Carlo Felice Manara 1,2, Massimo Robberto, Nicola Da Rio 3 Giuseppe Lodato 1, HST Orion Treasury Program Team HST MEASURES OF MASS ACCRETION RATES IN THE

Carlo Felice Manara1,2, Massimo Robberto, Nicola Da Rio3

Giuseppe Lodato1, HST Orion Treasury Program Team

HST MEASURES OF MASS ACCRETION RATES IN THE ORION NEBULA CLUSTER

1Università degli Studi di Milano (Italy), 2current address: ESO-Garching (Germany), 3current address: ESA (Netherlands)

From dust to stars and planets

Cloud collapse

104 yr

Disk formation

105 yr

Planetary system

109 yr107 yr

Low-mass binary

106 yr

C.F. Manara, M. Robberto, N. Da Rio et al. – Mass Accretion Rates Measures in the ONC

Fingerprints of acctretion

UV Excess

Calvet & Gullbring 1998 Gullbring et al. 2000

Muzerolle et al. 2001

Line emission (Hα)

T-Tauri star spectra


1

*1

m

accacc R

RGM

RLM

From tracers and accretion spectrum models

From Teff and Lstar(HRD)

From evolutionary modelsFrom models (~5 R*)

Rm

Camenzind 1990

Free-fall and accretion shock

From Rm to the star matter is in supersonic free-fall.

Material crashes on the star generating a shock.

Free-fall region:Line emission

Accretion Shock: UV excess

Magnetic field ~103 G

Magnetospheric accretion


Navier-Stokes equations and solutions

2/12/13

RR

RRRt

R

ttMacc)2/()2/5(

The azimuthal component of the Navier-Stokes equation is a diffusive equation of the surface density Σ:

With the assumption that the viscosity ν scales with the radius with a power law (self-similar solutions):

It is possible to obtain analytically a solution (Lynden-Bell & Pringle,1974) and, fort >> τᵥ, the mass accretion rate Ṁacc decreases with time with this power law:


Macc evolution with age and Mass

Hartmann et al. 1998, Robberto et al. 2004, Calvet et al. 2005,2008, Fedele et al. 2010, Sicilia-Aguilar et al. 2010

Calvet et al. 2004,Muzerolle et al. 2003, 2005, Natta et al 2004, 2006, Hartmann et al. 2006, Rigliaco et al. 2011


WFPC2 dataset


1643 sources

F336W (U) F439W (B) F656N (Ha) F814W (I)

Detected 1021 997 1342 1610

Upper limit 481 521 215 11

Lower limit 5 11 19 19

Not detected 136 114 67 3

For 1131 of the WFPC2 sources Teff from Da Rio et al. (2011) available.

For 439 sources U, B, I band photometry and Teff available. 339 of them are used (corrected for red

leak no proplyds, binaries, big errors…)

For 897 sources U, B, I band photometry available.

Method

UBI Diagram (2CD) with:

Two Colors Diagram


•Atmosphere Models (Allard et al.2010)

•Accretion spectrum (Calvet et al.98)•75% optically thick emission (blackbody at 7000K)•25% optically thin emission (HII region with n=104 cm-3)

• Extinction law (Cardelli et al. 1989)

Teff (K)

+ HII region (magnetospheric emission)

Two Colors Diagram – Accretion Spectrum


Observed 2CD


Observed 2CD




Dereddened 2CD



Calvet & Gullbring 98



C&G+Magnetosphere

Derivation of LACC and AV

The intersection of the reddening line (red) and the accretion curve (blue) determines simultaneously Lacc and AV.


Estimate of Lacc and AV obtained for 247 sources.

LHa estimation


LACC from LHa - calibration


Linear regression – no errors:

Linear regression – errors on LACC:

)20.027.2(log)05.023.1(log

Sun

H

Sun

acc

LL

LL

)05.069.2(log)01.031.1(log

Sun

H

Sun

acc

LL

LL

204 sources

LACC from LHa - calibration


Linear regression – no errors:

Herczeg & Hillenbrand 2008:

)20.027.2(log)05.023.1(log

Sun

H

Sun

acc

LL

LL

)70.027.2(log)16.031.1(log

Sun

H

Sun

acc

LL

LL

Dahm 2008: )64.019.2(log)26.018.1(log

Sun

H

Sun

acc

LL

LL

Linear regression – errors on LACC: )05.069.2(log)01.031.1(log

Sun

H

Sun

acc

LL

LL

De Marchi et al. 2010: )47.072.1(loglog

Sun

H

Sun

acc

LL

LL

LACC from LHa


Linear regression – no errors: )20.027.2(log)05.023.1(log

Sun

H

Sun

acc

LL

LL

Dahm 2008: )64.019.2(log)26.018.1(log

Sun

H

Sun

acc

LL

LL

497 sources with Lacc estimated from LHa

HR Diagram

With evolutionary models(e.g. D’Antona & Mazzitelli 1994)

derivation of M* and ageDerivation of Ṁacc for 743 sources (246 with 2CD and 497 from LHa)


Results

Final sample


Lacc vs Lstar


All data: b = 1.76 ± 0.01

Natta et al. 2006Clarke & Pringle 2006Tilling et al. 2008

*LLacc

2CD data: b = 1.60 ± 0.02Ha data: b = 1.77 ± 0.01

Tilling et al. 2008: b = 1.7 if h = 1.5 and D’Antona &

Mazzitelli 1994 models are used.

Macc decreases with time

tMaccHartmann et al., 1998: h=1.5.

Se si interpreta l’evoluzione del disco con modelli self similar (h>1) n~R, i.e. a= costante

Ṁacc ~ t-(1.44±0.02)


h = 1.14±0.02

tMacc



h = 1.14±0.02

h = 1.33±0.03

tMacc



h = 1.14±0.02 h = 1.33±0.03

h = 1.13±0.12

tMacc



h = 1.13±0.12

h = 0.56±0.08

tMacc


h = 1.14±0.02 h = 1.33±0.03


h = 0.56±0.08

h ≈ 0

tMacc


h = 1.13±0.12

h = 1.14±0.02 h = 1.33±0.03


Muzerolle et al., 2003: Ṁacc ~ M*2

Natta et al., 2006: Ṁacc ~ M*1.8±0.2

Rigliaco et al., 2011: Ṁacc~ M*1.6±0.4

Ṁacc ~ M*1.545±0.003


Macc increases with Mstar

Muzerolle et al., 2003: Ṁacc ~ M*2

Natta et al., 2006: Ṁacc ~ M*1.8±0.2

Rigliaco et al., 2011: Ṁacc~ M*1.6±0.4


Macc increases with Mstar


Macc spatial distribution


Conclusion

• We derived Lacc in two different ways: 2CD and Ha

• Obtained Macc for 743 sources

• Macc vs age: there is a dependence -> age spread,

hint of slower evolution for higher masses

• Macc vs M*: big spread, partly due to different ages


Future perspective

• Refine Lacc determination (accretion

spectrum…)

• Macc vs period

• Macc vs Mdisk

• Macc vs molteplicity (binaries)

• Other regions

Thanks

Documents

Carlo Felice Manara 1,2, Massimo Robberto, Nicola Da Rio 3 Giuseppe Lodato 1, HST Orion Treasury Program Team HST MEASURES OF MASS ACCRETION RATES IN THE