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

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))
Current internal library
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