<p><a href="https://astronomy.stackexchange.com/a/46772/42349">Rob's answer</a> already gives a rough estimate. I will try to make it more precise by relaxing some assumptions.</p>
<p><strong>How many star have been born in our universe?</strong></p>
<p>The cosmic star formation history <span class="math-container">$\psi(z)$</span> is a function that gives, for every redshift, the density of star formation rate. It is usually expressed in units of <span class="math-container">$M_\odot$</span> <span class="math-container">$yr^{-1}$</span> <span class="math-container">$cMpc^{-3}$</span>. The total mass of stars formed in a given comoving volume <span class="math-container">$dV$</span> at redshift <span class="math-container">$z$</span> in a time <span class="math-container">$dt$</span> is <span class="math-container">$\psi(z)dVdt$</span>.</p>
<p>You can find the state of the art of the estimation of the cosmic star formation history in figure 9 of <a href="https://arxiv.org/abs/1403.0007" rel="noreferrer">Piero Madau, Mark Dickinson (2014)</a>.</p>
<p><a href="https://i.sstatic.net/guiqU.png" rel="noreferrer"><img src="https://i.sstatic.net/guiqU.png" alt="figure 9 of Madau, Dickinson" /></a></p>
<p>You can see that star formation reached a peak around redshift 2 and now it has dropped very low. This means that the supernova rate that we measure now in the milky way is much lower that the rate we would have measured some billion years ago.</p>
<p>The authors also provide an analytic approximation.</p>
<p><span class="math-container">$$\psi(z) = 0.015 \frac{(1+z)^{2.7}}{1+[(1+z)/2.9]^{5.6}} M_\odot yr^{-1} Mpc^{-3}$$</span></p>
<p>We can calculate the total mass of stars that has ever formed in a given comoving volume as</p>
<p><span class="math-container">$$\int dt \psi(z) = \int dz \frac{dt}{dz} \psi(z)$$</span>
where the relation between <span class="math-container">$t$</span> and <span class="math-container">$z$</span> is given by</p>
<p><span class="math-container">$${dt \over dz} = {1 \over H_0} \frac{1}{(1+z)\sqrt{(1+z)^3 \Omega_m + \Omega_\Lambda}}$$</span></p>
<p>and <span class="math-container">$H_0 = 70 km\ s^{-1} Mpc^{-1} = 7.15 \times 10^{-11} yr^{-1}$</span>, <span class="math-container">$\Omega_m = 0.3$</span>, <span class="math-container">$\Omega_\Lambda = 0.7$</span></p>
<p>This gives</p>
<p><span class="math-container">$$\rho_{tot} = \int_0^8 dz \frac{dt}{dz} \psi(z) \approx 7.86 \times 10^8 M_\odot\ Mpc^{-3}$$</span></p>
<p>Above <span class="math-container">$z=8$</span> very few stars had formed, and we can ignore them.</p>
<p><strong>How many stars die as supernovae?</strong></p>
<p><span class="math-container">$\psi(z)$</span> tells us how many stars were born, so we need to know the fraction of these stars that died with a supernova. We know that small stars, like the Sun don't end their life as a supernova. Only more massive stars, with <span class="math-container">$m&gt;8M_\odot$</span> have a chance to explode, and they do it after a few million years since their birth: almost instantly from a cosmic point of view. For this calculation, we can assume that every star with <span class="math-container">$m&gt;m_{SN}=8M_\odot$</span> instantly goes supernova after its creation.</p>
<p>If we know (from <span class="math-container">$\psi(z)$</span>) that a certain mass <span class="math-container">$M$</span> of gas has converted into stars, how many of these stars will have <span class="math-container">$m&gt;8M_\odot$</span>? The answer to this question is provided by the <em>Initial Mass Function</em> (IMF) <span class="math-container">$\xi(m)$</span>. <span class="math-container">$\xi(m)dm$</span> is proportional to the number of stars that form with mass between <span class="math-container">$m$</span> and <span class="math-container">$m+dm$</span>.</p>
<p>We can choose to use the IMF provided by <a href="https://ui.adsabs.harvard.edu/abs/2001MNRAS.322..231K/abstract" rel="noreferrer">Kroupa (2001)</a>, that is defined as a broken power law</p>
<p><span class="math-container">$$\xi(m) \propto m^{-0.3}\ \text{if}\ 0.01 &lt; m \le 0.08 \\
\xi(m) \propto m^{-1.3}\ \text{if}\ 0.08 &lt; m \le 0.5 \\
\xi(m) \propto m^{-2.3}\ \text{if}\ 0.5 &lt; m$$</span></p>
<p><a href="https://i.sstatic.net/T2Si2.png" rel="noreferrer"><img src="https://i.sstatic.net/T2Si2.png" alt="kroupa imf" /></a></p>
<p>Here I have normalized the IMF such that <span class="math-container">$\int_{m_0}^{m_1} m \xi(m) dm = 1M_\odot$</span>. You can see that small mass stars are far more common than high mass stars. In particular, we can estimate that in a recently formed star population, the fraction of stars with <span class="math-container">$m&gt;m_SN=8M_\odot$</span> will be</p>
<p><span class="math-container">$$f_{SN} = \int_{8M_\odot}^{+\infty} \xi(m) dm \approx 0.01$$</span></p>
<p>Only 1% of the formed stars will become a supernova! Actually the integral shouldn't go up to <span class="math-container">$+\infty$</span>, because above <span class="math-container">$40M_\odot$</span> stars start to directly collapse into a black hole, but those stars are so rare that we can safely ignore their contribution.</p>
<p><strong>Summing things up</strong></p>
<p>The comoving volume between us and <span class="math-container">$z=8$</span> can be quickly found using <a href="http://astro.ucla.edu/%7Ewright/ACC.html" rel="noreferrer">Ned Wright's cosmic calculator</a>: <span class="math-container">$V = 3.59 \times 10^{12} Mpc^3$</span></p>
<p>Now we have everything we need to estimate the number of supernovae that ever took place in the observable universe.</p>
<p><span class="math-container">$$N_{SN} = f_{SN} \times\rho_{tot} \times V = 2.86 \times 10^{19}$$</span></p>
<p>This result is in good agreement with Rob's one.</p>
<p>Edit: This answer neglects type Ia supernovae. A good start may be this paper <a href="https://arxiv.org/pdf/2105.11954.pdf" rel="noreferrer">https://arxiv.org/pdf/2105.11954.pdf</a></p>

CC BY-SA 4.0
2021-09-22T14:58:39.753Z
Lovely answer, but you've neglected the [type Ia supernovae](https://en.wikipedia.org/wiki/Type_Ia_supernova)
PM 2Ring
CC BY-SA 4.0
2021-09-22T15:51:33.107Z
I'm amazed the value is so close. I guess a couple of my assumptions might be cancelling each other out.
Rob
CC BY-SA 4.0
2021-09-22T16:24:25.137Z
@Rob you are right, I'm amazed as well!
Prallax
CC BY-SA 4.0
2021-09-22T16:29:41.640Z
@PM2Ring That's true. Unfortunately I would not know how to account for them. I'll clarify this aspect in the answer
Prallax
CC BY-SA 4.0
2021-09-22T11:37:35.020Z
2021-09-22T16:47:14.293Z
2021-09-22T16:47:14.293Z
Prallax
<p>On average the Milky way has one supernovae per 100 hundred  (10^2) years. As the Galaxy is ~10 Billion (10^9) years old, then that is ~10^7 supernovae in the Milky way's life. Assuming the average galaxy looks like the Milky way and that there are an estimated ~1 Trillion (10^12) galaxies in the Universe, then that suggests there have been ~(10^12 x 10^9) / 10^2 supernovae or about <strong>10^19 supernovae so far.</strong></p>
<p>This ignores many things like whether the average of all galaxies look like the Milky way, whether the star formation rate changes over time, whether the fraction of stars that undergo a supernovae change over time, and probably many more things. Also ignores effects like how many supernovae would have had enough time for the light to reach us.</p>

CC BY-SA 4.0
2021-09-18T20:58:55.603Z
2021-09-18T20:58:55.603Z
Rob
<p>We know there are currently between 10^22 and 10^24 stars in the observable universe, but can we make an estimate of how many stars have died so far? Or, in other words, how many supernovæ have taken place so far?</p>

CC BY-SA 4.0
2021-09-18T09:37:32.063Z
There are other ways for stars to die, notably falling into a black hole.
PM 2Ring
CC BY-SA 4.0
2021-09-18T10:35:40.827Z
or, more commonly, by losing their outer layers in a planetary nebula
James K
CC BY-SA 4.0
2021-09-18T11:19:40.057Z
@JamesK Good point. ;) I suspect that the OP classes white dwarfs as still alive.
PM 2Ring
CC BY-SA 4.0
2021-09-18T12:35:59.560Z
Currently the question does not have enough detail. Can you please be specific on what you mean by "died" or if you just want to ask if we can estimate how many supernovae there have been then please edit the question to ask that.
Rory Alsop
CC BY-SA 4.0
2021-09-18T14:56:11.803Z
It might also be worth clarifying what is meant by "observable universe." Are you interested in the particle horizon, the hubble volume, etc...?
Daddy Kropotkin
<star><supernova><observable-universe>
Can we estimate the number of stars which have died in the observable universe?
user2906
# Can we estimate the number of stars which have died in the observable universe?

(Asked by: username_0 on 2021-09-18)

We know there are currently between 10^22 and 10^24 stars in the observable universe, but can we make an estimate of how many stars have died so far? Or, in other words, how many supernovæ have taken place so far?

**Tags:** star, supernova, observable-universe

> **Comments:**
> **username_1**: There are other ways for stars to die, notably falling into a black hole.  
> **username_2**: or, more commonly, by losing their outer layers in a planetary nebula  
> **username_1**: @JamesK Good point. ;) I suspect that the OP classes white dwarfs as still alive.  
> **username_3**: Currently the question does not have enough detail. Can you please be specific on what you mean by "died" or if you just want to ask if we can estimate how many supernovae there have been then please edit the question to ask that.  
> **username_4**: It might also be worth clarifying what is meant by "observable universe." Are you interested in the particle horizon, the hubble volume, etc...?  

---

## 2 answers

### Answer by username_5 on 2021-09-22. Score: 8

[username_6's answer](https://astronomy.stackexchange.com/a/46772/42349) already gives a rough estimate. I will try to make it more precise by relaxing some assumptions.

**How many star have been born in our universe?**

The cosmic star formation history $\psi(z)$ is a function that gives, for every redshift, the density of star formation rate. It is usually expressed in units of $M\_\odot$ $yr^{-1}$ $cMpc^{-3}$. The total mass of stars formed in a given comoving volume $dV$ at redshift $z$ in a time $dt$ is $\psi(z)dVdt$.

You can find the state of the art of the estimation of the cosmic star formation history in figure 9 of [Piero Madau, Mark Dickinson (2014)](https://arxiv.org/abs/1403.0007).

[![figure 9 of Madau, Dickinson](https://i.sstatic.net/guiqU.png)](https://i.sstatic.net/guiqU.png)

You can see that star formation reached a peak around redshift 2 and now it has dropped very low. This means that the supernova rate that we measure now in the milky way is much lower that the rate we would have measured some billion years ago.

The authors also provide an analytic approximation.

$$\psi(z) = 0.015 \frac{(1+z)^{2.7}}{1+[(1+z)/2.9]^{5.6}} M\_\odot yr^{-1} Mpc^{-3}$$

We can calculate the total mass of stars that has ever formed in a given comoving volume as

$$\int dt \psi(z) = \int dz \frac{dt}{dz} \psi(z)$$
where the relation between $t$ and $z$ is given by

$${dt \over dz} = {1 \over H\_0} \frac{1}{(1+z)\sqrt{(1+z)^3 \Omega\_m + \Omega\_\Lambda}}$$

and $H\_0 = 70 km\ s^{-1} Mpc^{-1} = 7.15 \times 10^{-11} yr^{-1}$, $\Omega\_m = 0.3$, $\Omega\_\Lambda = 0.7$

This gives

$$\rho\_{tot} = \int\_0^8 dz \frac{dt}{dz} \psi(z) \approx 7.86 \times 10^8 M\_\odot\ Mpc^{-3}$$

Above $z=8$ very few stars had formed, and we can ignore them.

**How many stars die as supernovae?**

$\psi(z)$ tells us how many stars were born, so we need to know the fraction of these stars that died with a supernova. We know that small stars, like the Sun don't end their life as a supernova. Only more massive stars, with $m>8M\_\odot$ have a chance to explode, and they do it after a few million years since their birth: almost instantly from a cosmic point of view. For this calculation, we can assume that every star with $m>m\_{SN}=8M\_\odot$ instantly goes supernova after its creation.

If we know (from $\psi(z)$) that a certain mass $M$ of gas has converted into stars, how many of these stars will have $m>8M\_\odot$? The answer to this question is provided by the *Initial Mass Function* (IMF) $\xi(m)$. $\xi(m)dm$ is proportional to the number of stars that form with mass between $m$ and $m+dm$.

We can choose to use the IMF provided by [Kroupa (2001)](https://ui.adsabs.harvard.edu/abs/2001MNRAS.322..231K/abstract), that is defined as a broken power law

$$\xi(m) \propto m^{-0.3}\ \text{if}\ 0.01 < m \le 0.08 \\
\xi(m) \propto m^{-1.3}\ \text{if}\ 0.08 < m \le 0.5 \\
\xi(m) \propto m^{-2.3}\ \text{if}\ 0.5 < m$$

[![kroupa imf](https://i.sstatic.net/T2Si2.png)](https://i.sstatic.net/T2Si2.png)

Here I have normalized the IMF such that $\int\_{m\_0}^{m\_1} m \xi(m) dm = 1M\_\odot$. You can see that small mass stars are far more common than high mass stars. In particular, we can estimate that in a recently formed star population, the fraction of stars with $m>m\_SN=8M\_\odot$ will be

$$f\_{SN} = \int\_{8M\_\odot}^{+\infty} \xi(m) dm \approx 0.01$$

Only 1% of the formed stars will become a supernova! Actually the integral shouldn't go up to $+\infty$, because above $40M\_\odot$ stars start to directly collapse into a black hole, but those stars are so rare that we can safely ignore their contribution.

**Summing things up**

The comoving volume between us and $z=8$ can be quickly found using [Ned Wright's cosmic calculator](http://astro.ucla.edu/%7Ewright/ACC.html): $V = 3.59 \times 10^{12} Mpc^3$

Now we have everything we need to estimate the number of supernovae that ever took place in the observable universe.

$$N\_{SN} = f\_{SN} \times\rho\_{tot} \times V = 2.86 \times 10^{19}$$

This result is in good agreement with username_6's one.

Edit: This answer neglects type Ia supernovae. A good start may be this paper <https://arxiv.org/pdf/2105.11954.pdf>

> **Comments:**
> **username_1**: Lovely answer, but you've neglected the [type Ia supernovae](https://en.wikipedia.org/wiki/Type_Ia_supernova)  
> **username_6**: I'm amazed the value is so close. I guess a couple of my assumptions might be cancelling each other out.  
> **username_5**: @username_6 you are right, I'm amazed as well!  
> **username_5**: @PM2Ring That's true. Unfortunately I would not know how to account for them. I'll clarify this aspect in the answer  

---

### Answer by username_6 on 2021-09-18. Score: 8

On average the Milky way has one supernovae per 100 hundred (10^2) years. As the Galaxy is ~10 Billion (10^9) years old, then that is ~10^7 supernovae in the Milky way's life. Assuming the average galaxy looks like the Milky way and that there are an estimated ~1 Trillion (10^12) galaxies in the Universe, then that suggests there have been ~(10^12 x 10^9) / 10^2 supernovae or about **10^19 supernovae so far.**

This ignores many things like whether the average of all galaxies look like the Milky way, whether the star formation rate changes over time, whether the fraction of stars that undergo a supernovae change over time, and probably many more things. Also ignores effects like how many supernovae would have had enough time for the light to reach us.


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