Measuring a Black Hole mass

[Martin]

back in March 2003 blike posted a news item about

people measuring the mass of a distant black hole and finding

that it was 3 billion solar masses.

 

http://www.spaceflightnow.com/news/n0303/20blackhole/

 

this is a good mass for a quasar-core black hole

the mass of the stars in Milky galaxy is about 200 billion solar, IIRC

anyway it is on the order of 100 billion

 

so this hole in the news item is massing a few percent of all the stars in our galaxy

 

how big is such a hole?

the radius of a solar mass BH is about 2 miles and it is proportional]

so the radius of the hole they got a mass for must be 6 billion miles.

that is not so big for something far away

 

How did they estimate the mass?

 

can anyone suggest a way or ways to determine the mass of a distant BH.

 

As it happens this one is about 13 billion lightyears away. How can you tell its mass? They give some hints in the news article. Does anyone understand the method, from these hints, and want to explain?

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I understand how they measured the mass of the black hole at the center of our galaxy. It is only some 30,000 lightyears away and they can see objects ( stars) orbiting it. So they can easily estimate the mass from the orbit.

IIRC it was I think around 6 million solar masses---not very big. this one in the news item is 3 billion solar--much bigger. But how did they tell since it is too far away to image things orbiting it.

[Martin]

I dug up the actual journal article that the news article was based on.

 

It gives more information.

Like the redshift of the quasar is z = 6.41, which the science journalist didnt bother including

 

http://arxiv.org/abs/astro-ph/0303062

 

"We present near-infrared H and K-band spectra of the z=6.41 quasar SDSS J114816.64+525150.3. The spectrum reveals a broad MgII 2799 emission line with a full-width half-maximium of 6000 km/s. From the peak wavelength of this emission line we obtain a more accurate redshift than is possible from the published optical spectrum and determine a redshift of z=6.41+/-0.01. If the true peak of the Lyman alpha emission is at the same redshift, then a large fraction of the flux blueward of the peak is absorbed. The equivalent width of the MgII emission line is similar to that of lower redshift quasars, suggesting that the UV continuum is not dominated by a beamed component. Making basic assumptions about the line-emitting gas we derive an estimate for the central black hole in this quasar of 3x10^9 solar masses. The very high luminosity of the quasar shows that it is accreting at the maximal allowable rate for a black hole of this mass adopting the Eddington limit criterion."

 

Some of the gas spiraling into the hole is coming at us at 6000 km/s and some is going away from us at 6000 km/s. they tell that from the width of the Magnesium line.

 

these speeds are superimposed on the recession speed that goes with redshift z = 6.41. we can calculate that using Morgan's calculator.

this will help make imagining the thing more concrete.

[Martin]

I plugged the numbers into Morgan's calculator to get the basic data on this quasar

 

http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html

 

using concordance model parameters (0.27, 0.73, 71) in the calculator

age of universe when light was emitted: 0.87 billion years

distance from us when light was emitted: 3.8 billion lightyears

recession speed when light was emitted: 2.9 c

 

present distance: 28 billion lightyears

present recession speed: 2.03 c

 

So this light we are now seeing, when it was emitted by the quasar (almost 13 billion years ago) the quasar was only 3.8 billion LY away from us

and it was going away from us at 2.9 times the speed of light.

Of course the light, even the part of the light "aimed" at us, at first was swept back and did not get any nearer to us, but eventually after almost 13 billion years it did make it (the expansion of the universe having slowed markedly until comparatively recently is what permitted this)

 

To imagine the thing is more detail. the whole quasar then, as we see it today, was receding at around 3 times the speed of light. And on top of that the gas on one side was going away from us at 6000 km/s and on the other side coming towards us at 6000 km/s. As the gas circled the black hole. This is two percent of the speed of light.

 

what I'm wondering is why do you say the mass of a black hole is 3 billion solar, based on observing that the gas circling the hole achieves a speed of 2 percent of c.

 

have to turn in, think some more about it tomorrow. this link may help

http://arxiv.org/abs/astro-ph/0204473

it looks like they studied reverberation of closer quasars---brightness fluctuations over time periods like a year---there being a delay between when we see peak excitment of the gas between the hole and us and when we see the same peak in the gas off to the side, and that delay gives an idea of the distance the ring of gas is out from the hole.

then knowing the distance and the speed of the ring of gas they got the mass of the hole.

then they correlated the radius of the gas ring to the brightness of a 3000 angstrom line and this let them estimate masses of more distant quasars. hope to clarify this tomorrow

[Martin]

formula (1) in http://arxiv.org/astro-ph/0303062

 

[math]\frac{M_{hole}}{M_{sol}} = 3.37\sqrt{\frac{\lambda L_{3000}}{10^{37} W}}}(\frac{\text{speed of ring}}{km/s})^2 [/math]

 

the mass of the hole, measured in solars is equal to 3.37 times

 

the square root of the 3000 Angstrom line brightness measured in units of 10^37 Watt

 

time the square of speed of the ring measured in km/s

 

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what they put in for the speed in the case of this quasar was

6000 km/s, and their symbol for the speed is FWHM(MgII) which means

"full-width-half-maximum speed reckoned from width of Magnesium II line"

the 3.37 is an empirical coefficient gotten by studying hundreds of closer quasars where they could use time-variation ("reverberation") to determine the radius of the speeding ring and determine the mass reliably.

then they found a correlation with the brightness of the 3000 line. And

using that they could reckon the mass of more distant quasars (assuming they are the same as nearby ones at least in this respect)

[[Tycho?]]

I think its funny how this thread of 4 posts was made entirely by one person.

 

And no, I dont have anything to contribute to this.

[fuhrerkeebs]

Couldn't you also estimate the mass by measuring how much light curves around the black hole?

[Martin]

Couldn't you also estimate the mass by measuring how much light curves around the black hole?

 

Keebs! nice to have someone to share this with. Like Tycho, I was myself thinking it was funny no one else chimed in.

 

You are absolutely right that they do judge the mass of things by gravitational lensing! Keebs you right on target.

 

It is maybe worth saying why that wouldnt work in this case:

this was a quasar and blindingly bright and billions of lightyears away.

 

At that distance you dont see individual stars

you can tell the mass of a distant galaxy by how it bends light from other galaxies behind it

 

but in the case of a quasar, which is a galaxy with a hole in it, how do you tell how much of the mass is the hole and how much is the rest of the galaxy-----the unfortunate stars that it may sometime gobble up, and gas and dust and dark matter (if it exists).

 

so it is a real challenge to finesse info about the mass of the actual hole which is powering this quasar.

 

it is a good idea Keebs but noway could they see the lightbending effect of just the hole not including all the crud around it