The Milky Way Galaxy With Only Half The Mass Originally Thought?

The recent research report released in Long Beach, CA at the 221st meeting of the American Astronomical Society (by a team at the University of California (Santa Cruz))  to the effect the Milky Way Galaxy has been awarded almost twice as much mass as it ought to have, has shocked may galactic astronomers. But in a way it really shouldn't. We have to bear in mind our mass determinations are merely estimates at best and based on inherently simplistic assumptions.

For example, we typically make use of Kepler's 3rd or harmonic law, viz.

M =   (a) ³ / (P) ²

to make a mass estimate for the galaxy, where a = the semi-major axis (mean distance of Sun estimated from the galactic center), and P is the period for revolution about the galactic mass center. We estimate that a =  2 x 10⁹ AU   and P = 2 x 10 ⁸ yrs  , so that we can write for M:

M = (2 x 10⁹ AU) ³ / (2 x 10 ⁸ yrs) ²

Or: 

M = (8 x 10 ²⁷) / (4 x 10 ¹⁶ ) = 2 x 10¹¹ (m) the mass of the Sun.

But examine it carefully! It essentially assumes the mean mass for all stars in the Milky Way is equal to one solar mass (2 x 10 ³⁰ kg ) which, if off, would mean the galactic mass is overestimated.

Anyway, what the UCSC researchers found is that  stars in the far outer reaches of the Milky Way, between 260,000 and 490,000 light-years from the galactic center, are moving surprisingly slowly   In some ways, this isn't suprising and merely discloses we jumped the gun in our assumptions. The precise parameters which defines this is the epicycle frequency ( k_o ) which is in turn related a given star's orbital angular speed ( W  ).

For example, in the Sun's case we first convert it's period (P - used in the Mass computation) to seconds, so: T(s) = (2 x 10 ⁸  yrs.) (365.25 days/yr.) (86,400 s/ day) = 6.3 x 10 ¹⁵ s


Then:  W  » 10 ^-15 rad s^-1

But clearly if the UCSC data show slower stars than this parameter will be off.  According to Alis Deason, one of the primary researchers:

"Because these velocities are so low, the mass of our galaxy may be much lower than we once thought,"

She added: "If we infer the properties of the stars that we think are reasonable, then we find the mass of the Milky Way could be half as massive as we currently believe,"

To be sure, Deason and her colleagues did far more than use seat of the pants estimates for angular velocity such as depicted above. Her team looked far out into the Milky Way's halo,  which extends far beyond the 100,000-light-year-wide disk. They measured the radial velocities of a sample of distant halo stars using two different instruments: the European Southern Observatory's 8.2-meter telescope in Chile and the 4.2-meter William Herschel Observatory in Spain. (Radial velocities are the arcsec differences in position measured along the line of sight.)

They found that the dispersion, or spread, of halo-star velocities was about half that seen for stars closer to the galactic center.


Using this information, the team calculated that the total mass of the Milky Way out to such extreme distances may be between 500 billion and 1 trillion times that of our sun — substantially lower than the current leading estimate. Note that if the upper limit here is accepted or  10 ¹²  solar  it means a total galactic mass of (2 x 10 ³⁰  kg ) ( 10 ¹²) =  2 x 10 ⁴² kg  compared to 4 x 10 ⁴¹ kg  obtained from the Kepler's law value. Thus, the problem doesn't enter until the lower value of mass is used.

Even so, the research results must be confirmed, and that may also necessitate assessing the amount of dark matter in our galaxy, including the degree to which black holes (especially the putative central black hole) contribute to the Milky Way's mass.  

Stay tuned!

A Mammoth Black Hole In a Small Galaxy?

The Biggest story in astronomy the past few days has been the discovery of an enormous black hole - the second most massive ever detected - in a relatively tiny galaxy. The galaxy: NGC 1277, is just a quarter the size of our own Milky Way, but hosts a black hole 4,000 times larger than the one at the Milky Way's centre.


A report in Nature shows it has a mass some 17 billion times that of our Sun. This surprise finding is hard to reconcile with existing models of black hole growth, which hold that they evolve in tandem with host galaxies. In any case, the black hole concept has always been tricky and even a few high profile astronomers like Lawrence Krausse have expressed skepticism.

But this skepticism is misplaced. The fact is black holes emerged out of Kurt Schwarzschild's specific solution of Einstein's general relativity equations, viz. for the interval ds:

ds² = -(1- 2M/r)dt² + dr² /1 - 2M/r + r²  (d Θ² +sin² Θ d φ²)


Now granted, no one has ever literally seen a black hole but we know how to recognize the physical evidence for its existence: very powerful and periodic bursts of x-rays, registered on sensitive satellite detectors. Mathematically, the very brief periods of less than a millisecond betray an extremely compact volume. The x-rays indicate accretion to a large mass. Together, these can be matched to predictions given in the Einstein general relativity equations and Voila! the black hole emerges as an object consistent with the observations.

In general black hole identification is predicated upon observing its effects as a member of a binary (double) star system. Thereby, the black hole presence is inferred from x-rays given off when the companion star’s gaseous layers are sucked into it. As those accreting gaseous layers are pulled through the hole's event horizon, they are condensed and the impacting plasma leads to intense heating and x-rays. It is the rapid periodicity of the x-ray signal that betrays the presence of the black hole since no truly massive object on the order of 3-4 solar masses (for typical stellar black holes) could possibly make single revolutions about a primary normal star in seconds timeframes!

Now, back to the recent find.  In galactic black holes of the type just found, we are looking at prolonged and progressive accretion of surrounding matter which 'feeds' the growth of the black hole. To detect these beasts,  the Hobby-Eberly Telescope was deployed to look specifically for massive holes in galaxies. It then undertook a survey that brought in a haul of nearly 900 host galaxies.

However, the counterintuitive surprise  has been that some of the most massive black holes have been identified in the smallest galaxies - like NGC 1277, 220 million light years distant.  What manner of technique was used? In a simplified sketch, the astronomers made a computer model of the target galaxy which incorporated all possible stellar orbits within it, allowed by the dynamics.   This approach would have reckoned in a certain parameter, c =  k_o / W .   Here c is the number of epicycle oscillations per orbit about the galactic center, which is given by the ratio of the star's epicycle frequency ( k_o ) to its orbital angular speed ( W  ).    For example, in the case of the Sun, we have  k_o = 1.35. From this we can find the other parameters.   We know that the Sun’s period around the galactic center is: 2 x 10 ⁸ yrs. We need to obtain this in seconds:

T(s) = (2 x 10⁸ yrs.) (365.25 days/yr.) (86,400 s/ day)


T(s) = 6.3 x 10 ¹⁵ s


Then: W = (2 π rad)/ T(s) = 2 π rad/ 6.3 x 10¹⁵ s


W  »  10 ^-15 rad s^-1

But: k_o = 1.35  W    = 1.35 x 10 ^-15 rad s^-1

Moving on, after the computer assembles all such model orbits from similar computations for other stars, the results are assembled so the final product galaxy exhibits the same stellar velocities as measured (again, deducible from the values of  W ).  The research team thereby found that the hole in NGC 1277 held 14% of its mass.

Astronomers whose specialty is black holes look forward to more of these amazing finds, and also whether NGC 1277 indicates the exception rather than the rule - as the current assay appears to suggest.