = 4.82, Mbol, = 4.74, BCv, = −0.08 and V = −26.75. Emperical relations for the V-band bolometric corrections have been computed by Flower (1996) and Torres (2010). Flower (1996) used a data sample of 335 stars to derive the following empirical relation between the Bolometric Correction and log(Teff ),

2 BCV = a + b log(Teff ) + c log(Teff ) + ... (5) The coefficients were later corrected by Torres (2010). The coefficients for different ranges of log(Teff ) from Torres (2010) are given in table 1.

1 Table 1: Coefficients from (Torres 2010)

Coefficient log(Teff ) > 3.90 3.90 > log(Teff ) > 3.70 log(Teff ) < 3.70 a 0.190537291496456E+05 0.370510203809015E+05 0.118115450538963E+06 b 0.155144866764412E+05 0.385672629965804E+05 0.137145973583929E+06 c 0.421278819301717E+04 0.150651486316025E+05 0.636233812100225E+05 d 0.381476328422343E+03 0.261724637119416E+04 0.147412923562646E+05 e ... 0.170623810323864E+03 0.170587278406872E+04 f ...... 0.788731721804990E+02

The studies mentioned above were only conducted to a lower limit of log(Teff ) ≈ 3.4 − 3.7. This is above the effective temperatures of brown dwarfs. The stellar radii of the brown dwarfs are hard to measure and this influences the accuracy of bolometric correction. Hence, the above mentioned studies skipped brown dwarfs in their sample set. Reid et al. (2001) have computed the bolometric corrections of brown dwarfs for the J band and Todorov et al. (2010) have computed them for the K band. Recent surveys have measured the stellar parameters of brown dwarfs like effective temperature, extinction, etc. with a high confidence level. Hence, we propose to observe a set of 45 brown dwarfs in Opiuchus and Upper Scorpious star forming regions (cf. Appendix A) for which the effective temperature, distance and the extinction have been measured by Alves de Oliveira et al. (2012, 2013) for the ρ Opiuchus region and Dawson et al. (2011) for Upper Scorpious. By measuring their magnitudes in 4 different photometric bands and fitting them with a black body of corresponding temperature, distance and extinction, we can estimate the radii of the brown dwarfs and thus their bolometric luminosities. As a pilot study, we selected a sample of 32 M, L and T dwarfs filtered from the online database of Gelino et al. (2004) as the ones which had known U, B, V, I, R, J, H and K photometric magnitudes. Some of the SEDs of the above mentioned objects are shown in Appendix B. The photometric magnitudes were downloaded from the SIMBAD database. Their Spectral Energy Distribution (SED) was fitted with a black body by assuming all the objects to be at the same distance and with same radius to estimate their corresponding effective temperatures. Thus from their SED we computed the bolometric corrections for each of the object. The bolometric correc- tions were over-plotted with the bolometric correction curves given by Allen (2000) and Flower (1996); Torres (2010) shown in Figure 1.

2 Figure 1: Bolometric correction of 32 brown dwarfs over plotted with cor- rections from Allen (2000) and Flower (1996); Torres (2010).

Technical Justification

We will observe brown dwarfs in the star forming regions ρ Ophiuchi and Upper Scorpius to obtain their photometry in order to determine a relation between the effective temperature Teff and the bolometric corrections using the WFC (FoV ∼ 0.3 deg2) on the INT. In order to observe the constellation of Scorpius it might be necessary to override the INT low shutter limit since it will be only above the shutter limit for two hours (on the 20th of April). The ρ Ophiuchi cloud complex can in principle be observed without overriding the low shutter limit since it lies above 33◦ for three hours (on the 20th of April). At least 17 brown dwarfs are expected to be observed in the wide–field image of ρ Ophiuchi (Alves de Oliveira et al. 2012, 2013) and 28 in Upper Scorpius (Dawson et al. 2011). We will be observing between 3 and 7 days after the full Moon, thus we chose the relatively red filters V, R, I and z, due to the high background and the proximity of the chosen objects to the Moon. We used the V, R, and I photometric points of the brown dwarf ρ Ophi- uchi 102 to estimate the exposure times and signal-to-noise ratios in this field (Wilking et al. 2005). This is a very bright brown dwarf hence we decided to offset the magnitudes by two orders for the exposure time cal- culation. This brown dwarf can also be used as a calibrator. Since there was no photometric data in the z band available for this source, we chose

3 Table 2: Filters and exposure times Object Band Filter mag exp. time [s] S to N ρ Orphiuchi V WFCHARV 15.6 60 652.52 R WFCHARR 17.6 60 212.52 I WFCRGOI 15.4 60 522.54 z WFCRGOZ 21.4 300 2.10 Upper Scorpius V WFCHARV - 60 - R WFCHARR 19.7 60 42.30 I WFCRGOI 16.5 60 311.28 z WFCRGOZ 19.3 60 6.38

CHFTWIR-OPH 9 (Alves de Oliveira et al. 2010) to estimate the exposure time in the z band. The results can be found in table 1. The exposure times were chosen such that a signal-to-noise ratio larger than 2 can be obtained. Other brown dwarf sources might be dimmer than ρ Ophiuchi 102, thus we decided for the relatively long exposure time. We are planning to take 10 images per filter which are slightly shifted in order to be able to correct for contaminations and the fact that there are gaps in between the four chips of the CCD. This amounts to a total of 1.5 hours of exposure time including an initialization and readout time of 1 minute. Similarly, we can use the brown dwarf 2MASS J15563311-1807421 as a reference for Upper Scorpius in the R and I band (Slesnick et al. 2006). In the z-band, the brown dwarf UGCS J154723.32-272907.3 (Dawson et al. 2011) was used. The exposure times were chosen such that a signal-to-noise ratio larger than 2 can be obtained. We could not find a brown dwarf in Upper Scorpius whose V band magnitude had already been determined. Comparing the signal to noise ratios of other bands, we expect to have a significant signal for 60 seconds of exposure. For 10 images this amounts to a total exposure time of 1 hour.

4 References

Allen, A. N. 2000, Allen’s astrophysical quantities

Alves de Oliveira, C., Abrah´am,P.,´ Marton, G., et al. 2013, Astronomy & Astrophysics, 559, A126

Alves de Oliveira, C., Moraux, E., Bouvier, J., & Bouy, H. 2012, Astronomy & Astrophysics, 539, A151

Alves de Oliveira, C., Moraux, E., Bouvier, J., et al. 2010, Astronomy & Astrophysics, 515, A75

Dawson, P., Scholz, A., & Ray, T. P. 2011, Monthly Notices of the Royal Astronomical Society, 418, 1231

Flower, P. J. 1996, The Astrophysical Journal, 469, 355

Gelino, C. R., Kirkpatrick, J. D., & Burgasser, A. J. 2004, in Bulletin of the American Astronomical Society, Vol. 36, American Astronomical Society Meeting Abstracts, 1354

Reid, I. N., Burgasser, A. J., Cruz, K. L., Kirkpatrick, J. D., & Gizis, J. E. 2001, The Astronomical Journal, 121, 1710

Slesnick, C. L., Carpenter, J. M., & Hillenbrand, L. A. 2006, The Astro- nomical Journal, 131, 3016

Todorov, K., Luhman, K. L., & McLeod, K. K. 2010, The Astrophysical Journal Letters, 714, L84

Torres, G. 2010, The Astronomical Journal, 140, 1158

Wilking, B. A., Meyer, M. R., Robinson, J. G., & Greene, T. P. 2005, The Astronomical Journal, 130, 1733

5 A Objects for the observation proposed

Table 3: Objects in ρ Ophiuchus region Object name (CHFTWIR-Oph-) RA (J2000) DEC (J2000) 9 16:26:03.28 24:30:25.9 16 16:26:18.58 24:29:51.6 18 16:26:19.41 24:27:43.9 30 16:26:36.82 24:19:00.3 31 16:26:37.81 24:39:03.3 33 16:26:39.69 24:22:06.2 37 16:26:40.84 24:30:51.1 66 16:27:14.34 24:31:32.0 77 16:27:25.64 24:37:28.6 78 16:27:26.23 24:19:23.1 90 16:27:36.59 24:51:36.1 96 16:27:40.84 24:29:00.8 98 16:27:44.20 23:58:52.4 100 16:27:46.54 24:05:59.2 101 16:27:47.25 24:46:45.9 103 16:28:10.46 24:24:20.4 107 16:28:48.71 24:26:31.8

6 Table 4: Objects in Upper Scorpius region Object name RA (J2000) DEC (J2000) 2MASS J155823762721435 15:58:23.76 27:21:43.7 2MASS J160901682740521 16:09:01.68 27:40:52.3 2MASS J160355732738248 16:03:55.73 27:38:25.1 2MASS J155857932758083 15:58:57.93 27:58:08.5 2MASS J155316982756369 15:53:16.98 27:56:37.2 2MASS J155519602751207 15:55:19.59 27:51:21.0 2MASS J155019582805237 15:50:19.58 28:05:23.9 2MASS J155834032803243 15:58:34.03 28:03:24.5 2MASS J160052652812087 16:00:52.66 28:12:09.0 2MASS J154929092815384 15:49:29.08 28:15:38.6 2MASS J154936602815141 15:49:36.59 28:15:14.3 2MASS J161923992818374 16:19:23.99 28:18:37.5 2MASS J154908032839550 15:49:08.02 28:39:55.2 2MASS J154857772837332 15:48:57.76 28:37:33.4 2MASS J161958272832276 16:19:58.26 28:32:27.8 2MASS J155444862843078 15:54:44.85 28:43:07.9 2MASS J155915132840411 15:59:15.12 28:40:41.3 2MASS J160628702856580 16:06:28.70 28:56:58.2 2MASS J161013162856308 16:10:13.15 28:56:31.0 2MASS J160515442802520 16:05:15.44 28:02:52.0 2MASS J155525132801085 15:55:25.11 28:01:08.8 2MASS J155029342835535 15:50:29.32 28:35:53.9 2MASS J161909832831390 16:19:09.82 28:31:39.5 2MASS J160356012743335 16:03:56.00 27:43:33.6 2MASS J161459362826214 16:14:59.37 28:26:21.8 2MASS J155517682856579 15:55:17.70 28:56:58.1 2MASS J155049202900030 15:50:49.19 29:00:03.1 UGCSJ 154723.32272907.3 15:47:23.33 27:29:07.3

7 B SED from the pilot study

Figure 2: M, L and T dwarfs filtered from Gelino et al. (2004)

8