# Calculating the mass of a galaxy bulge

• I
• Jules Winnfield
In summary, the conversation discusses the need for a method to calculate the bulge mass of galaxies such as the Milky Way and Andromeda. The de Vaucouleurs profile is commonly used for this calculation, but the speaker is unable to get an exact solution using Mathematica. They provide the general form of the integral and express their frustration with attempting to solve it in Mathematica. They then ask if anyone has an industry standard method for this calculation and mention using Young's tables as a current approach. They also provide links to two articles that address additional approaches for calculating rotation and mass in galaxies.
Jules Winnfield
I'm looking for a usable method to calculate the bulge mass of, say, the Milky Way or Andromeda. Most of the literature I've read agree that a de Vaucouleurs profile is the way to go. However, I'm unable to get an exact solution using Mathematica. The general form of the integral is:$$\Sigma_b(r)=\Sigma_{be}exp\left(-\kappa(\frac{r}{a_b})^{\frac{1}{4}}-1 \right)$$$$M_b=2\pi\int_{0}^{\infty}r\Sigma_b(r) dr=22.665 a_b^2 \Sigma_{be}$$ $$\rho_b(r)=\int_r^\infty\frac{d\Sigma_b(x)}{dx}\frac{1}{\sqrt{x^2-r^2}}dx$$$$M_b(R)=4\pi\int_0^R\rho_b(r)r^2 dr$$Attempting these integrals in Mathematica leaves me with meaningless results. Has anyone got an 'industry standard' method for doing this calculation. I've been using Young's tables until now and I was hoping there was a better method than just a table lookup.

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## 1. How is the mass of a galaxy bulge calculated?

The mass of a galaxy bulge is typically calculated by studying the rotational velocity of stars and gas within the bulge, as well as the distribution of matter within the bulge. This information is used to apply the laws of gravity and determine the total mass of the bulge.

## 2. What units are used to express the mass of a galaxy bulge?

The mass of a galaxy bulge is typically expressed in solar masses, which is a unit of mass equal to the mass of our Sun. This unit is commonly used in astronomy to measure the mass of celestial objects.

## 3. Can the mass of a galaxy bulge be measured directly?

No, the mass of a galaxy bulge cannot be measured directly. Instead, it is inferred from other measurements such as the rotational velocity and distribution of matter. This is due to the fact that the bulge is made up of a combination of stars, gas, and dark matter, which cannot be directly observed.

## 4. How does the mass of a galaxy bulge affect the overall mass of a galaxy?

The mass of a galaxy bulge is a significant factor in determining the overall mass of a galaxy. In most spiral galaxies, the bulge makes up a large portion of the total mass, and can even contribute up to half of the total mass in some cases. Therefore, accurately calculating the mass of the bulge is crucial in understanding the overall mass and dynamics of a galaxy.

## 5. Can the mass of a galaxy bulge change over time?

Yes, the mass of a galaxy bulge can change over time due to interactions with other galaxies or the accretion of matter from the surrounding environment. However, these changes happen slowly over millions of years and are not significant enough to drastically alter the overall mass of the bulge in a short period of time.

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