L. P. Singer, H.-Y. Chen, D. E. Holz, W. M. Farr, L. R. Price, V. Raymond, S. B. Cenko, N. Gehrels, J. Cannizzo, M. M. Kasliwal, S. Nissanke, M. Coughlin, B. Farr, Alex L. Urban, S. Vitale, J. Veitch, P. Graff, C. P. L. Berry, S. Mohapatra, and I. Mandel
Read at arXiv.orgThis web page provides additional online material related to the paper Going the Distance: Mapping Host Galaxies of LIGO Sources in Three Dimensions Using Local Cosmography and Targeted Follow-up.
The paper explores three-dimensional reconstruction positions of gravitational-wave transients that are detectable by LIGO and Virgo. It builds upon an earlier pair of papers on sky localization with gravitational-wave detectors, but adds directionally resolved LIGO distance estimates in order to facilitate deep searches of potential host galaxies for electromagnetic counterparts of LIGO sources.
The table below shows thumbnail images of 500 simulated Advanced LIGO volume reconstructions. Each image is a volume rendering of the probability distribution for a given event, projected in the plane of the distribution's two most significant principal axes.
Touch the O1 or O2 buttons in the toolbar to switch between Advanced LIGO observing runs. Touch any of the Sort by buttons to reorder the thumbnails by detector network, enclosed volume, enclosed area, network signal-to-noise ratio, or signal-to-noise ratio in LIGO Hanford (H) or LIGO Livingston (L).
Touch any thumbnail to show more detail about the simulated event or to download the FITS/HEALPix sky localization file.
The 3D localization files are easy to use in Python using the Healpy package. See sample code.
And now for the data...
First make sure that you have Python set up on your system. If you do not yet have a favorite Python environment, we suggest Anaconda.
We will need Healpy for reading the 3D localization file. For this example, we will also use Astropy/Astroquery for retrieving archival data, Matplotlib for plotting, and Scipy for statistics functions. Open a termianl and run the following commands:
$ conda install astropy scipy matplotlib $ pip install astroquery healpy
Fire up a Python interpreter and import packages:
$ python >>> import healpy as hp >>> import numpy as np >>> from matplotlib import pyplot as plt >>> from scipy.stats import norm >>> from astroquery.ned import Ned >>> from astropy.utils.data import download_file >>> from astropy.cosmology import default_cosmology >>> cosmo = default_cosmology.get()
Next, download an example 3D sky map:
>>> url = 'http://asd.gsfc.nasa.gov/Leo.Singer/going-the-distance/18951_bayestar.fits.gz' >>> filename = download_file(url, cache=True)
Read the four HEALPix layers with Healpy:
>>> prob, distmu, distsigma, distnorm = hp.read_map(filename, field=[0, 1, 2, 3])
Look up PGC 23997 in NED:
>>> pgc = Ned.query_object('PGC 23997')
Convert its RA and Dec to physicists' spherical polar coordinates (𝜃, 𝜙) with 𝜃=0 at the North celestial pole, and its redshift to a luminosity distance in Mpc:
>>> theta = 0.5 * np.pi - np.deg2rad(pgc[0]['DEC(deg)']) >>> phi = np.deg2rad(pgc[0]['RA(deg)']) >>> dist = cosmo.luminosity_distance(pgc[0]['Redshift']).value
Look up the HEALPix pixel that contains the galaxy:
>>> npix = len(prob) >>> nside = hp.npix2nside(npix) >>> ipix = hp.ang2pix(nside, theta, phi)
Finally, plot the conditional distance distribution in the of the galaxy:
>>> r = np.linspace(0, 120)
>>> p = norm(distmu[ipix], distsigma[ipix]).pdf(r) * distnorm[ipix] * r**2
>>> plt.plot(r, p)
>>> plt.axvline(dist)
>>> plt.xlabel('Distance (Mpc)')
>>> plt.ylabel('Probability / Mpc')
>>> plt.savefig('pgc23997.png')
