Extention to Lick indices¶
We also include functions to compute lick indices and provide a series of commonly use ones.
Lick index¶
The Lick system of spectral line indices is one of the most commonly used methods of determining ages and metallicities of unresolved (integrated light) stellar populations.
The calibration of the Lick / IDS system is complicated because the original Lick spectra were not flux calibrated, so there are usually systematic effects due to differences in continuum shape. Proper calibration involves observing many of the original Lick/IDS standard stars and deriving offsets to the standard system.
In Vazdekis et al. (2010), they propose a new Line Index System, hereafter LIS, with three new spectral resolutions at which to measure the Lick indices. Note that this new system should not be restricted to the Lick set of indices in a flux calibrated system. In fact, LIS can be used for any index in the literature (e.g., for the Rose (1984) indices), including newly defined indices (e.g., Cervantes & Vazdekis 2009).
The LIS system is defined for 3 different spectral resolutions which are best suited for the following astrophysical cases:
LIS-5.0AA: globular clusters
LIS-8.4AA: low and intermediate-mass galaxies
LIS-14.0AA: massive galaxies
Conversions to transform the data from the Lick/IDS system to LIS can be found in Johansson, Thomas & Maraston (2010), which provides a discussion of indices and the information content of them.
Quick start example¶
The lick extension is very similar to the broadband usage.
# convert to magnitudes
import numpy as np
from pyphot import LickLibrary
# using the internal collection of indices
lib = LickLibrary()
f = lib['CN_1']
# work on many spectra at once
index = f.get(lamb, spectra, axis=1)
Calculations¶
Suppose one has a spectrum \(f_\lambda\) defined over the wavelength \(\lambda\). First, we must adapt the resolution of the spectrum to match one of the LIS range. Indeed Lick definitions have different resolution elements as function of wavelength:
\(\lambda\) in \(\unicode{x212B}\) |
4000 |
4400 |
4900 |
5400 |
6000 |
resolution (FWHM in \(\unicode{x212B}\)) |
11.5 |
9.2 |
8.4 |
8.4 |
9.8 |
new_f = licks.reduce_resolution(w, f, sigma0=0.55, sigma_floor=0.2)
Indices are defined on continuum normalized spectra. Therefore all indices come with 3 intervals: a band that gives the index range but also a blue and a red interval on each side which are used to fit a polynomial function as local continuum.
see: licks.LickIndex.continuum_normalized_region_around_line().
Finally any index is calculated by integrated the continuum normalized flux. Some indices are given in magnitudes, and some in equivalent width units.
References¶
Worthey G., Faber S. M., Gonzalez J. J., Burstein D., 1994, ApJS, 94, 687
Worthey G., Ottaviani D. L., 1997, ApJS, 111, 377
Puzia et al. 2002
Zhang, Li & Han 2005, http://arxiv.org/abs/astro-ph/0508634v1
Vazdekis et al., 2010
Johansson, Thomas & Maraston, 2010, http://wwwmpa.mpa-garching.mpg.de/~jonasj/milesff/milesff.pdf
This page shows the content of the provided library with respective properties of the passband filters. The code to generate the table is also provided below.
Library content¶
import pyphot
# define header and table format (as csv)
hdr = ("name", "wavelength units", "index units", "min", "max" "min blue", "max blue", "min red", "max red")
fmt = "{0:s},{1:s},{2:s},{3:.3f},{4:.3f},{5:.3f},{6:.5f},{7:.3f},{8:.3f}\n"
l = pyphot.LickLibrary()
with open('licks_table.csv', 'w') as output:
output.write(','.join(hdr) + '\n')
for k in sorted(l.content):
fk = l[k]
# wavelength have units
band = fk.band.magnitude
blue = fk.blue.magnitude
red = fk.red.magnitude
rec = (fk.name, fk.wavelength_unit, fk.index_unit, band[0], band[1],
blue[0], blue[1], red[0], red[1])
output.write(fmt.format(*rec))
name |
wavelength units |
index units |
min |
maxmin blue |
max blue |
min red |
max red |
|
CN_1 |
AA |
mag |
4142.125 |
4177.125 |
4080.125 |
4117.62500 |
4244.125 |
4284.125 |
CN_2 |
AA |
mag |
4142.125 |
4177.125 |
4083.875 |
4096.37500 |
4244.125 |
4284.125 |
Ca1_LB13 |
AA |
ew |
8484.000 |
8513.000 |
8474.000 |
8484.00000 |
8563.000 |
8577.000 |
Ca2_LB13 |
AA |
ew |
8522.000 |
8562.000 |
8474.000 |
8484.00000 |
8563.000 |
8577.000 |
Ca3_LB13 |
AA |
ew |
8642.000 |
8682.000 |
8619.000 |
8642.00000 |
8700.000 |
8725.000 |
Ca4227 |
AA |
ew |
4222.250 |
4234.750 |
4211.000 |
4219.75000 |
4241.000 |
4251.000 |
Ca4455 |
AA |
ew |
4452.125 |
4474.625 |
4445.875 |
4454.62500 |
4477.125 |
4492.125 |
CaH |
AA |
ew |
6775.000 |
6817.000 |
6520.000 |
6545.00000 |
7035.000 |
7050.000 |
CaHK_LB13 |
AA |
ew |
3899.470 |
4003.470 |
3806.500 |
3833.82000 |
4020.690 |
4052.360 |
CaH_1 |
AA |
mag |
6357.500 |
6401.750 |
6342.125 |
6356.50000 |
6408.500 |
6429.750 |
CaH_2 |
AA |
mag |
6775.000 |
6900.000 |
6510.000 |
6539.25000 |
7017.000 |
7064.000 |
Fe4383 |
AA |
ew |
4369.125 |
4420.375 |
4359.125 |
4370.37500 |
4442.875 |
4455.375 |
Fe4531 |
AA |
ew |
4514.250 |
4559.250 |
4504.250 |
4514.25000 |
4560.500 |
4579.250 |
Fe4668 |
AA |
ew |
4634.000 |
4720.250 |
4611.500 |
4630.25000 |
4742.750 |
4756.500 |
Fe5015 |
AA |
ew |
4977.750 |
5054.000 |
4946.500 |
4977.75000 |
5054.000 |
5065.250 |
Fe5270 |
AA |
ew |
5245.650 |
5285.650 |
5233.150 |
5248.15000 |
5285.650 |
5318.150 |
Fe5335 |
AA |
ew |
5312.125 |
5352.125 |
5304.625 |
5315.87500 |
5353.375 |
5363.375 |
Fe5406 |
AA |
ew |
5387.500 |
5415.000 |
5376.250 |
5387.50000 |
5415.000 |
5425.000 |
Fe5709 |
AA |
ew |
5696.625 |
5720.375 |
5672.875 |
5696.62500 |
5722.875 |
5736.625 |
Fe5782 |
AA |
ew |
5776.625 |
5796.625 |
5765.375 |
5775.37500 |
5797.875 |
5811.625 |
G4300 |
AA |
ew |
4281.375 |
4316.375 |
4266.375 |
4282.62500 |
4318.875 |
4335.125 |
H_beta |
AA |
ew |
4847.875 |
4876.625 |
4827.875 |
4847.87500 |
4876.625 |
4891.625 |
Hbeta0 |
AA |
ew |
4839.275 |
4877.097 |
4821.175 |
4838.40400 |
4897.445 |
4915.845 |
HbetaEW |
AA |
ew |
4847.875 |
4876.625 |
4799.000 |
4839.00000 |
4886.000 |
4926.000 |
HdeltaEW |
AA |
ew |
4083.500 |
4122.250 |
4017.000 |
4057.00000 |
4153.000 |
4193.000 |
Hdelta_A |
AA |
ew |
4083.500 |
4122.250 |
4041.600 |
4079.75000 |
4128.500 |
4161.000 |
Hdelta_F |
AA |
ew |
4091.000 |
4112.250 |
4057.250 |
4088.50000 |
4114.750 |
4137.250 |
HgammaEW |
AA |
ew |
4319.750 |
4363.500 |
4242.000 |
4282.00000 |
4404.000 |
4444.000 |
Hgamma_A |
AA |
ew |
4319.750 |
4363.500 |
4283.500 |
4319.75000 |
4367.250 |
4419.750 |
Hgamma_F |
AA |
ew |
4331.250 |
4352.250 |
4283.500 |
4319.75000 |
4354.750 |
4384.750 |
Mg4780 |
AA |
ew |
4760.780 |
4798.800 |
4738.910 |
4757.31000 |
4819.780 |
4835.510 |
Mg_1 |
AA |
mag |
5069.125 |
5134.125 |
4895.125 |
4957.62500 |
5301.125 |
5366.125 |
Mg_2 |
AA |
mag |
5154.125 |
5196.625 |
4895.125 |
4957.62500 |
5301.125 |
5366.125 |
Mg_b |
AA |
ew |
5160.125 |
5192.625 |
5142.625 |
5161.37500 |
5191.375 |
5206.375 |
NaI |
AA |
ew |
8163.500 |
8229.125 |
8140.000 |
8163.50000 |
8230.250 |
8250.000 |
NaI_F13 |
AA |
ew |
8180.000 |
8200.000 |
8137.000 |
8147.00000 |
8233.000 |
8244.000 |
NaI_LB13 |
AA |
ew |
8180.000 |
8200.000 |
8143.000 |
8153.00000 |
8233.000 |
8244.000 |
NaI_V12 |
AA |
ew |
8180.000 |
8200.000 |
8164.000 |
8173.00000 |
8233.000 |
8244.000 |
Na_D |
AA |
ew |
5876.875 |
5909.375 |
5860.625 |
5875.62500 |
5922.125 |
5948.125 |
OIIEW |
AA |
ew |
3716.300 |
3738.300 |
3696.300 |
3716.30000 |
3738.300 |
3758.300 |
TiO2SDSS_LB13 |
AA |
mag |
6189.625 |
6272.125 |
6066.625 |
6141.62500 |
6442.000 |
6455.000 |
TiO3 |
AA |
ew |
6600.000 |
6723.000 |
6520.000 |
6545.00000 |
7035.000 |
7050.000 |
TiOCaH |
AA |
ew |
6600.000 |
6817.000 |
6520.000 |
6545.00000 |
7035.000 |
7050.000 |
TiO_1 |
AA |
mag |
5936.625 |
5994.125 |
5816.625 |
5849.12500 |
6038.625 |
6103.625 |
TiO_2 |
AA |
mag |
6189.625 |
6272.125 |
6066.625 |
6141.62500 |
6372.625 |
6415.125 |
TiO_3 |
AA |
mag |
7123.750 |
7162.500 |
7017.000 |
7064.00000 |
7234.000 |
7269.000 |
TiO_4 |
AA |
mag |
7643.250 |
7717.250 |
7527.000 |
7577.75000 |
7735.500 |
7782.750 |
aTiO |
AA |
mag |
5445.000 |
5600.000 |
5420.000 |
5442.00000 |
5630.000 |
5655.000 |
bTiO |
AA |
ew |
4758.500 |
4800.000 |
4742.750 |
4756.50000 |
4827.875 |
4847.875 |
