How to estimate the inclination of a galaxy between edge on and face on?

Question

I have the images of a galaxy and the field of view and I would like to determinte the inclination of a galaxy between edge-on and face-on. Would that information be enough to do the calculation? Or what other details would be needed?

Answer 1

If you tilt a circular object, then along one axis the length will appear to be shortened, while along a perpendicular axis the apparent size will be unchanged. So you can use that to determine the tilt angle (inclination).

If we define $0^\circ$ to be face-on, then when tilted at an angle $i$ away from face-on, the shorter axis will appear to be decreased in length by a factor of $\cos i$. Thus, assuming that the galaxy is circular in cross-section, you can determine its inclination from $\cos i = \frac{\rm short\ axis}{\rm long\ axis}$.

This should work for spiral galaxies, but won't work for elliptical galaxies, which aren't necessarily circular in projection when viewed face-on.

Answer 2

You can visit IncliNET which is a Web application that uses the power of Convolutional Neural Networks to evaluate the inclination of spiral galaxies. This online GUI allows users to submit a galaxy image through various methods. https://edd.ifa.hawaii.edu/inclinet/

1. Galaxy PGC ID

Entering the name of a galaxy by querying its PGC number (the ID of galaxy in the Principal Galaxy Catalog) - The PGC catalog is deployed with our model, and contains a table of galaxy coordinates and their sizes. Images are then queried from the SDSS quick-look image server.

2. Galaxy Name

Searching a galaxy by its common name. - The entered name is queried through the NASA/IPAC Extragalactic Database. Then, a python routine based on the package Beautiful Soup extracts the corresponding PGC number. Once the PGC ID is available, the galaxy image is imported from the SDSS quick-look.

3. Galaxy Coordinates

A specific location in the sky can be queried by entering the sky coordinates and the field size. In the first release we only provide access to the SDSS images, if they are available. The SDSS coverage is mainly limited to the Northern sky.

4. Galaxy Image

Uploading a galaxy image from the local computer of the user. User has the option of uploading a galaxy image for evaluation(s) by our model(s).

Please refer to the gitHub repository and the documentation of the GUI for further details on the entire process.

Each galaxy has its own unique morphology, luminosity, and surface brightness profiles. In addition, galaxy images are covered by foreground stars of the Milky Way galaxy. Therefore, it is challenging to design an algorithm that automatically determines the 3D inclination of spiral galaxies. The inclinations of spiral galaxies can be coarsely derived from the ellipticity of apertures used for photometry, assuming that the image of a spiral galaxy is the projection of a disk with the shape of an oblate spheroid. For ~1/3 of spirals, the approximation of axial ratios provides inclination estimates good to better than 5 degrees, with degradation to ~5 degrees for another 1/3. However in ~1/3 of cases, ellipticity-derived inclinations are problematic for a variety of reasons.

• Prominent bulges can dominate the axial ratio measurement.
• Some galaxies may not be axially symmetric due to tidal effects.
• High surface brightness bars within much lower surface brightness disks can lead to large errors. Simply the orientation of strong spiral features with respect to the tilt axis can be confusing.

The statistical derivation of inclinations for large samples has been unsatisfactory until recently. There is a report on how 20,000 spiral galaxies have been sorted manually in a collaborative project with the help of amateur astronomers using an online tool called Galaxy Inclination Zoo. Please refer to the section 2.3 of the following paper for more details.

Cosmicflows-4: The Catalog of ~10000 Tully-Fisher Distances (Journal ref: Kourkchi et al., 2020, ApJ, 902, 145, arXiv:2009.00733)