Question1 : I would like to know if possible the distance separating the elliptical galaxy M60 (NGC 4649) and some spiral galaxies belonging to its group such as: NGC 4019, NGC 4037, NGC 4049, NGC 4064, NGC 4116 and NGC 4123 ?
Question2 : Same question for galaxy M86 (NGC 4406) and members of its group: NGC 4435, NGC 4438, NGC 4458, NGC 4461, NGC 4473 and NGC 4477.
Question3 : Same question for galaxy M87 (NGC 4486) and members of its group: NGC 4206, NGC 4262, NGC 4298, NGC 4302, NGC 4307 and NGC 4313.
I thank you in advance for any information that can help me.
Hi Melati Rabia ,
The distances between galaxies that you seek may be obtained as follows:
Step 1: Look up each of the objects in your list by name from an online extragalactic database, such as this one: https://ned.ipac.caltech.edu/byname.
Step 2: Note the RA (right ascension) and DEC (declination) of each object, and convert the values to radians.
Step 3: Note the ‘Hubble Distance’ of each object. Also called the cosmological ‘proper distance’, this is what enters Hubble’s law (v = H_0. D). It is basically the present distance to the object from Earth, calculated by ‘freezing’ the expansion of the universe.
Step 4: Since the Hubble distance vector satisfies Hubble’s law, the following must hold:
D_12 = sqrt( (D_1)^2 + (D_2)^2 – 2.D_1.D_2*cos(theta) )
where D_1 and D_2 are the proper distances to objects #1 and #2 respectively ; theta is the angle between the unit vectors pointing to these objects ; and D_12 is the proper distance between these two objects that you wish to find.
You can find ‘theta’ like this:
r_1 = [sin(DEC_1), cos(DEC_1)cos(RA_1), cos(DEC_1)sin(RA_1)]
r_2 = [sin(DEC_2), cos(DEC_2)cos(RA_2), cos(DEC_2)sin(RA_2)]
theta = arccos( r_1.r_2 / (|r_1| |r_2|) )
where r_1.r_2 is a dot product between two unit vectors, r_1 and r_2, pointing towards the objects #1 and #2 respectively, constructed in 3D spherical coordinates.
Repeat these steps for every pair of objects that you wish to find the proper distance between. Hope this answers your question!
Hi-
The three galaxies (M60, M86, M87) of your imputed groups are the three brightest galaxies in the Virgo cluster, which contains about 1000 galaxies. It also has several subgroups of galaxies, and has been studied for decades. Using surface brightness fluctuations of E and S0 galaxies, which is a better distance indicator than Hubble distances, a series of papers summarized by Mei et al. (arXiv:astro-ph/0702510 or Article The ACS Virgo Cluster Survey. XIII. SBF distance catalog and...
) discuss these subgroups. (Unfortunately this technique has not been successfully applied to spiral or irregular galaxies, mainly due to internal dust.) Since these groups are members of the much larger dynamical system of the Virgo cluster, you cannot treat them as independent of the larger system, which the above article discusses.
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