T Tauri star properties using multi-wavelength survey photometry using multi-wavelength survey photometry Geert Barentsen Geert Barentsen University of Hertfordshire University of Hertfordshire
Near-infrared Near-infrared excess excess UV/optical UV/optical excess excess T Tauri objects T Tauri objects = young solar-like stars (< 10 Myr, = young solar-like stars (< 10 Myr, < 2 M < 2 M ☉ ☉ ) ) Emission lines Emission lines (H-alpha, Ca II, ...) (H-alpha, Ca II, ...)
survey (North) VPHAS survey (South) IPHAS/UVEX survey (North) 88% of T Tauri stars in SIMBAD are located at |b| > 5: 88% of T Tauri stars in SIMBAD are located at |b| > 5: our knowledge is dominated by the Gould Belt our knowledge is dominated by the Gould Belt b = +5 b = +5 b = -5 b = -5
IC1396 IC1396 log N ~ 3 log N ~ 3 Tarantula Tarantula log N ~ 6? log N ~ 6? 150 pc 150 pc (~ Gould Belt) (~ Gould Belt) 1 kpc 1 kpc > 1 kpc > 1 kpc Access to different regions at larger distances Access to different regions at larger distances Sun's birth environment likely log N = 3-4? (Adams 2010) Sun's birth environment likely log N = 3-4? (Adams 2010)
down to ~20 mag = typical brightness of a 0.2 M = typical brightness of a 0.2 M ☉ ☉ T Tauri star at 1 kpc T Tauri star at 1 kpc Image: Gaia mock catalogue (credit: X. Luri & DPAC-CU2) Image: Gaia mock catalogue (credit: X. Luri & DPAC-CU2) 5 kpc 5 kpc
but photometry is “ but photometry is “cheap & deep cheap & deep”: ”: 1) Readily available up to 20 mag (IPHAS, VPHAS, ...) Readily available up to 20 mag (IPHAS, VPHAS, ...) 2) Homogeneous instrumentation & calibration Homogeneous instrumentation & calibration 3) Narrow-band filters provide “a low-res spectrum” Narrow-band filters provide “a low-res spectrum” ... so what can we learn about star formation ... so what can we learn about star formation using photometry alone? using photometry alone?
5 (Barentsen et al. 2011) (Barentsen et al. 2011) Colours have been modelled using the Colours have been modelled using the Pickles (1998) library of observed stellar spectra Pickles (1998) library of observed stellar spectra
Solution: r'-i' / i'-J traces extinction for late-type stars Solution: r'-i' / i'-J traces extinction for late-type stars However: However: these colours are not independent of age/mass/emission these colours are not independent of age/mass/emission Av=1 Av=1
Parameters) Pr(Parameters) Pr(Parameters | Data) ~ Pr(Data | Parameters) Pr(Parameters) Likelihood Likelihood Prior Prior Posterior Posterior = generic solution to the problem of matching observations to models. = generic solution to the problem of matching observations to models. Increasingly being adopted, e.g. 3D extinction mapping (Sale et al. 2012), Increasingly being adopted, e.g. 3D extinction mapping (Sale et al. 2012), parameter determination of main-sequence stars (Bailer-Jones 2011), parameter determination of main-sequence stars (Bailer-Jones 2011), exoplanet light curve fitting (e.g. Ford 2005). exoplanet light curve fitting (e.g. Ford 2005).
Model(Accretion rate, Mass, Age, Extinction) = SED {r', Ha, i', J} Model(Accretion rate, Mass, Age, Extinction) = SED {r', Ha, i', J} ∑ ∑(SED (SED Model Model - SED - SED Observed Observed ) )2 2 ~ ~ σ σ2 2γ γ2 2 and a prior, e.g.: and a prior, e.g.: Pr(Parameters) ~ Uniform Pr(Parameters) ~ Uniform => => find the parameter-space regions where the posterior is high. find the parameter-space regions where the posterior is high. (Note: in this example, the maximum likelihood is equivalent to a (Note: in this example, the maximum likelihood is equivalent to a γ γ2 2-fit!) -fit!) For example ... For example ...
and hence very useful when data and model = fast and hence very useful when data and model uncertainties are small, uncertainties are small, but: but: 1) Photometric data is sparse Photometric data is sparse there is a family of degenerate solutions! there is a family of degenerate solutions! 2) Models are uncertain Models are uncertain the presence of “nuisance parameters” makes the the presence of “nuisance parameters” makes the likelihood more complicated than a Gaussian likelihood more complicated than a Gaussian => Estimate the full posterior distribution Pr(Parameters | Data) => Estimate the full posterior distribution Pr(Parameters | Data) So, why not simply use So, why not simply use γ γ2 2 fitting? fitting?
+ confidence intervals can summarize these distributions into numbers (maximum likelihoods can not!) distributions into numbers (maximum likelihoods can not!) Mass Mass Mass Mass Extinction Extinction Age Age
using a log-uniform prior The extinction can be constrained up to a factor ~2 using a log-uniform prior (or less using a more informative prior) (or less using a more informative prior) Mass Mass Extinction Extinction Future work: add more photometric bands to tighten our handle! Future work: add more photometric bands to tighten our handle!
be distributions. 2) Assume distributions depend 2) Assume distributions depend only on their parents. only on their parents. Hierarchical model Hierarchical model
Modelled colours of emission-line stars Modelled colours of emission-line stars Rules of probability theory allow the model Rules of probability theory allow the model to be written as a hierarchy of smaller sub-models to be written as a hierarchy of smaller sub-models Priors Priors (often uniform) (often uniform)
posterior with “brute force” would require >10^20 samples Computing the posterior with “brute force” would require >10^20 samples (i.e. 10 parameters, 100 values) = computationally intractable (i.e. 10 parameters, 100 values) = computationally intractable But: But: can be reduced to ~10^5 samples by only sampling the parameter space can be reduced to ~10^5 samples by only sampling the parameter space where the posterior probability is large where the posterior probability is large = = Markov Chain Monte Carlo Markov Chain Monte Carlo technique (MCMC.) technique (MCMC.) How to compute the posterior? How to compute the posterior?
candidates from IPHAS colour-colour diagram ... H-alpha EWs agree with literature H-alpha EWs agree with literature spectroscopy from (Sicilia-Aguilar et al.) spectroscopy from (Sicilia-Aguilar et al.)
Spitzer YSOs (< 1 Myr) (< 1 Myr) Hot star Hot star The spatial dispersion of objects in front of the globules suggests an The spatial dispersion of objects in front of the globules suggests an age gradient away from the central O-type star age gradient away from the central O-type star Consistent with Consistent with sequentially triggered star formation. sequentially triggered star formation. Detailed discussion in (Barentsen et al. 2011, MNRAS) Detailed discussion in (Barentsen et al. 2011, MNRAS)
et al. (2009) using Spitzer. Confirms earlier findings by Balog et al. (2006) & Sung et al. (2009) using Spitzer. Fraction of accreting stars lower within ~1 pc from hot O-type star? Fraction of accreting stars lower within ~1 pc from hot O-type star?
cheap & deep. • Large databases are waiting to be exploited. Large databases are waiting to be exploited. • Sophistication of knowledge inference tools is Sophistication of knowledge inference tools is increasingly becoming the limiting factor, rather increasingly becoming the limiting factor, rather than telescope time or processing power! than telescope time or processing power!
include radiation transfer Improve the likelihood model to include radiation transfer models (circumstellar environment, accretion shock) models (circumstellar environment, accretion shock) • Incorporate additional surveys (UVEX, UKIDSS, Spitzer) Incorporate additional surveys (UVEX, UKIDSS, Spitzer) • Carry out a homogeneous, comparative study across Carry out a homogeneous, comparative study across Galactic star-forming regions Galactic star-forming regions (but need Gaia for accurate cluster membership lists) (but need Gaia for accurate cluster membership lists)
being limited by the sophistication of knowledge inference methods. by the sophistication of knowledge inference methods. Rather than by the amount of data or processing power. Rather than by the amount of data or processing power.
explained by UV photo-evaporation? Might be explained by UV photo-evaporation? But models & observations suggest photo-evaporation is not effective But models & observations suggest photo-evaporation is not effective beyond ~1 pc from source (e.g. Richling & Yorke 1998; Balog et al. 2007) beyond ~1 pc from source (e.g. Richling & Yorke 1998; Balog et al. 2007) Hot star Hot star
decreasing ages We also find a gradient of increasing accretion rates and decreasing ages This is more difficult to explain from photo-evaporation! This is more difficult to explain from photo-evaporation!