Star formation rate/strength tracer calibrations

H. Otí-Floranes & J. M. Mas-Hesse

Departamento de Astrofísica

Centro de Astrobiología (INTA-CSIC)

ESA - ESAC Camino Bajo del Castillo, 28692 Villanueva de la Canada, Madrid, SPAIN

Choose the values which best describe your burst and input the value of the magnitude observed in order to obtain the value of the Star Formation Strength (IB models) or of the Star Formation Rate (EB models). Also, the intrinsic values expected for the rest of the magnitudes are output. For more information, read below.
Star formation history and age:
Initial Mass Function: Salpeter
Magnitude observed
Value of the magnitude observed =
Color excess: E(B-V)=
IB EW(Lyα)(Â)
t(Myr) Z=0.02 Z=0.008
1 207 227
2 139 182
3 75 102
4 41 53
5 41 34
6 13 24
EB EW(Lyα)(Â)
t(Myr) Z=0.02 Z=0.008
10 81 93
30 69 75
250 66 71
Predicted EW (Lyα) values for IB and EB star formation scenarios, assuming:
  • Salpeter IMF 2-120 Msun
  • No extinction
  • Lyman α escape fraction = 1.0
  • Fraction of Lyman continuum photons effectively participating in the ionization = 0.70
See below for more details. Computed by Sonia Torrejón de Pablos (CAB-UCM report, 2019).


STAR FORMATION MODELS: We consider two types of models for the star formation history: instantaneous (IB) and extended (EB) bursts. The former assumes an instantaneous formation of stars and is characterized by the total mass of gas transformed into stars, which we call Star Formation Strength (SFS). On the other hand, EB models assume a constant Star Formation Rate (SFR), which is the speed at which gas is being transformed into stars. Here, we show the calibrations of tracers at different energies for both SFS and SFR, obtained with the evolutionary synthesis models CMHK02 (Cerviño, Mas-Hesse, & Kunth 2002) and Starburst99 (Leitherer et al. 1999).

INPUT: The input needed is:

1) Star formation history and age: the user can choose between IB and EB models, being 4, 5 and 6 Myr the optional ages of the burst for the former models, and 10, 30 and 250 for the latter.

2) Initial Mass Function: a Salpeter Initial Mass Function is assumed (α=2.35), with three optional mass limits: 2-120, 0.1-100 or 1-100 Mo.

3) Magnitude observed: we have developed SFS and SFR calibrations for a large number of tracers at different energies, this way the user can choose among the monochromatic continuum luminosity at 1500, 2000, 3500 (U-band), 4400 (B-band), 5500 (V-band) and 22200 (K-band) Å, the infrared luminosity, the number of ionizing photons, the Hα and the Lyα emission, the mechanical energy injection rate, the soft X-ray (0.4-2.4 keV) luminosity and the radio luminosity at 1.4 GHz.

4) Value of the magnitude observed: the value given by the user for the magnitude chosen will be plugged into the appropiate SFS or SFR calibration.

5) Color excess: extinction is subject to be present in the observations carried out onto the studied burst, therefore the user can give an estimate of its value through E(B-V). Cardelli extinction law with RV=3.1 is assumed (Cardelli et al. 1989). IMPORTANT: the value given by the user to the observed magnitude is assumed to be the observed one, i.e. not corrected for extinction.

OUTPUT: The output yielded is:

1) the value of SFS/SFR assuming the observational value of the magnitude given, provided an extinction given by the colour excess value. Cardelli extinction law with RV=3.1 is assumed.

2) the expected values for the other magnitudes for which we have developed the calibrations under the same conditions of ages, IMF and extinction. IMPORTANT: the continuum luminosities and the emission nebular lines values are also affected by the extinction, so they represent the expected observational values for the E(B-V) value given by the user.

IONIZING PHOTONS & NEBULAR LINES: A mean fraction (1-f)=0.3 of ionizing photons, irrespective of their energy, is assumed to be absorbed by dust before they can ionize any atom. Therefore, their number NLyc, together with the nebular lines Hα and Lyα, are corrected for this effect. Both lines are calculated considering Case B recombination, with Te=104 K and ne=5×102 cm-3 (Storey & Hummer 1995). Since Lyα is a resonant line it can be resonantly trapped within the nebula, and even low amount of dust can lead to its suppression, depending on the kinematics and column density of the neutral gas. Here, Lyα calibration is obtained assuming that all Lyα photons can escape, which represents an upper value of L(Lyα). If SFS/SFR were to be calculated via the observational value L(Lyα), prior correction for this resonance effect should be made. The escape fraction values cover the whole range 0-1 (Atek et al. 2009), although in the nearby starburst galaxies its value is ~10% (Östlin et al. 2008). Both lines Hα and Ly&alpha are corrected for extinction assuming the E(B-V) value given by the user and Cardelli extinction law.

CONTINUUM LUMINOSITY: Monochromatic continuum luminosity is calculated at 1500, 2000, 3500 (U-band), 4400 (B-band), 5500 (V-band) and 22200 (K-band) Å, and they represent the value expected to be observed for the given E(B-V) value assuming Cardelli extinction law.

INFRARED LUMINOSITY: LFIR is the total infrared emission of the burst, i.e. in the range 1-1000 μm, and its contributions are: 1) the absorbed continuum, calculated through Cardelli extinction law assuming RV=3.1, 2) the fraction (1-f)=0.3 of ionizing photons absorbed, and 3) the total amount of Lyα photons emitted. Although we assume that all photons escape in order to calculate L(Lyα), we do consider for the LFIR calculation that all photons are absorbed by dust. This affects very weakly LFIR value (10% at most). In order to make a more realistic approach towards UV photons absorption by dust, extinction in the range 912-1250 Å was assumed to be A1250 (see Mezger et al. (1982)). Infrared emission saturates for E(B-V)>0.5 (Mas-Hesse, Otí-Floranes, & Cerviño 2008), therefore LFIR is only calculated for E(B-V)= 0.1, 0.2, 0.3, 1, whereas the E(B-V) value input by the user is not considered for this calculation.

RADIO EMISSION: Calibrations for thermal (Lth) and non-thermal (Lnth) radio emissions at 1.4 GHz are calculated. Prescriptions by Lequeux et al. (1981) were followed for the former, considering as before (1-f)=0.3. For the latter we assumed a similar relation than the one obtained by Condon, & Yin (1990), but considering αnth=-0.9. Our relation, as the one from Condon, & Yin (1990), reproduces the Galactic values for both Lnth at 408 MHz and the supernova rate from Berkhuijsen (1984) and Tammann (1982), respectively. Finally, we sum both Lth and Lnth in order to obtain Lrad.

MECHANICAL ENERGY AND X-RAY EMISSION: dEK/dt represents the rate at which mechanical energy is injected into the medium by stellar winds and supernova ejecta. When interstellar gas heats up due to this energy injected, its temperature reaches values of millions of Kelvin, and soft X-ray emission is produced. This component, together with the harder emission by supernova remnants, is used in order to obtain the calibration for LsoftX(0.4-2.4 keV), which was already published in Mas-Hesse, Otí-Floranes, & Cerviño (2008). As explained in Mas-Hesse, Otí-Floranes, & Cerviño (2008), a typical value εsoftx=0.05 is assumed, which indicates that ~5% of the mechanical energy yielded by stellar winds and supernovae is transfomed into X-ray emission.

For a more detailed description, see Otí-Floranes, & Mas-Hesse (2010) or send an e-mail to .

Acknowledgments: Partially funded by Spanish MICINN grants CSD2006-00070 (CONSOLIDER GTC) under the Consolider-Ingenio 2010 Program, and AYA 2007-67965 (ESTALLIDOS). Also, we thank Carlos Rodrigo Blanco and Raúl Gutiérrez Sánchez for their help in the implementation of this site.


If you use these calibrators while preparing a paper, please cite Otí-Floranes, & Mas-Hesse (2010).