We're going to construct the spatially-resolved mass-metallicity relation (MZR) for a MaNGA galaxy, where mass refers to stellar mass and metallicity refers to gas-phase oxygen abundance.
In [1]:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
In [2]:
import os
from os.path import join
path_notebooks = os.path.abspath('.')
path_data = join(path_notebooks, 'data')
In [3]:
We are going to use the N2 metallicity calibration (their Equation 1) from Pettini & Pagel (2004):
12 + log(O/H) = 8.90 + 0.57 $\times$ log( $\frac{F([NII])}{F(H\alpha)}$ ).
One of the benefits of this calibration is that the required lines are very close in wavelength, so the reddening correction is negligible.
Get [NII] 6585 and Halpha flux maps from the Marvin Maps object. Note: MaNGA (and Marvin) use the wavelengths of lines in vaccuum, whereas they are usually reported in air, hence the slight offsets.
In [4]:
Calculate the necessary line ratio.
Marvin can do map arithmetic, which propagates the inverse variances and masks, so you can just do +, -, *, /, and ** operations as normal. (Note: taking the log of a Marvin Map will work for the values but the inverse variance propagation does not correctly propagate the inverse variance yet.)
In [5]:
Finally, calculate the metallicity.
In [6]:
Metallicity indicators only work for star-forming spaxels, so we need a way to select only these spaxels.
The classic diagnostic diagram for classify the emission from galaxies (or galactic sub-regions) as star-forming or non-star-forming (i.e., from active galactic nuclei (AGN) or evolved stars) was originally proposed in Baldwin, Phillips, & Terlevich (1981) and is known as the BPT diagram.
The BPT diagram uses ratios of emission lines to separate thermal and non-thermal emission.
The classic BPT diagram uses [OIII]5007 / Hbeta vs. [NII]6583 / Halpha, but there are several versions of the BPT diagram that use different lines ratios.
Let's use Marvin's maps.get_bpt() method to make BPT diagrams for this galaxy.
red line: maximal starbust (Kewley et al 2001) -- everything to the right is non-star-forming.
dashed black line: conservative star-forming cut (Kauffmann et al. 2003) -- everything to the left is star-forming.
Line ratios that fall in between these two lines are designated "Composite" with contributions from both star-forming and non-star-forming emission.
blue line: separates non-star-forming spaxels into Seyferts and LINERs.
Seyferts are a type of AGNs.
LINERs (Low Ionization Nuclear Emission Regions) are not always nuclear (LIER is a better acronym) and not always AGN (oftern hot evolved stars).
Sometimes these diagnostic diagrams disagree with each other, hence the "Ambiguous" designation.
Try using maps.get_bpt? to read the documentation on how to use this function.
In [7]:
The BPT masks are dictionaries of dictionaries of a boolean (True/False) arrays. We are interested in the spaxels that are classified as star-forming in all three BPT diagrams are designated as True, which is designated with the global key. Print this mask.
In [8]:
Out[8]:
In [9]:
Out[9]:
Select non-star-forming spaxels (from the BPT mask) and set their mask value to the DAP's DONOTUSE value with the n2.pixmask.labels_to_value() method. Note that we are selecting spaxels that we want from the BPT mask (i.e., True is a spaxel to keep), whereas we are using the pixmask to select spaxels that we want to exclude (i.e., True is a spaxel to ignore).
In [10]:
Select spaxels classified by the DAP as bad data according to the masks for spaxels with no IFU coverage, with unreliable measurements, or otherwise unfit for science. Use the n2.pixmask.get_mask method.
In [11]:
Select spaxels with signal-to-noise ratios (SNRs) > 3 on both [NII] 6585 and Halpha.
ha.ivar = inverse variance = $\frac{1}{\sigma^2}$, where $\sigma$ is the error.
In [12]:
Do a bitwise (binary) OR to create a master mask of spaxels to ignore.
In [13]:
In [14]:
Use pandas to read in the csv file with stellar masses.
In [15]:
import pandas as pd
mstar = pd.read_csv(join(path_data, 'manga-{}_mstar.csv'.format(maps.plateifu)))
Plot stellar mass map using ax.imshow(). MaNGA maps are oriented such that you want to specify origin='lower'. Also include a labelled colorbar.
In [16]:
In [17]:
Get the redshift of the galaxy from the maps.nsa attribute.
In [18]:
We'll use the small angle approximation to estimate the physical scale:
$\theta = \mathrm{tan}^{-1}(\frac{d}{D}) \approx \frac{206,265 \, \mathrm{arcsec}}{1 \, \mathrm{radian}} \frac{d}{D}$,
where
$\theta$ is the angular size of the object (in our case spaxel) in arcsec,
$d$ is the diameter of the object (spaxel), and
$D$ is the angular diameter distance.
The distance (via the Hubble Law --- which is fairly accurate for low redshift objects) is
$D \approx \frac{cz}{H_0}$,
where
$c$ is the speed of light in km/s,
$z$ is the redshift, and
$H_0$ is the Hubble constant in km/s/Mpc.
Calculate $D$.
In [19]:
Rearrange the small angle formula to solve for the scale ($\frac{d}{\theta}$) in pc / arcsec.
In [20]:
Now convert the spaxel size from arcsec to parsecs and calculate the area of a spaxel.
In [21]:
Finally, we simply divide the stellar mass by the area to get the stellar mass surface density $\Sigma_\star$ in units of $\frac{M_\odot}{pc^2}$.
In [22]:
Let's plot metallicity as a function of $\Sigma_\star$! Remember to apply the mask. Also set the axis range to be [0, 4, 8, 8.8].
In [23]:
Out[23]:
We have constructed the spatially-resolved MZR for one galaxy, but we are interested in understanding the evolution of galaxies in general, so we want to repeat this exercise for many galaxies. In Barrera-Ballesteros et al. (2016), Jorge Barrera-Ballesteros (who gave a talk at Pitt in November 2017) did just this, and here is the analogous figure for 653 disk galaxies.
The best fit line from Barrera-Ballesteros et al. (2016) is given in the next cell.
In [24]:
# fitting formula
aa = 8.55
bb = 0.014
cc = 3.14
xx = np.linspace(1, 3, 1000)
yy = aa + bb * (xx - cc) * np.exp(-(xx - cc))
Remake the spatially-resolved MZR plot for our galaxy showing the he best fit line from Barrera-Ballesteros et al. (2016).
In [25]:
Out[25]:
The spaxels in our galaxy are typically above the best fit relation. Part of the offset may be due to systematic differences in the metallicity calibrator used, but the overal trend of flat metallicity as stellar mass surface densities decreases seems to be in tension with their best fit. It would be worth investigating this effect for more galaxies to understand if individual galaxies typically obey the best fit relation or whether they typically exhibit a flat trend in this space.
Ultimately, Barrera-Ballesteros et al. (2016) concluded that the spatially-resolved MZR is a scaled version of the global MZR (e.g., see Tremonti et al. 2004).
In [ ]: