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How to Activate Relay using Transistor?

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1. Jan 18, 2015

nicy12

As I searched the internet, transistors were configured in common-emitter configuration. They also show me that in order to activate the relay, the transistor should be operated in saturation and cut-off mode. How to make my BC547 Transistor operate to saturation mode (using common-emitter configuration) in order to activate my 24 VDC Relay using 24 VDC Source? How to decide proper Resistor Values?

2. Jan 18, 2015

Staff: Mentor

Hi nicy12. Your research covers a lot of the details. One more detail you need to supply is the source of the switching signal. What will you be using to control the switching transistor? A microswitch? A logic signal from some circuit? How many volts?

Your relay opeartes off 24VDC, but how much current does its solenoid draw while in operation?

Not enough information provided yet.

BTW, you'll also need a protection diode, because solenoids generate a spike in the voltage across the winding when you switch the current off

3. Jan 18, 2015

davenn

here's a couple of ideas I did for some one else
it will give you a starting point
BUT you need to answer NascentOxygen's questions so transistor type etc can be suggested

cheers
Dave

4. Jan 18, 2015

Mike_In_Plano

Most of your project sized 24 V relays need about 60 ma, 150 ma on the outside. The transistor should be fairly tough. A 2N2222 has a 500ma limit, which is pretty tough.
The following is a good starting point and can be tweeked to fit your needs:

Note that you'll need to supply at least 2 ma at 3.3V to be sure of driving a 150 ma coil.

5. Jan 19, 2015

nicy12

Sir NascentOxygen I want my 24 VDC Source to be the source of relay as well as transistor. The circuit should use only one Voltage Source. Regarding Relay, I don't know what details in the data sheet I downloaded (my relay is MY4N-J) were needed to be used so I will post an image so you can help me about this:

The Relay I am going to used has LED inside the casing that serve as an indicator so I think it also serve as a flyback diode.

6. Jan 19, 2015

nicy12

This is the circuit (which I designed) I really want to build:

As much as possible I don't want to replace the Transistor but if it was really needed so I will follow. The LDR values given was tested by me so it should be fixed.

7. Jan 19, 2015

Staff: Mentor

Yes, that 37.7 mA looks to be the current the relay coil needs.

But before going further, can you confirm that you already possess that LDR? They are not used so much now, I seem to recall them having limited long-term reliability. More common now are phototransistors.

If you have purchased that LDR, then you may require more than one transistor. You'll need to test the LDR for its dark and light resistances, under the light conditions you'll be relying on. Those R values in the schematic are probably just examples in a textbook figure.

Whatever the LED indicator does, you should not rely on it. Add the protection diode.

Last edited: Jan 19, 2015
8. Jan 19, 2015

nicy12

Yes I already bought one. The LDR values given were tested according to the situation or place where it will be placed. I am the one who tested it using multimeter ( I taped the LDR in the probes of my tester and measure its resistance at the location when there is light and when there is no light).

I used 10 M ohm Resistor because it will give me approx. 0.4 V at the base when there is light and approx. 3 V when there is no light ( greater than 0.7 of Vbe)

I have no idea on using phototransistor so research should be done in order to build circuit regarding that. I first want the LDR-Relay combination to this home project. I used transistor becuase my research says that transistors are also used in driving Relays.

If I am going to add 1N4001 Diode, Where it would be placed in the circuit?

9. Jan 19, 2015

nicy12

Sir Davenn does your circuit really drive the 24 VDC relay? Because you are only using 6 VDC as Vcc. Please explain.

10. Jan 19, 2015

Staff: Mentor

I can't get your circuit to work with even a pair of BC547s. I think it can be made to work by substituting a JFET for the BC547. The FET won't load down your divider network.

I don't have any favourite FETs for this voltage, but the 2N7000 seems available and should do the job.

http://www.futurlec.com/Transistors/2N7000.shtml

Are you in a position to purchase that FET?

11. Jan 19, 2015

nicy12

I am afraid to use FET because I haven't understand the BJT cleary in terms of practice. I have a little idea about BJT's in terms of theory where the type of transistor don't matter because needed parameters are given to solve the problem. To be specific, I don't know what details in the data sheet should be considered thus, I don't know what type of transistor should be used. I just found that BC547 as part of Dark Sensor Circuit here:
http://electronicpowersupply.blogspot.com/2014/04/simple-light-dark-detector-circuit.html
So I searched for the data sheet of that transistor here:
http://www.futurlec.com/Transistors/BC547.shtml
I found out that BC547 has maximum Emitter-Base Voltage of 6 V (I think that would be the maximum Vbe) and the minimum Base-Emiiter On Voltage was 0.55 V ( I believe that it was the needed Vbe to turn the transistor ON).

My problem now is I don't know what kind of transistor is going to be used so that I can drive the 24 VDC 3.7 mA Relay. Some website says that I should make my transistor to operate in Cut-off and Saturation Region. Operating in Cut-off is easy, I just need to Cut the supply in base (or supply it with less than 0.7 V). But operating in Saturation Mode makes me feel dumber given that I have already resistor values in the circuit.

I also don't want to use FET because I don't have any idea about it except it switches faster than BJT. Well, I don't want to mess in FET while I am having trouble to BJT.

One more thing, I honestly don't get it:
"I can't get your circuit to work with even a pair of BC547s. I think it can be made to work by substituting a JFET for the BC547. The FET won't load down your divider network."

12. Jan 19, 2015

Svein

Just off the top of my head - that 10M resistor seems way too large. Try removing the LDR (simulating "extremely dark") and see if the circuit energizes. I suspect it will not. The trouble lies in the current amplification of the BC 547. 24V through 10Mohm results in a current of 2.4μA. If the β of BC 547 is 200, then the collector current will be 4.8mA - this not nearly enough to energize the relay (the spec sheet says 37.7mA at 24V).

13. Jan 19, 2015

Staff: Mentor

It's all very well to look at the two resistor divider alone, but when you connect it to the transistor base that transistor must draw some current from the divider, and this messes up your calculations. The base needs a lot more current than your network can provide, so the resistor values are no good, and then the light vs. darkness voltage variations won't be what you'd hoped. Alas, it just won't work.

A FET is simpler, it doesn't need much gate current at all, so it will work just like you'd hoped!

14. Jan 19, 2015

nicy12

Why should I removed the LDR if I am going to simulate an "exteremely dark" situation if I can substitute it to be 3 M ohm (as I tested it in very very dark location)?
$$\frac{3x10^6 x 24}{10 x 10^6 + 3 x 10^6} = 5.54 V$$
It is enough to turn the transistor on without burning it (since the maximum is 6 Vdc)

15. Jan 19, 2015

Svein

That is correct - if you look at the resistor string alone. But the transistor base will lock at 0.7V and from there it is a question of supplying enough base current to the transistor. In order to turn on the relay, the transistor has to supply 38mA. Assuming a conservative β of 100, you need to supply 0.38mA into the base. 24V/0.38mA equals 63kΩ. 10MΩ is therefore way too large.

You could use an extra BC 547 as a source follower in front of your existing BC 547. Again assuming a β of 100, you need to supply 3.8μA into that base - which lets you get away with 6.3MΩ. Still less than 10MΩ, and you are now using a base current of the order of the leakage currents.

A FET draws no gate current at all, but it has other problems. A JFET needs to operate with a negative gate voltage and it has no defined "turn-on" point. An "enhancement-mode" MOSFET will work with a positive gate voltage, but it still has no clearly defined "turn-on" point.

Personally, I would have used a comparator and fed the comparator output into the BC 547 base.

16. Jan 19, 2015

nicy12

My little brain will going to burn! I can't make any circuit that comply the requirements.. If I will consider the voltage in Base-Emiiter Junction, there will be no enough current. If I'll consider the current, the voltage in Base-Emitter Junction is high that will burn the transistor. What should I do?

Can you provide me the circuit Sir?

17. Jan 19, 2015

Svein

18. Jan 19, 2015

nicy12

I tried to use the 6.3 M ohm you said and this is the circuit I produced. Please tell me if I made it correctly:

7.018 mA is also not enough to activate my Relay. If I will going to add another, this will activate the relay but it is not convenient because three (3) transistors were used.

Last edited: Jan 19, 2015
19. Jan 19, 2015

Svein

Sorry. The first transistor has to be connected as an emitter-follower, which means: Collector to +24V, base as you have drawn it and emitter connected to the base of the other transistor (with a 10kΩ resistor to ground).


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# 7. Similarities between preferred stock and long-term debt (bonds) include all of the following...

7. Similarities between preferred stock and long-term debt (bonds) include all of the following except

a. each has a fixed claim to annual income (dividends and interest, respectively).

b. each has a fixed claim on assets (liquidating value and principal amount, respectively).

c. each allows the corporation a tax deduction (dividends and interest, respectively).

d.  each may be callable and/or convertible.

e. All of the above are similarities between preferred stock and long-term debt (bonds).

## Related Questions in Financial Accounting - Others

• ### Similarities between preferred stock and long-term debt (bonds) include all of the following except...

(Solved) January 14, 2017

Similarities between preferred stock and long-term debt (bonds) include all of the following except a. each has a fixed claim to annual income (dividends and interest , respectively). b . each has a fixed claim on assets (liquidating value and principal amount , respectively). c . each

Since interest payments on long term debts are considered as the cost of operating a business it is tax deductible but the same is not applied for dividends because it is the distribution to...
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• ### Problem 1 How does P & P determine the value for Levels 1, 2 and 3 investments? Problem 3 Why would

(Solved) August 07, 2016

to the industry? Ratio Formula Use Evaluation as?Compared to the Industry Average Industry Average Net Profit Margin 3.1% Price to free cash flow -84.2 Return on Equity 5.4% Total Debt /Equity 77.9 Dividend Yield 3.6%

Problem 1 How does P & P determine the value for Levels 1, 2 and 3 investments? Problem 3 Why would foreign currency translation decrease from 2013 to 2014? Problem 5 Using the following...

(Solved) February 15, 2016

of Sales in Year 1: 110,000 Price per Unit: $11 Variable cost per unit: 30% Fixed Costs:$125,000 Income taxes : 15% Interest Expense: $200,000 In year 2, Price per unit increases to$11.50, and unit of sales increases by 5%, all other assumptions remain the same. 3) Calculate the sustainable growth

Unit I due 16 Feb 2016 at 6pm EST 1) Critique the benefits and drawbacks of proprietorships and partnerships as a form of business organization.Your response should be at least 250 words in...
• ### P16-1 Issuances of Stock The Cada Corporation is authorized to issue 10,000 shares of $100 par,... (Solved) November 07, 2015 per share. Common stock is currently selling for$42 per share. Stockholders elect not to convert into common stock . 8. Same as transaction 7 , except that stockholders owning 2,000 shares of preferred stock elect to convert each share into three shares of common stock . The remaining 5

Date particulars Amount($) Amount($) 2013 Cash A/c………………………………………………..Dr(10000*113) 1130000 Preferred Stocks at Par A/c(10000*\$100) 1000000 Additional paid in capital A/c 130000 Cash...

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# Halo Ellipsoid Analysis¶

Warning

This functionality is currently broken and needs to be updated to make use of the Halo Finding and Analysis framework. Anyone interested in doing so should contact the yt-dev list.

## Purpose¶

The purpose of creating this feature in yt is to analyze field properties that surround dark matter haloes. Originally, this was usually done with the sphere 3D container, but since many halo particles are linked together in a more elongated shape, I thought it would be better to use an ellipsoid 3D container to wrap around the particles. This way, less of the empty-of-particle space around the halo would be included when doing the analysis of field properties where the particles are suppose to occupy.

## General Overview¶

In order to use the ellipsoid 3D container object, one must supply it with a center, the magnitude of the semi-principle axes, the direction of the first semi-principle axis, the tilt angle (rotation angle about the y axis that will align the first semi-principle axis with the x axis once it is aligned in the x-z plane.)

Once those parameters are determined, the function “ellipsoid” will return the 3D object, and users will be able to get field attributes from the data object just as they would from spheres, cylinders etc.

## Example¶

To use the ellipsoid container to get field information, you will have to first determine the ellipsoid’s parameters. This can be done with the haloes obtained from halo finding, but essentially it takes the information:

1. Center position x,y,z
2. List of particles position x,y,z

And calculates the ellipsoid information needed for the 3D container.

What I usually do is get this information from the halo finder output files in the .h5 HDF5 binary format. I load them into memory using the LoadHaloes() function instead of reading in the ASCII output.

### Halo Finding¶

import yt
from yt.analysis_modules.halo_finding.api import *

halo_list = HaloFinder(ds)
halo_list.dump('MyHaloList')

### Ellipsoid Parameters¶

import yt
from yt.analysis_modules.halo_finding.api import *

Once the halo information is saved you can load it into the data object “haloes”, you can get loop over the list of haloes and do

ell_param = haloes[0].get_ellipsoid_parameters()

This will return 6 items

1. The center of mass as an array.
2. A as a float. (Must have A>=B)
3. B as a float. (Must have B>=C)
4. C as a float. (Must have C > cell size)
5. e0 vector as an array. (now normalized automatically in the code)
6. tilt as a float.

The center of mass would be the same one as returned by the halo finder. The A, B, C are the largest to smallest magnitude of the ellipsoid’s semi-principle axes. “e0” is the largest semi-principle axis vector direction that would have magnitude A but normalized. The “tilt” is an angle measured in radians. It can be best described as after the rotation about the z-axis to align e0 to x in the x-y plane, and then rotating about the y-axis to align e0 completely to the x-axis, the angle remaining to rotate about the x-axis to align both e1 to the y-axis and e2 to the z-axis.

### Ellipsoid 3D Container¶

Once the parameters are obtained from the get_ellipsoid_parameters() function, or picked at random by the user, it can be input into the ellipsoid container as:

ell = ds.ellipsoid(ell_param[0],
ell_param[1],
ell_param[2],
ell_param[3],
ell_param[4],
ell_param[5])
dens = ell.quantities['TotalQuantity']('density')[0]

This way, “ell” will be the ellipsoid container, and “dens” will be the total density of the ellipsoid in an unigrid simulation. One can of course use this container object with parameters that they come up with, the ellipsoid parameters do not have to come from the Halo Finder. And of course, one can use the ellipsoid container with other derived fields or fields that they are interested in.

## Drawbacks¶

Since this is a first attempt, there are many drawbacks and corners cut. Many things listed here will be amended when I have time.

• The ellipsoid 3D container like the boolean object, do not contain particle position and velocity information.
• This currently assume periodic boundary condition, so if an ellipsoid center is at the edge, it will return part of the opposite edge field information. Will try to put in the option to turn off periodicity in the future.
• This method gives a minimalistic ellipsoid centered around the center of mass that contains all the particles, but sometimes people prefer an inertial tensor triaxial ellipsoid described in Dubinski, Carlberg 1991. I have that method composed but it is not fully tested yet.
• The method to obtain information from the halo still uses the center of mass as the center of the ellipsoid, so it is not making the smallest ellipsoid that contains the particles as possible. To start at the center of the particles based on position will require an O($$N^2$$) operation, right now I’m trying to limit everything to O($$N$$) operations. If particle count does not get too large, I may implement the O($$N^2$$) operation.
• Currently the list of haloes can be analyzed using object parallelism (one halo per core), but I’m not sure if haloes will get big enough soon that other forms of parallelism will be needed to analyze them due to memory constraint.
• This has only been tested on unigrid simulation data, not AMR. In unigrid simulations, I can take “dens” from the example and divide it by the total number of cells to get the average density, in AMR one would need to do an volume weighted average instead.


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# What should I put in a “Go box”, “Go bag”, or “go kit” for emergency communications?

If I wanted to build a mostly-portable-but-still-comprehensive kit to use in emergencies, either my own, or simulated ones through ARES or RACES, what should I put in the kit? I'd prefer responses to be generic (see below), though I won't complain about specific gear lists.

I'm thinking no larger than a set of these Rigid boxes from Home Depot: top, middle, base. As far as antenna, no more poles and antennas than a single person can carry in a large/XXL duffle bag. I'm thinking tripod mount, vehicle tire mount, or rope-in-a-tree mount.

For example:

• 1 - 3 mobile radios
• Emergency scanner
• Power supplies for above
• Enough battery capacity to run them for xx hours
• SWR meters for the bands in use by the radios above
• One of these widgets
• Book with local repeaters
• Laptop with programming cables for radios
• Non-radio supplies wouldn't actually make this question off-topic; but there is a problem that this question will almost certainly get answers that are "here is my list", without substantial attempt to produce a comprehensive answer to get voted to the top. And someone can always say "Well what if this happened and you needed this?" Can you maybe figure out how to narrow down your question to be more objective? – Kevin Reid AG6YO Jun 26 '18 at 1:03
• In the ideal case, a question has one best answer. Here, a really well thought-out answer is still going to make an enormous number of assumptions about what situations might be encountered to make certain items useful, versus the cost of carrying them, and people can reasonably disagree with those assumptions, so there is no such thing as a best answer. – Kevin Reid AG6YO Jun 26 '18 at 1:25
• If you were to phrase this question as "how should I plan what to bring", it would be more asking for a comprehensive answer. But it would still be quite broad — what kind of outing are you doing? Field Day? DXpedition? SOTA? A not-overdoing-it day in the park? Emergency communications? If you could narrow down what range of scenarios you want to allow for then that would make a question that would be more answerable within a reasonable length (where by 'reasonable length' I mean that someone might actually put in the effort to answer it completely, not that there is a limit). – Kevin Reid AG6YO Jun 26 '18 at 1:28
• Oftentimes an organization will provide a gear list for its members to pack for an outing. That's the same thing I'm looking for here. Random first example in an Internet search: thetrek.co/thru-hiker-resources/… – YetAnotherRandomUser Jun 26 '18 at 23:28
• I'm still a bit skeptical, but let's see how this goes. I've reopened the question. – Kevin Reid AG6YO Jun 26 '18 at 23:31

If I wanted to build a mostly-portable-but-still-comprehensive kit to use in emergencies, either my own, or simulated ones through ARES or RACES, what should I put in the kit?

If you are active in ARES or RACES, they will support served agencies. The potential needs of these agencies and your role within the organization will determine the contents of your go-kit. My local ARES has a field operations manual that includes two levels of go-kits for the average member. The go-kit and your skills get tested and refined through regular drills, simulations, and desk-top exercises. We also update our field manuals based on the lessons learned from these drills.

You can imagine that if your role is to staff an EOC (Emergency Operations Center) or a Comms Trailer, your go-kit might be rather sparse - probably an HT and your personal effects. On the other hand, if your role is to provide comms support for your local SAR (Search and Rescue) team, your go-kit might be rather extensive including the ability to deploy cross band, hill top radios, for example. In my case, my go-kit is actually a go-truck as I have state wide responsibility to provide technical assistance in the event an emergency. I have spare repeaters, antennas, RFI kits, AC and DC distribution systems, a spectrum analyzer, technical reference manuals, etc. that get loaded into the truck based upon the needs. Clearly this go-kit is different from most people's idea of a go-kit. The point is knowing your role is the key to stocking your go-kit.

Deployment Location and Duration

The location and duration of your deployment has a profound impact on the contents of your go-kit. Most of us could comfortably operate for 8 hours or so with just our technical gear. Beyond that, issues such as personal hygiene, F&H (Food and Hydration), sleeping gear, etc. start to come into focus and must be addressed in the go-kit plan or in the site logistics plan.

The duration and location can also impact the power requirements of your portable/mobile operations. If your assignment is to do police or fire ride-alongs for support comms, do you have the right gear to plug into the vehicle power and to deploy an antenna on the vehicle? Your stack of batteries may only last for a few hours and then you may find that your cigarette adapter cord isn't usable because all sockets are already taken or at capacity. On the other hand, if you are providing comm relays for a wild fire team, your nifty solar panel may not be at all practical since the sun is too obscured by smoke.

Practice

Hopefully your ARES/RACES team conducts a couple of drills a year to test the environment, your skills, and your gear. This also helps to understand the served agency's command structure, their terminology, their temperament, and the type of comms they really need (perhaps contrasted to what they asked for). It also gives them a chance to experience your capabilities and expertise.

Practicing with the served agencies may also highlight unanticipated issues. For example, many are surprised when their trusty \$40 Chinese HT is rendered completely useless in an RF dense environment like an EOC. The lesson learned may be that a different radio is needed for the go-kit.

In the absence of organized practice drills you should, at the very least, setup your gear in the envisioned field conditions and try operating it for the duration you anticipate being deployed. This not only enhances your skills, but it will test the readiness and completeness of your gear. It is usually the basic things that get overlooked - things such as flashlights, pens, communication forms, frequency charts, a comfortable chair, headphones, medications, contact supplies, etc. that are not thought of in advance but become painfully obvious with realistic practice and drills.

Laptop with programming cables for radios

While at first glance, this would could fall under the category of "be prepared", I would cynically view this as a red flag indicating lack of preparation. Today's radios typically have a hundred or more memories in them. With proper planning, the radio can be programmed in advance for most scenarios. For example, our ARES field manual has all of the frequencies listed for all repeaters in our county and all adjoining counties. The list includes simplex, reverse repeater pairs, and predetermined cross banding frequencies. We regularly offer programming of radios with this list at our meetings. Our field manual also includes all FRS, GMRS, MURS, NWS, and served agency frequencies.

While the laptop could prove helpful, is there other gear that could take its place that would be more effective in helping you to carry out your role?

Identification

Emergency situations generally involve restricted access to certain locations. You must have the right identification with you to gain access. Your served agencies will facilitate gaining the proper credentials including recognized photo ID cards. For unanticipated issues, having your passport, drivers license, and a copy of your FCC license(s) may be helpful.

Grab Lists and Refresh Lists

While a basic go-kit can be prepared in advance, many times there are things that need to be grabbed at the last minute. Examples include medications, snacks, identification, or a generator and gas can. A list that is prominently attached to your go-kit can help you to avoid forgetting these items "in the heat of the battle". Force yourself to check-off items on the list as they are packed if your list includes more than a few items.

You can also use a grab list to enhance your go-kit for longer or different deployments. The grab list could include the items needed to expand your day go-kit to a three day go-kit, for example.

Several items in your go-kit may have expiration dates and should be replaced or refreshed on a periodic basis. Examples include alkaline batteries, bottled water, snack bars, hand warmers, and gasoline. Keep a "refresh" list of these items along with a "replace by" or "do by" date. Take this list in hand once a month and check for anything in need of attention. Don't forget to include charging rechargeable batteries on this list as well as periodic maintenance items such as generator start-up and test, oil changes, updating programmed frequencies, etc.

The Family

Emergency deployments usually involve leaving the family behind while you go on your assignment. Don't overlook their own safety/security and their concerns about your safety while you are deployed. Your go-kit should include plans and capability to communicate with your family. They should have a complementary plan accessible to them at home so they know how they can get in touch with you. Don't forget to practice this plan with them as well.

The Amateur Radio Emergency Service (ARES) for example uses the following checklist (source is http://www.arrl.org/files/file/ARES_FR_Manual.pdf):

Basic Deployment Equipment Checklist:
When responding to an emergency event, or even a training exercise,
there is a minimum set of equipment and personal gear you should bring
with you to get the job done. Basic items include:
• 2-meter hand-held
• 2-meter mag-mount antenna and coax
• Earphone
• Paper and pencil
• ARES ID card
• Extra batteries
• Appropriate clothing
• Food and water
The majority of these items should be kept in a “Ready Kit.” Just pick
it up on your way out the door for deployment. You might also consider the
items on the following list for inclusion in this ready kit, designed to
allow you to stay in the field for up to 72 hours.

The same document has a "72 hour" checklist, as well as some interesting info about the operations of ARES.

Hope this is a helpful starting point!


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# Why would it be true that people with longer legs walk faster than ones with shorter legs?

When a person walks, the only force acting on him is the force of friction between him and the ground (neglecting air resistance and all). The magnitude of acceleration due to this force is independent of the mass of the object (longer legs have more mass). Hence the person should move with with a velocity independent of the length of his legs.

But I have heard (also observed) that people with longer legs walk faster than ones with shorter legs. If that is true, then why?

One can argue that the torque about the pivot due to friction is more in case of longer legs, But then the torque due to gravity (when one raises his leg to move), which opposes the frictional torque, is also more for longer legs. And why would these torques make a difference anyway, as they have no effect on the acceleration of the center of mass?

-
 It is a relevant question, as students often don't discriminate between maximum static friction and actual static friction. Unless it is duplicate, leave it as it is. – Pygmalion Apr 17 '12 at 17:03

Think about the limiting cases. An ant-sized marching band would take a long time to march the length of a football field. The reason they take so long has nothing to with friction - it's just that their legs are smaller and so each stride moves them a shorter distance.

-
 Yes, but their legs weight less and the torque required to moev them is much less, so why can't they simply move their legs faster? – John Rennie Apr 18 '12 at 8:02 From their perspective their bodies are proportioned exactly as ours, and so the timing of their strides are the same as ours. Naturally this is an extreme example - it is just meant to indicate that someone with shorter legs (say, a child) will walk slower compared to someone with longer legs. They could, of course, hasten the timing of their strides, but that would require a noticeable extra input of effort – kleingordon Apr 18 '12 at 18:38

Note, in your problem you have static friction, and for static friction

$$F_\text{sf} \le F_\text{sf,max} = \mu_\text{sf} N = \mu_\text{sf} m g.$$

Note "less or equal" in the equation above, which means that actual static friction is less or equal than maximum static friction. So when you are walking, most of the time "less" sign applies, which means that mass of the body isn't relevant for the friction!

(Example: if you are standing still, $F_\text{sf} = 0$, despite the fact that $\mu_\text{sf} m g > 0$.)

People with longer legs walk faster simply because they are making bigger steps. I guess period between two steps for casual walking is some kind of a constant for all people... maybe has something to do with our heart beats.

Dynamic friction is different, there is always "equal" sign:

$$F_\text{df} = F_\text{df,max} = \mu_\text{df} N = \mu_\text{df} m g.$$

-
 Oh right! I don't know why I neglected that(maximum and actual static friction acting). – Megha Apr 17 '12 at 17:08 No problem. Students of traffic sciences have problem with this difference, and it is a very very important issue for them. – Pygmalion Apr 17 '12 at 17:15

Interesting question. I had a Google around and came across http://silver.neep.wisc.edu/~lakes/BME315ScalingWalk.html, which seems a reasonable discussion of the mechanics (very simplified). The conclusion is that the walking speed is proportional to the square root of leg length, so taller people do walk faster but the square root dependance means it's not not much faster.

-
 Hmmm it is nice. Thank You:) – Megha Apr 17 '12 at 17:07 From 12 to 14 I was very athletic, and excelled particularly in the long jump, my style chosen as an example for other students! Then the growth spurt came and I realized I could never compete since other girls grew much longer legs and could start jumping up to 5 meters, whereas I, with my short legs, good style or not, could only reach 4m or so :( . I then concentrated in mathematics and physics :). – anna v Apr 17 '12 at 17:18 But you could outperform them by jumping over pole, leaving your center of pass under pole ;) – Pygmalion Apr 17 '12 at 17:23 The simple pendulum mechanism works well if the person is walking casually but if we consider an athlete running a race, factors like muscle power have to be taken into account. – Megha Apr 18 '12 at 14:52

I think the simplest model that may be useful here is to treat the legs as simple pendula. In "steady state" comfortable walking, it is reasonable to assume that the legs oscillate close to their natural frequency. That is, the forward contacting leg lifts allowing the rear to swing forward freely over the stride. For a (simple) pendulum with:

$$\omega = \sqrt{\frac{g}{l}}$$ the velocity along the ground will be: $$v \propto l\omega = \sqrt{lg}$$

Note that this result is independent of the mass of the walker and the ground contact forces.

-


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# A point P moves inside the square A1 A2 A3 A4 of side length b such that distance of point P from O is less than its distance from

+1 vote
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A point P moves inside the square A1 A2 A3 A4 of side length b such that distance of point P from O is less than its distance from each of the four vertices of square. The area moved by the point P is

(A)  b2 sq. units

(B)  b2/2  sq. units

(C) 2b2

(D)  None of these

by (53.8k points)
selected

Correct option (B)  b2/2  sq. units

See Fig.

Point will lie inside the square PQRS


text:
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In the ﬁgure above, what is the value of

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In the ﬁgure above, what is the value of [#permalink]  01 Dec 2015, 07:14
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In the ﬁgure above, what is the value of $$\frac{x + y + z}{45}$$ ?

A. 2

B. 3

C. 4

D. 5

E. 6

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Re: In the ﬁgure above, what is the value of [#permalink]  01 Dec 2015, 07:44
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Solution

The interior angles of a triangle, no matter what, must sum to 180°

As such $$\frac{180}{45}=4$$

Answer is $$C$$
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Re: In the ﬁgure above, what is the value of   [#permalink] 01 Dec 2015, 07:44
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# メンバー

TOP　>　メンバー　>　河合 隆裕

## 河合 隆裕

E-Mail N.A.

U R L

[1] Microfunctions and pseudo-differential equations, Lect. Notes in Math., 287, Springer, 1973, pp.265-529. (with M. Sato and M. Kashiwara)

[2] On holonomic systems of micro-differential equations, III, Publ. RIMS, Kyoto Univ., 17 (1981), 813-979. (with M. Kashiwara)

[3] Algebraic Analysis of Singular Perturbation Theory, Amer. Math. Soc., 2005 (with Y. Takei; 日本語版 (岩波書店，1998)の英訳)

[4] The exact steepest descent method --- A new steepest descent method based on the exact WKB analysis, Adv. Stud. Pure Math., 42 (2004), 45-61. (with T. Aoki and Y. Takei)

[5] On the exact WKB analysis of operators admitting infinitely many phases, Adv. in Math., 181 (2004), 165--189. (with T. Aoki, T. Koike and Y. Takei)

[6] On the exact WKB analysis of microdifferential operators of WKB type, Ann. Inst. Fourier, 54 (2004), 1393-1421. (with T. Aoki, T. Koike and Y. Takei)

[7] On the Stokes geometry of higher order Painlev\'e equations, Ast\'erisque, 297 (2004), 117-166. (with T. Koike, Y. Nishikawa and Y. Takei)
[8] WKB analysis of higher order Painlev\'e equations with a large parameter --- Local reduction of 0-parameter solutions for Painlev\'e hierarchies $(P_{J})(J=\mathrm{I}, \mathrm{II}-1$ or $\mathrm{II}-2)$, Adv. in Math., in press.

[9] Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations, J. Phys., A38 (2005), 3317-3336 (with T. Aoki, S. Sasaki, A. Shudo and Y. Takei)

[10] Virtual turning points --- a gift of microlocal analysis to the exact WKB analysis, RIMS Preprint 1533, 2006. (with T. Aoki, N. Honda, T. Koike, Y. Nishikawa, S. Sasaki, A. Shudo and Y. Takei)

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# Question #03596

Dec 5, 2017

Undefined.

#### Explanation:

From the above graph:
If you were to take 2 arbitrary points on the line and determine the slope, the following would be the result;

$S l o p e \left(m\right) = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Taking coordinates (1,1) and (1,2), we get:

$m = \frac{2 - 1}{1 - 1} = \frac{1}{0}$
Since, anything divided by zero equals Undefined.

Therefore, the Slope(m) of the line is Undefined.

Dec 7, 2017

Undefined.

#### Explanation:

Even though it may seem irrelevant to the question, I will explain why the slop is undefined.

Here is one of the many reasons.
If $\frac{1}{0}$ is infinity, then we can say that $\frac{2}{0}$ is also infinity.(By the way, infinity is only a quantity, not a number)

By our rule that if $\frac{a}{b} = \frac{c}{b}$ then $a = c$, it results this:$1 = 2$ which we know is not true.

Therefore, the line is undefined.


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# Distribution of resources from providers to maximum number of receivers

Consider there is a city with $$n$$ residents who are in need of internet and there are $$m$$ internet providers in the city. Here in the city every resident needs internet and every resident knows what providers are available to him. Formally let resident $$i$$ has list of providers $$a_i$$. Also each provider has a maximum number of connections he can give, that is, provider $$i$$ can have at max $$k_i$$ connections. Find the optimal way of providing internet so that the number of residents having internet is maximum.

My thoughts on the question is that this question looks like a derivative of knack-pack problem with constraints, which suggests dynamic programing but i am unable to find the states. Could anyone help me?


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# reliability_test_duration¶

class reliability.Reliability_testing.reliability_test_duration

This function calculates the required duration for a reliability test to achieve the specified producers and consumers risks. This is done based on the specified MTBF required and MTBF design. For details please see the algorithm.

Parameters: MTBF_required (float, int) – The required MTBF that the equipment must demonstrate during the test. MTBF_design (float, int) – The design target for the MTBF that the producer aims to achieve. consumer_risk (float) – The risk the consumer is accepting. This is the probability that a bad product will be accepted as a good product by the consumer. producer_risk (float) – The risk the producer is accepting. This is the probability that a good product will be rejected as a bad product by the consumer. one_sided (bool, optional) – The risk is analogous to the confidence interval, and the confidence interval can be one sided or two sided. Default = True. time_terminated (bool, optional) – Whether the test is time terminated or failure terminated. Typically it will be time terminated if the required test duration is sought. Default = True show_plot (bool) – If True, this will create a plot of the risk vs test duration. Default = True. print_results (bool, optional) – If True, this will print the results to the console. Default = True. test_duration (float) – The required test duration to meet the input parameters.

Notes

The number of failures allowed is calculated but not provided by this function since the test will determine the actual number of failures so any prediction of number of failures ahead of time is not practical.

If the plot does not show automatically, use plt.show() to show it.


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# Texture Mapping jagged pixel edges

I'm currently writing a software renderer. I managed to implement texture mapping and it works fine. Only issue is, that the edges between the pixels are sometimes jagged in x direction as you can see here:

Could this be caused by a lack of precision? If so, how can I improve it? What I'm doing is simply stepping along the edges of a triangle and interpolating the UVs for each scanline.

EDIT: Here's my code for edge stepping and drawing of scanlines. The Edge class has a method step which increments the interpolants for each scanline.

edge.h

Edge(const Vertex& minY, const Vertex& maxY){
float dy = maxY.position.y - minY.position.y;

yStart = static_cast<int>(ceil(minY.position.y));
yEnd = static_cast<int>(ceil(maxY.position.y));

float prestep = yStart - minY.position.y;

xStep = (maxY.position.x - minY.position.x) / dy;
x = minY.position.x + xStep * prestep;

wStep = (1.0f / maxY.position.w - 1.0f / minY.position.w) / dy;
w = 1.0f / minY.position.w + wStep * prestep;

texCoordsStep = (maxY.textureCoordinates / maxY.position.w - minY.textureCoordinates / minY.position.w) / dy;
texCoords = minY.textureCoordinates / minY.position.w + texCoordsStep * prestep;
}

renderTarget.cpp

void RenderTarget::DrawScanLine(const Edge& left, const Edge& right, int y){
int xStart = static_cast<int>(ceil(left.GetCurX()));
int xEnd = static_cast<int>(ceil(right.GetCurX()));
float dx = static_cast<float>(xEnd - xStart);
float prestep = xStart - left.GetCurX();

float w = left.GetCurW();
float wStep = (right.GetCurW() - w) / dx;

glm::vec2 texCoordsStep = (right.GetCurTexCoords() - left.GetCurTexCoords()) / dx;
glm::vec2 texCoords = left.GetCurTexCoords() + texCoordsStep * prestep;

Uint32* p = pixels + xStart + y * surface->w;

for(int x = xStart; x < xEnd; x++){
float z = 1.0f / w;  //value for perspective correction
int s = static_cast<int>(texCoords.s * z * texture->surface->w) & texture->surface->w - 1;
int t = static_cast<int>(texCoords.t * z * texture->surface->h) & texture->surface->h - 1;

*p = texture->pixels[s + t * texture->surface->w];  //copying the texture's pixel to the framebuffer
p++;
w += wStep;
texCoords += texCoordsStep;
color += colorStep;
}
}

• I'm confused by why there are vertical lines at all. Is it deliberate that the texture is aligned with the image plane instead of the triangle? What happens when you rotate the texture (mapping)? – Dan Hulme Oct 10 '16 at 8:59
• @DanHulme It's actually aligned with the triangle, you just can't see it in the screenshot. I tried to change the uv mapping but no difference.Weird thing is though, if I rotate the triangle 90° it's perfect. I think this might have something to do with the triangle itself. The problems occur if one side of the triangle is aligned with the x-axis. When aligned with the y-axis it works... – Leon2806 Oct 10 '16 at 12:44
• The triangle edge jaggies in the top-right corner (against black background) strike me odd though. Why some pixels appear bigger than others? They should all be the same size. – JarkkoL Oct 11 '16 at 20:37
• @JarkkoL that's because I scaled the picture in Photoshop in order to make the issue more visible :) – Leon2806 Oct 11 '16 at 20:46
• I thought you might have (: You should scale it properly to make it less confusing. – JarkkoL Oct 11 '16 at 20:47

I strongly suspect that you are simply running out of floating point precision (at least in "U" dimension). With this sort of mathematics, the LSBs will soon become noisy resulting in the jagged appearance when you are (effectively) doing yes/no comparisons against known constants.

May I suggest instead that, rather than doing point sampling of your texture, try doing (at the very least) bilinear filtering which will hide the precision artefacts and also IMHO look better than having little squares.

UPDATE It just occurred to me that one of the possible causes of inaccuracy is that you are doing increments for each pixel X step, e.g. these two

w  += wStep;
texCoords += texCoordsStep;

These will soon cause errors to accumulate. Remove them and replace with multiplies by the X value and I expect things should improve.

UPDATE2 It will also be affected by how far away from the origin of the texture you are when you sample it. If, for example, your source texture is defined over [0..1]x[0..1] and then repeats outside of that range, you might expect sampling at uv = (1000000.125, 100000.125) to be the same as (0.125,0.125) but, because the precision of FP decreases with increasing magnitude (i.e. the steps between floats also increases), you might end up with something quite different.

• Yeah, that's kind of what I expected. But it has to work somehow... – Leon2806 Oct 11 '16 at 19:12
• I already have bilinear filtering but I like to have both. This gives it sort of a retro look – Leon2806 Oct 11 '16 at 19:13
• @Leon2806 see update re not doing per-pixel increments. – Simon F Oct 12 '16 at 8:14
• I'm not sure if I completely understand what you mean. Should I multiply the step value by x? because that gives me the exact same result. – Leon2806 Oct 12 '16 at 12:44
• In real mathematics it does, but not in the world of floating point. I believe the appropriate quote is "Floating point numbers are like piles of sand; every time you move them around, you lose a little sand and pick up a little dirt.” ( — Brian Kernighan and P. J. Plauger). Every time you do an operation (e.g an add or a mul) you'll typically lose up to 1/2 a ULP of accuracy. Replacing a sequence "+C+C+C...+C" with +N*C will thus improve your sand to dirt ratio :-) – Simon F Oct 12 '16 at 13:17

In my case, i fixed the problem adding Dx' for interpolation of x-direction. In edge scan line of x-direction, I use integer-type for speed-up but ingnored dx' as below. I changed variable type from interger to float and adding dx'. (picture 1)

• when you use interger type with shift, same as float-type – zeroe Jan 9 '17 at 10:12


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# Linear Regression#

Linear regression is a type of supervised machine learning algorithm that is used to model the relationship between a dependent variable (y) and one or more independent variables (X). The goal of linear regression is to find the best line (the line of best fit) that fits the data points in such a way that the sum of the squared distances between the data points and the line is minimized. This line is called the regression line, and it is used to make predictions about the dependent variable given the independent variables.

## How Does Linear Regression Work?#

Linear regression models the relationship between the dependent and independent variables as a linear equation of the form:

y = β0 + β1X1 + β2X2 + … + βnXn

$y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + ... + \beta_n X_n$

Where y is the dependent variable, X1, X2, …, Xn are the independent variables, and β0, β1, β2, …, βn are the coefficients. The coefficients are found using a method called least squares estimation, which minimizes the sum of the squared distances between the data points and the regression line.

## Types of Linear Regression#

There are two main types of linear regression:

1. Simple Linear Regression: This type of linear regression models the relationship between the dependent variable and one independent variable.

2. Multiple Linear Regression: This type of linear regression models the relationship between the dependent variable and multiple independent variables.

1. Simple and Easy to Implement: Linear regression is a simple and straightforward algorithm that is easy to implement.

2. Provides a Good Starting Point: Linear regression provides a good starting point for more complex models, and it can be used as a basis for comparison.

3. Fast and Efficient: Linear regression is fast and efficient, making it suitable for large datasets.

1. Linearity Assumption: Linear regression assumes that the relationship between the dependent and independent variables is linear. This assumption may not always hold, and the model may not be accurate if the relationship is not linear.

2. Outliers: Linear regression is sensitive to outliers, which can have a big impact on the results.

3. Non-Linear Relationships: Linear regression is not well-suited to modeling non-linear relationships between the dependent and independent variables.

## Example Code#

import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

# Load the Boston Housing dataset

# Convert the dataset into a pandas dataframe
df = pd.DataFrame(boston.data, columns=boston.feature_names)
df["Target"] = boston.target

# Assign the features and target
X = df.drop("Target", axis=1)
y = df["Target"]

# Split the dataset into training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

# Train the Linear Regression model
reg = LinearRegression()
reg.fit(X_train, y_train)

# Predict the target on the test set
y_pred = reg.predict(X_test)

# Calculate the mean squared error
mse = mean_squared_error(y_test, y_pred)
print("Mean Squared Error:", mse)

## Conclusion#

Linear regression is a simple and efficient type of machine learning algorithm that is widely used for modeling the relationship between a dependent variable and one or more independent variables. Despite its limitations, linear regression continues to be a valuable tool for any data scientist to have in their toolkit, and it provides a good starting point for more complex models. By understanding the strengths and limitations of linear regression, data scientists can make informed decisions about when to use this algorithm and when to consider alternative models.


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• ### The VANDELS ESO public spectroscopic survey: observations and first data release(1803.07373)

March 20, 2018 astro-ph.GA
This paper describes the observations and the first data release (DR1) of the ESO public spectroscopic survey "VANDELS, a deep VIMOS survey of the CANDELS CDFS and UDS fields". VANDELS' main targets are star-forming galaxies at 2.4<z<5.5 and massive passive galaxies at 1<z<2.5. By adopting a strategy of ultra-long exposure times, from 20 to 80 hours per source, VANDELS is designed to be the deepest ever spectroscopic survey of the high-redshift Universe. Exploiting the red sensitivity of the VIMOS spectrograph, the survey has obtained ultra-deep spectra covering the wavelength 4800-10000 A with sufficient signal-to-noise to investigate the astrophysics of high-redshift galaxy evolution via detailed absorption line studies. The VANDELS-DR1 is the release of all spectra obtained during the first season of observations and includes data for galaxies for which the total (or half of the total) scheduled integration time was completed. The release contains 879 individual objects with a measured redshift and includes fully wavelength and flux-calibrated 1D spectra, the associated error spectra, sky spectra and wavelength-calibrated 2D spectra. We also provide a catalog with the essential galaxy parameters, including spectroscopic redshifts and redshift quality flags. In this paper we present the survey layout and observations, the data reduction and redshift measurement procedure and the general properties of the VANDELS-DR1 sample. We also discuss the spectroscopic redshift distribution, the accuracy of the photometric redshifts and we provide some examples of data products. All VANDELS-DR1 data are publicly available and can be retrieved from the ESO archive. Two further data releases are foreseen in the next 2 years with a final release scheduled for June 2020 which will include improved re-reduction of the entire spectroscopic data set. (abridged)
• ### The VANDELS ESO spectroscopic survey(1803.07414)

March 20, 2018 astro-ph.GA
VANDELS is a uniquely-deep spectroscopic survey of high-redshift galaxies with the VIMOS spectrograph on ESO's Very Large Telescope (VLT). The survey has obtained ultra-deep optical (0.48 < lambda < 1.0 micron) spectroscopy of ~2100 galaxies within the redshift interval 1.0 < z < 7.0, over a total area of ~0.2 sq. degrees centred on the CANDELS UDS and CDFS fields. Based on accurate photometric redshift pre-selection, 85% of the galaxies targeted by VANDELS were selected to be at z>=3. Exploiting the red sensitivity of the refurbished VIMOS spectrograph, the fundamental aim of the survey is to provide the high signal-to-noise ratio spectra necessary to measure key physical properties such as stellar population ages, masses, metallicities and outflow velocities from detailed absorption-line studies. Using integration times calculated to produce an approximately constant signal-to-noise ratio (20 < t_int < 80 hours), the VANDELS survey targeted: a) bright star-forming galaxies at 2.4 < z < 5.5, b) massive quiescent galaxies at 1.0 < z < 2.5, c) fainter star-forming galaxies at 3.0 < z < 7.0 and d) X-ray/Spitzer-selected active galactic nuclei and Herschel-detected galaxies. By targeting two extragalactic survey fields with superb multi-wavelength imaging data, VANDELS will produce a unique legacy data set for exploring the physics underpinning high-redshift galaxy evolution. In this paper we provide an overview of the VANDELS survey designed to support the science exploitation of the first ESO public data release, focusing on the scientific motivation, survey design and target selection.
• ### The MUSE Hubble Ultra Deep Field Survey: III. Testing photometric redshifts to 30th magnitude(1710.05062)

Oct. 13, 2017 astro-ph.CO, astro-ph.GA
We tested the performance of photometric redshifts for galaxies in the Hubble Ultra Deep field down to 30th magnitude. We compared photometric redshift estimates from three spectral fitting codes from the literature (EAZY, BPZ and BEAGLE) to high quality redshifts for 1227 galaxies from the MUSE integral field spectrograph. All these codes can return photometric redshifts with bias |Dzn|=|z-z_phot|/(1+z)<0.05 down to F775W=30 and spectroscopic incompleteness is unlikely to strongly modify this statement. We have, however, identified clear systematic biases in the determination of photometric redshifts: in the 0.4<z<1.5 range, photometric redshifts are systematically biased low by as much as Dzn=-0.04 in the median, and at z>3 they are systematically biased high by up to Dzn = 0.05, an offset that can in part be explained by adjusting the amount of intergalactic absorption applied. In agreement with previous studies we find little difference in the performance of the different codes, but in contrast to those we find that adding extensive ground-based and IRAC photometry actually can worsen photo-z performance for faint galaxies. We find an outlier fraction, defined through |Dzn|>0.15, of 8% for BPZ and 10% for EAZY and BEAGLE, and show explicitly that this is a strong function of magnitude. While this outlier fraction is high relative to numbers presented in the literature for brighter galaxies, they are very comparable to literature results when the depth of the data is taken into account. Finally, we demonstrate that while a redshift might be of high confidence, the association of a spectrum to the photometric object can be very uncertain and lead to a contamination of a few percent in spectroscopic training samples that do not show up as catastrophic outliers, a problem that must be tackled in order to have sufficiently accurate photometric redshifts for future cosmological surveys.
• ### Modelling ultraviolet-line diagnostics of stars, the ionized and the neutral interstellar medium in star-forming galaxies(1705.10320)

Sept. 14, 2017 astro-ph.GA
We combine state-of-the-art models for the production of stellar radiation and its transfer through the interstellar medium (ISM) to investigate ultraviolet-line diagnostics of stars, the ionized and the neutral ISM in star-forming galaxies. We start by assessing the reliability of our stellar population synthesis modelling by fitting absorption-line indices in the ISM-free ultraviolet spectra of 10 Large-Magellanic-Cloud clusters. In doing so, we find that neglecting stochastic sampling of the stellar initial mass function in these young ($\sim10$-100 Myr), low-mass clusters affects negligibly ultraviolet-based age and metallicity estimates but can lead to significant overestimates of stellar mass. Then, we proceed and develop a simple approach, based on an idealized description of the main features of the ISM, to compute in a physically consistent way the combined influence of nebular emission and interstellar absorption on ultraviolet spectra of star-forming galaxies. Our model accounts for the transfer of radiation through the ionized interiors and outer neutral envelopes of short-lived stellar birth clouds, as well as for radiative transfer through a diffuse intercloud medium. We use this approach to explore the entangled signatures of stars, the ionized and the neutral ISM in ultraviolet spectra of star-forming galaxies. We find that, aside from a few notable exceptions, most standard ultraviolet indices defined in the spectra of ISM-free stellar populations are prone to significant contamination by the ISM, which increases with metallicity. We also identify several nebular-emission and interstellar-absorption features, which stand out as particularly clean tracers of the different phases of the ISM.
• ### WebPlotDigitizer, a polyvalent and free software to extract spectra from old astronomical publications: application to ultraviolet spectropolarimetry(1708.02025)

Aug. 7, 2017 astro-ph.IM
In this contribution, we present WebPlotDigitizer, a polyvalent and free software developed to facilitate easy and accurate data extraction from a variety of plot types. We describe the numerous features of this numerical tool and present its relevance when applied to astrophysical archival research. We exploit WebPlotDigitizer to extract ultraviolet spectropolarimetric spectra from old publications that used the Hubble Space Telescope, Lick Observatory 3m Shane telescope and Astro-2 mission to observe the Seyfert-2 AGN NGC 1068. By doing so, we compile all the existing ultraviolet polarimetric data on NGC 1068 to prepare the ground for further investigations with the future high-resolution spectropolarimeter POLLUX on-board of the proposed Large UV/Optical/Infrared Surveyor (LUVOIR) NASA mission.
• ### Resolving the age bimodality of galaxy stellar populations on kpc scales(1701.06570)

Jan. 26, 2017 astro-ph.GA
Galaxies in the local Universe are known to follow bimodal distributions in the global stellar populations properties. We analyze the distribution of the local average stellar-population ages of 654,053 sub-galactic regions resolved on ~1-kpc scales in a volume-corrected sample of 394 galaxies, drawn from the CALIFA-DR3 integral-field-spectroscopy survey and complemented by SDSS imaging. We find a bimodal local-age distribution, with an old and a young peak primarily due to regions in early-type galaxies and star-forming regions of spirals, respectively. Within spiral galaxies, the older ages of bulges and inter-arm regions relative to spiral arms support an internal age bimodality. Although regions of higher stellar-mass surface-density, mu*, are typically older, mu* alone does not determine the stellar population age and a bimodal distribution is found at any fixed mu*. We identify an "old ridge" of regions of age ~9 Gyr, independent of mu*, and a "young sequence" of regions with age increasing with mu* from 1-1.5 Gyr to 4-5 Gyr. We interpret the former as regions containing only old stars, and the latter as regions where the relative contamination of old stellar populations by young stars decreases as mu* increases. The reason why this bimodal age distribution is not inconsistent with the unimodal shape of the cosmic-averaged star-formation history is that i) the dominating contribution by young stars biases the age low with respect to the average epoch of star formation, and ii) the use of a single average age per region is unable to represent the full time-extent of the star-formation history of "young-sequence" regions.
• ### A deep ALMA image of the Hubble Ultra Deep Field(1606.00227)

Dec. 20, 2016 astro-ph.GA
We present the results of the first, deep ALMA imaging covering the full 4.5 sq arcmin of the Hubble Ultra Deep Field (HUDF) as previously imaged with WFC3/IR on HST. Using a mosaic of 45 pointings, we have obtained a homogeneous 1.3mm image of the HUDF, achieving an rms sensitivity of 35 microJy, at a resolution of 0.7 arcsec. From an initial list of ~50 >3.5sigma peaks, a rigorous analysis confirms 16 sources with flux densities S(1.3) > 120 microJy. All of these have secure galaxy counterparts with robust redshifts (<z> = 2.15), and 12 are also detected at 6GHz in new deep JVLA imaging. Due to the wealth of supporting data in this unique field, the physical properties of the ALMA sources are well constrained, including their stellar masses (M*) and UV+FIR star-formation rates (SFR). Our results show that stellar mass is the best predictor of SFR in the high-z Universe; indeed at z > 2 our ALMA sample contains 7 of the 9 galaxies in the HUDF with M* > 2 x 10^10 Msun and we detect only one galaxy at z > 3.5, reflecting the rapid drop-off of high-mass galaxies with increasing redshift. The detections, coupled with stacking, allow us to probe the redshift/mass distribution of the 1.3-mm background down to S(1.3) ~ 10 micro-Jy. We find strong evidence for a steep `main sequence' for star-forming galaxies at z ~ 2, with SFR \propto M* and a mean specific SFR = 2.2 /Gyr. Moreover, we find that ~85% of total star formation at z ~ 2 is enshrouded in dust, with ~65% of all star formation at this epoch occurring in high-mass galaxies (M* > 2 x 10^10 Msun), for which the average obscured:unobscured SF ratio is ~200. Finally, we combine our new ALMA results with the existing HST data to revisit the cosmic evolution of star-formation rate density; we find that this peaks at z ~ 2.5, and that the star-forming Universe transits from primarily unobscured to primarily obscured thereafter at z ~ 4.
• ### Self-similarity in the chemical evolution of galaxies and the delay time distribution of SNe Ia(1607.00015)

June 30, 2016 astro-ph.GA
Recent improvements in the age dating of stellar populations and single stars allow us to study the ages and abundance of stars and galaxies with unprecedented accuracy. We here compare the relation between age and \alpha-element abundances for stars in the solar neighborhood to that of local, early-type galaxies. We find both relations to be very similar. Both fall into two regimes with a flat slope for ages younger than ~9 Gyr and a steeper slope for ages older than that value. This quantitative similarity seems surprising, given the different types of galaxies and scales involved. For the sample of early-type galaxies we also show that the data are inconsistent with literature delay time distributions of either single or double Gaussian shape. The data are consistent with a power law delay time distribution. We thus confirm that the delay time distribution inferred for the Milky Way from chemical evolution arguments also must apply to massive early-type galaxies. We also offer a tentative explanation for the seeming universality of the age-[\alpha/Fe] relation as the manifestation of averaging of different stellar populations with varying chemical evolution histories.
• ### The impact of the Star Formation Histories on the SFR-M$_{*}$ relation at z$\ge$2(1606.04823)

June 15, 2016 astro-ph.GA
In this paper we investigate the impact of different star formation histories (SFHs) on the relation between stellar mass M$_{*}$ and star formation rate (SFR) using a sample of galaxies with reliable spectroscopic redshift zspec>2 drawn from the VIMOS Ultra-Deep Survey (VUDS). We produce an extensive database of dusty model galaxies, calculated starting from the new library of single stellar population (SSPs) models presented in Cassara' et al. 2013 and weighted by a set of 28 different SFHs based on the Schmidt function, and characterized by different ratios of the gas infall time scale $\tau_{infall}$ to the star formation efficiency $\nu$. The treatment of dust extinction and re-emission has been carried out by means of the radiative transfer calculation. The spectral energy distribution (SED) fitting technique is performed by using GOSSIP+, a tool able to combine both photometric and spectroscopic information to extract the best value of the physical quantities of interest, and to consider the Intergalactic Medium (IGM) attenuation as a free parameter. We find that the main contribution to the scatter observed in the $SFR-M_{*}$ plane is the possibility of choosing between different families of SFHs in the SED fitting procedure, while the redshift range plays a minor role. The majority of the galaxies, at all cosmic times, are best-fit by models with SFHs characterized by a high $\tau_{\rm infall}/\nu$ ratio. We discuss the reliability of the presence of a small percentage of dusty and highly star forming galaxies, in the light of their detection in the FIR.
• ### The VLT LEGA-C Spectroscopic Survey: The Physics of Galaxies at a Lookback Time of 7 Gyr(1603.05479)

March 17, 2016 astro-ph.GA
The Large Early Galaxy Census (LEGA-C) is a Public Spectroscopic Survey of $\sim3200$ $K$-band selected galaxies at redshifts $z=0.6-1.0$ with stellar masses M_star > 1e10M_sun, conducted with VIMOS on ESO's Very Large Telescope. The survey is embedded in the COSMOS field ($R.A. = 10h00$; $Dec.=+2\deg$). The 20-hour long integrations produce high-$S/N$ continuum spectra that reveal ages, metallicities and velocity dispersions of the stellar populations. LEGA-C's unique combination of sample size and depth will enable us for the first time to map the stellar content at large look-back time, across galaxies of different types and star-formation activity. Observations started in December 2014 and are planned to be completed by mid 2018, with early data releases of the spectra and value-added products. In this paper we present the science case, the observing strategy, an overview of the data reduction process and data products, and a first look at the relationship between galaxy structure and spectral properties, as it existed 7 Gyr ago.
• ### A Comprehensive Comparative Test of Seven Widely-Used Spectral Synthesis Models Against Multi-Band Photometry of Young Massive Star Clusters(1601.03850)

Jan. 15, 2016 astro-ph.GA
We test the predictions of spectral synthesis models based on seven different massive-star prescriptions against Legacy ExtraGalactic UV Survey (LEGUS) observations of eight young massive clusters in two local galaxies, NGC 1566 and NGC 5253, chosen because predictions of all seven models are available at the published galactic metallicities. The high angular resolution, extensive cluster inventory and full near-ultraviolet to near-infrared photometric coverage make the LEGUS dataset excellent for this study. We account for both stellar and nebular emission in the models and try two different prescriptions for attenuation by dust. From Bayesian fits of model libraries to the observations, we find remarkably low dispersion in the median E(B-V) (~0.03 mag), stellar masses (~10^4 M_\odot) and ages (~1 Myr) derived for individual clusters using different models, although maximum discrepancies in these quantities can reach 0.09 mag and factors of 2.8 and 2.5, respectively. This is for ranges in median properties of 0.05-0.54 mag, 1.8-10x10^4 M_\odot and 1.6-40 Myr spanned by the clusters in our sample. In terms of best fit, the observations are slightly better reproduced by models with interacting binaries and least well reproduced by models with single rotating stars. Our study provides a first quantitative estimate of the accuracies and uncertainties of the most recent spectral synthesis models of young stellar populations, demonstrates the good progress of models in fitting high-quality observations, and highlights the needs for a larger cluster sample and more extensive tests of the model parameter space.
• ### The VIMOS Ultra Deep Survey: Ly$\alpha$ Emission and Stellar Populations of Star-Forming Galaxies at 2<z<2.5(1503.01753)

Jan. 6, 2016 astro-ph.GA
The aim of this paper is to investigate spectral and photometric properties of 854 faint ($i_{AB}$<~25 mag) star-forming galaxies (SFGs) at 2<z<2.5 using the VIMOS Ultra-Deep Survey (VUDS) spectroscopic data and deep multi-wavelength photometric data in three extensively studied extragalactic fields (ECDFS, VVDS, COSMOS). These SFGs were targeted for spectroscopy based on their photometric redshifts. The VUDS spectra are used to measure the UV spectral slopes ($\beta$) as well as Ly$\alpha$ equivalent widths (EW). On average, the spectroscopically measured $\beta$ (-1.36$\pm$0.02), is comparable to the photometrically measured $\beta$ (-1.32$\pm$0.02), and has smaller measurement uncertainties. The positive correlation of $\beta$ with the Spectral Energy Distribution (SED)-based measurement of dust extinction, E$_{\rm s}$(B-V), emphasizes the importance of $\beta$ as an alternative dust indicator at high redshifts. To make a proper comparison, we divide these SFGs into three subgroups based on their rest-frame Ly$\alpha$ EW: SFGs with no Ly$\alpha$ emission (SFG$_{\rm N}$; EW$\le$0\AA), SFGs with Ly$\alpha$ emission (SFG$_{\rm L}$; EW$>$0\AA), and Ly$\alpha$ emitters (LAEs; EW$\ge$20\AA). The fraction of LAEs at these redshifts is $\sim$10%, which is consistent with previous observations. We compared best-fit SED-estimated stellar parameters of the SFG$_{\rm N}$, SFG$_{\rm L}$ and LAE samples. For the luminosities probed here ($\sim$L$^*$), we find that galaxies with and without Ly$\alpha$ in emission have small but significant differences in their SED-based properties. We find that LAEs have less dust, and lower star-formation rates (SFR) compared to non-LAEs. We also find that LAEs are less massive compared to non-LAEs, though the difference is smaller and less significant compared to the SFR and E$_{\rm s}$(B-V). [abridged]
• ### The Lyman Continuum escape fraction of galaxies at z=3.3 in the VUDS-LBC/COSMOS field(1509.01101)

Sept. 3, 2015 astro-ph.GA
The Lyman continuum (LyC) flux escaping from high-z galaxies into the IGM is a fundamental quantity to understand the physical processes involved in the reionization epoch. We have investigated a sample of star-forming galaxies at z~3.3 in order to search for possible detections of LyC photons escaping from galaxy halos. UV deep imaging in the COSMOS field obtained with the prime focus camera LBC at the LBT telescope was used together with a catalog of spectroscopic redshifts obtained by the VIMOS Ultra Deep Survey (VUDS) to build a sample of 45 galaxies at z~3.3 with L>0.5L*. We obtained deep LBC images of galaxies with spectroscopic redshifts in the interval 3.27<z<3.40 both in the R and deep U bands. A sub-sample of 10 galaxies apparently shows escape fractions>28% but a detailed analysis of their properties reveals that, with the exception of two marginal detections (S/N~2) in the U band, all the other 8 galaxies are most likely contaminated by the UV flux of low-z interlopers located close to the high-z targets. The average escape fraction derived from the stacking of the cleaned sample was constrained to fesc_rel<2%. The implied HI photo-ionization rate is a factor two lower than that needed to keep the IGM ionized at z~3, as observed in the Lyman forest of high-z QSO spectra or by the proximity effect. These results support a scenario where high redshift, relatively bright (L>0.5L*) star-forming galaxies alone are unable to sustain the level of ionization observed in the cosmic IGM at z~3. Star-forming galaxies at higher redshift and at fainter luminosities (L<<L*) can be the major contributors to the reionization of the Universe only if their physical properties are subject to rapid changes from z~3 to z~6-10. Alternatively, ionizing sources could be discovered looking for fainter sources among the AGN population at high-z.
• ### Abundance patterns in early-type galaxies: is there a 'knee' in the [Fe/H] vs. [alpha/Fe] relation?(1508.05103)

Aug. 20, 2015 astro-ph.GA
Early-type galaxies (ETGs) are known to be enhanced in alpha elements, in accordance with their old ages and short formation timescales. In this contribution we aim to resolve the enrichment histories of ETGs. This means we study the abundance of Fe ([Fe/H]) and the alpha-element groups ([alpha/Fe]) separately for stars older than 9.5 Gyr ([Fe/H]o, [alpha/Fe]o) and for stars between 1.5 and 9.5 Gyr ([Fe/H]i, [alpha/Fe]i). Through extensive simulation we show that we can indeed recover the enrichment history per galaxy. We then analyze a spectroscopic sample of 2286 early-type galaxies from the SDSS selected to be ETGs. We separate out those galaxies for which the abundance of iron in stars grows throughout the lifetime of the galaxy, i.e. in which [Fe/H]o < [Fe/H]i. We confirm earlier work where the [Fe/H] and [alpha/Fe] parameters are correlated with the mass and velocity dispersion of ETGs. We emphasize that the strongest relation is between [alpha/Fe] and age. This relation falls into two regimes, one with a steep slope for old galaxies and one with a shallow slope for younger ETGs. The vast majority of ETGs in our sample do not show the 'knee' in the plot of [Fe/H] vs. [alpha/Fe] commonly observed in local group galaxies. This implies that for the vast majority of ETGs, the stars younger than 9.5 Gyrs are likely to have been accreted or formed from accreted gas. The properties of the intermediate-age stars in accretion-dominated ETGs indicate that mass growth through late (minor) mergers in ETGs is dominated by galaxies with low [Fe/H] and low [alpha/Fe]. The method of reconstructing the stellar enrichment histories of ETGs introduced in this paper promises to constrain the star formation and mass assembly histories of large samples of galaxies in a unique way.
• ### Discovering extremely compact and metal-poor, star-forming dwarf galaxies out to z ~ 0.9 in the VIMOS Ultra-Deep Survey(1403.3692)

March 31, 2015 astro-ph.CO, astro-ph.GA
We report the discovery of 31 low-luminosity (-14.5 > M_{AB}(B) > -18.8), extreme emission line galaxies (EELGs) at 0.2 < z < 0.9 identified by their unusually high rest-frame equivalent widths (100 < EW[OIII] < 1700 A) as part of the VIMOS Ultra Deep Survey (VUDS). VIMOS optical spectra of unprecedented sensitivity ($I_{AB}$ ~ 25 mag) along with multiwavelength photometry and HST imaging are used to investigate spectrophotometric properties of this unique sample and explore, for the first time, the very low stellar mass end (M* < 10^8 M$_{\odot}$) of the luminosity-metallicity (LZR) and mass-metallicity (MZR) relations at z < 1. Characterized by their extreme compactness (R50 < 1 kpc), low stellar mass and enhanced specific star formation rates (SFR/M* ~ 10^{-9} - 10^{-7} yr^{-1}), the VUDS EELGs are blue dwarf galaxies likely experiencing the first stages of a vigorous galaxy-wide starburst. Using T_e-sensitive direct and strong-line methods, we find that VUDS EELGs are low-metallicity (7.5 < 12+log(O/H) < 8.3) galaxies with high ionization conditions, including at least three EELGs showing HeII 4686A emission and four EELGs of extremely metal-poor (<10% solar) galaxies. The LZR and MZR followed by EELGs show relatively large scatter, being broadly consistent with the extrapolation toward low luminosity and mass from previous studies at similar redshift. However, we find evidences that galaxies with younger and more vigorous star formation -- as characterized by their larger EWs, ionization and sSFR -- tend to be more metal-poor at a given stellar mass.
• ### The stellar mass - halo mass relation from galaxy clustering in VUDS: a high star formation efficiency at z~3(1412.5584)

Dec. 17, 2014 astro-ph.CO
The relation between the galaxy stellar mass M_star and the dark matter halo mass M_h gives important information on the efficiency in forming stars and assembling stellar mass in galaxies. We present the stellar mass to halo mass ratio (SMHR) measurements at redshifts 2<z<5, obtained from the VIMOS Ultra Deep Survey. We use halo occupation distribution (HOD) modelling of clustering measurements on ~3000 galaxies with spectroscopic redshifts to derive the dark matter halo mass M_h, and SED fitting over a large set of multi-wavelength data to derive the stellar mass M_star and compute the SMHR=M_star/M_h. We find that the SMHR ranges from 1% to 2.5% for galaxies with M_star=1.3x10^9 M_sun to M_star=7.4x10^9 M_sun in DM halos with M_h=1.3x10^{11} M_sun} to M_h=3x10^{11} M_sun. We derive the integrated star formation efficiency (ISFE) of these galaxies and find that the star formation efficiency is a moderate 6-9% for lower mass galaxies while it is relatively high at 16% for galaxies with the median stellar mass of the sample ~7x10^9 M_sun. The lower ISFE at lower masses may indicate that some efficient means of suppressing star formation is at work (like SNe feedback), while the high ISFE for the average galaxy at z~3 is indicating that these galaxies are efficiently building-up their stellar mass at a key epoch in the mass assembly process. We further infer that the average mass galaxy at z~3 will start experiencing star formation quenching within a few hundred millions years.
• ### VIMOS Ultra-Deep Survey (VUDS): Witnessing the Assembly of a Massive Cluster at z~3.3(1403.4230)

Dec. 1, 2014 astro-ph.CO
Using new spectroscopic observations obtained as part of the VIMOS Ultra-Deep Survey (VUDS), we perform a systematic search for overdense environments in the early universe ($z>2$) and report here on the discovery of Cl J0227-0421, a massive protocluster at $z=3.29$. This protocluster is characterized by both the large overdensity of spectroscopically confirmed members, $\delta_{gal}=10.5\pm2.8$, and a significant overdensity in photometric redshift members. The halo mass of this protocluster is estimated, by a variety of methods, to be roughly $3\times10^{14}$ $\mathcal{M}_{\odot}$ at $z\sim3.3$, which, evolved to $z=0$ results in a halo mass rivaling or exceeding that of the Coma cluster. The properties of 19 spectroscopically confirmed member galaxies are compared with a large sample of VUDS/VVDS galaxies in lower density field environments at similar redshifts. We find tentative evidence for an excess of redder, brighter, and more massive galaxies within the confines of the protocluster relative to the field population, which suggests that we may be observing the beginning of environmentally-induced quenching. The properties of these galaxies are investigated, including a discussion of the brightest protocluster galaxy which appears to be undergoing vigorous coeval nuclear and starburst activity. The remaining member galaxies appear to have characteristics which are largely similar to the field population. Though we find weaker evidence of the suppression of the median star formation rates amongst and differences in stacked spectra of member galaxies with respect to the field, we defer any conclusions of these trends to future work with the ensemble of protostructures that are found in the full VUDS sample.
• ### The stellar initial mass function at 0.9<z<1.5(1407.4455)

Nov. 24, 2014 astro-ph.GA
We explore the stellar initial mass function (IMF) of a sample of 49 massive quiescent galaxies (MQGs) at 0.9$<$z$<$1.5. We base our analysis on intermediate resolution spectro-photometric data in the GOODS-N field taken in the near-infrared and optical with the HST/WFC3 G141 grism and the Survey for High-z Absorption Red and Dead Sources (SHARDS). To constrain the slope of the IMF, we have measured the TiO$_2$ spectral feature, whose strength depends strongly on the content of low-mass stars, as well as on stellar age. Using ultraviolet to near-infrared individual and stacked spectral energy distributions, we have independently estimated the stellar ages of our galaxies. Knowing the age of the stellar population, we interpret the strong differences in the TiO$_2$ feature as an IMF variation. In particular, for the heaviest z$\sim$1 MQGs (M$>$10$^{11}$Msun) we find an average age of 1.7$\pm$0.3 Gyr and a bottom-heavy IMF ($\Gamma_b$=3.2$\pm$0.2). Lighter MQGs (2$\times$10$^{10}$$<$M$<$10$^{11}$ Msun) at the same redshift are younger on average (1.0$\pm$0.2 Gyr) and present a shallower IMF slope ($\Gamma_b=2.7^{+0.3}_{-0.4}$). Our results are in good agreement with the findings about the IMF slope in early-type galaxies of similar mass in the present-day Universe. This suggests that the IMF, a key characteristic of the stellar populations in galaxies, is bottom-heavier for more massive galaxies and has remained unchanged in the last $\sim$8 Gyr.
• ### The evolving SFR-M_star relation and sSFR since z~5 from the VUDS spectroscopic survey(1411.5687)

Nov. 20, 2014 astro-ph.CO, astro-ph.GA
We study the evolution of the star formation rate (SFR) - stellar mass (M_star) relation and specific star formation rate (sSFR) of star forming galaxies (SFGs) since a redshift z~5.5 using 2435 (4531) galaxies with highly reliable (reliable) spectroscopic redshifts in the VIMOS Ultra-Deep Survey (VUDS). It is the first time that these relations can be followed over such a large redshift range from a single homogeneously selected sample of galaxies with spectroscopic redshifts. The log(SFR) - log(M_star) relation for SFGs remains roughly linear all the way up to z=5 but the SFR steadily increases at fixed mass with increasing redshift. We find that for stellar masses M_star>3.2 x 10^9 M_sun the SFR increases by a factor ~13 between z=0.4 and z=2.3. We extend this relation up to z=5, finding an additional increase in SFR by a factor 1.7 from z=2.3 to z=4.8 for masses M_star > 10^10 M_sun. We observe a turn-off in the SFR-M_star relation at the highest mass end up to a redshift z~3.5. We interpret this turn-off as the signature of a strong on-going quenching mechanism and rapid mass growth. The sSFR increases strongly up to z~2 but it grows much less rapidly in 2<z<5. We find that the shape of the sSFR evolution is not well reproduced by cold gas accretion-driven models or the latest hydrodynamical models. Below z~2 these models have a flatter evolution (1+z)^{Phi} with Phi=2-2.25 compared to the data which evolves more rapidly with Phi=2.8+-0.2. Above z~2, the reverse is happening with the data evolving more slowly with Phi=1.2+-0.1. The observed sSFR evolution over a large redshift range 0<z<5 and our finding of a non linear main sequence at high mass both indicate that the evolution of SFR and M_star is not solely driven by gas accretion. The results presented in this paper emphasize the need to invoke a more complex mix of physical processes {abridge}
• ### The evolution of clustering length, large-scale bias and host halo mass at 2<z<5 in the VIMOS Ultra Deep Survey (VUDS)(1411.5688)

Nov. 20, 2014 astro-ph.CO
We investigate the evolution of galaxy clustering for galaxies in the redshift range 2.0<$z$<5.0 using the VIMOS Ultra Deep Survey (VUDS). We present the projected (real-space) two-point correlation function $w_p(r_p)$ measured by using 3022 galaxies with robust spectroscopic redshifts in two independent fields (COSMOS and VVDS-02h) covering in total 0.8 deg$^2$. We quantify how the scale dependent clustering amplitude $r_0$ changes with redshift making use of mock samples to evaluate and correct the survey selection function. Using a power-law model $\xi(r) = (r/r_0)^{-\gamma}$ we find that the correlation function for the general population is best fit by a model with a clustering length $r_0$=3.95$^{+0.48}_{-0.54}$ h$^{-1}$Mpc and slope $\gamma$=1.8$^{+0.02}_{-0.06}$ at $z$~2.5, $r_0$=4.35$\pm$0.60 h$^{-1}$Mpc and $\gamma$=1.6$^{+0.12}_{-0.13}$ at $z$~3.5. We use these clustering parameters to derive the large-scale linear galaxy bias $b_L^{PL}$, between galaxies and dark matter. We find $b_L^{PL}$ = 2.68$\pm$0.22 at redshift $z$~3 (assuming $\sigma_8$ = 0.8), significantly higher than found at intermediate and low redshifts. We fit an HOD model to the data and we obtain that the average halo mass at redshift $z$~3 is $M_h$=10$^{11.75\pm0.23}$ h$^{-1}$M$_{\odot}$. From this fit we confirm that the large-scale linear galaxy bias is relatively high at $b_L^{HOD}$ = 2.82$\pm$0.27. Comparing these measurements with similar measurements at lower redshifts we infer that the star-forming population of galaxies at $z$~3 should evolve into the massive and bright ($M_r$<-21.5) galaxy population which typically occupy haloes of mass $\langle M_h\rangle$ = 10$^{13.9}$ h$^{-1}$ $M_{\odot}$ at redshift $z$=0.
• ### The VIMOS Ultra-Deep Survey (VUDS): IGM transmission towards galaxies with 2.5<z<5.5 and the colour selection of high redshift galaxies(1411.5692)

Nov. 20, 2014 astro-ph.CO
(arXiv abridged abstract) The observed UV rest-frame spectra of distant galaxies are the result of their intrinsic emission combined with absorption along the line of sight produced by the inter-galactic medium (IGM). Here we analyse the evolution of the mean IGM transmission Tr(Ly_alpha) and its dispersion along the line of sight for 2127 galaxies with 2.5<z<5.5 in the VIMOS Ultra Deep Survey (VUDS). We fit model spectra combined with a range of IGM transmission to the galaxy spectra using the spectral fitting algorithm GOSSIP+. We use these fits to derive the mean IGM transmission towards each galaxy for several redshift slices from z=2.5 to z=5.5. We find that the mean IGM transmission defined as Tr(Ly_alpha)=e^{-tau} (with tau the HI optical depth) is 79%, 69%, 59%, 55% and 46% at redshifts 2.75, 3,22, 3.70, 4.23, 4.77, respectively. We compare these results to measurements obtained from quasars lines of sight and find that the IGM transmission towards galaxies is in excellent agreement with quasar values up to redshift z~4. We find tentative evidence for a higher IGM transmission at z>= 4 compared to results from QSOs, but a degeneracy between dust extinction and IGM prevents to draw firm conclusions if the internal dust extinction for star-forming galaxies at z>4 takes a mean value significantly in excess of E(B-V)>0.15. Most importantly, we find a large dispersion of IGM transmission along the lines of sight towards distant galaxies with 68% of the distribution within 10 to 17% of the median value in delta z=0.5 bins, similar to what is found on the LOS towards QSOs. We demonstrate the importance of taking into account this large range of IGM transmission when selecting high redshift galaxies based on their colour properties (e.g. LBG or photometric redshift selection) or otherwise face a significant incompleteness in selecting high redshift galaxy populations.
• ### The VIMOS Ultra-Deep Survey (VUDS): fast increase of the fraction of strong Lyman alpha emitters from z=2 to z=6(1403.3693)

Oct. 13, 2014 astro-ph.CO, astro-ph.GA
Aims. The aim of this work is to constrain the evolution of the fraction of Lya emitters among UV selected star forming galaxies at 2<z<6, and to measure the stellar escape fraction of Lya photons over the same redshift range. Methods. We exploit the ultradeep spectroscopic observations collected by the VIMOS Ultra Deep Survey (VUDS) to build an unique, complete and unbiased sample of 4000 spectroscopically confirmed star forming galaxies at 2<z<6. Our galaxy sample UV luminosities brighter than M* at 2<z<6, and luminosities down to one magnitude fainter than M* at 2<z<3.5. Results. We find that 80% of the star forming galaxies in our sample have EW0(Lya)<10A, and correspondingly fesc(Lya)<1%. By comparing these results with literature, we conclude that the bulk of the Lya luminosity at 2<z<6 comes from galaxies that are fainter in the UV than those we sample in this work. The strong Lya emitters constitute, at each redshift, the tail of the distribution of the galaxies with extreme EW0(Lya) and fesc(Lya) . This tail of large EW0 and fesc(Lya) becomes more important as the redshift increases, and causes the fraction of Lya with EW0> 25A to increase from 5% at z=2 to 30% at z=6, with the increase being relatively stronger beyond z=4. We observe no difference, for the narrow range of UV luminosities explored in this work, between the fraction of strong Lya emitters among galaxies fainter or brighter than M*, although the fraction for the FUV faint galaxies evolves faster, at 2<z<3.5, than for the bright ones. We do observe an anticorrelation between E(B-V) and fesc(Lya): generally galaxies with high fesc(Lya) have also small amounts of dust (and viceversa). However, when the dust content is low (E(B-V)<0.05) we observe a very broad range of fesc(Lya), ranging from 10^-3 to 1. This implies that the dust alone is not the only regulator of the amount of escaping Lya photons.
• ### Discovery of a rich proto-cluster at z=2.9 and associated diffuse cold gas in the VIMOS Ultra-Deep Survey (VUDS)(1403.3691)

Aug. 7, 2014 astro-ph.CO
[Abridged] We characterise a massive proto-cluster at z=2.895 that we found in the COSMOS field using the spectroscopic sample of the VIMOS Ultra-Deep Survey (VUDS). This is one of the rare structures at z~3 not identified around AGNs or radio galaxies, so it is an ideal laboratory to study galaxy formation in dense environments. The structure comprises 12 galaxies with secure spectroscopic redshift in an area of 7'x8', in a z bin of Dz=0.016. The measured galaxy number overdensity is delta_g=12+/-2. This overdensity has total mass of M~8.1x10^(14)M_sun in a volume of 13x15x17 Mpc^3. Simulations indicate that such an overdensity at z~2.9 is a proto-cluster that will collapse in a cluster of total mass M~2.5x10^(15)M_sun at z=0. We compare the properties of the galaxies within the overdensity with a control sample at the same z but outside the overdensity. We did not find any statistically significant difference between the properties (stellar mass, SFR, sSFR, NUV-r, r-K) of the galaxies inside and outside the overdensity. The stacked spectrum of galaxies in the overdensity background shows a significant absorption feature at the wavelength of Lya redshifted at z=2.895 (lambda=4736 A), with a rest frame EW = 4+/- 1.4 A. Stacking only background galaxies without intervening sources at z~2.9 along their line of sight, we find that this absorption feature has a rest frame EW of 10.8+/-3.7 A, with a detection S/N of ~4. These EW values imply a high column density (N(HI)~3-20x10^(19)cm^(-2)), consistent with a scenario where such absorption is due to intervening cold gas streams, falling into the halo potential wells of the proto-cluster galaxies. However, we cannot exclude the hypothesis that this absorption is due to the diffuse gas within the overdensity.
• ### Science Case and Requirements for the MOSAIC Concept for a Multi-Object Spectrograph for the European Extremely Large Telescope(1406.6369)

Over the past 18 months we have revisited the science requirements for a multi-object spectrograph (MOS) for the European Extremely Large Telescope (E-ELT). These efforts span the full range of E-ELT science and include input from a broad cross-section of astronomers across the ESO partner countries. In this contribution we summarise the key cases relating to studies of high-redshift galaxies, galaxy evolution, and stellar populations, with a more expansive presentation of a new case relating to detection of exoplanets in stellar clusters. A general requirement is the need for two observational modes to best exploit the large (>40 sq. arcmin) patrol field of the E-ELT. The first mode ('high multiplex') requires integrated-light (or coarsely resolved) optical/near-IR spectroscopy of >100 objects simultaneously. The second ('high definition'), enabled by wide-field adaptive optics, requires spatially-resolved, near-IR of >10 objects/sub-fields. Within the context of the conceptual study for an ELT-MOS called MOSAIC, we summarise the top-level requirements from each case and introduce the next steps in the design process.
• ### The VIMOS Ultra-Deep Survey: ~10,000 galaxies with spectroscopic redshifts to study galaxy assembly at early epochs 2<z<~6(1403.3938)

March 16, 2014 astro-ph.CO
We present the VIMOS Ultra Deep Survey (VUDS), a spectroscopic redshift survey of ~10.000 very faint galaxies to study the major phase of galaxy assembly 2<z<~6. The survey covers 1 deg^2 in 3 separate fields: COSMOS, ECDFS and VVDS-02h, with targets selection based on an inclusive combination of photometric redshifts and color properties. Spectra covering 3650<lambda<9350 A are obtained with VIMOS on the ESO-VLT with integration times of 14h. Here we present the survey strategy, the target selection, the data processing, as well as the redshift measurement process, emphasizing the specific methods adapted to this high redshift range. The spectra quality and redshift reliability are discussed, and we derive a completeness in redshift measurement of 91%, or 74% for the most reliable measurements, down to i_AB=25, and measurements are performed all the way down to i_AB=27. The redshift distribution of the main sample peaks at z=3-4 and extends over a large redshift range mainly in 2 < z < 6. At 3<z<5, the galaxies cover a large range of luminosities -23< M_U < -20.5, stellar mass 10^9 M_sun< M_star < 10^{11} M_sun, and star formation rates 1 M_sun/yr< SFR < 10^3 M_sun/yr. We discuss the spectral properties of galaxies using individual as well as stacked spectra. The comparison between spectroscopic and photometric redshifts as well as color selection demonstrate the effectiveness of our selection scheme. With ~6000 galaxies with reliable spectroscopic redshifts in 2<z<6 expected when complete, this survey is the largest at these redshifts and offers the opportunity for unprecedented studies of the star-forming galaxy population and its distribution in large scale structures during the major phase of galaxy assembly.


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# sum of torsion of an elliptic curve

It is clear from the isomorphism between elliptic curves over $\mathbb{C}$ and complex tori that the sum of the $m$-torsion points is the identity in the group law of the elliptic curve. How generally does this hold, and how can one see it (not using the Lefschetz principle, please)?

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Possibly helpful: If you have an abelian group of odd order, then the product of all the elements is the identity. –  Dylan Moreland Jun 10 '12 at 18:46

It's not true if $m$ is not prime to the characteristic of the field (e.g. take an ordinary elliptic curve in characteristic 2; it will have exactly one non-trivial 2-torsion point).

We also need the field to be algebraically closed, although you may have been assuming that anyway (e.g. take an elliptic curve over $\mathbb{R}$ whose real points have only one connected component - then there's a uniqut non-trivial two-torsion point).

Once we make these two assumptions on the ground field, the torsion is isomorphic to $(\mathbb{Z}/m)^2$ as an abelian group, and this is a property of that group.

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This more-or-less follows from abstract group theory:

Let $P$ = sum of all points of order $m$. Then $P$ is itself a point of order $m$. Now, let $k$ be any integer co-prime to $m$ and note that multiplication by $k$ is a permutation of $E[m]$. So $[k]P$ = sum of all points in $E[m] = P$. So $[k-1]P = 0$. Since $[m]P = 0$ too, then if $gcd( k-1, m ) = 1$ then it follows that $P = 0$.

The case $m = 2$ escapes this proof since $k$ is odd and $gcd( k-1, m ) = 2$.

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It really helps to format your answers using MathJax (see FAQ). I updated your answer as an example. Regards –  Amzoti Mar 25 '13 at 4:06
I think you mean to exclude the case $k\equiv 1\pmod m$, otherwise your argument fails. And, in the case $m=2$, your argument can never work, as you have pointed out. –  awllower Mar 25 '13 at 4:07