What is the Breakdown of the Milky Way's Mass?

[JoeOfTexas]

I have never seen a breakdown of the mass of the Milky Way, so I attempted to do it myself.

My horrible estimates left me with 5x10⁴⁰ mass of unknown origin, which is about 3% of the overall galaxy's mass. It appears the 3% could be explained if the estimates were a bit more accurate.

I'm just an amateur, so please let me know which variables cannot work and why. Thanks!--------------------------------------------------------------Here is my breakdown:

Variables

Solar Mass = 2 x 10³⁰ kg
Averaged to 2 from 1.989

Solar Lifetime = 10⁹ years = (3 x 10¹⁷) seconds
Used for every star

Solar Mass to Energy emitted = (4 x 10⁹) kg/sec
Source: http://www.Newton.dep.anl.gov/askasci/ast99/ast99441.htm

Milky Way Diameter = 100,000 light years

Milky Way Thickness = 1,000 light years

Milky Way Age = 13.2 x 10¹¹ years = (4.17 x 10¹⁹) seconds

Milky Way Mass = 8.5 x 10¹¹ solar masses = (8.5 x 10¹¹) (2 x 10³⁰) = (17 x 10⁴¹) kg

Milky Way Star Count = 200 to 400 billion stars = (300 billion midrange) = (3 x 10¹¹) stars
300 billion seems safe to use

Milky Way Planet Count = 100 billion planets
from Wiki http://en.wikipedia.org/wiki/Milky_Way#Stars_and_planets

Electromagnetic Radiation Mass

ER mass of all stars emitted per second = (4 x 10⁹) (3 x 10¹¹) = (4 x 10⁹) (300 x 10⁹) = (12 x 10²⁰) kg/sec
Using our sun as an average for all stars

Total Energy Mass Emitted over galaxy lifetime = (4.17 x 10¹⁹) (120 x 10¹⁹) = (5 x 10⁴⁰) kg

Energy Retained over lifetime of galaxy = 50% (random guess)
Energy is retained by sticking onto matter or just traveling through the galaxy, this number could be broken down properly, but still has a great significance even at 1%

ER Mass = (5 x 10⁴⁰) (0.5) = (2.5 x 10⁴⁰) kg

Milky Way Mass Breakdown

Stars Mass = (2 x 10³⁰) (3 x 10¹¹) = (6 x 10⁴¹) kg

Planets Mass = (10¹³) (6 x 10²⁴) = (6 x 10³⁷) kg

Molecular Cloud Mass = (60% of Milky Way mass) = (8.5 x 10¹¹) (0.6) = (10.2 x 10⁴¹)
Source: http://www.paulruffle.com/molecularclouds.htm

Milky Way Mass – (Stars Mass + Planets mass + Molecular Cloud Mass + ER Mass)

=> (6 x 10⁴¹) + (.0006 x 10⁴¹) + (10.2 x 10⁴¹) + (.25 x 10⁴¹) = (16.5 x 10⁴¹)

=> (17 x 10⁴¹) – (16.2 x 10⁴¹) = (0.5 x 10⁴¹) kg

Remaining Mass = (5 x 10⁴⁰) kg or 3% of total milky way mass

 

[Matterwave]

1. A bunch of those numbers have huge error bars on them, often with a variance of 50%-100% or more. How do you expect to get reasonable numbers from such poorly known estimates?

2. Your source on molecular clouds said 60% of the mass of the galaxy is not in stars, it did not say that 60% of the mass of the galaxy was in molecular clouds. You're going to have to come up with a better number for that.

Everything else is an order of magnitude smaller, so they don't matter much in comparison to the errors you have already incorporated in your calculations.

 

[JoeOfTexas]

1. A bunch of those numbers have huge error bars on them, often with a variance of 50%-100% or more. How do you expect to get reasonable numbers from such poorly known estimates?

I'm assuming you are talking about using Solar Mass across the board for each star, correct? In my reading, I noticed that stars and black holes come in many different sizes, with stars smaller than our sun being most popular; however, my thinking was that black holes and stars more massive than our sun would more than compensate in mass for the smaller stars, so I used our sun as an "average".

2. Your source on molecular clouds said 60% of the mass of the galaxy is not in stars, it did not say that 60% of the mass of the galaxy was in molecular clouds. You're going to have to come up with a better number for that.

I misinterpreted that part, thanks. The molecular cloud and ER mass are the two variables most unknown at the moment.

How exactly did we come to the conclusion of Dark Matter with so much inconclusive data?

 

[Matterwave]

I'm assuming you are talking about using Solar Mass across the board for each star, correct? In my reading, I noticed that stars and black holes come in many different sizes, with stars smaller than our sun being most popular; however, my thinking was that black holes and stars more massive than our sun would more than compensate in mass for the smaller stars, so I used our sun as an "average".

Many other numbers are quite uncertain. The mass of the milky way itself is anywhere between 850 billion solar masses to 1.5 trillion solar masses, for example. Also, as you mentioned in your post there are anywhere between 100 to 400 billion stars. Using 300 billion as "the middle of the range of guesses that we currently have" does not inspire very much confidence!

I misinterpreted that part, thanks. The molecular cloud and ER mass are the two variables most unknown at the moment.

How exactly did we come to the conclusion of Dark Matter with so much inconclusive data?

The Dark Matter conclusion was arrived at because although the luminous matter of the galaxy declines as we get to the outskirts of the galaxy, the rotation curve of galaxies stay constant. The constant rotation curves imply that there is much more unseen gravitational mass than we can account for by the luminous matter. Originally it was though that dark matter might be "MACHOs" or massive compact halo objects (e.g. dim white dwarves, or black holes), but a survey did not suggest enough of them existed to account for the mass deficit. I'm sure molecular clouds were considered at some point, but I think the percentage they actually account for is maybe a few percent...but a quick google did not turn up anything very promising for me. Perhaps someone else knows the % for molecular clouds.